Finite Group Databasebeta

← C24×D4×H(5,𝔽2) #72339175

Subgroups — C24×D4×H(5,𝔽2) #72339175

Order 4096.

475073979 conjugacy classes of subgroups.

The subgroup lattice has 1025 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×D4×#41C216yesmaximal, complemented
2C24×D4×Q8C2212yescomplemented
3C24×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
4C26×H(5,𝔽2)C212yesmaximal, complemented
5C24×#3498C216yesmaximal, complemented
6C24×C4×#41C2216yescomplemented
7C24×#3496C219yesmaximal, complemented
8C24×#547C22118yescomplemented
9C24×#532C22118yescomplemented
10C24×#3488C2112yesmaximal, complemented
11C26×#41C22112yescomplemented
12C24×#537C22118yescomplemented
13C24×#520C2216yescomplemented
14C24×#550C22112yescomplemented
15C24×#550C2216yescomplemented
16C24×#548C22112yescomplemented
17C23×D4×H(5,𝔽2)C21960yesmaximal, direct product factor
18C23×C4×H(5,𝔽2)C221480yescomplemented
19C24×#3484C2118yesmaximal, complemented
20C24×#535C22136yescomplemented
21C24×#518C2219yescomplemented
22C25×D42C219yesmaximal, complemented
23C25×#127C2219yescomplemented
24C25×#121C22118yescomplemented
25C25×#121C22118yescomplemented
26C25×C4×D4C2219yescomplemented
27C25×C4×D4C2219yescomplemented
28C24×#546C22136yescomplemented
29C24×#546C22172yescomplemented
30C23×#3498C2212880yescomplemented
31C23×#3488C2215760yescomplemented
32C24×#534C22136yescomplemented
33C23×#3496C2214320yescomplemented
34C27×D4C22118yescomplemented
35C27×D4C2216yescomplemented
36C24×#525C22136yescomplemented
37C23×D4×#41C2212880yescomplemented
38C25×#120C22136yescomplemented
39C25×H(5,𝔽2)—2512no—
40C25×H(5,𝔽2)C2211yescharacteristic
41C25×H(5,𝔽2)C22118yescomplemented
42C25×H(5,𝔽2)C22112yescomplemented
43C25×H(5,𝔽2)C221960yescomplemented
44C22×D4×H(5,𝔽2)C221143360yesdirect product factor
45C23×#3484C2218640yescomplemented
46C24×D42C22118yescomplemented
47C24×D42C22136yescomplemented
48C24×D42C22172yescomplemented
49C24×D42C2214320yescomplemented
50C24×D42C22136yescomplemented
51C29C23112yescomplemented
52C24×H(5,𝔽2)—2122880no—
53C24×H(5,𝔽2)—21536no—
54C24×H(5,𝔽2)—22304no—
55C24×H(5,𝔽2)D41256yesdirect product factor
56C24×H(5,𝔽2)C231240yes—
57C24×H(5,𝔽2)C2314320yescomplemented
58C24×H(5,𝔽2)C2312880yescomplemented
59C24×H(5,𝔽2)C23171680yescomplemented
60C25×#41—21536no—
61C25×#41C2316yes—
62C25×#41C23136yescomplemented
63C25×#41C23112yescomplemented
64C25×#41C23136yescomplemented
65C25×#41C2312880yescomplemented
66C26×Q8C2314yescomplemented
67C26×D4—22304no—
68C26×D4—4384no—
69C26×D4C2319yes—
70C26×D4C2319yes—
71C26×D4C23172yescomplemented
72C26×D4C23136yescomplemented
73C26×D4C23136yescomplemented
74C26×D4C23118yescomplemented
75C26×D4C23136yescomplemented
76C26×D4C23118yescomplemented
77C26×D4C23118yescomplemented
78C26×D4C2314320yescomplemented
79C26×D4C2311440yescomplemented
80C27×C4C23118yescomplemented
81C27×C4C2316yescomplemented
82C2×D4×H(5,𝔽2)C2313932160yesdirect product factor
83C22×#3498C231215040yescomplemented
84C22×#3488C231430080yescomplemented
85C22×#3496C231322560yescomplemented
86C22×#3484C231645120yescomplemented
87C22×D4×#41C231215040yescomplemented
88C23×#550C2311440yescomplemented
89C23×#550C2312880yescomplemented
90C23×#547C2314320yescomplemented
91C23×#548C2312880yescomplemented
92C23×#546C2318640yescomplemented
93C23×#546C23117280yescomplemented
94C23×D4×Q8C231480yescomplemented
95C23×D42C2314320yescomplemented
96C23×D42C231322560yescomplemented
97C23×D42C23117280yescomplemented
98C23×D42C2318640yescomplemented
99C23×D42C2318640yescomplemented
100C23×#537C2314320yescomplemented
101C23×#535C2318640yescomplemented
102C23×#534C2318640yescomplemented
103C23×#532C2314320yescomplemented
104C24×C4⋊Q8C2316yescomplemented
105C24×#127C23136yescomplemented
106C24×#127C23118yescomplemented
107C24×#127C2312160yescomplemented
108C24×#124C23136yescomplemented
109C23×#525C2318640yescomplemented
110C24×#123C23172yescomplemented
111C24×C22⋊Q8C23136yescomplemented
112C24×C22⋊Q8C23112yescomplemented
113C24×#121C23136yescomplemented
114C24×#121C23136yescomplemented
115C24×#121C23136yescomplemented
116C24×#121C23172yescomplemented
117C24×#121C23172yescomplemented
118C24×#121C23136yescomplemented
119C24×#121C2314320yescomplemented
120C24×#121C2314320yescomplemented
121C24×#120C23172yescomplemented
122C24×#120C231144yescomplemented
123C24×#120C2318640yescomplemented
124C22×C4×H(5,𝔽2)C23135840yescomplemented
125C23×#520C2311440yescomplemented
126C23×#518C2312160yescomplemented
127C23×C4×#41C2311440yescomplemented
128C24×C4×Q8C2316yescomplemented
129C24×C4×Q8C2312yescomplemented
130C24×C4×D4C2316yes—
131C24×C4×D4C23118yescomplemented
132C24×C4×D4C23118yescomplemented
133C24×C4×D4C23136yescomplemented
134C24×C4×D4C23136yescomplemented
135C24×C4×D4C23118yescomplemented
136C24×C4×D4C23136yescomplemented
137C24×C4×D4C2312160yescomplemented
138C24×C4×D4C2312160yescomplemented
139C24×#117C23118yescomplemented
140C25×C4⋊C4C2319yescomplemented
141C25×C4⋊C4C2319yescomplemented
142C25×C22⋊C4C23118yescomplemented
143C25×C22⋊C4C23118yescomplemented
144C25×C22⋊C4C23136yescomplemented
145C25×C42C2319yescomplemented
146C28—2768no—
147C28—4384no—
148C28—8192no—
149C28C24118yes—
150C28C24136yes—
151C28C2416yes—
152C28C2411440yescomplemented
153C23×H(5,𝔽2)—24587520no—
154C23×H(5,𝔽2)—2184320no—
155C23×H(5,𝔽2)—2276480no—
156C23×H(5,𝔽2)C2×D4130720yesdirect product factor
157C23×H(5,𝔽2)C2418960yes—
158C23×H(5,𝔽2)C241161280yescomplemented
159C23×H(5,𝔽2)C241107520yescomplemented
160C23×H(5,𝔽2)C241983040yescomplemented
161C24×#41—2184320no—
162C24×#41—2768no—
163C24×#41—22304no—
164C24×#41—22304no—
165C24×#41C2×D41768yescomplemented
166C24×#41C241720yes—
167C24×#41C2414320yescomplemented
168C24×#41C2414320yescomplemented
169C24×#41C2411440yescomplemented
170C24×#41C241107520yescomplemented
171C25×Q8—2256no—
172C25×Q8C24112yes—
173C25×Q8C2412yes—
174C25×Q8C241480yescomplemented
175C25×D4—22304no—
176C25×D4—22304no—
177C25×D4—24608no—
178C25×D4—2276480no—
179C25×D4—2576no—
180C25×D4—21152no—
181C25×D4—4576no—
182C25×D4—446080no—
183C25×D4—41152no—
184C25×D4—8288no—
185C25×D4C2×D411152yescomplemented
186C25×D4C24118yes—
187C25×D4C2419yes—
188C25×D4C2411080yes—
189C25×D4C24172yes—
190C25×D4C24136yes—
191C25×D4C24136yes—
192C25×D4C24136yes—
193C25×D4C24118yes—
194C25×D4C2411080yes—
195C25×D4C2411yescharacteristic
196C25×D4C2414320yescomplemented
197C25×D4C2412160yescomplemented
198C25×D4C2414320yescomplemented
199C25×D4C2418640yescomplemented
200C25×D4C2414320yescomplemented
201C25×D4C2412160yescomplemented
202C25×D4C2412160yescomplemented
203C25×D4C241161280yescomplemented
204C25×D4C24153760yescomplemented
205C26×C4—21152no—
206C26×C4—4192no—
207C26×C4C2419yes—
208C26×C4C24118yes—
209C26×C4C24112yes—
210C26×C4C24136yes—
211C26×C4C2419yes—
212C26×C4C24118yes—
213C26×C4C2419yes—
214C26×C4C2412160yescomplemented
215C26×C4C241720yescomplemented
216D4×H(5,𝔽2)C24116777216yesdirect product factor
217C2×#3498C2412949120yescomplemented
218C2×#3488C2415898240yescomplemented
219C2×#3496C2414423680yescomplemented
220C2×#3484C2418847360yescomplemented
221C2×D4×#41C2412949120yescomplemented
222C22×#550C24153760yescomplemented
223C22×#550C241107520yescomplemented
224C22×#547C241161280yescomplemented
225C22×#548C241107520yescomplemented
226C22×#546C241322560yescomplemented
227C22×#546C241645120yescomplemented
228C22×D4×Q8C24117920yescomplemented
229C22×D42C241161280yescomplemented
230C22×D42C241645120yescomplemented
231C22×D42C241322560yescomplemented
232C22×D42C2414423680yescomplemented
233C22×D42C241322560yescomplemented
234C22×#537C241161280yescomplemented
235C22×#535C241322560yescomplemented
236C22×#534C241322560yescomplemented
237C22×#532C241161280yescomplemented
238C23×C4⋊Q8C241720yescomplemented
239C23×#127C2412160yescomplemented
240C23×#127C2414320yescomplemented
241C23×#127C24180640yescomplemented
242C23×#124C2414320yescomplemented
243C22×#525C241322560yescomplemented
244C23×#123C2418640yescomplemented
245C23×C22⋊Q8C2411440yescomplemented
246C23×C22⋊Q8C2414320yescomplemented
247C23×#121C2414320yescomplemented
248C23×#121C2414320yescomplemented
249C23×#121C2418640yescomplemented
250C23×#121C2418640yescomplemented
251C23×#121C2414320yescomplemented
252C23×#121C2414320yescomplemented
253C23×#121C241161280yescomplemented
254C23×#121C241161280yescomplemented
255C23×#120C2418640yescomplemented
256C23×#120C24117280yescomplemented
257C23×#120C241322560yescomplemented
258C2×C4×H(5,𝔽2)C241491520yescomplemented
259C22×#520C24153760yescomplemented
260C22×#518C24180640yescomplemented
261C22×C4×#41C24153760yescomplemented
262C23×C4×Q8C241240yescomplemented
263C23×C4×Q8C241720yescomplemented
264C23×C4×D4C241720yes—
265C23×C4×D4C2412160yescomplemented
266C23×C4×D4C2414320yescomplemented
267C23×C4×D4C2414320yescomplemented
268C23×C4×D4C2412160yescomplemented
269C23×C4×D4C2412160yescomplemented
270C23×C4×D4C2414320yescomplemented
271C23×C4×D4C24180640yescomplemented
272C23×C4×D4C24180640yescomplemented
273C23×#117C2412160yescomplemented
274C24×C4⋊C4C2416yes—
275C24×C4⋊C4C24118yes—
276C24×C4⋊C4C24118yes—
277C24×C4⋊C4C2416yes—
278C24×C4⋊C4C24112yes—
279C24×C4⋊C4C2411080yescomplemented
280C24×C4⋊C4C2411080yescomplemented
281C24×C22⋊C4C24112yes—
282C24×C22⋊C4C24136yes—
283C24×C22⋊C4C24172yes—
284C24×C22⋊C4C24136yes—
285C24×C22⋊C4C2412160yescomplemented
286C24×C22⋊C4C2412160yescomplemented
287C24×C22⋊C4C2414320yescomplemented
288C24×C42C2416yes—
289C24×C42C24118yes—
290C24×C42C2411080yescomplemented
291C27—2576no—
292C27—2576no—
293C27—21152no—
294C27—246080no—
295C27—496no—
296C27—496no—
297C27—4288no—
298C27—4576no—
299C27—423040no—
300C27—4576no—
301C27—811520no—
302C27—824576no—
303C27C22×D41384yescomplemented
304C27C25118yes—
305C27C2511080yes—
306C27C2519yes—
307C27C2512yes—
308C27C2512160yes—
309C27C251360yes—
310C27C25126880yescomplemented
311C22×H(5,𝔽2)—231457280no—
312C22×H(5,𝔽2)—23440640no—
313C22×H(5,𝔽2)—25160960no—
314C22×H(5,𝔽2)C22×D41573440yesdirect product factor
315C22×H(5,𝔽2)C25161440yes—
316C22×H(5,𝔽2)C2511105920yescomplemented
317C22×H(5,𝔽2)C251737280yescomplemented
318C22×H(5,𝔽2)C2512097152yescomplemented
319C23×#41—23440640no—
320C23×#41—246080no—
321C23×#41—2138240no—
322C23×#41—2138240no—
323C23×#41C22×D4146080yescomplemented
324C23×#41C25113440yes—
325C23×#41C25180640yescomplemented
326C23×#41C25180640yescomplemented
327C23×#41C25126880yescomplemented
328C23×#41C251737280yescomplemented
329C24×Q8—215360no—
330C24×Q8—2384no—
331C24×Q8C22×D41128yescomplemented
332C24×Q8C251720yes—
333C24×Q8C251120yes—
334C24×Q8C2518960yescomplemented
335C24×D4—22304no—
336C24×D4—2138240no—
337C24×D4—2576no—
338C24×D4—2138240no—
339C24×D4—2276480no—
340C24×D4—25160960no—
341C24×D4—234560no—
342C24×D4—21152no—
343C24×D4—269120no—
344C24×D4—2288no—
345C24×D4—434560no—
346C24×D4—4576no—
347C24×D4—4576no—
348C24×D4—4860160no—
349C24×D4—469120no—
350C24×D4—817280no—
351C24×D4C22×D411152yescomplemented
352C24×D4C22×D4169120yescomplemented
353C24×D4H(5,𝔽2)164yesdirect product factor
354C24×D4C2511080yes—
355C24×D4C251540yes—
356C24×D4C25120160yes—
357C24×D4C2514320yes—
358C24×D4C2512160yes—
359C24×D4C2512160yes—
360C24×D4C2512160yes—
361C24×D4C2511080yes—
362C24×D4C25120160yes—
363C24×D4C25160yes—
364C24×D4C25180640yescomplemented
365C24×D4C25180640yescomplemented
366C24×D4C25140320yescomplemented
367C24×D4C251161280yescomplemented
368C24×D4C25180640yescomplemented
369C24×D4C25140320yescomplemented
370C24×D4C25140320yescomplemented
371C24×D4C2511105920yescomplemented
372C24×D4C251368640yescomplemented
373C25×C4—2576no—
374C25×C4—2384no—
375C25×C4—21152no—
376C25×C4—269120no—
377C25×C4—2288no—
378C25×C4—411520no—
379C25×C4—4288no—
380C25×C4—4144no—
381C25×C4C22×D41576yescomplemented
382C25×C4C251720yes—
383C25×C4C251540yes—
384C25×C4C2511080yes—
385C25×C4C2512160yes—
386C25×C4C25112yes—
387C25×C4C2519yes—
388C25×C4C2516yes—
389C25×C4C2511080yes—
390C25×C4C251540yes—
391C25×C4C2516yes—
392C25×C4C251540yes—
393C25×C4C2511yescharacteristic
394C25×C4C25140320yescomplemented
395C25×C4C25113440yescomplemented
396#3498C2516291456yescomplemented
397#3496C2519437184yescomplemented
398#3488C25112582912yescomplemented
399#3484C25118874368yescomplemented
400D4×#41C2516291456yescomplemented
401C2×#550C251737280yescomplemented
402C2×#550C251368640yescomplemented
403C2×D4×Q8C251122880yescomplemented
404C2×#548C251737280yescomplemented
405C2×#547C2511105920yescomplemented
406C2×#546C2512211840yescomplemented
407C2×#546C2514423680yescomplemented
408C2×D42C2511105920yescomplemented
409C2×D42C2519437184yescomplemented
410C2×D42C2512211840yescomplemented
411C2×D42C2514423680yescomplemented
412C2×D42C2512211840yescomplemented
413C2×#537C2511105920yescomplemented
414C2×#535C2512211840yescomplemented
415C2×#534C2512211840yescomplemented
416C2×#532C2511105920yescomplemented
417C22×C4⋊Q8C25113440yescomplemented
418C22×#127C25140320yescomplemented
419C22×#127C25180640yescomplemented
420C22×#127C251552960yescomplemented
421C22×#124C25180640yescomplemented
422C2×#525C2512211840yescomplemented
423C22×#123C251161280yescomplemented
424C22×C22⋊Q8C25126880yescomplemented
425C22×C22⋊Q8C25180640yescomplemented
426C22×#121C25180640yescomplemented
427C22×#121C25180640yescomplemented
428C22×#121C251161280yescomplemented
429C22×#121C251161280yescomplemented
430C22×#121C25180640yescomplemented
431C22×#121C25180640yescomplemented
432C22×#121C2511105920yescomplemented
433C22×#121C2511105920yescomplemented
434C22×#120C251161280yescomplemented
435C22×#120C251322560yescomplemented
436C22×#120C2512211840yescomplemented
437C4×H(5,𝔽2)C2511048576yescomplemented
438C2×#520C251368640yescomplemented
439C2×#518C251552960yescomplemented
440C2×C4×#41C251368640yescomplemented
441C22×C4×Q8C2514480yescomplemented
442C22×C4×Q8C25113440yescomplemented
443C22×C4×D4C25113440yes—
444C22×C4×D4C25140320yescomplemented
445C22×C4×D4C25180640yescomplemented
446C22×C4×D4C25180640yescomplemented
447C22×C4×D4C25140320yescomplemented
448C22×C4×D4C25140320yescomplemented
449C22×C4×D4C25180640yescomplemented
450C22×C4×D4C251552960yescomplemented
451C22×C4×D4C251552960yescomplemented
452C22×#117C25140320yescomplemented
453C23×C4⋊C4C251360yes—
454C23×C4⋊C4C2511080yes—
455C23×C4⋊C4C2511080yes—
456C23×C4⋊C4C251360yes—
457C23×C4⋊C4C251720yes—
458C23×C4⋊C4C25120160yescomplemented
459C23×C4⋊C4C25120160yescomplemented
460C23×C22⋊C4C251720yes—
461C23×C22⋊C4C2512160yes—
462C23×C22⋊C4C2514320yes—
463C23×C22⋊C4C2512160yes—
464C23×C22⋊C4C25140320yescomplemented
465C23×C22⋊C4C25140320yescomplemented
466C23×C22⋊C4C25180640yescomplemented
467C23×C42C251360yes—
468C23×C42C2511080yes—
469C23×C42C25120160yescomplemented
470C26—232no—
471C26—2144no—
472C26—2144no—
473C26—232no—
474C26—217280no—
475C26—2288no—
476C26—2288no—
477C26—217280no—
478C26—2288no—
479C26—234560no—
480C26—2430080no—
481C26—42880no—
482C26—46144no—
483C26—42880no—
484C26—48640no—
485C26—417280no—
486C26—4215040no—
487C26—417280no—
488C26—418432no—
489C26—818432no—
490C26—8107520no—
491C26—8737280no—
492C26C23×D41288yes—
493C26C23×D4111520yescomplemented
494C26C2×H(5,𝔽2)164yescomplemented
495C26C261540yes—
496C26C26110080yes—
497C26C261270yes—
498C26C26160yes—
499C26C26120160yes—
500C26C2613360yes—
501C26C2611yescharacteristic
502C26C26192160yescomplemented
503C2×H(5,𝔽2)—233554432no—
504C2×H(5,𝔽2)—211796480no—
505C2×H(5,𝔽2)—217694720no—
506C2×H(5,𝔽2)C23×D411966080yesdirect product factor
507C2×H(5,𝔽2)C26165536yes—
508C2×H(5,𝔽2)C2611179648yescomplemented
509C2×H(5,𝔽2)C261786432yescomplemented
510C22×#41—211796480no—
511C22×#41—2430080no—
512C22×#41—21290240no—
513C22×#41—21290240no—
514C22×#41C23×D41430080yescomplemented
515C22×#41C26146080yes—
516C22×#41C261276480yescomplemented
517C22×#41C261276480yescomplemented
518C22×#41C26192160yescomplemented
519C22×#41C261786432yescomplemented
520C23×Q8—2143360no—
521C23×Q8—211520no—
522C23×Q8C23×D413840yescomplemented
523C23×Q8C2616720yes—
524C23×Q8C2611120yes—
525C23×Q8C26130720yescomplemented
526C23×D4—269120no—
527C23×D4—21290240no—
528C23×D4—217280no—
529C23×D4—21290240no—
530C23×D4—22580480no—
531C23×D4—217694720no—
532C23×D4—2322560no—
533C23×D4—234560no—
534C23×D4—2645120no—
535C23×D4—28640no—
536C23×D4—4322560no—
537C23×D4—417280no—
538C23×D4—417280no—
539C23×D4—42949120no—
540C23×D4—4645120no—
541C23×D4—8161280no—
542C23×D4C23×D4134560yescomplemented
543C23×D4C23×D41645120yescomplemented
544C23×D4C2×H(5,𝔽2)11920yesdirect product factor
545C23×D4C26110080yes—
546C23×D4C2615040yes—
547C23×D4C26169120yes—
548C23×D4C26140320yes—
549C23×D4C26120160yes—
550C23×D4C26120160yes—
551C23×D4C26120160yes—
552C23×D4C26110080yes—
553C23×D4C26169120yes—
554C23×D4C261560yes—
555C23×D4C261276480yescomplemented
556C23×D4C261276480yescomplemented
557C23×D4C261138240yescomplemented
558C23×D4C261552960yescomplemented
559C23×D4C261276480yescomplemented
560C23×D4C261138240yescomplemented
561C23×D4C261138240yescomplemented
562C23×D4C2611179648yescomplemented
563C23×D4C261393216yescomplemented
564C24×C4—2192no—
565C24×C4—217280no—
566C24×C4—2144no—
567C24×C4—296no—
568C24×C4—211520no—
569C24×C4—234560no—
570C24×C4—2645120no—
571C24×C4—28640no—
572C24×C4—4107520no—
573C24×C4—48640no—
574C24×C4—44320no—
575C24×C4C23×D41192yes—
576C24×C4C23×D4117280yescomplemented
577C24×C4C2×H(5,𝔽2)132yescomplemented
578C24×C4C261360yes—
579C24×C4C261270yes—
580C24×C4C261180yes—
581C24×C4C2616720yes—
582C24×C4C2615040yes—
583C24×C4C26110080yes—
584C24×C4C26120160yes—
585C24×C4C26110080yes—
586C24×C4C2615040yes—
587C24×C4C261180yes—
588C24×C4C2615040yes—
589C24×C4C26130yes—
590C24×C4C261138240yescomplemented
591C24×C4C26146080yescomplemented
592#550C261393216yescomplemented
593#550C261786432yescomplemented
594D4×Q8C261131072yescomplemented
595#548C261786432yescomplemented
596#547C2611179648yescomplemented
597#546C2612359296yescomplemented
598#546C2614718592yescomplemented
599D42C2611179648yescomplemented
600D42C2614718592yescomplemented
601D42C2612359296yescomplemented
602D42C2612359296yescomplemented
603#537C2611179648yescomplemented
604#535C2612359296yescomplemented
605#534C2612359296yescomplemented
606#532C2611179648yescomplemented
607C2×C4⋊Q8C26146080yescomplemented
608C2×#127C261138240yescomplemented
609C2×#127C261276480yescomplemented
610C2×#127C261589824yescomplemented
611C2×#124C261276480yescomplemented
612#525C2612359296yescomplemented
613C2×#123C261552960yescomplemented
614C2×C22⋊Q8C26192160yescomplemented
615C2×C22⋊Q8C261276480yescomplemented
616C2×#121C261276480yescomplemented
617C2×#121C261276480yescomplemented
618C2×#121C261552960yescomplemented
619C2×#121C261552960yescomplemented
620C2×#121C261276480yescomplemented
621C2×#121C261276480yescomplemented
622C2×#121C2611179648yescomplemented
623C2×#121C2611179648yescomplemented
624C2×#120C261552960yescomplemented
625C2×#120C2611105920yescomplemented
626C2×#120C2612359296yescomplemented
627#520C261393216yescomplemented
628#518C261589824yescomplemented
629C4×#41C261393216yescomplemented
630C2×C4×Q8C26115360yescomplemented
631C2×C4×Q8C26146080yescomplemented
632C2×C4×D4C26146080yes—
633C2×C4×D4C261138240yescomplemented
634C2×C4×D4C261276480yescomplemented
635C2×C4×D4C261276480yescomplemented
636C2×C4×D4C261138240yescomplemented
637C2×C4×D4C261138240yescomplemented
638C2×C4×D4C261276480yescomplemented
639C2×C4×D4C261589824yescomplemented
640C2×C4×D4C261589824yescomplemented
641C2×#117C261138240yescomplemented
642C22×C4⋊C4C2613360yes—
643C22×C4⋊C4C26110080yes—
644C22×C4⋊C4C26110080yes—
645C22×C4⋊C4C2613360yes—
646C22×C4⋊C4C2616720yes—
647C22×C4⋊C4C26169120yescomplemented
648C22×C4⋊C4C26169120yescomplemented
649C22×C22⋊C4C2616720yes—
650C22×C22⋊C4C26120160yes—
651C22×C22⋊C4C26140320yes—
652C22×C22⋊C4C26120160yes—
653C22×C22⋊C4C261138240yescomplemented
654C22×C22⋊C4C261138240yescomplemented
655C22×C22⋊C4C261276480yescomplemented
656C22×C42C2613360yes—
657C22×C42C26110080yes—
658C22×C42C26169120yescomplemented
659C25—21024no—
660C25—24608no—
661C25—2480no—
662C25—22160no—
663C25—22160no—
664C25—2480no—
665C25—280640no—
666C25—24320no—
667C25—24320no—
668C25—280640no—
669C25—24320no—
670C25—2161280no—
671C25—2737280no—
672C25—413440no—
673C25—492160no—
674C25—413440no—
675C25—440320no—
676C25—480640no—
677C25—4368640no—
678C25—480640no—
679C25—4276480no—
680C25—44608no—
681C25—8276480no—
682C25—8184320no—
683C25—83440640no—
684C25C24×D414320yes—
685C25C24×D4116yes—
686C25C24×D4153760yescomplemented
687C25C22×H(5,𝔽2)116yes—
688C25C22×H(5,𝔽2)1960yescomplemented
689C25H(7,𝔽2)116yes—
690C25C2712520yes—
691C25C27117280yes—
692C25C2711260yes—
693C25C271280yes—
694C25C27134560yes—
695C25C2715760yes—
696C25C27115yes—
697C25C27149152yescomplemented
698H(5,𝔽2)—26291456no—
699H(5,𝔽2)—29437184no—
700H(5,𝔽2)C24×D411048576yesdirect product factor
701C2×#41—26291456no—
702C2×#41—2737280no—
703C2×#41—22211840no—
704C2×#41—22211840no—
705C2×#41C24×D41737280yescomplemented
706C2×#41C27124576yes—
707C2×#41C271147456yescomplemented
708C2×#41C271147456yescomplemented
709C2×#41C27149152yescomplemented
710C22×Q8—2245760no—
711C22×Q8—253760no—
712C22×Q8C24×D4117920yescomplemented
713C22×Q8C27111520yes—
714C22×Q8C2711920yes—
715C22×Q8C27116384yescomplemented
716C22×D4—2322560no—
717C22×D4—22211840no—
718C22×D4—280640no—
719C22×D4—22211840no—
720C22×D4—24423680no—
721C22×D4—29437184no—
722C22×D4—2552960no—
723C22×D4—2161280no—
724C22×D4—21105920no—
725C22×D4—240320no—
726C22×D4—4552960no—
727C22×D4—480640no—
728C22×D4—480640no—
729C22×D4—41572864no—
730C22×D4—41105920no—
731C22×D4—8276480no—
732C22×D4C24×D41161280yescomplemented
733C22×D4C24×D411105920yescomplemented
734C22×D4C22×H(5,𝔽2)18960yesdirect product factor
735C22×D4C27117280yes—
736C22×D4C2718640yes—
737C22×D4C27136864yes—
738C22×D4C27169120yes—
739C22×D4C27134560yes—
740C22×D4C27134560yes—
741C22×D4C27134560yes—
742C22×D4C27117280yes—
743C22×D4C27136864yes—
744C22×D4C271960yes—
745C22×D4C271147456yescomplemented
746C22×D4C27173728yescomplemented
747C22×D4C271147456yescomplemented
748C22×D4C271294912yescomplemented
749C22×D4C271147456yescomplemented
750C22×D4C27173728yescomplemented
751C22×D4C27173728yescomplemented
752C23×C4—22880no—
753C23×C4—280640no—
754C23×C4—22160no—
755C23×C4—21440no—
756C23×C4—253760no—
757C23×C4—2161280no—
758C23×C4—21105920no—
759C23×C4—240320no—
760C23×C4—4184320no—
761C23×C4—440320no—
762C23×C4—420160no—
763C23×C4C24×D412880yes—
764C23×C4C24×D4180640yescomplemented
765C23×C4C22×H(5,𝔽2)1480yescomplemented
766C23×C4C271840yes—
767C23×C4C2711260yes—
768C23×C4C2711680yes—
769C23×C4C27117280yes—
770C23×C4C2718640yes—
771C23×C4C27111520yes—
772C23×C4C27134560yes—
773C23×C4C2718640yes—
774C23×C4C27117280yes—
775C23×C4C271840yes—
776C23×C4C2718640yes—
777C23×C4C271140yes—
778C23×C4C27173728yescomplemented
779C23×C4C27124576yescomplemented
780C4⋊Q8C27124576yescomplemented
781#127C27173728yescomplemented
782#127C271147456yescomplemented
783#124C271147456yescomplemented
784#123C271294912yescomplemented
785C22⋊Q8C27149152yescomplemented
786C22⋊Q8C271147456yescomplemented
787#121C271147456yescomplemented
788#121C271147456yescomplemented
789#121C271294912yescomplemented
790#121C271294912yescomplemented
791#121C271147456yescomplemented
792#121C271147456yescomplemented
793#120C271294912yescomplemented
794#120C271589824yescomplemented
795C4×Q8C2718192yescomplemented
796C4×Q8C27124576yescomplemented
797C4×D4C27124576yes—
798C4×D4C27173728yescomplemented
799C4×D4C271147456yescomplemented
800C4×D4C271147456yescomplemented
801C4×D4C27173728yescomplemented
802C4×D4C27173728yescomplemented
803C4×D4C271147456yescomplemented
804#117C27173728yescomplemented
805C2×C4⋊C4C2715760yes—
806C2×C4⋊C4C27117280yes—
807C2×C4⋊C4C27117280yes—
808C2×C4⋊C4C2715760yes—
809C2×C4⋊C4C27111520yes—
810C2×C4⋊C4C27136864yescomplemented
811C2×C4⋊C4C27136864yescomplemented
812C2×C22⋊C4C27111520yes—
813C2×C22⋊C4C27134560yes—
814C2×C22⋊C4C27169120yes—
815C2×C22⋊C4C27134560yes—
816C2×C22⋊C4C27173728yescomplemented
817C2×C22⋊C4C27173728yescomplemented
818C2×C22⋊C4C271147456yescomplemented
819C2×C42C27117280yes—
820C2×C42C2715760yes—
821C2×C42C27136864yescomplemented
822C24—21120no—
823C24—25040no—
824C24—25040no—
825C24—21120no—
826C24—27680no—
827C24—234560no—
828C24—269120no—
829C24—210080no—
830C24—210080no—
831C24—269120no—
832C24—210080no—
833C24—2138240no—
834C24—2196608no—
835C24—411520no—
836C24—4215040no—
837C24—411520no—
838C24—434560no—
839C24—469120no—
840C24—498304no—
841C24—469120no—
842C24—4645120no—
843C24—434560no—
844C24—8645120no—
845C24—849152no—
846C24—82949120no—
847C24D4×H(5,𝔽2)1256yesdirect product factor
848C24C25×D4110080yes—
849C24C25×D41120yes—
850C24C25×D4146080yescomplemented
851C24C23×H(5,𝔽2)1120yes—
852C24C23×H(5,𝔽2)12240yescomplemented
853C24C2×H(7,𝔽2)1120yes—
854C24C2812160yes—
855C24C2814608yes—
856C24C2811080yes—
857C24C281240yes—
858C24C2819216yes—
859C24C2811536yes—
860C24C28135yes—
861#41—2196608no—
862#41—2589824no—
863#41—2589824no—
864#41C25×D41196608yescomplemented
865C2×Q8—265536no—
866C2×Q8—246080no—
867C2×Q8C25×D4115360yescomplemented
868C2×Q8C2813072yes—
869C2×Q8C281512yes—
870C2×D4—2276480no—
871C2×D4—2589824no—
872C2×D4—269120no—
873C2×D4—2589824no—
874C2×D4—21179648no—
875C2×D4—2147456no—
876C2×D4—2138240no—
877C2×D4—2294912no—
878C2×D4—234560no—
879C2×D4—4147456no—
880C2×D4—469120no—
881C2×D4—469120no—
882C2×D4—4294912no—
883C2×D4—873728no—
884C2×D4C25×D41138240yescomplemented
885C2×D4C25×D41294912yescomplemented
886C2×D4C23×H(5,𝔽2)17680yesdirect product factor
887C2×D4C2814608yes—
888C2×D4C2812304yes—
889C2×D4C28118432yes—
890C2×D4C2819216yes—
891C2×D4C2819216yes—
892C2×D4C2819216yes—
893C2×D4C2814608yes—
894C2×D4C281256yes—
895C22×C4—26720no—
896C22×C4—269120no—
897C22×C4—25040no—
898C22×C4—23360no—
899C22×C4—246080no—
900C22×C4—2138240no—
901C22×C4—2294912no—
902C22×C4—234560no—
903C22×C4—449152no—
904C22×C4—434560no—
905C22×C4—417280no—
906C22×C4C25×D416720yes—
907C22×C4C25×D4169120yescomplemented
908C22×C4C23×H(5,𝔽2)11120yescomplemented
909C22×C4C281720yes—
910C22×C4C2811080yes—
911C22×C4C2812304yes—
912C22×C4C2811440yes—
913C22×C4C2814608yes—
914C22×C4C2813072yes—
915C22×C4C2819216yes—
916C22×C4C2812304yes—
917C22×C4C2814608yes—
918C22×C4C281720yes—
919C22×C4C2812304yes—
920C22×C4C281120yes—
921C4⋊C4C2811536yes—
922C4⋊C4C2814608yes—
923C4⋊C4C2814608yes—
924C4⋊C4C2811536yes—
925C4⋊C4C2813072yes—
926C22⋊C4C2813072yes—
927C22⋊C4C2819216yes—
928C22⋊C4C28118432yes—
929C22⋊C4C2819216yes—
930C42C2811536yes—
931C42C2814608yes—
932C23—28960no—
933C23—240320no—
934C23—22160no—
935C23—22160no—
936C23—2480no—
937C23—2480no—
938C23—24320no—
939C23—29216no—
940C23—24320no—
941C23—29216no—
942C23—24320no—
943C23—218432no—
944C23—41536no—
945C23—492160no—
946C23—41536no—
947C23—44608no—
948C23—49216no—
949C23—49216no—
950C23—4276480no—
951C23—440320no—
952C23—8276480no—
953C23—8393216no—
954C23C2×D4×H(5,𝔽2)1960yesdirect product factor
955C23C26×D414320yes—
956C23C26×D41140yes—
957C23C26×D416144yescomplemented
958C23C24×H(5,𝔽2)1140yes—
959C23C24×H(5,𝔽2)1960yescomplemented
960C23C22×H(7,𝔽2)1140yes—
961C23C291288yes—
962C23C29132yes—
963C23C291144yes—
964C23C29115yes—
965Q8—26144no—
966Q8C26×D412048yescomplemented
967D4—29216no—
968D4—236864no—
969D4—24608no—
970D4—218432no—
971D4—49216no—
972D4—49216no—
973D4C26×D4118432yescomplemented
974D4C24×H(5,𝔽2)11024yesdirect product factor
975C2×C4—22160no—
976C2×C4—21440no—
977C2×C4—22880no—
978C2×C4—29216no—
979C2×C4—24608no—
980C2×C4—26144no—
981C2×C4—218432no—
982C2×C4—44608no—
983C2×C4—42304no—
984C2×C4C26×D412880yes—
985C2×C4C26×D419216yescomplemented
986C2×C4C24×H(5,𝔽2)1480yescomplemented
987C2×C4C29196yes—
988C2×C4C291144yes—
989C2×C4C291192yes—
990C2×C4C29116yes—
991C2×C4C29196yes—
992C22—232no—
993C22—2144no—
994C22—232no—
995C22—21920no—
996C22—28640no—
997C22—2144no—
998C22—2288no—
999C22—2288no—
1000C22—2288no—
1001C22—46144no—
1002C22—418432no—
1003C22—48640no—
1004C22—818432no—
1005C22C21011yescharacteristic
1006C22C22×D4×H(5,𝔽2)1560yesdirect product factor
1007C22C23×H(7,𝔽2)130yes—
1008C22C25×H(5,𝔽2)130yes—
1009C22C25×H(5,𝔽2)164yescomplemented
1010C22C27×D41288yes—
1011C22C27×D4130yes—
1012C4—2192no—
1013C4—296no—
1014C4—2144no—
1015C4C25×H(5,𝔽2)132yescomplemented
1016C4C27×D41192yes—
1017C2—264no—
1018C2—2288no—
1019C2—4288no—
1020C2C24×H(7,𝔽2)11yescharacteristic
1021C2C23×D4×H(5,𝔽2)160yesdirect product factor
1022C2C28×D411yescharacteristic
1023C2C26×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, socleC26C26
commutator, Frattini, cosocleC22C210
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C26 ◁ G
LECSG ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C24×D4×#41C2semidirect
2. C24×D4×Q8C22semidirect
3. C24×C4×H(5,𝔽2)C2semidirect
4. C26×H(5,𝔽2)C2semidirect
5. C24×#3498C2semidirect
6. C24×C4×#41C22semidirect
7. C24×#3496C2semidirect
8. C24×#547C22semidirect
9. C24×#532C22semidirect
10. C24×#3488C2semidirect
11. C26×#41C22semidirect
12. C24×#537C22semidirect
13. C24×#520C22semidirect
14. C24×#550C22semidirect
15. C24×#550C22semidirect
16. C24×#548C22semidirect
17. C23×D4×H(5,𝔽2)C2direct (N × H)
18. C23×C4×H(5,𝔽2)C22semidirect
19. C24×#3484C2semidirect
20. C24×#535C22semidirect
21. C24×#518C22semidirect
22. C25×D42C2semidirect
23. C25×#127C22semidirect
24. C25×#121C22semidirect
25. C25×#121C22semidirect
26. C25×C4×D4C22semidirect
27. C25×C4×D4C22semidirect
28. C24×#546C22semidirect
29. C24×#546C22semidirect
30. C23×#3498C22semidirect
31. C23×#3488C22semidirect
32. C24×#534C22semidirect
33. C23×#3496C22semidirect
34. C27×D4C22semidirect
35. C27×D4C22semidirect
36. C24×#525C22semidirect
37. C23×D4×#41C22semidirect
38. C25×#120C22semidirect
41. C25×H(5,𝔽2)C22semidirect
42. C25×H(5,𝔽2)C22semidirect
43. C25×H(5,𝔽2)C22semidirect
44. C22×D4×H(5,𝔽2)C22direct (N × H)
45. C23×#3484C22semidirect
46. C24×D42C22semidirect
47. C24×D42C22semidirect
48. C24×D42C22semidirect
49. C24×D42C22semidirect
50. C24×D42C22semidirect
51. C29C23semidirect
55. C24×H(5,𝔽2)D4direct (N × H)
57. C24×H(5,𝔽2)C23semidirect
58. C24×H(5,𝔽2)C23semidirect
59. C24×H(5,𝔽2)C23semidirect
62. C25×#41C23semidirect
63. C25×#41C23semidirect
64. C25×#41C23semidirect
65. C25×#41C23semidirect
66. C26×Q8C23semidirect
71. C26×D4C23semidirect
72. C26×D4C23semidirect
73. C26×D4C23semidirect
74. C26×D4C23semidirect
75. C26×D4C23semidirect
76. C26×D4C23semidirect
77. C26×D4C23semidirect
78. C26×D4C23semidirect
79. C26×D4C23semidirect
80. C27×C4C23semidirect
81. C27×C4C23semidirect
82. C2×D4×H(5,𝔽2)C23direct (N × H)
83. C22×#3498C23semidirect
84. C22×#3488C23semidirect
85. C22×#3496C23semidirect
86. C22×#3484C23semidirect
87. C22×D4×#41C23semidirect
88. C23×#550C23semidirect
89. C23×#550C23semidirect
90. C23×#547C23semidirect
91. C23×#548C23semidirect
92. C23×#546C23semidirect
93. C23×#546C23semidirect
94. C23×D4×Q8C23semidirect
95. C23×D42C23semidirect
96. C23×D42C23semidirect
97. C23×D42C23semidirect
98. C23×D42C23semidirect
99. C23×D42C23semidirect
100. C23×#537C23semidirect
101. C23×#535C23semidirect
102. C23×#534C23semidirect
103. C23×#532C23semidirect
104. C24×C4⋊Q8C23semidirect
105. C24×#127C23semidirect
106. C24×#127C23semidirect
107. C24×#127C23semidirect
108. C24×#124C23semidirect
109. C23×#525C23semidirect
110. C24×#123C23semidirect
111. C24×C22⋊Q8C23semidirect
112. C24×C22⋊Q8C23semidirect
113. C24×#121C23semidirect
114. C24×#121C23semidirect
115. C24×#121C23semidirect
116. C24×#121C23semidirect
117. C24×#121C23semidirect
118. C24×#121C23semidirect
119. C24×#121C23semidirect
120. C24×#121C23semidirect
121. C24×#120C23semidirect
122. C24×#120C23semidirect
123. C24×#120C23semidirect
124. C22×C4×H(5,𝔽2)C23semidirect
125. C23×#520C23semidirect
126. C23×#518C23semidirect
127. C23×C4×#41C23semidirect
128. C24×C4×Q8C23semidirect
129. C24×C4×Q8C23semidirect
131. C24×C4×D4C23semidirect
132. C24×C4×D4C23semidirect
133. C24×C4×D4C23semidirect
134. C24×C4×D4C23semidirect
135. C24×C4×D4C23semidirect
136. C24×C4×D4C23semidirect
137. C24×C4×D4C23semidirect
138. C24×C4×D4C23semidirect
139. C24×#117C23semidirect
140. C25×C4⋊C4C23semidirect
141. C25×C4⋊C4C23semidirect
142. C25×C22⋊C4C23semidirect
143. C25×C22⋊C4C23semidirect
144. C25×C22⋊C4C23semidirect
145. C25×C42C23semidirect
152. C28C24semidirect
156. C23×H(5,𝔽2)C2×D4direct (N × H)
158. C23×H(5,𝔽2)C24semidirect
159. C23×H(5,𝔽2)C24semidirect
160. C23×H(5,𝔽2)C24semidirect
165. C24×#41C2×D4semidirect
167. C24×#41C24semidirect
168. C24×#41C24semidirect
169. C24×#41C24semidirect
170. C24×#41C24semidirect
174. C25×Q8C24semidirect
185. C25×D4C2×D4semidirect
196. C25×D4C24semidirect
197. C25×D4C24semidirect
198. C25×D4C24semidirect
199. C25×D4C24semidirect
200. C25×D4C24semidirect
201. C25×D4C24semidirect
202. C25×D4C24semidirect
203. C25×D4C24semidirect
204. C25×D4C24semidirect
214. C26×C4C24semidirect
215. C26×C4C24semidirect
216. D4×H(5,𝔽2)C24direct (N × H)
217. C2×#3498C24semidirect
218. C2×#3488C24semidirect
219. C2×#3496C24semidirect
220. C2×#3484C24semidirect
221. C2×D4×#41C24semidirect
222. C22×#550C24semidirect
223. C22×#550C24semidirect
224. C22×#547C24semidirect
225. C22×#548C24semidirect
226. C22×#546C24semidirect
227. C22×#546C24semidirect
228. C22×D4×Q8C24semidirect
229. C22×D42C24semidirect
230. C22×D42C24semidirect
231. C22×D42C24semidirect
232. C22×D42C24semidirect
233. C22×D42C24semidirect
234. C22×#537C24semidirect
235. C22×#535C24semidirect
236. C22×#534C24semidirect
237. C22×#532C24semidirect
238. C23×C4⋊Q8C24semidirect
239. C23×#127C24semidirect
240. C23×#127C24semidirect
241. C23×#127C24semidirect
242. C23×#124C24semidirect
243. C22×#525C24semidirect
244. C23×#123C24semidirect
245. C23×C22⋊Q8C24semidirect
246. C23×C22⋊Q8C24semidirect
247. C23×#121C24semidirect
248. C23×#121C24semidirect
249. C23×#121C24semidirect
250. C23×#121C24semidirect
251. C23×#121C24semidirect
252. C23×#121C24semidirect
253. C23×#121C24semidirect
254. C23×#121C24semidirect
255. C23×#120C24semidirect
256. C23×#120C24semidirect
257. C23×#120C24semidirect
258. C2×C4×H(5,𝔽2)C24semidirect
259. C22×#520C24semidirect
260. C22×#518C24semidirect
261. C22×C4×#41C24semidirect
262. C23×C4×Q8C24semidirect
263. C23×C4×Q8C24semidirect
265. C23×C4×D4C24semidirect
266. C23×C4×D4C24semidirect
267. C23×C4×D4C24semidirect
268. C23×C4×D4C24semidirect
269. C23×C4×D4C24semidirect
270. C23×C4×D4C24semidirect
271. C23×C4×D4C24semidirect
272. C23×C4×D4C24semidirect
273. C23×#117C24semidirect
279. C24×C4⋊C4C24semidirect
280. C24×C4⋊C4C24semidirect
285. C24×C22⋊C4C24semidirect
286. C24×C22⋊C4C24semidirect
287. C24×C22⋊C4C24semidirect
290. C24×C42C24semidirect
303. C27C22×D4semidirect
310. C27C25semidirect
314. C22×H(5,𝔽2)C22×D4direct (N × H)
316. C22×H(5,𝔽2)C25semidirect
317. C22×H(5,𝔽2)C25semidirect
318. C22×H(5,𝔽2)C25semidirect
323. C23×#41C22×D4semidirect
325. C23×#41C25semidirect
326. C23×#41C25semidirect
327. C23×#41C25semidirect
328. C23×#41C25semidirect
331. C24×Q8C22×D4semidirect
334. C24×Q8C25semidirect
351. C24×D4C22×D4semidirect
352. C24×D4C22×D4semidirect
353. C24×D4H(5,𝔽2)direct (N × H)
364. C24×D4C25semidirect
365. C24×D4C25semidirect
366. C24×D4C25semidirect
367. C24×D4C25semidirect
368. C24×D4C25semidirect
369. C24×D4C25semidirect
370. C24×D4C25semidirect
371. C24×D4C25semidirect
372. C24×D4C25semidirect
381. C25×C4C22×D4semidirect
394. C25×C4C25semidirect
395. C25×C4C25semidirect
396. #3498C25semidirect
397. #3496C25semidirect
398. #3488C25semidirect
399. #3484C25semidirect
400. D4×#41C25semidirect
401. C2×#550C25semidirect
402. C2×#550C25semidirect
403. C2×D4×Q8C25semidirect
404. C2×#548C25semidirect
405. C2×#547C25semidirect
406. C2×#546C25semidirect
407. C2×#546C25semidirect
408. C2×D42C25semidirect
409. C2×D42C25semidirect
410. C2×D42C25semidirect
411. C2×D42C25semidirect
412. C2×D42C25semidirect
413. C2×#537C25semidirect
414. C2×#535C25semidirect
415. C2×#534C25semidirect
416. C2×#532C25semidirect
417. C22×C4⋊Q8C25semidirect
418. C22×#127C25semidirect
419. C22×#127C25semidirect
420. C22×#127C25semidirect
421. C22×#124C25semidirect
422. C2×#525C25semidirect
423. C22×#123C25semidirect
424. C22×C22⋊Q8C25semidirect
425. C22×C22⋊Q8C25semidirect
426. C22×#121C25semidirect
427. C22×#121C25semidirect
428. C22×#121C25semidirect
429. C22×#121C25semidirect
430. C22×#121C25semidirect
431. C22×#121C25semidirect
432. C22×#121C25semidirect
433. C22×#121C25semidirect
434. C22×#120C25semidirect
435. C22×#120C25semidirect
436. C22×#120C25semidirect
437. C4×H(5,𝔽2)C25semidirect
438. C2×#520C25semidirect
439. C2×#518C25semidirect
440. C2×C4×#41C25semidirect
441. C22×C4×Q8C25semidirect
442. C22×C4×Q8C25semidirect
444. C22×C4×D4C25semidirect
445. C22×C4×D4C25semidirect
446. C22×C4×D4C25semidirect
447. C22×C4×D4C25semidirect
448. C22×C4×D4C25semidirect
449. C22×C4×D4C25semidirect
450. C22×C4×D4C25semidirect
451. C22×C4×D4C25semidirect
452. C22×#117C25semidirect
458. C23×C4⋊C4C25semidirect
459. C23×C4⋊C4C25semidirect
464. C23×C22⋊C4C25semidirect
465. C23×C22⋊C4C25semidirect
466. C23×C22⋊C4C25semidirect
469. C23×C42C25semidirect
493. C26C23×D4semidirect
494. C26C2×H(5,𝔽2)semidirect
502. C26C26semidirect
506. C2×H(5,𝔽2)C23×D4direct (N × H)
508. C2×H(5,𝔽2)C26semidirect
509. C2×H(5,𝔽2)C26semidirect
514. C22×#41C23×D4semidirect
516. C22×#41C26semidirect
517. C22×#41C26semidirect
518. C22×#41C26semidirect
519. C22×#41C26semidirect
522. C23×Q8C23×D4semidirect
525. C23×Q8C26semidirect
542. C23×D4C23×D4semidirect
543. C23×D4C23×D4semidirect
544. C23×D4C2×H(5,𝔽2)direct (N × H)
555. C23×D4C26semidirect
556. C23×D4C26semidirect
557. C23×D4C26semidirect
558. C23×D4C26semidirect
559. C23×D4C26semidirect
560. C23×D4C26semidirect
561. C23×D4C26semidirect
562. C23×D4C26semidirect
563. C23×D4C26semidirect
576. C24×C4C23×D4semidirect
577. C24×C4C2×H(5,𝔽2)semidirect
590. C24×C4C26semidirect
591. C24×C4C26semidirect
592. #550C26semidirect
593. #550C26semidirect
594. D4×Q8C26semidirect
595. #548C26semidirect
596. #547C26semidirect
597. #546C26semidirect
598. #546C26semidirect
599. D42C26semidirect
600. D42C26semidirect
601. D42C26semidirect
602. D42C26semidirect
603. #537C26semidirect
604. #535C26semidirect
605. #534C26semidirect
606. #532C26semidirect
607. C2×C4⋊Q8C26semidirect
608. C2×#127C26semidirect
609. C2×#127C26semidirect
610. C2×#127C26semidirect
611. C2×#124C26semidirect
612. #525C26semidirect
613. C2×#123C26semidirect
614. C2×C22⋊Q8C26semidirect
615. C2×C22⋊Q8C26semidirect
616. C2×#121C26semidirect
617. C2×#121C26semidirect
618. C2×#121C26semidirect
619. C2×#121C26semidirect
620. C2×#121C26semidirect
621. C2×#121C26semidirect
622. C2×#121C26semidirect
623. C2×#121C26semidirect
624. C2×#120C26semidirect
625. C2×#120C26semidirect
626. C2×#120C26semidirect
627. #520C26semidirect
628. #518C26semidirect
629. C4×#41C26semidirect
630. C2×C4×Q8C26semidirect
631. C2×C4×Q8C26semidirect
633. C2×C4×D4C26semidirect
634. C2×C4×D4C26semidirect
635. C2×C4×D4C26semidirect
636. C2×C4×D4C26semidirect
637. C2×C4×D4C26semidirect
638. C2×C4×D4C26semidirect
639. C2×C4×D4C26semidirect
640. C2×C4×D4C26semidirect
641. C2×#117C26semidirect
647. C22×C4⋊C4C26semidirect
648. C22×C4⋊C4C26semidirect
653. C22×C22⋊C4C26semidirect
654. C22×C22⋊C4C26semidirect
655. C22×C22⋊C4C26semidirect
658. C22×C42C26semidirect
686. C25C24×D4semidirect
688. C25C22×H(5,𝔽2)semidirect
697. C25C27semidirect
700. H(5,𝔽2)C24×D4direct (N × H)
705. C2×#41C24×D4semidirect
707. C2×#41C27semidirect
708. C2×#41C27semidirect
709. C2×#41C27semidirect
712. C22×Q8C24×D4semidirect
715. C22×Q8C27semidirect
732. C22×D4C24×D4semidirect
733. C22×D4C24×D4semidirect
734. C22×D4C22×H(5,𝔽2)direct (N × H)
745. C22×D4C27semidirect
746. C22×D4C27semidirect
747. C22×D4C27semidirect
748. C22×D4C27semidirect
749. C22×D4C27semidirect
750. C22×D4C27semidirect
751. C22×D4C27semidirect
764. C23×C4C24×D4semidirect
765. C23×C4C22×H(5,𝔽2)semidirect
778. C23×C4C27semidirect
779. C23×C4C27semidirect
780. C4⋊Q8C27semidirect
781. #127C27semidirect
782. #127C27semidirect
783. #124C27semidirect
784. #123C27semidirect
785. C22⋊Q8C27semidirect
786. C22⋊Q8C27semidirect
787. #121C27semidirect
788. #121C27semidirect
789. #121C27semidirect
790. #121C27semidirect
791. #121C27semidirect
792. #121C27semidirect
793. #120C27semidirect
794. #120C27semidirect
795. C4×Q8C27semidirect
796. C4×Q8C27semidirect
798. C4×D4C27semidirect
799. C4×D4C27semidirect
800. C4×D4C27semidirect
801. C4×D4C27semidirect
802. C4×D4C27semidirect
803. C4×D4C27semidirect
804. #117C27semidirect
810. C2×C4⋊C4C27semidirect
811. C2×C4⋊C4C27semidirect
816. C2×C22⋊C4C27semidirect
817. C2×C22⋊C4C27semidirect
818. C2×C22⋊C4C27semidirect
821. C2×C42C27semidirect
847. C24D4×H(5,𝔽2)direct (N × H)
850. C24C25×D4semidirect
852. C24C23×H(5,𝔽2)semidirect
864. #41C25×D4semidirect
867. C2×Q8C25×D4semidirect
884. C2×D4C25×D4semidirect
885. C2×D4C25×D4semidirect
886. C2×D4C23×H(5,𝔽2)direct (N × H)
907. C22×C4C25×D4semidirect
908. C22×C4C23×H(5,𝔽2)semidirect
954. C23C2×D4×H(5,𝔽2)direct (N × H)
957. C23C26×D4semidirect
959. C23C24×H(5,𝔽2)semidirect
966. Q8C26×D4semidirect
973. D4C26×D4semidirect
974. D4C24×H(5,𝔽2)direct (N × H)
985. C2×C4C26×D4semidirect
986. C2×C4C24×H(5,𝔽2)semidirect
1006. C22C22×D4×H(5,𝔽2)direct (N × H)
1009. C22C25×H(5,𝔽2)semidirect
1015. C4C25×H(5,𝔽2)semidirect
1021. C2C23×D4×H(5,𝔽2)direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C24×D4×#412
C24×C4×H(5,𝔽2)2
C26×H(5,𝔽2)2
C24×#34982
C24×#34962
C24×#34882
C23×D4×H(5,𝔽2)2
C24×#34842
C25×D422