Finite Group Databasebeta

← C2×#72239580 #72317087

Subgroups — C2×#72239580 #72317087

Order 2048.

At least 6947 conjugacy classes of subgroups; only the 9192 normal subgroups are shown.

The subgroup lattice has 939 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#357420C211yesmaximal, characteristic, complemented
2C2×#357426C211yesmaximal, characteristic, complemented
3C22×#10776C212yesmaximal, complemented
4C22×#11006C212yesmaximal, complemented
5C22×#10984C212yesmaximal, complemented
6C2×#357440C212yesmaximal, complemented
7C22×#20598C212yesmaximal, complemented
8C23×#1795C212yesmaximal, complemented
9#72239580C2116yesmaximal, direct product factor
10C23×#3484C211yesmaximal, characteristic
11C24×H(5,𝔽2)C2211yescharacteristic
12C26×D4C2211yescharacteristic
13C22×#3484C418yescomplemented
14C22×#3484C2218yes—
15C23×#546C414yescomplemented
16C23×D42C414yescomplemented
17C23×#535C2211yescharacteristic
18C23×#535C2211yescharacteristic
19C23×#525C2211yescharacteristic
20C23×#525C2211yescharacteristic
21C23×#518C2211yescharacteristic
22C23×#407C2212yescomplemented
23C23×#410C2212yescomplemented
24C23×#413C2212yescomplemented
25C23×#421C2214yescomplemented
26C23×#418C2214yes—
27C23×#418C2214yescomplemented
28C22×#2280C2212yescomplemented
29C22×#1795C22116yescomplemented
30C2×#20598C22116yescomplemented
31C22×#1742C2212yescomplemented
32C22×#1740C2212yescomplemented
33C22×#1733C2214yescomplemented
34C2×#11006C22116yescomplemented
35C2×#10984C22116yescomplemented
36#357440C22116yescomplemented
37#357426C2218yescomplemented
38#357420C2218yescomplemented
39C2×#10776C22116yescomplemented
40C23×H(5,𝔽2)C2×C414yes—
41C23×H(5,𝔽2)D4116yes—
42C23×H(5,𝔽2)C2314yes—
43C24×#41C2×C412yes—
44C24×#41C2311yescharacteristic
45C24×#41C2311yescharacteristic
46C25×D4C2×C414yes—
47C25×D4C2×C414yes—
48C25×D4C2×C412yes—
49C25×D4D418yes—
50C25×D4D418yes—
51C25×D4C2311yescharacteristic
52C25×D4C2314yes—
53C25×D4C2311yescharacteristic
54C26×C4C2311yescharacteristic
55C24×M16C2314yes—
56C22×#546C2×C4132yescomplemented
57C22×D42C2×C4132yescomplemented
58C22×#535C2×C414yes—
59C22×#535C2×C414yes—
60C22×#535D4116yes—
61C22×#535D4116yes—
62C22×#535C2314yes—
63C22×#535C2314yes—
64C23×#127C2×C412yes—
65C23×#124C2×C412yes—
66C22×#525C2×C414yes—
67C22×#525C2×C414yes—
68C22×#525D418yes—
69C22×#525D418yes—
70C22×#525D414yes—
71C22×#525D414yes—
72C22×#525C2314yes—
73C22×#525C2314yes—
74C23×#123D412yes—
75C23×C22⋊Q8C2×C412yes—
76C23×C22⋊Q8D412yes—
77C23×#121C2×C412yes—
78C23×#121C2×C414yes—
79C23×#121D412yes—
80C23×#120D412yes—
81C22×#518C2×C414yes—
82C22×#518D4116yes—
83C22×#518C2314yes—
84C23×C4×D4C2×C414yes—
85C23×C4×D4C2×C414yes—
86C23×#117C2314yes—
87C23×#117C2311yescharacteristic
88C23×#117C2311yescharacteristic
89C22×#421C23116yescomplemented
90C22×#418D4132yescomplemented
91C22×#418C23116yes—
92C22×#418C23116yescomplemented
93C22×#413C2318yescomplemented
94C22×#410C2318yescomplemented
95C22×#407C2318yescomplemented
96C2×#2280C2318yescomplemented
97C2×#1742C2318yescomplemented
98C2×#1740C2318yescomplemented
99C2×#1733C23116yescomplemented
100C27C2×D411yescharacteristic
101C22×H(5,𝔽2)C22⋊C4132yescomplemented
102C22×H(5,𝔽2)C2×D4132yes—
103C23×#41C22⋊C4116yescomplemented
104C23×#41C22×C412yes—
105C23×#41C22×C418yes—
106C23×#41C22×C412yes—
107C23×#41C2×D414yes—
108C23×#41C2×D418yes—
109C23×#41C2×D414yes—
110C23×#41C2×D418yes—
111C23×#41C2×D412yes—
112C23×#41C2×D412yes—
113C23×#41C2×D418yes—
114C23×#41C2×D418yes—
115C23×#41C2412yes—
116C23×#41C2412yes—
117C24×Q8C22×C411yescharacteristic
118C24×Q8C2×D411yescharacteristic
119C24×D4C22⋊C4132yes—
120C24×D4C22⋊C4116yes—
121C24×D4C22⋊C4116yes—
122C24×D4C22⋊C414yes—
123C24×D4C22⋊C4116yescomplemented
124C24×D4C22×C412yes—
125C24×D4C22×C412yes—
126C24×D4C22×C411yescharacteristic
127C24×D4C22×C4116yes—
128C24×D4C22×C418yes—
129C24×D4C22×C412yes—
130C24×D4C22×C412yes—
131C24×D4C2×D412yes—
132C24×D4C2×D411yescharacteristic
133C24×D4C2×D418yes—
134C24×D4C2×D418yes—
135C24×D4C2×D414yes—
136C24×D4C2×D414yes—
137C24×D4C2×D4132yes—
138C24×D4C2×D418yes—
139C24×D4C2×D414yes—
140C24×D4C2×D414yes—
141C24×D4C2×D418yes—
142C24×D4C2×D4116yes—
143C24×D4#41116yes—
144C24×D4C2412yes—
145C24×D4C2412yes—
146C25×C4C22×C412yes—
147C25×C4C22×C412yes—
148C25×C4C22×C412yes—
149C25×C4C2×D411yescharacteristic
150C25×C4C2×D412yes—
151C25×C4C2×D414yes—
152C25×C4C2×D414yes—
153C25×C4C2×D414yes—
154C25×C4C2×D414yes—
155C25×C4C2×D412yes—
156C25×C4C2×D412yes—
157C25×C4C2412yes—
158C25×C4C2411yescharacteristic
159C23×M16C2×D4116yescomplemented
160C23×M16C2418yes—
161C2×#535C22⋊C4132yescomplemented
162C2×#535C22⋊C4132yescomplemented
163C2×#535C2×D4132yes—
164C2×#535C2×D4132yes—
165C22×#127C22⋊C4116yescomplemented
166C22×#127C22×C418yes—
167C22×#124C22⋊C4116yescomplemented
168C22×#124C22×C418yes—
169C2×#525C22⋊C4132yes—
170C2×#525C2×D4132yes—
171C22×#123C22⋊C418yes—
172C22×#123C2×D418yes—
173C22×C22⋊Q8C22⋊C418yes—
174C22×C22⋊Q8C22⋊C418yes—
175C22×C22⋊Q8C22⋊C418yes—
176C22×C22⋊Q8C22×C418yes—
177C22×C22⋊Q8C2×D418yes—
178C22×#121C22⋊C418yes—
179C22×#121C22⋊C418yes—
180C22×#121C22⋊C418yes—
181C22×#121C22⋊C4132yescomplemented
182C22×#121C22×C418yes—
183C22×#121C22×C4116yes—
184C22×#121C2×D418yes—
185C22×#120C22⋊C418yes—
186C22×#120C2×D418yes—
187C2×#518C22⋊C4132yescomplemented
188C2×#518C2×D4132yes—
189C22×C4×D4C22⋊C4116yes—
190C22×C4×D4C22⋊C4132yescomplemented
191C22×C4×D4C22×C4116yes—
192C22×C4×D4C22×C4116yes—
193C22×#117C22×C412yes—
194C22×#117C22×C412yes—
195C22×#117C2×D414yes—
196C22×#117C2×D418yes—
197C22×#117C2×D414yes—
198C22×#117C2×D418yes—
199C22×#117C2×D412yes—
200C22×#117C2×D418yes—
201C22×#117C2×D418yes—
202C22×#117C2×D412yes—
203C22×#117C2×D4116yescomplemented
204C22×#117C2418yes—
205C22×#117C2412yes—
206C22×#117C2412yes—
207C23×C4⋊C4C22⋊C414yes—
208C23×C4⋊C4C22×C412yes—
209C23×C4⋊C4C2×D412yes—
210C23×C22⋊C4C22⋊C414yes—
211C23×C22⋊C4C22⋊C414yes—
212C23×C22⋊C4C2×D412yes—
213C23×C42C22×C412yes—
214C2×#418C2×D4164yescomplemented
215C26C2×C22⋊C412yes—
216C26C2×C22⋊C412yes—
217C26C2×C22⋊C412yes—
218C26#12014yes—
219C26#12014yes—
220C26C22×D412yes—
221C26C22×D411yescharacteristic
222C22×#41C2×C22⋊C418yes—
223C22×#41C2×C22⋊C418yes—
224C22×#41C2×C22⋊C418yes—
225C22×#41C2×C22⋊C418yes—
226C22×#41C2×C22⋊C418yes—
227C22×#41C2×C22⋊C4132yescomplemented
228C22×#41#120132yes—
229C22×#41#120132yes—
230C22×#41#120116yes—
231C22×#41#120116yes—
232C22×#41C22×D418yes—
233C22×#41C22×D418yes—
234C22×#41C22×D418yes—
235C22×#41C22×D418yes—
236C22×#41C22×D418yes—
237C23×Q8C2×C22⋊C414yes—
238C23×Q8C2×C22⋊C412yes—
239C23×Q8C2×C22⋊C412yes—
240C23×Q8C2×C22⋊C414yes—
241C23×Q8C2×C22⋊C412yes—
242C23×Q8#12018yes—
243C23×Q8C23×C412yes—
244C23×Q8C22×D412yes—
245C23×D4C2×C22⋊C414yes—
246C23×D4C2×C22⋊C412yes—
247C23×D4C2×C22⋊C418yes—
248C23×D4C2×C22⋊C418yes—
249C23×D4C2×C22⋊C418yes—
250C23×D4C2×C22⋊C418yes—
251C23×D4C2×C22⋊C414yes—
252C23×D4C2×C22⋊C412yes—
253C23×D4C2×C22⋊C412yes—
254C23×D4C2×C22⋊C414yes—
255C23×D4C2×C22⋊C414yes—
256C23×D4C2×C22⋊C418yes—
257C23×D4C2×C22⋊C414yes—
258C23×D4C2×C22⋊C4164yes—
259C23×D4C2×C22⋊C418yes—
260C23×D4C2×C22⋊C418yes—
261C23×D4C2×C22⋊C414yes—
262C23×D4C2×C22⋊C414yes—
263C23×D4C2×C22⋊C418yes—
264C23×D4C2×C22⋊C418yes—
265C23×D4C2×C22⋊C418yes—
266C23×D4C2×C22⋊C4116yes—
267C23×D4C2×C22⋊C4132yescomplemented
268C23×D4C4×D4132yes—
269C23×D4C4×D4132yes—
270C23×D4#12018yes—
271C23×D4#120132yes—
272C23×D4#120132yes—
273C23×D4#120132yes—
274C23×D4#120132yes—
275C23×D4#120116yes—
276C23×D4#120116yes—
277C23×D4#120132yes—
278C23×D4#120116yes—
279C23×D4#121132yes—
280C23×D4#121132yes—
281C23×D4#121164yes—
282C23×D4#121164yes—
283C23×D4#123116yes—
284C23×D4#123116yes—
285C23×D4#123132yes—
286C23×D4#124132yes—
287C23×D4#127132yes—
288C23×D4C23×C414yes—
289C23×D4C23×C412yes—
290C23×D4C23×C414yes—
291C23×D4C22×D414yes—
292C23×D4C22×D412yes—
293C23×D4C22×D418yes—
294C23×D4C22×D418yes—
295C23×D4C22×D418yes—
296C23×D4C22×D418yes—
297C23×D4C22×D418yes—
298C23×D4C22×D418yes—
299C23×D4C22×D4116yes—
300C23×D4C2×#41116yes—
301C24×C4C2×C22⋊C414yes—
302C24×C4C2×C22⋊C414yes—
303C24×C4C2×C22⋊C418yes—
304C24×C4C2×C22⋊C414yes—
305C24×C4C2×C22⋊C414yes—
306C24×C4C2×C22⋊C418yes—
307C24×C4C2×C22⋊C418yes—
308C24×C4C2×C22⋊C418yes—
309C24×C4C2×C22⋊C412yes—
310C24×C4C2×C22⋊C412yes—
311C24×C4C2×C22⋊C414yes—
312C24×C4C2×C22⋊C414yes—
313C24×C4C2×C22⋊C412yes—
314C24×C4C2×C22⋊C414yes—
315C24×C4C2×C22⋊C414yes—
316C24×C4#12018yes—
317C24×C4#12018yes—
318C24×C4#12018yes—
319C24×C4#12018yes—
320C24×C4#12014yes—
321C24×C4#12014yes—
322C24×C4#12018yes—
323C24×C4#12018yes—
324C24×C4C23×C414yes—
325C24×C4C23×C414yes—
326C24×C4C23×C411yescharacteristic
327C24×C4C23×C411yescharacteristic
328C24×C4C22×D412yes—
329C24×C4C22×D418yes—
330C24×C4C22×D418yes—
331C24×C4C22×D414yes—
332C24×C4C22×D414yes—
333C24×C4C22×D412yes—
334C24×C4C22×D412yes—
335C24×C4C22×D411yescharacteristic
336C24×C4C22×D414yes—
337C24×C4C22×D414yes—
338C24×C4C22×D414yes—
339C24×C4C22×D412yes—
340C24×C4C22×D412yes—
341C24×C4C22×D411yescharacteristic
342C24×C4C22×D411yescharacteristic
343C24×C4C22×D418yes—
344C24×C4C2×#4118yes—
345C24×C4H(5,𝔽2)18yes—
346C24×C4H(5,𝔽2)18yes—
347C24×C4C2511yescharacteristic
348C22×M16C22×D4116yescomplemented
349C2×#127C2×C22⋊C4132yescomplemented
350C2×#124C2×C22⋊C4132yescomplemented
351C2×C22⋊Q8C2×C22⋊C4132yes—
352C2×#121C2×C22⋊C4132yes—
353C2×#121C2×C22⋊C4164yescomplemented
354C2×C4×D4C2×C22⋊C4164yescomplemented
355C2×#117C2×C22⋊C418yes—
356C2×#117C2×C22⋊C418yes—
357C2×#117C2×C22⋊C418yes—
358C2×#117C2×C22⋊C418yes—
359C2×#117C2×C22⋊C418yes—
360C2×#117#120132yes—
361C2×#117#120132yes—
362C2×#117#120116yes—
363C2×#117#120116yes—
364C2×#117C22×D418yes—
365C2×#117C22×D418yes—
366C2×#117C22×D418yes—
367C2×#117C22×D418yes—
368C2×#117C22×D418yes—
369C2×#117C22×D4116yescomplemented
370C22×C4⋊C4C2×C22⋊C4116yes—
371C22×C4⋊C4C2×C22⋊C414yes—
372C22×C4⋊C4C2×C22⋊C414yes—
373C22×C4⋊C4C2×C22⋊C414yes—
374C22×C4⋊C4C2×C22⋊C418yes—
375C22×C4⋊C4C2×C22⋊C418yes—
376C22×C4⋊C4#120116yes—
377C22×C4⋊C4C23×C414yes—
378C22×C4⋊C4C22×D414yes—
379C22×C22⋊C4C2×C22⋊C4116yes—
380C22×C22⋊C4C2×C22⋊C4116yes—
381C22×C22⋊C4C2×C22⋊C414yes—
382C22×C22⋊C4#120116yes—
383C22×C22⋊C4C22×D414yes—
384C22×C42C2×C22⋊C418yes—
385C22×C42C2×C22⋊C418yes—
386C22×C42C2×C22⋊C414yes—
387C22×C42C23×C414yes—
388C25#37914yes—
389C25#37914yes—
390C25#37918yes—
391C25#37918yes—
392C25C22×C22⋊C414yes—
393C25C22×C22⋊C411yescharacteristic
394C25C22×C22⋊C414yes—
395C25C22×C22⋊C411yescharacteristic
396C25C2×#12018yes—
397C25C2×#12012yes—
398C25C2×#12014yes—
399C25C2×#12012yes—
400C25C2×#12014yes—
401C25D4218yes—
402C25#54618yes—
403C25C23×D411yescharacteristic
404C2×#41#379132yes—
405C2×#41C2×#120132yes—
406C22×Q8#37918yes—
407C22×Q8#37918yes—
408C22×Q8#37918yes—
409C22×Q8C22×C22⋊C414yes—
410C22×Q8C22×C22⋊C414yes—
411C22×Q8C22×C22⋊C414yes—
412C22×Q8C2×#12018yes—
413C22×D4#379116yes—
414C22×D4#37918yes—
415C22×D4#379116yes—
416C22×D4#379116yes—
417C22×D4#37918yes—
418C22×D4#37918yes—
419C22×D4#379132yes—
420C22×D4#379116yes—
421C22×D4#379116yes—
422C22×D4#379132yes—
423C22×D4#386132yes—
424C22×D4#386132yes—
425C22×D4#386132yes—
426C22×D4#386132yes—
427C22×D4#386164yes—
428C22×D4#386164yes—
429C22×D4#390164yes—
430C22×D4#390164yes—
431C22×D4#3921128yes—
432C22×D4#3921128yes—
433C22×D4#3941128yes—
434C22×D4#3941128yes—
435C22×D4C22×C22⋊C418yes—
436C22×D4C22×C22⋊C418yes—
437C22×D4C22×C22⋊C414yes—
438C22×D4C22×C22⋊C414yes—
439C22×D4C22×C22⋊C414yes—
440C22×D4C22×C22⋊C418yes—
441C22×D4C22×C22⋊C418yes—
442C22×D4C22×C22⋊C418yes—
443C22×D4C22×C22⋊C418yes—
444C22×D4C2×C4×D4132yes—
445C22×D4C2×#12018yes—
446C22×D4C2×#120132yes—
447C22×D4C2×#120116yes—
448C22×D4C2×#120116yes—
449C22×D4C2×#120132yes—
450C22×D4C2×#120116yes—
451C22×D4C2×#121132yes—
452C22×D4C2×#121132yes—
453C22×D4C2×#121132yes—
454C22×D4C2×#123116yes—
455C22×D4C2×#123116yes—
456C22×D4C2×#124116yes—
457C22×D4C2×#127116yes—
458C23×C4#37918yes—
459C23×C4#37914yes—
460C23×C4#379116yes—
461C23×C4#379116yes—
462C23×C4#37918yes—
463C23×C4#37918yes—
464C23×C4#37918yes—
465C23×C4#37914yes—
466C23×C4#379116yes—
467C23×C4C22×C22⋊C418yes—
468C23×C4C22×C22⋊C418yes—
469C23×C4C22×C22⋊C418yes—
470C23×C4C22×C22⋊C418yes—
471C23×C4C22×C22⋊C414yes—
472C23×C4C22×C22⋊C414yes—
473C23×C4C22×C22⋊C418yes—
474C23×C4C22×C22⋊C412yes—
475C23×C4C22×C22⋊C411yescharacteristic
476C23×C4C22×C22⋊C412yes—
477C23×C4C22×C22⋊C412yes—
478C23×C4C22×C22⋊C411yescharacteristic
479C23×C4C22×C22⋊C412yes—
480C23×C4C22×C22⋊C412yes—
481C23×C4C22×C22⋊C412yes—
482C23×C4C22×C22⋊C411yescharacteristic
483C23×C4C22×C22⋊C412yes—
484C23×C4C22×C22⋊C412yes—
485C23×C4C22×C22⋊C412yes—
486C23×C4C22×C22⋊C412yes—
487C23×C4C22×C22⋊C411yescharacteristic
488C23×C4C22×C22⋊C411yescharacteristic
489C23×C4C22×C22⋊C411yescharacteristic
490C23×C4C2×C4×D418yes—
491C23×C4C2×C4×D418yes—
492C23×C4#51818yes—
493C23×C4#51818yes—
494C23×C4C2×#120116yes—
495C23×C4C2×#12018yes—
496C23×C4C2×#12014yes—
497C23×C4C2×#12012yes—
498C23×C4C2×#12012yes—
499C23×C4C2×#12014yes—
500C23×C4C2×#12012yes—
501C23×C4C2×#12012yes—
502C23×C4C2×#12012yes—
503C23×C4C2×#12014yes—
504C23×C4C2×#12012yes—
505C23×C4C2×#12014yes—
506C23×C4C2×#12014yes—
507C23×C4C2×#12014yes—
508C23×C4C2×#12018yes—
509C23×C4C2×#12018yes—
510C23×C4C2×#12018yes—
511C23×C4C2×#12018yes—
512C23×C4C2×#12018yes—
513C23×C4C2×#12018yes—
514C23×C4C2×#12018yes—
515C23×C4C2×#12018yes—
516C23×C4C2×#12014yes—
517C23×C4C2×#12014yes—
518C23×C4C2×#12018yes—
519C23×C4C2×#121116yes—
520C23×C4C2×#12118yes—
521C23×C4C2×#12118yes—
522C23×C4C2×#121116yes—
523C23×C4C2×#12314yes—
524C23×C4C2×#12314yes—
525C23×C4C2×#12318yes—
526C23×C4C2×#12418yes—
527C23×C4C2×#12718yes—
528C23×C4#53418yes—
529C23×C4#53418yes—
530C23×C4#534116yes—
531C23×C4#53414yes—
532C23×C4#53414yes—
533C23×C4#53418yes—
534C23×C4#53414yes—
535C23×C4#53414yes—
536C23×C4#53418yes—
537C23×C4#53518yes—
538C23×C4#53518yes—
539C23×C4#535116yes—
540C23×C4D4218yes—
541C23×C4D42116yes—
542C23×C4D4218yes—
543C23×C4D42116yes—
544C23×C4D4218yes—
545C23×C4D42116yes—
546C23×C4D4218yes—
547C23×C4D42116yes—
548C23×C4D4218yes—
549C23×C4D4218yes—
550C23×C4D4218yes—
551C23×C4#54618yes—
552C23×C4#546116yes—
553C23×C4#54618yes—
554C23×C4#546116yes—
555C23×C4#54618yes—
556C23×C4#546116yes—
557C23×C4#54618yes—
558C23×C4#54618yes—
559C23×C4#546116yes—
560C23×C4#54618yes—
561C23×C4#54618yes—
562C23×C4C24×C411yescharacteristic
563C23×C4C23×D412yes—
564C23×C4C23×D412yes—
565C23×C4C23×D412yes—
566C23×C4C23×D412yes—
567C23×C4C23×D412yes—
568C23×C4C23×D412yes—
569C23×C4C23×D414yes—
570C23×C4C23×D411yescharacteristic
571C23×C4C22×#4114yes—
572C23×C4C2×H(5,𝔽2)14yes—
573C23×C4C2×H(5,𝔽2)14yes—
574#117#379132yes—
575#117C2×#120132yes—
576C2×C4⋊C4#379116yes—
577C2×C4⋊C4#379116yes—
578C2×C4⋊C4#379116yes—
579C2×C4⋊C4C22×C22⋊C418yes—
580C2×C4⋊C4C22×C22⋊C418yes—
581C2×C4⋊C4C22×C22⋊C418yes—
582C2×C4⋊C4C2×#120116yes—
583C2×C22⋊C4#379116yes—
584C2×C22⋊C4C2×#120116yes—
585C2×C42#379116yes—
586C2×C42C22×C22⋊C418yes—
587C2×C42C22×C22⋊C418yes—
588C24#1795116yescomplemented
589C24C2×#37918yes—
590C24C2×#37912yes—
591C24C2×#37911yescharacteristic
592C24C2×#37912yes—
593C24C2×#37912yes—
594C24C2×#37918yes—
595C24C2×#37912yes—
596C24C2×#37912yes—
597C24C2×#37911yescharacteristic
598C24D4×C22⋊C418yes—
599C24D4×C22⋊C418yes—
600C24#240314yes—
601C24#240314yes—
602C24#240318yes—
603C24#240514yes—
604C24#240514yes—
605C24#240518yes—
606C24#2408116yes—
607C24#241018yes—
608C24#241018yes—
609C24#2410116yes—
610C24#243318yes—
611C24#243518yes—
612C24#284618yes—
613C24#284618yes—
614C24C23×C22⋊C411yescharacteristic
615C24C22×#12012yes—
616C24C22×#12012yes—
617C24C22×#12012yes—
618C24C2×D4214yes—
619C24C2×#54614yes—
620C2×Q8C2×#37918yes—
621C2×D4#1438164yes—
622C2×D4#1438164yes—
623C2×D4#14381128yes—
624C2×D4C2×#379116yes—
625C2×D4C2×#37918yes—
626C2×D4C2×#379116yes—
627C2×D4C2×#386132yes—
628C2×D4C2×#386132yes—
629C2×D4C2×#390132yes—
630C2×D4C2×#392164yes—
631C2×D4C2×#394164yes—
632C22×C4C2×#37918yes—
633C22×C4C2×#37918yes—
634C22×C4C2×#379116yes—
635C22×C4C2×#37912yes—
636C22×C4C2×#37912yes—
637C22×C4C2×#37914yes—
638C22×C4C2×#37912yes—
639C22×C4C2×#37912yes—
640C22×C4C2×#37911yescharacteristic
641C22×C4C2×#37911yescharacteristic
642C22×C4C2×#37912yes—
643C22×C4C2×#37912yes—
644C22×C4C2×#37912yes—
645C22×C4C2×#37912yes—
646C22×C4C2×#37912yes—
647C22×C4C2×#37914yes—
648C22×C4C2×#37914yes—
649C22×C4C2×#37912yes—
650C22×C4C2×#37912yes—
651C22×C4C2×#37912yes—
652C22×C4C2×#37912yes—
653C22×C4C2×#37914yes—
654C22×C4C2×#38614yes—
655C22×C4C2×#38614yes—
656C22×C4C2×#38618yes—
657C22×C4C2×#38614yes—
658C22×C4C2×#38614yes—
659C22×C4C2×#38618yes—
660C22×C4C2×#39018yes—
661C22×C4C2×#39018yes—
662C22×C4#230814yes—
663C22×C4#230814yes—
664C22×C4#230818yes—
665C22×C4#230814yes—
666C22×C4#230814yes—
667C22×C4#230818yes—
668C22×C4#230918yes—
669C22×C4#230918yes—
670C22×C4D4×C22⋊C4116yes—
671C22×C4D4×C22⋊C4116yes—
672C22×C4D4×C22⋊C418yes—
673C22×C4D4×C22⋊C418yes—
674C22×C4D4×C22⋊C4116yes—
675C22×C4D4×C22⋊C418yes—
676C22×C4D4×C22⋊C418yes—
677C22×C4D4×C22⋊C418yes—
678C22×C4D4×C22⋊C418yes—
679C22×C4D4×C22⋊C4116yes—
680C22×C4C2×#392116yes—
681C22×C4C2×#392116yes—
682C22×C4C2×#394116yes—
683C22×C4C2×#394116yes—
684C22×C4#2403116yes—
685C22×C4#2403116yes—
686C22×C4#2403116yes—
687C22×C4#2403116yes—
688C22×C4#240314yes—
689C22×C4#240314yes—
690C22×C4#240318yes—
691C22×C4#240314yes—
692C22×C4#240314yes—
693C22×C4#240314yes—
694C22×C4#240314yes—
695C22×C4#240318yes—
696C22×C4#240318yes—
697C22×C4#2405116yes—
698C22×C4#2405116yes—
699C22×C4#2405116yes—
700C22×C4#2405116yes—
701C22×C4#240514yes—
702C22×C4#240514yes—
703C22×C4#240518yes—
704C22×C4#240514yes—
705C22×C4#240514yes—
706C22×C4#240514yes—
707C22×C4#240514yes—
708C22×C4#240518yes—
709C22×C4#240518yes—
710C22×C4#2408116yes—
711C22×C4#2408116yes—
712C22×C4#2408116yes—
713C22×C4#2408116yes—
714C22×C4#2408116yes—
715C22×C4#2408116yes—
716C22×C4#2408116yes—
717C22×C4#2410116yes—
718C22×C4#2410116yes—
719C22×C4#2410116yes—
720C22×C4#2410116yes—
721C22×C4#2410116yes—
722C22×C4#2410116yes—
723C22×C4#2410116yes—
724C22×C4#2410116yes—
725C22×C4#241018yes—
726C22×C4#241018yes—
727C22×C4#2410116yes—
728C22×C4#241018yes—
729C22×C4#241018yes—
730C22×C4#241018yes—
731C22×C4#241018yes—
732C22×C4#2410116yes—
733C22×C4#2410116yes—
734C22×C4#2433116yes—
735C22×C4#2433116yes—
736C22×C4#243318yes—
737C22×C4#243318yes—
738C22×C4#243318yes—
739C22×C4#243518yes—
740C22×C4#2435116yes—
741C22×C4#2435116yes—
742C22×C4#243518yes—
743C22×C4#243518yes—
744C22×C4#2613116yes—
745C22×C4#2613116yes—
746C22×C4#2613116yes—
747C22×C4#2613116yes—
748C22×C4#284618yes—
749C22×C4#284618yes—
750C22×C4#284618yes—
751C22×C4#284618yes—
752C22×C4#284618yes—
753C22×C4#284618yes—
754C22×C4C23×C22⋊C411yescharacteristic
755C22×C4C23×C22⋊C411yescharacteristic
756C22×C4C23×C22⋊C411yescharacteristic
757C22×C4C23×C22⋊C411yescharacteristic
758C22×C4C23×C22⋊C411yescharacteristic
759C22×C4C23×C22⋊C411yescharacteristic
760C22×C4C22×C4×D414yes—
761C22×C4C2×#51814yes—
762C22×C4C22×#12012yes—
763C22×C4C22×#12012yes—
764C22×C4C22×#12012yes—
765C22×C4C22×#12014yes—
766C22×C4C22×#12014yes—
767C22×C4C22×#12014yes—
768C22×C4C22×#12014yes—
769C22×C4C22×#12012yes—
770C22×C4C22×#12012yes—
771C22×C4C22×#12114yes—
772C22×C4C22×#12114yes—
773C22×C4C22×#12114yes—
774C22×C4C22×#12312yes—
775C22×C4C22×#12312yes—
776C22×C4C22×#12412yes—
777C22×C4C22×#12712yes—
778C22×C4C2×#53412yes—
779C22×C4C2×#53412yes—
780C22×C4C2×#53414yes—
781C22×C4C2×#53414yes—
782C22×C4C2×#53412yes—
783C22×C4C2×#53412yes—
784C22×C4C2×#53512yes—
785C22×C4C2×#53512yes—
786C22×C4C2×#53514yes—
787C22×C4C2×D4214yes—
788C22×C4C2×D4214yes—
789C22×C4C2×D4214yes—
790C22×C4C2×D4214yes—
791C22×C4C2×D4214yes—
792C22×C4C2×D4214yes—
793C22×C4C2×D4214yes—
794C22×C4C2×#54614yes—
795C22×C4C2×#54614yes—
796C22×C4C2×#54614yes—
797C22×C4C2×#54614yes—
798C22×C4C2×#54614yes—
799C22×C4C2×#54614yes—
800C22×C4C2×#54614yes—
801C4⋊C4C2×#379116yes—
802C23#1386714yes—
803C23#1386718yes—
804C23#1386714yes—
805C23#1386714yes—
806C23#1386718yes—
807C23#1386714yes—
808C23#1390218yes—
809C23#1390218yes—
810C23#1467914yes—
811C23#1467912yes—
812C23#1467912yes—
813C23#14715116yes—
814C23#14715116yes—
815C23#14724116yes—
816C23#14724116yes—
817C23C2×#179518yes—
818C23C2×#1795116yescomplemented
819C23C22×#37911yescharacteristic
820C23C22×#37911yescharacteristic
821C23C22×#37911yescharacteristic
822C23C2×D4×C22⋊C414yes—
823C23C2×#240312yes—
824C23C2×#240312yes—
825C23C2×#241014yes—
826C23C2×#241014yes—
827C23C2×#240512yes—
828C23C2×#240512yes—
829C23C2×#240814yes—
830C23C2×#243312yes—
831C23C2×#243512yes—
832C23C2×#284614yes—
833D4C2×#1438132yes—
834C2×C4C2×#143814yes—
835C2×C4C2×#143814yes—
836C2×C4C2×#143818yes—
837C2×C4#1386718yes—
838C2×C4#1386714yes—
839C2×C4#1386714yes—
840C2×C4#1386714yes—
841C2×C4#1386714yes—
842C2×C4#1386718yes—
843C2×C4#1386718yes—
844C2×C4#1386718yes—
845C2×C4#1386718yes—
846C2×C4#1386718yes—
847C2×C4#1386718yes—
848C2×C4#1386718yes—
849C2×C4#13867116yes—
850C2×C4#1390218yes—
851C2×C4#1390218yes—
852C2×C4#13902116yes—
853C2×C4#1390218yes—
854C2×C4#1390218yes—
855C2×C4#1433514yes—
856C2×C4#1433514yes—
857C2×C4#1433518yes—
858C2×C4#1467914yes—
859C2×C4#1467912yes—
860C2×C4#1467912yes—
861C2×C4#14715116yes—
862C2×C4#14715116yes—
863C2×C4#14715116yes—
864C2×C4#14715116yes—
865C2×C4#14715116yes—
866C2×C4#14715116yes—
867C2×C4#14724116yes—
868C2×C4#14724116yes—
869C2×C4#14724116yes—
870C2×C4#14724116yes—
871C2×C4#14724116yes—
872C2×C4#14724116yes—
873C2×C4C22×#37911yescharacteristic
874C2×C4C22×#37911yescharacteristic
875C2×C4C22×#37911yescharacteristic
876C2×C4C22×#37911yescharacteristic
877C2×C4C22×#38612yes—
878C2×C4C22×#38612yes—
879C2×C4C22×#39012yes—
880C2×C4C2×#230812yes—
881C2×C4C2×#230812yes—
882C2×C4C2×#230912yes—
883C2×C4C2×D4×C22⋊C414yes—
884C2×C4C2×D4×C22⋊C414yes—
885C2×C4C2×D4×C22⋊C414yes—
886C2×C4C22×#39214yes—
887C2×C4C22×#39414yes—
888C2×C4C2×#261314yes—
889C2×C4C2×#261314yes—
890C2×C4C2×#240312yes—
891C2×C4C2×#240312yes—
892C2×C4C2×#240314yes—
893C2×C4C2×#240314yes—
894C2×C4C2×#241014yes—
895C2×C4C2×#241014yes—
896C2×C4C2×#241014yes—
897C2×C4C2×#241014yes—
898C2×C4C2×#241014yes—
899C2×C4C2×#241014yes—
900C2×C4C2×#240512yes—
901C2×C4C2×#240512yes—
902C2×C4C2×#240514yes—
903C2×C4C2×#240514yes—
904C2×C4C2×#240814yes—
905C2×C4C2×#240814yes—
906C2×C4C2×#240814yes—
907C2×C4C2×#243314yes—
908C2×C4C2×#243312yes—
909C2×C4C2×#243514yes—
910C2×C4C2×#243512yes—
911C2×C4C2×#284614yes—
912C22#15409414yes—
913C22#15409418yes—
914C22#15409414yes—
915C22#359639116yes—
916C22#39213218yes—
917C22C2×#1386712yes—
918C22C2×#1386712yes—
919C22C2×#1390212yes—
920C22C2×#1467911yescharacteristic
921C22C2×#1471514yes—
922C22C2×#1472414yes—
923C22C22×#179514yes—
924C4#15409414yes—
925C4#15409414yes—
926C4#15409418yes—
927C4C22×#143811yescharacteristic
928C4C2×#1386712yes—
929C4C2×#1386712yes—
930C4C2×#1390212yes—
931C4C2×#1433511yescharacteristic
932C4C2×#1471514yes—
933C4C2×#1472414yes—
934C2C2×#39213212yes—
935C2C2×#35963914yes—
936C2#7223958018yesdirect product factor
937C2C2×#15409411yescharacteristic
subgroupG/H
center, socleC24C2×#379
commutatorC23×C4C24×C4
Frattini, cosocleC24×C4C25
prime radicalC23×#3484C2
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C26×C4 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#357420C2semidirect
2. C2×#357426C2semidirect
3. C22×#10776C2semidirect
4. C22×#11006C2semidirect
5. C22×#10984C2semidirect
6. C2×#357440C2semidirect
7. C22×#20598C2semidirect
8. C23×#1795C2semidirect
9. #72239580C2direct (N × H)
13. C22×#3484C4semidirect
15. C23×#546C4semidirect
16. C23×D42C4semidirect
22. C23×#407C22semidirect
23. C23×#410C22semidirect
24. C23×#413C22semidirect
25. C23×#421C22semidirect
27. C23×#418C22semidirect
28. C22×#2280C22semidirect
29. C22×#1795C22semidirect
30. C2×#20598C22semidirect
31. C22×#1742C22semidirect
32. C22×#1740C22semidirect
33. C22×#1733C22semidirect
34. C2×#11006C22semidirect
35. C2×#10984C22semidirect
36. #357440C22semidirect
37. #357426C22semidirect
38. #357420C22semidirect
39. C2×#10776C22semidirect
56. C22×#546C2×C4semidirect
57. C22×D42C2×C4semidirect
89. C22×#421C23semidirect
90. C22×#418D4semidirect
92. C22×#418C23semidirect
93. C22×#413C23semidirect
94. C22×#410C23semidirect
95. C22×#407C23semidirect
96. C2×#2280C23semidirect
97. C2×#1742C23semidirect
98. C2×#1740C23semidirect
99. C2×#1733C23semidirect
101. C22×H(5,𝔽2)C22⋊C4semidirect
103. C23×#41C22⋊C4semidirect
123. C24×D4C22⋊C4semidirect
159. C23×M16C2×D4semidirect
161. C2×#535C22⋊C4semidirect
162. C2×#535C22⋊C4semidirect
165. C22×#127C22⋊C4semidirect
167. C22×#124C22⋊C4semidirect
181. C22×#121C22⋊C4semidirect
187. C2×#518C22⋊C4semidirect
190. C22×C4×D4C22⋊C4semidirect
203. C22×#117C2×D4semidirect
214. C2×#418C2×D4semidirect
227. C22×#41C2×C22⋊C4semidirect
267. C23×D4C2×C22⋊C4semidirect
348. C22×M16C22×D4semidirect
349. C2×#127C2×C22⋊C4semidirect
350. C2×#124C2×C22⋊C4semidirect
353. C2×#121C2×C22⋊C4semidirect
354. C2×C4×D4C2×C22⋊C4semidirect
369. C2×#117C22×D4semidirect
588. C24#1795semidirect
818. C23C2×#1795semidirect
936. C2#72239580direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#3574202
C2×#3574262
C22×#107762
C22×#110062
C22×#109842
C2×#3574402
C22×#205982
C23×#17952
#722395802
C23×#34842