Finite Group Databasebeta

← C2×#72286197 #72315793

Subgroups — C2×#72286197 #72315793

Order 2048.

Only the 41816 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 858 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6438001C216yesmaximal, complemented
2C2×#6379015C213yesmaximal, complemented
3C2×#6442726C213yesmaximal, complemented
4C2×#6573723C218yesmaximal, complemented
5C2×C4×#3027C211yesmaximal, characteristic, complemented
6C2×#10586097C211yesmaximal, characteristic, complemented
7#72286197C2164yesmaximal, direct product factor
8C2×#6628982C211yesmaximal, characteristic, complemented
9C2×#6443348C213yesmaximal, complemented
10C2×#6437633C216yesmaximal, complemented
11C2×#6573715C2116yesmaximal, complemented
12C2×#6628898C212yesmaximal, complemented
13C2×#7677118C213yesmaximal, complemented
14C2×D4×B(4,𝔽2)C218yesmaximal, complemented
15C22×#60399C212yesmaximal, complemented
16C22×H(7,𝔽2)C2212yescomplemented
17#10586097C22132yescomplemented
18C2×D4×H(5,𝔽2)C2218yescomplemented
19C2×D4×H(5,𝔽2)C2218yescomplemented
20C2×#62852C2216yescomplemented
21C2×#62812C2213yescomplemented
22C22×#3498C2213yes—
23C22×#3484C2216yescomplemented
24C23×D42C2211yescharacteristic, complemented
25C2×C4×#585C2211yescharacteristic, complemented
26C22×#3027C2211yescharacteristic
27C22×#3027C2216yescomplemented
28C22×#3025C2212yescomplemented
29C22×#3025C2216yescomplemented
30C22×#3025C2216yescomplemented
31C2×#60399C22164yescomplemented
32C22×#3026C22116yescomplemented
33C23×B(4,𝔽2)C22116yescomplemented
34C22×#2883C2216yescomplemented
35#7677118C22196yescomplemented
36C2×#39338C22112yescomplemented
37C2×#37644C22124yescomplemented
38C2×D4×#120C22112yescomplemented
39C2×#35514C2216yescomplemented
40C2×#35512C2216yescomplemented
41C2×#35222C2216yescomplemented
42C2×#35165C2213yescomplemented
43C2×#34936C2213yescomplemented
44C2×#34935C2213yescomplemented
45C2×#34210C2213yescomplemented
46C2×C4×#535C2213yescomplemented
47#6628982C22132yescomplemented
48C2×#32928C2218yescomplemented
49C2×#32927C2214yescomplemented
50C2×#32926C2214yescomplemented
51#6628898C22164yescomplemented
52C2×#32900C22116yescomplemented
53C2×#32898C22116yescomplemented
54#6573723C221256yescomplemented
55#6573715C221512yescomplemented
56D4×B(4,𝔽2)C221256yescomplemented
57#6443348C22196yescomplemented
58C2×#25773C22124yescomplemented
59C2×#25772C22112yescomplemented
60C2×#25771C22112yescomplemented
61#6442726C22196yescomplemented
62C2×#24262C22124yescomplemented
63C2×#24260C22124yescomplemented
64#6438001C221192yescomplemented
65C2×#24405C22148yescomplemented
66C2×#24404C22148yescomplemented
67#6437633C221192yescomplemented
68C2×#23903C22148yescomplemented
69C2×#23900C22148yescomplemented
70C2×#23516C2216yescomplemented
71C2×#23445C2216yescomplemented
72C2×#23443C22112yescomplemented
73#6379015C22196yescomplemented
74C2×D4×#99C22124yescomplemented
75C2×D4×#99C22124yescomplemented
76C4×#3027C22132yescomplemented
77C2×#21482C2218yescomplemented
78C2×C4×B(4,𝔽2)C2218yescomplemented
79C2×#21212C2216yescomplemented
80C2×#20985C22112yescomplemented
81C2×#20961C2213yescomplemented
82C2×#20959C2216yescomplemented
83C2×#20890C2213yescomplemented
84C2×#20632C2213yescomplemented
85C2×#20610C2211yescharacteristic, complemented
86C2×#20610C2216yescomplemented
87C2×#20586C2216yescomplemented
88C2×C4×#410C2213yescomplemented
89C2×H(7,𝔽2)C23132yescomplemented
90C22×#585C2311yescharacteristic
91C22×#585C2316yes—
92C23×H(5,𝔽2)C2316yes—
93C23×H(5,𝔽2)C23116yes—
94C25×D4C2312yescomplemented
95C25×D4C2312yescomplemented
96D4×H(5,𝔽2)C231128yescomplemented
97D4×H(5,𝔽2)C231128yescomplemented
98#62852C23196yescomplemented
99#62812C23148yescomplemented
100C2×#3498D4148yescomplemented
101C2×#3498C23148yes—
102C2×#3496C23112yes—
103C2×#3496C23112yes—
104C2×#3484C23148yes—
105C2×#3484C23196yescomplemented
106C22×#550D416yescomplemented
107C22×#550D416yescomplemented
108C22×D42D416yescomplemented
109C22×D42D416yescomplemented
110C22×D42C23112yes—
111C22×D42C23112yes—
112C22×D42C23116yescomplemented
113C2×#3449C2316yes—
114C22×#535D4112yescomplemented
115C22×#535C2316yes—
116C22×#535C2313yes—
117C22×#535C2316yescomplemented
118C22×#534C23124yescomplemented
119C22×#532D416yescomplemented
120C22×#532C2313yes—
121C23×#127D416yescomplemented
122C23×#127C2311yescharacteristic
123C22×#525C2316yes—
124C22×#525C2316yescomplemented
125C22×#525C2316yescomplemented
126C23×#121C2312yescomplemented
127C23×#121C2312yescomplemented
128C23×#120C2314yescomplemented
129C23×#120C23124yescomplemented
130C4×#585C23116yescomplemented
131C2×C4×H(5,𝔽2)C2314yes—
132C2×C4×H(5,𝔽2)C2314yes—
133C2×#3428C2313yes—
134C22×#518C2316yescomplemented
135C22×C4×#41C2313yes—
136C23×C4×D4C2311yescharacteristic, complemented
137C23×C4×D4C2311yescharacteristic, complemented
138C2×#3027D4132yescomplemented
139C2×#3027C23116yes—
140C2×#3027C23196yescomplemented
141C2×#3026C231256yescomplemented
142C2×#3025C23132yescomplemented
143C2×#3025C23196yescomplemented
144C2×#3025C23196yescomplemented
145C22×#458C2318yes—
146C22×#458C23124yescomplemented
147C22×#458C23124yescomplemented
148C22×B(4,𝔽2)C2318yes—
149C22×B(4,𝔽2)C2318yes—
150C22×B(4,𝔽2)C23124yescomplemented
151C22×B(4,𝔽2)C23148yescomplemented
152C22×B(4,𝔽2)C23124yescomplemented
153C22×B(4,𝔽2)C231256yescomplemented
154C2×#2883C23196yescomplemented
155C22×#410C2313yes—
156C22×#410C2313yes—
157C22×#410C2316yes—
158C22×#410C23112yescomplemented
159C22×#410C23112yescomplemented
160C23×#99C23148yescomplemented
161#39338C231192yescomplemented
162#37644C231384yescomplemented
163C2×#2847C23112yescomplemented
164C2×#2846C23124yescomplemented
165D4×#120C231192yescomplemented
166#35514C23196yescomplemented
167#35512C23196yescomplemented
168#35222C23196yescomplemented
169#35165C23148yescomplemented
170#34936C23148yescomplemented
171#34935C23148yescomplemented
172C2×#2539C23112yescomplemented
173C2×#2534C23112yescomplemented
174C2×#2501C2316yescomplemented
175C2×#2486C2316yescomplemented
176C2×#2433C2316yescomplemented
177C2×#2408C2316yescomplemented
178C2×#2412C23124yescomplemented
179C2×#2405C23124yescomplemented
180C2×#2410C23124yescomplemented
181C2×#2403C23124yescomplemented
182C2×#2617C23112yescomplemented
183C2×#2613C23124yescomplemented
184#34210C23148yescomplemented
185C2×D4×C22⋊C4C23112yescomplemented
186C2×D4×C22⋊C4C23112yescomplemented
187C4×#535C23148yescomplemented
188C2×#2321C23112yescomplemented
189C2×#2317C2313yescomplemented
190C2×#2311C2313yes—
191C2×#2311C2316yescomplemented
192C2×#2309C2313yescomplemented
193C2×#2309C2316yescomplemented
194C2×C4×#120C23112yescomplemented
195C2×#2285C2313yescomplemented
196C2×#2280C2316yescomplemented
197C2×C4×#117C2313yescomplemented
198#32928C231128yescomplemented
199#32927C23164yescomplemented
200#32926C23164yescomplemented
201#32900C231256yescomplemented
202#32898C231256yescomplemented
203#25773C231384yescomplemented
204#25772C231192yescomplemented
205#25771C231192yescomplemented
206#24405C231768yescomplemented
207#24404C231768yescomplemented
208#24262C231384yescomplemented
209#24260C231384yescomplemented
210#23903C231768yescomplemented
211#23900C231768yescomplemented
212#23516C23196yescomplemented
213C2×#2044C23148yescomplemented
214#23445C23196yescomplemented
215#23443C231192yescomplemented
216C2×#2022C23148yescomplemented
217C2×#2021C23148yescomplemented
218C2×#2021C23148yescomplemented
219D4×#99C231384yescomplemented
220D4×#99C231384yescomplemented
221#21482C231128yescomplemented
222C4×B(4,𝔽2)C231128yescomplemented
223#21212C23196yescomplemented
224C2×#1964C23124yescomplemented
225C2×#1964C23124yescomplemented
226#20985C231192yescomplemented
227C2×#1898C23196yescomplemented
228#20961C23148yescomplemented
229#20959C23196yescomplemented
230C2×#1890C23124yescomplemented
231C2×#1889C23124yescomplemented
232C2×#1889C23124yescomplemented
233#20890C23148yescomplemented
234C2×#1867C23124yescomplemented
235#20632C23148yescomplemented
236C2×#1799C23112yescomplemented
237C2×#1799C23112yescomplemented
238#20610C23116yescomplemented
239#20610C23196yescomplemented
240C2×#1790C2318yes—
241C2×#1790C23148yescomplemented
242#20586C23196yescomplemented
243C2×#1781C23148yescomplemented
244C4×#410C23148yescomplemented
245C2×C4×#99C23112yescomplemented
246C2×C4×#99C23112yescomplemented
247C2×#1740C2316yescomplemented
248C2×#1740C2316yescomplemented
249C27C2414yes—
250C2×#585C2×D4116yescomplemented
251C2×#585C24148yes—
252C2×#585C2418yes—
253C22×H(5,𝔽2)C2×D4148yescomplemented
254C22×H(5,𝔽2)C24148yes—
255C22×H(5,𝔽2)C2414yes—
256C22×H(5,𝔽2)C241128yes—
257C22×H(5,𝔽2)C24124yes—
258C23×#41C2×D4112yescomplemented
259C23×#41C2×D4112yescomplemented
260C23×#41C2413yes—
261C23×#41C2416yes—
262C24×D4C2×D4112yescomplemented
263C24×D4C2×D4112yescomplemented
264C24×D4C2×D4112yescomplemented
265C24×D4C2×D4112yescomplemented
266C24×D4C24124yes—
267C24×D4C2412yes—
268C24×D4C2412yes—
269C24×D4C2412yes—
270C24×D4C2411yescharacteristic
271C24×D4C2414yes—
272C24×D4C2411yescharacteristic
273C24×D4C2414yes—
274C24×D4C24116yescomplemented
275C24×D4C24116yescomplemented
276C25×C4C2412yes—
277C25×C4C2412yes—
278#3496C24196yes—
279#3496C24196yes—
280#3484C241384yes—
281C2×#550C2×D4196yescomplemented
282C2×#550C2×D4196yescomplemented
283C2×D42C2×D4196yescomplemented
284C2×D42C2×D4196yescomplemented
285C2×D42C2×D4196yescomplemented
286C2×D42C2×D4196yescomplemented
287C2×D42C24196yes—
288C2×D42C24196yes—
289#3449C24148yes—
290C2×#535C2×D4148yescomplemented
291C2×#535C2×D41192yescomplemented
292C2×#535C2×D4148yescomplemented
293C2×#535C24148yes—
294C2×#535C24124yes—
295C2×#535C24148yescomplemented
296C2×#534C24124yes—
297C2×#534C241192yescomplemented
298C2×#532C2×D4124yescomplemented
299C2×#532C2×D4196yescomplemented
300C2×#532C24124yes—
301C22×C4⋊Q8C2×D413yescomplemented
302C22×#127C2×D4124yes—
303C22×#127C2×D416yes—
304C22×#127C2×D416yes—
305C22×#127C2×D416yes—
306C22×#127C2×D416yes—
307C22×#127C2×D4196yescomplemented
308C22×#127C2×D413yescomplemented
309C22×#127C2×D4112yescomplemented
310C22×#127C2×D4112yescomplemented
311C22×#127C2×D4112yescomplemented
312C22×#127C2418yes—
313C22×#124C2×D4112yescomplemented
314C22×#124C2×D416yescomplemented
315C2×#525C24148yes—
316C2×#525C24148yescomplemented
317C2×#525C24148yescomplemented
318C22×#123C24112yes—
319C22×#123C24112yes—
320C22×#123C24112yes—
321C22×#121C2×D4112yescomplemented
322C22×#121C2×D4112yescomplemented
323C22×#121C2×D4124yescomplemented
324C22×#121C2×D4124yescomplemented
325C22×#121C2×D4112yescomplemented
326C22×#121C2×D4112yescomplemented
327C22×#121C2416yes—
328C22×#121C2416yes—
329C22×#121C24116yescomplemented
330C22×#121C24116yescomplemented
331C22×#120C2×D4124yescomplemented
332C22×#120C2×D4124yescomplemented
333C22×#120C24124yes—
334C22×#120C24112yes—
335C22×#120C24112yes—
336C22×#120C24112yes—
337C22×#120C24124yes—
338C22×#120C24112yes—
339C22×#120C24132yescomplemented
340C22×#120C241192yescomplemented
341C4×H(5,𝔽2)C24132yes—
342C4×H(5,𝔽2)C24132yes—
343#3428C24124yes—
344C2×#518C24112yes—
345C2×#518C24148yescomplemented
346C2×C4×#41C2×D4124yescomplemented
347C2×C4×#41C24124yes—
348C22×C4×Q8C2×D413yescomplemented
349C22×C4×Q8C2×D413yescomplemented
350C22×C4×D4C2×D413yescomplemented
351C22×C4×D4C2×D413yescomplemented
352C22×C4×D4C2×D4112yescomplemented
353C22×C4×D4C2×D4112yescomplemented
354C22×C4×D4C2×D416yescomplemented
355C22×C4×D4C2×D416yescomplemented
356C22×C4×D4C2416yes—
357C22×C4×D4C2416yes—
358C22×C4×D4C2418yescomplemented
359C22×C4×D4C2418yescomplemented
360C22×#117C2×D416yescomplemented
361C22×#117C2413yes—
362C22×#117C2413yes—
363C22×#117C2416yes—
364C22×#117C2413yes—
365C23×C4⋊C4C2411yescharacteristic
366C23×C4⋊C4C2411yescharacteristic
367C23×C22⋊C4C24124yes—
368C23×C22⋊C4C2412yes—
369C23×C22⋊C4C2412yes—
370C23×C22⋊C4C2414yes—
371C23×C42C2×D416yescomplemented
372C23×C42C2411yescharacteristic
373#3027C2×D41256yescomplemented
374C2×#458C24164yes—
375C2×#458C241192yescomplemented
376C2×#458C241192yescomplemented
377C2×B(4,𝔽2)C2×D41128yescomplemented
378C2×B(4,𝔽2)C24164yes—
379C2×B(4,𝔽2)C24164yes—
380C2×B(4,𝔽2)C241192yescomplemented
381C2×B(4,𝔽2)C241192yescomplemented
382C2×B(4,𝔽2)C241384yescomplemented
383C2×#410C2×D4148yescomplemented
384C2×#410C24124yes—
385C2×#410C24148yes—
386C2×#410C24124yes—
387C2×#410C24196yescomplemented
388C2×#410C24196yescomplemented
389C22×#99C24112yes—
390C22×#99C24112yes—
391C22×#99C24148yes—
392C22×#99C24124yes—
393C22×#99C24148yes—
394C22×#99C241384yescomplemented
395#2847C24196yescomplemented
396#2846C241192yescomplemented
397#2617C24196yescomplemented
398#2613C241192yescomplemented
399#2539C24196yescomplemented
400#2534C24196yescomplemented
401#2501C24148yescomplemented
402#2486C24148yescomplemented
403#2433C24148yescomplemented
404#2412C241192yescomplemented
405#2410C241192yescomplemented
406#2408C24148yescomplemented
407#2405C241192yescomplemented
408#2403C241192yescomplemented
409D4×C22⋊C4C24196yescomplemented
410D4×C22⋊C4C24196yescomplemented
411#2321C24196yescomplemented
412#2317C24124yescomplemented
413#2311C24124yes—
414#2311C24148yescomplemented
415#2309C24124yescomplemented
416#2309C24148yescomplemented
417C4×#120C24196yescomplemented
418C2×#386C24124yes—
419C2×#386C24112yes—
420C2×#385C24112yes—
421#2285C24124yescomplemented
422#2280C24148yescomplemented
423C2×#381C24112yes—
424C2×#380C2416yes—
425C2×#380C2416yes—
426C2×#379C24112yes—
427C2×#379C24112yes—
428C2×#379C24124yes—
429C4×#117C24124yescomplemented
430C2×C4×C22⋊C4C2416yes—
431C2×C4×C22⋊C4C2416yes—
432#2044C241384yescomplemented
433#2022C241384yescomplemented
434#2021C241384yescomplemented
435#2021C241384yescomplemented
436#1964C241192yescomplemented
437#1964C241192yescomplemented
438#1898C241768yescomplemented
439#1890C241192yescomplemented
440#1889C241192yescomplemented
441#1889C241192yescomplemented
442#1867C241192yescomplemented
443#1799C24196yescomplemented
444#1799C24196yescomplemented
445#1790C24164yes—
446#1790C241384yescomplemented
447#1781C241384yescomplemented
448C4×#99C24196yescomplemented
449C4×#99C24196yescomplemented
450#1740C24148yescomplemented
451#1740C24148yescomplemented
452C2×#342C24124yes—
453C2×#342C24124yes—
454C26C22×D4124yes—
455C26C2514yes—
456C26C2512yes—
457C26C2512yes—
458C26C25116yes—
459#585C22×D4164yescomplemented
460C2×H(5,𝔽2)C22×D4132yes—
461C2×H(5,𝔽2)C25196yes—
462C2×H(5,𝔽2)C25116yes—
463C22×#41C22×D4124yes—
464C22×#41C22×D4124yes—
465C22×#41C22×D4112yes—
466C22×#41C22×D4196yescomplemented
467C22×#41C22×D4196yescomplemented
468C22×#41H(5,𝔽2)124yes—
469C22×#41C25124yes—
470C22×#41C25112yes—
471C23×Q8C22×D413yes—
472C23×Q8C22×D416yes—
473C23×D4C22×D4112yes—
474C23×D4C22×D4112yes—
475C23×D4C22×D4112yes—
476C23×D4C22×D4112yes—
477C23×D4C22×D4124yes—
478C23×D4C22×D4112yes—
479C23×D4C22×D4112yes—
480C23×D4C22×D4124yes—
481C23×D4C22×D4124yes—
482C23×D4C22×D413yes—
483C23×D4C22×D416yes—
484C23×D4C22×D416yes—
485C23×D4C22×D416yes—
486C23×D4C22×D4124yes—
487C23×D4C22×D4124yes—
488C23×D4C22×D4124yes—
489C23×D4C22×D4124yes—
490C23×D4C22×D4196yes—
491C23×D4C22×D4196yescomplemented
492C23×D4C22×D4196yescomplemented
493C23×D4C22×D4196yescomplemented
494C23×D4C22×D4196yescomplemented
495C23×D4C22×D418yescomplemented
496C23×D4C2516yes—
497C23×D4C25112yes—
498C23×D4C25196yes—
499C23×D4C2518yes—
500C23×D4C2518yes—
501C23×D4C2518yes—
502C23×D4C2514yes—
503C23×D4C2514yes—
504C23×D4C25116yes—
505C23×D4C25116yes—
506C24×C4C22×D416yes—
507C24×C4C22×D416yes—
508C24×C4C22×D416yes—
509C24×C4C22×D4112yes—
510C24×C4C22×D4124yes—
511C24×C4C2511yescharacteristic
512C24×C4C2511yescharacteristic
513C24×C4C2511yescharacteristic
514C24×C4C2512yes—
515C24×C4C2512yes—
516C24×C4C2518yes—
517C24×C4C2518yes—
518#535C22×D41192yescomplemented
519#534C25196yes—
520C2×C4⋊Q8C22×D4124yescomplemented
521C2×#127#120148yes—
522C2×#127#120148yes—
523C2×#127#120148yes—
524C2×#127#120148yes—
525C2×#127#12014yes—
526C2×#127#120112yes—
527C2×#127#120112yes—
528C2×#127#120112yes—
529C2×#127#120124yes—
530C2×#127C22×D4148yes—
531C2×#127C22×D4148yes—
532C2×#127C22×D4148yes—
533C2×#127C22×D4148yes—
534C2×#127C22×D4124yescomplemented
535C2×#127C22×D4196yescomplemented
536C2×#127C22×D4196yescomplemented
537C2×#127C22×D4196yescomplemented
538C2×#124C22×D4196yescomplemented
539C2×#124C22×D4148yescomplemented
540C2×#123C25148yes—
541C2×#123C25148yes—
542C2×#123C25148yes—
543C2×#121C22×D4124yes—
544C2×#121C22×D4124yes—
545C2×#121C22×D4196yescomplemented
546C2×#121C22×D4196yescomplemented
547C2×#121C22×D41192yescomplemented
548C2×#121C22×D41192yescomplemented
549C2×#121C22×D4196yescomplemented
550C2×#121C22×D4196yescomplemented
551C2×#121C25124yes—
552C2×#121C25124yes—
553C2×#120C22×D4196yes—
554C2×#120C22×D41192yescomplemented
555C2×#120C22×D41192yescomplemented
556C2×#120C22×D4196yescomplemented
557C2×#120C25196yes—
558C2×#120C25148yes—
559C2×#120C25148yes—
560C2×#120C25196yes—
561C2×#120C25148yes—
562C2×#120C25148yes—
563#518C25148yes—
564C2×C4×Q8C22×D4124yescomplemented
565C2×C4×Q8C22×D4124yescomplemented
566C2×C4×D4C22×D4124yes—
567C2×C4×D4C22×D4124yes—
568C2×C4×D4C22×D4124yescomplemented
569C2×C4×D4C22×D4124yescomplemented
570C2×C4×D4C22×D4196yescomplemented
571C2×C4×D4C22×D4196yescomplemented
572C2×C4×D4C22×D4148yescomplemented
573C2×C4×D4C22×D4148yescomplemented
574C2×C4×D4C25124yes—
575C2×C4×D4C25124yes—
576C2×#117C22×D4112yes—
577C2×#117C22×D4148yescomplemented
578C2×#117C22×D4124yescomplemented
579C2×#117C25112yes—
580C2×#117C25112yes—
581C2×#117C25112yes—
582C2×#117C25124yes—
583C22×C4⋊C4C22×D416yes—
584C22×C4⋊C4C22×D416yes—
585C22×C4⋊C4C22×D413yes—
586C22×C4⋊C4C22×D413yes—
587C22×C4⋊C4C22×D416yes—
588C22×C4⋊C4C22×D416yes—
589C22×C4⋊C4C2514yes—
590C22×C4⋊C4C2514yes—
591C22×C22⋊C4C22×D416yes—
592C22×C22⋊C4C22×D416yes—
593C22×C22⋊C4C22×D4112yes—
594C22×C22⋊C4C22×D4112yes—
595C22×C22⋊C4C22×D4124yes—
596C22×C22⋊C4C22×D4124yes—
597C22×C22⋊C4C2516yes—
598C22×C22⋊C4C2516yes—
599C22×C22⋊C4C25196yes—
600C22×C22⋊C4C25112yes—
601C22×C22⋊C4C2516yes—
602C22×C22⋊C4C2518yes—
603C22×C22⋊C4C2518yes—
604C22×C22⋊C4C25116yes—
605C22×C42C22×D413yes—
606C22×C42C22×D413yes—
607C22×C42C22×D413yes—
608C22×C42C22×D413yes—
609C22×C42C22×D4112yes—
610C22×C42C22×D416yes—
611C22×C42C22×D416yes—
612C22×C42C22×D416yes—
613C22×C42C22×D4148yescomplemented
614C22×C42C2514yes—
615B(4,𝔽2)C22×D41512yescomplemented
616#410C22×D41192yescomplemented
617C2×#99C22×D4196yescomplemented
618C2×#99C25148yes—
619C2×#99C25196yes—
620C2×#99C251192yes—
621C2×#99C25148yes—
622C2×#99C251192yes—
623#386C25148yes—
624#386C25196yes—
625#385C25148yes—
626#381C25148yes—
627#380C25124yes—
628#380C25124yes—
629#379C25148yes—
630#379C25196yes—
631#379C25148yes—
632C4×C22⋊C4C25124yes—
633C4×C22⋊C4C25124yes—
634#342C25196yes—
635#342C25196yes—
636C25C23×D4112yes—
637C25C23×D418yes—
638C25C23×D4196yes—
639C25C23×D4124yes—
640C25C23×D4124yes—
641C25C23×D416yes—
642C25C2611yescharacteristic
643C25C2618yes—
644C25C2614yes—
645C25C2614yes—
646H(5,𝔽2)C23×D4164yes—
647C2×#41D42196yescomplemented
648C2×#41C23×D4148yes—
649C2×#41C2×H(5,𝔽2)148yes—
650C22×Q8D42124yescomplemented
651C22×Q8C23×D4124yes—
652C22×Q8C23×D4112yes—
653C22×D4C2×#12018yes—
654C22×D4C2×#120148yes—
655C22×D4C2×#120148yes—
656C22×D4C2×#120124yes—
657C22×D4C2×#12018yes—
658C22×D4C2×#120148yes—
659C22×D4C2×#120148yes—
660C22×D4C2×#120148yes—
661C22×D4C2×#120148yes—
662C22×D4C2×#12018yes—
663C22×D4C2×#120124yes—
664C22×D4C2×#120124yes—
665C22×D4D42124yescomplemented
666C22×D4C23×D4148yes—
667C22×D4C23×D4148yes—
668C22×D4C23×D4148yes—
669C22×D4C23×D4148yes—
670C22×D4C23×D4148yes—
671C22×D4C23×D4148yes—
672C22×D4C23×D4112yes—
673C22×D4C23×D4112yes—
674C22×D4C23×D4124yes—
675C22×D4C23×D4124yes—
676C22×D4C23×D4124yes—
677C22×D4C23×D4196yes—
678C22×D4C23×D4196yes—
679C22×D4C23×D4196yes—
680C22×D4C23×D4196yes—
681C22×D4C23×D4124yes—
682C22×D4C23×D4124yes—
683C22×D4C23×D4116yescomplemented
684C22×D4C2×H(5,𝔽2)124yes—
685C22×D4C26112yes—
686C22×D4C26124yes—
687C23×C4D42148yescomplemented
688C23×C4C23×D413yes—
689C23×C4C23×D416yes—
690C23×C4C23×D413yes—
691C23×C4C23×D413yes—
692C23×C4C23×D413yes—
693C23×C4C23×D413yes—
694C23×C4C23×D413yes—
695C23×C4C23×D416yes—
696C23×C4C23×D416yes—
697C23×C4C23×D414yes—
698C23×C4C23×D416yes—
699C23×C4C23×D4124yes—
700C23×C4C23×D4112yes—
701C23×C4C23×D416yes—
702C23×C4C23×D416yes—
703C23×C4C23×D4124yes—
704C23×C4C23×D4124yes—
705C23×C4C23×D4196yes—
706C23×C4C23×D4148yes—
707C23×C4C2×H(5,𝔽2)112yes—
708C23×C4C2612yes—
709C23×C4C2612yes—
710C23×C4C2612yes—
711C23×C4C2614yes—
712C23×C4C2614yes—
713#127C2×#120132yes—
714#127C2×#120196yes—
715#127C2×#120196yes—
716#127C2×#120196yes—
717#127C2×#1201192yes—
718#120C23×D41192yescomplemented
719#117C23×D4148yescomplemented
720C2×C4⋊C4C23×D4112yes—
721C2×C4⋊C4C23×D4112yes—
722C2×C4⋊C4C23×D4124yes—
723C2×C4⋊C4C23×D4124yes—
724C2×C4⋊C4C23×D4124yes—
725C2×C4⋊C4C23×D4124yes—
726C2×C22⋊C4C23×D4124yes—
727C2×C22⋊C4C23×D4124yes—
728C2×C22⋊C4C23×D4124yes—
729C2×C22⋊C4C23×D4196yes—
730C2×C22⋊C4C23×D4196yes—
731C2×C22⋊C4C23×D4148yes—
732C2×C22⋊C4C23×D4148yes—
733C2×C22⋊C4C23×D4112yes—
734C2×C22⋊C4C26112yes—
735C2×C22⋊C4C26112yes—
736C2×C22⋊C4C26124yes—
737C2×C22⋊C4C26112yes—
738C2×C42C2×#12011yescharacteristic
739C2×C42C2×#12013yes—
740C2×C42C2×#120112yes—
741C2×C42C2×#120112yes—
742C2×C42C2×#120112yes—
743C2×C42C2×#120112yes—
744C2×C42C2×#12013yes—
745C2×C42C2×#12013yes—
746C2×C42C2×#12016yes—
747C2×C42C23×D4112yes—
748C2×C42C23×D4112yes—
749C2×C42C23×D4112yes—
750C2×C42C23×D4112yes—
751C2×C42C23×D4124yes—
752C2×C42C23×D4124yes—
753C2×C42C23×D4124yes—
754#99C23×D41192yescomplemented
755C24C22×#120148yes—
756C24C22×#120116yes—
757C24C2×D42124yes—
758C24C24×D413yes—
759C24C24×D413yes—
760C24C24×D4124yes—
761C24C24×D418yes—
762C24C24×D4148yes—
763C24C24×D4112yes—
764C24C24×D412yes—
765C24C22×H(5,𝔽2)16yes—
766C24C2711yescharacteristic
767C2×Q8C2×D42148yescomplemented
768C2×D4C22×#120132yes—
769C2×D4C22×#120196yes—
770C2×D4C22×#120132yes—
771C2×D4C22×#120132yes—
772C2×D4C22×#120196yes—
773C2×D4C22×#120196yes—
774C2×D4C2×D42148yes—
775C2×D4C2×D42148yescomplemented
776C2×D4C24×D4124yes—
777C2×D4C22×H(5,𝔽2)124yes—
778C22×C4C22×#12011yescharacteristic
779C22×C4C22×#12016yes—
780C22×C4C22×#12016yes—
781C22×C4C22×#12013yes—
782C22×C4C22×#12011yescharacteristic
783C22×C4C22×#12016yes—
784C22×C4C22×#12016yes—
785C22×C4C22×#12016yes—
786C22×C4C22×#12016yes—
787C22×C4C22×#12013yes—
788C22×C4C22×#12013yes—
789C22×C4C22×#12011yescharacteristic
790C22×C4C2×D42112yes—
791C22×C4C2×D42112yes—
792C22×C4C2×D42124yes—
793C22×C4C2×D42124yes—
794C22×C4C2×D42196yescomplemented
795C22×C4#3484112yes—
796C22×C4#3484124yes—
797C22×C4#3484112yes—
798C22×C4C24×D416yes—
799C22×C4C24×D416yes—
800C22×C4C24×D416yes—
801C22×C4C24×D416yes—
802C22×C4C24×D416yes—
803C22×C4C24×D416yes—
804C22×C4C24×D414yes—
805C22×C4C24×D4112yes—
806C22×C4C24×D4112yes—
807C22×C4C24×D4112yes—
808C22×C4C24×D4124yes—
809C22×C4C22×H(5,𝔽2)112yes—
810C22⋊C4C24×D4124yes—
811C42C22×#120112yes—
812C42C22×#12014yes—
813C42C22×#120112yes—
814C42C22×#120124yes—
815C42C22×#120112yes—
816C23C23×#120132yes—
817C23C23×#12013yes—
818C23C23×#12011yescharacteristic
819C23C22×D42124yes—
820C23C22×D4216yes—
821C23C22×D4216yes—
822C23C2×#348416yes—
823C23C2×#348416yes—
824C23C25×D413yes—
825C23C25×D411yescharacteristic
826C23C23×H(5,𝔽2)13yes—
827C2×C4D4×#120124yes—
828C2×C4D4×#120124yes—
829C2×C4D4×#12014yes—
830C2×C4D4×#120112yes—
831C2×C4#6039914yescomplemented
832C2×C4C23×#12012yes—
833C2×C4C23×#12012yes—
834C2×C4C23×#12016yes—
835C2×C4C23×#12012yes—
836C2×C4C23×#12016yes—
837C2×C4C23×#12016yes—
838C2×C4C22×D42112yes—
839C2×C4C22×D42112yes—
840C2×C4C22×D42124yes—
841C2×C4C2×#3484112yes—
842C2×C4C2×#3484112yes—
843C22C2×D4×#12016yes—
844C22C2×D4×#12012yes—
845C22C2×#6039912yes—
846C22#1057487312yes—
847C22C24×#12011yescharacteristic
848C22C23×D4213yes—
849C22C22×#348413yes—
850C4C2×D4×#12014yes—
851C4C2×D4×#120112yes—
852C4C2×#6039914yescomplemented
853C2C22×D4×#12011yescharacteristic
854C2C22×#6039911yescharacteristic
855C2C2×#1057487311yescharacteristic
856C2#7228619714yesdirect product factor
subgroupG/H
center, socleC23C23×#120
commutator, Frattini, cosocleC24C27
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×#127 ◁ G
LECSG ▷ C24 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#6438001C2semidirect
2. C2×#6379015C2semidirect
3. C2×#6442726C2semidirect
4. C2×#6573723C2semidirect
5. C2×C4×#3027C2semidirect
6. C2×#10586097C2semidirect
7. #72286197C2direct (N × H)
8. C2×#6628982C2semidirect
9. C2×#6443348C2semidirect
10. C2×#6437633C2semidirect
11. C2×#6573715C2semidirect
12. C2×#6628898C2semidirect
13. C2×#7677118C2semidirect
14. C2×D4×B(4,𝔽2)C2semidirect
15. C22×#60399C2semidirect
16. C22×H(7,𝔽2)C22semidirect
17. #10586097C22semidirect
18. C2×D4×H(5,𝔽2)C22semidirect
19. C2×D4×H(5,𝔽2)C22semidirect
20. C2×#62852C22semidirect
21. C2×#62812C22semidirect
23. C22×#3484C22semidirect
24. C23×D42C22semidirect
25. C2×C4×#585C22semidirect
27. C22×#3027C22semidirect
28. C22×#3025C22semidirect
29. C22×#3025C22semidirect
30. C22×#3025C22semidirect
31. C2×#60399C22semidirect
32. C22×#3026C22semidirect
33. C23×B(4,𝔽2)C22semidirect
34. C22×#2883C22semidirect
35. #7677118C22semidirect
36. C2×#39338C22semidirect
37. C2×#37644C22semidirect
38. C2×D4×#120C22semidirect
39. C2×#35514C22semidirect
40. C2×#35512C22semidirect
41. C2×#35222C22semidirect
42. C2×#35165C22semidirect
43. C2×#34936C22semidirect
44. C2×#34935C22semidirect
45. C2×#34210C22semidirect
46. C2×C4×#535C22semidirect
47. #6628982C22semidirect
48. C2×#32928C22semidirect
49. C2×#32927C22semidirect
50. C2×#32926C22semidirect
51. #6628898C22semidirect
52. C2×#32900C22semidirect
53. C2×#32898C22semidirect
54. #6573723C22semidirect
55. #6573715C22semidirect
56. D4×B(4,𝔽2)C22semidirect
57. #6443348C22semidirect
58. C2×#25773C22semidirect
59. C2×#25772C22semidirect
60. C2×#25771C22semidirect
61. #6442726C22semidirect
62. C2×#24262C22semidirect
63. C2×#24260C22semidirect
64. #6438001C22semidirect
65. C2×#24405C22semidirect
66. C2×#24404C22semidirect
67. #6437633C22semidirect
68. C2×#23903C22semidirect
69. C2×#23900C22semidirect
70. C2×#23516C22semidirect
71. C2×#23445C22semidirect
72. C2×#23443C22semidirect
73. #6379015C22semidirect
74. C2×D4×#99C22semidirect
75. C2×D4×#99C22semidirect
76. C4×#3027C22semidirect
77. C2×#21482C22semidirect
78. C2×C4×B(4,𝔽2)C22semidirect
79. C2×#21212C22semidirect
80. C2×#20985C22semidirect
81. C2×#20961C22semidirect
82. C2×#20959C22semidirect
83. C2×#20890C22semidirect
84. C2×#20632C22semidirect
85. C2×#20610C22semidirect
86. C2×#20610C22semidirect
87. C2×#20586C22semidirect
88. C2×C4×#410C22semidirect
89. C2×H(7,𝔽2)C23semidirect
94. C25×D4C23semidirect
95. C25×D4C23semidirect
96. D4×H(5,𝔽2)C23semidirect
97. D4×H(5,𝔽2)C23semidirect
98. #62852C23semidirect
99. #62812C23semidirect
100. C2×#3498D4semidirect
105. C2×#3484C23semidirect
106. C22×#550D4semidirect
107. C22×#550D4semidirect
108. C22×D42D4semidirect
109. C22×D42D4semidirect
112. C22×D42C23semidirect
114. C22×#535D4semidirect
117. C22×#535C23semidirect
118. C22×#534C23semidirect
119. C22×#532D4semidirect
121. C23×#127D4semidirect
124. C22×#525C23semidirect
125. C22×#525C23semidirect
126. C23×#121C23semidirect
127. C23×#121C23semidirect
128. C23×#120C23semidirect
129. C23×#120C23semidirect
130. C4×#585C23semidirect
134. C22×#518C23semidirect
136. C23×C4×D4C23semidirect
137. C23×C4×D4C23semidirect
138. C2×#3027D4semidirect
140. C2×#3027C23semidirect
141. C2×#3026C23semidirect
142. C2×#3025C23semidirect
143. C2×#3025C23semidirect
144. C2×#3025C23semidirect
146. C22×#458C23semidirect
147. C22×#458C23semidirect
150. C22×B(4,𝔽2)C23semidirect
151. C22×B(4,𝔽2)C23semidirect
152. C22×B(4,𝔽2)C23semidirect
153. C22×B(4,𝔽2)C23semidirect
154. C2×#2883C23semidirect
158. C22×#410C23semidirect
159. C22×#410C23semidirect
160. C23×#99C23semidirect
161. #39338C23semidirect
162. #37644C23semidirect
163. C2×#2847C23semidirect
164. C2×#2846C23semidirect
165. D4×#120C23semidirect
166. #35514C23semidirect
167. #35512C23semidirect
168. #35222C23semidirect
169. #35165C23semidirect
170. #34936C23semidirect
171. #34935C23semidirect
172. C2×#2539C23semidirect
173. C2×#2534C23semidirect
174. C2×#2501C23semidirect
175. C2×#2486C23semidirect
176. C2×#2433C23semidirect
177. C2×#2408C23semidirect
178. C2×#2412C23semidirect
179. C2×#2405C23semidirect
180. C2×#2410C23semidirect
181. C2×#2403C23semidirect
182. C2×#2617C23semidirect
183. C2×#2613C23semidirect
184. #34210C23semidirect
185. C2×D4×C22⋊C4C23semidirect
186. C2×D4×C22⋊C4C23semidirect
187. C4×#535C23semidirect
188. C2×#2321C23semidirect
189. C2×#2317C23semidirect
191. C2×#2311C23semidirect
192. C2×#2309C23semidirect
193. C2×#2309C23semidirect
194. C2×C4×#120C23semidirect
195. C2×#2285C23semidirect
196. C2×#2280C23semidirect
197. C2×C4×#117C23semidirect
198. #32928C23semidirect
199. #32927C23semidirect
200. #32926C23semidirect
201. #32900C23semidirect
202. #32898C23semidirect
203. #25773C23semidirect
204. #25772C23semidirect
205. #25771C23semidirect
206. #24405C23semidirect
207. #24404C23semidirect
208. #24262C23semidirect
209. #24260C23semidirect
210. #23903C23semidirect
211. #23900C23semidirect
212. #23516C23semidirect
213. C2×#2044C23semidirect
214. #23445C23semidirect
215. #23443C23semidirect
216. C2×#2022C23semidirect
217. C2×#2021C23semidirect
218. C2×#2021C23semidirect
219. D4×#99C23semidirect
220. D4×#99C23semidirect
221. #21482C23semidirect
222. C4×B(4,𝔽2)C23semidirect
223. #21212C23semidirect
224. C2×#1964C23semidirect
225. C2×#1964C23semidirect
226. #20985C23semidirect
227. C2×#1898C23semidirect
228. #20961C23semidirect
229. #20959C23semidirect
230. C2×#1890C23semidirect
231. C2×#1889C23semidirect
232. C2×#1889C23semidirect
233. #20890C23semidirect
234. C2×#1867C23semidirect
235. #20632C23semidirect
236. C2×#1799C23semidirect
237. C2×#1799C23semidirect
238. #20610C23semidirect
239. #20610C23semidirect
241. C2×#1790C23semidirect
242. #20586C23semidirect
243. C2×#1781C23semidirect
244. C4×#410C23semidirect
245. C2×C4×#99C23semidirect
246. C2×C4×#99C23semidirect
247. C2×#1740C23semidirect
248. C2×#1740C23semidirect
250. C2×#585C2×D4semidirect
253. C22×H(5,𝔽2)C2×D4semidirect
258. C23×#41C2×D4semidirect
259. C23×#41C2×D4semidirect
262. C24×D4C2×D4semidirect
263. C24×D4C2×D4semidirect
264. C24×D4C2×D4semidirect
265. C24×D4C2×D4semidirect
274. C24×D4C24semidirect
275. C24×D4C24semidirect
281. C2×#550C2×D4semidirect
282. C2×#550C2×D4semidirect
283. C2×D42C2×D4semidirect
284. C2×D42C2×D4semidirect
285. C2×D42C2×D4semidirect
286. C2×D42C2×D4semidirect
290. C2×#535C2×D4semidirect
291. C2×#535C2×D4semidirect
292. C2×#535C2×D4semidirect
295. C2×#535C24semidirect
297. C2×#534C24semidirect
298. C2×#532C2×D4semidirect
299. C2×#532C2×D4semidirect
301. C22×C4⋊Q8C2×D4semidirect
307. C22×#127C2×D4semidirect
308. C22×#127C2×D4semidirect
309. C22×#127C2×D4semidirect
310. C22×#127C2×D4semidirect
311. C22×#127C2×D4semidirect
313. C22×#124C2×D4semidirect
314. C22×#124C2×D4semidirect
316. C2×#525C24semidirect
317. C2×#525C24semidirect
321. C22×#121C2×D4semidirect
322. C22×#121C2×D4semidirect
323. C22×#121C2×D4semidirect
324. C22×#121C2×D4semidirect
325. C22×#121C2×D4semidirect
326. C22×#121C2×D4semidirect
329. C22×#121C24semidirect
330. C22×#121C24semidirect
331. C22×#120C2×D4semidirect
332. C22×#120C2×D4semidirect
339. C22×#120C24semidirect
340. C22×#120C24semidirect
345. C2×#518C24semidirect
346. C2×C4×#41C2×D4semidirect
348. C22×C4×Q8C2×D4semidirect
349. C22×C4×Q8C2×D4semidirect
350. C22×C4×D4C2×D4semidirect
351. C22×C4×D4C2×D4semidirect
352. C22×C4×D4C2×D4semidirect
353. C22×C4×D4C2×D4semidirect
354. C22×C4×D4C2×D4semidirect
355. C22×C4×D4C2×D4semidirect
358. C22×C4×D4C24semidirect
359. C22×C4×D4C24semidirect
360. C22×#117C2×D4semidirect
371. C23×C42C2×D4semidirect
373. #3027C2×D4semidirect
375. C2×#458C24semidirect
376. C2×#458C24semidirect
377. C2×B(4,𝔽2)C2×D4semidirect
380. C2×B(4,𝔽2)C24semidirect
381. C2×B(4,𝔽2)C24semidirect
382. C2×B(4,𝔽2)C24semidirect
383. C2×#410C2×D4semidirect
387. C2×#410C24semidirect
388. C2×#410C24semidirect
394. C22×#99C24semidirect
395. #2847C24semidirect
396. #2846C24semidirect
397. #2617C24semidirect
398. #2613C24semidirect
399. #2539C24semidirect
400. #2534C24semidirect
401. #2501C24semidirect
402. #2486C24semidirect
403. #2433C24semidirect
404. #2412C24semidirect
405. #2410C24semidirect
406. #2408C24semidirect
407. #2405C24semidirect
408. #2403C24semidirect
409. D4×C22⋊C4C24semidirect
410. D4×C22⋊C4C24semidirect
411. #2321C24semidirect
412. #2317C24semidirect
414. #2311C24semidirect
415. #2309C24semidirect
416. #2309C24semidirect
417. C4×#120C24semidirect
421. #2285C24semidirect
422. #2280C24semidirect
429. C4×#117C24semidirect
432. #2044C24semidirect
433. #2022C24semidirect
434. #2021C24semidirect
435. #2021C24semidirect
436. #1964C24semidirect
437. #1964C24semidirect
438. #1898C24semidirect
439. #1890C24semidirect
440. #1889C24semidirect
441. #1889C24semidirect
442. #1867C24semidirect
443. #1799C24semidirect
444. #1799C24semidirect
446. #1790C24semidirect
447. #1781C24semidirect
448. C4×#99C24semidirect
449. C4×#99C24semidirect
450. #1740C24semidirect
451. #1740C24semidirect
459. #585C22×D4semidirect
466. C22×#41C22×D4semidirect
467. C22×#41C22×D4semidirect
491. C23×D4C22×D4semidirect
492. C23×D4C22×D4semidirect
493. C23×D4C22×D4semidirect
494. C23×D4C22×D4semidirect
495. C23×D4C22×D4semidirect
518. #535C22×D4semidirect
520. C2×C4⋊Q8C22×D4semidirect
534. C2×#127C22×D4semidirect
535. C2×#127C22×D4semidirect
536. C2×#127C22×D4semidirect
537. C2×#127C22×D4semidirect
538. C2×#124C22×D4semidirect
539. C2×#124C22×D4semidirect
545. C2×#121C22×D4semidirect
546. C2×#121C22×D4semidirect
547. C2×#121C22×D4semidirect
548. C2×#121C22×D4semidirect
549. C2×#121C22×D4semidirect
550. C2×#121C22×D4semidirect
554. C2×#120C22×D4semidirect
555. C2×#120C22×D4semidirect
556. C2×#120C22×D4semidirect
564. C2×C4×Q8C22×D4semidirect
565. C2×C4×Q8C22×D4semidirect
568. C2×C4×D4C22×D4semidirect
569. C2×C4×D4C22×D4semidirect
570. C2×C4×D4C22×D4semidirect
571. C2×C4×D4C22×D4semidirect
572. C2×C4×D4C22×D4semidirect
573. C2×C4×D4C22×D4semidirect
577. C2×#117C22×D4semidirect
578. C2×#117C22×D4semidirect
613. C22×C42C22×D4semidirect
615. B(4,𝔽2)C22×D4semidirect
616. #410C22×D4semidirect
617. C2×#99C22×D4semidirect
647. C2×#41D42semidirect
650. C22×Q8D42semidirect
665. C22×D4D42semidirect
683. C22×D4C23×D4semidirect
687. C23×C4D42semidirect
718. #120C23×D4semidirect
719. #117C23×D4semidirect
754. #99C23×D4semidirect
767. C2×Q8C2×D42semidirect
775. C2×D4C2×D42semidirect
794. C22×C4C2×D42semidirect
831. C2×C4#60399semidirect
852. C4C2×#60399semidirect
856. C2#72286197direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#64380012
C2×#63790152
C2×#64427262
C2×#65737232
C2×C4×#30272
C2×#105860972
#722861972
C2×#66289822
C2×#64433482
C2×#64376332
C2×#65737152
C2×#66288982
C2×#76771182
C2×D4×B(4,𝔽2)2
C22×#603992