Finite Group Databasebeta

← C2×#72216646 #72241066

Subgroups — C2×#72216646 #72241066

Order 2048.

Only the 6496 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 516 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#374004C211yesmaximal, characteristic, complemented
2C2×#417824C212yesmaximal, complemented
3C2×#394273C214yesmaximal, complemented
4C2×#359591C212yesmaximal, complemented
5C2×#417538C214yesmaximal, complemented
6C2×#364532C214yesmaximal, complemented
7C2×#6628896C211yesmaximal, characteristic, complemented
8C2×#394064C214yesmaximal, complemented
9C22×#60399C212yesmaximal, complemented
10C2×#7670203C211yesmaximal, characteristic, complemented
11C22×#23900C214yesmaximal, complemented
12C2×#449475C212yesmaximal, complemented
13#72216646C2132yesmaximal, direct product factor
14C22×H(7,𝔽2)C2211yescharacteristic, complemented
15C22×#3484C2212yes—
16C22×#3484C2214yescomplemented
17C24×#120C2212yescomplemented
18C2×#60399C22132yescomplemented
19C22×#3026C2214yescomplemented
20C22×#3026C2214yescomplemented
21C23×B(4,𝔽2)C2214yes—
22C23×B(4,𝔽2)C2214yescomplemented
23C23×B(4,𝔽2)C2214yescomplemented
24C22×#2883C2214yescomplemented
25C22×#2883C2212yescomplemented
26#7670203C22116yescomplemented
27C22×#2846C2211yescharacteristic, complemented
28C22×#2846C2214yescomplemented
29C2×#35390C2211yescharacteristic, complemented
30C2×#35348C2212yescomplemented
31C2×#35346C2211yescharacteristic
32C2×#35346C2212yescomplemented
33C2×#34981C2212yescomplemented
34C2×#34980C2212yescomplemented
35C2×#34198C2212yescomplemented
36#6628896C22116yescomplemented
37C2×#23900C22164yescomplemented
38C2×#23444C2214yescomplemented
39C22×#2021C2218yescomplemented
40C22×#2021C2218yescomplemented
41C22×#1913C2214yescomplemented
42C22×#1898C2218yescomplemented
43C22×#1889C2214yescomplemented
44C22×#1889C2214yescomplemented
45C2×#20609C2214yescomplemented
46C2×#20585C2212yescomplemented
47C2×#20585C2211yescharacteristic, complemented
48C22×#1781C2214yescomplemented
49#449475C22132yescomplemented
50#417824C22132yescomplemented
51#417538C22164yescomplemented
52#394273C22164yescomplemented
53#394064C22164yescomplemented
54#374004C22116yescomplemented
55#364532C22164yescomplemented
56#359591C22132yescomplemented
57C2×#11169C2212yescomplemented
58C2×#11089C2218yescomplemented
59C2×#10991C2218yescomplemented
60C2×#10991C2214yescomplemented
61C2×#10972C2218yescomplemented
62C2×#10972C2214yescomplemented
63C2×#10965C2214yescomplemented
64C2×#10965C2212yescomplemented
65C2×#10938C2214yescomplemented
66C2×#10754C2214yescomplemented
67C2×#10768C2214yescomplemented
68C28C2311yescharacteristic, complemented
69C2×H(7,𝔽2)C2318yescomplemented
70C23×H(5,𝔽2)C2311yescharacteristic
71C23×H(5,𝔽2)C2314yes—
72C23×H(5,𝔽2)C2312yes—
73C25×D4C2312yes—
74C2×#3484D4116yescomplemented
75C2×#3484C23116yes—
76C2×#3484C23132yescomplemented
77C22×#535D414yescomplemented
78C22×#534D414yescomplemented
79C22×#534C2312yes—
80C22×#534C2312yes—
81C22×#534C2318yes—
82C22×#534C2311yescharacteristic, complemented
83C22×#525D414yescomplemented
84C23×#120D414yescomplemented
85C23×#120C2311yescharacteristic
86C23×#120C2312yes—
87C23×#120C2318yes—
88C23×#120C2312yes—
89C23×#120C2312yes—
90C23×#120C2314yes—
91C23×#120C2312yescomplemented
92C23×#120C2312yescomplemented
93C23×#120C23116yescomplemented
94C22×#518C2312yes—
95C22×#518C2314yes—
96C24×C22⋊C4C2312yescomplemented
97C2×#3026C23132yescomplemented
98C2×#3026C23132yescomplemented
99C22×B(4,𝔽2)D4164yescomplemented
100C22×B(4,𝔽2)C23132yes—
101C22×B(4,𝔽2)C23132yescomplemented
102C22×B(4,𝔽2)C23132yescomplemented
103C2×#2883C23132yescomplemented
104C2×#2883C23116yescomplemented
105C23×#99C2318yes—
106C23×#99C2314yes—
107C23×#99C2318yes—
108C23×#99C2314yes—
109C23×#99C2318yes—
110C23×#99C2314yes—
111C23×#99C2318yescomplemented
112C2×#2846C2318yescomplemented
113C2×#2846C23132yescomplemented
114#35390C2318yescomplemented
115#35348C23116yescomplemented
116#35346D418yescomplemented
117#35346C2318yes—
118#35346C23116yescomplemented
119#34981C23116yescomplemented
120#34980C23116yescomplemented
121C2×#2404D414yescomplemented
122C2×#2403D414yescomplemented
123#34198C23116yescomplemented
124C2×#2315C2312yescomplemented
125C2×#2308C2311yescharacteristic
126C2×#2308C2312yes—
127C2×#2308C2314yes—
128C2×#2308C2312yes—
129C2×#2308C2312yescomplemented
130C22×#379C2311yescharacteristic, complemented
131C22×#379C2314yescomplemented
132C22×#379C2318yescomplemented
133C22×#379C2312yescomplemented
134C2×#2273C2311yescharacteristic, complemented
135#23444C23132yescomplemented
136C2×#2021C23164yescomplemented
137C2×#2021C23164yescomplemented
138C2×#1913C23132yescomplemented
139C2×#1898C23164yescomplemented
140C2×#1889C23132yescomplemented
141C2×#1889C23132yescomplemented
142#20609C23132yescomplemented
143#20585C23116yescomplemented
144#20585C2318yescomplemented
145C2×#1781C23132yescomplemented
146C22×#342C2314yescomplemented
147C22×#342C2318yescomplemented
148C22×#342C2318yescomplemented
149C22×#342C2318yescomplemented
150#11169C23116yescomplemented
151#11089C23164yescomplemented
152#10991C23132yescomplemented
153#10991C23164yescomplemented
154#10972C23132yescomplemented
155#10972C23164yescomplemented
156#10965C23116yescomplemented
157#10965C23132yescomplemented
158#10938C23132yescomplemented
159#10768C23132yescomplemented
160#10754C23132yescomplemented
161C27C2×D412yescomplemented
162C27C2412yes—
163C27C2411yescharacteristic
164C27C2414yescomplemented
165C22×H(5,𝔽2)C2×D414yes—
166C22×H(5,𝔽2)C2×D418yes—
167C22×H(5,𝔽2)C2×D4132yescomplemented
168C22×H(5,𝔽2)C2414yes—
169C22×H(5,𝔽2)C2418yes—
170C22×H(5,𝔽2)C24116yes—
171C23×#41C2×D412yes—
172C23×#41C2×D414yes—
173C24×D4C2×D412yes—
174C24×D4C2×D414yes—
175C24×D4C2×D412yescomplemented
176C24×D4C2×D412yescomplemented
177C24×D4C2×D412yescomplemented
178C24×D4C2×D418yescomplemented
179C24×D4C2412yes—
180C24×D4C2411yescharacteristic
181C24×D4C2412yes—
182C24×D4C2418yes—
183C24×D4C2414yes—
184C25×C4C2×D412yescomplemented
185C2×#535C2×D4132yescomplemented
186C2×#534C2×D418yes—
187C2×#534C2×D418yescomplemented
188C2×#534C2×D4132yescomplemented
189C2×#534C2418yes—
190C2×#534C2418yes—
191C2×#534C24132yes—
192C2×#534C2414yescomplemented
193C2×#525C2×D4132yescomplemented
194C22×#123C2×D414yes—
195C22×#123C2×D414yescomplemented
196C22×#120C2×D418yes—
197C22×#120C2×D414yes—
198C22×#120C2×D414yes—
199C22×#120C2×D4132yes—
200C22×#120C2×D414yes—
201C22×#120C2×D414yescomplemented
202C22×#120C2×D418yescomplemented
203C22×#120C2×D418yescomplemented
204C22×#120C2×D418yescomplemented
205C22×#120C2×D414yescomplemented
206C22×#120C2×D414yescomplemented
207C22×#120C2×D414yescomplemented
208C22×#120C2×D4164yescomplemented
209C22×#120C2×D4132yescomplemented
210C22×#120C2414yes—
211C22×#120C2418yes—
212C22×#120C2418yes—
213C22×#120C24132yes—
214C22×#120C2418yes—
215C22×#120C24116yes—
216C22×#120C2418yescomplemented
217C22×#120C2418yescomplemented
218C2×#518C2×D418yescomplemented
219C2×#518C2418yes—
220C2×#518C24116yes—
221C22×#117C2×D414yescomplemented
222C23×C22⋊C4C2×D414yescomplemented
223C23×C22⋊C4C2×D412yescomplemented
224C23×C22⋊C4C2412yes—
225C23×C22⋊C4C2412yes—
226C23×C22⋊C4C2412yes—
227C23×C22⋊C4C2418yes—
228C23×C22⋊C4C2411yescharacteristic
229C23×C22⋊C4C2414yes—
230C23×C22⋊C4C2418yescomplemented
231C2×B(4,𝔽2)C2×D41256yescomplemented
232C22×#99C2×D4164yescomplemented
233C22×#99C2×D4132yescomplemented
234C22×#99C24116yes—
235C22×#99C24132yes—
236C22×#99C24132yes—
237C22×#99C24116yes—
238C22×#99C24116yes—
239C22×#99C24132yes—
240C22×#99C24132yescomplemented
241#2404C2×D4132yescomplemented
242#2403C2×D4132yescomplemented
243#2315C2418yescomplemented
244#2308C2×D414yescomplemented
245#2308C2×D418yescomplemented
246#2308C2418yes—
247#2308C24116yes—
248#2308C2414yes—
249#2308C2418yes—
250#2308C2418yescomplemented
251C2×#386C2×D418yescomplemented
252C2×#381C2×D412yescomplemented
253C2×#379C2×D412yescomplemented
254C2×#379C2414yescomplemented
255C2×#379C24132yescomplemented
256C2×#379C24116yescomplemented
257C2×#379C2418yescomplemented
258#2273C2414yescomplemented
259C2×#342C24116yescomplemented
260C2×#342C24132yescomplemented
261C2×#342C24132yescomplemented
262C2×#342C24132yescomplemented
263C26#12012yescomplemented
264C26C22×D412yes—
265C26C22×D412yes—
266C26C22×D411yescharacteristic
267C26C22×D414yes—
268C26C22×D412yes—
269C26C22×D4116yes—
270C26C22×D412yes—
271C26C22×D412yes—
272C26C22×D412yes—
273C26C22×D418yescomplemented
274C26H(5,𝔽2)14yes—
275C26C2514yes—
276C26C2512yes—
277C26C2511yescharacteristic
278C2×H(5,𝔽2)C22×D4164yescomplemented
279C22×#41#120116yescomplemented
280C22×#41#12018yescomplemented
281C22×#41C22×D418yes—
282C22×#41C22×D4116yes—
283C23×Q8#12012yescomplemented
284C23×D4#12014yescomplemented
285C23×D4#12012yescomplemented
286C23×D4#12018yescomplemented
287C23×D4#120116yescomplemented
288C23×D4C22×D414yes—
289C23×D4C22×D414yes—
290C23×D4C22×D414yes—
291C23×D4C22×D414yes—
292C23×D4C22×D414yes—
293C23×D4C22×D414yes—
294C23×D4C22×D418yes—
295C23×D4C22×D4116yes—
296C23×D4C22×D4116yes—
297C23×D4C22×D4132yes—
298C23×D4C22×D414yes—
299C23×D4C22×D412yes—
300C23×D4C22×D414yes—
301C23×D4C22×D418yescomplemented
302C23×D4C22×D418yescomplemented
303C23×D4C22×D418yescomplemented
304C23×D4H(5,𝔽2)116yes—
305C23×D4H(5,𝔽2)18yes—
306C23×D4C2514yes—
307C23×D4C2512yes—
308C23×D4C2514yes—
309C23×D4C2518yes—
310C24×C4#12012yescomplemented
311C24×C4#12014yescomplemented
312C24×C4C22×D412yes—
313C24×C4C22×D411yescharacteristic
314C24×C4C22×D412yes—
315C24×C4C22×D412yes—
316C24×C4C22×D418yescomplemented
317C24×C4H(5,𝔽2)14yes—
318C2×#123C22×D4116yes—
319C2×#123C22×D4116yescomplemented
320C2×#120#120164yescomplemented
321C2×#120#120132yescomplemented
322C2×#120#120132yescomplemented
323C2×#120C22×D4116yes—
324C2×#120C22×D4116yes—
325C2×#120C22×D4164yes—
326C2×#120C22×D4116yes—
327C2×#120C22×D4132yescomplemented
328C2×#120C22×D4116yescomplemented
329C2×#120C22×D4116yescomplemented
330C2×#120C22×D4116yescomplemented
331C2×#120C22×D41128yescomplemented
332C2×#117C22×D4116yescomplemented
333C22×C22⋊C4C22×D4116yes—
334C22×C22⋊C4C22×D414yes—
335C22×C22⋊C4C22×D414yes—
336C22×C22⋊C4C22×D414yes—
337C22×C22⋊C4C22×D4132yes—
338C22×C22⋊C4C22×D414yes—
339C22×C22⋊C4C22×D414yes—
340C22×C22⋊C4C22×D414yes—
341C22×C22⋊C4C22×D412yes—
342C22×C22⋊C4C22×D4116yescomplemented
343C22×C22⋊C4C22×D418yescomplemented
344C22×C22⋊C4C2514yes—
345C22×C22⋊C4C2514yes—
346C22×C22⋊C4C2514yes—
347C22×C22⋊C4C25116yes—
348C22×C22⋊C4C2512yes—
349C22×C22⋊C4C2518yes—
350C2×#99C22×D41128yescomplemented
351C2×#99C22×D4164yescomplemented
352#386C22×D4132yescomplemented
353#381C22×D418yescomplemented
354#379C22×D418yescomplemented
355C25C2×#12014yes—
356C25C2×#12014yes—
357C25C2×#12018yes—
358C25C2×#12018yes—
359C25C2×#120116yes—
360C25C2×#12012yes—
361C25C2×#12012yes—
362C25C2×#12018yescomplemented
363C25D42116yes—
364C25D42116yescomplemented
365C25C23×D414yes—
366C25C23×D414yes—
367C25C23×D4116yes—
368C25C23×D414yes—
369C25C23×D414yes—
370C25C23×D412yes—
371C25C23×D412yes—
372C25C23×D412yes—
373C25C23×D414yes—
374C25C23×D418yes—
375C25C23×D411yescharacteristic
376C25C23×D411yescharacteristic
377C25C2×H(5,𝔽2)18yes—
378C25C2×H(5,𝔽2)14yes—
379C25C2×H(5,𝔽2)14yes—
380C25C2×H(5,𝔽2)18yes—
381C25C2611yescharacteristic
382C22×Q8C2×#12018yescomplemented
383C22×D4C2×#120116yes—
384C22×D4C2×#120116yes—
385C22×D4C2×#12018yes—
386C22×D4C2×#12018yes—
387C22×D4C2×#12018yes—
388C22×D4C2×#120116yescomplemented
389C22×D4C2×#12018yescomplemented
390C22×D4#534116yes—
391C22×D4#534116yes—
392C22×D4D42132yes—
393C22×D4D42132yes—
394C22×D4D42132yes—
395C22×D4D42132yescomplemented
396C22×D4C23×D418yes—
397C22×D4C23×D418yes—
398C22×D4C23×D418yes—
399C22×D4C23×D4116yes—
400C22×D4C23×D4132yes—
401C22×D4C2×H(5,𝔽2)116yes—
402C23×C4C2×#12014yes—
403C23×C4C2×#12014yes—
404C23×C4C2×#12012yes—
405C23×C4C2×#12012yes—
406C23×C4C2×#12018yescomplemented
407C23×C4C2×#120116yescomplemented
408C23×C4D42116yes—
409C23×C4D42116yescomplemented
410C23×C4C23×D414yes—
411C23×C4C23×D412yes—
412C23×C4C23×D414yes—
413C23×C4C23×D414yes—
414C23×C4C2×H(5,𝔽2)18yes—
415#120C2×#120164yescomplemented
416#120C2×#120164yescomplemented
417C2×C22⋊C4C2×#120116yes—
418C2×C22⋊C4C2×#120116yes—
419C2×C22⋊C4C23×D418yes—
420C2×C22⋊C4C23×D4116yes—
421C2×C22⋊C4C23×D418yes—
422C2×C22⋊C4C23×D418yes—
423C2×C22⋊C4C23×D4132yes—
424C24#2403116yes—
425C24#2403116yes—
426C24C22×#12012yes—
427C24C22×#12011yescharacteristic
428C24C22×#12011yescharacteristic
429C24C22×#12018yes—
430C24C22×#12014yes—
431C24C22×#12014yes—
432C24C22×#12018yes—
433C24C22×#12018yes—
434C24C22×#12014yes—
435C24C2×#53414yes—
436C24C2×#53414yes—
437C24C2×D4218yes—
438C24C2×D4218yes—
439C24C2×D4218yes—
440C24C2×D4218yes—
441C24C2×D42116yes—
442C24C2×D4218yes—
443C24C2×D4218yes—
444C24C2×D42116yescomplemented
445C24#348414yes—
446C24#348418yes—
447C24#348414yes—
448C24#3484116yes—
449C24#3484116yes—
450C24#348414yes—
451C24#348412yes—
452C24#348412yes—
453C24#353218yes—
454C24#353218yes—
455C24C24×D412yes—
456C24C24×D414yes—
457C24C24×D411yescharacteristic
458C24C22×H(5,𝔽2)14yes—
459C24C22×H(5,𝔽2)14yes—
460C2×D4#2403132yes—
461C2×D4#2403132yes—
462C2×D4C22×#120116yes—
463C2×D4C2×#534116yes—
464C2×D4C2×D42132yes—
465C22×C4#2403116yes—
466C22×C4#2403116yes—
467C22×C4C22×#12018yes—
468C22×C4C22×#12014yes—
469C22×C4C2×D42116yes—
470C22×C4C2×D42116yescomplemented
471C22⋊C4C22×#120116yes—
472C23C2×#2403116yes—
473C23C2×#240314yes—
474C23C2×#240314yes—
475C23C2×#240314yes—
476C23C2×#240314yes—
477C23#3534612yes—
478C23#3534614yes—
479C23#3534611yescharacteristic
480C23#3534611yescharacteristic
481C23D4×#12018yes—
482C23D4×#12018yes—
483C23D4×#120116yes—
484C23#3764418yes—
485C23#3764418yes—
486C23#37644116yes—
487C23#5899018yes—
488C23#5899018yes—
489C23#5899018yes—
490C23#5899018yes—
491C23C23×#12011yescharacteristic
492C23C23×#12012yes—
493C23C22×#53412yes—
494C23C22×D4214yes—
495C23C22×D4214yes—
496C23C22×D4214yes—
497C23C2×#353214yes—
498C23C2×#348412yes—
499C23C2×#348418yes—
500C23C2×#348414yes—
501C2×C4C2×#2403116yes—
502C22#64765612yes—
503C22#64765612yes—
504C22#64765618yes—
505C22#64765614yes—
506C22#649987414yes—
507C22C22×#240312yes—
508C22C2×#3534611yescharacteristic
509C22C2×D4×#12014yes—
510C22C2×#3764414yes—
511C22C2×#5899014yes—
512C2#7221664614yesdirect product factor
513C2C2×#649987412yes—
514C2C2×#64765611yescharacteristic
subgroupG/H
center, socleC23#35346
commutator, Frattini, cosocleC25C26
LCSG ▷ C25 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C26 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#374004C2semidirect
2. C2×#417824C2semidirect
3. C2×#394273C2semidirect
4. C2×#359591C2semidirect
5. C2×#417538C2semidirect
6. C2×#364532C2semidirect
7. C2×#6628896C2semidirect
8. C2×#394064C2semidirect
9. C22×#60399C2semidirect
10. C2×#7670203C2semidirect
11. C22×#23900C2semidirect
12. C2×#449475C2semidirect
13. #72216646C2direct (N × H)
14. C22×H(7,𝔽2)C22semidirect
16. C22×#3484C22semidirect
17. C24×#120C22semidirect
18. C2×#60399C22semidirect
19. C22×#3026C22semidirect
20. C22×#3026C22semidirect
22. C23×B(4,𝔽2)C22semidirect
23. C23×B(4,𝔽2)C22semidirect
24. C22×#2883C22semidirect
25. C22×#2883C22semidirect
26. #7670203C22semidirect
27. C22×#2846C22semidirect
28. C22×#2846C22semidirect
29. C2×#35390C22semidirect
30. C2×#35348C22semidirect
32. C2×#35346C22semidirect
33. C2×#34981C22semidirect
34. C2×#34980C22semidirect
35. C2×#34198C22semidirect
36. #6628896C22semidirect
37. C2×#23900C22semidirect
38. C2×#23444C22semidirect
39. C22×#2021C22semidirect
40. C22×#2021C22semidirect
41. C22×#1913C22semidirect
42. C22×#1898C22semidirect
43. C22×#1889C22semidirect
44. C22×#1889C22semidirect
45. C2×#20609C22semidirect
46. C2×#20585C22semidirect
47. C2×#20585C22semidirect
48. C22×#1781C22semidirect
49. #449475C22semidirect
50. #417824C22semidirect
51. #417538C22semidirect
52. #394273C22semidirect
53. #394064C22semidirect
54. #374004C22semidirect
55. #364532C22semidirect
56. #359591C22semidirect
57. C2×#11169C22semidirect
58. C2×#11089C22semidirect
59. C2×#10991C22semidirect
60. C2×#10991C22semidirect
61. C2×#10972C22semidirect
62. C2×#10972C22semidirect
63. C2×#10965C22semidirect
64. C2×#10965C22semidirect
65. C2×#10938C22semidirect
66. C2×#10754C22semidirect
67. C2×#10768C22semidirect
68. C28C23semidirect
69. C2×H(7,𝔽2)C23semidirect
74. C2×#3484D4semidirect
76. C2×#3484C23semidirect
77. C22×#535D4semidirect
78. C22×#534D4semidirect
82. C22×#534C23semidirect
83. C22×#525D4semidirect
84. C23×#120D4semidirect
91. C23×#120C23semidirect
92. C23×#120C23semidirect
93. C23×#120C23semidirect
96. C24×C22⋊C4C23semidirect
97. C2×#3026C23semidirect
98. C2×#3026C23semidirect
99. C22×B(4,𝔽2)D4semidirect
101. C22×B(4,𝔽2)C23semidirect
102. C22×B(4,𝔽2)C23semidirect
103. C2×#2883C23semidirect
104. C2×#2883C23semidirect
111. C23×#99C23semidirect
112. C2×#2846C23semidirect
113. C2×#2846C23semidirect
114. #35390C23semidirect
115. #35348C23semidirect
116. #35346D4semidirect
118. #35346C23semidirect
119. #34981C23semidirect
120. #34980C23semidirect
121. C2×#2404D4semidirect
122. C2×#2403D4semidirect
123. #34198C23semidirect
124. C2×#2315C23semidirect
129. C2×#2308C23semidirect
130. C22×#379C23semidirect
131. C22×#379C23semidirect
132. C22×#379C23semidirect
133. C22×#379C23semidirect
134. C2×#2273C23semidirect
135. #23444C23semidirect
136. C2×#2021C23semidirect
137. C2×#2021C23semidirect
138. C2×#1913C23semidirect
139. C2×#1898C23semidirect
140. C2×#1889C23semidirect
141. C2×#1889C23semidirect
142. #20609C23semidirect
143. #20585C23semidirect
144. #20585C23semidirect
145. C2×#1781C23semidirect
146. C22×#342C23semidirect
147. C22×#342C23semidirect
148. C22×#342C23semidirect
149. C22×#342C23semidirect
150. #11169C23semidirect
151. #11089C23semidirect
152. #10991C23semidirect
153. #10991C23semidirect
154. #10972C23semidirect
155. #10972C23semidirect
156. #10965C23semidirect
157. #10965C23semidirect
158. #10938C23semidirect
159. #10768C23semidirect
160. #10754C23semidirect
161. C27C2×D4semidirect
164. C27C24semidirect
167. C22×H(5,𝔽2)C2×D4semidirect
175. C24×D4C2×D4semidirect
176. C24×D4C2×D4semidirect
177. C24×D4C2×D4semidirect
178. C24×D4C2×D4semidirect
184. C25×C4C2×D4semidirect
185. C2×#535C2×D4semidirect
187. C2×#534C2×D4semidirect
188. C2×#534C2×D4semidirect
192. C2×#534C24semidirect
193. C2×#525C2×D4semidirect
195. C22×#123C2×D4semidirect
201. C22×#120C2×D4semidirect
202. C22×#120C2×D4semidirect
203. C22×#120C2×D4semidirect
204. C22×#120C2×D4semidirect
205. C22×#120C2×D4semidirect
206. C22×#120C2×D4semidirect
207. C22×#120C2×D4semidirect
208. C22×#120C2×D4semidirect
209. C22×#120C2×D4semidirect
216. C22×#120C24semidirect
217. C22×#120C24semidirect
218. C2×#518C2×D4semidirect
221. C22×#117C2×D4semidirect
222. C23×C22⋊C4C2×D4semidirect
223. C23×C22⋊C4C2×D4semidirect
230. C23×C22⋊C4C24semidirect
231. C2×B(4,𝔽2)C2×D4semidirect
232. C22×#99C2×D4semidirect
233. C22×#99C2×D4semidirect
240. C22×#99C24semidirect
241. #2404C2×D4semidirect
242. #2403C2×D4semidirect
243. #2315C24semidirect
244. #2308C2×D4semidirect
245. #2308C2×D4semidirect
250. #2308C24semidirect
251. C2×#386C2×D4semidirect
252. C2×#381C2×D4semidirect
253. C2×#379C2×D4semidirect
254. C2×#379C24semidirect
255. C2×#379C24semidirect
256. C2×#379C24semidirect
257. C2×#379C24semidirect
258. #2273C24semidirect
259. C2×#342C24semidirect
260. C2×#342C24semidirect
261. C2×#342C24semidirect
262. C2×#342C24semidirect
263. C26#120semidirect
273. C26C22×D4semidirect
278. C2×H(5,𝔽2)C22×D4semidirect
279. C22×#41#120semidirect
280. C22×#41#120semidirect
283. C23×Q8#120semidirect
284. C23×D4#120semidirect
285. C23×D4#120semidirect
286. C23×D4#120semidirect
287. C23×D4#120semidirect
301. C23×D4C22×D4semidirect
302. C23×D4C22×D4semidirect
303. C23×D4C22×D4semidirect
310. C24×C4#120semidirect
311. C24×C4#120semidirect
316. C24×C4C22×D4semidirect
319. C2×#123C22×D4semidirect
320. C2×#120#120semidirect
321. C2×#120#120semidirect
322. C2×#120#120semidirect
327. C2×#120C22×D4semidirect
328. C2×#120C22×D4semidirect
329. C2×#120C22×D4semidirect
330. C2×#120C22×D4semidirect
331. C2×#120C22×D4semidirect
332. C2×#117C22×D4semidirect
342. C22×C22⋊C4C22×D4semidirect
343. C22×C22⋊C4C22×D4semidirect
350. C2×#99C22×D4semidirect
351. C2×#99C22×D4semidirect
352. #386C22×D4semidirect
353. #381C22×D4semidirect
354. #379C22×D4semidirect
362. C25C2×#120semidirect
364. C25D42semidirect
382. C22×Q8C2×#120semidirect
388. C22×D4C2×#120semidirect
389. C22×D4C2×#120semidirect
395. C22×D4D42semidirect
406. C23×C4C2×#120semidirect
407. C23×C4C2×#120semidirect
409. C23×C4D42semidirect
415. #120C2×#120semidirect
416. #120C2×#120semidirect
444. C24C2×D42semidirect
470. C22×C4C2×D42semidirect
512. C2#72216646direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#3740042
C2×#4178242
C2×#3942732
C2×#3595912
C2×#4175382
C2×#3645322
C2×#66288962
C2×#3940642
C22×#603992
C2×#76702032
C22×#239002
C2×#4494752
#722166462