Finite Group Databasebeta

← #72338579

Subgroups — #72338579

Order 2048.

Only the 5076 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 670 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72338578C211yesmaximal, characteristic, complemented
2#72338577C214yesmaximal, complemented
3#72338575C212yesmaximal, complemented
4#72338207C211yesmaximal, characteristic, complemented
5#72317711C2116yesmaximal, complemented
6#72306375C218yesmaximal, complemented
7#72306361C214yesmaximal, complemented
8#72305972C214yesmaximal, complemented
9#72302157C212yesmaximal, complemented
10#72302148C212yesmaximal, complemented
11C2×#6348967C212yesmaximal, complemented
12C2×#7737411C211yesmaximal, characteristic, complemented
13#72213685C2116yesmaximal, complemented
14#10585995C2211yescharacteristic, complemented
15C22×#3498C2211yescharacteristic
16C23×D42C2211yescharacteristic, complemented
17#10575560C2218yescomplemented
18#10575552C2214yescomplemented
19#10575547C2218yescomplemented
20#10575509C2212yescomplemented
21C2×#60798C2212yes—
22#10575254C2212yescomplemented
23#10575219C2212yescomplemented
24C2×#60558C2214yescomplemented
25#10574126C2211yescharacteristic, complemented
26#7737411C2214yes—
27#7737411C2218yescomplemented
28#7737411C2214yescomplemented
29C2×#52004C2218yescomplemented
30C2×#35237C2212yescomplemented
31C2×#34963C2212yes—
32C2×#34364C2211yescharacteristic, complemented
33#6348967C22116yescomplemented
34#6348967C22116yescomplemented
35C2×#18529C2218yescomplemented
36C2×#18524C2218yescomplemented
37#6346641C2218yescomplemented
38#6346639C2214yescomplemented
39#6346637C2214yescomplemented
40#6346626C22116yescomplemented
41#6346414C22116yescomplemented
42C2×#17741C2212yescomplemented
43#6343804C2212yescomplemented
44#6343372C2214yescomplemented
45C2×#17448C2214yescomplemented
46#6342561C2212yescomplemented
47#246957C221128yescomplemented
48#246930C22164yescomplemented
49#246927C22164yescomplemented
50#235463C22116yescomplemented
51#235462C22116yescomplemented
52#235456C22132yescomplemented
53#235444C22132yescomplemented
54#201616C22116yescomplemented
55#201614C22116yescomplemented
56#201611C2218yescomplemented
57#201605C2218yescomplemented
58#200885C22116yescomplemented
59#200876C22116yescomplemented
60#200851C2218yescomplemented
61#200848C2218yescomplemented
62#187836C2218yescomplemented
63#187824C2214yescomplemented
64#187824C2214yescomplemented
65#187811C2218yescomplemented
66#181215C2214yescomplemented
67C23×H(5,𝔽2)D412yes—
68#62815C2312yescomplemented
69#62814C2314yescomplemented
70#62813C2311yescharacteristic, complemented
71#62812C2311yescharacteristic, complemented
72C2×#3498D412yes—
73C2×#3498D412yes—
74C2×#3498D414yes—
75C2×#3498C2312yes—
76C2×#3498C2312yes—
77C2×#3498C2314yes—
78C22×D42C2314yes—
79C22×D42C2314yes—
80C22×D42C2314yes—
81#62686C2314yescomplemented
82C22×#535D412yes—
83C22×#535C2314yes—
84C2×#3444C2312yes—
85C22×#532D412yes—
86C22×#532C2311yescharacteristic
87C23×#127D412yes—
88C23×#127C2311yescharacteristic
89C22×C4×#41C2311yescharacteristic
90C23×C4×D4C2312yes—
91#60806C23132yescomplemented
92#60802C2318yescomplemented
93#60799C2318yescomplemented
94#60798D4116yescomplemented
95#60798C2318yes—
96#60798C2318yes—
97C2×#3208D418yescomplemented
98C2×#3205D418yescomplemented
99#60644C23116yescomplemented
100#60639C2314yescomplemented
101C2×#3151C2314yes—
102#60619C23116yescomplemented
103#60618C2314yescomplemented
104C2×#3138C2314yes—
105#60558C23116yes—
106#60558C23116yescomplemented
107C2×#3110C2318yescomplemented
108C2×#3109C2318yescomplemented
109#60125C2314yescomplemented
110#60124C2314yescomplemented
111#60123C2312yescomplemented
112C2×#2920C2312yes—
113C2×#2920C2314yes—
114C4×#568C2312yescomplemented
115#52004C23132yes—
116#52004C23132yes—
117#35237C2318yes—
118#35237C2318yes—
119#34963D414yes—
120#34963D414yes—
121#34963D418yes—
122#34963C2314yes—
123#34963C2314yes—
124#34963C2318yes—
125C2×#2598C2318yes—
126C2×#2487D414yes—
127C2×#2408D414yes—
128C2×#2631C2318yes—
129C2×#2398D414yes—
130C2×#2397D414yes—
131#34364C2314yes—
132#34364C2314yes—
133C2×#2380C2314yes—
134C2×#2283C2312yes—
135#18529C23164yescomplemented
136#18524C23164yescomplemented
137#18156C23164yescomplemented
138#18154C23132yescomplemented
139#18152C23132yescomplemented
140#17741C2318yes—
141#17741C2318yes—
142C2×#1555C2318yes—
143#17675C2318yescomplemented
144#17666C2318yescomplemented
145#17663C2318yescomplemented
146#17596C2318yescomplemented
147#17595C2318yescomplemented
148#17593C23116yescomplemented
149#17558C23116yescomplemented
150#17448C23116yes—
151#17448C23116yescomplemented
152C2×#1490C23116yescomplemented
153#17366C2318yescomplemented
154#17363C2314yescomplemented
155#17363C2314yescomplemented
156#17357C2318yescomplemented
157#10022C231128yescomplemented
158#10018C231128yescomplemented
159#9494C23164yescomplemented
160#9492C23164yescomplemented
161#9428C23164yescomplemented
162#9425C23164yescomplemented
163#8522C23132yescomplemented
164#8522C23132yescomplemented
165#7976C23116yescomplemented
166#7975C23116yescomplemented
167#7972C23116yescomplemented
168C22×H(5,𝔽2)C2×D414yes—
169C22×H(5,𝔽2)C2×D414yes—
170C22×H(5,𝔽2)C2×D418yes—
171C23×#41C2×D411yescharacteristic
172C23×#41C2×D414yes—
173C23×#41C2×D412yes—
174C24×D4C2×D412yes—
175C24×D4C2×D412yes—
176C24×D4C2×D414yes—
177C2×D42C24116yes—
178#3458C2414yescomplemented
179#3455C2418yescomplemented
180#3449C2414yescomplemented
181C2×#535C2×D418yes—
182C2×#535C2×D418yes—
183C2×#535C2×D414yes—
184C2×#535C2×D414yes—
185C2×#535C2×D418yes—
186C2×#535C2418yes—
187C2×#535C2418yes—
188#3444C2×D418yescomplemented
189#3444C2414yes—
190#3444C2414yes—
191C2×#533C2×D414yescomplemented
192C2×#533C2412yes—
193C2×#532C2×D412yes—
194C2×#532C2×D412yes—
195C2×#532C2×D414yes—
196C2×#532C2×D414yes—
197C2×#532C2×D414yes—
198C2×#532C2×D414yes—
199C2×#532C2×D414yescomplemented
200C2×#532C2412yes—
201C2×#532C2412yes—
202C2×#532C2412yes—
203C22×C4⋊Q8C2×D411yescharacteristic
204C22×#127C2×D412yes—
205C22×#127C2×D412yes—
206C22×#127C2×D412yes—
207C22×#127C2×D418yes—
208C22×#127C2×D418yes—
209C22×#127C2×D414yes—
210C22×#127C2×D414yes—
211C22×#127C2×D414yes—
212C22×#127C2×D414yes—
213C22×#127C2×D411yescharacteristic
214C22×#127C2×D414yes—
215C22×#127C2412yes—
216C22×#127C2412yes—
217C22×#127C2412yes—
218C22×#124C2×D414yes—
219C22×#124C2412yes—
220C2×C4×#41C2×D414yes—
221C2×C4×#41C2×D412yes—
222C2×C4×#41C2×D412yes—
223C2×C4×#41C2×D411yescharacteristic
224C2×C4×#41C2×D411yescharacteristic
225C2×C4×#41C2×D412yes—
226C2×C4×#41C2411yescharacteristic
227C2×C4×#41C2411yescharacteristic
228C2×C4×#41C2412yes—
229C22×C4×Q8C2×D412yes—
230C22×C4×D4C2×D414yes—
231C22×C4×D4C2×D412yes—
232C22×C4×D4C2×D414yes—
233C22×C4×D4C2×D414yes—
234C22×C4×D4C2×D414yes—
235C22×C4×D4C2414yes—
236C22×C4×D4C2414yes—
237C22×C4×D4C2414yes—
238C22×#117C2×D411yescharacteristic
239C22×#117C2412yes—
240C23×C4⋊C4C2×D412yes—
241C23×C42C2×D412yes—
242C23×C42C2411yescharacteristic
243#3208C2×D4132yescomplemented
244#3208C2×D4132yescomplemented
245#3205C2×D4132yescomplemented
246#3205C2×D4132yescomplemented
247#3153C24116yescomplemented
248#3151C2×D4116yescomplemented
249#3151C24116yes—
250C2×#493C2×D418yescomplemented
251C2×#492C2×D418yescomplemented
252#3140C24116yescomplemented
253#3138C2×D4116yescomplemented
254#3138C24116yes—
255C2×#486C2×D4116yescomplemented
256#3110C24132yes—
257#3109C24132yes—
258#2921C2418yescomplemented
259#2920C2×D418yescomplemented
260#2920C2414yes—
261#2920C2414yes—
262#2920C2418yes—
263#2920C2418yes—
264C2×#432C2418yes—
265C2×#431C2×D418yescomplemented
266#2873C2418yescomplemented
267C2×C4×M16C2414yes—
268#2631C24132yes—
269#2598C2×D4116yes—
270#2598C2×D4116yes—
271#2598C24116yes—
272#2598C24116yes—
273#2487C2×D418yes—
274#2487C2×D418yes—
275#2487C2×D418yes—
276#2487C2×D418yes—
277#2408C2×D418yes—
278#2408C2×D418yes—
279#2408C2×D418yes—
280#2408C2×D418yes—
281#2398C2×D418yes—
282#2398C2×D418yes—
283#2398C2×D4116yes—
284#2397C2×D418yes—
285#2397C2×D418yes—
286#2397C2×D4116yes—
287C2×#400C2×D418yes—
288C2×#399C2×D418yes—
289C2×#394C2×D418yes—
290C2×#392C2×D418yes—
291#2380C24116yes—
292#2283C2×D414yes—
293#2283C2×D414yes—
294#2283C2414yes—
295#2283C2414yes—
296C2×#383C2414yes—
297C2×#380C2×D414yes—
298C2×#376C2×D414yes—
299#1555C24132yes—
300#1533C24132yescomplemented
301#1515C24132yescomplemented
302#1514C24132yescomplemented
303#1490C24164yes—
304#1464C24116yescomplemented
305#1464C24116yescomplemented
306#1288C24164yescomplemented
307C22×#41#12012yes—
308C22×#41#12011yescharacteristic
309C22×#41#12011yescharacteristic
310C22×#41C22×D411yescharacteristic
311C22×#41C22×D411yescharacteristic
312C22×#41C22×D412yes—
313C22×#41C22×D418yes—
314C22×#41C22×D418yes—
315C22×#41C22×D414yes—
316C22×#41C22×D414yes—
317C23×Q8#12011yescharacteristic
318C23×Q8C22×D412yes—
319C23×D4#120116yes—
320C23×D4#12011yescharacteristic
321C23×D4#12012yes—
322C23×D4C22×D414yes—
323C23×D4C22×D414yes—
324C23×D4C22×D414yes—
325C23×D4C22×D412yes—
326C23×D4C22×D418yes—
327C23×D4C22×D418yes—
328C23×D4C22×D414yes—
329C23×D4C22×D414yes—
330C23×D4C22×D414yes—
331C24×C4#12014yes—
332C24×C4C22×D411yescharacteristic
333C24×C4C22×D412yes—
334C24×C4C22×D412yes—
335#533C22×D418yes—
336#533C22×D414yescomplemented
337#533C22×D418yescomplemented
338#533C2514yes—
339#532C22×D418yes—
340#532C22×D414yescomplemented
341#532C22×D418yescomplemented
342#532C2514yes—
343C2×C4⋊Q8C22×D412yes—
344C2×C4⋊Q8C22×D412yes—
345C2×C4⋊Q8C22×D414yescomplemented
346C2×C4⋊Q8C22×D412yescomplemented
347C2×#127#12018yes—
348C2×#127#120116yes—
349C2×#127#12018yes—
350C2×#127#12018yes—
351C2×#127#12018yes—
352C2×#127C22×D414yes—
353C2×#127C22×D414yes—
354C2×#127C22×D414yes—
355C2×#127C22×D418yes—
356C2×#127C22×D418yes—
357C2×#127C22×D4116yes—
358C2×#127C22×D4116yes—
359C2×#127C22×D412yes—
360C2×#127C22×D412yes—
361C2×#127C22×D418yes—
362C2×#127C22×D418yes—
363C2×#127C22×D412yescomplemented
364C2×#127C2514yes—
365C2×#124C22×D418yes—
366C2×#124C22×D418yes—
367C2×#124C22×D414yes—
368C2×#124C2514yes—
369C2×C4×Q8#12012yes—
370C2×C4×Q8#12014yes—
371C2×C4×Q8#12012yes—
372C2×C4×Q8C22×D412yes—
373C2×C4×Q8C22×D412yes—
374C2×C4×Q8C22×D414yes—
375C2×C4×D4#12012yes—
376C2×C4×D4#12014yes—
377C2×C4×D4#12012yes—
378C2×C4×D4#12014yes—
379C2×C4×D4#12014yes—
380C2×C4×D4#12014yes—
381C2×C4×D4#12014yes—
382C2×C4×D4C22×D414yes—
383C2×C4×D4C22×D414yes—
384C2×C4×D4C22×D414yes—
385C2×C4×D4C22×D414yes—
386C2×C4×D4C22×D412yes—
387C2×C4×D4C22×D412yes—
388C2×C4×D4C22×D414yes—
389C2×C4×D4C22×D418yes—
390C2×C4×D4C22×D418yes—
391C2×C4×D4C22×D418yes—
392C2×C4×D4C2518yes—
393C2×#117#12012yes—
394C2×#117#12012yes—
395C2×#117C22×D414yes—
396C2×#117C22×D414yes—
397C2×#117C22×D411yescharacteristic
398C2×#117C22×D411yescharacteristic
399C2×#117C22×D412yes—
400C2×#117C22×D412yes—
401C2×#117C22×D412yes—
402C2×#117C2512yes—
403C2×#117C2512yes—
404C22×C4⋊C4#12012yes—
405C22×C4⋊C4C22×D414yes—
406C22×C4⋊C4C22×D414yes—
407C22×C4⋊C4C22×D414yes—
408C22×C4⋊C4C22×D414yes—
409C22×C22⋊C4#12012yes—
410C22×C22⋊C4C22×D414yes—
411C22×C42#12014yes—
412C22×C42#12014yes—
413C22×C42#12014yes—
414C22×C42C22×D411yescharacteristic
415C22×C42C22×D411yescharacteristic
416C22×C42C22×D411yescharacteristic
417C22×C42C22×D414yes—
418C22×C42C22×D414yes—
419C22×C42C22×D412yes—
420C22×C42C22×D412yes—
421C22×C42C22×D412yes—
422C22×C42C22×D412yes—
423C22×C42C22×D412yes—
424C22×C42C22×D412yes—
425C22×C42C22×D412yes—
426C22×C42C22×D412yes—
427C22×C42H(5,𝔽2)14yes—
428C22×C42H(5,𝔽2)14yes—
429C22×C42C2511yescharacteristic
430C22×C42C2511yescharacteristic
431C22×C42C2511yescharacteristic
432#493C22×D4132yescomplemented
433#492C22×D4132yescomplemented
434#486C22×D4164yescomplemented
435#432C25116yes—
436#431C22×D4116yes—
437#431C22×D4116yescomplemented
438C4×M16C22×D418yescomplemented
439C4×M16C2518yes—
440C2×C4×C8C22×D418yescomplemented
441#400C22×D4116yes—
442#400C22×D4116yes—
443#399C22×D4116yes—
444#399C22×D4116yes—
445#394C22×D4116yes—
446#394C22×D4116yes—
447#392C22×D4116yes—
448#392C22×D4116yes—
449#383C22×D418yes—
450#383C2518yes—
451#380C22×D418yes—
452#380C22×D418yes—
453#376C22×D418yes—
454#376C22×D418yes—
455C2×#95C22×D418yes—
456C25C2×#12011yescharacteristic
457C25C2×#12012yes—
458C22×Q8C2×#12011yescharacteristic
459C22×Q8C2×#12012yes—
460C22×Q8C2×#12011yescharacteristic
461C22×Q8C23×D414yes—
462C22×D4C2×#120116yes—
463C22×D4C2×#120116yes—
464C22×D4C2×#120116yes—
465C22×D4C2×#12012yes—
466C22×D4C2×#12011yescharacteristic
467C22×D4C2×#12012yes—
468C22×D4C2×#12011yescharacteristic
469C22×D4C2×#12012yes—
470C22×D4C2×#12012yes—
471C22×D4C2×#12012yes—
472C22×D4C23×D418yes—
473C22×D4C23×D414yes—
474C22×D4C23×D418yes—
475C23×C4C2×#12011yescharacteristic
476C23×C4C2×#12011yescharacteristic
477C23×C4C2×#12011yescharacteristic
478C23×C4C2×#12012yes—
479C23×C4C2×#12012yes—
480C23×C4C2×#12012yes—
481C23×C4C2×#12014yes—
482C23×C4C2×#12014yes—
483C23×C4C2×#12012yes—
484C23×C4C2×#12012yes—
485C23×C4C2×#12012yes—
486C23×C4C2×#12014yes—
487C23×C4C2×#12014yes—
488C23×C4C2×#12014yes—
489C23×C4C2×#12014yes—
490C23×C4#53414yes—
491C23×C4D4214yes—
492C23×C4D4214yes—
493C23×C4D4214yes—
494C23×C4D4214yes—
495C23×C4C23×D411yescharacteristic
496C23×C4C23×D411yescharacteristic
497C23×C4C23×D411yescharacteristic
498C23×C4C23×D412yes—
499C23×C4C23×D412yes—
500C23×C4C23×D412yes—
501C23×C4C23×D412yes—
502C23×C4C23×D412yes—
503C4⋊Q8C23×D418yes—
504C4⋊Q8C23×D414yes—
505#127C2×#12018yes—
506#127C2×#12018yes—
507#127C2×#120116yes—
508#127C2×#120116yes—
509#127C23×D414yes—
510#127C23×D4116yes—
511C2×C4⋊C4C2×#12012yes—
512C2×C4⋊C4C2×#12012yes—
513C2×C4⋊C4C2×#12014yes—
514C2×C4⋊C4C2×#12014yes—
515C2×C4⋊C4C2×#12014yes—
516C2×C4⋊C4C23×D418yes—
517C2×C4⋊C4C23×D414yes—
518C2×C4⋊C4C23×D414yes—
519C2×C22⋊C4C2×#12014yes—
520C2×C22⋊C4C2×#12012yes—
521C2×C22⋊C4C2×#12012yes—
522C2×C22⋊C4C2×#12014yes—
523C2×C22⋊C4C2×#12014yes—
524C2×C22⋊C4C23×D414yes—
525C2×C22⋊C4C23×D414yes—
526C2×C42C2×#12012yes—
527C2×C42C2×#12012yes—
528C2×C42C2×#12012yes—
529C2×C42C2×#12012yes—
530C2×C42C2×#12012yes—
531C2×C42C2×#12012yes—
532C2×C42C2×#12014yes—
533C2×C42C2×#12012yes—
534C2×C42C2×#12014yes—
535C2×C42C2×#12014yes—
536C2×C42C2×#12014yes—
537C2×C42C2×#12014yes—
538C2×C42C2×#12014yes—
539C2×C42#53412yes—
540C2×C42#53412yes—
541C2×C42#53412yes—
542C2×C42#53414yes—
543C2×C42#53412yes—
544C2×C42D4214yes—
545C2×C42D4214yes—
546C2×C42D4214yes—
547C2×C42D4214yes—
548C2×C42D4214yes—
549C2×C42D4214yes—
550C2×C42D4214yes—
551C2×C42D4214yes—
552C2×C42D4214yes—
553C2×C42D4214yes—
554C2×C42D4214yes—
555C2×C42D4214yes—
556C2×C42C23×D412yes—
557C2×C42C23×D414yes—
558C2×C42C23×D412yes—
559C2×C42C23×D414yes—
560C2×C42C23×D411yescharacteristic
561C2×C42C23×D411yescharacteristic
562C2×C42C23×D411yescharacteristic
563C2×C42C23×D412yes—
564C2×C42C23×D412yes—
565C2×C42C23×D412yes—
566C2×C42C23×D412yes—
567C2×C42C23×D412yes—
568C2×C42C2×H(5,𝔽2)14yes—
569C2×C42C2×H(5,𝔽2)14yes—
570C2×C42C2×H(5,𝔽2)12yes—
571C2×C42C2×H(5,𝔽2)12yes—
572C2×C42C2611yescharacteristic
573C4×C8C23×D4116yes—
574#95C23×D4116yes—
575C24#240314yes—
576C24C22×#12011yescharacteristic
577C24C22×#12011yescharacteristic
578C24C22×#12011yescharacteristic
579C24C22×#12012yes—
580C24C22×#12012yes—
581C2×D4#301918yes—
582C2×D4C22×#120116yes—
583C22×C4#240312yes—
584C22×C4#240314yes—
585C22×C4#240314yes—
586C22×C4#240312yes—
587C22×C4#240312yes—
588C22×C4#240314yes—
589C22×C4#240314yes—
590C22×C4#240312yes—
591C22×C4#240314yes—
592C22×C4#240314yes—
593C22×C4#240314yes—
594C22×C4C22×#12012yes—
595C22×C4C22×#12012yes—
596C22×C4C22×#12011yescharacteristic
597C22×C4C22×#12012yes—
598C22×C4C22×#12011yescharacteristic
599C22×C4C22×#12011yescharacteristic
600C22×C4C22×#12012yes—
601C22×C4C22×#12012yes—
602C22×C4C22×#12012yes—
603C22×C4C22×#12012yes—
604C22×C4C22×#12012yes—
605C22×C4C22×#12014yes—
606C22×C4C22×#12014yes—
607C22×C4C2×#53412yes—
608C22×C4C2×#53412yes—
609C22×C4C2×#53412yes—
610C22×C4C2×D4214yes—
611C22×C4C2×D4214yes—
612C22×C4C2×D4214yes—
613C22×C4C2×D4214yes—
614C22×C4C2×D4214yes—
615C22×C4C2×D4214yes—
616C22×C4C24×D411yescharacteristic
617C22×C4C24×D412yes—
618C42#240312yes—
619C42#240314yes—
620C42#240314yes—
621C42#240312yes—
622C42#240312yes—
623C42#240314yes—
624C42#240314yes—
625C42#240312yes—
626C42C22×#12011yescharacteristic
627C42C22×#12012yes—
628C42C22×#12012yes—
629C42C22×#12011yescharacteristic
630C42C2×#53411yescharacteristic
631C42C2×#53412yes—
632C42C2×#53412yes—
633C42C2×#53411yescharacteristic
634C42C2×D4214yes—
635C42C2×D4214yes—
636C42C2×D4214yes—
637C42C2×D4214yes—
638C42C2×D4214yes—
639C42C2×D4214yes—
640C42C24×D412yes—
641C42C22×H(5,𝔽2)12yes—
642C23C2×#240312yes—
643C23C2×#240312yes—
644C23C2×#240312yes—
645C23C2×#301914yes—
646C23C2×#301914yes—
647C23C23×#12011yescharacteristic
648C2×C4#2388218yes—
649C2×C4C2×#240312yes—
650C2×C4C2×#240312yes—
651C2×C4C2×#240312yes—
652C2×C4C2×#240312yes—
653C2×C4C2×#240314yes—
654C2×C4C2×#240312yes—
655C2×C4C2×#240312yes—
656C2×C4C2×#240312yes—
657C2×C4C2×#301914yes—
658C2×C4C23×#12011yescharacteristic
659C2×C4C22×#53411yescharacteristic
660C2×C4C22×D4214yes—
661C22#643744514yes—
662C22C2×#2388214yes—
663C22C22×#240311yescharacteristic
664C22C22×#301912yes—
665C4C2×#2388214yes—
666C4C2×#2388214yes—
667C2C22×#2388212yes—
668C2C2×#643744511yescharacteristic
subgroupG/H
center, socleC22C22×#2403
commutator, Frattini, cosocleC2×C42C26
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C23×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72338578C2semidirect
2. #72338577C2semidirect
3. #72338575C2semidirect
4. #72338207C2semidirect
5. #72317711C2semidirect
6. #72306375C2semidirect
7. #72306361C2semidirect
8. #72305972C2semidirect
9. #72302157C2semidirect
10. #72302148C2semidirect
11. C2×#6348967C2semidirect
12. C2×#7737411C2semidirect
13. #72213685C2semidirect
14. #10585995C22semidirect
16. C23×D42C22semidirect
17. #10575560C22semidirect
18. #10575552C22semidirect
19. #10575547C22semidirect
20. #10575509C22semidirect
22. #10575254C22semidirect
23. #10575219C22semidirect
24. C2×#60558C22semidirect
25. #10574126C22semidirect
27. #7737411C22semidirect
28. #7737411C22semidirect
29. C2×#52004C22semidirect
30. C2×#35237C22semidirect
32. C2×#34364C22semidirect
33. #6348967C22semidirect
34. #6348967C22semidirect
35. C2×#18529C22semidirect
36. C2×#18524C22semidirect
37. #6346641C22semidirect
38. #6346639C22semidirect
39. #6346637C22semidirect
40. #6346626C22semidirect
41. #6346414C22semidirect
42. C2×#17741C22semidirect
43. #6343804C22semidirect
44. #6343372C22semidirect
45. C2×#17448C22semidirect
46. #6342561C22semidirect
47. #246957C22semidirect
48. #246930C22semidirect
49. #246927C22semidirect
50. #235463C22semidirect
51. #235462C22semidirect
52. #235456C22semidirect
53. #235444C22semidirect
54. #201616C22semidirect
55. #201614C22semidirect
56. #201611C22semidirect
57. #201605C22semidirect
58. #200885C22semidirect
59. #200876C22semidirect
60. #200851C22semidirect
61. #200848C22semidirect
62. #187836C22semidirect
63. #187824C22semidirect
64. #187824C22semidirect
65. #187811C22semidirect
66. #181215C22semidirect
68. #62815C23semidirect
69. #62814C23semidirect
70. #62813C23semidirect
71. #62812C23semidirect
81. #62686C23semidirect
91. #60806C23semidirect
92. #60802C23semidirect
93. #60799C23semidirect
94. #60798D4semidirect
97. C2×#3208D4semidirect
98. C2×#3205D4semidirect
99. #60644C23semidirect
100. #60639C23semidirect
102. #60619C23semidirect
103. #60618C23semidirect
106. #60558C23semidirect
107. C2×#3110C23semidirect
108. C2×#3109C23semidirect
109. #60125C23semidirect
110. #60124C23semidirect
111. #60123C23semidirect
114. C4×#568C23semidirect
135. #18529C23semidirect
136. #18524C23semidirect
137. #18156C23semidirect
138. #18154C23semidirect
139. #18152C23semidirect
143. #17675C23semidirect
144. #17666C23semidirect
145. #17663C23semidirect
146. #17596C23semidirect
147. #17595C23semidirect
148. #17593C23semidirect
149. #17558C23semidirect
151. #17448C23semidirect
152. C2×#1490C23semidirect
153. #17366C23semidirect
154. #17363C23semidirect
155. #17363C23semidirect
156. #17357C23semidirect
157. #10022C23semidirect
158. #10018C23semidirect
159. #9494C23semidirect
160. #9492C23semidirect
161. #9428C23semidirect
162. #9425C23semidirect
163. #8522C23semidirect
164. #8522C23semidirect
165. #7976C23semidirect
166. #7975C23semidirect
167. #7972C23semidirect
178. #3458C24semidirect
179. #3455C24semidirect
180. #3449C24semidirect
188. #3444C2×D4semidirect
191. C2×#533C2×D4semidirect
199. C2×#532C2×D4semidirect
243. #3208C2×D4semidirect
244. #3208C2×D4semidirect
245. #3205C2×D4semidirect
246. #3205C2×D4semidirect
247. #3153C24semidirect
248. #3151C2×D4semidirect
250. C2×#493C2×D4semidirect
251. C2×#492C2×D4semidirect
252. #3140C24semidirect
253. #3138C2×D4semidirect
255. C2×#486C2×D4semidirect
258. #2921C24semidirect
259. #2920C2×D4semidirect
265. C2×#431C2×D4semidirect
266. #2873C24semidirect
300. #1533C24semidirect
301. #1515C24semidirect
302. #1514C24semidirect
304. #1464C24semidirect
305. #1464C24semidirect
306. #1288C24semidirect
336. #533C22×D4semidirect
337. #533C22×D4semidirect
340. #532C22×D4semidirect
341. #532C22×D4semidirect
345. C2×C4⋊Q8C22×D4semidirect
346. C2×C4⋊Q8C22×D4semidirect
363. C2×#127C22×D4semidirect
432. #493C22×D4semidirect
433. #492C22×D4semidirect
434. #486C22×D4semidirect
437. #431C22×D4semidirect
438. C4×M16C22×D4semidirect
440. C2×C4×C8C22×D4semidirect

Maximal subgroups

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

subgroupindex
#723385782
#723385772
#723385752
#723382072
#723177112
#723063752
#723063612
#723059722
#723021572
#723021482
C2×#63489672
C2×#77374112
#722136852