Finite Group Databasebeta

← #72334316

Subgroups — #72334316

Order 2048.

At least 6399 conjugacy classes of subgroups; only the 10296 normal subgroups are shown.

The subgroup lattice has 810 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72334311C211yesmaximal, characteristic, complemented
2#72334303C216yesmaximal, complemented
3#72332588C216yesmaximal, complemented
4#72332558C216yesmaximal, complemented
5#72317648C211yesmaximal, characteristic, complemented
6#72298513C216yesmaximal, complemented
7#72298443C216yesmaximal, complemented
8#72298421C216yesmaximal, complemented
9C25×#121C211yesmaximal, characteristic, complemented
10#72287875C211yesmaximal, characteristic, complemented
11#72286446C211yesmaximal, characteristic, complemented
12#72286433C211yesmaximal, characteristic, complemented
13#72286409C211yesmaximal, characteristic, complemented
14#72286393C211yesmaximal, characteristic, complemented
15#72279059C216yesmaximal, complemented
16C2×#612433C211yesmaximal, characteristic, complemented
17C22×#14694C211yesmaximal, characteristic, complemented
18#72250308C211yesmaximal, characteristic, complemented
19#72240113C211yesmaximal, characteristic, complemented
20C2×#647714C216yesmaximal, complemented
21C2×#612424C211yesmaximal, characteristic, complemented
22C2×#612424C211yesmaximal, characteristic, complemented
23C22×D4×#120C211yesmaximal, characteristic, complemented
24C26×D4C2211yescharacteristic
25C26×D4C2211yescharacteristic, complemented
26C26×D4C2211yescharacteristic, complemented
27C27×C4C2211yescharacteristic, complemented
28C23×D42C2213yescomplemented
29C24×#121C2216yes—
30C24×#121C2216yescomplemented
31C24×#121C2216yescomplemented
32C24×#121C2216yescomplemented
33C24×#120C2211yescharacteristic
34C24×#120C2211yescharacteristic
35C25×C4⋊C4C2211yescharacteristic, complemented
36C25×C22⋊C4C2211yescharacteristic, complemented
37C25×C22⋊C4C2211yescharacteristic, complemented
38C22×#2847C2211yescharacteristic
39C22×#2846C2211yescharacteristic
40C22×#2846C2211yescharacteristic
41C22×#2846C2211yescharacteristic
42C22×#2846C2211yescharacteristic, complemented
43C22×#2846C2211yescharacteristic, complemented
44C22×#2433C2213yescomplemented
45C22×#2408C2213yescomplemented
46C22×#2410C2213yescomplemented
47C22×#2410C2213yescomplemented
48C22×#2410C2214yescomplemented
49C22×#2410C2216yescomplemented
50C22×#2403C2213yescomplemented
51C22×#2403C2213yescomplemented
52C22×#2403C2216yescomplemented
53C22×#2403C2216yescomplemented
54C22×D4×C22⋊C4C2213yescomplemented
55C22×C4×#120C2211yescharacteristic
56C23×#386C2216yescomplemented
57C23×#379C2211yescharacteristic, complemented
58C2×#15310C22112yescomplemented
59C2×#15278C22112yescomplemented
60C2×#15263C22112yescomplemented
61C2×#15257C22112yescomplemented
62C2×#14757C22112yescomplemented
63C2×#14724C2216yescomplemented
64C2×#14719C2216yescomplemented
65C2×#14718C2216yescomplemented
66C2×#14716C2216yescomplemented
67C2×#14716C22112yescomplemented
68C2×#14715C2216yescomplemented
69C2×#14715C2216yescomplemented
70C2×#14715C2216yescomplemented
71C2×#14715C2216yescomplemented
72C2×#14715C2216yescomplemented
73C2×#14715C2216yescomplemented
74C2×#14715C2216yescomplemented
75C2×#14694C2211yescharacteristic
76C2×#14694C2211yescharacteristic
77C2×#14694C2211yescharacteristic
78C2×#14694C2211yescharacteristic, complemented
79C2×#14694C2211yescharacteristic, complemented
80C2×#14694C2211yescharacteristic, complemented
81C2×#14694C2211yescharacteristic, complemented
82C2×#14694C2211yescharacteristic, complemented
83C2×#14694C2216yescomplemented
84C2×#14694C2216yescomplemented
85C2×#14694C2216yescomplemented
86C2×#14694C2211yescharacteristic, complemented
87C2×#14694C2216yescomplemented
88C2×#14693C2211yescharacteristic, complemented
89C2×#14679C2211yescharacteristic, complemented
90C2×#14679C2211yescharacteristic, complemented
91C2×#14679C2211yescharacteristic, complemented
92C2×#14679C2211yescharacteristic, complemented
93C2×#14023C22112yescomplemented
94C2×#14015C2216yescomplemented
95C2×#13967C2216yescomplemented
96C2×#13867C2216yescomplemented
97C2×#13867C2216yescomplemented
98C2×#13867C2216yescomplemented
99C2×#13867C2216yescomplemented
100C2×#13867C2216yescomplemented
101C2×#13867C2216yescomplemented
102C22×C22⋊#95C2216yescomplemented
103#156824C22124yescomplemented
104#156706C22124yescomplemented
105#156706C22124yescomplemented
106#156706C22124yescomplemented
107#154729C22124yescomplemented
108#154674C22124yescomplemented
109#154255C22124yescomplemented
110#154248C2216yescomplemented
111#154248C2216yescomplemented
112#154248C2216yescomplemented
113#154247C2216yescomplemented
114#154195C2216yescomplemented
115#154195C2216yescomplemented
116#154195C2216yescomplemented
117#154195C2216yescomplemented
118#154195C2216yescomplemented
119#154195C2216yescomplemented
120#154194C2216yescomplemented
121#154194C2216yescomplemented
122#154097C2216yescomplemented
123#154096C2216yescomplemented
124#154095C2216yescomplemented
125#154094C2216yescomplemented
126#154094C2216yescomplemented
127#154094C2216yescomplemented
128#154094C2216yescomplemented
129#154077C2211yescharacteristic, complemented
130#154077C2211yescharacteristic, complemented
131#154077C2211yescharacteristic, complemented
132#154077C2211yescharacteristic, complemented
133#154077C2216yescomplemented
134#154077C2216yescomplemented
135#153851C2216yescomplemented
136#153759C2216yescomplemented
137#153749C2216yescomplemented
138C28C2311yescharacteristic
139C28C2311yescharacteristic
140C28C2311yescharacteristic
141C25×D4D4116yescomplemented
142C25×D4C2313yes—
143C25×D4C2316yes—
144C25×D4C2316yes—
145C25×D4C2316yes—
146C25×D4C2313yes—
147C25×D4C2313yes—
148C25×D4C2313yes—
149C25×D4C2316yes—
150C25×D4C2313yes—
151C25×D4C2313yes—
152C25×D4C2311yescharacteristic, complemented
153C26×C4C2311yescharacteristic
154C26×C4C2311yescharacteristic
155C26×C4C2311yescharacteristic
156C26×C4C2316yes—
157C26×C4C2311yescharacteristic
158C26×C4C2316yes—
159C23×#127C2313yescomplemented
160C23×#121D4196yescomplemented
161C23×#121C23124yes—
162C23×#121C23112yes—
163C23×#121C23112yes—
164C23×#121C23112yes—
165C23×#121C2313yes—
166C23×#121C2314yes—
167C23×#121C2313yescomplemented
168C23×#121C2313yescomplemented
169C23×#121C2313yescomplemented
170C23×#121C2314yescomplemented
171C23×#120D4116yescomplemented
172C23×#120C2311yescharacteristic
173C23×#120C2311yescharacteristic
174C23×#120C2313yes—
175C23×#120C2313yes—
176C23×#120C2313yes—
177C23×#120C2313yes—
178C23×#120C2316yes—
179C23×#120C2313yes—
180C23×#120C2313yes—
181C23×#120C2311yescharacteristic
182C23×#120C2316yes—
183C23×#120C2313yes—
184C23×#120C2316yes—
185C23×#120C2313yes—
186C23×#120C2313yescomplemented
187C23×#120C2313yescomplemented
188C23×#120C2314yescomplemented
189C23×#120C2314yescomplemented
190C23×C4×D4C2313yes—
191C23×C4×D4C2313yescomplemented
192C24×C4⋊C4C2316yes—
193C24×C4⋊C4C2316yes—
194C24×C22⋊C4C2316yes—
195C24×C22⋊C4C2316yes—
196C24×C22⋊C4C2316yes—
197C24×C22⋊C4C2316yes—
198C24×C22⋊C4C2313yes—
199C24×C22⋊C4C2316yes—
200C24×C22⋊C4C2313yes—
201C24×C22⋊C4C2314yescomplemented
202C2×#2846D4116yescomplemented
203C22×#394C2316yescomplemented
204C22×#394C2314yescomplemented
205C22×#394C2314yescomplemented
206C22×#394C23112yescomplemented
207C22×#392C2316yescomplemented
208C22×#392C2316yescomplemented
209C22×#392C2316yescomplemented
210C22×#392C2314yescomplemented
211C22×#392C2314yescomplemented
212C22×#392C23112yescomplemented
213C22×#392C23112yescomplemented
214C22×#392C23112yescomplemented
215C22×#392C23112yescomplemented
216C22×#392C23112yescomplemented
217C22×#392C23112yescomplemented
218C22×#390C2316yescomplemented
219C22×#386C2316yes—
220C22×#386C2313yes—
221C22×#386C2313yes—
222C22×#386C2313yes—
223C22×#386C2316yes—
224C22×#386C2316yes—
225C22×#386C2316yes—
226C22×#386C2316yes—
227C22×#386C2316yes—
228C22×#386C2316yes—
229C22×#386C2316yes—
230C22×#386C2316yes—
231C22×#386C2314yescomplemented
232C22×#386C2314yescomplemented
233C22×#386C2316yescomplemented
234C22×#386C2316yescomplemented
235C22×#386C2314yescomplemented
236C22×#386C23112yescomplemented
237C22×#386C23112yescomplemented
238C22×#386C23112yescomplemented
239C22×#386C23112yescomplemented
240C22×#386C23112yescomplemented
241C22×#386C23112yescomplemented
242C22×#386C23112yescomplemented
243C22×#385C2313yes—
244C22×#385C2316yes—
245C22×#385C2314yescomplemented
246C22×#380C2313yes—
247C22×#379C2311yescharacteristic
248C22×#379C2316yes—
249C22×#379C2313yes—
250C22×#379C2313yes—
251C22×#379C2311yescharacteristic
252C22×#379C2311yescharacteristic
253C22×#379C2316yes—
254C22×#379C2316yes—
255C22×#379C2316yes—
256C22×#379C2316yes—
257C22×#379C2316yes—
258C22×#379C2311yescharacteristic
259C22×#379C2311yescharacteristic
260C22×#379C2313yes—
261C22×#379C2313yes—
262C22×#379C2316yes—
263C22×#379C2316yes—
264C22×#379C2316yes—
265C22×#379C2316yes—
266C22×#379C2316yes—
267C22×#379C2316yes—
268C22×#379C2314yescomplemented
269C22×C4×C22⋊C4C2313yes—
270C23×#95C23112yescomplemented
271#14694D4116yescomplemented
272C2×#1444C23112yescomplemented
273C2×#1441C23112yescomplemented
274C2×#1440C23112yescomplemented
275C2×#1439C23112yescomplemented
276C2×#1439C23112yescomplemented
277C2×#1439C23112yescomplemented
278C2×#1439C23112yescomplemented
279C2×#1439C23112yescomplemented
280C2×#1439C23112yescomplemented
281C2×#1438C23112yescomplemented
282C2×#1438C23112yescomplemented
283C2×#1438C23112yescomplemented
284C2×#1438C23112yescomplemented
285C2×#1438C23112yescomplemented
286C2×#1438C23112yescomplemented
287C2×#1438C23112yescomplemented
288C2×#1438C23112yescomplemented
289C2×#1438C23124yescomplemented
290C2×#1438C23112yescomplemented
291C2×#1438C23112yescomplemented
292C2×#1438C23124yescomplemented
293C2×#1438C23124yescomplemented
294C2×#1438C23124yescomplemented
295C2×#1438C23124yescomplemented
296C2×#1437C23112yescomplemented
297C2×#1436C23112yescomplemented
298C2×C22⋊#95C2316yes—
299C2×C22⋊#95C2316yes—
300C2×C22⋊#95C2316yes—
301C2×C22⋊#95C2316yes—
302C2×C22⋊#95C2316yes—
303C2×C22⋊#95C2316yes—
304C2×C22⋊#95C2316yes—
305C2×C22⋊#95C2316yes—
306C2×C22⋊#95C2316yes—
307C2×C22⋊#95C2316yes—
308C2×C22⋊#95C2316yes—
309C2×C22⋊#95C2316yes—
310C2×C22⋊#95C2316yes—
311C2×C22⋊#95C2316yes—
312C2×C22⋊#95C2316yes—
313C2×C22⋊#95C2316yes—
314C2×C22⋊#95C2316yes—
315C2×C22⋊#95C2316yes—
316C2×C22⋊#95C23112yescomplemented
317C2×C22⋊#95C23112yescomplemented
318C2×C22⋊#95C23112yescomplemented
319C2×C22⋊#95C23124yescomplemented
320C2×C22⋊#95C23124yescomplemented
321#7557C23124yescomplemented
322#7557C23124yescomplemented
323#7555C23124yescomplemented
324#7555C23124yescomplemented
325#7555C23124yescomplemented
326#7555C23124yescomplemented
327C27C2×D418yes—
328C27C2×D418yes—
329C27C2×D418yes—
330C27C2×D418yes—
331C27C2411yescharacteristic
332C27C2413yes—
333C27C2413yes—
334C27C2416yes—
335C27C2411yescharacteristic
336C27C2413yes—
337C27C2413yes—
338C27C2411yescharacteristic
339C24×D4C2×D4124yes—
340C24×D4C2×D4124yes—
341C24×D4C2×D4124yes—
342C24×D4C2×D4148yes—
343C24×D4C2×D4124yes—
344C24×D4C2×D4148yescomplemented
345C24×D4C2×D4148yescomplemented
346C24×D4C2×D4124yescomplemented
347C24×D4C2413yes—
348C24×D4C2413yes—
349C24×D4C2411yescharacteristic
350C24×D4C2413yes—
351C24×D4C2414yes—
352C24×D4C2413yes—
353C24×D4C24112yes—
354C24×D4C2416yes—
355C24×D4C24112yes—
356C24×D4C2411yescharacteristic
357C24×D4C2411yescharacteristic
358C24×D4C2413yes—
359C24×D4C2413yes—
360C24×D4C2413yes—
361C24×D4C2413yes—
362C24×D4C2414yes—
363C24×D4C2411yescharacteristic
364C24×D4C2413yes—
365C24×D4C2413yes—
366C24×D4C2414yes—
367C24×D4C2413yes—
368C24×D4C2413yes—
369C24×D4C2414yes—
370C24×D4C2414yes—
371C25×C4C2×D418yes—
372C25×C4C2×D418yescomplemented
373C25×C4C2×D4148yescomplemented
374C25×C4C2416yes—
375C25×C4C2416yes—
376C25×C4C24112yes—
377C25×C4C2416yes—
378C25×C4C2413yes—
379C25×C4C2411yescharacteristic
380C25×C4C2414yes—
381C25×C4C2413yes—
382C25×C4C2414yes—
383C25×C4C2413yes—
384C25×C4C2413yes—
385C22×#121C2×D4196yes—
386C22×#121C2×D4196yescomplemented
387C22×#121C2×D4196yescomplemented
388C22×#121C2×D4196yescomplemented
389C22×#120C2×D418yes—
390C22×#120C2×D418yes—
391C22×#120C2×D418yes—
392C22×#120C2×D418yes—
393C22×#120C2×D4124yescomplemented
394C22×#120C2×D4124yescomplemented
395C22×#120C2×D4124yescomplemented
396C22×#120C2×D4124yescomplemented
397C22×#120#4118yes—
398C23×C4⋊C4C2×D4148yescomplemented
399C23×C4⋊C4C24112yes—
400C23×C4⋊C4C2413yes—
401C23×C4⋊C4C2413yes—
402C23×C4⋊C4C2414yes—
403C23×C4⋊C4C2414yes—
404C23×C22⋊C4C2×D4148yescomplemented
405C23×C22⋊C4C2×D4148yescomplemented
406C23×C22⋊C4C2×D4124yescomplemented
407C23×C22⋊C4C2414yes—
408C23×C22⋊C4C2414yes—
409C23×C22⋊C4C2416yes—
410C23×C22⋊C4C2416yes—
411C23×C22⋊C4C2416yes—
412C23×C22⋊C4C2414yes—
413C23×C22⋊C4C24112yes—
414C23×C22⋊C4C24112yes—
415C23×C22⋊C4C2413yes—
416C23×C22⋊C4C2413yes—
417C23×C22⋊C4C2416yes—
418C23×C22⋊C4C2413yes—
419C23×C22⋊C4C2413yes—
420C23×C22⋊C4C2414yes—
421C23×C22⋊C4C2413yes—
422C23×C22⋊C4C2413yes—
423C23×C22⋊C4C2413yes—
424C23×C22⋊C4C2413yes—
425C23×C22⋊C4C2413yes—
426C23×C22⋊C4C2413yes—
427C23×C22⋊C4C2413yes—
428C23×C22⋊C4C2416yes—
429C23×C22⋊C4C24112yes—
430C23×C22⋊C4C2414yes—
431C23×C22⋊C4C2414yes—
432C23×C22⋊C4C24112yes—
433C23×C22⋊C4C2414yes—
434C23×C22⋊C4C2414yes—
435C23×C22⋊C4C2414yes—
436C23×C22⋊C4C2414yes—
437C23×C22⋊C4C2414yes—
438C23×C22⋊C4C2416yes—
439C23×C22⋊C4C2414yes—
440C23×C22⋊C4C2414yes—
441C23×C22⋊C4C2413yes—
442C23×C22⋊C4C2414yes—
443C23×C22⋊C4C24112yes—
444C23×C22⋊C4C2414yes—
445C23×C22⋊C4C24112yes—
446C23×C22⋊C4C2416yes—
447C23×C22⋊C4C24112yes—
448C23×C22⋊C4C24112yes—
449C23×C22⋊C4C24112yes—
450C23×C22⋊C4C2416yes—
451C23×C22⋊C4C24112yes—
452C23×C42C2413yes—
453C2×#386C2×D4148yescomplemented
454C2×#379C2×D418yes—
455C2×#379C2×D418yescomplemented
456C2×#379C2×D4124yescomplemented
457C2×#379C2×D4124yescomplemented
458C22×#95C24112yes—
459C22×#95C2414yes—
460C22×#95C24112yes—
461C22×#95C2414yes—
462C22×#95C2414yes—
463C22×#95C24112yes—
464C22×#95C2414yes—
465C22×#95C2416yes—
466C22×#95C2416yes—
467C22×#95C24112yes—
468C22×#95C24112yes—
469C22×#95C24112yes—
470C22×#95C24112yes—
471C22×#95C24112yes—
472C22×#95C24112yes—
473C22×#95C24112yes—
474C22×#95C24112yes—
475C22×#95C24112yes—
476C22×#95C24112yes—
477C22×#95C24112yes—
478C22⋊#95C2×D4148yescomplemented
479C26#120164yescomplemented
480C26C22×D414yes—
481C26C22×D414yes—
482C26C22×D414yes—
483C26C22×D414yes—
484C26C22×D4112yes—
485C26C22×D4112yes—
486C26C22×D4112yes—
487C26C22×D4112yes—
488C26C22×D4124yes—
489C26C22×D4112yes—
490C26C22×D4124yes—
491C26C22×D4112yes—
492C26C22×D4124yes—
493C26C22×D4112yes—
494C26C22×D4112yes—
495C26C22×D414yescomplemented
496C26C2×#4114yes—
497C26H(5,𝔽2)14yes—
498C26H(5,𝔽2)14yes—
499C26H(5,𝔽2)124yes—
500C26C2511yescharacteristic
501C26C2511yescharacteristic
502C26C2514yes—
503C26C2513yes—
504C26C2511yescharacteristic
505C26C2511yescharacteristic
506C26C2513yes—
507C26C2511yescharacteristic
508C26C2513yes—
509C23×D4#1201192yescomplemented
510C23×D4C22×D4112yes—
511C23×D4C22×D4112yes—
512C23×D4C22×D4124yes—
513C23×D4C22×D4112yes—
514C23×D4C22×D4148yes—
515C23×D4C22×D4112yes—
516C23×D4C22×D4112yes—
517C23×D4C22×D4148yes—
518C23×D4C22×D4148yes—
519C23×D4C22×D4124yes—
520C23×D4C22×D4124yes—
521C23×D4C22×D4124yes—
522C23×D4C22×D4112yes—
523C23×D4C22×D4112yes—
524C23×D4C22×D4148yes—
525C23×D4C22×D4124yes—
526C23×D4C22×D414yes—
527C23×D4C22×D414yescomplemented
528C23×D4C22×D4112yescomplemented
529C23×D4C22×D4112yescomplemented
530C23×D4C22×D4112yescomplemented
531C23×D4C2×#41112yes—
532C24×C4C22×D4124yes—
533C24×C4C22×D4124yes—
534C24×C4C22×D4124yes—
535C24×C4C22×D4148yes—
536C24×C4C22×D4124yes—
537C24×C4C22×D4112yes—
538C24×C4C22×D4124yes—
539C24×C4C22×D4112yes—
540C24×C4C22×D4148yes—
541C24×C4C22×D4112yescomplemented
542C24×C4H(5,𝔽2)124yes—
543C24×C4C2514yes—
544C24×C4C2514yes—
545C24×C4C2514yes—
546C24×C4C2511yescharacteristic
547C24×C4C2513yes—
548C24×C4C2513yes—
549C24×C4C2514yes—
550C24×C4C2513yes—
551C24×C4C2514yes—
552C24×C4C2513yes—
553C24×C4C2514yes—
554C24×C4C2513yes—
555C24×C4C2511yescharacteristic
556C24×C4C2514yes—
557C2×#121#1201256yescomplemented
558C2×#120#121164yescomplemented
559C22×C4⋊C4C22×D4148yes—
560C22×C4⋊C4C22×D4148yes—
561C22×C22⋊C4C22×D4148yes—
562C22×C22⋊C4C22×D4148yes—
563C22×C22⋊C4C22×D4112yes—
564C22×C22⋊C4C22×D4124yes—
565C22×C22⋊C4C22×D4112yes—
566C22×C22⋊C4C22×D4112yes—
567C22×C22⋊C4C22×D4112yes—
568C22×C22⋊C4C22×D4148yes—
569C22×C22⋊C4C22×D4148yes—
570C22×C22⋊C4C22×D4112yes—
571C22×C22⋊C4C22×D4112yes—
572C22×C22⋊C4C22×D4116yescomplemented
573C22×C22⋊C4C22×D4112yescomplemented
574C22×C22⋊C4C22×D4112yescomplemented
575C22×C22⋊C4C22×D4124yescomplemented
576C22×C22⋊C4C22×D4124yescomplemented
577C22×C22⋊C4C2×#41112yes—
578C2×#95C22×D4148yescomplemented
579C25C2×#120116yes—
580C25C2×#120148yes—
581C25C2×#120148yes—
582C25C2×#120148yes—
583C25C2×#120148yes—
584C25C2×#121116yes—
585C25#534116yes—
586C25#534148yes—
587C25D42116yes—
588C25D42116yes—
589C25D42196yes—
590C25D42196yes—
591C25#546116yes—
592C25#546116yes—
593C25C23×D412yes—
594C25C23×D412yes—
595C25C23×D416yes—
596C25C23×D4112yes—
597C25C23×D4124yes—
598C25C23×D412yes—
599C25C23×D412yes—
600C25C23×D4112yes—
601C25C23×D412yes—
602C25C23×D416yes—
603C25C23×D416yes—
604C25C23×D416yes—
605C25C23×D4112yes—
606C25C23×D412yes—
607C25C23×D4112yes—
608C25C23×D416yes—
609C25C23×D416yes—
610C25C23×D412yes—
611C25C23×D412yes—
612C25C23×D416yes—
613C25C23×D4112yes—
614C25C23×D416yes—
615C25C22×#4112yes—
616C25C22×#4116yes—
617C25C2×H(5,𝔽2)112yes—
618C25C2×H(5,𝔽2)112yes—
619C25C2×H(5,𝔽2)112yes—
620C25C2×H(5,𝔽2)16yes—
621C25C2×H(5,𝔽2)16yes—
622C25C2×H(5,𝔽2)112yes—
623C25#585112yes—
624C25C2611yescharacteristic
625C22×D4C2×#120148yes—
626C22×D4C2×#120148yes—
627C22×D4C2×#120148yes—
628C22×D4C2×#120148yes—
629C22×D4C2×#120164yes—
630C22×D4C2×#120164yescomplemented
631C22×D4C2×#120164yescomplemented
632C22×D4C2×#121148yescomplemented
633C23×C4C2×#120148yes—
634C23×C4C2×#120164yescomplemented
635C23×C4D42196yescomplemented
636C23×C4C23×D418yes—
637C23×C4C23×D416yes—
638C23×C4C23×D416yes—
639C23×C4C23×D412yes—
640C23×C4C23×D416yes—
641C23×C4C23×D4124yes—
642C23×C4C23×D416yes—
643C23×C4C23×D4112yes—
644C23×C4C23×D4124yes—
645C23×C4C23×D416yes—
646C23×C4C23×D416yes—
647C23×C4C23×D412yes—
648C23×C4C23×D4112yes—
649C23×C4C23×D4124yes—
650C23×C4C23×D418yes—
651C23×C4C22×#4116yes—
652C23×C4C2×H(5,𝔽2)124yes—
653C2×C4⋊C4C2×#120164yescomplemented
654C2×C22⋊C4C2×#120164yescomplemented
655C2×C22⋊C4C2×#120164yescomplemented
656C2×C22⋊C4C2×#121148yescomplemented
657C24#24031192yescomplemented
658C24#2410164yescomplemented
659C24C22×#120112yes—
660C24C22×#120116yes—
661C24C22×#120112yes—
662C24C22×#120116yes—
663C24C22×#120112yes—
664C24C22×#120112yes—
665C24C22×#120112yes—
666C24C22×#120116yes—
667C24C22×#120112yes—
668C24C22×#12014yes—
669C24C22×#120112yes—
670C24C22×#121112yes—
671C24C22×#12114yescomplemented
672C24C2×#534112yes—
673C24C2×#534112yes—
674C24C2×#534112yes—
675C24C2×#534112yes—
676C24C2×D42124yes—
677C24C2×D42124yes—
678C24C2×D42112yes—
679C24C2×D42124yes—
680C24C2×D42124yes—
681C24C2×D42124yes—
682C24C2×D42124yes—
683C24C2×D42112yes—
684C24C2×D42124yes—
685C24C2×#546112yes—
686C24C2×#546112yes—
687C24D4×#41124yes—
688C24#3484112yes—
689C24#3484124yes—
690C24#3484148yes—
691C24#3485112yes—
692C24#3488124yes—
693C24#3488124yes—
694C24#3496124yes—
695C24#3496124yes—
696C24#3519124yes—
697C24#3534124yes—
698C24#3537124yes—
699C24C24×D416yes—
700C24C24×D411yescharacteristic
701C24C24×D411yescharacteristic
702C24C24×D411yescharacteristic
703C24C24×D411yescharacteristic
704C24C23×#4111yescharacteristic
705C24C22×H(5,𝔽2)11yescharacteristic
706C24C22×H(5,𝔽2)16yes—
707C24C22×H(5,𝔽2)11yescharacteristic
708C24C22×H(5,𝔽2)16yes—
709C24C2×#58516yes—
710C2×D4#2846164yescomplemented
711C22×C4C22×#120116yes—
712C22×C4C22×#120112yes—
713C22×C4C22×#120116yes—
714C22×C4C22×#120116yes—
715C22×C4C22×#120112yes—
716C22×C4C22×#120116yes—
717C22×C4C22×#121112yescomplemented
718C22×C4C2×D42148yes—
719C22×C4#3484148yes—
720C23C2×#2403124yes—
721C23C2×#2403124yes—
722C23C2×#2403124yes—
723C23C2×#2410124yes—
724C23#34980124yes—
725C23#35347124yes—
726C23D4×#120124yes—
727C23D4×#120132yes—
728C23D4×#120132yes—
729C23D4×#121148yes—
730C23#36212124yes—
731C23C2×#284618yes—
732C23C2×#284618yes—
733C23#37646124yes—
734C23#37672148yes—
735C23#38020124yes—
736C23#58997148yes—
737C23#59123148yes—
738C23C23×#12011yescharacteristic
739C23C23×#12013yes—
740C23C23×#12014yes—
741C23C23×#12111yescharacteristic
742C23C22×#53413yes—
743C23C22×#53411yescharacteristic
744C23C22×D4211yescharacteristic
745C23C22×D4216yes—
746C23C22×D4216yes—
747C23C22×D4211yescharacteristic
748C23C22×D4216yes—
749C23C22×#54611yescharacteristic
750C23C22×#54611yescharacteristic
751C23C2×D4×#4116yes—
752C23C2×#353416yes—
753C23C2×#353716yes—
754C23C2×#3484112yes—
755C23C2×#3484112yes—
756C23C2×#348416yes—
757C23C2×#348413yes—
758C23C2×#349616yes—
759C23C2×#349616yes—
760C23C2×#351916yes—
761C23C2×#348513yes—
762C23C2×#348816yes—
763C23C2×#348816yes—
764C23#62811112yes—
765C23#62818124yes—
766C2×C4D4×#120132yescomplemented
767C2×C4C2×#284618yes—
768C22#612424116yescomplemented
769C22#647714148yescomplemented
770C22C22×#240313yes—
771C22C22×#241011yescharacteristic
772C22C2×#3498013yes—
773C22C2×#3534713yes—
774C22C2×D4×#12014yes—
775C22C2×D4×#12014yes—
776C22C2×D4×#12013yes—
777C22C2×D4×#12014yes—
778C22C2×D4×#12116yes—
779C22C2×#3621213yes—
780C22#41×#12014yes—
781C22#763093913yes—
782C22#763093914yes—
783C22#763103213yes—
784C22#763120214yes—
785C22C22×#284611yescharacteristic
786C22C2×#3767216yes—
787C22C2×#3764613yes—
788C22C2×#3802013yes—
789C22#764225716yes—
790C22C2×#5912316yes—
791C22C2×#5899716yes—
792C22#7670204112yes—
793C22#7670204112yes—
794C22#7670220112yes—
795C22#7671870112yes—
796C22#7708710112yes—
797C22#7711159112yes—
798C2C2×#61242411yescharacteristic
799C2#7223352414yes—
800C2D4×#284611yescharacteristic
801C2#7223354914yes—
802C2#7223357714yes—
803C2#120×#12114yes—
804C2C2×#64771413yes—
805C2#7223709913yes—
806C2#7225658513yes—
807C2#7233013413yes—
808C2#7233429911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC25C26
LCSG ▷ C25 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72334311C2semidirect
2. #72334303C2semidirect
3. #72332588C2semidirect
4. #72332558C2semidirect
5. #72317648C2semidirect
6. #72298513C2semidirect
7. #72298443C2semidirect
8. #72298421C2semidirect
9. C25×#121C2semidirect
10. #72287875C2semidirect
11. #72286446C2semidirect
12. #72286433C2semidirect
13. #72286409C2semidirect
14. #72286393C2semidirect
15. #72279059C2semidirect
16. C2×#612433C2semidirect
17. C22×#14694C2semidirect
18. #72250308C2semidirect
19. #72240113C2semidirect
20. C2×#647714C2semidirect
21. C2×#612424C2semidirect
22. C2×#612424C2semidirect
23. C22×D4×#120C2semidirect
25. C26×D4C22semidirect
26. C26×D4C22semidirect
27. C27×C4C22semidirect
28. C23×D42C22semidirect
30. C24×#121C22semidirect
31. C24×#121C22semidirect
32. C24×#121C22semidirect
35. C25×C4⋊C4C22semidirect
36. C25×C22⋊C4C22semidirect
37. C25×C22⋊C4C22semidirect
42. C22×#2846C22semidirect
43. C22×#2846C22semidirect
44. C22×#2433C22semidirect
45. C22×#2408C22semidirect
46. C22×#2410C22semidirect
47. C22×#2410C22semidirect
48. C22×#2410C22semidirect
49. C22×#2410C22semidirect
50. C22×#2403C22semidirect
51. C22×#2403C22semidirect
52. C22×#2403C22semidirect
53. C22×#2403C22semidirect
54. C22×D4×C22⋊C4C22semidirect
56. C23×#386C22semidirect
57. C23×#379C22semidirect
58. C2×#15310C22semidirect
59. C2×#15278C22semidirect
60. C2×#15263C22semidirect
61. C2×#15257C22semidirect
62. C2×#14757C22semidirect
63. C2×#14724C22semidirect
64. C2×#14719C22semidirect
65. C2×#14718C22semidirect
66. C2×#14716C22semidirect
67. C2×#14716C22semidirect
68. C2×#14715C22semidirect
69. C2×#14715C22semidirect
70. C2×#14715C22semidirect
71. C2×#14715C22semidirect
72. C2×#14715C22semidirect
73. C2×#14715C22semidirect
74. C2×#14715C22semidirect
78. C2×#14694C22semidirect
79. C2×#14694C22semidirect
80. C2×#14694C22semidirect
81. C2×#14694C22semidirect
82. C2×#14694C22semidirect
83. C2×#14694C22semidirect
84. C2×#14694C22semidirect
85. C2×#14694C22semidirect
86. C2×#14694C22semidirect
87. C2×#14694C22semidirect
88. C2×#14693C22semidirect
89. C2×#14679C22semidirect
90. C2×#14679C22semidirect
91. C2×#14679C22semidirect
92. C2×#14679C22semidirect
93. C2×#14023C22semidirect
94. C2×#14015C22semidirect
95. C2×#13967C22semidirect
96. C2×#13867C22semidirect
97. C2×#13867C22semidirect
98. C2×#13867C22semidirect
99. C2×#13867C22semidirect
100. C2×#13867C22semidirect
101. C2×#13867C22semidirect
102. C22×C22⋊#95C22semidirect
103. #156824C22semidirect
104. #156706C22semidirect
105. #156706C22semidirect
106. #156706C22semidirect
107. #154729C22semidirect
108. #154674C22semidirect
109. #154255C22semidirect
110. #154248C22semidirect
111. #154248C22semidirect
112. #154248C22semidirect
113. #154247C22semidirect
114. #154195C22semidirect
115. #154195C22semidirect
116. #154195C22semidirect
117. #154195C22semidirect
118. #154195C22semidirect
119. #154195C22semidirect
120. #154194C22semidirect
121. #154194C22semidirect
122. #154097C22semidirect
123. #154096C22semidirect
124. #154095C22semidirect
125. #154094C22semidirect
126. #154094C22semidirect
127. #154094C22semidirect
128. #154094C22semidirect
129. #154077C22semidirect
130. #154077C22semidirect
131. #154077C22semidirect
132. #154077C22semidirect
133. #154077C22semidirect
134. #154077C22semidirect
135. #153851C22semidirect
136. #153759C22semidirect
137. #153749C22semidirect
141. C25×D4D4semidirect
152. C25×D4C23semidirect
159. C23×#127C23semidirect
160. C23×#121D4semidirect
167. C23×#121C23semidirect
168. C23×#121C23semidirect
169. C23×#121C23semidirect
170. C23×#121C23semidirect
171. C23×#120D4semidirect
186. C23×#120C23semidirect
187. C23×#120C23semidirect
188. C23×#120C23semidirect
189. C23×#120C23semidirect
191. C23×C4×D4C23semidirect
201. C24×C22⋊C4C23semidirect
202. C2×#2846D4semidirect
203. C22×#394C23semidirect
204. C22×#394C23semidirect
205. C22×#394C23semidirect
206. C22×#394C23semidirect
207. C22×#392C23semidirect
208. C22×#392C23semidirect
209. C22×#392C23semidirect
210. C22×#392C23semidirect
211. C22×#392C23semidirect
212. C22×#392C23semidirect
213. C22×#392C23semidirect
214. C22×#392C23semidirect
215. C22×#392C23semidirect
216. C22×#392C23semidirect
217. C22×#392C23semidirect
218. C22×#390C23semidirect
231. C22×#386C23semidirect
232. C22×#386C23semidirect
233. C22×#386C23semidirect
234. C22×#386C23semidirect
235. C22×#386C23semidirect
236. C22×#386C23semidirect
237. C22×#386C23semidirect
238. C22×#386C23semidirect
239. C22×#386C23semidirect
240. C22×#386C23semidirect
241. C22×#386C23semidirect
242. C22×#386C23semidirect
245. C22×#385C23semidirect
268. C22×#379C23semidirect
270. C23×#95C23semidirect
271. #14694D4semidirect
272. C2×#1444C23semidirect
273. C2×#1441C23semidirect
274. C2×#1440C23semidirect
275. C2×#1439C23semidirect
276. C2×#1439C23semidirect
277. C2×#1439C23semidirect
278. C2×#1439C23semidirect
279. C2×#1439C23semidirect
280. C2×#1439C23semidirect
281. C2×#1438C23semidirect
282. C2×#1438C23semidirect
283. C2×#1438C23semidirect
284. C2×#1438C23semidirect
285. C2×#1438C23semidirect
286. C2×#1438C23semidirect
287. C2×#1438C23semidirect
288. C2×#1438C23semidirect
289. C2×#1438C23semidirect
290. C2×#1438C23semidirect
291. C2×#1438C23semidirect
292. C2×#1438C23semidirect
293. C2×#1438C23semidirect
294. C2×#1438C23semidirect
295. C2×#1438C23semidirect
296. C2×#1437C23semidirect
297. C2×#1436C23semidirect
316. C2×C22⋊#95C23semidirect
317. C2×C22⋊#95C23semidirect
318. C2×C22⋊#95C23semidirect
319. C2×C22⋊#95C23semidirect
320. C2×C22⋊#95C23semidirect
321. #7557C23semidirect
322. #7557C23semidirect
323. #7555C23semidirect
324. #7555C23semidirect
325. #7555C23semidirect
326. #7555C23semidirect
344. C24×D4C2×D4semidirect
345. C24×D4C2×D4semidirect
346. C24×D4C2×D4semidirect
372. C25×C4C2×D4semidirect
373. C25×C4C2×D4semidirect
386. C22×#121C2×D4semidirect
387. C22×#121C2×D4semidirect
388. C22×#121C2×D4semidirect
393. C22×#120C2×D4semidirect
394. C22×#120C2×D4semidirect
395. C22×#120C2×D4semidirect
396. C22×#120C2×D4semidirect
398. C23×C4⋊C4C2×D4semidirect
404. C23×C22⋊C4C2×D4semidirect
405. C23×C22⋊C4C2×D4semidirect
406. C23×C22⋊C4C2×D4semidirect
453. C2×#386C2×D4semidirect
455. C2×#379C2×D4semidirect
456. C2×#379C2×D4semidirect
457. C2×#379C2×D4semidirect
478. C22⋊#95C2×D4semidirect
479. C26#120semidirect
495. C26C22×D4semidirect
509. C23×D4#120semidirect
527. C23×D4C22×D4semidirect
528. C23×D4C22×D4semidirect
529. C23×D4C22×D4semidirect
530. C23×D4C22×D4semidirect
541. C24×C4C22×D4semidirect
557. C2×#121#120semidirect
558. C2×#120#121semidirect
572. C22×C22⋊C4C22×D4semidirect
573. C22×C22⋊C4C22×D4semidirect
574. C22×C22⋊C4C22×D4semidirect
575. C22×C22⋊C4C22×D4semidirect
576. C22×C22⋊C4C22×D4semidirect
578. C2×#95C22×D4semidirect
630. C22×D4C2×#120semidirect
631. C22×D4C2×#120semidirect
632. C22×D4C2×#121semidirect
634. C23×C4C2×#120semidirect
635. C23×C4D42semidirect
653. C2×C4⋊C4C2×#120semidirect
654. C2×C22⋊C4C2×#120semidirect
655. C2×C22⋊C4C2×#120semidirect
656. C2×C22⋊C4C2×#121semidirect
657. C24#2403semidirect
658. C24#2410semidirect
671. C24C22×#121semidirect
710. C2×D4#2846semidirect
717. C22×C4C22×#121semidirect
766. C2×C4D4×#120semidirect
768. C22#612424semidirect
769. C22#647714semidirect

Maximal subgroups

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

subgroupindex
#723343112
#723343032
#723325882
#723325582
#723176482
#722985132
#722984432
#722984212
C25×#1212
#722878752
#722864462
#722864332
#722864092
#722863932
#722790592
C2×#6124332
C22×#146942
#722503082
#722401132
C2×#6477142
C2×#6124242
C22×D4×#1202