Finite Group Databasebeta

← #779710

Subgroups — #779710

Order 512.

4896 conjugacy classes of subgroups.

The subgroup lattice has 1354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#559C211yesmaximal, characteristic, complemented
2C2×#2432C211yesmaximal, characteristic, complemented
3C2×#2431C211yesmaximal, characteristic
4C2×#2339C211yesmaximal, characteristic, complemented
5#16654C212yesmaximal, complemented
6#16032C212yesmaximal, complemented
7#15982C212yesmaximal, complemented
8#15314C212yesmaximal, complemented
9#15270C212yesmaximal, complemented
10#15243C211yesmaximal, characteristic, complemented
11#15215C211yesmaximal, characteristic, complemented
12#15201C211yesmaximal, characteristic, complemented
13#14912C212yesmaximal, complemented
14#14730C212yesmaximal, complemented
15#14027C211yesmaximal, characteristic, complemented
16#14027C211yesmaximal, characteristic, complemented
17#14025C211yesmaximal, characteristic, complemented
18#14024C211yesmaximal, characteristic, complemented
19#14016C212yesmaximal, complemented
20#13970C211yesmaximal, characteristic, complemented
21#13969C211yesmaximal, characteristic, complemented
22#13916C211yesmaximal, characteristic, complemented
23C4×#393C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C2×#559—28no—
26C2×#559—28no—
27C2×#559—28no—
28C22×C4⋊Q8C2211yescharacteristic
29C22×#127C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C22×#124C2212yes—
32C22×#124C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C22×#123C2212yes—
35C22×#123C2212yes—
36C22×C22⋊Q8C2211yescharacteristic
37C22×#121C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×D4C2212yes—
41C22×C4×D4C2211yescharacteristic
42C22×C4×D4C2211yescharacteristic
43C22×C4×D4C2211yescharacteristic
44#2432—28no—
45#2431—28no—
46C2×#394C2212yes—
47C2×#394C2212yes—
48C2×#393C2211yescharacteristic
49C2×#392C2212yes—
50C2×#392C2212yes—
51#2339—28no—
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#391C2211yescharacteristic
58C2×#390C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#390C2211yescharacteristic
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#386C2212yes—
69C2×#385C2212yes—
70C2×#385C2212yes—
71C2×#381C2212yes—
72C2×#381C2212yes—
73C2×#380C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C22×#95C2212yes—
78#1446C2211yescharacteristic
79#1446C2212yes—
80#1442C2212yes—
81#1442C2211yescharacteristic
82#1442C2211yescharacteristic
83#1442C2211yescharacteristic
84#1442C2212yes—
85#1442C2212yes—
86#1441C2212yes—
87#1441C2212yes—
88#1441C2212yes—
89#1440C2212yes—
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yes—
93#1440C2212yes—
94#1440C2212yes—
95#1440C2212yes—
96#1439C2211yescharacteristic
97#1439C2212yes—
98#1439C2212yes—
99#1439C2211yescharacteristic
100#1439C2211yescharacteristic
101#1439C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yes—
111#1437C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2212yes—
115C4⋊#95C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
126C4×#95C2211yescharacteristic
127C4×#95C2211yescharacteristic
128C4×#95C2211yescharacteristic
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—24no—
133C22×#41—24no—
134C22×#41—42no—
135C22×#41—42no—
136C23×Q8C2311yescharacteristic
137C23×Q8C2311yescharacteristic
138C23×Q8C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2312yes—
142C23×D4C2311yescharacteristic
143C23×D4C2312yes—
144C23×D4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2312yes—
147C24×C4C2312yes—
148C24×C4C2312yes—
149C24×C4C2312yes—
150#559—2128no—
151C2×C4⋊Q8—24no—
152C2×C4⋊Q8—24no—
153C2×C4⋊Q8—42no—
154C2×#127—24no—
155C2×#127—24no—
156C2×#127D418yes—
157C2×#124—24no—
158C2×#124—24no—
159C2×#124—28no—
160C2×#124—24no—
161C2×#124—24no—
162C2×#124—24no—
163C2×#124—24no—
164C2×#124—28no—
165C2×#124—28no—
166C2×#124—24no—
167C2×#124—42no—
168C2×#124D418yescomplemented
169C2×#123—28no—
170C2×#123—28no—
171C2×#123—28no—
172C2×#123—28no—
173C2×#123—28no—
174C2×#123—28no—
175C2×C22⋊Q8—24no—
176C2×C22⋊Q8—24no—
177C2×C22⋊Q8—42no—
178C2×#121—24no—
179C2×#121—24no—
180C2×#121—42no—
181C2×C4×Q8—24no—
182C2×C4×Q8—24no—
183C2×C4×Q8—24no—
184C2×C4×Q8—24no—
185C2×C4×Q8—24no—
186C2×C4×Q8—24no—
187C2×C4×D4—24no—
188C2×C4×D4—28no—
189C2×C4×D4—24no—
190C2×C4×D4—24no—
191C2×C4×D4—28no—
192C2×C4×D4—24no—
193C2×C4×D4—24no—
194C2×C4×D4—28no—
195C2×C4×D4—24no—
196C2×C4×D4—42no—
197C2×C4×D4—42no—
198C2×C4×D4D418yescomplemented
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2312yes—
209C22×C4⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2312yes—
236C22×C42C2312yes—
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243#394—28no—
244#394—28no—
245#393—24no—
246#392—28no—
247#392—28no—
248#391—24no—
249#391—24no—
250#391—24no—
251#391—24no—
252#391—42no—
253#391—42no—
254#390—24no—
255#390—24no—
256#390—42no—
257#390—42no—
258#386—28no—
259#386—28no—
260#386—28no—
261#386—28no—
262#386—28no—
263#386—44no—
264#386—44no—
265#385—28no—
266#385—28no—
267#381—28no—
268#381—44no—
269#380—24no—
270C4×C22⋊C4—24no—
271C4×C22⋊C4—24no—
272C4×C22⋊C4—24no—
273C2×#95—28no—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2311yescharacteristic
315C25C2412yes—
316C25C2411yescharacteristic
317C25C2412yes—
318C2×#41—232no—
319C2×#41—416no—
320C2×#41—416no—
321C2×#41—416no—
322C2×#41—416no—
323C2×#41—416no—
324C2×#41—416no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8—41no—
343C22×Q8—41no—
344C22×Q8C2×D414yes—
345C22×Q8#4114yes—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—24no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4C2×D414yes—
383C22×D4C2×D418yes—
384C22×D4C2×D414yes—
385C22×D4C2×D414yes—
386C22×D4C2×D414yes—
387C22×D4C2×D418yes—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4C2×D418yes—
422C23×C4#4114yes—
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2412yes—
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C4⋊Q8—416no—
444#127—232no—
445#124—264no—
446#124—232no—
447#124—232no—
448#124—416no—
449#123—264no—
450#123—264no—
451C22⋊Q8—416no—
452#121—416no—
453C4×Q8—232no—
454C4×Q8—232no—
455C4×D4—264no—
456C4×D4—232no—
457C4×D4—232no—
458C4×D4—416no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4C2×D414yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—41no—
539C2×C22⋊C4—41no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—41no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—41no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4C2×D418yes—
568C2×C22⋊C4C2×D418yes—
569C2×C22⋊C4C2×D418yes—
570C2×C42—24no—
571C2×C42—24no—
572C2×C42—24no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—22no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42C2×D414yes—
589C2×C42C2×D414yes—
590C2×C42C2×D414yes—
591#95—22no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—24no—
611#95—22no—
612#95—22no—
613#95—42no—
614#95—41no—
615#95—42no—
616#95—42no—
617#95—41no—
618#95—41no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95—42no—
630#95—42no—
631#95#4114yescomplemented
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—21no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—21no—
649C24—21no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—21no—
654C24—21no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—22no—
662C24—21no—
663C24—21no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—22no—
672C24C22×D414yes—
673C24C22×D414yes—
674C24C22×D414yes—
675C24C22×D414yes—
676C24C2×#4112yes—
677C24C2511yescharacteristic
678#41—4128no—
679C2×Q8—28no—
680C2×Q8—28no—
681C2×Q8—28no—
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—28no—
685C2×Q8—28no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8—44no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×D4—216no—
701C2×D4—216no—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—216no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—84no—
733C2×D4—84no—
734C2×D4—84no—
735C2×D4—84no—
736C2×D4—84no—
737C2×D4—84no—
738C2×D4—84no—
739C2×D4—84no—
740C2×D4—84no—
741C2×D4#120116yes—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—216no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—216no—
820C22×C4—216no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—28no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—22no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—48no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—48no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4—84no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4C22×D414yes—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D414yes—
902C22×C4C22×D412yes—
903C22×C4C22×D412yes—
904C22×C4C22×D412yes—
905C22×C4C22×D412yes—
906C22×C4C2×#4112yes—
907C22×C4C2×#4112yes—
908C22×C4C2×#4112yes—
909C22×C4C2×#4114yes—
910C22×C4C2×#4112yes—
911C22×C4C2×#4112yes—
912C22×C4C2×#4112yes—
913C22×C4H(5,𝔽2)12yes—
914C22×C4H(5,𝔽2)12yes—
915C22×C4H(5,𝔽2)12yes—
916C22×C42−1+412yes—
917C4⋊C4—28no—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—216no—
921C4⋊C4—28no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C22⋊C4—216no—
929C22⋊C4—216no—
930C22⋊C4—216no—
931C22⋊C4—216no—
932C22⋊C4—216no—
933C22⋊C4—216no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C42—216no—
955C42—28no—
956C42—28no—
957C42—28no—
958C42—44no—
959C42—44no—
960C42—44no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—24no—
984C23—22no—
985C23—24no—
986C23—22no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—42no—
1011C23—41no—
1012C23—42no—
1013C23—41no—
1014C23—41no—
1015C23—42no—
1016C23—42no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—41no—
1024C23—42no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—41no—
1029C23—41no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—42no—
1037C23—41no—
1038C23—42no—
1039C23—41no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—41no—
1044C23—42no—
1045C23—42no—
1046C23—41no—
1047C23—42no—
1048C23—41no—
1049C23—41no—
1050C23—42no—
1051C23—42no—
1052C23—41no—
1053C23—42no—
1054C23—41no—
1055C23—42no—
1056C23—41no—
1057C23—42no—
1058C23—41no—
1059C23—42no—
1060C23—41no—
1061C23—42no—
1062C23—41no—
1063C23—42no—
1064C23—41no—
1065C23C2×#12018yes—
1066C23C23×D411yescharacteristic
1067C23C23×D411yescharacteristic
1068C23C23×D411yescharacteristic
1069C23C22×#4111yescharacteristic
1070C23C22×#4111yescharacteristic
1071C23C22×#4111yescharacteristic
1072C23C2×H(5,𝔽2)11yescharacteristic
1073C23C2×H(5,𝔽2)11yescharacteristic
1074C23C2×H(5,𝔽2)11yescharacteristic
1075C23C2×2−1+411yescharacteristic
1076C23#58511yescharacteristic
1077C23#58511yescharacteristic
1078C23#58511yescharacteristic
1079C23#58511yescharacteristic
1080C23#58511yescharacteristic
1081Q8—416no—
1082Q8—416no—
1083Q8—416no—
1084D4—232no—
1085D4—432no—
1086D4—432no—
1087D4—416no—
1088D4—816no—
1089D4—816no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—432no—
1133C2×C4—41no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—416no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—41no—
1218C2×C4—42no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—816no—
1225C2×C4—816no—
1226C2×C4—816no—
1227C2×C4C2×#12014yes—
1228C2×C4#52514yes—
1229C2×C4#53514yes—
1230C2×C4#54614yes—
1231C2×C4#54614yes—
1232C2×C4#54614yes—
1233C2×C4#54614yes—
1234C2×C4#54714yes—
1235C22—28no—
1236C22—28no—
1237C22—28no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—42no—
1251C22—44no—
1252C22—42no—
1253C22—44no—
1254C22—42no—
1255C22—44no—
1256C22—42no—
1257C22—44no—
1258C22—44no—
1259C22—42no—
1260C22—44no—
1261C22—44no—
1262C22—42no—
1263C22—42no—
1264C22—81no—
1265C22—82no—
1266C22—82no—
1267C22—81no—
1268C22—82no—
1269C22—81no—
1270C22—81no—
1271C22—82no—
1272C22—82no—
1273C22—81no—
1274C22—82no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—82no—
1279C22—82no—
1280C22C22×#12011yescharacteristic
1281C22C2×#52511yescharacteristic
1282C22C2×#53511yescharacteristic
1283C22C2×#54611yescharacteristic
1284C22C2×#54611yescharacteristic
1285C22C2×#54611yescharacteristic
1286C22C2×#54611yescharacteristic
1287C22C2×#54711yescharacteristic
1288C22D4×#4111yescharacteristic
1289C22D4×#4111yescharacteristic
1290C22#348011yescharacteristic
1291C22#348011yescharacteristic
1292C22#348511yescharacteristic
1293C22#348511yescharacteristic
1294C22#348511yescharacteristic
1295C22#348811yescharacteristic
1296C22#348911yescharacteristic
1297C22#348911yescharacteristic
1298C22#349611yescharacteristic
1299C22#349611yescharacteristic
1300C22#350011yescharacteristic
1301C22#350611yescharacteristic
1302C22#350711yescharacteristic
1303C22#350811yescharacteristic
1304C22#351011yescharacteristic
1305C22#351411yescharacteristic
1306C22#352211yescharacteristic
1307C22#352411yescharacteristic
1308C22#352411yescharacteristic
1309C22#355411yescharacteristic
1310C22#355411yescharacteristic
1311C22#355811yescharacteristic
1312C22#356211yescharacteristic
1313C22#356211yescharacteristic
1314C22#356211yescharacteristic
1315C4—24no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—44no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—44no—
1327C4—44no—
1328C4—82no—
1329C4—82no—
1330C4—81no—
1331C4—82no—
1332C4—81no—
1333C4—81no—
1334C4#240418yes—
1335C2—48no—
1336C2—82no—
1337C2—84no—
1338C2C2×#240411yescharacteristic
1339C2#3575011yescharacteristic
1340C2#3577811yescharacteristic
1341C2#3621311yescharacteristic
1342C2#3643711yescharacteristic
1343C2#3995311yescharacteristic
1344C2#4268311yescharacteristic
1345C2#4509711yescharacteristic
1346C2#4514111yescharacteristic
1347C2#4514611yescharacteristic
1348C2#4531911yescharacteristic
1349C2#5906411yescharacteristic
1350C2#5914511yescharacteristic
1351C2#5941111yescharacteristic
1352C2#5941711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2431C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#559C2semidirect
2. C2×#2432C2semidirect
4. C2×#2339C2semidirect
5. #16654C2semidirect
6. #16032C2semidirect
7. #15982C2semidirect
8. #15314C2semidirect
9. #15270C2semidirect
10. #15243C2semidirect
11. #15215C2semidirect
12. #15201C2semidirect
13. #14912C2semidirect
14. #14730C2semidirect
15. #14027C2semidirect
16. #14027C2semidirect
17. #14025C2semidirect
18. #14024C2semidirect
19. #14016C2semidirect
20. #13970C2semidirect
21. #13969C2semidirect
22. #13916C2semidirect
23. C4×#393C2semidirect
168. C2×#124D4semidirect
198. C2×C4×D4D4semidirect
631. #95#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5592
C2×#24322
C2×#24312
C2×#23392
#166542
#160322
#159822
#153142
#152702
#152432
#152152
#152012
#149122
#147302
#140272
#140252
#140242
#140162
#139702
#139692
#139162
C4×#3932