Finite Group Databasebeta

← #522681

Subgroups — #522681

Order 512.

3940 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2616C211yesmaximal, characteristic
2C2×#2362C211yesmaximal, characteristic, complemented
3C2×#2323C211yesmaximal, characteristic, complemented
4C2×#2311C211yesmaximal, characteristic
5C2×#2297C211yesmaximal, characteristic
6#14702C211yesmaximal, characteristic, complemented
7#14573C212yesmaximal, complemented
8#14571C212yesmaximal, complemented
9#14524C212yesmaximal, complemented
10#14523C212yesmaximal, complemented
11#14264C211yesmaximal, characteristic, complemented
12#14224C212yesmaximal, complemented
13#14214C212yesmaximal, complemented
14#14205C212yesmaximal, complemented
15#14201C212yesmaximal, complemented
16#14139C211yesmaximal, characteristic, complemented
17#14129C211yesmaximal, characteristic, complemented
18#13997C211yesmaximal, characteristic, complemented
19#13994C211yesmaximal, characteristic, complemented
20#13973C211yesmaximal, characteristic, complemented
21#13969C211yesmaximal, characteristic, complemented
22C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
23C4×#380C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C42C2211yescharacteristic
33#2616C4116yescomplemented
34C2×#395C2212yes—
35C2×#394C2212yes—
36C2×#394C2212yes—
37C2×#394C2212yes—
38#2362—28no—
39#2323—28no—
40#2311—28no—
41#2297—28no—
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2212yes—
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#390C2212yes—
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#389C2212yes—
53C2×#389C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#388C2212yes—
56C2×#388C2212yes—
57C2×#388C2212yes—
58C2×#388C2212yes—
59C2×#388C2212yes—
60C2×#387C2212yes—
61C2×#387C2212yes—
62C2×#386C2211yescharacteristic
63C2×#386C2212yes—
64C2×#386C2211yescharacteristic
65C2×#386C2212yes—
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic
68C2×#380C2211yescharacteristic
69C2×#380C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×#380C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C4⋊C4C2212yes—
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82C2×C4×C22⋊C4C2212yes—
83C2×C4×C22⋊C4C2212yes—
84C2×C4×C22⋊C4C2211yescharacteristic
85#1445C2212yes—
86#1444C2212yes—
87#1442C2212yes—
88#1442C2212yes—
89#1442C2212yes—
90#1441C2212yes—
91#1441C2212yes—
92#1441C2212yes—
93#1440C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1437C2212yes—
102#1437C2212yes—
103#1437C2212yes—
104#1436C2212yes—
105#1436C2212yes—
106#1436C2212yes—
107#1436C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111C4⋊#95C2211yescharacteristic
112C4⋊#95C2211yescharacteristic
113C4⋊#95C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2211yescharacteristic
116C4⋊#95C2212yes—
117C4⋊#95C2211yescharacteristic
118#1434C2212yes—
119#1434C2212yes—
120#1434C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C4×#95C2212yes—
128C22×#41—24no—
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—42no—
133C22×#41—42no—
134C22×#41C2×C418yes—
135C23×Q8C2311yescharacteristic
136C23×Q8C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C2×C22⋊Q8—24no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—42no—
151C2×C22⋊Q8—42no—
152C2×C22⋊Q8C2×C418yescomplemented
153C2×C22⋊Q8C2×C418yescomplemented
154C2×C22⋊Q8C2×C418yescomplemented
155C2×C4×Q8—24no—
156C2×C4×Q8—24no—
157C2×C4×Q8—42no—
158C2×#117—24no—
159C2×#117—24no—
160C2×#117—24no—
161C2×#117—24no—
162C2×#117—42no—
163C2×#117—42no—
164C22×C4⋊C4—24no—
165C22×C4⋊C4—24no—
166C22×C4⋊C4—42no—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C42—24no—
206C22×C42—24no—
207C22×C42—42no—
208C22×C42C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2312yes—
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2312yes—
218C22×C42C2312yes—
219#395C2×C4116yescomplemented
220#394C2×C4116yes—
221#394C2×C4116yescomplemented
222#394C2×C4116yescomplemented
223#391—24no—
224#391—24no—
225#391—28no—
226#391—24no—
227#391—24no—
228#391—42no—
229#390—28no—
230#390—24no—
231#390—24no—
232#389—24no—
233#389—24no—
234#389—28no—
235#389—42no—
236#388—28no—
237#388—28no—
238#388—28no—
239#388—28no—
240#388—44no—
241#387—28no—
242#387—28no—
243#386—28no—
244#386—24no—
245#386—24no—
246#386—28no—
247#386—24no—
248#386—24no—
249#380—24no—
250#380—24no—
251#380—24no—
252#380C2×C418yescomplemented
253#380C2×C418yescomplemented
254#380C2×C418yescomplemented
255#380D418yes—
256C4×C4⋊C4—24no—
257C4×C4⋊C4—24no—
258C4×C4⋊C4—28no—
259C4×C4⋊C4—42no—
260C4×C22⋊C4—24no—
261C4×C22⋊C4—24no—
262C4×C22⋊C4—24no—
263C4×C22⋊C4—44no—
264C4×C22⋊C4—44no—
265C4×C22⋊C4D418yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C25C2411yescharacteristic
306C25C2411yescharacteristic
307C25C2411yescharacteristic
308C2×#41—232no—
309C2×#41—232no—
310C2×#41—416no—
311C2×#41—416no—
312C2×#41—416no—
313C2×#41—416no—
314C2×#41—416no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—41no—
326C22×Q8—41no—
327C22×Q8C22×C414yes—
328C22×Q8C22×C414yes—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—41no—
342C22×D4—41no—
343C22×D4—41no—
344C22×D4—41no—
345C22×D4—41no—
346C22×D4—41no—
347C22×D4C22×C414yes—
348C22×D4C22×C414yes—
349C22×D4C22×C414yes—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—24no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—24no—
374C23×C4—41no—
375C23×C4—41no—
376C23×C4—41no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4—41no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4C22×C414yes—
386C23×C4C22×C414yes—
387C23×C4C22×C414yes—
388C23×C4C2×D414yes—
389C23×C4C2×D414yes—
390C23×C4#4114yes—
391C23×C4#4114yes—
392C23×C4C2411yescharacteristic
393C23×C4C2412yes—
394C23×C4C2411yescharacteristic
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2412yes—
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2412yes—
403C23×C4C2411yescharacteristic
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C22⋊Q8—232no—
413C22⋊Q8—232no—
414C22⋊Q8—416no—
415C4×Q8—416no—
416#117—416no—
417#117—416no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—416no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4C22×C414yes—
463C2×C4⋊C4C22×C414yes—
464C2×C4⋊C4C22×C414yes—
465C2×C4⋊C4C22×C418yes—
466C2×C4⋊C4C22×C418yes—
467C2×C4⋊C4C22×C418yes—
468C2×C4⋊C4C2×D414yes—
469C2×C4⋊C4C2×D414yes—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—41no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—41no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—41no—
510C2×C22⋊C4—41no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4C22×C418yes—
525C2×C22⋊C4C22×C418yes—
526C2×C22⋊C4C22×C418yes—
527C2×C22⋊C4C22×C418yes—
528C2×C22⋊C4C22×C418yes—
529C2×C22⋊C4C22×C418yes—
530C2×C22⋊C4C2×D414yes—
531C2×C22⋊C4C2×D414yes—
532C2×C22⋊C4C2×D418yes—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—24no—
539C2×C42—22no—
540C2×C42—24no—
541C2×C42—24no—
542C2×C42—24no—
543C2×C42—22no—
544C2×C42—24no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—24no—
552C2×C42—22no—
553C2×C42—24no—
554C2×C42—24no—
555C2×C42—24no—
556C2×C42—416no—
557C2×C42—42no—
558C2×C42—42no—
559C2×C42—41no—
560C2×C42—41no—
561C2×C42—42no—
562C2×C42—42no—
563C2×C42—42no—
564C2×C42—42no—
565C2×C42C2×D414yes—
566C2×C42C2×D414yes—
567#95—22no—
568#95—22no—
569#95—22no—
570#95—22no—
571#95—22no—
572#95—22no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95C22×C418yes—
601#95C22×C418yes—
602#95C22×C418yes—
603#95C2×D414yes—
604#95C2×D414yes—
605#95C2×D418yes—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24C23×C412yes—
645C24C23×C412yes—
646C24C23×C412yes—
647C24C22×D412yes—
648C24C22×D412yes—
649C24C2×#4112yes—
650C24C2×#4112yes—
651C24C2511yescharacteristic
652#41—4128no—
653C2×Q8—28no—
654C2×Q8—28no—
655C2×Q8—28no—
656C2×Q8—28no—
657C2×Q8—28no—
658C2×Q8—44no—
659C2×Q8—44no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×Q8—44no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8—44no—
666C2×Q8—44no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—28no—
708C22×C4—28no—
709C22×C4—28no—
710C22×C4—28no—
711C22×C4—28no—
712C22×C4—28no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—48no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—48no—
835C22×C4—84no—
836C22×C4—84no—
837C22×C4—84no—
838C22×C4—84no—
839C22×C4—84no—
840C22×C4C4×D4116yes—
841C22×C4C4×D4116yes—
842C22×C4C23×C414yes—
843C22×C4C23×C414yes—
844C22×C4C23×C414yes—
845C22×C4C23×C412yes—
846C22×C4C23×C414yes—
847C22×C4C23×C412yes—
848C22×C4C23×C412yes—
849C22×C4C23×C412yes—
850C22×C4C22×D412yes—
851C22×C4C22×D414yes—
852C22×C4C22×D412yes—
853C22×C4C22×D414yes—
854C22×C4C22×D412yes—
855C22×C4C22×D412yes—
856C22×C4C22×D412yes—
857C22×C4C22×D412yes—
858C22×C4C22×D412yes—
859C22×C4C22×D412yes—
860C22×C4C2×#4112yes—
861C22×C4C2×#4112yes—
862C22×C4C2×#4112yes—
863C22×C4C2×#4112yes—
864C22×C4H(5,𝔽2)12yes—
865C22×C4H(5,𝔽2)12yes—
866C22×C4H(5,𝔽2)12yes—
867C22×C42−1+412yes—
868C22×C42−1+412yes—
869C22×C42−1+412yes—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—216no—
873C4⋊C4—216no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—84no—
886C4⋊C4—84no—
887C22⋊C4—216no—
888C22⋊C4—216no—
889C22⋊C4—28no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—44no—
895C22⋊C4—48no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—84no—
906C22⋊C4—84no—
907C22⋊C4—84no—
908C42—28no—
909C42—28no—
910C42—44no—
911C42—44no—
912C42—48no—
913C42—48no—
914C42—48no—
915C42—44no—
916C42—44no—
917C42—84no—
918C42—84no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23C2×C4×D414yes—
1023C23C2×C4×D414yes—
1024C23C24×C411yescharacteristic
1025C23C23×D411yescharacteristic
1026C23C23×D411yescharacteristic
1027C23C22×#4111yescharacteristic
1028C23C22×#4111yescharacteristic
1029C23C2×H(5,𝔽2)11yescharacteristic
1030C23C2×H(5,𝔽2)11yescharacteristic
1031C23C2×H(5,𝔽2)11yescharacteristic
1032C23C2×2−1+411yescharacteristic
1033C23C2×2−1+411yescharacteristic
1034C23C2×2−1+411yescharacteristic
1035C23#58511yescharacteristic
1036C23#58511yescharacteristic
1037C23#58511yescharacteristic
1038C23#58511yescharacteristic
1039Q8—416no—
1040Q8—416no—
1041D4—416no—
1042D4—416no—
1043D4—416no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—232no—
1063C2×C4—232no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—416no—
1101C2×C4—416no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—41no—
1105C2×C4—42no—
1106C2×C4—41no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—42no—
1110C2×C4—42no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—41no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—416no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—816no—
1180C2×C4C2×C4×D414yes—
1181C2×C4C2×C4×D414yes—
1182C2×C4C2×C4×D414yes—
1183C2×C4C2×C4×D414yes—
1184C2×C4#51814yes—
1185C2×C4#53714yes—
1186C2×C4D4214yes—
1187C2×C4#54614yes—
1188C2×C4#54614yes—
1189C2×C4#55114yes—
1190C22—24no—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—24no—
1195C22—24no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22C22×C4×D411yescharacteristic
1236C22C22×C4×D411yescharacteristic
1237C22C2×#51811yescharacteristic
1238C22C4×H(5,𝔽2)11yescharacteristic
1239C22C4×2−1+411yescharacteristic
1240C22C4×2−1+411yescharacteristic
1241C22C4×2−1+411yescharacteristic
1242C22C2×#53711yescharacteristic
1243C22#344911yescharacteristic
1244C22#346011yescharacteristic
1245C22#346111yescharacteristic
1246C22C2×D4211yescharacteristic
1247C22C2×#54611yescharacteristic
1248C22C2×#54611yescharacteristic
1249C22C2×#55111yescharacteristic
1250C22#348911yescharacteristic
1251C22#348911yescharacteristic
1252C22#349211yescharacteristic
1253C22#349311yescharacteristic
1254C22#349511yescharacteristic
1255C22#349511yescharacteristic
1256C22#349611yescharacteristic
1257C22#349711yescharacteristic
1258C22#349911yescharacteristic
1259C22#350011yescharacteristic
1260C22#350911yescharacteristic
1261C22#351011yescharacteristic
1262C22#353811yescharacteristic
1263C22#354011yescharacteristic
1264C22#354111yescharacteristic
1265C22#354211yescharacteristic
1266C22#354711yescharacteristic
1267C22#354711yescharacteristic
1268C22#354811yescharacteristic
1269C22#355111yescharacteristic
1270C4—24no—
1271C4—24no—
1272C4—24no—
1273C4—44no—
1274C4—44no—
1275C4—42no—
1276C4—44no—
1277C4—44no—
1278C4—42no—
1279C4—42no—
1280C4—44no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—44no—
1285C4—82no—
1286C4—81no—
1287C4—82no—
1288C4—81no—
1289C4#235818yes—
1290C2—44no—
1291C2—44no—
1292C2—82no—
1293C2C4×#53711yescharacteristic
1294C2C2×#235811yescharacteristic
1295C2#3426811yescharacteristic
1296C2#3427411yescharacteristic
1297C2#3427611yescharacteristic
1298C2#3441211yescharacteristic
1299C2#3441411yescharacteristic
1300C2#3783711yescharacteristic
1301C2#3784411yescharacteristic
1302C2#3797111yescharacteristic
1303C2#3797411yescharacteristic
1304C2#3933511yescharacteristic
1305C2#3934011yescharacteristic
1306C2#3943511yescharacteristic
1307C2#3943811yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×#41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2362C2semidirect
3. C2×#2323C2semidirect
6. #14702C2semidirect
7. #14573C2semidirect
8. #14571C2semidirect
9. #14524C2semidirect
10. #14523C2semidirect
11. #14264C2semidirect
12. #14224C2semidirect
13. #14214C2semidirect
14. #14205C2semidirect
15. #14201C2semidirect
16. #14139C2semidirect
17. #14129C2semidirect
18. #13997C2semidirect
19. #13994C2semidirect
20. #13973C2semidirect
21. #13969C2semidirect
22. C22⋊C4×C4⋊C4C2semidirect
23. C4×#380C2semidirect
33. #2616C4semidirect
152. C2×C22⋊Q8C2×C4semidirect
153. C2×C22⋊Q8C2×C4semidirect
154. C2×C22⋊Q8C2×C4semidirect
219. #395C2×C4semidirect
221. #394C2×C4semidirect
222. #394C2×C4semidirect
252. #380C2×C4semidirect
253. #380C2×C4semidirect
254. #380C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#26162
C2×#23622
C2×#23232
C2×#23112
C2×#22972
#147022
#145732
#145712
#145242
#145232
#142642
#142242
#142142
#142052
#142012
#141392
#141292
#139972
#139942
#139732
#139692
C22⋊C4×C4⋊C42
C4×#3802