Finite Group Databasebeta

← #4929014

Subgroups — #4929014

Order 512.

5892 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#518C211yesmaximal, characteristic, complemented
2C2×#2609C211yesmaximal, characteristic, complemented
3C2×#2598C211yesmaximal, characteristic, complemented
4C2×#2392C211yesmaximal, characteristic, complemented
5#14906C211yesmaximal, characteristic, complemented
6#14905C211yesmaximal, characteristic, complemented
7#14860C211yesmaximal, characteristic, complemented
8#14801C211yesmaximal, characteristic, complemented
9#14796C211yesmaximal, characteristic, complemented
10#14795C211yesmaximal, characteristic, complemented
11#14733C212yesmaximal, complemented
12#14732C212yesmaximal, complemented
13#14726C212yesmaximal, complemented
14#14725C212yesmaximal, complemented
15#14724C211yesmaximal, characteristic, complemented
16#14715C211yesmaximal, characteristic
17#14345C211yesmaximal, characteristic, complemented
18#14173C212yesmaximal, complemented
19#14171C212yesmaximal, complemented
20#13991C212yesmaximal, complemented
21#13967C212yesmaximal, complemented
22#13938C211yesmaximal, characteristic, complemented
23#13905C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#120C2212yes—
26C2×#518—28no—
27C2×#518—28no—
28C2×#518—28no—
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2212yes—
31C22×C4×D4C2212yes—
32C22×C4×D4C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×C4×D4C2212yescomplemented
36C22×#117C2211yescharacteristic
37C22×#117C2211yescharacteristic
38C22×#117C2211yescharacteristic, complemented
39C23×C22⋊C4C2212yes—
40C23×C22⋊C4C2212yes—
41#2609—28no—
42#2598—28no—
43C2×#400C2211yescharacteristic, complemented
44C2×#399C2211yescharacteristic, complemented
45#2392—28no—
46C2×#398C2211yescharacteristic, complemented
47C2×#398C2211yescharacteristic, complemented
48C2×#397C2211yescharacteristic, complemented
49C2×#396C2211yescharacteristic
50C2×#396C2211yescharacteristic, complemented
51C2×#396C2212yescomplemented
52C2×#394C2211yescharacteristic
53C2×#394C2211yescharacteristic
54C2×#394C2211yescharacteristic
55C2×#394C2212yes—
56C2×#394C2212yescomplemented
57C2×#392C2211yescharacteristic
58C2×#392C2212yes—
59C2×#392C2211yescharacteristic
60C2×#388C2211yescharacteristic
61C2×#388C2212yescomplemented
62C2×#388C2211yescharacteristic, complemented
63C2×#387C2211yescharacteristic, complemented
64C2×#387C2211yescharacteristic, complemented
65C2×#386C2211yescharacteristic
66C2×#386C2211yescharacteristic
67C2×#386C2212yescomplemented
68C2×#386C2212yescomplemented
69C2×#386C2212yescomplemented
70C2×#386C2212yescomplemented
71C2×#385C2211yescharacteristic
72C2×#385C2212yescomplemented
73C2×#385C2211yescharacteristic, complemented
74C2×#385C2212yescomplemented
75C2×#385C2212yescomplemented
76C2×#383C2211yescharacteristic, complemented
77C2×#382C2211yescharacteristic, complemented
78C2×#380C2212yescomplemented
79C2×#380C2212yescomplemented
80C2×#379C2212yes—
81C2×#379C2212yes—
82C2×#379C2212yes—
83C2×C4×C4⋊C4C2211yescharacteristic, complemented
84C2×C4×C22⋊C4C2212yescomplemented
85#1445C2211yescharacteristic, complemented
86#1445C2211yescharacteristic, complemented
87#1445C2211yescharacteristic, complemented
88#1445C2211yescharacteristic, complemented
89#1441C2212yescomplemented
90#1440C2212yes—
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1438C2211yescharacteristic
103#1438C2211yescharacteristic
104#1438C2212yes—
105#1438C2211yescharacteristic
106#1438C2211yescharacteristic
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1437C2212yes—
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119#1434C2211yescharacteristic, complemented
120#1434C2211yescharacteristic, complemented
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C22⋊#95C2212yescomplemented
128C22⋊#95C2212yescomplemented
129C26C2312yes—
130C23×D4—28no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—28no—
134C23×D4—24no—
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2312yes—
144C24×C4C2312yes—
145C24×C4C2312yes—
146C24×C4C2312yes—
147C2×#120—28no—
148C2×#120—44no—
149C2×#120—44no—
150#518—2128no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—28no—
154C2×C4×D4—28no—
155C2×C4×D4—28no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4—28no—
159C2×C4×D4—28no—
160C2×C4×D4—28no—
161C2×C4×D4—28no—
162C2×C4×D4—24no—
163C2×C4×D4—24no—
164C2×C4×D4—24no—
165C2×C4×D4—24no—
166C2×C4×D4—24no—
167C2×C4×D4—24no—
168C2×C4×D4—44no—
169C2×C4×D4—44no—
170C2×C4×D4D418yescomplemented
171C2×C4×D4D418yescomplemented
172C2×#117—24no—
173C2×#117—24no—
174C2×#117—24no—
175C2×#117—24no—
176C2×#117—24no—
177C2×#117—24no—
178C2×#117—24no—
179C2×#117—24no—
180C2×#117D418yescomplemented
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2312yes—
195C22×C22⋊C4—28no—
196C22×C22⋊C4—28no—
197C22×C22⋊C4—28no—
198C22×C22⋊C4—28no—
199C22×C22⋊C4—28no—
200C22×C22⋊C4—28no—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2312yes—
238C22×C42C2311yescharacteristic
239#400—24no—
240#399—24no—
241#398—24no—
242#398—24no—
243#397—24no—
244#396—24no—
245#396—24no—
246#396—28no—
247#394—24no—
248#394—24no—
249#394—28no—
250#394—24no—
251#394—28no—
252#392—24no—
253#392—24no—
254#392—28no—
255#388—28no—
256#388—24no—
257#388—24no—
258#387—24no—
259#387—24no—
260#386—28no—
261#386—24no—
262#386—28no—
263#386—24no—
264#386—44no—
265#386—44no—
266#385—28no—
267#385—24no—
268#385—24no—
269#385—44no—
270#385—44no—
271#383—24no—
272#382—24no—
273#380—44no—
274#380—44no—
275#379—28no—
276#379—44no—
277#379—44no—
278C4×C4⋊C4—24no—
279C4×C22⋊C4—28no—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C25—24no—
315C25—24no—
316C25—24no—
317C25—24no—
318C25—24no—
319C25—24no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25#4118yes—
329C25C2411yescharacteristic
330C25C2411yescharacteristic
331C25C2412yes—
332C25C2412yes—
333C22×D4—232no—
334C22×D4—264no—
335C22×D4—264no—
336C22×D4—232no—
337C22×D4—232no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—41no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4C2×D414yes—
372C22×D4C2×D414yes—
373C22×D4#4118yes—
374C23×C4—24no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—41no—
394C23×C4—41no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4C2×D414yes—
412C23×C4C2×D418yes—
413C23×C4C2×D418yes—
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2412yes—
420C23×C4C2412yes—
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433#120—432no—
434C4×D4—264no—
435C4×D4—264no—
436C4×D4—232no—
437C4×D4—232no—
438C4×D4—232no—
439C4×D4—232no—
440C4×D4—432no—
441#117—232no—
442#117—232no—
443#117—416no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4C2×D414yes—
479C2×C4⋊C4C2×D414yes—
480C2×C4⋊C4C2×D414yes—
481C2×C4⋊C4C2×D414yes—
482C2×C22⋊C4—264no—
483C2×C22⋊C4—264no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
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—22no—
506C2×C22⋊C4—22no—
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—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—41no—
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⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4C2×D414yes—
576C2×C22⋊C4C2×D414yes—
577C2×C22⋊C4C2×D418yes—
578C2×C22⋊C4C2×D418yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—24no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—24no—
588C2×C42—42no—
589C2×C42—42no—
590C2×C42C2×D414yes—
591C2×C42C2×D414yes—
592C2×C42C2×D414yes—
593C2×C42C2×D414yes—
594#95—24no—
595#95—24no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—24no—
603#95—24no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—24no—
608#95—22no—
609#95—22no—
610#95—24no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—24no—
615#95—24no—
616#95—24no—
617#95—24no—
618#95—24no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95—42no—
628C24—216no—
629C24—216no—
630C24—216no—
631C24—216no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—21no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—21no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—21no—
665C24—216no—
666C24—216no—
667C24—216no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—22no—
672C24—22no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—22no—
677C24—21no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24C22×D412yes—
707C24C22×D414yes—
708C24C22×D414yes—
709C24C2×#4114yes—
710C24C2×#4114yes—
711C24C2×#4114yes—
712C24C2×#4114yes—
713C24C2×#4114yes—
714C24H(5,𝔽2)12yes—
715C24C2511yescharacteristic
716C2×D4—216no—
717C2×D4—2256no—
718C2×D4—216no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—216no—
724C2×D4—216no—
725C2×D4—216no—
726C2×D4—216no—
727C2×D4—216no—
728C2×D4—216no—
729C2×D4—216no—
730C2×D4—216no—
731C2×D4—216no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—216no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—44no—
745C2×D4—48no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—84no—
749C2×D4—84no—
750C2×D4—82no—
751C2×D4—84no—
752C2×D4—84no—
753C22×C4—216no—
754C22×C4—216no—
755C22×C4—28no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
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—21no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—216no—
805C22×C4—216no—
806C22×C4—216no—
807C22×C4—216no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—22no—
857C22×C4—21no—
858C22×C4—22no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—84no—
870C22×C4—84no—
871C22×C4—84no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—84no—
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×C4C22×D414yes—
890C22×C4C22×D414yes—
891C22×C4C22×D412yes—
892C22×C4C22×D412yes—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D412yes—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D412yes—
902C22×C4C22×D412yes—
903C22×C4C2×#4114yes—
904C22×C4H(5,𝔽2)14yes—
905C22×C4H(5,𝔽2)12yes—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—82no—
917C4⋊C4—82no—
918C4⋊C4—84no—
919C4⋊C4—82no—
920C22⋊C4—216no—
921C22⋊C4—216no—
922C22⋊C4—216no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—216no—
926C22⋊C4—216no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—84no—
945C22⋊C4—82no—
946C22⋊C4—84no—
947C22⋊C4—84no—
948C22⋊C4—82no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C42—216no—
954C42—28no—
955C42—48no—
956C42—44no—
957C42#120116yescomplemented
958C23—264no—
959C23—22no—
960C23—24no—
961C23—24no—
962C23—22no—
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—22no—
980C23—24no—
981C23—24no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—22no—
992C23—22no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—24no—
1011C23—24no—
1012C23—42no—
1013C23—41no—
1014C23—42no—
1015C23—41no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—41no—
1055C23—41no—
1056C23—42no—
1057C23—41no—
1058C23—42no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—41no—
1066C23—41no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—816no—
1073C23—816no—
1074C23—816no—
1075C23—816no—
1076C23—816no—
1077C23—816no—
1078C23—816no—
1079C23—816no—
1080C23—816no—
1081C23—816no—
1082C23—816no—
1083C23—816no—
1084C23—816no—
1085C23—816no—
1086C23#52514yes—
1087C23#52518yes—
1088C23#52518yes—
1089C23C23×D411yescharacteristic
1090C23C23×D411yescharacteristic
1091C23C23×D411yescharacteristic
1092C23C22×#4112yes—
1093C23C22×#4112yes—
1094C23C2×H(5,𝔽2)11yescharacteristic
1095C23C2×H(5,𝔽2)11yescharacteristic
1096C23C2×H(5,𝔽2)12yes—
1097C23#58511yescharacteristic
1098C23#58511yescharacteristic
1099C23#58512yes—
1100D4—232no—
1101D4—232no—
1102D4—264no—
1103D4—432no—
1104D4—88no—
1105D4—816no—
1106C2×C4—232no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—416no—
1144C2×C4—41no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—816no—
1218C2×C4—816no—
1219C2×C4—816no—
1220C2×C4—816no—
1221C2×C4C2×#12014yes—
1222C2×C4C2×#12014yes—
1223C2×C4C2×#12014yes—
1224C2×C4#52514yes—
1225C22—24no—
1226C22—28no—
1227C22—28no—
1228C22—28no—
1229C22—24no—
1230C22—28no—
1231C22—24no—
1232C22—28no—
1233C22—28no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—42no—
1247C22—44no—
1248C22—44no—
1249C22—42no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—42no—
1259C22—44no—
1260C22—44no—
1261C22—42no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—42no—
1268C22—42no—
1269C22—44no—
1270C22—42no—
1271C22—864no—
1272C22—81no—
1273C22—82no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—82no—
1278C22C22×#12011yescharacteristic
1279C22C2×#52512yes—
1280C22C2×#52511yescharacteristic
1281C22C2×#52511yescharacteristic
1282C22C2×#52512yes—
1283C22#348411yescharacteristic
1284C22#348511yescharacteristic
1285C22#348812yes—
1286C22#348811yescharacteristic
1287C22#348811yescharacteristic
1288C22#348811yescharacteristic
1289C22#348811yescharacteristic
1290C22#349012yes—
1291C22#349112yes—
1292C22#349612yes—
1293C22#349811yescharacteristic
1294C22#350011yescharacteristic
1295C22#350512yes—
1296C22#350512yes—
1297C22#351312yes—
1298C22#351412yes—
1299C22#351912yes—
1300C22#352112yes—
1301C4—24no—
1302C4—24no—
1303C4—24no—
1304C4—24no—
1305C4—44no—
1306C4—42no—
1307C4—44no—
1308C4—42no—
1309C4—44no—
1310C4—42no—
1311C4—81no—
1312C4—82no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—82no—
1318C4—81no—
1319C4—82no—
1320C2—48no—
1321C2—48no—
1322C2—44no—
1323C2—82no—
1324C2#3535212yes—
1325C2#3544912yes—
1326C2#3551211yescharacteristic
1327C2#3551311yescharacteristic
1328C2#3568311yescharacteristic
1329C2#3575311yescharacteristic
1330C2#3576212yes—
1331C2#3577712yes—
1332C2#3598211yescharacteristic
1333C2#3600411yescharacteristic
1334C2#3661411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14715C2
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×#518C2semidirect
2. C2×#2609C2semidirect
3. C2×#2598C2semidirect
4. C2×#2392C2semidirect
5. #14906C2semidirect
6. #14905C2semidirect
7. #14860C2semidirect
8. #14801C2semidirect
9. #14796C2semidirect
10. #14795C2semidirect
11. #14733C2semidirect
12. #14732C2semidirect
13. #14726C2semidirect
14. #14725C2semidirect
15. #14724C2semidirect
17. #14345C2semidirect
18. #14173C2semidirect
19. #14171C2semidirect
20. #13991C2semidirect
21. #13967C2semidirect
22. #13938C2semidirect
23. #13905C2semidirect
35. C22×C4×D4C22semidirect
38. C22×#117C22semidirect
43. C2×#400C22semidirect
44. C2×#399C22semidirect
46. C2×#398C22semidirect
47. C2×#398C22semidirect
48. C2×#397C22semidirect
50. C2×#396C22semidirect
51. C2×#396C22semidirect
56. C2×#394C22semidirect
61. C2×#388C22semidirect
62. C2×#388C22semidirect
63. C2×#387C22semidirect
64. C2×#387C22semidirect
67. C2×#386C22semidirect
68. C2×#386C22semidirect
69. C2×#386C22semidirect
70. C2×#386C22semidirect
72. C2×#385C22semidirect
73. C2×#385C22semidirect
74. C2×#385C22semidirect
75. C2×#385C22semidirect
76. C2×#383C22semidirect
77. C2×#382C22semidirect
78. C2×#380C22semidirect
79. C2×#380C22semidirect
83. C2×C4×C4⋊C4C22semidirect
84. C2×C4×C22⋊C4C22semidirect
85. #1445C22semidirect
86. #1445C22semidirect
87. #1445C22semidirect
88. #1445C22semidirect
89. #1441C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. #1434C22semidirect
120. #1434C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
127. C22⋊#95C22semidirect
128. C22⋊#95C22semidirect
170. C2×C4×D4D4semidirect
171. C2×C4×D4D4semidirect
180. C2×#117D4semidirect
957. C42#120semidirect

Maximal subgroups

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

subgroupindex
C22×#5182
C2×#26092
C2×#25982
C2×#23922
#149062
#149052
#148602
#148012
#147962
#147952
#147332
#147322
#147262
#147252
#147242
#147152
#143452
#141732
#141712
#139912
#139672
#139382
#139052