Finite Group Databasebeta

← #644680

Subgroups — #644680

Order 512.

5756 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×#525C211yesmaximal, characteristic, complemented
2C2×#2630C212yesmaximal, complemented
3C2×C4×#120C211yesmaximal, characteristic, complemented
4#16265C211yesmaximal, characteristic, complemented
5#16264C211yesmaximal, characteristic, complemented
6#16261C211yesmaximal, characteristic, complemented
7#16260C211yesmaximal, characteristic, complemented
8#16255C212yesmaximal, complemented
9#16249C212yesmaximal, complemented
10#15001C211yesmaximal, characteristic, complemented
11#14996C211yesmaximal, characteristic, complemented
12#14892C211yesmaximal, characteristic, complemented
13#14889C211yesmaximal, characteristic, complemented
14#14888C211yesmaximal, characteristic, complemented
15#14885C211yesmaximal, characteristic, complemented
16#14733C212yesmaximal, complemented
17#14732C212yesmaximal, complemented
18#14723C211yesmaximal, characteristic, complemented
19#14722C211yesmaximal, characteristic, complemented
20#14680C211yesmaximal, characteristic, complemented
21#14287C212yesmaximal, complemented
22#14173C212yesmaximal, complemented
23#14171C212yesmaximal, complemented
24C23×#41C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C2×#525—28no—
27C2×#525—216no—
28C22×#123C2212yes—
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C22×#120C2211yescharacteristic
34C22×#120C2212yes—
35C22×C4×D4C2212yes—
36C22×C4×D4C2212yes—
37C22×C4×D4C2211yescharacteristic
38C22×C4×D4C2211yescharacteristic
39C22×C4×D4C2211yescharacteristic
40C22×#117C2211yescharacteristic
41#2630—216no—
42C2×#398C2212yescomplemented
43C2×#397C2212yes—
44C2×#396C2212yescomplemented
45C2×#396C2212yescomplemented
46C2×#395C2211yescharacteristic, complemented
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2212yes—
50C2×#394C2212yes—
51C2×#394C2212yescomplemented
52C2×#394C2211yescharacteristic, complemented
53C2×#393C2211yescharacteristic, complemented
54C2×#392C2212yes—
55C2×#392C2212yes—
56C2×#392C2212yes—
57C2×#392C2211yescharacteristic, complemented
58C4×#120—28no—
59C2×#388C2212yescomplemented
60C2×#387C2212yescomplemented
61C2×#386C2211yescharacteristic
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2212yescomplemented
65C2×#386C2212yescomplemented
66C2×#385C2211yescharacteristic
67C2×#385C2211yescharacteristic
68C2×#385C2211yescharacteristic
69C2×#385C2212yescomplemented
70C2×#385C2212yescomplemented
71C2×#380C2212yes—
72C2×#380C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×#380C2212yes—
75C2×#379C2211yescharacteristic
76C2×#379C2212yes—
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80#1446C2211yescharacteristic, complemented
81#1446C2211yescharacteristic, complemented
82#1444C2211yescharacteristic, complemented
83#1444C2211yescharacteristic, complemented
84#1442C2211yescharacteristic, complemented
85#1442C2211yescharacteristic, complemented
86#1441C2211yescharacteristic, complemented
87#1441C2211yescharacteristic, complemented
88#1441C2212yescomplemented
89#1441C2212yescomplemented
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yes—
93#1440C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2211yescharacteristic, complemented
99#1439C2211yescharacteristic, complemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1438C2211yescharacteristic, complemented
111#1438C2211yescharacteristic, complemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119#1436C2212yescomplemented
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C22×#41—28no—
129C22×#41—24no—
130C22×#41—44no—
131C22×#41—42no—
132C22×#41—42no—
133C23×Q8C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C24×C4—28no—
143C24×C4—42no—
144C24×C4—42no—
145C24×C4—44no—
146C24×C4D418yescomplemented
147C24×C4C2311yescharacteristic
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155#525—2128no—
156C2×#123—28no—
157C2×#123—28no—
158C2×#123D4116yescomplemented
159C2×C22⋊Q8—24no—
160C2×C22⋊Q8—24no—
161C2×C22⋊Q8—28no—
162C2×C22⋊Q8—28no—
163C2×#121—24no—
164C2×#121—24no—
165C2×#121—28no—
166C2×#121—28no—
167C2×#120—28no—
168C2×#120—24no—
169C2×#120—28no—
170C2×#120—24no—
171C2×#120—28no—
172C2×#120—24no—
173C2×C4×D4—28no—
174C2×C4×D4—28no—
175C2×C4×D4—28no—
176C2×C4×D4—24no—
177C2×C4×D4—24no—
178C2×C4×D4—24no—
179C2×C4×D4—28no—
180C2×C4×D4—28no—
181C2×C4×D4—28no—
182C2×C4×D4—28no—
183C2×C4×D4—44no—
184C2×C4×D4—42no—
185C2×C4×D4—42no—
186C2×#117—24no—
187C2×#117—28no—
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C42C2312yes—
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237#398—28no—
238#397—28no—
239#396—28no—
240#396—28no—
241#395—42no—
242#394—28no—
243#394—28no—
244#394—28no—
245#394—28no—
246#394—42no—
247#394—44no—
248#393—42no—
249#392—28no—
250#392—28no—
251#392—42no—
252#392—44no—
253#388—28no—
254#387—28no—
255#386—24no—
256#386—24no—
257#386—24no—
258#386—28no—
259#386—44no—
260#385—24no—
261#385—24no—
262#385—24no—
263#385—28no—
264#385—44no—
265#380—28no—
266#380—44no—
267#380—42no—
268#380—42no—
269#379—24no—
270#379—44no—
271C4×C22⋊C4—24no—
272C4×C22⋊C4—24no—
273C4×C22⋊C4—24no—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C25—24no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—41no—
312C25—41no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25C2×D414yes—
317C25C2412yes—
318C25C2411yescharacteristic
319C25C2411yescharacteristic
320C25C2411yescharacteristic
321C25C2411yescharacteristic
322C2×#41—232no—
323C2×#41—432no—
324C2×#41—432no—
325C2×#41—416no—
326C2×#41—416no—
327C22×Q8—24no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—42no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—24no—
350C22×D4—22no—
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—41no—
362C22×D4—42no—
363C22×D4—41no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
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×D4C2×D418yes—
381C22×D4#4114yescomplemented
382C23×C4—24no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—232no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—24no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—416no—
405C23×C4—416no—
406C23×C4—42no—
407C23×C4—41no—
408C23×C4—41no—
409C23×C4—41no—
410C23×C4—41no—
411C23×C4—42no—
412C23×C4—41no—
413C23×C4—41no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—41no—
418C23×C4—42no—
419C23×C4—41no—
420C23×C4—432no—
421C23×C4—432no—
422C23×C4C2×D414yes—
423C23×C4C2×D414yes—
424C23×C4C2×D414yes—
425C23×C4C2×D414yes—
426C23×C4C2×D414yes—
427C23×C4C2×D414yes—
428C23×C4C2×D418yes—
429C23×C4C2412yes—
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2412yes—
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447#123—264no—
448C22⋊Q8—232no—
449C22⋊Q8—232no—
450#121—232no—
451#121—232no—
452#120—232no—
453#120—264no—
454C4×D4—264no—
455C4×D4—264no—
456C4×D4—416no—
457C4×D4—416no—
458C4×D4—416no—
459#117—232no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4C2×D418yes—
491C2×C4⋊C4C2×D418yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
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—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
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—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—41no—
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⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4C2×D418yes—
582C2×C22⋊C4C2×D418yes—
583C2×C22⋊C4C2×D418yes—
584C2×C22⋊C4#4114yescomplemented
585C2×C42—24no—
586C2×C42—24no—
587C2×C42—24no—
588C2×C42—22no—
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—24no—
592C2×C42—41no—
593C2×C42—42no—
594C2×C42—41no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627C24—22no—
628C24—22no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—22no—
638C24—22no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—28no—
653C24—28no—
654C24—28no—
655C24—22no—
656C24—21no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—21no—
662C24—21no—
663C24—22no—
664C24—21no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—21no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24—44no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—44no—
688C24—44no—
689C24—44no—
690C24—44no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24C22×D414yes—
700C24C22×D412yes—
701C24C22×D414yes—
702C24C22×D412yes—
703C24C22×D412yes—
704C24C2×#4112yes—
705C24C2×#4112yes—
706C24C2×#4112yes—
707C24H(5,𝔽2)12yes—
708C242−1+412yes—
709C24C2511yescharacteristic
710#41—4128no—
711C2×Q8—28no—
712C2×Q8—48no—
713C2×Q8—48no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×D4—216no—
717C2×D4—216no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—216no—
722C2×D4—28no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—44no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—44no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—44no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—44no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C22×C4—216no—
767C22×C4—216no—
768C22×C4—28no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—216no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—28no—
819C22×C4—28no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—48no—
887C22×C4—48no—
888C22×C4—48no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—4128no—
892C22×C4—48no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—48no—
896C22×C4—44no—
897C22×C4—84no—
898C22×C4—84no—
899C22×C4#120116yes—
900C22×C4C22×D414yes—
901C22×C4C22×D414yes—
902C22×C4C22×D414yes—
903C22×C4C22×D414yes—
904C22×C4C22×D412yes—
905C22×C4C22×D412yes—
906C22×C4C22×D414yes—
907C22×C4C22×D412yes—
908C22×C4C22×D412yes—
909C22×C4C2×#4112yes—
910C22×C4C2×#4112yes—
911C22×C4C2×#4112yes—
912C22×C4H(5,𝔽2)14yes—
913C22×C4H(5,𝔽2)12yes—
914C22×C4H(5,𝔽2)12yes—
915C4⋊C4—28no—
916C4⋊C4—28no—
917C4⋊C4—216no—
918C4⋊C4—216no—
919C4⋊C4—48no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—84no—
924C4⋊C4—84no—
925C4⋊C4—84no—
926C4⋊C4—84no—
927C22⋊C4—216no—
928C22⋊C4—216no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—216no—
932C22⋊C4—28no—
933C22⋊C4—216no—
934C22⋊C4—216no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C22⋊C4—84no—
958C22⋊C4—84no—
959C22⋊C4—84no—
960C42—216no—
961C42—44no—
962C42—44no—
963C42—44no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—22no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—22no—
1015C23—22no—
1016C23—416no—
1017C23—416no—
1018C23—416no—
1019C23—416no—
1020C23—416no—
1021C23—416no—
1022C23—416no—
1023C23—432no—
1024C23—432no—
1025C23—432no—
1026C23—432no—
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—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—41no—
1054C23—42no—
1055C23—41no—
1056C23—41no—
1057C23—42no—
1058C23—42no—
1059C23—41no—
1060C23—42no—
1061C23—41no—
1062C23—41no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—41no—
1083C23—42no—
1084C23—41no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23C2×#12014yes—
1100C23#52514yes—
1101C23#53714yes—
1102C23C23×D411yescharacteristic
1103C23C23×D412yes—
1104C23C22×#4111yescharacteristic
1105C23C22×#4111yescharacteristic
1106C23C2×H(5,𝔽2)12yes—
1107C23C2×H(5,𝔽2)11yescharacteristic
1108C23C2×H(5,𝔽2)11yescharacteristic
1109C23C2×H(5,𝔽2)11yescharacteristic
1110C23C2×2−1+411yescharacteristic
1111C23#58512yes—
1112C23#58512yes—
1113Q8—416no—
1114D4—416no—
1115D4—416no—
1116D4—416no—
1117D4—432no—
1118D4—416no—
1119D4—432no—
1120D4—432no—
1121D4—816no—
1122C2×C4—232no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—416no—
1156C2×C4—416no—
1157C2×C4—416no—
1158C2×C4—416no—
1159C2×C4—416no—
1160C2×C4—432no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
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—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—88no—
1232C2×C4C2×#12014yes—
1233C2×C4C2×#12014yes—
1234C2×C4#53414yes—
1235C2×C4#53414yes—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—24no—
1245C22—464no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—42no—
1271C22—42no—
1272C22—44no—
1273C22—44no—
1274C22—42no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—82no—
1283C22—82no—
1284C22—81no—
1285C22—82no—
1286C22—81no—
1287C22—82no—
1288C22—81no—
1289C22—81no—
1290C22—82no—
1291C22—82no—
1292C22—82no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22C22×#12011yescharacteristic
1297C22C2×#52511yescharacteristic
1298C22C2×#53411yescharacteristic
1299C22C2×#53411yescharacteristic
1300C22C2×#53711yescharacteristic
1301C22#344911yescharacteristic
1302C22#344911yescharacteristic
1303C22#345912yes—
1304C22#346012yes—
1305C22D4×#4112yes—
1306C22D4×#4112yes—
1307C22#348412yes—
1308C22#348412yes—
1309C22#348812yes—
1310C22#348912yes—
1311C22#351911yescharacteristic
1312C22#351911yescharacteristic
1313C22#352011yescharacteristic
1314C22#352011yescharacteristic
1315C22#353912yes—
1316C22#354012yes—
1317C22#354112yes—
1318C22#354212yes—
1319C4—24no—
1320C4—24no—
1321C4—24no—
1322C4—24no—
1323C4—42no—
1324C4—42no—
1325C4—44no—
1326C4—44no—
1327C4—42no—
1328C4—44no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—82no—
1334C4—82no—
1335C4—82no—
1336C4—82no—
1337C2—44no—
1338C2—44no—
1339C2—44no—
1340C2—82no—
1341C2—84no—
1342C2#3456211yescharacteristic
1343C2#3473611yescharacteristic
1344C2#3498011yescharacteristic
1345C2#3507711yescharacteristic
1346C2#3525111yescharacteristic
1347C2#3744411yescharacteristic
1348C2#3745511yescharacteristic
1349C2#3782412yes—
1350C2#3782512yes—
1351C2#3782612yes—
1352C2#3782712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#525C2semidirect
2. C2×#2630C2semidirect
3. C2×C4×#120C2semidirect
4. #16265C2semidirect
5. #16264C2semidirect
6. #16261C2semidirect
7. #16260C2semidirect
8. #16255C2semidirect
9. #16249C2semidirect
10. #15001C2semidirect
11. #14996C2semidirect
12. #14892C2semidirect
13. #14889C2semidirect
14. #14888C2semidirect
15. #14885C2semidirect
16. #14733C2semidirect
17. #14732C2semidirect
18. #14723C2semidirect
19. #14722C2semidirect
20. #14680C2semidirect
21. #14287C2semidirect
22. #14173C2semidirect
23. #14171C2semidirect
42. C2×#398C22semidirect
44. C2×#396C22semidirect
45. C2×#396C22semidirect
46. C2×#395C22semidirect
51. C2×#394C22semidirect
52. C2×#394C22semidirect
53. C2×#393C22semidirect
57. C2×#392C22semidirect
59. C2×#388C22semidirect
60. C2×#387C22semidirect
64. C2×#386C22semidirect
65. C2×#386C22semidirect
69. C2×#385C22semidirect
70. C2×#385C22semidirect
80. #1446C22semidirect
81. #1446C22semidirect
82. #1444C22semidirect
83. #1444C22semidirect
84. #1442C22semidirect
85. #1442C22semidirect
86. #1441C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. #1436C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
146. C24×C4D4semidirect
158. C2×#123D4semidirect
381. C22×D4#41semidirect
584. C2×C22⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5252
C2×#26302
C2×C4×#1202
#162652
#162642
#162612
#162602
#162552
#162492
#150012
#149962
#148922
#148892
#148882
#148852
#147332
#147322
#147232
#147222
#146802
#142872
#141732
#141712