Finite Group Databasebeta

← #644688

Subgroups — #644688

Order 512.

5700 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#525C211yesmaximal, characteristic, complemented
2C2×#2638C211yesmaximal, characteristic, complemented
3C2×#2635C211yesmaximal, characteristic, complemented
4C2×C4×#120C211yesmaximal, characteristic, complemented
5#16601C211yesmaximal, characteristic, complemented
6#16600C211yesmaximal, characteristic, complemented
7#16501C211yesmaximal, characteristic, complemented
8#16500C211yesmaximal, characteristic, complemented
9#16255C212yesmaximal, complemented
10#16249C212yesmaximal, complemented
11#14964C212yesmaximal, complemented
12#14906C211yesmaximal, characteristic, complemented
13#14905C211yesmaximal, characteristic, complemented
14#14889C211yesmaximal, characteristic, complemented
15#14885C211yesmaximal, characteristic, complemented
16#14731C212yesmaximal, complemented
17#14730C212yesmaximal, complemented
18#14721C212yesmaximal, complemented
19#14681C211yesmaximal, characteristic, complemented
20#14292C211yesmaximal, characteristic, complemented
21#14290C211yesmaximal, characteristic, complemented
22#14173C212yesmaximal, complemented
23#14171C212yesmaximal, complemented
24C23×#41C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C2×#525—28no—
27C2×#525—28no—
28C2×#525—28no—
29C22×#123C2212yes—
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C22×#120C2211yescharacteristic
35C22×#120C2212yes—
36C22×C4×D4C2211yescharacteristic
37C22×C4×D4C2212yes—
38C22×C4×D4C2212yes—
39C22×C4×D4C2211yescharacteristic
40C22×C4×D4C2211yescharacteristic
41C22×#117C2211yescharacteristic
42#2638—28no—
43#2635—28no—
44C2×#400C2211yescharacteristic, complemented
45C2×#399C2211yescharacteristic, complemented
46C2×#398C2211yescharacteristic, complemented
47C2×#397C2212yes—
48C2×#397C2211yescharacteristic, complemented
49C2×#395C2211yescharacteristic, complemented
50C2×#394C2212yes—
51C2×#394C2212yes—
52C2×#394C2212yes—
53C2×#394C2212yes—
54C2×#394C2211yescharacteristic, complemented
55C2×#393C2211yescharacteristic, complemented
56C2×#392C2212yes—
57C2×#392C2212yes—
58C2×#392C2212yes—
59C2×#392C2211yescharacteristic, complemented
60C4×#120—28no—
61C2×#388C2212yescomplemented
62C2×#387C2212yescomplemented
63C2×#386C2211yescharacteristic
64C2×#386C2211yescharacteristic
65C2×#386C2211yescharacteristic
66C2×#386C2212yescomplemented
67C2×#386C2212yescomplemented
68C2×#385C2211yescharacteristic
69C2×#385C2211yescharacteristic
70C2×#385C2211yescharacteristic
71C2×#385C2212yescomplemented
72C2×#385C2212yescomplemented
73C2×#381C2211yescharacteristic
74C2×#381C2211yescharacteristic
75C2×#381C2212yes—
76C2×#379C2211yescharacteristic
77C2×#379C2212yes—
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81#1446C2211yescharacteristic, complemented
82#1446C2211yescharacteristic, complemented
83#1445C2211yescharacteristic, complemented
84#1445C2211yescharacteristic, complemented
85#1445C2211yescharacteristic, complemented
86#1445C2211yescharacteristic, complemented
87#1444C2212yescomplemented
88#1442C2212yescomplemented
89#1441C2212yescomplemented
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yes—
93#1440C2212yes—
94#1440C2212yescomplemented
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yescomplemented
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#1438C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1437C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119#1436C2212yescomplemented
120#1436C2212yescomplemented
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2212yescomplemented
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—24no—
133C22×#41—44no—
134C22×#41—44no—
135C23×Q8C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C23×D4C2312yes—
143C23×D4C2311yescharacteristic
144C24×C4—24no—
145C24×C4—24no—
146C24×C4—44no—
147C24×C4—44no—
148C24×C4D418yescomplemented
149C24×C4C2311yescharacteristic
150C24×C4C2312yes—
151C24×C4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2311yescharacteristic
156C24×C4C2311yescharacteristic
157#525—2128no—
158C2×#123—28no—
159C2×#123—28no—
160C2×#123—28no—
161C2×C22⋊Q8—24no—
162C2×C22⋊Q8—24no—
163C2×C22⋊Q8—24no—
164C2×C22⋊Q8—24no—
165C2×C22⋊Q8—24no—
166C2×C22⋊Q8D418yescomplemented
167C2×#121—24no—
168C2×#121—24no—
169C2×#121—24no—
170C2×#121—24no—
171C2×#121—24no—
172C2×#121D418yescomplemented
173C2×#120—28no—
174C2×#120—24no—
175C2×#120—28no—
176C2×#120—24no—
177C2×#120—28no—
178C2×#120—24no—
179C2×C4×D4—28no—
180C2×C4×D4—28no—
181C2×C4×D4—28no—
182C2×C4×D4—24no—
183C2×C4×D4—24no—
184C2×C4×D4—24no—
185C2×C4×D4—24no—
186C2×C4×D4—24no—
187C2×C4×D4—28no—
188C2×C4×D4—28no—
189C2×C4×D4—28no—
190C2×C4×D4—44no—
191C2×C4×D4—44no—
192C2×#117—24no—
193C2×#117—24no—
194C2×#117—24no—
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C42C2312yes—
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242#400—24no—
243#399—24no—
244#398—24no—
245#397—24no—
246#397—28no—
247#395—24no—
248#394—28no—
249#394—24no—
250#394—28no—
251#394—28no—
252#394—44no—
253#393—24no—
254#392—28no—
255#392—24no—
256#392—28no—
257#392—44no—
258#388—28no—
259#387—28no—
260#386—24no—
261#386—24no—
262#386—24no—
263#386—28no—
264#386—44no—
265#385—24no—
266#385—24no—
267#385—24no—
268#385—28no—
269#385—44no—
270#381—24no—
271#381—24no—
272#381—44no—
273#379—24no—
274#379—44no—
275C4×C22⋊C4—24no—
276C4×C22⋊C4—24no—
277C4×C22⋊C4—24no—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—24no—
317C25—42no—
318C25—42no—
319C25—41no—
320C25—41no—
321C25—42no—
322C25C2×D414yes—
323C25C2412yes—
324C25C2411yescharacteristic
325C25C2411yescharacteristic
326C25C2411yescharacteristic
327C25C2411yescharacteristic
328C2×#41—232no—
329C2×#41—432no—
330C2×#41—432no—
331C2×#41—416no—
332C2×#41—416no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—42no—
336C22×Q8—42no—
337C22×Q8C2×D414yes—
338C22×D4—24no—
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—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—22no—
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—41no—
375C22×D4—41no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4C2×D418yes—
386C22×D4C2×D414yes—
387C22×D4#4114yescomplemented
388C23×C4—24no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—24no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—232no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—22no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—416no—
413C23×C4—416no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—42no—
425C23×C4—432no—
426C23×C4—432no—
427C23×C4C2×D414yes—
428C23×C4C2×D414yes—
429C23×C4C2×D414yes—
430C23×C4C2×D414yes—
431C23×C4C2×D414yes—
432C23×C4C2×D414yes—
433C23×C4C2×D414yes—
434C23×C4C2×D414yes—
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2412yes—
438C23×C4C2412yes—
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2411yescharacteristic
446C23×C4C2412yes—
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453#123—264no—
454C22⋊Q8—232no—
455C22⋊Q8—232no—
456#121—232no—
457#121—232no—
458#120—232no—
459#120—264no—
460C4×D4—264no—
461C4×D4—264no—
462C4×D4—416no—
463C4×D4—416no—
464C4×D4—416no—
465#117—232no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—24no—
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—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4C2×D414yes—
492C2×C4⋊C4C2×D414yes—
493C2×C4⋊C4C2×D418yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
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—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
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—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
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—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—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
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⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4C2×D418yes—
585C2×C22⋊C4C2×D418yes—
586C2×C22⋊C4#4114yescomplemented
587C2×C42—24no—
588C2×C42—24no—
589C2×C42—24no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—22no—
595C2×C42—42no—
596C2×C42—42no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—24no—
604#95—24no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—24no—
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—
628#95—42no—
629#95—42no—
630#95—42no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—21no—
647C24—21no—
648C24—22no—
649C24—21no—
650C24—21no—
651C24—22no—
652C24—21no—
653C24—21no—
654C24—22no—
655C24—22no—
656C24—28no—
657C24—28no—
658C24—28no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—21no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—21no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—21no—
683C24—44no—
684C24—44no—
685C24—44no—
686C24—44no—
687C24—48no—
688C24—48no—
689C24—44no—
690C24—44no—
691C24—44no—
692C24—44no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—48no—
700C24—48no—
701C24—48no—
702C24—48no—
703C24C22×D414yes—
704C24C22×D412yes—
705C24C22×D412yes—
706C24C22×D412yes—
707C24C22×D412yes—
708C24C22×D412yes—
709C24C2×#4112yes—
710C24C2×#4112yes—
711C24C2×#4112yes—
712C24H(5,𝔽2)14yes—
713C24C2511yescharacteristic
714#41—4128no—
715C2×Q8—28no—
716C2×Q8—48no—
717C2×Q8—44no—
718C2×Q8—44no—
719C2×Q8—48no—
720C2×D4—216no—
721C2×D4—216no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—216no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—44no—
732C2×D4—48no—
733C2×D4—44no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—44no—
760C2×D4—48no—
761C2×D4—44no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—84no—
769C2×D4—84no—
770C22×C4—216no—
771C22×C4—216no—
772C22×C4—28no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—216no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—28no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
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—48no—
892C22×C4—48no—
893C22×C4—4128no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—48no—
900C22×C4—44no—
901C22×C4—84no—
902C22×C4—84no—
903C22×C4#120116yes—
904C22×C4C22×D414yes—
905C22×C4C22×D414yes—
906C22×C4C22×D412yes—
907C22×C4C22×D414yes—
908C22×C4C22×D412yes—
909C22×C4C22×D412yes—
910C22×C4C22×D412yes—
911C22×C4C22×D412yes—
912C22×C4C22×D412yes—
913C22×C4C22×D412yes—
914C22×C4C22×D412yes—
915C22×C4C2×#4112yes—
916C22×C4C2×#4112yes—
917C22×C4C2×#4112yes—
918C22×C4H(5,𝔽2)14yes—
919C4⋊C4—216no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—216no—
923C4⋊C4—48no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—84no—
928C4⋊C4—84no—
929C22⋊C4—216no—
930C22⋊C4—216no—
931C22⋊C4—216no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—216no—
935C22⋊C4—28no—
936C22⋊C4—216no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
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—
960C22⋊C4—84no—
961C22⋊C4—84no—
962C42—216no—
963C42—44no—
964C42—44no—
965C42—44no—
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—22no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
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—24no—
1009C23—22no—
1010C23—24no—
1011C23—22no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—416no—
1019C23—416no—
1020C23—416no—
1021C23—416no—
1022C23—416no—
1023C23—416no—
1024C23—416no—
1025C23—432no—
1026C23—432no—
1027C23—432no—
1028C23—432no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
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—42no—
1055C23—41no—
1056C23—42no—
1057C23—41no—
1058C23—41no—
1059C23—42no—
1060C23—42no—
1061C23—41no—
1062C23—42no—
1063C23—42no—
1064C23—41no—
1065C23—42no—
1066C23—41no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—41no—
1074C23—41no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
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—
1099C23—42no—
1100C23—42no—
1101C23C2×#12014yes—
1102C23#52514yes—
1103C23#53414yes—
1104C23C23×D411yescharacteristic
1105C23C23×D411yescharacteristic
1106C23C23×D411yescharacteristic
1107C23C22×#4111yescharacteristic
1108C23C22×#4111yescharacteristic
1109C23C2×H(5,𝔽2)12yes—
1110C23C2×H(5,𝔽2)12yes—
1111C23#58512yes—
1112C23#58511yescharacteristic
1113C23#58511yescharacteristic
1114C23#58512yes—
1115Q8—416no—
1116D4—416no—
1117D4—416no—
1118D4—432no—
1119D4—432no—
1120D4—416no—
1121D4—416no—
1122D4—432no—
1123D4—816no—
1124C2×C4—232no—
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—22no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—416no—
1157C2×C4—416no—
1158C2×C4—416no—
1159C2×C4—416no—
1160C2×C4—416no—
1161C2×C4—432no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
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—41no—
1196C2×C4—41no—
1197C2×C4—41no—
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—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—88no—
1235C2×C4C2×#12014yes—
1236C2×C4C2×#12014yes—
1237C2×C4#53414yes—
1238C22—24no—
1239C22—24no—
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—24no—
1245C22—24no—
1246C22—24no—
1247C22—464no—
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—42no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—42no—
1283C22—42no—
1284C22—82no—
1285C22—81no—
1286C22—82no—
1287C22—81no—
1288C22—81no—
1289C22—82no—
1290C22—81no—
1291C22—82no—
1292C22—82no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22C22×#12011yescharacteristic
1299C22C2×#52511yescharacteristic
1300C22C2×#53411yescharacteristic
1301C22C2×#53411yescharacteristic
1302C22#344911yescharacteristic
1303C22#344911yescharacteristic
1304C22#344911yescharacteristic
1305C22#345912yes—
1306C22#346012yes—
1307C22D4×#4111yescharacteristic
1308C22D4×#4111yescharacteristic
1309C22D4×#4111yescharacteristic
1310C22D4×#4111yescharacteristic
1311C22#348412yes—
1312C22#348412yes—
1313C22#348512yes—
1314C22#348712yes—
1315C22#351312yes—
1316C22#351312yes—
1317C22#353312yes—
1318C22#353312yes—
1319C22#353912yes—
1320C22#354012yes—
1321C4—24no—
1322C4—24no—
1323C4—24no—
1324C4—42no—
1325C4—44no—
1326C4—42no—
1327C4—44no—
1328C4—44no—
1329C4—42no—
1330C4—42no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—82no—
1336C4—82no—
1337C4—82no—
1338C4—82no—
1339C2—44no—
1340C2—44no—
1341C2—44no—
1342C2—82no—
1343C2—84no—
1344C2#3456211yescharacteristic
1345C2#3473611yescharacteristic
1346C2#3498011yescharacteristic
1347C2#3506311yescharacteristic
1348C2#3514911yescharacteristic
1349C2#3744511yescharacteristic
1350C2#3745411yescharacteristic
1351C2#3780012yes—
1352C2#3780112yes—
1353C2#3780212yes—
1354C2#3780312yes—
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×#2638C2semidirect
3. C2×#2635C2semidirect
4. C2×C4×#120C2semidirect
5. #16601C2semidirect
6. #16600C2semidirect
7. #16501C2semidirect
8. #16500C2semidirect
9. #16255C2semidirect
10. #16249C2semidirect
11. #14964C2semidirect
12. #14906C2semidirect
13. #14905C2semidirect
14. #14889C2semidirect
15. #14885C2semidirect
16. #14731C2semidirect
17. #14730C2semidirect
18. #14721C2semidirect
19. #14681C2semidirect
20. #14292C2semidirect
21. #14290C2semidirect
22. #14173C2semidirect
23. #14171C2semidirect
44. C2×#400C22semidirect
45. C2×#399C22semidirect
46. C2×#398C22semidirect
48. C2×#397C22semidirect
49. C2×#395C22semidirect
54. C2×#394C22semidirect
55. C2×#393C22semidirect
59. C2×#392C22semidirect
61. C2×#388C22semidirect
62. C2×#387C22semidirect
66. C2×#386C22semidirect
67. C2×#386C22semidirect
71. C2×#385C22semidirect
72. C2×#385C22semidirect
81. #1446C22semidirect
82. #1446C22semidirect
83. #1445C22semidirect
84. #1445C22semidirect
85. #1445C22semidirect
86. #1445C22semidirect
87. #1444C22semidirect
88. #1442C22semidirect
89. #1441C22semidirect
94. #1440C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1437C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. #1436C22semidirect
120. #1436C22semidirect
127. C22⋊#95C22semidirect
128. C22⋊#95C22semidirect
148. C24×C4D4semidirect
166. C2×C22⋊Q8D4semidirect
172. C2×#121D4semidirect
387. C22×D4#41semidirect
586. 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×#26382
C2×#26352
C2×C4×#1202
#166012
#166002
#165012
#165002
#162552
#162492
#149642
#149062
#149052
#148892
#148852
#147312
#147302
#147212
#146812
#142922
#142902
#141732
#141712