Finite Group Databasebeta

← #617197

Subgroups — #617197

Order 512.

5034 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2437C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic, complemented
3C2×#2308C211yesmaximal, characteristic
4C22×#386C211yesmaximal, characteristic
5#15506C212yesmaximal, complemented
6#15439C212yesmaximal, complemented
7#15439C212yesmaximal, complemented
8#15429C212yesmaximal, complemented
9#15328C212yesmaximal, complemented
10#15327C212yesmaximal, complemented
11#15324C212yesmaximal, complemented
12#15323C212yesmaximal, complemented
13#14936C211yesmaximal, characteristic, complemented
14#14935C211yesmaximal, characteristic, complemented
15#14935C211yesmaximal, characteristic, complemented
16#14934C211yesmaximal, characteristic, complemented
17#14693C211yesmaximal, characteristic, complemented
18#14680C211yesmaximal, characteristic, complemented
19#14335C211yesmaximal, characteristic
20#14262C211yesmaximal, characteristic, complemented
21#14127C211yesmaximal, characteristic, complemented
22#13877C211yesmaximal, characteristic, complemented
23#13877C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic, complemented
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33#2626—28no—
34#2437—28no—
35C2×#399C2211yescharacteristic, complemented
36C2×#399C2212yescomplemented
37C2×#396C2211yescharacteristic, complemented
38C2×#396C2212yescomplemented
39C2×#396C2211yescharacteristic, complemented
40C2×#396C2212yescomplemented
41C2×#393C2211yescharacteristic, complemented
42C2×#393C2212yescomplemented
43#2308—28no—
44C2×#386—28no—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#385C2211yescharacteristic
54C2×#385C2211yescharacteristic
55C2×#385C2211yescharacteristic
56C2×#385C2211yescharacteristic
57C2×#385C2211yescharacteristic
58C2×#385C2211yescharacteristic
59C2×#385C2211yescharacteristic, complemented
60C2×#385C2211yescharacteristic, complemented
61C2×#385C2212yescomplemented
62C2×#385C2212yescomplemented
63C2×#385C2212yescomplemented
64C2×#385C2212yescomplemented
65C2×#381C2211yescharacteristic
66C2×#381C2211yescharacteristic
67C2×#381C2211yescharacteristic
68C2×#381C2211yescharacteristic
69C2×#380C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic, complemented
73C2×#380C2212yescomplemented
74C2×#380C2212yescomplemented
75C2×#380C2212yescomplemented
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×#379C2211yescharacteristic
82C22×#95C2211yescharacteristic
83C22×#95C2211yescharacteristic
84#1446C2212yescomplemented
85#1445C2212yescomplemented
86#1445C2212yescomplemented
87#1445C2212yescomplemented
88#1444C2212yescomplemented
89#1443C2212yescomplemented
90#1443C2212yescomplemented
91#1442C2212yescomplemented
92#1442C2212yescomplemented
93#1442C2212yescomplemented
94#1441C2212yescomplemented
95#1441C2212yescomplemented
96#1441C2212yescomplemented
97#1441C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yes—
113#1438C2212yes—
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2212yescomplemented
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—24no—
134C23×D4—42no—
135C23×D4—42no—
136C23×D4Q818yescomplemented
137C23×D4C2312yes—
138C23×D4C2312yes—
139C24×C4—24no—
140C24×C4—24no—
141C24×C4—44no—
142C24×C4—44no—
143C24×C4—42no—
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2312yes—
147C24×C4C2311yescharacteristic
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2312yes—
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8—24no—
156C2×C22⋊Q8—24no—
157C2×C22⋊Q8—42no—
158C2×C22⋊Q8—44no—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—42no—
184C22×C22⋊C4—42no—
185C22×C22⋊C4—42no—
186C22×C22⋊C4D418yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220#399—28no—
221#399—24no—
222#396—28no—
223#396—28no—
224#396—24no—
225#396—24no—
226#393—28no—
227#393—24no—
228#386—28no—
229#386—28no—
230#386—28no—
231#386—28no—
232#386—28no—
233#386—28no—
234#386—28no—
235#386—28no—
236#385—24no—
237#385—24no—
238#385—24no—
239#385—24no—
240#385—24no—
241#385—24no—
242#385—44no—
243#385—44no—
244#385—44no—
245#385—44no—
246#385—42no—
247#385—42no—
248#381—24no—
249#381—24no—
250#381—42no—
251#381—42no—
252#380—24no—
253#380—24no—
254#380—24no—
255#380—44no—
256#380—44no—
257#380—42no—
258#380—44no—
259#379—24no—
260#379—24no—
261#379—24no—
262#379—24no—
263#379—24no—
264#379D418yes—
265C2×#95—24no—
266C2×#95—24no—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
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—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25C2×D414yes—
320C25C2×D414yes—
321C25C2×Q814yes—
322C25C2×Q814yes—
323C25#4114yes—
324C25#4114yes—
325C25C2411yescharacteristic
326C25C2411yescharacteristic
327C25C2412yes—
328C25C2411yescharacteristic
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—42no—
332C22×Q8—41no—
333C22×Q8—42no—
334C22×D4—232no—
335C22×D4—232no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—416no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—416no—
350C22×D4—416no—
351C22×D4—416no—
352C22×D4—416no—
353C22×D4C2×Q818yes—
354C22×D4C2×Q818yes—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—24no—
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—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—22no—
372C23×C4—24no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—41no—
398C23×C4—41no—
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—416no—
411C23×C4—416no—
412C23×C4—432no—
413C23×C4—416no—
414C23×C4—432no—
415C23×C4C2×D414yes—
416C23×C4C2×D414yes—
417C23×C4C2×Q814yes—
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2412yes—
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2412yes—
435C23×C4C2412yes—
436C23×C4C2411yescharacteristic
437C22⋊Q8—416no—
438C22⋊Q8—416no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—41no—
459C2×C4⋊C4—41no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
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×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—416no—
529C2×C22⋊C4—416no—
530C2×C22⋊C4—416no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—416no—
549C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
567C2×C22⋊C4C2×D414yes—
568C2×C22⋊C4C2×D414yes—
569C2×C22⋊C4C2×D414yes—
570C2×C22⋊C4C2×D414yes—
571C2×C22⋊C4C2×D414yes—
572C2×C22⋊C4C2×D418yes—
573C2×C22⋊C4C2×D418yes—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—28no—
615C24—28no—
616C24—28no—
617C24—28no—
618C24—28no—
619C24—28no—
620C24—22no—
621C24—21no—
622C24—21no—
623C24—22no—
624C24—21no—
625C24—21no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—22no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—28no—
649C24—28no—
650C24—28no—
651C24—28no—
652C24—28no—
653C24—28no—
654C24—48no—
655C24—48no—
656C24—48no—
657C24—48no—
658C24—48no—
659C24—48no—
660C24—44no—
661C24—44no—
662C24—44no—
663C24—44no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—44no—
669C24—44no—
670C24—48no—
671C24—44no—
672C24—48no—
673C24—44no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24C22⋊Q8116yes—
687C24C22⋊Q8116yescomplemented
688C24C22×D412yes—
689C24C22×D414yes—
690C24C22×D412yes—
691C24C22×D412yes—
692C24C22×D412yes—
693C24C22×Q812yes—
694C24C22×Q812yes—
695C24C22×Q814yes—
696C24C22×Q812yes—
697C24C2×#4112yes—
698C24C2×#4112yes—
699C24C2×#4114yes—
700C24C2×#4112yes—
701C24C2×#4112yes—
702C24H(5,𝔽2)12yes—
703C24H(5,𝔽2)12yes—
704C24C2511yescharacteristic
705C2×Q8—44no—
706C2×Q8—44no—
707C2×Q8—82no—
708C2×Q8—84no—
709C2×Q8—84no—
710C2×D4—216no—
711C2×D4—216no—
712C2×D4—216no—
713C2×D4—216no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—4128no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—216no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—21no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—21no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—22no—
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—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
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—44no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—48no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—4128no—
855C22×C4—48no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—48no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—84no—
869C22×C4—84no—
870C22×C4—84no—
871C22×C4—84no—
872C22×C4—82no—
873C22×C4—82no—
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×C4C22×D412yes—
884C22×C4C22×D414yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×D412yes—
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×Q814yes—
891C22×C4H(5,𝔽2)14yes—
892C22×C4H(5,𝔽2)14yes—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—82no—
900C4⋊C4—84no—
901C4⋊C4—82no—
902C4⋊C4—82no—
903C4⋊C4—84no—
904C4⋊C4—84no—
905C4⋊C4—84no—
906C4⋊C4—84no—
907C4⋊C4—84no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—82no—
933C22⋊C4—82no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C23—22no—
942C23—22no—
943C23—24no—
944C23—22no—
945C23—22no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—22no—
958C23—22no—
959C23—24no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—22no—
966C23—22no—
967C23—24no—
968C23—24no—
969C23—232no—
970C23—24no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—22no—
978C23—22no—
979C23—24no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—232no—
1005C23—432no—
1006C23—416no—
1007C23—416no—
1008C23—416no—
1009C23—432no—
1010C23—432no—
1011C23—432no—
1012C23—416no—
1013C23—416no—
1014C23—416no—
1015C23—416no—
1016C23—416no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
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—816no—
1050C23—816no—
1051C23—816no—
1052C23—816no—
1053C23—88no—
1054C23—88no—
1055C23—88no—
1056C23—88no—
1057C23C2×C22⋊Q814yes—
1058C23C2×C22⋊Q814yes—
1059C23C2×C22⋊Q818yes—
1060C23C2×C22⋊Q814yes—
1061C23C2×C22⋊Q814yes—
1062C23#54314yes—
1063C23D4214yes—
1064C23#54614yes—
1065C23#54614yes—
1066C23#55114yes—
1067C23C23×D411yescharacteristic
1068C23C23×D411yescharacteristic
1069C23C23×Q811yescharacteristic
1070C23C22×#4111yescharacteristic
1071C23C22×#4111yescharacteristic
1072C23C2×H(5,𝔽2)12yes—
1073C23C2×H(5,𝔽2)11yescharacteristic
1074C23C2×H(5,𝔽2)11yescharacteristic
1075C23C2×H(5,𝔽2)12yes—
1076C23#58512yes—
1077C23#58512yes—
1078Q8—88no—
1079D4—432no—
1080D4—432no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—416no—
1108C2×C4—432no—
1109C2×C4—416no—
1110C2×C4—432no—
1111C2×C4—41no—
1112C2×C4—42no—
1113C2×C4—41no—
1114C2×C4—42no—
1115C2×C4—416no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
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—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—88no—
1195C2×C4—816no—
1196C2×C4—88no—
1197C2×C4—88no—
1198C2×C4—88no—
1199C2×C4#53414yes—
1200C22—28no—
1201C22—28no—
1202C22—28no—
1203C22—28no—
1204C22—24no—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—28no—
1211C22—28no—
1212C22—28no—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—24no—
1219C22—464no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—42no—
1235C22—44no—
1236C22—42no—
1237C22—44no—
1238C22—42no—
1239C22—44no—
1240C22—42no—
1241C22—44no—
1242C22—44no—
1243C22—42no—
1244C22—42no—
1245C22—44no—
1246C22—42no—
1247C22—42no—
1248C22—832no—
1249C22#243718yes—
1250C22C22×C22⋊Q811yescharacteristic
1251C22C22×C22⋊Q811yescharacteristic
1252C22C2×#53411yescharacteristic
1253C22#344911yescharacteristic
1254C22C2×#54311yescharacteristic
1255C22#345912yes—
1256C22C2×D4211yescharacteristic
1257C22C2×#54611yescharacteristic
1258C22C2×#54611yescharacteristic
1259C22C2×#55111yescharacteristic
1260C22#348411yescharacteristic
1261C22#348511yescharacteristic
1262C22#349012yes—
1263C22#349112yes—
1264C22#349612yes—
1265C22#349612yes—
1266C22#350112yes—
1267C22#350112yes—
1268C22#350512yes—
1269C22#353212yes—
1270C22#353312yes—
1271C22#354212yes—
1272C22#354212yes—
1273C4—24no—
1274C4—44no—
1275C4—44no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—44no—
1282C4—82no—
1283C4—82no—
1284C4—82no—
1285C4—81no—
1286C4—82no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C2—28no—
1293C2—48no—
1294C2—44no—
1295C2—44no—
1296C2C2×#243711yescharacteristic
1297C2#3498511yescharacteristic
1298C2#3501011yescharacteristic
1299C2#3535912yes—
1300C2#3674712yes—
1301C2#3783211yescharacteristic
1302C2#3784211yescharacteristic
1303C2#3796412yes—
1304C2#3933211yescharacteristic
1305C2#3933811yescharacteristic
1306C2#3942812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2437C2semidirect
2. C2×#2626C2semidirect
5. #15506C2semidirect
6. #15439C2semidirect
7. #15439C2semidirect
8. #15429C2semidirect
9. #15328C2semidirect
10. #15327C2semidirect
11. #15324C2semidirect
12. #15323C2semidirect
13. #14936C2semidirect
14. #14935C2semidirect
15. #14935C2semidirect
16. #14934C2semidirect
17. #14693C2semidirect
18. #14680C2semidirect
20. #14262C2semidirect
21. #14127C2semidirect
22. #13877C2semidirect
23. #13877C2semidirect
27. C22×C22⋊Q8C22semidirect
35. C2×#399C22semidirect
36. C2×#399C22semidirect
37. C2×#396C22semidirect
38. C2×#396C22semidirect
39. C2×#396C22semidirect
40. C2×#396C22semidirect
41. C2×#393C22semidirect
42. C2×#393C22semidirect
59. C2×#385C22semidirect
60. C2×#385C22semidirect
61. C2×#385C22semidirect
62. C2×#385C22semidirect
63. C2×#385C22semidirect
64. C2×#385C22semidirect
72. C2×#380C22semidirect
73. C2×#380C22semidirect
74. C2×#380C22semidirect
75. C2×#380C22semidirect
84. #1446C22semidirect
85. #1445C22semidirect
86. #1445C22semidirect
87. #1445C22semidirect
88. #1444C22semidirect
89. #1443C22semidirect
90. #1443C22semidirect
91. #1442C22semidirect
92. #1442C22semidirect
93. #1442C22semidirect
94. #1441C22semidirect
95. #1441C22semidirect
96. #1441C22semidirect
97. #1441C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
136. C23×D4Q8semidirect
687. C24C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24372
C2×#26262
C2×#23082
C22×#3862
#155062
#154392
#154292
#153282
#153272
#153242
#153232
#149362
#149352
#149342
#146932
#146802
#143352
#142622
#141272
#138772