Finite Group Databasebeta

← #636115

Subgroups — #636115

Order 512.

5216 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2450C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic, complemented
3C2×C4×#120C211yesmaximal, characteristic, complemented
4C22×#386C211yesmaximal, characteristic, complemented
5#16357C212yesmaximal, complemented
6#16352C212yesmaximal, complemented
7#16288C212yesmaximal, complemented
8#16271C212yesmaximal, complemented
9#14817C212yesmaximal, complemented
10#14796C212yesmaximal, complemented
11#14756C212yesmaximal, complemented
12#14732C212yesmaximal, complemented
13#14725C211yesmaximal, characteristic, complemented
14#14724C211yesmaximal, characteristic, complemented
15#14717C211yesmaximal, characteristic, complemented
16#14715C211yesmaximal, characteristic
17#14693C211yesmaximal, characteristic, complemented
18#14265C211yesmaximal, characteristic, complemented
19#14259C211yesmaximal, characteristic, complemented
20#14255C211yesmaximal, characteristic, complemented
21#13971C211yesmaximal, characteristic, complemented
22#13967C211yesmaximal, characteristic, complemented
23#13883C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#120C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2212yescomplemented
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34#2626—28no—
35#2450—28no—
36C2×#400C2211yescharacteristic, complemented
37C2×#399C2212yescomplemented
38C2×#398C2211yescharacteristic, complemented
39C2×#396C2211yescharacteristic, complemented
40C2×#396C2212yescomplemented
41C2×#396C2212yescomplemented
42C2×#394C2212yes—
43C2×#394C2212yes—
44C2×#394C2212yescomplemented
45C2×#393C2211yescharacteristic, complemented
46C2×#393C2212yescomplemented
47C2×#393C2212yescomplemented
48C2×#392C2212yes—
49C2×#392C2212yes—
50C4×#120—28no—
51C2×#391C2211yescharacteristic, complemented
52C2×#388C2212yescomplemented
53C2×#387C2211yescharacteristic, complemented
54C2×#386—28no—
55C2×#386C2211yescharacteristic
56C2×#386C2211yescharacteristic
57C2×#386C2211yescharacteristic
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2211yescharacteristic
62C2×#386C2212yes—
63C2×#386C2212yescomplemented
64C2×#386C2212yescomplemented
65C2×#385C2211yescharacteristic
66C2×#385C2211yescharacteristic
67C2×#385C2211yescharacteristic
68C2×#385C2211yescharacteristic
69C2×#385C2211yescharacteristic, complemented
70C2×#385C2212yescomplemented
71C2×#385C2212yescomplemented
72C2×#385C2212yescomplemented
73C2×#380C2211yescharacteristic
74C2×#380C2211yescharacteristic, complemented
75C2×#379C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82C2×C4×C22⋊C4C2212yescomplemented
83C22×#95C2211yescharacteristic
84C22×#95C2211yescharacteristic
85#1445C2212yescomplemented
86#1443C2212yescomplemented
87#1443C2212yescomplemented
88#1443C2212yescomplemented
89#1442C2212yescomplemented
90#1442C2212yescomplemented
91#1442C2212yescomplemented
92#1441C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1440C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1438C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1436C2212yescomplemented
116#1434C2212yescomplemented
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—44no—
134C23×D4—44no—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2312yes—
140C24×C4—24no—
141C24×C4—24no—
142C24×C4—44no—
143C24×C4—42no—
144C24×C4—44no—
145C24×C4C2312yes—
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8—42no—
156C2×#120—24no—
157C2×#120—24no—
158C2×#120—24no—
159C2×#120—24no—
160C2×#120—24no—
161C2×#120—42no—
162C2×C4×D4—24no—
163C2×C4×D4—28no—
164C2×C4×D4—24no—
165C2×C4×D4—44no—
166C2×C4×D4—42no—
167C2×C4×D4—44no—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4—44no—
185C22×C22⋊C4—42no—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
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×C42C2311yescharacteristic
221C22×C42C2312yes—
222#400—24no—
223#399—28no—
224#398—24no—
225#396—28no—
226#396—24no—
227#396—28no—
228#394—44no—
229#394—44no—
230#394—44no—
231#393—24no—
232#393—28no—
233#393—44no—
234#392—44no—
235#392—44no—
236#391—24no—
237#388—44no—
238#387—24no—
239#386—24no—
240#386—24no—
241#386—24no—
242#386—24no—
243#386—28no—
244#386—28no—
245#386—28no—
246#386—28no—
247#386—28no—
248#386—44no—
249#385—24no—
250#385—24no—
251#385—24no—
252#385—28no—
253#385—24no—
254#385—44no—
255#385—44no—
256#385D418yescomplemented
257#380—24no—
258#380—24no—
259#379—24no—
260#379—24no—
261#379—24no—
262#379—24no—
263#379—24no—
264#379—42no—
265C4×C22⋊C4—24no—
266C4×C22⋊C4—28no—
267C2×#95—24no—
268C2×#95D418yescomplemented
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C25—22no—
306C25—22no—
307C25—24no—
308C25—24no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25#4114yes—
326C25#4114yes—
327C25C2412yes—
328C25C2411yescharacteristic
329C25C2412yes—
330C25C2411yescharacteristic
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—41no—
334C22×Q8—42no—
335C22×Q8—42no—
336C22×D4—232no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
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—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—416no—
372C22×D4—416no—
373C22×D4—432no—
374C22×D4—432no—
375C22×D4#4114yes—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—22no—
389C23×C4—24no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—24no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—22no—
398C23×C4—24no—
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—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—41no—
416C23×C4—42no—
417C23×C4—432no—
418C23×C4—416no—
419C23×C4—416no—
420C23×C4—432no—
421C23×C4C2×D414yes—
422C23×C4C2×D414yes—
423C23×C4C2×D414yes—
424C23×C4C2×D414yes—
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2412yes—
438C23×C4C2412yes—
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C22⋊Q8—416no—
445#120—232no—
446#120—416no—
447C4×D4—416no—
448C4×D4—432no—
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—22no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—41no—
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⋊C4C2×D418yescomplemented
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—22no—
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—24no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
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—41no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—416no—
556C2×C22⋊C4—416no—
557C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
578C2×C22⋊C4C2×D414yes—
579C2×C42—22no—
580C2×C42—24no—
581C2×C42—22no—
582C2×C42—24no—
583C2×C42—42no—
584C2×C42—41no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—22no—
590#95—24no—
591#95—22no—
592#95—22no—
593#95—24no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—24no—
600#95—24no—
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—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95C2×D414yes—
617#95C2×D414yes—
618#95C2×D414yes—
619#95C2×D414yes—
620#95C2×D418yescomplemented
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—28no—
626C24—28no—
627C24—216no—
628C24—28no—
629C24—216no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—28no—
643C24—28no—
644C24—28no—
645C24—22no—
646C24—21no—
647C24—22no—
648C24—21no—
649C24—22no—
650C24—21no—
651C24—21no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—21no—
662C24—22no—
663C24—22no—
664C24—21no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—28no—
670C24—28no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—44no—
683C24—44no—
684C24—48no—
685C24—44no—
686C24—48no—
687C24—44no—
688C24—44no—
689C24—44no—
690C24—48no—
691C24—44no—
692C24—44no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24—84no—
707C24C22×D412yes—
708C24C22×D412yes—
709C24C2×#4114yes—
710C24C2×#4112yes—
711C24C2×#4114yes—
712C24C2×#4112yes—
713C24C2×#4112yes—
714C24C2×#4112yes—
715C24H(5,𝔽2)14yes—
716C24H(5,𝔽2)14yes—
717C24H(5,𝔽2)12yes—
718C242−1+412yes—
719C24C2511yescharacteristic
720C2×Q8—44no—
721C2×Q8—44no—
722C2×Q8—82no—
723C2×Q8—84no—
724C2×Q8—84no—
725C2×D4—216no—
726C2×D4—216no—
727C2×D4—216no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
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—4128no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—44no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—84no—
757C2×D4—84no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—84no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—216no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
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—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
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—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—22no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—48no—
875C22×C4—48no—
876C22×C4—48no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—48no—
887C22×C4—48no—
888C22×C4—48no—
889C22×C4—48no—
890C22×C4—4128no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—82no—
898C22×C4—84no—
899C22×C4—84no—
900C22×C4—84no—
901C22×C4—84no—
902C22×C4—84no—
903C22×C4C22×D412yes—
904C22×C4C22×D412yes—
905C22×C4C22×D414yes—
906C22×C4C22×D414yes—
907C22×C4C22×D412yes—
908C22×C4C22×D412yes—
909C22×C4C22×D412yes—
910C22×C4C22×D412yes—
911C22×C4C22×D412yes—
912C22×C4C22×D412yes—
913C22×C4C2×#4112yes—
914C22×C4H(5,𝔽2)14yes—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—84no—
922C4⋊C4—82no—
923C4⋊C4—82no—
924C4⋊C4—82no—
925C4⋊C4—84no—
926C22⋊C4—216no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—84no—
950C22⋊C4—82no—
951C22⋊C4—84no—
952C22⋊C4—82no—
953C22⋊C4—82no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C22⋊C4—84no—
958C22⋊C4—84no—
959C22⋊C4—84no—
960C42—44no—
961C42—48no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—232no—
979C23—24no—
980C23—24no—
981C23—24no—
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—24no—
995C23—24no—
996C23—24no—
997C23—22no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—22no—
1002C23—24no—
1003C23—24no—
1004C23—22no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—432no—
1010C23—432no—
1011C23—416no—
1012C23—416no—
1013C23—416no—
1014C23—432no—
1015C23—432no—
1016C23—416no—
1017C23—416no—
1018C23—416no—
1019C23—416no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—416no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—41no—
1038C23—42no—
1039C23—42no—
1040C23—41no—
1041C23—41no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—41no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—41no—
1054C23—41no—
1055C23—42no—
1056C23—42no—
1057C23—41no—
1058C23—41no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—416no—
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—42no—
1083C23—42no—
1084C23—816no—
1085C23—816no—
1086C23—88no—
1087C23—88no—
1088C23—816no—
1089C23—816no—
1090C23—88no—
1091C23—88no—
1092C23#52514yes—
1093C23#52514yes—
1094C23#53818yes—
1095C23#53914yes—
1096C23D4214yes—
1097C23#54814yes—
1098C23#54814yes—
1099C23#55114yes—
1100C23C23×D411yescharacteristic
1101C23C23×D411yescharacteristic
1102C23C22×#4111yescharacteristic
1103C23C22×#4111yescharacteristic
1104C23C22×#4111yescharacteristic
1105C23C2×H(5,𝔽2)12yes—
1106C23C2×H(5,𝔽2)12yes—
1107C23C2×H(5,𝔽2)12yes—
1108C23C2×H(5,𝔽2)11yescharacteristic
1109C23C2×2−1+411yescharacteristic
1110C23#58512yes—
1111Q8—88no—
1112D4—432no—
1113D4—432no—
1114D4—432no—
1115D4—416no—
1116D4—816no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
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—22no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—416no—
1150C2×C4—432no—
1151C2×C4—416no—
1152C2×C4—416no—
1153C2×C4—432no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
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—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—41no—
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—88no—
1231C2×C4—88no—
1232C2×C4—88no—
1233C2×C4#53514yes—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—28no—
1238C22—28no—
1239C22—28no—
1240C22—24no—
1241C22—28no—
1242C22—24no—
1243C22—24no—
1244C22—28no—
1245C22—28no—
1246C22—28no—
1247C22—464no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—42no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—42no—
1271C22—42no—
1272C22—832no—
1273C22—81no—
1274C22—82no—
1275C22—81no—
1276C22—82no—
1277C22—81no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—81no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22#246318yes—
1288C22C2×#52511yescharacteristic
1289C22C2×#52511yescharacteristic
1290C22C2×#53511yescharacteristic
1291C22#344911yescharacteristic
1292C22C2×#53812yes—
1293C22C2×#53911yescharacteristic
1294C22#345912yes—
1295C22#345912yes—
1296C22C2×D4211yescharacteristic
1297C22C2×#54811yescharacteristic
1298C22C2×#54811yescharacteristic
1299C22C2×#55111yescharacteristic
1300C22#348412yes—
1301C22#348411yescharacteristic
1302C22#348411yescharacteristic
1303C22#348812yes—
1304C22#349012yes—
1305C22#351312yes—
1306C22#351912yes—
1307C22#353212yes—
1308C22#353412yes—
1309C22#353512yes—
1310C22#353612yes—
1311C4—24no—
1312C4—42no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—44no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—82no—
1326C4—82no—
1327C4—81no—
1328C4—82no—
1329C4—82no—
1330C2—28no—
1331C2—48no—
1332C2—82no—
1333C2—84no—
1334C2#3459311yescharacteristic
1335C2C2×#246311yescharacteristic
1336C2#3498811yescharacteristic
1337C2#3499012yes—
1338C2#3748212yes—
1339C2#3764511yescharacteristic
1340C2#3765211yescharacteristic
1341C2#3775212yes—
1342C2#3903612yes—
1343C2#3911611yescharacteristic
1344C2#3912011yescharacteristic
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. C2×#2450C2semidirect
2. C2×#2626C2semidirect
3. C2×C4×#120C2semidirect
4. C22×#386C2semidirect
5. #16357C2semidirect
6. #16352C2semidirect
7. #16288C2semidirect
8. #16271C2semidirect
9. #14817C2semidirect
10. #14796C2semidirect
11. #14756C2semidirect
12. #14732C2semidirect
13. #14725C2semidirect
14. #14724C2semidirect
15. #14717C2semidirect
17. #14693C2semidirect
18. #14265C2semidirect
19. #14259C2semidirect
20. #14255C2semidirect
21. #13971C2semidirect
22. #13967C2semidirect
23. #13883C2semidirect
30. C22×C4×D4C22semidirect
36. C2×#400C22semidirect
37. C2×#399C22semidirect
38. C2×#398C22semidirect
39. C2×#396C22semidirect
40. C2×#396C22semidirect
41. C2×#396C22semidirect
44. C2×#394C22semidirect
45. C2×#393C22semidirect
46. C2×#393C22semidirect
47. C2×#393C22semidirect
51. C2×#391C22semidirect
52. C2×#388C22semidirect
53. C2×#387C22semidirect
63. C2×#386C22semidirect
64. C2×#386C22semidirect
69. C2×#385C22semidirect
70. C2×#385C22semidirect
71. C2×#385C22semidirect
72. C2×#385C22semidirect
74. C2×#380C22semidirect
82. C2×C4×C22⋊C4C22semidirect
85. #1445C22semidirect
86. #1443C22semidirect
87. #1443C22semidirect
88. #1443C22semidirect
89. #1442C22semidirect
90. #1442C22semidirect
91. #1442C22semidirect
92. #1441C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1440C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. #1434C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
256. #385D4semidirect
268. C2×#95D4semidirect
477. C2×C4⋊C4C2×D4semidirect
620. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24502
C2×#26262
C2×C4×#1202
C22×#3862
#163572
#163522
#162882
#162712
#148172
#147962
#147562
#147322
#147252
#147242
#147172
#147152
#146932
#142652
#142592
#142552
#139712
#139672
#138832