Finite Group Databasebeta

← #722612

Subgroups — #722612

Order 512.

4650 conjugacy classes of subgroups.

The subgroup lattice has 1275 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic, complemented
3C22×#396C211yesmaximal, characteristic, complemented
4C2×#2321C211yesmaximal, characteristic
5#16604C212yesmaximal, complemented
6#16265C212yesmaximal, complemented
7#15846C212yesmaximal, complemented
8#15325C212yesmaximal, complemented
9#15322C212yesmaximal, complemented
10#15280C212yesmaximal, complemented
11#14914C211yesmaximal, characteristic, complemented
12#14877C212yesmaximal, complemented
13#14729C212yesmaximal, complemented
14#14720C211yesmaximal, characteristic, complemented
15#14717C211yesmaximal, characteristic, complemented
16#14717C211yesmaximal, characteristic, complemented
17#14139C211yesmaximal, characteristic, complemented
18#14016C211yesmaximal, characteristic, complemented
19#14015C211yesmaximal, characteristic, complemented
20#13967C211yesmaximal, characteristic
21#13967C211yesmaximal, characteristic
22#13923C211yesmaximal, characteristic, complemented
23#13872C211yesmaximal, characteristic, complemented
24C2×#554—28no—
25C2×#554—28no—
26C2×#554—28no—
27C22×C4⋊Q8C2211yescharacteristic, complemented
28C22×#125C2211yescharacteristic, complemented
29C22×#125C2211yescharacteristic, complemented
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic, complemented
34C22×C22⋊Q8C2211yescharacteristic, complemented
35C22×C22⋊Q8C2211yescharacteristic, complemented
36C22×#120C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic, complemented
38C22×C4×D4C2211yescharacteristic
39C22×C4×D4C2211yescharacteristic
40C22×C4×D4C2211yescharacteristic
41C23×C4⋊C4C2211yescharacteristic
42C23×C4⋊C4C2211yescharacteristic
43C23×C4⋊C4C2211yescharacteristic
44C23×C4⋊C4C2211yescharacteristic, complemented
45C23×C22⋊C4C2211yescharacteristic
46C23×C22⋊C4C2211yescharacteristic
47C23×C22⋊C4C2211yescharacteristic
48#2626—28no—
49C2×#399C2212yes—
50C2×#396—28no—
51C2×#396C2212yes—
52C2×#396C2212yes—
53C2×#396C2212yes—
54C2×#396C2212yes—
55C2×#396C2212yes—
56C2×#396C2212yes—
57C2×#395C2212yescomplemented
58C2×#393C2212yes—
59C2×#393C2212yes—
60C2×#393C2212yes—
61#2321—28no—
62C2×#391C2212yescomplemented
63C2×#390C2212yes—
64C2×#388C2212yes—
65C2×#388C2212yes—
66C2×#386C2212yes—
67C2×#386C2211yescharacteristic
68C2×#386C2211yescharacteristic
69C2×#386C2211yescharacteristic
70C2×#386C2212yes—
71C2×#386C2212yes—
72C2×#385C2211yescharacteristic
73C2×#385C2211yescharacteristic
74C2×#385C2211yescharacteristic
75C2×#385C2212yescomplemented
76C2×#380C2211yescharacteristic
77C2×#380C2212yescomplemented
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82C22×#95C2211yescharacteristic
83#1446C2212yescomplemented
84#1444C2212yescomplemented
85#1444C2212yescomplemented
86#1444C2212yescomplemented
87#1444C2212yescomplemented
88#1442C2212yescomplemented
89#1441C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1441C2212yescomplemented
93#1441C2212yescomplemented
94#1441C2212yescomplemented
95#1441C2212yescomplemented
96#1441C2212yescomplemented
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1438C2212yes—
109#1438C2212yes—
110#1437C2212yes—
111#1437C2212yes—
112#1436C2212yescomplemented
113#1436C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116C4⋊#95C2212yescomplemented
117C4⋊#95C2212yescomplemented
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2211yescharacteristic
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C23×Q8C2311yescharacteristic
131C23×Q8C2311yescharacteristic
132C23×Q8C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C23×D4C2312yes—
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144#554—2128no—
145C2×C4⋊Q8—24no—
146C2×C4⋊Q8—24no—
147C2×C4⋊Q8—24no—
148C2×#125—24no—
149C2×#125—24no—
150C2×#125—24no—
151C2×#125—24no—
152C2×#125—24no—
153C2×#125—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8—24no—
156C2×C22⋊Q8—24no—
157C2×C22⋊Q8—24no—
158C2×C22⋊Q8—24no—
159C2×C22⋊Q8—24no—
160C2×C22⋊Q8—24no—
161C2×C22⋊Q8—24no—
162C2×C22⋊Q8—24no—
163C2×C22⋊Q8—24no—
164C2×C22⋊Q8—24no—
165C2×C22⋊Q8—24no—
166C2×C22⋊Q8—24no—
167C2×C22⋊Q8—24no—
168C2×C22⋊Q8—24no—
169C2×C22⋊Q8—24no—
170C2×C22⋊Q8—24no—
171C2×C22⋊Q8D418yescomplemented
172C2×#120—24no—
173C2×#120—24no—
174C2×#120Q818yescomplemented
175C2×C4×Q8—24no—
176C2×C4×Q8—24no—
177C2×C4×Q8—24no—
178C2×C4×D4—24no—
179C2×C4×D4—24no—
180C2×C4×D4—24no—
181C2×C4×D4—24no—
182C2×C4×D4—24no—
183C2×C4×D4—24no—
184C2×C4×D4—24no—
185C2×C4×D4—24no—
186C2×C4×D4D418yes—
187C22×C4⋊C4—24no—
188C22×C4⋊C4—24no—
189C22×C4⋊C4—24no—
190C22×C4⋊C4—24no—
191C22×C4⋊C4—24no—
192C22×C4⋊C4—24no—
193C22×C4⋊C4—24no—
194C22×C4⋊C4—44no—
195C22×C4⋊C4—44no—
196C22×C4⋊C4D418yescomplemented
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2312yes—
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2312yes—
221C22×C22⋊C4—24no—
222C22×C22⋊C4—24no—
223C22×C22⋊C4—24no—
224C22×C22⋊C4—24no—
225C22×C22⋊C4—24no—
226C22×C22⋊C4—44no—
227C22×C22⋊C4—44no—
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×C22⋊C4C2312yes—
239C22×C22⋊C4C2311yescharacteristic
240C22×C22⋊C4C2311yescharacteristic
241C22×C22⋊C4C2311yescharacteristic
242C22×C22⋊C4C2311yescharacteristic
243C22×C22⋊C4C2311yescharacteristic
244C22×C22⋊C4C2312yes—
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2312yes—
250C22×C22⋊C4C2312yes—
251C22×C22⋊C4C2312yes—
252C22×C22⋊C4C2312yes—
253C22×C22⋊C4C2312yes—
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2312yes—
258#399—28no—
259#396—28no—
260#396—28no—
261#396—28no—
262#396—28no—
263#396—28no—
264#396—28no—
265#395—44no—
266#393—28no—
267#393—44no—
268#393—44no—
269#391—44no—
270#390—28no—
271#388—28no—
272#388—28no—
273#386—24no—
274#386—24no—
275#386—24no—
276#386—28no—
277#386—44no—
278#386—44no—
279#385—24no—
280#385—24no—
281#385—24no—
282#385—44no—
283#380—24no—
284#380—44no—
285#379—24no—
286#379—24no—
287#379—24no—
288C4×C22⋊C4—24no—
289C2×#95—24no—
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—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C2×#95C2312yes—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—22no—
325C25—22no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25—42no—
330C25C2×Q814yes—
331C25C2412yes—
332C25C2411yescharacteristic
333C25C2411yescharacteristic
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8—24no—
343C22×Q8—42no—
344C22×Q8—42no—
345C22×Q8—42no—
346C22×Q8—42no—
347C22×Q8—42no—
348C22×Q8C2×D414yes—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4C2×D414yes—
360C22×D4C2×Q814yes—
361C22×D4C2×Q818yes—
362C22×D4#4114yes—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—24no—
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—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4C2×D414yes—
403C23×C4C2×D414yes—
404C23×C4C2×D414yes—
405C23×C4C2×D414yes—
406C23×C4C2×D414yes—
407C23×C4C2×D414yes—
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C4⋊Q8—232no—
429#125—232no—
430#125—232no—
431C22⋊Q8—232no—
432C22⋊Q8—232no—
433C22⋊Q8—232no—
434C22⋊Q8—232no—
435C22⋊Q8—232no—
436C22⋊Q8—232no—
437#120—232no—
438C4×Q8—232no—
439C4×D4—232no—
440C4×D4—232no—
441C4×D4—232no—
442C2×C4⋊C4—232no—
443C2×C4⋊C4—232no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4—42no—
499C2×C4⋊C4—42no—
500C2×C4⋊C4—416no—
501C2×C4⋊C4—416no—
502C2×C4⋊C4—42no—
503C2×C4⋊C4—42no—
504C2×C4⋊C4—42no—
505C2×C4⋊C4—42no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—42no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—42no—
510C2×C4⋊C4C2×D414yes—
511C2×C4⋊C4C2×D414yes—
512C2×C4⋊C4C2×D414yes—
513C2×C4⋊C4C2×D414yes—
514C2×C4⋊C4C2×D414yes—
515C2×C4⋊C4C2×D414yes—
516C2×C4⋊C4C2×D414yes—
517C2×C4⋊C4C2×D414yes—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—416no—
575C2×C22⋊C4—416no—
576C2×C22⋊C4—416no—
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⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4—42no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4C2×D414yes—
594C2×C22⋊C4C2×D414yes—
595C2×C22⋊C4C2×D414yes—
596C2×C22⋊C4C2×D414yes—
597C2×C22⋊C4C2×Q814yes—
598C2×C22⋊C4C2×Q818yes—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—24no—
608C2×C42—42no—
609C2×C42—42no—
610C2×C42C2×D414yes—
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—24no—
620#95—24no—
621#95—24no—
622#95—24no—
623#95—24no—
624#95—24no—
625#95—24no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95—42no—
630#95—42no—
631#95—42no—
632#95—42no—
633#95—42no—
634#95—42no—
635#95—42no—
636#95—42no—
637#95—42no—
638#95—42no—
639#95—42no—
640#95—42no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—21no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—21no—
650C24—21no—
651C24—22no—
652C24—22no—
653C24—28no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—28no—
669C24—28no—
670C24—48no—
671C24—48no—
672C24—44no—
673C24—44no—
674C24—44no—
675C24—44no—
676C24—48no—
677C24—48no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24C22×D412yes—
691C24C22×D412yes—
692C24C22×D412yes—
693C24C22×D412yes—
694C24C22×Q814yes—
695C24C22×Q812yes—
696C24C22×Q812yes—
697C24C2×#4112yes—
698C24C2×#4112yes—
699C242−1+412yes—
700C242−1+412yes—
701C24C2511yescharacteristic
702C2×Q8—28no—
703C2×Q8—28no—
704C2×Q8—28no—
705C2×Q8—48no—
706C2×Q8—48no—
707C2×Q8—48no—
708C2×Q8—44no—
709C2×Q8—44no—
710C2×Q8—82no—
711C2×Q8—82no—
712C2×Q8—84no—
713C2×Q8—82no—
714C2×Q8—82no—
715C2×Q8—84no—
716C2×Q8—84no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—216no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—84no—
727C2×D4—84no—
728C2×D4—84no—
729C2×D4—84no—
730C2×D4C22⋊Q8116yes—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—22no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
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—28no—
794C22×C4—28no—
795C22×C4—28no—
796C22×C4—28no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
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—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—44no—
834C22×C4—44no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—44no—
839C22×C4—48no—
840C22×C4—44no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—82no—
857C22×C4—82no—
858C22×C4—84no—
859C22×C4—82no—
860C22×C4—82no—
861C22×C4—84no—
862C22×C4—84no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4—84no—
866C22×C4—84no—
867C22×C4—84no—
868C22×C4—84no—
869C22×C4#120116yes—
870C22×C4C22×D412yes—
871C22×C4C22×D412yes—
872C22×C4C22×D412yes—
873C22×C4C22×D412yes—
874C22×C4C22×D412yes—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C22×D412yes—
878C22×C4C22×D412yes—
879C22×C4C22×D412yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×Q814yes—
888C22×C4C22×Q812yes—
889C22×C4C2×#4112yes—
890C22×C4H(5,𝔽2)14yes—
891C22×C4H(5,𝔽2)14yes—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—84no—
913C4⋊C4—84no—
914C4⋊C4—84no—
915C4⋊C4—84no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—216no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C42—28no—
943C42—28no—
944C42—28no—
945C42—84no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—416no—
982C23—416no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—416no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—816no—
1023C23—816no—
1024C23—88no—
1025C23—816no—
1026C23—816no—
1027C23—88no—
1028C23—88no—
1029C23—88no—
1030C23C2×#12014yes—
1031C23C2×C22⋊Q814yes—
1032C23C2×C22⋊Q814yes—
1033C23#53614yes—
1034C23#54814yes—
1035C23#54814yes—
1036C23D4×Q814yes—
1037C23D4×Q814yes—
1038C23C23×D411yescharacteristic
1039C23C23×D411yescharacteristic
1040C23C23×D411yescharacteristic
1041C23C23×Q811yescharacteristic
1042C23C22×#4111yescharacteristic
1043C23C2×H(5,𝔽2)12yes—
1044C23C2×H(5,𝔽2)12yes—
1045C23C2×2−1+411yescharacteristic
1046C23C2×2−1+411yescharacteristic
1047C23#58512yes—
1048C23#58512yes—
1049Q8—416no—
1050Q8—88no—
1051Q8—88no—
1052D4—232no—
1053D4—816no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—416no—
1100C2×C4—416no—
1101C2×C4—416no—
1102C2×C4—416no—
1103C2×C4—42no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—42no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
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—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—88no—
1171C2×C4—88no—
1172C2×C4—88no—
1173C2×C4—88no—
1174C2×C4—88no—
1175C2×C4C2×#12014yes—
1176C2×C4C2×#12014yes—
1177C2×C4C2×C22⋊Q814yes—
1178C2×C4#53514yes—
1179C22—28no—
1180C22—24no—
1181C22—28no—
1182C22—28no—
1183C22—24no—
1184C22—24no—
1185C22—24no—
1186C22—28no—
1187C22—24no—
1188C22—24no—
1189C22—24no—
1190C22—28no—
1191C22—44no—
1192C22—42no—
1193C22—44no—
1194C22—44no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—44no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—44no—
1205C22—44no—
1206C22—44no—
1207C22—832no—
1208C22—82no—
1209C22—82no—
1210C22—82no—
1211C22—82no—
1212C22—82no—
1213C22—82no—
1214C22—82no—
1215C22—82no—
1216C22#240918yes—
1217C22C22×#12011yescharacteristic
1218C22C22×C22⋊Q811yescharacteristic
1219C22C2×#53511yescharacteristic
1220C22C2×#53611yescharacteristic
1221C22#344911yescharacteristic
1222C22C2×#54811yescharacteristic
1223C22C2×#54811yescharacteristic
1224C22C2×D4×Q811yescharacteristic
1225C22C2×D4×Q811yescharacteristic
1226C22#348411yescharacteristic
1227C22#348511yescharacteristic
1228C22#348812yes—
1229C22#348812yes—
1230C22#349612yes—
1231C22#349612yes—
1232C22#350112yes—
1233C22#350112yes—
1234C22#351912yes—
1235C22#352112yes—
1236C22#353612yes—
1237C22#354112yes—
1238C22#354112yes—
1239C22#356412yes—
1240C4—24no—
1241C4—24no—
1242C4—24no—
1243C4—24no—
1244C4—42no—
1245C4—42no—
1246C4—42no—
1247C4—42no—
1248C4—42no—
1249C4—42no—
1250C4—42no—
1251C4—42no—
1252C4—42no—
1253C4—44no—
1254C4—44no—
1255C4—82no—
1256C4—82no—
1257C4—82no—
1258C4—82no—
1259C4—82no—
1260C2—28no—
1261C2—44no—
1262C2—84no—
1263C2C2×#240911yescharacteristic
1264C2#3525011yescharacteristic
1265C2#3534711yescharacteristic
1266C2#3577612yes—
1267C2#3911711yescharacteristic
1268C2#3912011yescharacteristic
1269C2#3958811yescharacteristic
1270C2#3959411yescharacteristic
1271C2#4051312yes—
1272C2#4302512yes—
1273C2#4391212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
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×#554C2semidirect
2. C2×#2626C2semidirect
3. C22×#396C2semidirect
5. #16604C2semidirect
6. #16265C2semidirect
7. #15846C2semidirect
8. #15325C2semidirect
9. #15322C2semidirect
10. #15280C2semidirect
11. #14914C2semidirect
12. #14877C2semidirect
13. #14729C2semidirect
14. #14720C2semidirect
15. #14717C2semidirect
16. #14717C2semidirect
17. #14139C2semidirect
18. #14016C2semidirect
19. #14015C2semidirect
22. #13923C2semidirect
23. #13872C2semidirect
27. C22×C4⋊Q8C22semidirect
28. C22×#125C22semidirect
29. C22×#125C22semidirect
33. C22×C22⋊Q8C22semidirect
34. C22×C22⋊Q8C22semidirect
35. C22×C22⋊Q8C22semidirect
37. C22×C4×Q8C22semidirect
44. C23×C4⋊C4C22semidirect
57. C2×#395C22semidirect
62. C2×#391C22semidirect
75. C2×#385C22semidirect
77. C2×#380C22semidirect
83. #1446C22semidirect
84. #1444C22semidirect
85. #1444C22semidirect
86. #1444C22semidirect
87. #1444C22semidirect
88. #1442C22semidirect
89. #1441C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1441C22semidirect
93. #1441C22semidirect
94. #1441C22semidirect
95. #1441C22semidirect
96. #1441C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
112. #1436C22semidirect
113. #1436C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. C4⋊#95C22semidirect
117. C4⋊#95C22semidirect
128. C22⋊#95C22semidirect
171. C2×C22⋊Q8D4semidirect
174. C2×#120Q8semidirect
196. C22×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#26262
C22×#3962
C2×#23212
#166042
#162652
#158462
#153252
#153222
#152802
#149142
#148772
#147292
#147202
#147172
#141392
#140162
#140152
#139672
#139232
#138722