Finite Group Databasebeta

← #686276

Subgroups — #686276

Order 512.

4548 conjugacy classes of subgroups.

The subgroup lattice has 1353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2487C211yesmaximal, characteristic, complemented
2C22×#396C211yesmaximal, characteristic, complemented
3C2×D4×C22⋊C4C211yesmaximal, characteristic
4C2×#2308C211yesmaximal, characteristic
5#16301C212yesmaximal, complemented
6#16298C212yesmaximal, complemented
7#15508C212yesmaximal, complemented
8#15439C212yesmaximal, complemented
9#15324C212yesmaximal, complemented
10#15309C212yesmaximal, complemented
11#15091C211yesmaximal, characteristic, complemented
12#14946C211yesmaximal, characteristic, complemented
13#14769C212yesmaximal, complemented
14#14729C211yesmaximal, characteristic, complemented
15#14729C211yesmaximal, characteristic, complemented
16#14726C212yesmaximal, complemented
17#14262C211yesmaximal, characteristic, complemented
18#14015C211yesmaximal, characteristic, complemented
19#14015C211yesmaximal, characteristic, complemented
20#13960C211yesmaximal, characteristic, complemented
21#13877C211yesmaximal, characteristic, complemented
22#13877C211yesmaximal, characteristic, complemented
23#13867C211yesmaximal, characteristic
24C24×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic, complemented
28C23×C4⋊C4C2211yescharacteristic, complemented
29C23×C4⋊C4C2211yescharacteristic, complemented
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35#2487—28no—
36C2×#400C2212yescomplemented
37C2×#399C2212yescomplemented
38C2×#396—28no—
39C2×#396C2212yes—
40C2×#396C2212yes—
41C2×#396C2212yescomplemented
42C2×#396C2212yescomplemented
43C2×#396C2212yescomplemented
44C2×#396C2212yescomplemented
45D4×C22⋊C4—28no—
46#2308—28no—
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#389C2212yescomplemented
50C2×#386C2211yescharacteristic
51C2×#386C2211yescharacteristic
52C2×#386C2211yescharacteristic
53C2×#386C2211yescharacteristic
54C2×#386C2211yescharacteristic
55C2×#386C2211yescharacteristic
56C2×#386C2212yes—
57C2×#386C2211yescharacteristic
58C2×#386C2211yescharacteristic
59C2×#386C2211yescharacteristic
60C2×#386C2212yes—
61C2×#386C2211yescharacteristic
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#385C2211yescharacteristic, complemented
65C2×#385C2211yescharacteristic, complemented
66C2×#385C2211yescharacteristic, complemented
67C2×#385C2212yescomplemented
68C2×#385C2212yescomplemented
69C2×#385C2211yescharacteristic, complemented
70C2×#385C2212yescomplemented
71C2×#381C2212yes—
72C2×#380C2211yescharacteristic
73C2×#380C2211yescharacteristic, complemented
74C2×#380C2212yescomplemented
75C2×#380C2212yescomplemented
76C2×#380C2211yescharacteristic, complemented
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2212yes—
81C2×#379C2212yes—
82C2×C4×C22⋊C4C2211yescharacteristic
83C22×#95C2211yescharacteristic, complemented
84#1445C2212yescomplemented
85#1445C2212yescomplemented
86#1444C2212yescomplemented
87#1444C2212yescomplemented
88#1442C2212yescomplemented
89#1442C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1441C2212yescomplemented
93#1441C2212yescomplemented
94#1441C2212yescomplemented
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1438C2212yes—
113#1438C2212yes—
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116#1434C2212yescomplemented
117C22⋊#95C2212yes—
118C22⋊#95C2212yescomplemented
119C22⋊#95C2211yescharacteristic, complemented
120C22⋊#95C2211yescharacteristic, complemented
121C22⋊#95C2211yescharacteristic, complemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2211yescharacteristic, complemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2211yescharacteristic, complemented
126C22⋊#95C2211yescharacteristic, complemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—42no—
134C23×D4—42no—
135C23×D4Q818yes—
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C2×C4×D4—24no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—24no—
154C2×C4×D4—42no—
155C2×C4×D4—42no—
156C22×C4⋊C4—24no—
157C22×C4⋊C4—24no—
158C22×C4⋊C4—24no—
159C22×C4⋊C4—24no—
160C22×C4⋊C4—44no—
161C22×C4⋊C4—44no—
162C22×C4⋊C4—42no—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
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—44no—
186C22×C22⋊C4—42no—
187C22×C22⋊C4—42no—
188C22×C22⋊C4D418yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2312yes—
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226#400—28no—
227#399—28no—
228#396—28no—
229#396—28no—
230#396—28no—
231#396—28no—
232#396—44no—
233#396—44no—
234#390—24no—
235#390—24no—
236#389—28no—
237#386—24no—
238#386—24no—
239#386—24no—
240#386—24no—
241#386—24no—
242#386—24no—
243#386—28no—
244#386—24no—
245#386—24no—
246#386—24no—
247#386—28no—
248#386—42no—
249#386—42no—
250#386D418yes—
251#385—24no—
252#385—24no—
253#385—44no—
254#385—44no—
255#385—42no—
256#385—42no—
257#385—44no—
258#381—28no—
259#380—24no—
260#380—28no—
261#380—24no—
262#380—44no—
263#380—42no—
264#379—24no—
265#379—24no—
266#379—28no—
267#379—24no—
268#379—44no—
269C4×C22⋊C4—24no—
270C2×#95—24no—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
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—41no—
315C25—41no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25—42no—
321C25C2×D414yes—
322C25C2×Q814yes—
323C25C2×Q814yes—
324C25#4114yes—
325C25C2411yescharacteristic
326C25C2411yescharacteristic
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C25C2411yescharacteristic
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—232no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—232no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—41no—
351C22×D4—41no—
352C22×D4—41no—
353C22×D4—41no—
354C22×D4—416no—
355C22×D4—416no—
356C22×D4—416no—
357C22×D4—416no—
358C22×D4—416no—
359C22×D4C2×D414yes—
360C22×D4C2×Q814yes—
361C22×D4C2×Q814yes—
362C22×D4C2×Q814yes—
363C22×D4C2×Q814yes—
364C22×D4#4114yes—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—24no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—24no—
392C23×C4—24no—
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—41no—
406C23×C4—41no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4C2×D414yes—
416C23×C4C2×D414yes—
417C23×C4C2×D414yes—
418C23×C4C2×Q814yes—
419C23×C4C2411yescharacteristic
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2412yes—
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C4×D4—416no—
438C4×D4—416no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—42no—
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—41no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—416no—
470C2×C4⋊C4—416no—
471C2×C4⋊C4—416no—
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×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—416no—
536C2×C22⋊C4—416no—
537C2×C22⋊C4—416no—
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—42no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—416no—
554C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
577C2×C22⋊C4C2×D414yes—
578C2×C22⋊C4C2×D414yes—
579C2×C22⋊C4C2×D414yes—
580C2×C22⋊C4C2×D414yes—
581C2×C22⋊C4C2×D418yes—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—41no—
587C2×C42—41no—
588#95—24no—
589#95—24no—
590#95—22no—
591#95—22no—
592#95—24no—
593#95—24no—
594#95—22no—
595#95—22no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—24no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
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#95—42no—
617#95—42no—
618#95—42no—
619#95C2×D418yes—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
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—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—22no—
659C24—22no—
660C24—21no—
661C24—21no—
662C24—22no—
663C24—22no—
664C24—28no—
665C24—28no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—44no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24—44no—
683C24—48no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—82no—
693C24—82no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24C22⋊Q8116yes—
704C24C22×D412yes—
705C24C22×D412yes—
706C24C22×D412yes—
707C24C22×D412yes—
708C24C22×D412yes—
709C24C22×Q812yes—
710C24C22×Q812yes—
711C24C22×Q812yes—
712C24C22×Q812yes—
713C24C22×Q812yes—
714C24C2×#4112yes—
715C24C2×#4112yes—
716C24C2×#4112yes—
717C24C2×#4112yes—
718C24C2×#4112yes—
719C24H(5,𝔽2)12yes—
720C24H(5,𝔽2)12yes—
721C24C2511yescharacteristic
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—4128no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4C22⋊Q8116yes—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
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—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—28no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—21no—
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—22no—
855C22×C4—22no—
856C22×C4—44no—
857C22×C4—48no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—48no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—48no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—48no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—48no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—82no—
888C22×C4—84no—
889C22×C4—82no—
890C22×C4—84no—
891C22×C4—84no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4—84no—
896C22×C4—84no—
897C22×C4—84no—
898C22×C4—84no—
899C22×C4—84no—
900C22×C4—84no—
901C22×C4—84no—
902C22×C4—84no—
903C22×C4C22×D414yes—
904C22×C4C22×D412yes—
905C22×C4C22×D412yes—
906C22×C4C22×D414yes—
907C22×C4C22×D412yes—
908C22×C4C22×D412yes—
909C22×C4C22×D412yes—
910C22×C4C22×Q812yes—
911C22×C4C22×Q812yes—
912C22×C4C2×#4112yes—
913C22×C4H(5,𝔽2)14yes—
914C22×C4H(5,𝔽2)14yes—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—84no—
925C4⋊C4—84no—
926C4⋊C4—84no—
927C4⋊C4—84no—
928C4⋊C4—84no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
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—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—82no—
953C22⋊C4—82no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C22⋊C4—82no—
958C22⋊C4—82no—
959C22⋊C4—84no—
960C22⋊C4—84no—
961C22⋊C4—84no—
962C22⋊C4—84no—
963C22⋊C4—84no—
964C42—44no—
965C42—44no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—232no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—24no—
1027C23—24no—
1028C23—416no—
1029C23—416no—
1030C23—416no—
1031C23—416no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
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—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—88no—
1077C23—816no—
1078C23—816no—
1079C23—88no—
1080C23—816no—
1081C23—88no—
1082C23—816no—
1083C23—88no—
1084C23—88no—
1085C23—816no—
1086C23—816no—
1087C23—88no—
1088C23—816no—
1089C23—816no—
1090C23—88no—
1091C23—88no—
1092C23—88no—
1093C23C2×C22⋊Q814yes—
1094C23C2×C22⋊Q814yes—
1095C23C2×C22⋊Q814yes—
1096C23C2×C22⋊Q814yes—
1097C23C2×C22⋊Q814yes—
1098C23#54314yes—
1099C23D4214yes—
1100C23#54614yes—
1101C23#54614yes—
1102C23#55114yes—
1103C23C23×D411yescharacteristic
1104C23C23×D411yescharacteristic
1105C23C23×Q811yescharacteristic
1106C23C22×#4111yescharacteristic
1107C23C22×#4111yescharacteristic
1108C23C2×H(5,𝔽2)12yes—
1109C23C2×H(5,𝔽2)11yescharacteristic
1110C23C2×H(5,𝔽2)11yescharacteristic
1111C23C2×H(5,𝔽2)12yes—
1112C23#58512yes—
1113C23#58512yes—
1114D4—232no—
1115D4—416no—
1116D4—416no—
1117D4—416no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—416no—
1150C2×C4—416no—
1151C2×C4—416no—
1152C2×C4—416no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
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—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—88no—
1231C2×C4—88no—
1232C2×C4—816no—
1233C2×C4—88no—
1234C2×C4—88no—
1235C2×C4—88no—
1236C2×C4C2×C22⋊Q814yes—
1237C2×C4#53414yes—
1238C22—24no—
1239C22—28no—
1240C22—24no—
1241C22—28no—
1242C22—24no—
1243C22—28no—
1244C22—24no—
1245C22—28no—
1246C22—24no—
1247C22—24no—
1248C22—24no—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—28no—
1254C22—24no—
1255C22—24no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—42no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—44no—
1276C22—44no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—44no—
1284C22—44no—
1285C22—42no—
1286C22—832no—
1287C22—832no—
1288C22—81no—
1289C22—82no—
1290C22—82no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22#243718yes—
1295C22C22×C22⋊Q811yescharacteristic
1296C22C22×C22⋊Q811yescharacteristic
1297C22C2×#53411yescharacteristic
1298C22#344911yescharacteristic
1299C22C2×#54311yescharacteristic
1300C22C2×D4211yescharacteristic
1301C22C2×#54611yescharacteristic
1302C22C2×#54611yescharacteristic
1303C22C2×#55111yescharacteristic
1304C22#348411yescharacteristic
1305C22#348511yescharacteristic
1306C22#348812yes—
1307C22#349612yes—
1308C22#350112yes—
1309C22#350112yes—
1310C22#350512yes—
1311C22#350512yes—
1312C22#351912yes—
1313C22#352112yes—
1314C22#353412yes—
1315C22#353712yes—
1316C22#354212yes—
1317C22#356012yes—
1318C4—24no—
1319C4—24no—
1320C4—42no—
1321C4—44no—
1322C4—42no—
1323C4—44no—
1324C4—44no—
1325C4—42no—
1326C4—42no—
1327C4—81no—
1328C4—82no—
1329C4—82no—
1330C4—82no—
1331C4—82no—
1332C4—81no—
1333C4—81no—
1334C4—82no—
1335C4—81no—
1336C2—28no—
1337C2—44no—
1338C2—44no—
1339C2—44no—
1340C2—82no—
1341C2C2×#243711yescharacteristic
1342C2#3501011yescharacteristic
1343C2#3534911yescharacteristic
1344C2#3577612yes—
1345C2#3764611yescharacteristic
1346C2#3803011yescharacteristic
1347C2#3890411yescharacteristic
1348C2#3933211yescharacteristic
1349C2#4060912yes—
1350C2#4302212yes—
1351C2#4314912yes—
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×#2487C2semidirect
2. C22×#396C2semidirect
5. #16301C2semidirect
6. #16298C2semidirect
7. #15508C2semidirect
8. #15439C2semidirect
9. #15324C2semidirect
10. #15309C2semidirect
11. #15091C2semidirect
12. #14946C2semidirect
13. #14769C2semidirect
14. #14729C2semidirect
15. #14729C2semidirect
16. #14726C2semidirect
17. #14262C2semidirect
18. #14015C2semidirect
19. #14015C2semidirect
20. #13960C2semidirect
21. #13877C2semidirect
22. #13877C2semidirect
27. C23×C4⋊C4C22semidirect
28. C23×C4⋊C4C22semidirect
29. C23×C4⋊C4C22semidirect
36. C2×#400C22semidirect
37. C2×#399C22semidirect
41. C2×#396C22semidirect
42. C2×#396C22semidirect
43. C2×#396C22semidirect
44. C2×#396C22semidirect
49. C2×#389C22semidirect
64. C2×#385C22semidirect
65. C2×#385C22semidirect
66. C2×#385C22semidirect
67. C2×#385C22semidirect
68. C2×#385C22semidirect
69. C2×#385C22semidirect
70. C2×#385C22semidirect
73. C2×#380C22semidirect
74. C2×#380C22semidirect
75. C2×#380C22semidirect
76. C2×#380C22semidirect
83. C22×#95C22semidirect
84. #1445C22semidirect
85. #1445C22semidirect
86. #1444C22semidirect
87. #1444C22semidirect
88. #1442C22semidirect
89. #1442C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1441C22semidirect
93. #1441C22semidirect
94. #1441C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. #1434C22semidirect
118. C22⋊#95C22semidirect
119. C22⋊#95C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24872
C22×#3962
C2×D4×C22⋊C42
C2×#23082
#163012
#162982
#155082
#154392
#153242
#153092
#150912
#149462
#147692
#147292
#147262
#142622
#140152
#139602
#138772
#138672