Finite Group Databasebeta

← #636099

Subgroups — #636099

Order 512.

5186 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2437C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic, complemented
3C22×#386C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic, complemented
5#16323C212yesmaximal, complemented
6#16323C212yesmaximal, complemented
7#16320C212yesmaximal, complemented
8#16319C212yesmaximal, complemented
9#14920C211yesmaximal, characteristic, complemented
10#14914C211yesmaximal, characteristic, complemented
11#14777C212yesmaximal, complemented
12#14759C212yesmaximal, complemented
13#14748C212yesmaximal, complemented
14#14734C211yesmaximal, characteristic, complemented
15#14729C212yesmaximal, complemented
16#14726C211yesmaximal, characteristic, complemented
17#14693C211yesmaximal, characteristic, complemented
18#14275C211yesmaximal, characteristic, complemented
19#14265C211yesmaximal, characteristic, complemented
20#14262C211yesmaximal, characteristic, complemented
21#13877C211yesmaximal, characteristic, complemented
22#13867C211yesmaximal, characteristic
23#13867C211yesmaximal, characteristic
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic, complemented
28C23×C4⋊C4C2212yescomplemented
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34#2626—28no—
35#2437—28no—
36C2×#399C2211yescharacteristic, complemented
37C2×#399C2212yescomplemented
38C2×#399C2212yescomplemented
39C2×#396C2211yescharacteristic, complemented
40C2×#396C2211yescharacteristic, complemented
41C2×#396C2212yescomplemented
42C2×#396C2212yescomplemented
43C2×#396C2212yescomplemented
44C2×#393C2211yescharacteristic, complemented
45C2×#393C2212yescomplemented
46C2×#386—28no—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#385—28no—
56C2×#385C2211yescharacteristic
57C2×#385C2211yescharacteristic
58C2×#385C2211yescharacteristic
59C2×#385C2211yescharacteristic
60C2×#385C2211yescharacteristic
61C2×#385C2211yescharacteristic
62C2×#385C2211yescharacteristic
63C2×#385C2211yescharacteristic
64C2×#385C2211yescharacteristic, complemented
65C2×#385C2211yescharacteristic, complemented
66C2×#385C2212yescomplemented
67C2×#385C2212yescomplemented
68C2×#385C2212yescomplemented
69C2×#385C2212yescomplemented
70C2×#385C2212yescomplemented
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×#380C2211yescharacteristic, complemented
75C2×#379C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C22×#95C2211yescharacteristic
82C22×#95C2211yescharacteristic
83C22×#95C2212yescomplemented
84#1446C2212yescomplemented
85#1445C2212yescomplemented
86#1445C2212yescomplemented
87#1444C2212yescomplemented
88#1444C2212yescomplemented
89#1443C2212yescomplemented
90#1442C2212yescomplemented
91#1442C2212yescomplemented
92#1442C2212yescomplemented
93#1441C2212yescomplemented
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#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yes—
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—44no—
133C23×D4—44no—
134C23×D4Q818yescomplemented
135C23×D4C2312yes—
136C23×D4C2312yes—
137C24×C4—24no—
138C24×C4—24no—
139C24×C4—44no—
140C24×C4—42no—
141C24×C4—44no—
142C24×C4C2311yescharacteristic
143C24×C4C2312yes—
144C24×C4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C2×C22⋊Q8—24no—
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8—42no—
156C2×C22⋊Q8—44no—
157C22×C4⋊C4—28no—
158C22×C4⋊C4—44no—
159C22×C4⋊C4—44no—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
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—24no—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4—44no—
187C22×C22⋊C4—42no—
188C22×C22⋊C4—42no—
189C22×C22⋊C4D418yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223#399—28no—
224#399—24no—
225#399—44no—
226#396—28no—
227#396—24no—
228#396—24no—
229#396—28no—
230#396—44no—
231#393—24no—
232#393—28no—
233#386—28no—
234#386—28no—
235#386—28no—
236#386—28no—
237#386—44no—
238#386—44no—
239#386—44no—
240#386—44no—
241#385—24no—
242#385—24no—
243#385—24no—
244#385—24no—
245#385—28no—
246#385—24no—
247#385—24no—
248#385—24no—
249#385—24no—
250#385—28no—
251#385—44no—
252#385—42no—
253#385—44no—
254#385—44no—
255#385D418yescomplemented
256#380—24no—
257#380—24no—
258#380—24no—
259#380—24no—
260#379—24no—
261#379—24no—
262#379—24no—
263#379—24no—
264#379—24no—
265#379—42no—
266C2×#95—24no—
267C2×#95—24no—
268C2×#95—28no—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
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—24no—
307C25—24no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25—42no—
321C25C2×D414yes—
322C25C2×Q814yes—
323C25C2×Q814yes—
324C25#4114yes—
325C25C2412yes—
326C25C2411yescharacteristic
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—42no—
332C22×Q8—41no—
333C22×Q8—42no—
334C22×D4—232no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—42no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—432no—
348C22×D4—416no—
349C22×D4—416no—
350C22×D4—432no—
351C22×D4C2×Q818yes—
352C22×D4C2×Q818yes—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—24no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—24no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—22no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
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—41no—
401C23×C4—41no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—416no—
406C23×C4—416no—
407C23×C4—432no—
408C23×C4—416no—
409C23×C4—432no—
410C23×C4C2×D414yes—
411C23×C4C2×D414yes—
412C23×C4C2×D414yes—
413C23×C4C2×Q814yes—
414C23×C4C2411yescharacteristic
415C23×C4C2412yes—
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2412yes—
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2412yes—
433C22⋊Q8—416no—
434C22⋊Q8—416no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
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—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—41no—
464C2×C4⋊C4—41no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—432no—
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×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4C2×D418yescomplemented
481C2×C22⋊C4—232no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
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—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
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—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
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—41no—
545C2×C22⋊C4—41no—
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⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4C2×D414yes—
571C2×C22⋊C4C2×D414yes—
572C2×C22⋊C4C2×D414yes—
573C2×C22⋊C4C2×D414yes—
574C2×C22⋊C4C2×D414yes—
575C2×C22⋊C4C2×D414yes—
576C2×C22⋊C4#4114yes—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—24no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—42no—
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—
610#95C2×D418yescomplemented
611C24—21no—
612C24—21no—
613C24—22no—
614C24—22no—
615C24—21no—
616C24—22no—
617C24—22no—
618C24—21no—
619C24—22no—
620C24—22no—
621C24—28no—
622C24—28no—
623C24—28no—
624C24—216no—
625C24—28no—
626C24—216no—
627C24—28no—
628C24—28no—
629C24—28no—
630C24—28no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—21no—
638C24—22no—
639C24—28no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—44no—
657C24—44no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—48no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—44no—
671C24—44no—
672C24—44no—
673C24—48no—
674C24—48no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24—44no—
679C24—44no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24C22⋊Q8116yes—
689C24C22×D412yes—
690C24C22×D412yes—
691C24C22×D412yes—
692C24C22×D412yes—
693C24C22×Q814yes—
694C24C22×Q812yes—
695C24C22×Q812yes—
696C24C22×Q812yes—
697C24C2×#4112yes—
698C24C2×#4112yes—
699C24C2×#4112yes—
700C24C2×#4112yes—
701C24H(5,𝔽2)14yes—
702C24H(5,𝔽2)14yes—
703C24H(5,𝔽2)12yes—
704C242−1+412yes—
705C24C2511yescharacteristic
706C2×Q8—44no—
707C2×Q8—44no—
708C2×Q8—82no—
709C2×Q8—84no—
710C2×Q8—84no—
711C2×D4—216no—
712C2×D4—216no—
713C2×D4—216no—
714C2×D4—216no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—4128no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C22×C4—216no—
727C22×C4—28no—
728C22×C4—216no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—21no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—21no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
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—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
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—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—44no—
835C22×C4—44no—
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—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—4128no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—82no—
874C22×C4—82no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C22×D414yes—
887C22×C4C22×D414yes—
888C22×C4C22×D412yes—
889C22×C4C22×Q814yes—
890C22×C4C2×#4114yes—
891C22×C4H(5,𝔽2)14yes—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—82no—
903C4⋊C4—82no—
904C4⋊C4—84no—
905C4⋊C4—82no—
906C4⋊C4—84no—
907C4⋊C4—84no—
908C4⋊C4—84no—
909C22⋊C4—216no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—82no—
939C22⋊C4—82no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—24no—
946C23—22no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—24no—
955C23—22no—
956C23—22no—
957C23—24no—
958C23—22no—
959C23—22no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—232no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—24no—
981C23—22no—
982C23—24no—
983C23—24no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—232no—
989C23—22no—
990C23—22no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—416no—
1000C23—416no—
1001C23—416no—
1002C23—432no—
1003C23—432no—
1004C23—416no—
1005C23—416no—
1006C23—432no—
1007C23—432no—
1008C23—416no—
1009C23—416no—
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—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—416no—
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—816no—
1048C23—816no—
1049C23—88no—
1050C23—88no—
1051C23—816no—
1052C23—88no—
1053C23—88no—
1054C23—816no—
1055C23C2×C22⋊Q814yes—
1056C23C2×C22⋊Q814yes—
1057C23C2×C22⋊Q814yes—
1058C23#52514yes—
1059C23#53414yes—
1060C23#53514yes—
1061C23#53818yes—
1062C23#53914yes—
1063C23#54318yes—
1064C23D4214yes—
1065C23#54714yes—
1066C23D4×Q814yes—
1067C23#55414yes—
1068C23C23×D411yescharacteristic
1069C23C23×D411yescharacteristic
1070C23C23×Q811yescharacteristic
1071C23C22×#4111yescharacteristic
1072C23C22×#4111yescharacteristic
1073C23C2×H(5,𝔽2)12yes—
1074C23C2×H(5,𝔽2)12yes—
1075C23C2×H(5,𝔽2)11yescharacteristic
1076C23C2×H(5,𝔽2)12yes—
1077C23C2×2−1+411yescharacteristic
1078C23#58512yes—
1079Q8—88no—
1080D4—432no—
1081D4—432no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—432no—
1114C2×C4—432no—
1115C2×C4—416no—
1116C2×C4—416no—
1117C2×C4—416no—
1118C2×C4—432no—
1119C2×C4—41no—
1120C2×C4—42no—
1121C2×C4—41no—
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—41no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—41no—
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—41no—
1155C2×C4—41no—
1156C2×C4—41no—
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—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
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—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—88no—
1198C2×C4—88no—
1199C2×C4—88no—
1200C2×C4—88no—
1201C22—24no—
1202C22—24no—
1203C22—24no—
1204C22—24no—
1205C22—28no—
1206C22—28no—
1207C22—24no—
1208C22—28no—
1209C22—28no—
1210C22—24no—
1211C22—24no—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—28no—
1217C22—28no—
1218C22—28no—
1219C22—28no—
1220C22—24no—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—464no—
1225C22—42no—
1226C22—42no—
1227C22—44no—
1228C22—44no—
1229C22—42no—
1230C22—42no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—832no—
1241C22—82no—
1242C22—82no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22#244918yes—
1250C22#262618yescomplemented
1251C22C22×C22⋊Q811yescharacteristic
1252C22C2×#52511yescharacteristic
1253C22C2×#53411yescharacteristic
1254C22C2×#53511yescharacteristic
1255C22C2×#53812yes—
1256C22C2×#53911yescharacteristic
1257C22C2×#54312yes—
1258C22#345912yes—
1259C22C2×D4211yescharacteristic
1260C22C2×#54711yescharacteristic
1261C22C2×D4×Q811yescharacteristic
1262C22C2×#55411yescharacteristic
1263C22#348412yes—
1264C22#348411yescharacteristic
1265C22#348511yescharacteristic
1266C22#348812yes—
1267C22#350112yes—
1268C22#351312yes—
1269C22#351912yes—
1270C22#353212yes—
1271C22#353412yes—
1272C22#353512yes—
1273C22#353612yes—
1274C4—44no—
1275C4—44no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—44no—
1283C4—44no—
1284C4—44no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—82no—
1290C4—81no—
1291C4—81no—
1292C4—82no—
1293C2—28no—
1294C2—28no—
1295C2—44no—
1296C2—84no—
1297C2C2×#262611yescharacteristic
1298C2C2×#244911yescharacteristic
1299C2#3498511yescharacteristic
1300C2#3499012yes—
1301C2#3748212yes—
1302C2#3764511yescharacteristic
1303C2#3764611yescharacteristic
1304C2#3768412yes—
1305C2#3803611yescharacteristic
1306C2#3803911yescharacteristic
1307C2#3809612yes—
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
4. C22×#385C2semidirect
5. #16323C2semidirect
6. #16323C2semidirect
7. #16320C2semidirect
8. #16319C2semidirect
9. #14920C2semidirect
10. #14914C2semidirect
11. #14777C2semidirect
12. #14759C2semidirect
13. #14748C2semidirect
14. #14734C2semidirect
15. #14729C2semidirect
16. #14726C2semidirect
17. #14693C2semidirect
18. #14275C2semidirect
19. #14265C2semidirect
20. #14262C2semidirect
21. #13877C2semidirect
27. C22×C22⋊Q8C22semidirect
28. C23×C4⋊C4C22semidirect
36. C2×#399C22semidirect
37. C2×#399C22semidirect
38. C2×#399C22semidirect
39. C2×#396C22semidirect
40. C2×#396C22semidirect
41. C2×#396C22semidirect
42. C2×#396C22semidirect
43. C2×#396C22semidirect
44. C2×#393C22semidirect
45. C2×#393C22semidirect
64. C2×#385C22semidirect
65. C2×#385C22semidirect
66. C2×#385C22semidirect
67. C2×#385C22semidirect
68. C2×#385C22semidirect
69. C2×#385C22semidirect
70. C2×#385C22semidirect
74. C2×#380C22semidirect
83. C22×#95C22semidirect
84. #1446C22semidirect
85. #1445C22semidirect
86. #1445C22semidirect
87. #1444C22semidirect
88. #1444C22semidirect
89. #1443C22semidirect
90. #1442C22semidirect
91. #1442C22semidirect
92. #1442C22semidirect
93. #1441C22semidirect
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
110. #1439C22semidirect
111. #1439C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
134. C23×D4Q8semidirect
255. #385D4semidirect
480. C2×C4⋊C4C2×D4semidirect
610. #95C2×D4semidirect
1250. C22#2626semidirect

Maximal subgroups

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

subgroupindex
C2×#24372
C2×#26262
C22×#3862
C22×#3852
#163232
#163202
#163192
#149202
#149142
#147772
#147592
#147482
#147342
#147292
#147262
#146932
#142752
#142652
#142622
#138772
#138672