Finite Group Databasebeta

← #4420638

Subgroups — #4420638

Order 512.

4455 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2557C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
3#17077C211yesmaximal, characteristic, complemented
4#16884C211yesmaximal, characteristic, complemented
5#16884C211yesmaximal, characteristic, complemented
6#16810C211yesmaximal, characteristic, complemented
7#16357C212yesmaximal, complemented
8#16270C212yesmaximal, complemented
9#15948C212yesmaximal, complemented
10#15795C212yesmaximal, complemented
11#15273C212yesmaximal, complemented
12#15259C212yesmaximal, complemented
13#15123C211yesmaximal, characteristic, complemented
14#14865C211yesmaximal, characteristic, complemented
15#14820C212yesmaximal, complemented
16#14716C212yesmaximal, complemented
17#14715C211yesmaximal, characteristic, complemented
18#14715C211yesmaximal, characteristic, complemented
19#14623C211yesmaximal, characteristic, complemented
20#14351C211yesmaximal, characteristic, complemented
21#14311C211yesmaximal, characteristic, complemented
22#14299C211yesmaximal, characteristic, complemented
23#14175C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#121C2212yescomplemented
28C22×#120C2212yes—
29C22×#120C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C23×C22⋊C4C2212yes—
33#2557—28no—
34C2×#397C2211yescharacteristic
35C2×#397C2211yescharacteristic, complemented
36C2×#397C2212yescomplemented
37C2×#393C2211yescharacteristic, complemented
38C2×#393C2212yescomplemented
39C2×#393C2212yescomplemented
40C2×#392C2211yescharacteristic
41C2×#392C2211yescharacteristic
42C2×#392C2211yescharacteristic
43C2×#392C2211yescharacteristic
44C2×#392C2211yescharacteristic
45C2×#392C2212yes—
46C2×#392C2212yes—
47C2×#392C2212yescomplemented
48D4×C22⋊C4—28no—
49C2×#391C2211yescharacteristic, complemented
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic, complemented
53C2×#388C2211yescharacteristic, complemented
54C2×#387C2211yescharacteristic, complemented
55C2×#386C2211yescharacteristic
56C2×#386C2211yescharacteristic
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#386C2211yescharacteristic, complemented
60C2×#386C2212yescomplemented
61C2×#386C2212yescomplemented
62C2×#386C2212yescomplemented
63C2×#386C2212yescomplemented
64C2×#380C2211yescharacteristic
65C2×#380C2212yescomplemented
66C2×#379C2212yes—
67C2×#379C2212yes—
68C2×#379C2212yes—
69C2×C4×C22⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic, complemented
71#1443C2212yescomplemented
72#1443C2212yescomplemented
73#1443C2212yescomplemented
74#1442C2212yescomplemented
75#1442C2211yescharacteristic, complemented
76#1442C2211yescharacteristic, complemented
77#1442C2211yescharacteristic, complemented
78#1442C2211yescharacteristic, complemented
79#1440C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1440C2212yescomplemented
83#1440C2212yescomplemented
84#1440C2212yescomplemented
85#1440C2212yescomplemented
86#1439C2212yes—
87#1439C2212yescomplemented
88#1439C2211yescharacteristic, complemented
89#1439C2211yescharacteristic, complemented
90#1439C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2211yescharacteristic, complemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2211yescharacteristic, complemented
97#1438C2211yescharacteristic
98#1438C2211yescharacteristic
99#1438C2211yescharacteristic
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2211yescharacteristic
104#1438C2212yes—
105#1438C2212yescomplemented
106#1438C2212yescomplemented
107#1438C2212yescomplemented
108#1438C2212yescomplemented
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1438C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115C4⋊#95C2211yescharacteristic, complemented
116#1434C2211yescharacteristic, complemented
117#1434C2211yescharacteristic, complemented
118#1434C2211yescharacteristic, complemented
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C26C2312yes—
126C23×Q8C2311yescharacteristic
127C23×D4—24no—
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—44no—
131C23×D4—44no—
132C23×D4C2311yescharacteristic
133C23×D4C2312yes—
134C23×D4C2312yes—
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2311yescharacteristic
141C23×D4C2312yes—
142C24×C4C2312yes—
143C24×C4C2312yes—
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C2×#124—24no—
147C2×#124—44no—
148C2×#123—24no—
149C2×#123—44no—
150C2×#121—44no—
151C2×#121—44no—
152C2×#121—44no—
153C2×#120—44no—
154C2×#120—44no—
155C2×#120—44no—
156C2×#120—44no—
157C2×#120—44no—
158C2×#120—44no—
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4—44no—
162C2×C4×D4—44no—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C22⋊C4—28no—
170C22×C22⋊C4—44no—
171C22×C22⋊C4—44no—
172C22×C22⋊C4C2311yescharacteristic
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213#397—24no—
214#397—24no—
215#397—44no—
216#393—24no—
217#393—44no—
218#393—44no—
219#392—24no—
220#392—24no—
221#392—24no—
222#392—24no—
223#392—24no—
224#392—44no—
225#392—44no—
226#392—44no—
227#391—24no—
228#390—24no—
229#390—24no—
230#390—24no—
231#388—24no—
232#387—24no—
233#386—24no—
234#386—24no—
235#386—28no—
236#386—28no—
237#386—24no—
238#386—44no—
239#386—44no—
240#386—44no—
241#386—44no—
242#380—24no—
243#380—44no—
244#379—28no—
245#379—44no—
246#379—44no—
247C4×C22⋊C4—24no—
248C4×C22⋊C4D418yescomplemented
249C2×#95C2311yescharacteristic
250C2×#95C2311yescharacteristic
251C2×#95C2311yescharacteristic
252C2×#95C2311yescharacteristic
253C2×#95C2311yescharacteristic
254C2×#95C2312yes—
255C2×#95C2311yescharacteristic
256C2×#95C2312yes—
257C2×#95C2311yescharacteristic
258C2×#95C2311yescharacteristic
259C2×#95C2311yescharacteristic
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C25—24no—
286C25—24no—
287C25—24no—
288C25—24no—
289C25—24no—
290C25—24no—
291C25—24no—
292C25—42no—
293C25—42no—
294C25—42no—
295C25—42no—
296C25—42no—
297C25—42no—
298C25—42no—
299C25—42no—
300C25C2411yescharacteristic
301C25C2412yes—
302C25C2411yescharacteristic
303C25C2411yescharacteristic
304C25C2412yes—
305C22×Q8—22no—
306C22×Q8—22no—
307C22×Q8—42no—
308C22×Q8—41no—
309C22×Q8—42no—
310C22×D4—24no—
311C22×D4—24no—
312C22×D4—232no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—22no—
316C22×D4—24no—
317C22×D4—24no—
318C22×D4—22no—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—24no—
341C22×D4—42no—
342C22×D4—42no—
343C22×D4—42no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—41no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—416no—
370C22×D4—416no—
371C22×D4—432no—
372C22×D4—432no—
373C22×D4#4114yes—
374C22×D4#4114yes—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—22no—
383C23×C4—24no—
384C23×C4—24no—
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—41no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4C2×D414yes—
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417#124—416no—
418#123—416no—
419#121—432no—
420#120—432no—
421#120—432no—
422C4×D4—416no—
423C4×D4—416no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—42no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—432no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—41no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4C2×D414yes—
541C2×C22⋊C4C2×D414yes—
542C2×C42—22no—
543C2×C42—42no—
544C2×C42—42no—
545C2×C42—42no—
546C2×C42C2×D414yes—
547C2×C42C2×D414yes—
548#95—22no—
549#95—22no—
550#95—24no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—24no—
562#95—24no—
563#95—42no—
564#95—42no—
565#95—42no—
566#95—42no—
567#95—42no—
568#95—42no—
569#95—42no—
570#95—42no—
571#95—42no—
572#95—42no—
573#95—42no—
574#95—42no—
575#95—42no—
576#95—42no—
577#95—42no—
578#95—42no—
579#95—42no—
580#95—42no—
581#95—42no—
582#95C2×D414yes—
583#95C2×D414yes—
584C24—22no—
585C24—21no—
586C24—21no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—21no—
593C24—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—21no—
604C24—21no—
605C24—216no—
606C24—21no—
607C24—22no—
608C24—21no—
609C24—21no—
610C24—22no—
611C24—22no—
612C24—21no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—21no—
627C24—22no—
628C24—22no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—21no—
637C24—22no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—48no—
642C24—48no—
643C24—48no—
644C24—48no—
645C24—48no—
646C24—48no—
647C24—48no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—48no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—48no—
657C24—84no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24—84no—
662C24—84no—
663C24—84no—
664C24—84no—
665C24—84no—
666C24—84no—
667C24—84no—
668C24—84no—
669C24—84no—
670C24—84no—
671C24—84no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24C22×D412yes—
676C24C2×#4114yes—
677C24C2×#4114yes—
678C24H(5,𝔽2)12yes—
679C24H(5,𝔽2)14yes—
680C24H(5,𝔽2)14yes—
681C24H(5,𝔽2)14yes—
682C24C2511yescharacteristic
683C2×Q8—44no—
684C2×Q8—44no—
685C2×Q8—82no—
686C2×Q8—84no—
687C2×Q8—84no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—216no—
691C2×D4—216no—
692C2×D4—216no—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—4128no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—44no—
725C2×D4—82no—
726C2×D4—84no—
727C2×D4—82no—
728C2×D4—84no—
729C2×D4—82no—
730C2×D4—84no—
731C2×D4—84no—
732C2×D4—84no—
733C2×D4—84no—
734C2×D4—84no—
735C2×D4—84no—
736C2×D4—84no—
737C2×D4—84no—
738C2×D4—84no—
739C2×D4—84no—
740C2×D4—84no—
741C2×D4—84no—
742C2×D4—84no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4—84no—
746C2×D4—84no—
747C2×D4—84no—
748C2×D4—84no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—28no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—21no—
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—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—44no—
851C22×C4—48no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—82no—
858C22×C4—84no—
859C22×C4—84no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4—84no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4C22×D412yes—
866C22×C4C22×D412yes—
867C22×C4C22×D412yes—
868C22×C4C22×D412yes—
869C22×C4C22×D412yes—
870C22×C4C22×D412yes—
871C22×C4C2×#4112yes—
872C22×C4C2×#4112yes—
873C22×C4H(5,𝔽2)12yes—
874C22×C4H(5,𝔽2)14yes—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—44no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—48no—
904C22⋊C4—82no—
905C22⋊C4—82no—
906C22⋊C4—82no—
907C22⋊C4—84no—
908C22⋊C4—84no—
909C22⋊C4—84no—
910C22⋊C4—84no—
911C22⋊C4—84no—
912C22⋊C4—84no—
913C22⋊C4—84no—
914C22⋊C4—84no—
915C22⋊C4—84no—
916C22⋊C4—84no—
917C22⋊C4—84no—
918C22⋊C4—84no—
919C42—44no—
920C42—44no—
921C42—44no—
922C23—22no—
923C23—24no—
924C23—22no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—22no—
954C23—24no—
955C23—24no—
956C23—22no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—432no—
965C23—432no—
966C23—42no—
967C23—42no—
968C23—42no—
969C23—42no—
970C23—42no—
971C23—42no—
972C23—42no—
973C23—41no—
974C23—42no—
975C23—41no—
976C23—42no—
977C23—42no—
978C23—41no—
979C23—41no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—41no—
993C23—42no—
994C23—41no—
995C23—41no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—41no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—41no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—41no—
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—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—42no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—42no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—42no—
1051C23—42no—
1052C23—41no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—816no—
1062C23—816no—
1063C23—816no—
1064C23—816no—
1065C23—816no—
1066C23—816no—
1067C23—816no—
1068C23—816no—
1069C23—816no—
1070C23—816no—
1071C23—816no—
1072C23—816no—
1073C23—816no—
1074C23#53514yes—
1075C23#53818yes—
1076C23C23×D411yescharacteristic
1077C23C22×#4111yescharacteristic
1078C23C22×#4111yescharacteristic
1079C23C2×H(5,𝔽2)12yes—
1080C23C2×H(5,𝔽2)12yes—
1081C23C2×H(5,𝔽2)12yes—
1082C23C2×H(5,𝔽2)12yes—
1083C23C2×H(5,𝔽2)11yescharacteristic
1084C23C2×H(5,𝔽2)11yescharacteristic
1085C23#58511yescharacteristic
1086C23#58511yescharacteristic
1087Q8—88no—
1088D4—232no—
1089D4—416no—
1090D4—432no—
1091D4—88no—
1092D4—88no—
1093D4—816no—
1094D4—88no—
1095D4—816no—
1096D4—816no—
1097D4—816no—
1098C2×C4—24no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—416no—
1121C2×C4—41no—
1122C2×C4—42no—
1123C2×C4—41no—
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—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
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—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—816no—
1200C2×C4—88no—
1201C2×C4—816no—
1202C2×C4#52514yes—
1203C2×C4#53514yes—
1204C22—28no—
1205C22—28no—
1206C22—24no—
1207C22—24no—
1208C22—24no—
1209C22—28no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—42no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—42no—
1226C22—44no—
1227C22—42no—
1228C22—44no—
1229C22—42no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—42no—
1234C22—42no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—42no—
1241C22—44no—
1242C22—864no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—81no—
1250C22—82no—
1251C22—82no—
1252C22—82no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—82no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22C2×#52511yescharacteristic
1269C22C2×#53511yescharacteristic
1270C22C2×#53511yescharacteristic
1271C22C2×#53812yes—
1272C22#348411yescharacteristic
1273C22#348411yescharacteristic
1274C22#348811yescharacteristic
1275C22#348811yescharacteristic
1276C22#349012yes—
1277C22#351311yescharacteristic
1278C22#351411yescharacteristic
1279C22#351911yescharacteristic
1280C22#351912yes—
1281C22#351912yes—
1282C22#352111yescharacteristic
1283C22#353212yes—
1284C22#353212yes—
1285C22#353212yes—
1286C22#353412yes—
1287C22#353412yes—
1288C22#353412yes—
1289C22#354312yes—
1290C22#355812yes—
1291C4—24no—
1292C4—24no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—82no—
1299C4—82no—
1300C4—82no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—82no—
1305C4—81no—
1306C4—81no—
1307C4—82no—
1308C4—82no—
1309C2—48no—
1310C2—44no—
1311C2—82no—
1312C2—84no—
1313C2—161no—
1314C2#3498811yescharacteristic
1315C2#3523711yescharacteristic
1316C2#3552211yescharacteristic
1317C2#4058811yescharacteristic
1318C2#4058811yescharacteristic
1319C2#4059011yescharacteristic
1320C2#4072812yes—
1321C2#4079012yes—
1322C2#4248411yescharacteristic
1323C2#4855512yes—
1324C2#5001112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2557C2semidirect
2. C2×D4×C22⋊C4C2semidirect
3. #17077C2semidirect
4. #16884C2semidirect
5. #16884C2semidirect
6. #16810C2semidirect
7. #16357C2semidirect
8. #16270C2semidirect
9. #15948C2semidirect
10. #15795C2semidirect
11. #15273C2semidirect
12. #15259C2semidirect
13. #15123C2semidirect
14. #14865C2semidirect
15. #14820C2semidirect
16. #14716C2semidirect
17. #14715C2semidirect
18. #14715C2semidirect
19. #14623C2semidirect
20. #14351C2semidirect
21. #14311C2semidirect
22. #14299C2semidirect
23. #14175C2semidirect
27. C22×#121C22semidirect
35. C2×#397C22semidirect
36. C2×#397C22semidirect
37. C2×#393C22semidirect
38. C2×#393C22semidirect
39. C2×#393C22semidirect
47. C2×#392C22semidirect
49. C2×#391C22semidirect
52. C2×#390C22semidirect
53. C2×#388C22semidirect
54. C2×#387C22semidirect
59. C2×#386C22semidirect
60. C2×#386C22semidirect
61. C2×#386C22semidirect
62. C2×#386C22semidirect
63. C2×#386C22semidirect
65. C2×#380C22semidirect
70. C2×C4×C22⋊C4C22semidirect
71. #1443C22semidirect
72. #1443C22semidirect
73. #1443C22semidirect
74. #1442C22semidirect
75. #1442C22semidirect
76. #1442C22semidirect
77. #1442C22semidirect
78. #1442C22semidirect
82. #1440C22semidirect
83. #1440C22semidirect
84. #1440C22semidirect
85. #1440C22semidirect
87. #1439C22semidirect
88. #1439C22semidirect
89. #1439C22semidirect
90. #1439C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
105. #1438C22semidirect
106. #1438C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. C4⋊#95C22semidirect
116. #1434C22semidirect
117. #1434C22semidirect
118. #1434C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
248. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25572
C2×D4×C22⋊C42
#170772
#168842
#168102
#163572
#162702
#159482
#157952
#152732
#152592
#151232
#148652
#148202
#147162
#147152
#146232
#143512
#143112
#142992
#141752