Finite Group Databasebeta

← #779706

Subgroups — #779706

Order 512.

4784 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#556C211yesmaximal, characteristic, complemented
2C2×#2432C211yesmaximal, characteristic, complemented
3C2×#2431C211yesmaximal, characteristic
4C2×#2341C211yesmaximal, characteristic, complemented
5#16655C212yesmaximal, complemented
6#16004C212yesmaximal, complemented
7#15909C212yesmaximal, complemented
8#15453C212yesmaximal, complemented
9#15323C212yesmaximal, complemented
10#15227C211yesmaximal, characteristic, complemented
11#15215C211yesmaximal, characteristic, complemented
12#15157C211yesmaximal, characteristic, complemented
13#14917C212yesmaximal, complemented
14#14886C212yesmaximal, complemented
15#14064C212yesmaximal, complemented
16#14026C211yesmaximal, characteristic, complemented
17#14026C211yesmaximal, characteristic, complemented
18#14025C211yesmaximal, characteristic, complemented
19#14024C211yesmaximal, characteristic, complemented
20#13970C211yesmaximal, characteristic, complemented
21#13969C211yesmaximal, characteristic, complemented
22#13931C211yesmaximal, characteristic, complemented
23C4×#393C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C2×#556—28no—
26C2×#556—28no—
27C2×#556—28no—
28C22×C4⋊Q8C2211yescharacteristic
29C22×#127C2211yescharacteristic
30C22×#126C2212yes—
31C22×#126C2212yes—
32C22×#124C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C22×#124C2211yescharacteristic
35C22×C22⋊Q8C2212yes—
36C22×C22⋊Q8C2211yescharacteristic
37C22×#121C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42C22×C4×D4C2211yescharacteristic
43C22×#117C2212yes—
44#2432—28no—
45#2431—28no—
46C2×#394C2212yes—
47C2×#394C2212yes—
48C2×#393C2211yescharacteristic
49C2×#393C2212yes—
50C2×#392C2212yes—
51C2×#392C2212yes—
52#2341—28no—
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#390C2212yes—
58C2×#390C2212yes—
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#390C2211yescharacteristic
62C2×#390C2211yescharacteristic
63C2×#390C2211yescharacteristic
64C2×#390C2211yescharacteristic
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#386C2212yes—
69C2×#386C2212yes—
70C2×#385C2212yes—
71C2×#385C2212yes—
72C2×#380C2212yes—
73C2×#380C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2212yes—
78#1446C2211yescharacteristic
79#1445C2212yes—
80#1445C2212yes—
81#1442C2211yescharacteristic
82#1442C2211yescharacteristic
83#1442C2211yescharacteristic
84#1441C2212yes—
85#1441C2212yes—
86#1441C2212yes—
87#1440C2212yes—
88#1439C2211yescharacteristic
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2211yescharacteristic
94#1439C2211yescharacteristic
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1437C2212yes—
111#1437C2212yes—
112#1437C2212yes—
113#1437C2212yes—
114#1437C2212yes—
115#1436C2212yes—
116#1436C2212yes—
117#1436C2212yes—
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120C4⋊#95C2211yescharacteristic
121C4⋊#95C2211yescharacteristic
122C4⋊#95C2211yescharacteristic
123#1434C2212yes—
124#1434C2212yes—
125C22⋊#95C2212yes—
126C4×#95C2211yescharacteristic
127C4×#95C2211yescharacteristic
128C4×#95C2211yescharacteristic
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—24no—
133C22×#41—24no—
134C22×#41—42no—
135C22×#41—42no—
136C23×Q8C2311yescharacteristic
137C23×Q8C2311yescharacteristic
138C23×Q8C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2311yescharacteristic
141C23×D4C2312yes—
142C23×D4C2312yes—
143C23×D4C2312yes—
144C23×D4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2312yes—
147C24×C4C2312yes—
148#556—2128no—
149C2×C4⋊Q8—24no—
150C2×C4⋊Q8—24no—
151C2×C4⋊Q8D418yescomplemented
152C2×#127—24no—
153C2×#127—24no—
154C2×#127—42no—
155C2×#126—28no—
156C2×#126—28no—
157C2×#126—28no—
158C2×#126—28no—
159C2×#126—28no—
160C2×#126—28no—
161C2×#124—24no—
162C2×#124—24no—
163C2×#124—24no—
164C2×#124—24no—
165C2×#124—24no—
166C2×#124—24no—
167C2×#124—24no—
168C2×#124—42no—
169C2×#124D418yes—
170C2×C22⋊Q8—24no—
171C2×C22⋊Q8—24no—
172C2×C22⋊Q8—28no—
173C2×C22⋊Q8—28no—
174C2×C22⋊Q8—28no—
175C2×C22⋊Q8—42no—
176C2×#121—24no—
177C2×#121—24no—
178C2×#121—42no—
179C2×C4×Q8—24no—
180C2×C4×Q8—24no—
181C2×C4×Q8—24no—
182C2×C4×Q8—24no—
183C2×C4×Q8—24no—
184C2×C4×Q8—24no—
185C2×C4×Q8—24no—
186C2×C4×Q8—24no—
187C2×C4×Q8—24no—
188C2×C4×Q8—42no—
189C2×C4×Q8—42no—
190C2×C4×Q8D418yescomplemented
191C2×C4×D4—24no—
192C2×C4×D4—24no—
193C2×C4×D4—24no—
194C2×#117—28no—
195C2×#117—28no—
196C2×#117—28no—
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2312yes—
209C22×C4⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C42C2312yes—
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2312yes—
247#394—28no—
248#394—28no—
249#393—24no—
250#393—44no—
251#392—28no—
252#392—28no—
253#391—24no—
254#391—24no—
255#391—42no—
256#391—42no—
257#390—24no—
258#390—28no—
259#390—28no—
260#390—24no—
261#390—24no—
262#390—24no—
263#390—42no—
264#390—42no—
265#386—28no—
266#386—28no—
267#386—28no—
268#386—44no—
269#386—44no—
270#385—28no—
271#385—28no—
272#380—24no—
273#380—28no—
274C4×C22⋊C4—28no—
275C4×C22⋊C4—24no—
276C4×C22⋊C4—24no—
277C4×C22⋊C4—24no—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2311yescharacteristic
315C25C2412yes—
316C25C2411yescharacteristic
317C25C2412yes—
318C2×#41—232no—
319C2×#41—416no—
320C2×#41—416no—
321C2×#41—416no—
322C2×#41—416no—
323C2×#41—416no—
324C2×#41—416no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—41no—
341C22×Q8—41no—
342C22×Q8C2×D414yes—
343C22×Q8C2×D414yes—
344C22×Q8C2×D414yes—
345C22×Q8C2×D414yes—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—22no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—24no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4C2×D414yes—
387C22×D4#4114yes—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—22no—
396C23×C4—24no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4#4114yes—
409C23×C4C2412yes—
410C23×C4C2412yes—
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C4⋊Q8—232no—
430#127—416no—
431#126—264no—
432#126—264no—
433#124—232no—
434#124—232no—
435#124—416no—
436C22⋊Q8—264no—
437C22⋊Q8—416no—
438#121—416no—
439C4×Q8—232no—
440C4×Q8—232no—
441C4×Q8—232no—
442C4×Q8—416no—
443C4×D4—232no—
444#117—264no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—22no—
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—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4C2×D418yes—
481C2×C4⋊C4C2×D414yes—
482C2×C4⋊C4C2×D418yes—
483C2×C4⋊C4C2×D418yes—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—41no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—41no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—41no—
540C2×C22⋊C4—41no—
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—42no—
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⋊C4C2×D418yes—
567C2×C22⋊C4C2×D418yes—
568C2×C42—24no—
569C2×C42—24no—
570C2×C42—24no—
571C2×C42—24no—
572C2×C42—24no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—22no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—24no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—42no—
590C2×C42—42no—
591C2×C42C2×D418yes—
592C2×C42C2×D414yes—
593C2×C42C2×D414yes—
594C2×C42C2×D414yes—
595#95—22no—
596#95—24no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—24no—
611#95—22no—
612#95—22no—
613#95—41no—
614#95—41no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—41no—
619#95—41no—
620#95—42no—
621#95—41no—
622#95—41no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95—42no—
630#95—42no—
631#95#4114yescomplemented
632C24—22no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—22no—
638C24—21no—
639C24—22no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—21no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—21no—
649C24—22no—
650C24—21no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—21no—
655C24—22no—
656C24—21no—
657C24—22no—
658C24—22no—
659C24—21no—
660C24—21no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—22no—
674C24C22×D414yes—
675C24C2×#4114yes—
676C24C2×#4112yes—
677C24C2511yescharacteristic
678#41—4128no—
679C2×Q8—28no—
680C2×Q8—28no—
681C2×Q8—28no—
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—28no—
685C2×Q8—28no—
686C2×Q8—28no—
687C2×Q8—28no—
688C2×Q8—28no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8—44no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8#120116yes—
700C2×D4—216no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—84no—
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—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—216no—
751C22×C4—216no—
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—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—28no—
819C22×C4—28no—
820C22×C4—28no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—22no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—48no—
879C22×C4C22×D412yes—
880C22×C4C22×D414yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D414yes—
886C22×C4C22×D414yes—
887C22×C4C22×D414yes—
888C22×C4C22×D414yes—
889C22×C4C22×D412yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D412yes—
893C22×C4C2×#4112yes—
894C22×C4C2×#4112yes—
895C22×C4C2×#4112yes—
896C22×C4C2×#4112yes—
897C22×C4C2×#4112yes—
898C22×C4C2×#4112yes—
899C22×C4H(5,𝔽2)12yes—
900C22×C4H(5,𝔽2)12yes—
901C22×C4H(5,𝔽2)12yes—
902C22×C42−1+412yes—
903C4⋊C4—28no—
904C4⋊C4—216no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—216no—
908C4⋊C4—28no—
909C4⋊C4—216no—
910C4⋊C4—216no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C22⋊C4—216no—
917C22⋊C4—216no—
918C22⋊C4—216no—
919C22⋊C4—216no—
920C22⋊C4—216no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—44no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—48no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C42—216no—
945C42—216no—
946C42—28no—
947C42—28no—
948C42—28no—
949C42—48no—
950C42—44no—
951C42—44no—
952C42—44no—
953C23—24no—
954C23—24no—
955C23—22no—
956C23—22no—
957C23—24no—
958C23—24no—
959C23—22no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—22no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—42no—
975C23—41no—
976C23—42no—
977C23—42no—
978C23—41no—
979C23—42no—
980C23—42no—
981C23—41no—
982C23—41no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—41no—
988C23—42no—
989C23—41no—
990C23—41no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—41no—
996C23—42no—
997C23—42no—
998C23—41no—
999C23—42no—
1000C23—41no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—41no—
1006C23—42no—
1007C23—42no—
1008C23—41no—
1009C23—42no—
1010C23—42no—
1011C23—41no—
1012C23—41no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—41no—
1018C23—41no—
1019C23—42no—
1020C23—42no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—41no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—41no—
1034C23—42no—
1035C23—41no—
1036C23—42no—
1037C23—42no—
1038C23—41no—
1039C23—41no—
1040C23—42no—
1041C23—42no—
1042C23—41no—
1043C23—42no—
1044C23—42no—
1045C23—41no—
1046C23—42no—
1047C23—42no—
1048C23—41no—
1049C23—42no—
1050C23—41no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—41no—
1055C23—41no—
1056C23—42no—
1057C23—42no—
1058C23C23×D411yescharacteristic
1059C23C23×D411yescharacteristic
1060C23C23×D411yescharacteristic
1061C23C22×#4111yescharacteristic
1062C23C22×#4111yescharacteristic
1063C23C22×#4111yescharacteristic
1064C23C2×H(5,𝔽2)11yescharacteristic
1065C23C2×H(5,𝔽2)11yescharacteristic
1066C23C2×H(5,𝔽2)11yescharacteristic
1067C23C2×2−1+411yescharacteristic
1068C23#58511yescharacteristic
1069C23#58511yescharacteristic
1070C23#58511yescharacteristic
1071C23#58511yescharacteristic
1072C23#58511yescharacteristic
1073Q8—232no—
1074Q8—416no—
1075Q8—416no—
1076D4—432no—
1077D4—416no—
1078D4—416no—
1079D4—816no—
1080D4—816no—
1081D4—816no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
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—22no—
1127C2×C4—432no—
1128C2×C4—432no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—416no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—41no—
1212C2×C4—42no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—42no—
1216C2×C4C2×#12018yes—
1217C2×C4C2×#12014yes—
1218C2×C4#52514yes—
1219C2×C4#53514yes—
1220C2×C4#54614yes—
1221C2×C4#54614yes—
1222C2×C4#54614yes—
1223C2×C4#54614yes—
1224C2×C4#55014yes—
1225C22—44no—
1226C22—42no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—42no—
1235C22—42no—
1236C22—44no—
1237C22—44no—
1238C22—42no—
1239C22—44no—
1240C22—42no—
1241C22—44no—
1242C22—42no—
1243C22—42no—
1244C22—44no—
1245C22—44no—
1246C22—82no—
1247C22—82no—
1248C22—81no—
1249C22—82no—
1250C22—81no—
1251C22—82no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—82no—
1256C22—82no—
1257C22—81no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—81no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—81no—
1269C22—82no—
1270C22C22×#12011yescharacteristic
1271C22C2×#52511yescharacteristic
1272C22C2×#53511yescharacteristic
1273C22C2×#54611yescharacteristic
1274C22C2×#54611yescharacteristic
1275C22C2×#54611yescharacteristic
1276C22C2×#54611yescharacteristic
1277C22C2×#55011yescharacteristic
1278C22D4×#4111yescharacteristic
1279C22D4×#4111yescharacteristic
1280C22#347511yescharacteristic
1281C22#348011yescharacteristic
1282C22#348711yescharacteristic
1283C22#348711yescharacteristic
1284C22#348711yescharacteristic
1285C22#348811yescharacteristic
1286C22#348811yescharacteristic
1287C22#348911yescharacteristic
1288C22#349711yescharacteristic
1289C22#349711yescharacteristic
1290C22#350011yescharacteristic
1291C22#350611yescharacteristic
1292C22#350711yescharacteristic
1293C22#351011yescharacteristic
1294C22#351111yescharacteristic
1295C22#351411yescharacteristic
1296C22#352011yescharacteristic
1297C22#352111yescharacteristic
1298C22#352111yescharacteristic
1299C22#354611yescharacteristic
1300C22#354611yescharacteristic
1301C22#356111yescharacteristic
1302C22#356211yescharacteristic
1303C22#356211yescharacteristic
1304C22#356211yescharacteristic
1305C4—24no—
1306C4—28no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—44no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—44no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—81no—
1319C4—81no—
1320C4—82no—
1321C4—82no—
1322C4—82no—
1323C4—81no—
1324C4#240418yes—
1325C2—84no—
1326C2—82no—
1327C2—84no—
1328C2C2×#240411yescharacteristic
1329C2#3575711yescharacteristic
1330C2#3578711yescharacteristic
1331C2#3622911yescharacteristic
1332C2#3642911yescharacteristic
1333C2#3995411yescharacteristic
1334C2#4288911yescharacteristic
1335C2#4495511yescharacteristic
1336C2#4508411yescharacteristic
1337C2#4524011yescharacteristic
1338C2#4526911yescharacteristic
1339C2#5904911yescharacteristic
1340C2#5914611yescharacteristic
1341C2#5941011yescharacteristic
1342C2#5941611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2431C2
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×#556C2semidirect
2. C2×#2432C2semidirect
4. C2×#2341C2semidirect
5. #16655C2semidirect
6. #16004C2semidirect
7. #15909C2semidirect
8. #15453C2semidirect
9. #15323C2semidirect
10. #15227C2semidirect
11. #15215C2semidirect
12. #15157C2semidirect
13. #14917C2semidirect
14. #14886C2semidirect
15. #14064C2semidirect
16. #14026C2semidirect
17. #14026C2semidirect
18. #14025C2semidirect
19. #14024C2semidirect
20. #13970C2semidirect
21. #13969C2semidirect
22. #13931C2semidirect
23. C4×#393C2semidirect
151. C2×C4⋊Q8D4semidirect
190. C2×C4×Q8D4semidirect
631. #95#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5562
C2×#24322
C2×#24312
C2×#23412
#166552
#160042
#159092
#154532
#153232
#152272
#152152
#151572
#149172
#148862
#140642
#140262
#140252
#140242
#139702
#139692
#139312
C4×#3932