Finite Group Databasebeta

← #642355

Subgroups — #642355

Order 512.

4484 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic, complemented
2C2×#2854C211yesmaximal, characteristic, complemented
3C2×#2656C211yesmaximal, characteristic
4C2×#2639C211yesmaximal, characteristic, complemented
5#16682C212yesmaximal, complemented
6#16680C212yesmaximal, complemented
7#16674C212yesmaximal, complemented
8#16655C212yesmaximal, complemented
9#14926C214yesmaximal, complemented
10#14893C212yesmaximal, complemented
11#14886C212yesmaximal, complemented
12#14875C212yesmaximal, complemented
13#14795C212yesmaximal, complemented
14#14281C211yesmaximal, characteristic, complemented
15#14271C211yesmaximal, characteristic, complemented
16#14023C214yesmaximal, complemented
17C2×#1434C211yesmaximal, characteristic, complemented
18C2×#529—28no—
19C2×#529—28no—
20C2×#529—28no—
21C22×#126C2212yes—
22C22×#125C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×#123C2212yes—
25C22×#123C2212yes—
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#121C2214yes—
29C22×#121C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×D4C2212yes—
32C22×C4×D4C2211yescharacteristic
33C22×#117C2212yes—
34C23×C42C2211yescharacteristic
35#2854—28no—
36#2656—28no—
37#2639—28no—
38C2×#400C2212yes—
39C2×#399C2212yes—
40C2×#399C2212yes—
41C2×#397C2212yes—
42C2×#394C2212yes—
43C2×#393C2212yes—
44C2×#392C2212yes—
45C2×#392C2212yes—
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#388C2212yes—
51C2×#388C2212yes—
52C2×#386C2214yes—
53C2×#386C2212yes—
54C2×#386C2214yes—
55C2×#386C2214yes—
56C2×#380C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2212yes—
60C22×#95C2212yes—
61#1446C2212yes—
62#1445C2212yes—
63#1445C2212yes—
64#1444C2214yes—
65#1444C2214yes—
66#1441C2212yes—
67#1441C2212yes—
68#1441C2214yes—
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1438C2214yes—
80#1438C2212yes—
81#1437C2214yes—
82#1436C2214yes—
83#1434C2212yes—
84#1434C2212yes—
85#1434C2212yes—
86#1434C2212yes—
87C22⋊#95C2214yes—
88C22⋊#95C2214yes—
89C23×Q8C2311yescharacteristic
90C23×D4C2312yes—
91C23×D4C2312yes—
92C23×D4C2311yescharacteristic
93C23×D4C2314yes—
94C23×D4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2312yes—
100C24×C4C2311yescharacteristic
101#529—2128no—
102C2×#126—28no—
103C2×#126—28no—
104C2×#126—28no—
105C2×#125—24no—
106C2×#125—24no—
107C2×#125—24no—
108C2×#124—24no—
109C2×#124—24no—
110C2×#124—24no—
111C2×#123—28no—
112C2×#123—28no—
113C2×#123—28no—
114C2×#123—28no—
115C2×#123—48no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8D418yescomplemented
119C2×#121—24no—
120C2×#121—24no—
121C2×#121—216no—
122C2×#121—24no—
123C2×#121—24no—
124C2×#121—24no—
125C2×#121—216no—
126C2×#121—48no—
127C2×#121D418yes—
128C2×C4×Q8—24no—
129C2×C4×Q8—24no—
130C2×C4×Q8—24no—
131C2×C4×D4—28no—
132C2×C4×D4—24no—
133C2×C4×D4—28no—
134C2×C4×D4—24no—
135C2×C4×D4—28no—
136C2×C4×D4—24no—
137C2×#117—28no—
138C2×#117—28no—
139C2×#117—28no—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2314yes—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42D418yescomplemented
172C22×C42C2312yes—
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177#400—28no—
178#399—28no—
179#399—28no—
180#397—28no—
181#394—28no—
182#393—28no—
183#392—28no—
184#392—28no—
185#390—24no—
186#390—24no—
187#389—24no—
188#389—24no—
189#388—28no—
190#388—28no—
191#386—28no—
192#386—216no—
193#386—48no—
194#386—48no—
195#380—24no—
196C2×#95—24no—
197C2×#95—24no—
198C2×#95—28no—
199C2×#95—44no—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C25C2412yes—
220C25C2412yes—
221C25C2411yescharacteristic
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—42no—
225C22×Q8—42no—
226C22×Q8C2×D414yes—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—28no—
230C22×D4—28no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—28no—
235C22×D4—28no—
236C22×D4—28no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—28no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—44no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4C2×D418yes—
253C22×D4C2×D414yes—
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—41no—
276C23×C4—41no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4#4118yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2414yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2412yes—
302C23×C4C2414yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306#126—264no—
307#125—232no—
308#124—232no—
309#123—264no—
310#123—432no—
311C22⋊Q8—232no—
312#121—232no—
313#121—464no—
314#121—416no—
315C4×Q8—232no—
316C4×D4—264no—
317C4×D4—232no—
318#117—264no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4C2×D418yes—
349C2×C4⋊C4C2×D414yes—
350C2×C4⋊C4C2×D414yes—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4C2×D418yes—
398C2×C22⋊C4C2×D418yes—
399C2×C42—232no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42C2×D414yes—
412C2×C42C2×D414yes—
413C2×C42C2×D414yes—
414C2×C42C2×D414yes—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—28no—
423#95—28no—
424#95—28no—
425#95—28no—
426#95—28no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—21no—
439C24—21no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24—24no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—24no—
448C24—24no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—24no—
454C24—22no—
455C24—24no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—24no—
460C24—24no—
461C24C22×D414yes—
462C24C22×D412yes—
463C24C22×D412yes—
464C24C22×D412yes—
465C24C2×#4114yes—
466C24H(5,𝔽2)14yes—
467C24C2511yescharacteristic
468C2×Q8—28no—
469C2×Q8—48no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—48no—
473C2×D4—216no—
474C2×D4—232no—
475C2×D4—28no—
476C2×D4—48no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—48no—
480C2×D4—416no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—416no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—416no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—416no—
491C2×D4—416no—
492C2×D4—44no—
493C2×D4—84no—
494C2×D4—84no—
495C2×D4—88no—
496C2×D4—88no—
497C2×D4—88no—
498C2×D4—88no—
499C2×D4—88no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—216no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—24no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—216no—
548C22×C4—28no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—48no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4#120116yes—
602C22×C4C22×D414yes—
603C22×C4C22×D412yes—
604C22×C4C22×D414yes—
605C22×C4C22×D414yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C2×#4118yes—
616C22×C4H(5,𝔽2)12yes—
617C22×C42−1+412yes—
618C4⋊C4—216no—
619C4⋊C4—216no—
620C4⋊C4—216no—
621C4⋊C4—216no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—416no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—44no—
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—216no—
633C22⋊C4—216no—
634C22⋊C4—216no—
635C22⋊C4—416no—
636C22⋊C4—416no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—88no—
644C22⋊C4—88no—
645C22⋊C4—88no—
646C22⋊C4—88no—
647C42—216no—
648C42—28no—
649C42—28no—
650C42—28no—
651C42—28no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—28no—
672C23—28no—
673C23—24no—
674C23—24no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—42no—
686C23—42no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23C2×#12014yes—
717C23#53214yes—
718C23#53514yes—
719C23#54618yes—
720C23#55018yes—
721C23C23×D411yescharacteristic
722C23C23×D411yescharacteristic
723C23C23×D411yescharacteristic
724C23C22×#4112yes—
725C23C2×H(5,𝔽2)12yes—
726C23C2×H(5,𝔽2)11yescharacteristic
727C23C2×2−1+411yescharacteristic
728C23#58512yes—
729C23#58512yes—
730C23#58511yescharacteristic
731C23#58511yescharacteristic
732Q8—416no—
733D4—416no—
734D4—432no—
735D4—88no—
736D4—832no—
737D4—816no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—28no—
771C2×C4—416no—
772C2×C4—416no—
773C2×C4—432no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—416no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—44no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—816no—
820C2×C4—816no—
821C2×C4C2×#12014yes—
822C2×C4C2×#12014yes—
823C2×C4#53714yes—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—28no—
828C22—28no—
829C22—28no—
830C22—28no—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—44no—
835C22—48no—
836C22—48no—
837C22—44no—
838C22—44no—
839C22—82no—
840C22—82no—
841C22—84no—
842C22—84no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—84no—
849C22—84no—
850C22—84no—
851C22—84no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22#243118yes—
857C22C22×#12011yescharacteristic
858C22C2×#53211yescharacteristic
859C22C2×#53511yescharacteristic
860C22C2×#53711yescharacteristic
861C22#344911yescharacteristic
862C22#344911yescharacteristic
863C22#344911yescharacteristic
864C22#345912yes—
865C22#346112yes—
866C22C2×#54612yes—
867C22C2×#55012yes—
868C22#348512yes—
869C22#348512yes—
870C22#348811yescharacteristic
871C22#348811yescharacteristic
872C22#348911yescharacteristic
873C22#348911yescharacteristic
874C22#349112yes—
875C22#349312yes—
876C22#355812yes—
877C22#355912yes—
878C22#356012yes—
879C22#356012yes—
880C4—24no—
881C4—24no—
882C4—24no—
883C4—44no—
884C4—48no—
885C4—42no—
886C4—42no—
887C4—44no—
888C4—42no—
889C4—44no—
890C4—84no—
891C4—82no—
892C4—82no—
893C4—82no—
894C2—28no—
895C2—84no—
896C2—162no—
897C2#3459411yescharacteristic
898C2C2×#243111yescharacteristic
899C2#3508811yescharacteristic
900C2#3511911yescharacteristic
901C2#3525111yescharacteristic
902C2#3755411yescharacteristic
903C2#3755611yescharacteristic
904C2#3774612yes—
905C2#3774712yes—
906C2#3777012yes—
907C2#3777112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2656C2
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×#529C2semidirect
2. C2×#2854C2semidirect
4. C2×#2639C2semidirect
5. #16682C2semidirect
6. #16680C2semidirect
7. #16674C2semidirect
8. #16655C2semidirect
9. #14926C2semidirect
10. #14893C2semidirect
11. #14886C2semidirect
12. #14875C2semidirect
13. #14795C2semidirect
14. #14281C2semidirect
15. #14271C2semidirect
16. #14023C2semidirect
17. C2×#1434C2semidirect
118. C2×C22⋊Q8D4semidirect
171. C22×C42D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5292
C2×#28542
C2×#26562
C2×#26392
#166822
#166802
#166742
#166552
#149262
#148932
#148862
#148752
#147952
#142812
#142712
#140232
C2×#14342