Finite Group Databasebeta

← #482886

Subgroups — #482886

Order 512.

905 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40595C211yesmaximal, characteristic
2#22477C211yesmaximal, characteristic
3#17412C211yesmaximal, characteristic
4#11898C211yesmaximal, characteristic, complemented
5#11845C211yesmaximal, characteristic, complemented
6#11842C211yesmaximal, characteristic, complemented
7#11826C211yesmaximal, characteristic, complemented
8#11812C211yesmaximal, characteristic, complemented
9#11808C211yesmaximal, characteristic, complemented
10#11785C211yesmaximal, characteristic, complemented
11#11759C211yesmaximal, characteristic, complemented
12#11756C211yesmaximal, characteristic, complemented
13#11731C211yesmaximal, characteristic, complemented
14#11717C211yesmaximal, characteristic, complemented
15C2×#1351C211yesmaximal, characteristic, complemented
16C2×#551C2211yescharacteristic
17C2×D4×Q8C411yescharacteristic, complemented
18#2924—21no—
19#2821C411yescharacteristic, complemented
20#2814C411yescharacteristic, complemented
21#2716—21no—
22#2687—21no—
23#2677—21no—
24#2674—21no—
25#2659C411yescharacteristic, complemented
26#2638C2211yescharacteristic
27#2637C411yescharacteristic, complemented
28#2628C2211yescharacteristic
29#2614C411yescharacteristic, complemented
30#2599C2211yescharacteristic
31#2561C2211yescharacteristic
32#2438—21no—
33#2437—21no—
34#2434C411yescharacteristic, complemented
35#2419—21no—
36#2418—21no—
37#2409C2211yescharacteristic
38C2×#393C2211yescharacteristic
39#2342—21no—
40#2318C411yescharacteristic, complemented
41#1996—21no—
42#1899—21no—
43#1898—21no—
44#1820C2211yescharacteristic
45#1819C2211yescharacteristic
46#1799C2211yescharacteristic
47C4×#99C2211yescharacteristic
48#1740C2211yescharacteristic
49C2×#342C2211yescharacteristic
50#1473—21no—
51#1469—21no—
52#1468—21no—
53#1466C2211yescharacteristic
54#1464C2211yescharacteristic
55#1462C2211yescharacteristic
56#1460C2211yescharacteristic
57#1458C2211yescharacteristic
58C2×#323C2211yescharacteristic
59#1351C2211yescharacteristic
60#1351C2211yescharacteristic
61#1351C2211yescharacteristic
62#1351C2211yescharacteristic
63#1351C2211yescharacteristic
64#1351C2211yescharacteristic
65#1351C2211yescharacteristic
66#1351C2211yescharacteristic
67#1351C2211yescharacteristic
68#1351C2211yescharacteristic
69#1351C2211yescharacteristic
70#1351C2211yescharacteristic
71#1344C2211yescharacteristic
72#1344C2211yescharacteristic
73#1344C2211yescharacteristic
74#1344C2211yescharacteristic
75C23×Q8C2×C411yescharacteristic
76C23×Q8C2×C411yescharacteristic, complemented
77#551—41no—
78#551—41no—
79#551—41no—
80#551—41no—
81D4×Q8—41no—
82D4×Q8—41no—
83D4×Q8—41no—
84D4×Q8—41no—
85C2×C4⋊Q8—21no—
86C2×C4⋊Q8—21no—
87C2×C4⋊Q8C2×C411yescharacteristic, complemented
88C2×#126C2×C411yescharacteristic
89C2×#126D411yescharacteristic
90C2×#124D411yescharacteristic
91C2×#123—21no—
92C2×#123C2×C411yescharacteristic
93C2×#123D411yescharacteristic
94C2×#123D411yescharacteristic
95C2×C22⋊Q8—21no—
96C2×C22⋊Q8—21no—
97C2×C22⋊Q8—21no—
98C2×C22⋊Q8C2×C411yescharacteristic
99C2×C22⋊Q8C2×C411yescharacteristic
100C2×C22⋊Q8C2×C411yescharacteristic, complemented
101C2×C22⋊Q8D411yescharacteristic
102C2×#120D411yescharacteristic
103C2×C4×Q8C2×C411yescharacteristic, complemented
104C2×C4×D4—21no—
105C2×C4×D4C2×C411yescharacteristic
106C2×C4×D4C2311yescharacteristic
107C2×#117—21no—
108C2×#117D411yescharacteristic
109C2×#117C2311yescharacteristic
110C22×C22⋊C4—21no—
111C22×C22⋊C4—21no—
112C22×C22⋊C4D411yescharacteristic
113C22×C22⋊C4C2311yescharacteristic
114#433—41no—
115#433—41no—
116#432—21no—
117#432—21no—
118#431—21no—
119#431—21no—
120#424—41no—
121C2×#99—21no—
122C2×#99—21no—
123#407—21no—
124C2×C22⋊C8—21no—
125#405—41no—
126#400—21no—
127#400—21no—
128#399—21no—
129#399—21no—
130#398—21no—
131#398—21no—
132#398—21no—
133#398—21no—
134#398C2×C411yescharacteristic, complemented
135#398C2×C411yescharacteristic, complemented
136#397—21no—
137#397—21no—
138#397—21no—
139#397C2×C411yescharacteristic
140#397C2311yescharacteristic
141#396—21no—
142#396—21no—
143#395—21no—
144#395—21no—
145#395C2×C411yescharacteristic, complemented
146#395C2×C411yescharacteristic, complemented
147#395C2×C411yescharacteristic, complemented
148#395C2×C411yescharacteristic, complemented
149#395C2×C411yescharacteristic, complemented
150#395C2×C411yescharacteristic, complemented
151#394—21no—
152#394—21no—
153#393—21no—
154#393—21no—
155#393—21no—
156#393C2×C411yescharacteristic
157#393C2×C411yescharacteristic
158#393C2×C411yescharacteristic
159#393C2311yescharacteristic
160#393C2311yescharacteristic
161#393C2311yescharacteristic
162#391—21no—
163#391—21no—
164#389—21no—
165#388—21no—
166#388—21no—
167#388—21no—
168#388—21no—
169#388—21no—
170#388—41no—
171#388—41no—
172#387—21no—
173#387—21no—
174#387—21no—
175#387—21no—
176#387—21no—
177#386—21no—
178#386—21no—
179#385—21no—
180#385—21no—
181#385—21no—
182#385—21no—
183#385—21no—
184#385—21no—
185#385—41no—
186#383C2×C411yescharacteristic, complemented
187#382C2×C411yescharacteristic, complemented
188#381—21no—
189#381—21no—
190#381—21no—
191#381C2×C411yescharacteristic, complemented
192#380—21no—
193#380—21no—
194#380—21no—
195#380—21no—
196#380C2×C411yescharacteristic, complemented
197#379—21no—
198#379—21no—
199C4×C22⋊C4—21no—
200C4×C22⋊C4—41no—
201C4×C22⋊C4C2×C411yescharacteristic
202C2×#95—21no—
203C2×#95C2×C411yescharacteristic
204#342—21no—
205#342—21no—
206#342—21no—
207#342—21no—
208#342C2311yescharacteristic
209#342C2311yescharacteristic
210#342C2311yescharacteristic
211#342C2311yescharacteristic
212#324—21no—
213#324—21no—
214#323—21no—
215#323—21no—
216#323—21no—
217#323—21no—
218#323C2311yescharacteristic
219#323C2311yescharacteristic
220#323C2311yescharacteristic
221#323C2311yescharacteristic
222C25C2×D411yescharacteristic
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—41no—
226C22×Q8—41no—
227C22×Q8—41no—
228C22×Q8—41no—
229C22×Q8—82no—
230C22×Q8—82no—
231C22×Q8C22⋊C411yescharacteristic
232C22×Q8C22×C411yescharacteristic
233C22×Q8C22×C411yescharacteristic
234C22×Q8C22×C411yescharacteristic
235C22×D4C22⋊C411yescharacteristic
236C22×D4C22⋊C411yescharacteristic
237C22×D4C2×D411yescharacteristic
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—41no—
242C23×C4C22×C411yescharacteristic
243C23×C4C22×C411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C2×M16—41no—
248C22×C8—41no—
249C4⋊Q8—41no—
250C4⋊Q8—41no—
251C4⋊Q8—42no—
252C4⋊Q8—42no—
253C4⋊Q8—82no—
254#126—41no—
255#126—41no—
256#126—41no—
257#126—41no—
258#124—41no—
259#124—41no—
260#123—41no—
261#123—41no—
262#123—41no—
263#123—41no—
264#123—41no—
265#123—41no—
266#123—82no—
267C22⋊Q8—41no—
268C22⋊Q8—41no—
269C22⋊Q8—42no—
270C22⋊Q8—42no—
271C22⋊Q8—41no—
272C22⋊Q8—41no—
273C22⋊Q8—41no—
274C22⋊Q8—41no—
275C22⋊Q8—41no—
276C22⋊Q8—41no—
277C22⋊Q8—41no—
278C22⋊Q8—41no—
279C22⋊Q8—41no—
280C22⋊Q8—41no—
281C22⋊Q8—82no—
282#120—41no—
283#120—41no—
284C4×Q8—41no—
285C4×Q8—41no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—41no—
291C4×D4—41no—
292C4×D4—42no—
293C4×D4—42no—
294#117—21no—
295#117—21no—
296#117—21no—
297#117—21no—
298#117—41no—
299#117—41no—
300#117—42no—
301#117—81no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4C22⋊C411yescharacteristic
320C2×C4⋊C4C22⋊C411yescharacteristic
321C2×C4⋊C4C22⋊C411yescharacteristic
322C2×C4⋊C4C22⋊C411yescharacteristic
323C2×C4⋊C4C22⋊C411yescharacteristic
324C2×C4⋊C4C22×C411yescharacteristic
325C2×C4⋊C4C22×C411yescharacteristic
326C2×C4⋊C4C22×C411yescharacteristic
327C2×C4⋊C4C2×D411yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—82no—
356C2×C22⋊C4—81no—
357C2×C22⋊C4C22⋊C411yescharacteristic
358C2×C22⋊C4C22⋊C411yescharacteristic
359C2×C22⋊C4C22⋊C411yescharacteristic
360C2×C22⋊C4C22⋊C411yescharacteristic
361C2×C22⋊C4C22⋊C411yescharacteristic
362C2×C22⋊C4C22⋊C411yescharacteristic
363C2×C22⋊C4C22⋊C411yescharacteristic
364C2×C22⋊C4C22⋊C411yescharacteristic
365C2×C22⋊C4C22×C411yescharacteristic
366C2×C22⋊C4C2×D411yescharacteristic
367C2×C22⋊C4C2×D411yescharacteristic
368C2×C22⋊C4C2×D411yescharacteristic
369C2×C22⋊C4C2×D411yescharacteristic
370C2×C22⋊C4C2411yescharacteristic
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—41no—
374C2×C42—41no—
375C2×C42C22×C411yescharacteristic
376C2×C42C2×D411yescharacteristic
377C2×C42C2×D411yescharacteristic
378C4⋊C8—41no—
379C4⋊C8—41no—
380C4⋊C8—41no—
381C4⋊C8—41no—
382#99—42no—
383#99—81no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386C22⋊C8—21no—
387C22⋊C8—21no—
388C22⋊C8—41no—
389C22⋊C8—41no—
390#97—41no—
391#97—41no—
392C4×C8—41no—
393C4×C8—41no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—41no—
416#95—41no—
417#95—41no—
418#95—41no—
419#95C22×C411yescharacteristic
420#95C22×C411yescharacteristic
421#95C22×C411yescharacteristic
422#95C22×C411yescharacteristic
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—41no—
428C24—42no—
429C24—81no—
430C24C2×C22⋊C411yescharacteristic
431C24C2×C22⋊C411yescharacteristic
432C24C2×C22⋊C411yescharacteristic
433C24C22×D411yescharacteristic
434C2×Q8—41no—
435C2×Q8—42no—
436C2×Q8—42no—
437C2×Q8—42no—
438C2×Q8—42no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—81no—
445C2×Q8—81no—
446C2×Q8—81no—
447C2×Q8—81no—
448C2×Q8—81no—
449C2×Q8—82no—
450C2×Q8—82no—
451C2×Q8—82no—
452C2×Q8—82no—
453C2×Q8—82no—
454C2×Q8—82no—
455C2×Q8—82no—
456C2×Q8—82no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—42no—
465C2×D4—81no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—41no—
491C22×C4—42no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—42no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4—82no—
506C22×C4—82no—
507C22×C4—161no—
508C22×C4C2×C22⋊C411yescharacteristic
509C22×C4C2×C22⋊C411yescharacteristic
510C22×C4C2×C22⋊C411yescharacteristic
511C22×C4C2×C22⋊C411yescharacteristic
512C22×C4C2×C22⋊C411yescharacteristic
513C22×C4C2×C22⋊C411yescharacteristic
514C22×C4C2×C22⋊C411yescharacteristic
515C22×C4C2×C22⋊C411yescharacteristic
516C22×C4C2×C22⋊C411yescharacteristic
517C22×C4C23×C411yescharacteristic
518C22×C4C22×D411yescharacteristic
519M16—82no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—82no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—81no—
548C4⋊C4—81no—
549C4⋊C4—81no—
550C4⋊C4—81no—
551C4⋊C4—81no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4—81no—
555C4⋊C4—82no—
556C4⋊C4—161no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—22no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—82no—
599C22⋊C4—82no—
600C22⋊C4—161no—
601C22⋊C4#9911yescharacteristic
602C22⋊C4#9911yescharacteristic
603C22⋊C4#9911yescharacteristic
604C22⋊C4#9911yescharacteristic
605C42—21no—
606C42—21no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—42no—
612C42—81no—
613C42—82no—
614C42—161no—
615C23—21no—
616C23—22no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—82no—
642C23—82no—
643C23—162no—
644C23C2×#9911yescharacteristic
645C23C2×#9911yescharacteristic
646C23C22×C22⋊C411yescharacteristic
647C23#57711yescharacteristic
648C23#57811yescharacteristic
649Q8—42no—
650Q8—42no—
651Q8—82no—
652Q8—82no—
653Q8—84no—
654Q8—81no—
655Q8—81no—
656Q8—81no—
657Q8—81no—
658Q8—161no—
659D4—42no—
660D4—42no—
661D4—81no—
662D4—81no—
663D4—161no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4—84no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—162no—
739C2×C4—164no—
740C2×C4C2×#9911yescharacteristic
741C2×C4C2×#9911yescharacteristic
742C2×C4C2×#9911yescharacteristic
743C2×C4C2×#9911yescharacteristic
744C8—81no—
745C8—81no—
746C8—81no—
747C8—81no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—42no—
758C22—42no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—81no—
770C22—82no—
771C22—82no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—161no—
777C22—161no—
778C22#212912yes—
779C22C22×#9911yescharacteristic
780C22#289811yescharacteristic
781C22#290111yescharacteristic
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—81no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—82no—
801C4—81no—
802C4—81no—
803C4—81no—
804C4—161no—
805C4—161no—
806C4—161no—
807C2—21no—
808C2—21no—
809C2—22no—
810C2—41no—
811C2—41no—
812C2—41no—
813C2—81no—
814C2—81no—
815C2#1760811yescharacteristic
816C2#3334811yescharacteristic
817C2C2×#212911yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC2×#120D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#551 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #11898C2semidirect
5. #11845C2semidirect
6. #11842C2semidirect
7. #11826C2semidirect
8. #11812C2semidirect
9. #11808C2semidirect
10. #11785C2semidirect
11. #11759C2semidirect
12. #11756C2semidirect
13. #11731C2semidirect
14. #11717C2semidirect
15. C2×#1351C2semidirect
17. C2×D4×Q8C4semidirect
19. #2821C4semidirect
20. #2814C4semidirect
25. #2659C4semidirect
27. #2637C4semidirect
29. #2614C4semidirect
34. #2434C4semidirect
40. #2318C4semidirect
76. C23×Q8C2×C4semidirect
87. C2×C4⋊Q8C2×C4semidirect
100. C2×C22⋊Q8C2×C4semidirect
103. C2×C4×Q8C2×C4semidirect
134. #398C2×C4semidirect
135. #398C2×C4semidirect
145. #395C2×C4semidirect
146. #395C2×C4semidirect
147. #395C2×C4semidirect
148. #395C2×C4semidirect
149. #395C2×C4semidirect
150. #395C2×C4semidirect
186. #383C2×C4semidirect
187. #382C2×C4semidirect
191. #381C2×C4semidirect
196. #380C2×C4semidirect

Maximal subgroups

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

subgroupindex
#405952
#224772
#174122
#118982
#118452
#118422
#118262
#118122
#118082
#117852
#117592
#117562
#117312
#117172
C2×#13512