Finite Group Databasebeta

← #216834

Subgroups — #216834

Order 512.

1206 conjugacy classes of subgroups.

The subgroup lattice has 951 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35261C211yesmaximal, characteristic
2#20716C211yesmaximal, characteristic, complemented
3#13962C211yesmaximal, characteristic, complemented
4#9887C211yesmaximal, characteristic, complemented
5#9886C211yesmaximal, characteristic, complemented
6#9684C211yesmaximal, characteristic, complemented
7#9680C211yesmaximal, characteristic, complemented
8#9158C211yesmaximal, characteristic, complemented
9#9158C211yesmaximal, characteristic, complemented
10#9147C211yesmaximal, characteristic, complemented
11#9147C211yesmaximal, characteristic, complemented
12#8577C211yesmaximal, characteristic, complemented
13#8575C211yesmaximal, characteristic, complemented
14#8573C211yesmaximal, characteristic, complemented
15#8571C211yesmaximal, characteristic, complemented
16C2×#540C411yescharacteristic, complemented
17C22×#117C2211yescharacteristic
18C2×#433—21no—
19#2856C2211yescharacteristic
20#2851C2211yescharacteristic
21#2847C2211yescharacteristic
22#2847C2211yescharacteristic
23#2629C411yescharacteristic, complemented
24#2624C411yescharacteristic, complemented
25#2624C411yescharacteristic, complemented
26#2619C411yescharacteristic, complemented
27#2476—21no—
28#2476—21no—
29#2471—21no—
30#2471—21no—
31#2443—21no—
32#2443—21no—
33#2424—21no—
34#2424—21no—
35#2324C411yescharacteristic, complemented
36#2324C411yescharacteristic, complemented
37#2314C411yescharacteristic, complemented
38C4×#121C2211yescharacteristic
39C4×#121C2211yescharacteristic
40C2×#385—21no—
41C2×#381C2211yescharacteristic
42C22×#95C2211yescharacteristic
43#1818—21no—
44#1798—21no—
45#1797C2211yescharacteristic
46#1797C2211yescharacteristic
47#1779C2211yescharacteristic
48#1779C2211yescharacteristic
49#1750—21no—
50#1749C2211yescharacteristic
51C4×C22⋊C8C2211yescharacteristic
52C2×#327C2211yescharacteristic
53C2×#327C2211yescharacteristic
54C2×#327C2211yescharacteristic
55C2×#327C2211yescharacteristic
56C2×#327C2211yescharacteristic
57C2×#327C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60#1441—21no—
61#1441—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64#1434C2211yescharacteristic
65#1434C2211yescharacteristic
66C22⋊#95—21no—
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C24×C4—21no—
76C24×C4C2311yescharacteristic
77#540—44no—
78C2×#127C2×C411yescharacteristic, complemented
79C2×#125C2×C411yescharacteristic, complemented
80C2×#123—21no—
81C2×#123—21no—
82C2×#121—21no—
83C2×#121—21no—
84C2×#121—21no—
85C2×#121—21no—
86C2×#121C2×C411yescharacteristic
87C2×#121C2×C411yescharacteristic
88C2×#121C2×C411yescharacteristic
89C2×#121C2×C411yescharacteristic
90C2×#121C2311yescharacteristic
91C2×#121C2311yescharacteristic
92C2×#120—21no—
93C2×#120—21no—
94C2×C4×D4—21no—
95C2×C4×D4—21no—
96C2×C4×D4C2×C411yescharacteristic, complemented
97C2×C4×D4C2×C411yescharacteristic, complemented
98C2×#117—44no—
99C2×#117C2×C411yescharacteristic
100C2×#117C2×C411yescharacteristic
101C2×#117C2×C411yescharacteristic
102C2×#117C2×C411yescharacteristic
103C2×#117D411yescharacteristic
104C2×#117D411yescharacteristic
105C2×#117D411yescharacteristic
106C2×#117D411yescharacteristic
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4D411yescharacteristic
110C22×C4⋊C4D411yescharacteristic
111C22×C22⋊C4—21no—
112C22×C22⋊C4D411yescharacteristic
113C22×C22⋊C4D411yescharacteristic
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116#433—44no—
117C2×C4⋊C8—21no—
118C2×C4⋊C8—21no—
119C2×C22⋊C8—21no—
120C2×C22⋊C8—21no—
121C2×C22⋊C8—21no—
122C2×C22⋊C8—21no—
123C2×C22⋊C8C2311yescharacteristic
124C2×C22⋊C8C2311yescharacteristic
125C2×C22⋊C8C2311yescharacteristic
126C2×C22⋊C8C2311yescharacteristic
127C2×#97—21no—
128C2×C4×C8—21no—
129#399—21no—
130#399—21no—
131#398—21no—
132#398—21no—
133#397—21no—
134#397—21no—
135#396—21no—
136#396—21no—
137#394—21no—
138#394—21no—
139#394—21no—
140#394—21no—
141#394—21no—
142#394—21no—
143#392—21no—
144#392—21no—
145#390—21no—
146#390—21no—
147#390—21no—
148#390—21no—
149#390C2×C411yescharacteristic, complemented
150#390C2×C411yescharacteristic, complemented
151#390C2×C411yescharacteristic, complemented
152#390C2×C411yescharacteristic, complemented
153#389C2×C411yescharacteristic, complemented
154#389C2×C411yescharacteristic, complemented
155#389C2×C411yescharacteristic, complemented
156#389C2×C411yescharacteristic, complemented
157#388—21no—
158#388—21no—
159#388—21no—
160#388—21no—
161#388—21no—
162#388—21no—
163#387—21no—
164#387—21no—
165#387—21no—
166#387—21no—
167#386—21no—
168#386—21no—
169#386—21no—
170#386—21no—
171#386—21no—
172#386—21no—
173#386—21no—
174#386—21no—
175#386—21no—
176#386—21no—
177#385—21no—
178#385—21no—
179#385—21no—
180#385—21no—
181#385—44no—
182#384C2×C411yescharacteristic, complemented
183#382C2×C411yescharacteristic, complemented
184#381—41no—
185#381—41no—
186#380C2×C411yescharacteristic
187#380C2×C411yescharacteristic
188#380C2×C411yescharacteristic
189#380C2×C411yescharacteristic
190#380C2311yescharacteristic
191#380C2311yescharacteristic
192C4×C4⋊C4C2×C411yescharacteristic, complemented
193C4×C4⋊C4C2×C411yescharacteristic, complemented
194C4×C22⋊C4—21no—
195C4×C22⋊C4—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—41no—
205C2×#95—41no—
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210#336—21no—
211#336—21no—
212#336—21no—
213#336—21no—
214#327—41no—
215#327—41no—
216#327—41no—
217#327—41no—
218#327—41no—
219#327—41no—
220#327—41no—
221#327—41no—
222C25C2×D411yescharacteristic
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—21no—
231C22×D4C22×C411yescharacteristic
232C22×D4C22×C411yescharacteristic
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—81no—
251C23×C4—81no—
252C23×C4C22×C411yescharacteristic
253C23×C4C22×C411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C23×C4C2×D411yescharacteristic
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D411yescharacteristic
261C23×C4C2411yescharacteristic
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266#127—42no—
267#125—42no—
268#123—44no—
269#123—44no—
270#121—21no—
271#121—21no—
272#121—21no—
273#121—21no—
274#121—21no—
275#121—21no—
276#121—21no—
277#121—21no—
278#121—44no—
279#121—42no—
280#121—42no—
281#121—42no—
282#121—42no—
283#121—44no—
284#121—81no—
285#121—81no—
286#121—81no—
287#121—81no—
288#120—81no—
289#120—81no—
290#120—81no—
291#120—81no—
292C4×D4—42no—
293C4×D4—42no—
294C4×D4—81no—
295C4×D4—81no—
296C4×D4—81no—
297C4×D4—81no—
298#117—24no—
299#117—24no—
300#117—42no—
301#117—42no—
302#117—42no—
303#117—42no—
304#117—42no—
305#117—42no—
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—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—81no—
321C2×C4⋊C4—81no—
322C2×C4⋊C4C22⋊C411yescharacteristic
323C2×C4⋊C4C22⋊C411yescharacteristic
324C2×C4⋊C4C22⋊C411yescharacteristic
325C2×C4⋊C4C22⋊C411yescharacteristic
326C2×C4⋊C4C22⋊C411yescharacteristic
327C2×C4⋊C4C22⋊C411yescharacteristic
328C2×C4⋊C4C22⋊C411yescharacteristic
329C2×C4⋊C4C22⋊C411yescharacteristic
330C2×C4⋊C4C22×C411yescharacteristic
331C2×C4⋊C4C22×C411yescharacteristic
332C2×C4⋊C4C22×C411yescharacteristic
333C2×C4⋊C4C22×C411yescharacteristic
334C2×C4⋊C4C22×C411yescharacteristic
335C2×C4⋊C4C22×C411yescharacteristic
336C2×C22⋊C4—24no—
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—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4C22⋊C411yescharacteristic
364C2×C22⋊C4C22⋊C411yescharacteristic
365C2×C22⋊C4C22⋊C411yescharacteristic
366C2×C22⋊C4C22⋊C411yescharacteristic
367C2×C22⋊C4C22⋊C411yescharacteristic
368C2×C22⋊C4C22⋊C411yescharacteristic
369C2×C22⋊C4C22⋊C411yescharacteristic
370C2×C22⋊C4C22⋊C411yescharacteristic
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42C22×C411yescharacteristic
376C2×C42C22×C411yescharacteristic
377C2×C42C22×C411yescharacteristic
378C2×C42C22×C411yescharacteristic
379C2×C42C2×D411yescharacteristic
380C2×C42C2×D411yescharacteristic
381C2×C42C2×D411yescharacteristic
382C2×C42C2×D411yescharacteristic
383C4⋊C8—42no—
384C4⋊C8—42no—
385C22⋊C8—21no—
386C22⋊C8—21no—
387C22⋊C8—21no—
388C22⋊C8—21no—
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8—42no—
394C22⋊C8—42no—
395C22⋊C8—42no—
396C22⋊C8—42no—
397#97—42no—
398C4×C8—42no—
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—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—81no—
428#95—81no—
429C24—21no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—41no—
440C24—41no—
441C24C2×C22⋊C411yescharacteristic
442C24C2×C22⋊C411yescharacteristic
443C24C22×D411yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—42no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4—81no—
473C2×D4—81no—
474C2×D4—81no—
475C2×D4—81no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4—81no—
479C2×D4—81no—
480C2×D4—81no—
481C2×D4—81no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—42no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—48no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—42no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—81no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4—81no—
565C22×C4—84no—
566C22×C4—84no—
567C22×C4—84no—
568C22×C4—84no—
569C22×C4—84no—
570C22×C4—84no—
571C22×C4C2×C22⋊C411yescharacteristic
572C22×C4C2×C22⋊C411yescharacteristic
573C22×C4C2×C22⋊C411yescharacteristic
574C22×C4C2×C22⋊C411yescharacteristic
575C22×C4C2×C22⋊C411yescharacteristic
576C22×C4C2×C22⋊C411yescharacteristic
577C22×C4C2×C22⋊C411yescharacteristic
578C22×C4C2×C22⋊C411yescharacteristic
579C22×C4C2×C22⋊C411yescharacteristic
580C22×C4C2×C22⋊C411yescharacteristic
581C22×C4C23×C411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4H(5,𝔽2)11yescharacteristic
584C22×C4H(5,𝔽2)11yescharacteristic
585C22×C42−1+411yescharacteristic
586C22×C42−1+411yescharacteristic
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4—41no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—81no—
618C4⋊C4—81no—
619C4⋊C4—81no—
620C4⋊C4—81no—
621C4⋊C4—81no—
622C4⋊C4—81no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—41no—
631C22⋊C4—41no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—41no—
638C22⋊C4—41no—
639C22⋊C4—41no—
640C22⋊C4—41no—
641C22⋊C4—41no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C22⋊C4—41no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C22⋊C4—81no—
650C22⋊C4—81no—
651C22⋊C4—81no—
652C22⋊C4—81no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C22⋊C4—81no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C22⋊C4—84no—
659C22⋊C4#9914yes—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—41no—
668C42—81no—
669C42—81no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—24no—
675C23—24no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23C2×#9912yes—
717C23#41012yes—
718C23C22×C22⋊C411yescharacteristic
719C23#53511yescharacteristic
720C23#53611yescharacteristic
721C23#57611yescharacteristic
722C23#57611yescharacteristic
723C23#57711yescharacteristic
724C23#57711yescharacteristic
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—81no—
731D4—81no—
732D4—81no—
733D4—81no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4—162no—
738D4—162no—
739D4—162no—
740D4—162no—
741D4—162no—
742D4—162no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—816no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—162no—
845C2×C4—162no—
846C2×C4C2×#9912yes—
847C2×C4C2×#9912yes—
848C2×C4#52011yescharacteristic
849C2×C4#52011yescharacteristic
850C2×C4#53711yescharacteristic
851C2×C4#53711yescharacteristic
852C8—81no—
853C8—81no—
854C8—81no—
855C8—81no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22#231111yescharacteristic
901C22C22×#9911yescharacteristic
902C22C2×#41011yescharacteristic
903C22#289711yescharacteristic
904C22#289711yescharacteristic
905C22#290111yescharacteristic
906C22#290111yescharacteristic
907C22#322011yescharacteristic
908C22#322111yescharacteristic
909C22#324111yescharacteristic
910C22#324111yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—22no—
916C4—22no—
917C4—41no—
918C4—41no—
919C4—41no—
920C4—41no—
921C4—41no—
922C4—41no—
923C4—41no—
924C4—41no—
925C4—82no—
926C4—82no—
927C4—81no—
928C4—81no—
929C4—81no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—161no—
934C4—161no—
935C2—21no—
936C2—21no—
937C2—21no—
938C2—21no—
939C2—42no—
940C2—42no—
941C2—161no—
942C2—161no—
943C2#1760311yescharacteristic
944C2#1760311yescharacteristic
945C2#1760411yescharacteristic
946C2#1760411yescharacteristic
947C2#2187211yescharacteristic
948C2#2187411yescharacteristic
949C2#2190111yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#35261C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #20716C2semidirect
3. #13962C2semidirect
4. #9887C2semidirect
5. #9886C2semidirect
6. #9684C2semidirect
7. #9680C2semidirect
8. #9158C2semidirect
9. #9158C2semidirect
10. #9147C2semidirect
11. #9147C2semidirect
12. #8577C2semidirect
13. #8575C2semidirect
14. #8573C2semidirect
15. #8571C2semidirect
16. C2×#540C4semidirect
23. #2629C4semidirect
24. #2624C4semidirect
25. #2624C4semidirect
26. #2619C4semidirect
35. #2324C4semidirect
36. #2324C4semidirect
37. #2314C4semidirect
78. C2×#127C2×C4semidirect
79. C2×#125C2×C4semidirect
96. C2×C4×D4C2×C4semidirect
97. C2×C4×D4C2×C4semidirect
149. #390C2×C4semidirect
150. #390C2×C4semidirect
151. #390C2×C4semidirect
152. #390C2×C4semidirect
153. #389C2×C4semidirect
154. #389C2×C4semidirect
155. #389C2×C4semidirect
156. #389C2×C4semidirect
182. #384C2×C4semidirect
183. #382C2×C4semidirect
192. C4×C4⋊C4C2×C4semidirect
193. C4×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#352612
#207162
#139622
#98872
#98862
#96842
#96802
#91582
#91472
#85772
#85752
#85732
#85712