Finite Group Databasebeta

← #223699

Subgroups — #223699

Order 512.

1208 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36183C211yesmaximal, characteristic
2#22552C211yesmaximal, characteristic, complemented
3#13896C211yesmaximal, characteristic, complemented
4#9912C211yesmaximal, characteristic, complemented
5#9885C211yesmaximal, characteristic, complemented
6#9156C211yesmaximal, characteristic, complemented
7#9147C211yesmaximal, characteristic
8#9114C211yesmaximal, characteristic, complemented
9#9113C211yesmaximal, characteristic
10#8716C211yesmaximal, characteristic, complemented
11#8712C211yesmaximal, characteristic, complemented
12#8571C211yesmaximal, characteristic, complemented
13#8220C211yesmaximal, characteristic, complemented
14#8026C211yesmaximal, characteristic, complemented
15C2×#1294C211yesmaximal, characteristic, complemented
16C2×#551—21no—
17C2×#431C2211yescharacteristic
18C22×C22⋊C8C2211yescharacteristic
19#2857C2211yescharacteristic
20#2854C2211yescharacteristic
21#2847C2211yescharacteristic
22#2564—21no—
23#2553—21no—
24#2521—21no—
25#2501C411yescharacteristic, complemented
26#2498—21no—
27#2496C411yescharacteristic, complemented
28#2496C411yescharacteristic, complemented
29#2491C411yescharacteristic, complemented
30#2488—21no—
31#2440C411yescharacteristic, complemented
32#2422C411yescharacteristic, complemented
33#2412—21no—
34#2361C411yescharacteristic, complemented
35#2359—21no—
36#2344C411yescharacteristic, complemented
37C4×#121C2211yescharacteristic
38C2×#385—21no—
39#2285C2211yescharacteristic
40C2×#382C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C22×#95C2211yescharacteristic
44#1923—21no—
45#1923—21no—
46#1850—21no—
47#1817C2211yescharacteristic
48#1797C2211yescharacteristic
49#1779C2211yescharacteristic
50C8×C22⋊C4—21no—
51C4×C22⋊C8C2211yescharacteristic
52C2×#327C2211yescharacteristic
53C2×#327C2211yescharacteristic
54C2×#327C2211yescharacteristic
55C2×#327C2211yescharacteristic
56#1442—21no—
57#1442—21no—
58C4⋊#95C2211yescharacteristic
59#1434C2211yescharacteristic
60#1434C2211yescharacteristic
61C22⋊#95—21no—
62C22⋊#95C2211yescharacteristic
63#1294C2211yescharacteristic
64#1294C2211yescharacteristic
65#1294C2211yescharacteristic
66#1294C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C24×C4—21no—
76C24×C4C2311yescharacteristic
77C23×C8—21no—
78#551—44no—
79#551—44no—
80C2×C4⋊Q8C2×C411yescharacteristic, complemented
81C2×#126—21no—
82C2×#126—21no—
83C2×#124—21no—
84C2×#123—21no—
85C2×#123—21no—
86C2×#123—21no—
87C2×#123—21no—
88C2×C22⋊Q8—21no—
89C2×C22⋊Q8—21no—
90C2×#121C2×C411yescharacteristic
91C2×#121C2×C411yescharacteristic
92C2×#121C2311yescharacteristic
93C2×#120—21no—
94C2×C4×D4—21no—
95C2×C4×D4—21no—
96C2×C4×D4C2×C411yescharacteristic, complemented
97C2×#117—21no—
98C2×#117—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4C2×C411yescharacteristic
102C22×C4⋊C4C2×C411yescharacteristic
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4D411yescharacteristic
106C22×C22⋊C4D411yescharacteristic
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109#431—22no—
110#431—41no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—21no—
113C2×C22⋊C8—22no—
114C2×C22⋊C8—21no—
115C2×C22⋊C8—21no—
116C2×C22⋊C8—21no—
117C2×C22⋊C8—41no—
118C2×C22⋊C8C2311yescharacteristic
119C2×C22⋊C8C2311yescharacteristic
120C2×C22⋊C8C2311yescharacteristic
121C2×C22⋊C8C2311yescharacteristic
122C2×C4×C8—21no—
123C2×C4×C8—21no—
124#400—21no—
125#400—21no—
126#399—21no—
127#399—21no—
128#398—21no—
129#397—21no—
130#397—21no—
131#397—21no—
132#395—21no—
133#394—21no—
134#394—21no—
135#393—21no—
136#391—21no—
137#390C2×C411yescharacteristic, complemented
138#390C2×C411yescharacteristic, complemented
139#390C2×C411yescharacteristic, complemented
140#389—21no—
141#389C2×C411yescharacteristic, complemented
142#389C2×C411yescharacteristic, complemented
143#389C2×C411yescharacteristic, complemented
144#389C2×C411yescharacteristic, complemented
145#389C2×C411yescharacteristic, complemented
146#388—21no—
147#388—21no—
148#388—21no—
149#388—21no—
150#388—21no—
151#387—21no—
152#387—21no—
153#387—21no—
154#387—21no—
155#386—21no—
156#386—21no—
157#386—21no—
158#386—21no—
159#386—21no—
160#386—21no—
161#385—21no—
162#385—21no—
163#385—21no—
164#385—44no—
165#384C2×C411yescharacteristic, complemented
166#384C2×C411yescharacteristic, complemented
167#384C2×C411yescharacteristic, complemented
168#382—21no—
169#382—22no—
170#382—41no—
171#381—21no—
172#380—21no—
173#380—21no—
174#380—21no—
175#380—21no—
176#380C2×C411yescharacteristic
177#380C2×C411yescharacteristic
178#380C2×C411yescharacteristic
179#380C2×C411yescharacteristic
180#380C2311yescharacteristic
181#380C2311yescharacteristic
182#380C2311yescharacteristic
183C4×C4⋊C4—21no—
184C4×C4⋊C4C2×C411yescharacteristic, complemented
185C4×C4⋊C4C2×C411yescharacteristic, complemented
186C4×C4⋊C4C2×C411yescharacteristic, complemented
187C4×C22⋊C4—21no—
188C4×C22⋊C4C2×C411yescharacteristic
189C4×C22⋊C4C2×C411yescharacteristic
190C4×C22⋊C4C2×C411yescharacteristic
191C4×C22⋊C4C2×C411yescharacteristic
192C4×C22⋊C4D411yescharacteristic
193C4×C22⋊C4D411yescharacteristic
194C4×C22⋊C4D411yescharacteristic
195C4×C22⋊C4D411yescharacteristic
196C2×#95—21no—
197C2×#95—22no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—41no—
207C2×#95D411yescharacteristic
208C2×#95D411yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213#336—21no—
214#336—21no—
215#336—21no—
216#336—21no—
217#327—22no—
218#327—22no—
219#327—41no—
220#327—41no—
221C25C2×D411yescharacteristic
222C22×Q8—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4C22×C411yescharacteristic
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—81no—
245C23×C4—81no—
246C23×C4—81no—
247C23×C4C22×C411yescharacteristic
248C23×C4C22×C411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2411yescharacteristic
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—42no—
262C22×C8—42no—
263C22×C8—81no—
264C4⋊Q8—81no—
265#126—44no—
266#126—44no—
267#124—44no—
268#123—44no—
269#123—42no—
270#123—42no—
271#123—44no—
272#123—44no—
273C22⋊Q8—42no—
274C22⋊Q8—42no—
275C22⋊Q8—44no—
276#121—21no—
277#121—21no—
278#121—21no—
279#121—21no—
280#121—42no—
281#121—81no—
282#120—42no—
283#120—42no—
284C4×D4—42no—
285C4×D4—42no—
286C4×D4—44no—
287C4×D4—81no—
288#117—42no—
289#117—42no—
290#117—44no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—81no—
311C2×C4⋊C4—81no—
312C2×C4⋊C4—81no—
313C2×C4⋊C4C22×C411yescharacteristic
314C2×C4⋊C4C22×C411yescharacteristic
315C2×C4⋊C4C22×C411yescharacteristic
316C2×C4⋊C4C22×C411yescharacteristic
317C2×C4⋊C4C22×C411yescharacteristic
318C2×C4⋊C4C22×C411yescharacteristic
319C2×C4⋊C4C22×C411yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
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—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4C22⋊C411yescharacteristic
344C2×C22⋊C4C22⋊C411yescharacteristic
345C2×C22⋊C4C22⋊C411yescharacteristic
346C2×C22⋊C4C22⋊C411yescharacteristic
347C2×C22⋊C4C22⋊C411yescharacteristic
348C2×C22⋊C4C22⋊C411yescharacteristic
349C2×C22⋊C4C22⋊C411yescharacteristic
350C2×C22⋊C4C22⋊C411yescharacteristic
351C2×C22⋊C4D814yes—
352C2×C22⋊C4SD1614yes—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—81no—
361C2×C42C22×C411yescharacteristic
362C2×C42C22×C411yescharacteristic
363C2×C42C22×C411yescharacteristic
364C2×C42C22×C411yescharacteristic
365C2×C42C2×D411yescharacteristic
366C2×C42C2×D411yescharacteristic
367C2×C42C2×D411yescharacteristic
368C2×C42C2×D411yescharacteristic
369C4⋊C8—42no—
370C4⋊C8—81no—
371C22⋊C8—21no—
372C22⋊C8—21no—
373C22⋊C8—21no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8—21no—
378C22⋊C8—42no—
379C22⋊C8—42no—
380C22⋊C8—81no—
381C22⋊C8#4112yes—
382C4×C8—42no—
383C4×C8—81no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
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—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—81no—
412#95—81no—
413#95—81no—
414#95C22⋊C411yescharacteristic
415#95C22⋊C411yescharacteristic
416#95C22⋊C411yescharacteristic
417#95C22⋊C411yescharacteristic
418#95C22⋊C411yescharacteristic
419#95C22⋊C411yescharacteristic
420#95C22⋊C411yescharacteristic
421#95C22⋊C411yescharacteristic
422#95#4112yes—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—22no—
428C24—22no—
429C24—21no—
430C24—41no—
431C24—41no—
432C24C2×C22⋊C411yescharacteristic
433C24C2×C22⋊C411yescharacteristic
434C24C2×D812yes—
435C24C2×SD1612yes—
436C24C22×D411yescharacteristic
437C2×Q8—42no—
438C2×Q8—81no—
439C2×Q8—81no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—81no—
455C2×D4—81no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
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—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—48no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
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—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—82no—
536C22×C4—82no—
537C22×C4—82no—
538C22×C4—82no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4—84no—
542C22×C4—84no—
543C22×C4—84no—
544C22×C4—84no—
545C22×C4—84no—
546C22×C4—84no—
547C22×C4C2×C22⋊C411yescharacteristic
548C22×C4C2×C22⋊C411yescharacteristic
549C22×C4C2×C22⋊C411yescharacteristic
550C22×C4C2×C22⋊C411yescharacteristic
551C22×C4C2×C22⋊C411yescharacteristic
552C22×C4C2×C22⋊C411yescharacteristic
553C22×C4C2×C22⋊C411yescharacteristic
554C22×C4C2×C22⋊C411yescharacteristic
555C22×C4C2×C22⋊C411yescharacteristic
556C22×C4C2×C22⋊C411yescharacteristic
557C22×C4C2×D812yes—
558C22×C4C2×D812yes—
559C22×C4C2×SD1612yes—
560C22×C4C2×SD1612yes—
561C22×C4C23×C411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C2×#4111yescharacteristic
564C22×C4C2×#4111yescharacteristic
565C22×C4H(5,𝔽2)11yescharacteristic
566C22×C42−1+411yescharacteristic
567C2×C8—22no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—84no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—81no—
600C4⋊C4—81no—
601C4⋊C4—81no—
602C4⋊C4—84no—
603C4⋊C4—84no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—41no—
622C22⋊C4—41no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—84no—
630C22⋊C4#10214yes—
631C22⋊C4#10214yes—
632C22⋊C4#10214yes—
633C22⋊C4#10214yes—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—42no—
647C42—42no—
648C42—42no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—22no—
658C23—22no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23#41012yes—
687C23C2×#10212yes—
688C23C2×#10212yes—
689C23#42112yes—
690C23C22×C22⋊C411yescharacteristic
691C23#54611yescharacteristic
692C23#54711yescharacteristic
693C23C22×D811yescharacteristic
694C23C22×SD1611yescharacteristic
695C23#57711yescharacteristic
696C23#57811yescharacteristic
697Q8—162no—
698D4—81no—
699D4—81no—
700D4—81no—
701D4—81no—
702D4—81no—
703D4—81no—
704D4—84no—
705D4—162no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—816no—
795C2×C4—81no—
796C2×C4—84no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—162no—
812C2×C4—162no—
813C2×C4C2×#10212yes—
814C2×C4C2×#10212yes—
815C2×C4C2×#10212yes—
816C2×C4C2×#10212yes—
817C2×C4C4×#4111yescharacteristic
818C2×C4#52011yescharacteristic
819C2×C4#54611yescharacteristic
820C2×C4#54711yescharacteristic
821C8—42no—
822C8—81no—
823C8—81no—
824C8—81no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—22no—
830C22—21no—
831C22—21no—
832C22—22no—
833C22—21no—
834C22—21no—
835C22—22no—
836C22—21no—
837C22—22no—
838C22—21no—
839C22—22no—
840C22—21no—
841C22—21no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22#151714yes—
862C22#233911yescharacteristic
863C22C2×#41011yescharacteristic
864C22#288311yescharacteristic
865C22C22×#10211yescharacteristic
866C22#289811yescharacteristic
867C22C2×#42111yescharacteristic
868C22#290111yescharacteristic
869C22#329411yescharacteristic
870C22#329811yescharacteristic
871C22#333411yescharacteristic
872C22#333511yescharacteristic
873C4—22no—
874C4—22no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—22no—
880C4—22no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—82no—
888C4—82no—
889C4—81no—
890C4—81no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4—161no—
897C4—161no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—24no—
903C2—42no—
904C2—161no—
905C2C2×#151711yescharacteristic
906C2#1759811yescharacteristic
907C2#1760911yescharacteristic
908C2#1761311yescharacteristic
909C2#2247711yescharacteristic
910C2#2248511yescharacteristic
911C2#2250611yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#2847C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22552C2semidirect
3. #13896C2semidirect
4. #9912C2semidirect
5. #9885C2semidirect
6. #9156C2semidirect
8. #9114C2semidirect
10. #8716C2semidirect
11. #8712C2semidirect
12. #8571C2semidirect
13. #8220C2semidirect
14. #8026C2semidirect
15. C2×#1294C2semidirect
25. #2501C4semidirect
27. #2496C4semidirect
28. #2496C4semidirect
29. #2491C4semidirect
31. #2440C4semidirect
32. #2422C4semidirect
34. #2361C4semidirect
36. #2344C4semidirect
80. C2×C4⋊Q8C2×C4semidirect
96. C2×C4×D4C2×C4semidirect
137. #390C2×C4semidirect
138. #390C2×C4semidirect
139. #390C2×C4semidirect
141. #389C2×C4semidirect
142. #389C2×C4semidirect
143. #389C2×C4semidirect
144. #389C2×C4semidirect
145. #389C2×C4semidirect
165. #384C2×C4semidirect
166. #384C2×C4semidirect
167. #384C2×C4semidirect
184. C4×C4⋊C4C2×C4semidirect
185. C4×C4⋊C4C2×C4semidirect
186. C4×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#361832
#225522
#138962
#99122
#98852
#91562
#91472
#91142
#91132
#87162
#87122
#85712
#82202
#80262
C2×#12942