Finite Group Databasebeta

← #208502

Subgroups — #208502

Order 512.

1049 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34914C211yesmaximal, characteristic
2#20812C211yesmaximal, characteristic, complemented
3C8×#117C211yesmaximal, characteristic, complemented
4#9874C211yesmaximal, characteristic, complemented
5#9870C211yesmaximal, characteristic, complemented
6#9644C211yesmaximal, characteristic, complemented
7#9638C211yesmaximal, characteristic, complemented
8#9076C211yesmaximal, characteristic, complemented
9#9076C211yesmaximal, characteristic, complemented
10#9072C211yesmaximal, characteristic, complemented
11#9072C211yesmaximal, characteristic, complemented
12#8183C211yesmaximal, characteristic, complemented
13#8177C211yesmaximal, characteristic, complemented
14#8174C211yesmaximal, characteristic, complemented
15C4×D4⋊C8C211yesmaximal, characteristic, complemented
16C2×#529—21no—
17C2×#433—21no—
18C2×#431C2211yescharacteristic
19C22×C4×C8C2211yescharacteristic
20#2560—21no—
21#2559—21no—
22#2558—21no—
23#2557—21no—
24#2512C411yescharacteristic
25#2506C411yescharacteristic
26#2496C411yescharacteristic
27#2491C411yescharacteristic
28#2452C411yescharacteristic
29#2445C411yescharacteristic
30#2428C411yescharacteristic
31#2422C411yescharacteristic
32#2398—21no—
33#2392—21no—
34C4×C4⋊Q8C2211yescharacteristic
35C4×#127C2211yescharacteristic
36C4×#121C2211yescharacteristic
37C4×#121C2211yescharacteristic
38#2293C2211yescharacteristic
39#2290—21no—
40C42×D4C2211yescharacteristic
41C4×#117C2211yescharacteristic
42#1842C2211yescharacteristic
43#1842C2211yescharacteristic
44#1832—21no—
45#1798—21no—
46#1797C2211yescharacteristic
47#1797C2211yescharacteristic
48C8×C4⋊C4—21no—
49C8×C4⋊C4—21no—
50#1768—21no—
51#1767C2211yescharacteristic
52C4×C4⋊C8C2211yescharacteristic
53C8×C22⋊C4—21no—
54C8×C22⋊C4—21no—
55#1744C2211yescharacteristic
56#1744C2211yescharacteristic
57C42×C8C2211yescharacteristic
58C42×C8C2211yescharacteristic
59C2×D4⋊C8C2211yescharacteristic
60C2×D4⋊C8C2211yescharacteristic
61C2×D4⋊C8C2211yescharacteristic
62C2×D4⋊C8C2211yescharacteristic
63C2×D4⋊C8C2211yescharacteristic
64C2×D4⋊C8C2211yescharacteristic
65C2×D4⋊C8C2211yescharacteristic
66C2×D4⋊C8C2211yescharacteristic
67#1279C2211yescharacteristic
68#1279C2211yescharacteristic
69#1279C2211yescharacteristic
70#1279C2211yescharacteristic
71#1279C2211yescharacteristic
72#1279C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75C23×C8—21no—
76C2×C4⋊Q8C2×C411yescharacteristic
77C2×#127C2×C411yescharacteristic
78#529—44no—
79#529—44no—
80C2×#126—21no—
81C2×#126—21no—
82C2×#125—21no—
83C2×#124—21no—
84C2×#123—21no—
85C2×#123—21no—
86C2×C22⋊Q8—21no—
87C2×#121—21no—
88C2×#121C2×C411yescharacteristic
89C2×#121C2×C411yescharacteristic
90C2×C4×Q8—21no—
91C2×C4×D4—21no—
92C2×C4×D4—21no—
93C2×C4×D4—21no—
94C2×C4×D4—21no—
95C2×C4×D4C2×C411yescharacteristic
96C2×C4×D4C2×C411yescharacteristic
97C2×C4×D4C2311yescharacteristic
98C2×C4×D4C2311yescharacteristic
99C2×#117—21no—
100C2×#117D411yescharacteristic
101C2×#117D411yescharacteristic
102C22×C42—21no—
103C22×C42C2311yescharacteristic
104#433—44no—
105#431—22no—
106#431—22no—
107C2×C4⋊C8—21no—
108C2×C4⋊C8—21no—
109C2×C4⋊C8—21no—
110C2×C4⋊C8—21no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8C2311yescharacteristic
113C2×C4⋊C8C2311yescharacteristic
114C2×C4⋊C8C2311yescharacteristic
115C2×C4⋊C8C2311yescharacteristic
116C2×C22⋊C8—21no—
117C2×C22⋊C8—21no—
118C2×C22⋊C8—21no—
119C2×#97—21no—
120C2×C4×C8—21no—
121C2×C4×C8—22no—
122C2×C4×C8—22no—
123C2×C4×C8—21no—
124C2×C4×C8—21no—
125C2×C4×C8—21no—
126C2×C4×C8—21no—
127C2×C4×C8—21no—
128C2×C4×C8C2311yescharacteristic
129C2×C4×C8C2311yescharacteristic
130C2×C4×C8C2311yescharacteristic
131C2×C4×C8C2311yescharacteristic
132#400—21no—
133#400—21no—
134#398—21no—
135#397—21no—
136#397—21no—
137#397—21no—
138#396—21no—
139#396—21no—
140#394—21no—
141#394—21no—
142#394—21no—
143#394—21no—
144#394—21no—
145#393—21no—
146#393—21no—
147#392—21no—
148#391—21no—
149#390—21no—
150#390—21no—
151#390C2×C411yescharacteristic
152#390C2×C411yescharacteristic
153#390C2×C411yescharacteristic
154#390C2×C411yescharacteristic
155#390C2×C411yescharacteristic
156#390C2×C411yescharacteristic
157#389—21no—
158#389C2×C411yescharacteristic
159#389C2×C411yescharacteristic
160#389C2×C411yescharacteristic
161#389C2×C411yescharacteristic
162#389C2×C411yescharacteristic
163#389C2×C411yescharacteristic
164#388—21no—
165#388—21no—
166#388—21no—
167#388—21no—
168#388—21no—
169#388—21no—
170#387—21no—
171#387—21no—
172#386—21no—
173#386—21no—
174#386—21no—
175#386—21no—
176#385—21no—
177#385—21no—
178#384C2×C411yescharacteristic
179#384C2×C411yescharacteristic
180#380C2×C411yescharacteristic
181#380C2×C411yescharacteristic
182C4×C4⋊C4—21no—
183C4×C4⋊C4C2×C411yescharacteristic
184C4×C4⋊C4C2×C411yescharacteristic
185C4×C4⋊C4C2×C411yescharacteristic
186C4×C4⋊C4C2×C411yescharacteristic
187C4×C4⋊C4D411yescharacteristic
188C4×C4⋊C4D411yescharacteristic
189C4×C4⋊C4C2311yescharacteristic
190C4×C4⋊C4C2311yescharacteristic
191C4×C22⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4—21no—
194C4×C22⋊C4—21no—
195C4×C22⋊C4—21no—
196C4×C22⋊C4—21no—
197C4×C22⋊C4C2×C411yescharacteristic
198C4×C22⋊C4C2×C411yescharacteristic
199C4×C22⋊C4D411yescharacteristic
200C4×C22⋊C4D411yescharacteristic
201#376D411yescharacteristic
202#376D411yescharacteristic
203C43C2311yescharacteristic
204C43C2311yescharacteristic
205#336—21no—
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210#336—21no—
211#336—21no—
212#336—21no—
213D4⋊C8—22no—
214D4⋊C8—22no—
215D4⋊C8—22no—
216D4⋊C8—22no—
217D4⋊C8—22no—
218D4⋊C8—22no—
219D4⋊C8—22no—
220D4⋊C8—22no—
221C22×Q8—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4C22×C411yescharacteristic
227C22×D4C22×C411yescharacteristic
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4C22×C411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C22×C8—21no—
236C22×C8—24no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—42no—
245C22×C8—42no—
246C4⋊Q8—22no—
247C4⋊Q8—41no—
248#127—22no—
249#127—41no—
250#126—44no—
251#126—44no—
252#125—44no—
253#124—44no—
254#123—44no—
255#123—44no—
256C22⋊Q8—44no—
257#121—22no—
258#121—22no—
259#121—41no—
260#121—41no—
261#121—44no—
262C4×Q8—42no—
263C4×Q8—42no—
264C4×D4—22no—
265C4×D4—22no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—41no—
275C4×D4—41no—
276C4×D4—42no—
277C4×D4—42no—
278C4×D4—42no—
279C4×D4—42no—
280C4×D4—42no—
281C4×D4—42no—
282C4×D4—42no—
283C4×D4—42no—
284#117—22no—
285#117—22no—
286#117—42no—
287#117—42no—
288#117D814yes—
289#117SD1614yes—
290C2×C4⋊C4—21no—
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⋊C4C22⋊C411yescharacteristic
302C2×C4⋊C4C22⋊C411yescharacteristic
303C2×C4⋊C4C22⋊C411yescharacteristic
304C2×C4⋊C4C22⋊C411yescharacteristic
305C2×C4⋊C4C22×C411yescharacteristic
306C2×C4⋊C4C22×C411yescharacteristic
307C2×C4⋊C4C22×C411yescharacteristic
308C2×C4⋊C4C22×C411yescharacteristic
309C2×C4⋊C4C22×C411yescharacteristic
310C2×C4⋊C4C22×C411yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
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⋊C4C22⋊C411yescharacteristic
332C2×C22⋊C4C22⋊C411yescharacteristic
333C2×C22⋊C4C22⋊C411yescharacteristic
334C2×C22⋊C4C22⋊C411yescharacteristic
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—42no—
344C2×C42—42no—
345C2×C42C22×C411yescharacteristic
346C2×C42C22×C411yescharacteristic
347C2×C42C22×C411yescharacteristic
348C2×C42C22×C411yescharacteristic
349C2×C42C22×C411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C2×C42C2×D411yescharacteristic
356C2×C42C2×D411yescharacteristic
357C2×C42C2×D411yescharacteristic
358C2×C42C2×D411yescharacteristic
359C2×C42C2×D411yescharacteristic
360C2×C42C2411yescharacteristic
361C4⋊C8—24no—
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8—21no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8—21no—
370C4⋊C8—42no—
371C4⋊C8—42no—
372C4⋊C8—42no—
373C4⋊C8—42no—
374C22⋊C8—24no—
375C22⋊C8—42no—
376C22⋊C8—42no—
377#97—42no—
378C4×C8—24no—
379C4×C8—21no—
380C4×C8—21no—
381C4×C8—21no—
382C4×C8—21no—
383C4×C8—42no—
384C4×C8—42no—
385C4×C8—42no—
386C4×C8—42no—
387C4×C8—42no—
388C4×C8#4112yes—
389C4×C8#4112yes—
390C4×C8#4112yes—
391C4×C8#4112yes—
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#95C22⋊C411yescharacteristic
405#95C22⋊C411yescharacteristic
406#95C22⋊C411yescharacteristic
407#95C22⋊C411yescharacteristic
408#95C22⋊C411yescharacteristic
409#95C22⋊C411yescharacteristic
410#95C22⋊C411yescharacteristic
411#95C22⋊C411yescharacteristic
412C24—21no—
413C24—21no—
414C24C2×C22⋊C411yescharacteristic
415C2×Q8—42no—
416C2×Q8—42no—
417C2×Q8—81no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—81no—
438C2×D4—81no—
439C2×D4—81no—
440C2×D4—81no—
441C2×D4#13112yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4C2×C22⋊C411yescharacteristic
481C22×C4C2×C22⋊C411yescharacteristic
482C22×C4C2×C22⋊C411yescharacteristic
483C22×C4C2×C22⋊C411yescharacteristic
484C22×C4C2×C22⋊C411yescharacteristic
485C22×C4C2×C22⋊C411yescharacteristic
486C22×C4C2×C22⋊C411yescharacteristic
487C22×C4C2×C22⋊C411yescharacteristic
488C22×C4C2×C22⋊C411yescharacteristic
489C22×C4C2×C22⋊C411yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×D812yes—
492C22×C4C2×SD1612yes—
493C22×C4C23×C411yescharacteristic
494C22×C4C22×D411yescharacteristic
495C22×C4C22×D411yescharacteristic
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—48no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—81no—
545C4⋊C4#10214yes—
546C4⋊C4#10214yes—
547C4⋊C4#13112yes—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4#10214yes—
573C22⋊C4#10214yes—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—41no—
591C42—41no—
592C42—41no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—42no—
599C42—42no—
600C42C2×D812yes—
601C42C2×D812yes—
602C42C2×SD1612yes—
603C42C2×SD1612yes—
604C42#13512yes—
605C42#13512yes—
606C42C2×#4111yescharacteristic
607C42C2×#4111yescharacteristic
608C42C2×#4111yescharacteristic
609C42C2×#4111yescharacteristic
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23C2×#10212yes—
631C23C22×C22⋊C411yescharacteristic
632Q8—84no—
633D4—22no—
634D4—22no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—84no—
642D4—84no—
643D4—84no—
644D4—84no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
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—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—84no—
702C2×C4—84no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4C2×#10212yes—
712C2×C4C2×#10212yes—
713C2×C4C2×#10212yes—
714C2×C4C2×#10212yes—
715C2×C4C2×#10212yes—
716C2×C4#41612yes—
717C2×C4#41612yes—
718C2×C4C4×#4111yescharacteristic
719C2×C4C4×#4111yescharacteristic
720C2×C4#52511yescharacteristic
721C2×C4#52511yescharacteristic
722C2×C4#53211yescharacteristic
723C2×C4#53211yescharacteristic
724C2×C4C2×#13111yescharacteristic
725C2×C4C2×#13111yescharacteristic
726C2×C4#56811yescharacteristic
727C2×C4#56811yescharacteristic
728C2×C4C22×D811yescharacteristic
729C2×C4C22×SD1611yescharacteristic
730C2×C4C2×#13511yescharacteristic
731C2×C4C2×#13511yescharacteristic
732C8—24no—
733C8—42no—
734C8—42no—
735C8—42no—
736C8—81no—
737C8—81no—
738C8—81no—
739C8—81no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22#229711yescharacteristic
762C22#288011yescharacteristic
763C22#288011yescharacteristic
764C22C22×#10211yescharacteristic
765C22C2×#41611yescharacteristic
766C22#290111yescharacteristic
767C22#290111yescharacteristic
768C4—22no—
769C4—22no—
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—21no—
776C4—21no—
777C4—42no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—81no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4#296611yescharacteristic
788C4#296711yescharacteristic
789C4#296811yescharacteristic
790C4#296911yescharacteristic
791C4#316711yescharacteristic
792C4#316711yescharacteristic
793C4#316911yescharacteristic
794C4#316911yescharacteristic
795C2—42no—
796C2—82no—
797C2—161no—
798C2#1750711yescharacteristic
799C2#1750711yescharacteristic
800C2#1750811yescharacteristic
801C2#1751011yescharacteristic
802C2#2138111yescharacteristic
803C2#2140111yescharacteristic
804C2#2141911yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radical#2428C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C4×#117 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #20812C2semidirect
3. C8×#117C2semidirect
4. #9874C2semidirect
5. #9870C2semidirect
6. #9644C2semidirect
7. #9638C2semidirect
8. #9076C2semidirect
9. #9076C2semidirect
10. #9072C2semidirect
11. #9072C2semidirect
12. #8183C2semidirect
13. #8177C2semidirect
14. #8174C2semidirect
15. C4×D4⋊C8C2semidirect

Maximal subgroups

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

subgroupindex
#349142
#208122
C8×#1172
#98742
#98702
#96442
#96382
#90762
#90722
#81832
#81772
#81742
C4×D4⋊C82