Finite Group Databasebeta

← #223508

Subgroups — #223508

Order 512.

982 conjugacy classes of subgroups.

The subgroup lattice has 803 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34763C211yesmaximal, characteristic
2#22797C211yesmaximal, characteristic, complemented
3#21264C211yesmaximal, characteristic, complemented
4#9870C211yesmaximal, characteristic, complemented
5#9869C211yesmaximal, characteristic, complemented
6#9074C211yesmaximal, characteristic, complemented
7#9074C211yesmaximal, characteristic, complemented
8#8943C211yesmaximal, characteristic, complemented
9#8940C211yesmaximal, characteristic, complemented
10#8710C211yesmaximal, characteristic, complemented
11#8707C211yesmaximal, characteristic, complemented
12#8567C211yesmaximal, characteristic, complemented
13#8177C211yesmaximal, characteristic, complemented
14#7900C211yesmaximal, characteristic, complemented
15#7892C211yesmaximal, characteristic, complemented
16C2×#529—21no—
17C2×#432C2211yescharacteristic
18C2×#431C2211yescharacteristic
19C2×#431C2211yescharacteristic
20C2×#431C2211yescharacteristic
21#2521—21no—
22#2519—21no—
23#2512C411yescharacteristic
24#2506C411yescharacteristic
25#2501C411yescharacteristic
26#2496C411yescharacteristic
27#2491C411yescharacteristic
28#2488—21no—
29#2486C411yescharacteristic
30#2440C411yescharacteristic
31#2425—21no—
32#2416C411yescharacteristic
33#2396—21no—
34#2395—21no—
35C4×C4⋊Q8C2211yescharacteristic
36C4×#123—21no—
37C4×#121C2211yescharacteristic
38C4×#121C2211yescharacteristic
39#2293C2211yescharacteristic
40#2285C2211yescharacteristic
41C42×D4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43#1955—21no—
44#1954—21no—
45#1939—21no—
46#1924—21no—
47#1923—21no—
48#1923—21no—
49#1923—21no—
50#1842C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53#1771—21no—
54#1767C2211yescharacteristic
55C4×C4⋊C8C2211yescharacteristic
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58C42×C8C2211yescharacteristic
59C2×D4⋊C8C2211yescharacteristic
60C2×D4⋊C8C2211yescharacteristic
61C2×D4⋊C8C2211yescharacteristic
62C2×D4⋊C8C2211yescharacteristic
63#1279C2211yescharacteristic
64#1279C2211yescharacteristic
65#1279C2211yescharacteristic
66#1279C2211yescharacteristic
67#1279C2211yescharacteristic
68#1279C2211yescharacteristic
69#1279C2211yescharacteristic
70#1279C2211yescharacteristic
71#1279C2211yescharacteristic
72#1279C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75C2×C4⋊Q8C2×C411yescharacteristic
76#529—44no—
77#529—44no—
78C2×#126—21no—
79C2×#126—21no—
80C2×#125—21no—
81C2×#124—21no—
82C2×#123—21no—
83C2×#123—21no—
84C2×#123—21no—
85C2×C22⋊Q8—21no—
86C2×#121—21no—
87C2×#121C2×C411yescharacteristic
88C2×#121C2×C411yescharacteristic
89C2×C4×Q8—21no—
90C2×C4×D4—21no—
91C2×C4×D4—21no—
92C2×C4×D4C2×C411yescharacteristic
93C2×C4×D4D411yescharacteristic
94C2×C4×D4D411yescharacteristic
95C2×C4×D4C2311yescharacteristic
96C2×#117—21no—
97C2×#117—21no—
98C22×C4⋊C4C2×C411yescharacteristic
99C22×C4⋊C4C2×C411yescharacteristic
100C22×C42—21no—
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103#432—22no—
104#432—41no—
105#431—22no—
106#431—22no—
107#431—22no—
108#431—41no—
109#431—41no—
110#431—41no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—21no—
113C2×C4⋊C8—21no—
114C2×C4⋊C8—21no—
115C2×C4⋊C8—21no—
116C2×C4⋊C8C2311yescharacteristic
117C2×C4⋊C8C2311yescharacteristic
118C2×C4⋊C8C2311yescharacteristic
119C2×C4⋊C8C2311yescharacteristic
120C2×C22⋊C8—21no—
121C2×C22⋊C8—21no—
122C2×C22⋊C8—21no—
123C2×C22⋊C8—21no—
124C2×C22⋊C8—21no—
125C2×C22⋊C8—21no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8—21no—
128C2×#97—21no—
129C2×#97—21no—
130C2×C4×C8—21no—
131C2×C4×C8—21no—
132C2×C4×C8—21no—
133C2×C4×C8C2311yescharacteristic
134C2×C4×C8C2311yescharacteristic
135C2×C4×C8C2311yescharacteristic
136C2×C4×C8C2311yescharacteristic
137#400—21no—
138#400—21no—
139#399—21no—
140#399—21no—
141#398—21no—
142#398—21no—
143#398—21no—
144#397—21no—
145#397—21no—
146#397—21no—
147#396—21no—
148#396—21no—
149#395—21no—
150#394—21no—
151#394—21no—
152#393—21no—
153#391—21no—
154#390C2×C411yescharacteristic
155#390C2×C411yescharacteristic
156#390C2×C411yescharacteristic
157#390C2×C411yescharacteristic
158#389—21no—
159#389C2×C411yescharacteristic
160#389C2×C411yescharacteristic
161#389C2×C411yescharacteristic
162#389C2×C411yescharacteristic
163#389C2×C411yescharacteristic
164#389C2×C411yescharacteristic
165#388—21no—
166#388—21no—
167#388—21no—
168#388—21no—
169#388—21no—
170#388—21no—
171#387—21no—
172#387—21no—
173#386—21no—
174#386—21no—
175#386—21no—
176#385—21no—
177#384C2×C411yescharacteristic
178#384C2×C411yescharacteristic
179#384C2×C411yescharacteristic
180#382—21no—
181#381—21no—
182#380—21no—
183#380C2×C411yescharacteristic
184#380C2×C411yescharacteristic
185#380C2×C411yescharacteristic
186#380C2×C411yescharacteristic
187C4×C4⋊C4—21no—
188C4×C4⋊C4—21no—
189C4×C4⋊C4—21no—
190C4×C4⋊C4—21no—
191C4×C4⋊C4C2×C411yescharacteristic
192C4×C4⋊C4C2×C411yescharacteristic
193C4×C4⋊C4C2×C411yescharacteristic
194C4×C4⋊C4D411yescharacteristic
195C4×C4⋊C4D411yescharacteristic
196C4×C4⋊C4C2311yescharacteristic
197C4×C4⋊C4C2311yescharacteristic
198C4×C4⋊C4C2311yescharacteristic
199C4×C22⋊C4—21no—
200C4×C22⋊C4—21no—
201C4×C22⋊C4—21no—
202C4×C22⋊C4C2×C411yescharacteristic
203C4×C22⋊C4C2×C411yescharacteristic
204C4×C22⋊C4D411yescharacteristic
205C4×C22⋊C4D411yescharacteristic
206C4×C22⋊C4D411yescharacteristic
207C4×C22⋊C4D411yescharacteristic
208C2×#95—21no—
209C43C2311yescharacteristic
210#336—21no—
211#336—21no—
212#336—21no—
213#336—21no—
214#336—21no—
215#336—21no—
216D4⋊C8—22no—
217D4⋊C8—22no—
218D4⋊C8—41no—
219D4⋊C8—41no—
220C22×Q8—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4C22⋊C411yescharacteristic
224C22×D4C22×C411yescharacteristic
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4C22×C411yescharacteristic
229C23×C4C22×C411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C4⋊Q8—22no—
243C4⋊Q8—41no—
244#126—44no—
245#126—44no—
246#125—44no—
247#124—44no—
248#123—44no—
249#123—44no—
250#123—44no—
251C22⋊Q8—44no—
252#121—22no—
253#121—22no—
254#121—22no—
255#121—41no—
256#121—44no—
257C4×Q8—42no—
258C4×Q8—42no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—42no—
268C4×D4—42no—
269C4×D4—42no—
270C4×D4—42no—
271C4×D4—42no—
272#117—42no—
273#117—42no—
274#117—42no—
275#117—42no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4C22⋊C411yescharacteristic
296C2×C4⋊C4C22⋊C411yescharacteristic
297C2×C4⋊C4C22⋊C411yescharacteristic
298C2×C4⋊C4C22×C411yescharacteristic
299C2×C4⋊C4C22×C411yescharacteristic
300C2×C4⋊C4C22×C411yescharacteristic
301C2×C4⋊C4C22×C411yescharacteristic
302C2×C4⋊C4C22×C411yescharacteristic
303C2×C4⋊C4C22×C411yescharacteristic
304C2×C4⋊C4C22×C411yescharacteristic
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
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⋊C4C22⋊C411yescharacteristic
321C2×C22⋊C4C22⋊C411yescharacteristic
322C2×C22⋊C4C22⋊C411yescharacteristic
323C2×C22⋊C4C22⋊C411yescharacteristic
324C2×C22⋊C4C22⋊C411yescharacteristic
325C2×C22⋊C4C22⋊C411yescharacteristic
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42C22×C411yescharacteristic
342C2×C42C22×C411yescharacteristic
343C2×C42C22×C411yescharacteristic
344C2×C42C22×C411yescharacteristic
345C2×C42C2×D411yescharacteristic
346C2×C42C2×D411yescharacteristic
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2411yescharacteristic
354C4⋊C8—21no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—42no—
362C4⋊C8—42no—
363C4⋊C8—42no—
364C4⋊C8—42no—
365C4⋊C8—81no—
366C4⋊C8#4112yes—
367C22⋊C8—42no—
368C22⋊C8—42no—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8—81no—
374C22⋊C8—81no—
375#97—42no—
376#97—42no—
377C4×C8—21no—
378C4×C8—21no—
379C4×C8—21no—
380C4×C8—21no—
381C4×C8—21no—
382C4×C8—21no—
383C4×C8—21no—
384C4×C8—42no—
385C4×C8—42no—
386C4×C8—42no—
387C4×C8#4112yes—
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#95C22⋊C411yescharacteristic
404#95C22⋊C411yescharacteristic
405#95C22⋊C411yescharacteristic
406#95C22⋊C411yescharacteristic
407#95C22⋊C411yescharacteristic
408#95C22⋊C411yescharacteristic
409C24—21no—
410C24C2×C22⋊C411yescharacteristic
411C24C2×C22⋊C411yescharacteristic
412C2×Q8—42no—
413C2×Q8—42no—
414C2×Q8—81no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—41no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4—81no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
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—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—81no—
479C22×C4C2×C22⋊C411yescharacteristic
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×C4#13112yes—
490C22×C4#13112yes—
491C22×C4C23×C411yescharacteristic
492C22×C4C22×D411yescharacteristic
493C22×C4C22×D411yescharacteristic
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
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—
518C4⋊C4—21no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
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—41no—
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—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—81no—
549C4⋊C4#13112yes—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C42—21no—
573C42—21no—
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—22no—
591C42—41no—
592C42—42no—
593C42—42no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42AGL(1,ℤ/8)12yes—
601C42AGL(1,ℤ/8)12yes—
602C42C2×#4111yescharacteristic
603C42C2×#4111yescharacteristic
604C42H(5,𝔽2)11yescharacteristic
605C422−1+411yescharacteristic
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23#40812yes—
627C23C22×C22⋊C411yescharacteristic
628Q8—84no—
629D4—44no—
630D4—41no—
631D4—41no—
632D4—41no—
633D4—41no—
634D4—84no—
635D4—84no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
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—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
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—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—84no—
706C2×C4—84no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4#40812yes—
712C2×C4#41812yes—
713C2×C4#41812yes—
714C2×C4#42112yes—
715C2×C4C4×#4111yescharacteristic
716C2×C4#52011yescharacteristic
717C2×C4#54611yescharacteristic
718C2×C4#54611yescharacteristic
719C2×C4#54711yescharacteristic
720C2×C4#54711yescharacteristic
721C2×C4C2×#13111yescharacteristic
722C2×C4C2×#13111yescharacteristic
723C2×C4C2×#13111yescharacteristic
724C2×C4#56811yescharacteristic
725C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
726C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
727C2×C4#57711yescharacteristic
728C2×C4#57811yescharacteristic
729C8—42no—
730C8—42no—
731C8—42no—
732C8—81no—
733C8—81no—
734C8—81no—
735C8—81no—
736C8—81no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22#233911yescharacteristic
759C22C2×#40811yescharacteristic
760C22#288011yescharacteristic
761C22C2×#41811yescharacteristic
762C22#289811yescharacteristic
763C22C2×#42111yescharacteristic
764C22#290111yescharacteristic
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—21no—
770C4—21no—
771C4—41no—
772C4—42no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4#296611yescharacteristic
785C4#296811yescharacteristic
786C4#299211yescharacteristic
787C4#299411yescharacteristic
788C4#333011yescharacteristic
789C4#333211yescharacteristic
790C4#335311yescharacteristic
791C4#335411yescharacteristic
792C2—42no—
793C2—81no—
794C2—161no—
795C2#1747811yescharacteristic
796C2#1748411yescharacteristic
797C2#1751111yescharacteristic
798C2#1752411yescharacteristic
799C2#2247011yescharacteristic
800C2#2250011yescharacteristic
801C2#2250711yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radical#2416C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22797C2semidirect
3. #21264C2semidirect
4. #9870C2semidirect
5. #9869C2semidirect
6. #9074C2semidirect
7. #9074C2semidirect
8. #8943C2semidirect
9. #8940C2semidirect
10. #8710C2semidirect
11. #8707C2semidirect
12. #8567C2semidirect
13. #8177C2semidirect
14. #7900C2semidirect
15. #7892C2semidirect

Maximal subgroups

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

subgroupindex
#347632
#227972
#212642
#98702
#98692
#90742
#89432
#89402
#87102
#87072
#85672
#81772
#79002
#78922