Finite Group Databasebeta

← #363007

Subgroups — #363007

Order 512.

1116 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34145C211yesmaximal, characteristic
2#21023C211yesmaximal, characteristic
3#13846C211yesmaximal, characteristic
4#11386C211yesmaximal, characteristic
5#11386C211yesmaximal, characteristic
6#11226C211yesmaximal, characteristic
7#11209C211yesmaximal, characteristic
8#10886C211yesmaximal, characteristic
9#10879C211yesmaximal, characteristic
10#10852C211yesmaximal, characteristic
11#10808C211yesmaximal, characteristic
12#10808C211yesmaximal, characteristic
13#10808C211yesmaximal, characteristic
14#10808C211yesmaximal, characteristic
15#10701C211yesmaximal, characteristic
16C2×#533C2211yescharacteristic
17C2×#423C2211yescharacteristic
18C2×C4×M16C2211yescharacteristic
19#2370C411yescharacteristic, complemented
20#2370C411yescharacteristic, complemented
21#2370C411yescharacteristic, complemented
22#2370C411yescharacteristic, complemented
23#2369C411yescharacteristic, complemented
24#2369C411yescharacteristic, complemented
25#2368—21no—
26#2368—21no—
27#2365C411yescharacteristic, complemented
28#2365C411yescharacteristic, complemented
29#2360—21no—
30#2360—21no—
31#2296C2211yescharacteristic
32#2296C2211yescharacteristic
33#2295—21no—
34#2295—21no—
35#2295—21no—
36C42×Q8—21no—
37C4×#117C2211yescharacteristic
38C4×#117C2211yescharacteristic
39C4×#117C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×#376C2211yescharacteristic
43#1917—21no—
44#1917—21no—
45#1916—21no—
46#1916—21no—
47C2×#339C2211yescharacteristic
48C2×#339C2211yescharacteristic
49C2×#339C2211yescharacteristic
50C2×#339C2211yescharacteristic
51C2×#339C2211yescharacteristic
52C2×#339C2211yescharacteristic
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63#1728C2211yescharacteristic
64#1728C2211yescharacteristic
65#1728C2211yescharacteristic
66#1728C2211yescharacteristic
67#1445—21no—
68#1443—21no—
69#1442—21no—
70#1441—21no—
71C4×#95C2211yescharacteristic
72C4×#95C2211yescharacteristic
73C4×#95C2211yescharacteristic
74C4×#95C2211yescharacteristic
75C22×M16C2311yescharacteristic
76C22×M16C2311yescharacteristic
77C22×M16C2311yescharacteristic
78C22×M16C2311yescharacteristic
79#533—22no—
80#533—22no—
81#533—22no—
82#533—22no—
83C2×C4⋊Q8C2×C411yescharacteristic
84C2×C4⋊Q8C2×C411yescharacteristic
85C2×#125C2×C411yescharacteristic
86C2×#125C2×C411yescharacteristic
87C2×C22⋊Q8—21no—
88C2×C22⋊Q8—21no—
89C2×C4×Q8—21no—
90C2×C4×Q8—21no—
91C2×C4×Q8—21no—
92C2×C4×Q8—21no—
93C2×#117C2311yescharacteristic
94C2×#117C2311yescharacteristic
95C2×#117C2311yescharacteristic
96C2×#117C2311yescharacteristic
97C22×C4⋊C4—21no—
98C22×C4⋊C4D411yescharacteristic
99C22×C4⋊C4D411yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107#423—22no—
108#423—41no—
109C2×C4⋊C8—21no—
110C2×C4⋊C8—21no—
111C4×M16—22no—
112C4×M16—41no—
113C2×#97—21no—
114C2×C4×C8—21no—
115#391—21no—
116#391—21no—
117#391—21no—
118#391—21no—
119#391—21no—
120#391—21no—
121#389—21no—
122#389—21no—
123#389—21no—
124#389—21no—
125#389—21no—
126#389—21no—
127#389C2×C411yescharacteristic
128#389C2×C411yescharacteristic
129#389C2×C411yescharacteristic
130#389C2×C411yescharacteristic
131#389C2×C411yescharacteristic
132#389C2×C411yescharacteristic
133#389C2×C411yescharacteristic
134#389C2×C411yescharacteristic
135#387—21no—
136#387—21no—
137#387—21no—
138#387—21no—
139#387—21no—
140#387—21no—
141#387—21no—
142#387—21no—
143#387—21no—
144#387—21no—
145#387—21no—
146#387—21no—
147#385—21no—
148#385—21no—
149#385—21no—
150#385—21no—
151C4×C4⋊C4—21no—
152C4×C4⋊C4—21no—
153C4×C4⋊C4—21no—
154C4×C4⋊C4—21no—
155C4×C4⋊C4—21no—
156C4×C4⋊C4—21no—
157C4×C4⋊C4—21no—
158C4×C4⋊C4—21no—
159C4×C4⋊C4—21no—
160C4×C4⋊C4—21no—
161C4×C4⋊C4—22no—
162C4×C4⋊C4—41no—
163C4×C4⋊C4C2×C411yescharacteristic
164C4×C4⋊C4C2×C411yescharacteristic
165C4×C4⋊C4C2×C411yescharacteristic
166C4×C4⋊C4C2×C411yescharacteristic
167C4×C4⋊C4C2×C411yescharacteristic
168C4×C4⋊C4C2×C411yescharacteristic
169C4×C4⋊C4C2×C411yescharacteristic
170C4×C4⋊C4C2×C411yescharacteristic
171C4×C4⋊C4C2×C411yescharacteristic
172C4×C4⋊C4C2×C411yescharacteristic
173C4×C4⋊C4C2×C411yescharacteristic
174C4×C4⋊C4C2×C411yescharacteristic
175C4×C4⋊C4C2×C411yescharacteristic
176C4×C4⋊C4C2×C411yescharacteristic
177C4×C4⋊C4C2×C411yescharacteristic
178C4×C4⋊C4C2×C411yescharacteristic
179C4×C4⋊C4D411yescharacteristic
180C4×C4⋊C4D411yescharacteristic
181C4×C4⋊C4D411yescharacteristic
182C4×C4⋊C4D411yescharacteristic
183C4×C22⋊C4—21no—
184C4×C22⋊C4—21no—
185C4×C22⋊C4—21no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4—21no—
189#376—21no—
190#376—21no—
191#376—21no—
192#376—22no—
193#376—41no—
194C2×#95—21no—
195C2×#95—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—21no—
205C2×#95D411yescharacteristic
206C2×#95D411yescharacteristic
207C43—21no—
208C43—21no—
209C43—21no—
210#339—22no—
211#339—22no—
212#339—22no—
213#339—22no—
214#339—22no—
215#339—22no—
216#339—22no—
217#339—22no—
218#339—22no—
219#339—22no—
220#339—22no—
221#339—22no—
222#339—22no—
223#339—41no—
224#339—41no—
225#339Q814yescomplemented
226#336—21no—
227#336—21no—
228#336—21no—
229#336—21no—
230#336—21no—
231#336—21no—
232#336—21no—
233#336—21no—
234C22×Q8—21no—
235C22×Q8—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2411yescharacteristic
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—21no—
269C2×M16C2×Q812yes—
270C2×M16#4112yes—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C4⋊Q8—22no—
276C4⋊Q8—22no—
277C4⋊Q8—22no—
278C4⋊Q8—22no—
279#125—22no—
280#125—22no—
281#125—22no—
282#125—22no—
283C22⋊Q8—24no—
284C22⋊Q8—24no—
285C22⋊Q8—24no—
286C22⋊Q8—24no—
287C4×Q8—24no—
288C4×Q8—24no—
289C4×Q8—24no—
290C4×Q8—24no—
291C4×Q8—44no—
292C4×Q8—44no—
293#117—21no—
294#117—21no—
295#117—21no—
296#117—21no—
297#117—21no—
298#117—21no—
299#117—21no—
300#117—21no—
301#117—21no—
302#117—21no—
303#117C2×Q812yes—
304#117#4112yes—
305#117#4112yes—
306#117#4112yes—
307#117#4112yes—
308#117#4112yes—
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—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
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×C4⋊C4C22×C411yescharacteristic
337C2×C4⋊C4C22×C411yescharacteristic
338C2×C4⋊C4C22×C411yescharacteristic
339C2×C4⋊C4C22×C411yescharacteristic
340C2×C4⋊C4C22×C411yescharacteristic
341C2×C4⋊C4C22×C411yescharacteristic
342C2×C4⋊C4C22×C411yescharacteristic
343C2×C4⋊C4C22×C411yescharacteristic
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C22×C411yescharacteristic
399C2×C42C22×C411yescharacteristic
400C2×C42C22×C411yescharacteristic
401C2×C42C22×C411yescharacteristic
402C2×C42C22×C411yescharacteristic
403C2×C42C22×C411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×Q812yes—
411C2×C42#4112yes—
412C4⋊C8—42no—
413C4⋊C8—42no—
414#97—42no—
415C4×C8—42no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95C22⋊C411yescharacteristic
448#95C22⋊C411yescharacteristic
449#95C22⋊C411yescharacteristic
450#95C22⋊C411yescharacteristic
451#95C22⋊C411yescharacteristic
452#95C22⋊C411yescharacteristic
453#95C22⋊C411yescharacteristic
454#95C22⋊C411yescharacteristic
455C24C22×D411yescharacteristic
456C2×Q8—24no—
457C2×Q8—24no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—81no—
461C2×Q8—81no—
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—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
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—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
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×C4C2×C22⋊C411yescharacteristic
523C22×C4C2×C22⋊C411yescharacteristic
524C22×C4C2×C22⋊C411yescharacteristic
525C22×C4C2×C22⋊C411yescharacteristic
526C22×C4C2×C22⋊C411yescharacteristic
527C22×C4C2×C22⋊C411yescharacteristic
528C22×C4C2×C22⋊C411yescharacteristic
529C22×C4C2×C22⋊C411yescharacteristic
530C22×C4C2×C22⋊C411yescharacteristic
531C22×C4C2×C22⋊C411yescharacteristic
532C22×C4C2×C22⋊C411yescharacteristic
533C22×C4C2×C22⋊C411yescharacteristic
534C22×C4C23×C411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×Q811yescharacteristic
537C22×C4C2×#4111yescharacteristic
538C22×C4C2×#4111yescharacteristic
539C22×C4C2×#4111yescharacteristic
540C22×C4C2×#4111yescharacteristic
541C22×C4C2×#4111yescharacteristic
542C22×C4C2×#4111yescharacteristic
543C22×C4C2×#4111yescharacteristic
544C22×C4H(5,𝔽2)11yescharacteristic
545C22×C42−1+411yescharacteristic
546C22×C42−1+411yescharacteristic
547C22×C42−1+411yescharacteristic
548M16—22no—
549M16—22no—
550M16—22no—
551M16—22no—
552M16—41no—
553M16—41no—
554M16—41no—
555M16—41no—
556M16—41no—
557M16—41no—
558M16—41no—
559M16—41no—
560M16—41no—
561M16—41no—
562M16—41no—
563M16—41no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—48no—
604C4⋊C4—42no—
605C4⋊C4—81no—
606C4⋊C4—81no—
607C4⋊C4—81no—
608C4⋊C4—81no—
609C4⋊C4#11712yes—
610C4⋊C4#11712yes—
611C4⋊C4#11712yes—
612C4⋊C4#11712yes—
613C4⋊C4C4×Q812yes—
614C4⋊C4C4×Q812yes—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—41no—
622C22⋊C4—41no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—42no—
658C42—42no—
659C42—42no—
660C42—42no—
661C42—41no—
662C42—41no—
663C42—41no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—42no—
668C42—42no—
669C42—41no—
670C42—41no—
671C42—41no—
672C42—41no—
673C42—41no—
674C42—41no—
675C42—41no—
676C42—41no—
677C42—81no—
678C42—81no—
679C42—81no—
680C42—81no—
681C42—81no—
682C42—81no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23C22×C22⋊C411yescharacteristic
688C23#52511yescharacteristic
689C23#52511yescharacteristic
690C23#54611yescharacteristic
691C23#54711yescharacteristic
692C23#54811yescharacteristic
693C23D4×Q811yescharacteristic
694Q8—48no—
695Q8—84no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
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—21no—
721C2×C4—21no—
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—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
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#42112yes—
795C2×C4#42112yes—
796C2×C4C2×#11711yescharacteristic
797C2×C4C2×#11711yescharacteristic
798C2×C4C2×C4×Q811yescharacteristic
799C2×C4C4×#4111yescharacteristic
800C2×C4#51911yescharacteristic
801C2×C4#52011yescharacteristic
802C2×C4#52511yescharacteristic
803C2×C4#52511yescharacteristic
804C2×C4#52911yescharacteristic
805C2×C4#52911yescharacteristic
806C2×C4#53311yescharacteristic
807C2×C4#53311yescharacteristic
808C2×C4#54111yescharacteristic
809C2×C4#54111yescharacteristic
810C2×C4#54211yescharacteristic
811C2×C4#54211yescharacteristic
812C2×C4#54611yescharacteristic
813C2×C4#54711yescharacteristic
814C2×C4#54811yescharacteristic
815C2×C4D4×Q811yescharacteristic
816C2×C4#55211yescharacteristic
817C2×C4#55211yescharacteristic
818C2×C4#55411yescharacteristic
819C2×C4#55611yescharacteristic
820C2×C4#55611yescharacteristic
821C2×C4#55611yescharacteristic
822C2×C4#55711yescharacteristic
823C2×C4#55911yescharacteristic
824C8—42no—
825C8—42no—
826C8—81no—
827C8—81no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22#228011yescharacteristic
841C22#233911yescharacteristic
842C22Q8×C22⋊C411yescharacteristic
843C22#245811yescharacteristic
844C22#246211yescharacteristic
845C22#246511yescharacteristic
846C22#246911yescharacteristic
847C22C2×#42111yescharacteristic
848C22C2×#42111yescharacteristic
849C22#290111yescharacteristic
850C22#290111yescharacteristic
851C4—22no—
852C4—22no—
853C4—42no—
854C4—42no—
855C4—41no—
856C4—42no—
857C4—42no—
858C4—41no—
859C4—41no—
860C4—42no—
861C4—42no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4—81no—
874C4—81no—
875C4#229511yescharacteristic
876C4#232011yescharacteristic
877C4#235511yescharacteristic
878C4#235611yescharacteristic
879C4#245811yescharacteristic
880C4#246211yescharacteristic
881C4#246511yescharacteristic
882C4#246911yescharacteristic
883C2—21no—
884C2—21no—
885C2—21no—
886C2—21no—
887C2#1392711yescharacteristic
888C2#2074811yescharacteristic
889C2#2074911yescharacteristic
890C2#2250611yescharacteristic
891C2#2250711yescharacteristic
892C2#2252911yescharacteristic
893C2#2252911yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
19. #2370C4semidirect
20. #2370C4semidirect
21. #2370C4semidirect
22. #2370C4semidirect
23. #2369C4semidirect
24. #2369C4semidirect
27. #2365C4semidirect
28. #2365C4semidirect
225. #339Q8semidirect

Maximal subgroups

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

subgroupindex
#341452
#210232
#138462
#113862
#112262
#112092
#108862
#108792
#108522
#108082
#107012