Finite Group Databasebeta

← C2×#35958 #7629561

Subgroups — C2×#35958 #7629561

Order 512.

5046 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35958C2132yesmaximal, direct product factor
2C2×#2582C211yesmaximal, characteristic
3C2×#2568C211yesmaximal, characteristic
4C2×#2571C211yesmaximal, characteristic
5C2×#2581C211yesmaximal, characteristic
6C2×#2570C211yesmaximal, characteristic
7C2×#2565C211yesmaximal, characteristic
8C2×#2612C212yesmaximal
9C2×#2605C212yesmaximal
10C2×#2586C212yesmaximal
11C2×#2585C212yesmaximal
12C2×#2520C212yesmaximal
13C2×#2520C212yesmaximal
14C2×#2660C211yesmaximal, characteristic
15C2×#2666C212yesmaximal
16C2×#2402C212yesmaximal
17C2×#2399C211yesmaximal, characteristic
18C2×#2370C211yesmaximal, characteristic
19C2×#2369C211yesmaximal, characteristic
20C2×#2356C211yesmaximal, characteristic
21C2×#2355C211yesmaximal, characteristic
22C2×#2355C211yesmaximal, characteristic
23C2×#2355C211yesmaximal, characteristic
24C2×#2276C211yesmaximal, characteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×#125C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32#2666C22132yes—
33#2660C22116yes—
34#2612C22132yes—
35#2605C22132yes—
36#2586C22132yes—
37#2585C22132yes—
38#2582C22116yes—
39#2581C22116yes—
40#2571C22116yes—
41#2570C22116yes—
42#2568C22116yes—
43#2565C22116yes—
44#2520C22132yes—
45#2520C22132yes—
46#2402C22132yes—
47#2399C22116yes—
48C2×#400C2212yes—
49C2×#400C2212yes—
50C2×#400C2212yes—
51C2×#400C2212yes—
52C2×#400C2212yes—
53C2×#400C2212yes—
54C2×#398C2211yescharacteristic
55C2×#398C2212yes—
56C2×#398C2212yes—
57C2×#398C2212yes—
58C2×#398C2212yes—
59C2×#398C2212yes—
60C2×#398C2212yes—
61C2×#398C2211yescharacteristic
62C2×#398C2212yes—
63C2×#398C2211yescharacteristic
64C2×#398C2211yescharacteristic
65C2×#395C2211yescharacteristic
66C2×#395C2212yes—
67C2×#395C2212yes—
68C2×#395C2211yescharacteristic
69C2×#395C2211yescharacteristic
70C2×#395C2212yes—
71C2×#395C2211yescharacteristic
72#2370C22116yes—
73#2369C22116yes—
74#2356C22116yes—
75#2355C22116yes—
76#2355C22116yes—
77#2355C22116yes—
78C2×#391C2212yes—
79C2×#391C2212yes—
80C2×#391C2212yes—
81C2×#391C2212yes—
82C2×#391C2212yes—
83C2×#391C2212yes—
84C2×#391C2212yes—
85C2×#391C2211yescharacteristic
86C2×#391C2211yescharacteristic
87C2×#391C2211yescharacteristic
88C2×#391C2211yescharacteristic
89C2×#389C2212yes—
90C2×#389C2212yes—
91C2×#389C2212yes—
92C2×#389C2212yes—
93C2×#389C2211yescharacteristic
94C2×#389C2211yescharacteristic
95C2×#389C2211yescharacteristic
96C2×#389C2211yescharacteristic
97C2×#387C2212yes—
98C2×#387C2212yes—
99C2×#387C2212yes—
100C2×#387C2212yes—
101C2×#387C2212yes—
102C2×#387C2212yes—
103C2×#387C2212yes—
104C2×#387C2212yes—
105C2×#387C2212yes—
106C2×#387C2212yes—
107C2×#387C2212yes—
108C2×#387C2212yes—
109C2×#387C2212yes—
110C2×#387C2212yes—
111C2×#387C2212yes—
112C2×#387C2212yes—
113C2×#384C2211yescharacteristic
114C2×#384C2211yescharacteristic
115C2×#384C2211yescharacteristic
116C2×#383C2212yes—
117C2×#382C2212yes—
118C2×#382C2211yescharacteristic
119C2×#382C2211yescharacteristic
120C2×#382C2211yescharacteristic
121C2×#382C2211yescharacteristic
122C2×#382C2211yescharacteristic
123C2×#382C2212yes—
124#2276C22116yes—
125C2×C4×C4⋊C4C2212yes—
126C2×C4×C4⋊C4C2212yes—
127C2×C4×C4⋊C4C2212yes—
128C2×C4×C4⋊C4C2212yes—
129C2×C4×C4⋊C4C2212yes—
130C2×C4×C4⋊C4C2212yes—
131C2×C4×C4⋊C4C2211yescharacteristic
132C2×C4×C4⋊C4C2211yescharacteristic
133C2×C4×C4⋊C4C2211yescharacteristic
134C2×C4×C4⋊C4C2211yescharacteristic
135C2×C4×C4⋊C4C2211yescharacteristic
136C2×C4×C4⋊C4C2211yescharacteristic
137C2×C4×C4⋊C4C2212yes—
138C2×C4×C4⋊C4C2211yescharacteristic
139C2×C4×C4⋊C4C2211yescharacteristic
140C2×C4×C4⋊C4C2211yescharacteristic
141C2×C4×C4⋊C4C2211yescharacteristic
142C2×C4×C4⋊C4C2212yes—
143C2×C4×C4⋊C4C2211yescharacteristic
144C2×#376C2212yes—
145C2×#376C2212yes—
146C2×#376C2211yescharacteristic
147C23×Q8C2311yescharacteristic
148C23×Q8C2311yescharacteristic
149C23×Q8C2311yescharacteristic
150C23×Q8C2312yes—
151C2×C4⋊Q8—28no—
152C2×C4⋊Q8C2318yes—
153C2×#125—28no—
154C2×#125C2318yes—
155C2×C4×Q8—28no—
156C2×C4×Q8—28no—
157C2×C4×Q8—28no—
158C2×C4×Q8—28no—
159C2×C4×Q8Q8116yescomplemented
160C2×C4×Q8C2318yes—
161C2×C4×Q8C2318yes—
162C2×C4×Q8C2318yes—
163C2×C4×Q8C2318yes—
164C2×C4×Q8C2318yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2312yes—
202C22×C42C2312yes—
203C22×C42C2312yes—
204C22×C42C2311yescharacteristic
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2312yes—
209C22×C42C2312yes—
210C22×C42C2312yes—
211C22×C42C2312yes—
212C22×C42C2312yes—
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2312yes—
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219#400C23116yes—
220#400C23116yes—
221#400C23116yes—
222#400C23116yes—
223#400C23116yes—
224#400C23116yes—
225#398C23116yes—
226#398C23116yes—
227#398C23116yes—
228#398C23116yes—
229#398C23116yes—
230#398C2318yes—
231#398C23116yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C23116yes—
236#395C23116yes—
237#395C2318yes—
238#395C23116yes—
239#395C2318yes—
240#395C23116yes—
241#395C2318yes—
242#395C2318yes—
243#391C2318yes—
244#391C2318yes—
245#391C2318yes—
246#391C2318yes—
247#391C23116yes—
248#391C23116yes—
249#391C23116yes—
250#391C23116yes—
251#391C23116yes—
252#391C23116yes—
253#391C23116yes—
254#389C2318yes—
255#389C2318yes—
256#389C2318yes—
257#389C2318yes—
258#389C23116yes—
259#389C23116yes—
260#389C23116yes—
261#389C23116yes—
262#387C23116yes—
263#387C23116yes—
264#387C23116yes—
265#387C23116yes—
266#387C23116yes—
267#387C23116yes—
268#387C23116yes—
269#387C23116yes—
270#387C23116yes—
271#387C23116yes—
272#387C23116yes—
273#387C23116yes—
274#387C23116yes—
275#387C23116yes—
276#387C23116yes—
277#387C23116yes—
278#384C2318yes—
279#384C2318yes—
280#384C2318yes—
281#383C23116yes—
282#382C2318yes—
283#382C2318yes—
284#382C2318yes—
285#382C2318yes—
286#382C23116yes—
287#382C2318yes—
288#382C23116yes—
289C4×C4⋊C4C2318yes—
290C4×C4⋊C4C2318yes—
291C4×C4⋊C4C2318yes—
292C4×C4⋊C4C2318yes—
293C4×C4⋊C4C2318yes—
294C4×C4⋊C4C23116yes—
295C4×C4⋊C4C23116yes—
296C4×C4⋊C4C23116yes—
297C4×C4⋊C4C23116yes—
298C4×C4⋊C4C23116yes—
299C4×C4⋊C4C2318yes—
300C4×C4⋊C4C2318yes—
301C4×C4⋊C4C2318yes—
302C4×C4⋊C4C2318yes—
303C4×C4⋊C4C2318yes—
304C4×C4⋊C4C23116yes—
305C4×C4⋊C4C2318yes—
306C4×C4⋊C4C23116yes—
307C4×C4⋊C4C23116yes—
308#376C23116yes—
309#376C23116yes—
310#376C2318yes—
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313C2×#95C2312yes—
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2311yescharacteristic
320C2×#95C2312yes—
321C2×#95C2312yes—
322C2×#95C2312yes—
323C2×#95C2312yes—
324C2×#95C2312yes—
325C2×#95C2311yescharacteristic
326C2×#95C2311yescharacteristic
327C2×#95C2311yescharacteristic
328C2×#95C2311yescharacteristic
329C2×#95C2312yes—
330C2×#95C2312yes—
331C2×#95C2312yes—
332C2×#95C2312yes—
333C2×#95C2312yes—
334C2×#95C2312yes—
335C2×#95C2312yes—
336C2×#95C2312yes—
337C2×#95C2312yes—
338C2×#95C2312yes—
339C2×#95C2312yes—
340C2×#95C2312yes—
341C2×#95C2312yes—
342C2×#95C2312yes—
343C2×#95C2312yes—
344C2×#95C2312yes—
345C2×#95C2312yes—
346C2×#95C2312yes—
347C2×#95C2312yes—
348C2×#95C2312yes—
349C2×#95C2312yes—
350C2×#95C2312yes—
351C2×#95C2312yes—
352C22×Q8—24no—
353C22×Q8—24no—
354C22×Q8—24no—
355C22×Q8—24no—
356C22×Q8—28no—
357C22×Q8—24no—
358C22×Q8—42no—
359C22×Q8—42no—
360C22×Q8—42no—
361C22×Q8—44no—
362C22×Q8—44no—
363C22×Q8C2×Q818yes—
364C22×Q8C2414yes—
365C22×Q8C2414yes—
366C22×Q8C2414yes—
367C22×Q8C2418yes—
368C23×C4C2411yescharacteristic
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2411yescharacteristic
372C23×C4C2412yes—
373C23×C4C2411yescharacteristic
374C23×C4C2411yescharacteristic
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2412yes—
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C23×C4C2411yescharacteristic
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C4⋊Q8—232no—
392#125—232no—
393C4×Q8—232no—
394C4×Q8—232no—
395C4×Q8—232no—
396C4×Q8—232no—
397C4×Q8C2×Q8164yescomplemented
398C2×C4⋊C4—28no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—28no—
409C2×C4⋊C4—28no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—28no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—28no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—44no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—44no—
424C2×C4⋊C4—44no—
425C2×C4⋊C4—44no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—44no—
429C2×C4⋊C4—44no—
430C2×C4⋊C4—44no—
431C2×C4⋊C4—44no—
432C2×C4⋊C4—44no—
433C2×C4⋊C4C2×Q8116yes—
434C2×C4⋊C4C2×Q818yes—
435C2×C4⋊C4C2414yes—
436C2×C4⋊C4C2414yes—
437C2×C4⋊C4C2414yes—
438C2×C4⋊C4C2418yes—
439C2×C4⋊C4C2414yes—
440C2×C4⋊C4C2418yes—
441C2×C4⋊C4C2414yes—
442C2×C4⋊C4C2414yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C2414yes—
445C2×C4⋊C4C2414yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2418yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C2414yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C2418yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2418yes—
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C2414yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2418yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2418yes—
467C2×C4⋊C4C2418yes—
468C2×C4⋊C4C2418yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2418yes—
472C2×C42—28no—
473C2×C42—28no—
474C2×C42—24no—
475C2×C42—24no—
476C2×C42—24no—
477C2×C42—24no—
478C2×C42—44no—
479C2×C42—44no—
480C2×C42—44no—
481C2×C42—44no—
482C2×C42—44no—
483C2×C42—44no—
484C2×C42—44no—
485C2×C42C2×Q8116yes—
486C2×C42C2×Q818yes—
487C2×C42#4118yes—
488C2×C42#4118yes—
489C2×C42C2418yes—
490C2×C42C2418yes—
491C2×C42C2414yes—
492C2×C42C2414yes—
493C2×C42C2414yes—
494C2×C42C2414yes—
495C2×C42C2418yes—
496C2×C42C2418yes—
497C2×C42C2418yes—
498C2×C42C2418yes—
499C2×C42C2418yes—
500C2×C42C2418yes—
501C2×C42C2418yes—
502C2×C42C2418yes—
503C2×C42C2414yes—
504C2×C42C2414yes—
505C2×C42C2414yes—
506#95C2414yes—
507#95C2414yes—
508#95C2418yes—
509#95C2418yes—
510#95C2414yes—
511#95C2414yes—
512#95C2414yes—
513#95C2418yes—
514#95C2418yes—
515#95C2418yes—
516#95C2418yes—
517#95C2414yes—
518#95C2418yes—
519#95C2418yes—
520#95C2418yes—
521#95C2418yes—
522#95C2418yes—
523#95C2418yes—
524#95C2418yes—
525#95C2414yes—
526#95C2418yes—
527#95C2418yes—
528#95C2414yes—
529#95C2414yes—
530#95C2418yes—
531#95C2414yes—
532#95C2414yes—
533#95C2418yes—
534#95C2418yes—
535#95C2414yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C2418yes—
545#95C2418yes—
546#95C2418yes—
547C24C2511yescharacteristic
548C2×Q8—232no—
549C2×Q8—28no—
550C2×Q8—28no—
551C2×Q8—28no—
552C2×Q8—28no—
553C2×Q8—216no—
554C2×Q8—28no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—44no—
558C2×Q8—48no—
559C2×Q8—48no—
560C2×Q8—416no—
561C2×Q8—416no—
562C2×Q8—816no—
563C2×Q8C22×Q8116yes—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—24no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—22no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4C22×Q814yes—
622C22×C4C22×Q814yes—
623C22×C4C22×Q818yes—
624C22×C4C22×Q818yes—
625C22×C4C22×Q814yes—
626C22×C4C2×#4114yes—
627C22×C4C2×#4114yes—
628C22×C4C2×#4114yes—
629C22×C4C2×#4114yes—
630C22×C4C2×#4114yes—
631C22×C4C2×#4114yes—
632C22×C42−1+414yes—
633C22×C4C2512yes—
634C22×C4C2512yes—
635C22×C4C2514yes—
636C22×C4C2512yes—
637C22×C4C2514yes—
638C22×C4C2512yes—
639C22×C4C2512yes—
640C22×C4C2514yes—
641C22×C4C2514yes—
642C22×C4C2512yes—
643C22×C4C2514yes—
644C22×C4C2512yes—
645C22×C4C2514yes—
646C22×C4C2512yes—
647C22×C4C2514yes—
648C22×C4C2514yes—
649C22×C4C2512yes—
650C22×C4C2512yes—
651C22×C4C2512yes—
652C22×C4C2512yes—
653C22×C4C2512yes—
654C22×C4C2512yes—
655C22×C4C2512yes—
656C4⋊C4—216no—
657C4⋊C4—28no—
658C4⋊C4—216no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—28no—
666C4⋊C4—216no—
667C4⋊C4—216no—
668C4⋊C4—28no—
669C4⋊C4—28no—
670C4⋊C4—216no—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—28no—
675C4⋊C4—216no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—48no—
680C4⋊C4—44no—
681C4⋊C4—48no—
682C4⋊C4—48no—
683C4⋊C4—48no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—48no—
687C4⋊C4—48no—
688C4⋊C4—48no—
689C4⋊C4—48no—
690C4⋊C4—48no—
691C4⋊C4C22×Q8132yes—
692C4⋊C4C22×Q8116yes—
693C42—216no—
694C42—216no—
695C42—28no—
696C42—28no—
697C42—28no—
698C42—28no—
699C42—48no—
700C42—48no—
701C42—48no—
702C42—48no—
703C42—48no—
704C42—48no—
705C42—48no—
706C42C22×Q8132yes—
707C42C22×Q8116yes—
708C42C2×#41116yes—
709C42C2×#41116yes—
710C23C23×Q812yes—
711C23C22×#4112yes—
712C23C22×#4112yes—
713C23C2×2−1+412yes—
714C23#58512yes—
715C23#58512yes—
716C23#58512yes—
717C23C2611yescharacteristic
718Q8—232no—
719Q8—416no—
720Q8—416no—
721Q8—816no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—216no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—216no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—48no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—48no—
797C2×C4—48no—
798C2×C4—48no—
799C2×C4—48no—
800C2×C4—48no—
801C2×C4#533116yes—
802C2×C4C23×Q814yes—
803C2×C4C23×Q818yes—
804C2×C4C23×Q814yes—
805C2×C4C23×Q818yes—
806C2×C4C23×Q814yes—
807C2×C4C22×#4114yes—
808C2×C4C22×#4114yes—
809C2×C4C22×#4114yes—
810C2×C4C22×#4114yes—
811C2×C4C22×#4114yes—
812C2×C4C22×#4114yes—
813C2×C4C2×2−1+414yes—
814C22C2×#53314yes—
815C22#349314yes—
816C22#349514yes—
817C22#350214yes—
818C22#350414yes—
819C22#350714yes—
820C22#351014yes—
821C22C24×Q811yescharacteristic
822C22C23×#4111yescharacteristic
823C22C23×#4111yescharacteristic
824C22C22×2−1+411yescharacteristic
825C22C2×#58511yescharacteristic
826C22C2×#58511yescharacteristic
827C22C2×#58511yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—24no—
833C4—28no—
834C4—24no—
835C4—24no—
836C4—28no—
837C4—44no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—44no—
843C4—44no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—44no—
848C4—44no—
849C4—44no—
850C4C2×#53318yes—
851C2#3595818yesdirect product factor
852C2C22×#53311yescharacteristic
853C2C2×#349311yescharacteristic
854C2C2×#350711yescharacteristic
855C2C2×#350211yescharacteristic
856C2C2×#349511yescharacteristic
857C2C2×#350411yescharacteristic
858C2C2×#351011yescharacteristic
subgroupG/H
center, socle, prime radicalC24C25
commutator, Frattini, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35958C2direct (N × H)
159. C2×C4×Q8Q8semidirect
397. C4×Q8C2×Q8semidirect
851. C2#35958direct (N × H)

Maximal subgroups

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

subgroupindex
#359582
C2×#25822
C2×#25682
C2×#25712
C2×#25812
C2×#25702
C2×#25652
C2×#26122
C2×#26052
C2×#25862
C2×#25852
C2×#25202
C2×#26602
C2×#26662
C2×#24022
C2×#23992
C2×#23702
C2×#23692
C2×#23562
C2×#23552
C2×#22762