Finite Group Databasebeta

← C2×#35643 #7629049

Subgroups — C2×#35643 #7629049

Order 512.

5046 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35643C2132yesmaximal, direct product factor
2C2×#2568C211yesmaximal, characteristic
3C2×#2567C211yesmaximal, characteristic
4C2×#2581C211yesmaximal, characteristic
5C2×#2570C212yesmaximal
6C2×#2550C211yesmaximal, characteristic
7C2×#2612C212yesmaximal
8C2×#2605C212yesmaximal
9C2×#2605C212yesmaximal
10C2×#2588C212yesmaximal
11C2×#2586C212yesmaximal
12C2×#2509C211yesmaximal, characteristic
13C2×#2508C211yesmaximal, characteristic
14C2×#2511C212yesmaximal
15C2×#2520C212yesmaximal
16C2×#2453C211yesmaximal, characteristic
17C2×#2451C211yesmaximal, characteristic
18C2×#2331C211yesmaximal, characteristic
19C2×#2331C211yesmaximal, characteristic
20C2×#2320C211yesmaximal, characteristic
21C2×C4×#125C211yesmaximal, characteristic
22C2×#2295C211yesmaximal, characteristic
23C2×#2295C211yesmaximal, characteristic
24C2×#2276C211yesmaximal, characteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×#125C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32#2612C22132yes—
33#2605C22132yes—
34#2605C22132yes—
35#2588C22132yes—
36#2586C22132yes—
37#2581C22116yes—
38#2570C22132yes—
39#2568C22116yes—
40#2567C22116yes—
41#2550C22116yes—
42#2520C22132yes—
43#2511C22132yes—
44#2509C22116yes—
45#2508C22116yes—
46#2453C22116yes—
47#2451C22116yes—
48C2×#400C2212yes—
49C2×#400C2212yes—
50C2×#400C2212yes—
51C2×#400C2212yes—
52C2×#400C2212yes—
53C2×#400C2212yes—
54C2×#400C2212yes—
55C2×#398C2212yes—
56C2×#398C2212yes—
57C2×#398C2212yes—
58C2×#398C2212yes—
59C2×#395C2212yes—
60C2×#395C2212yes—
61C2×#395C2212yes—
62C2×#395C2212yes—
63C2×#395C2212yes—
64#2331C22116yes—
65#2331C22116yes—
66#2320C22116yes—
67C4×#125C22116yes—
68#2295C22116yes—
69#2295C22116yes—
70C2×#391C2211yescharacteristic
71C2×#391C2211yescharacteristic
72C2×#391C2212yes—
73C2×#391C2212yes—
74C2×#391C2212yes—
75C2×#391C2211yescharacteristic
76C2×#391C2212yes—
77C2×#391C2212yes—
78C2×#391C2212yes—
79C2×#391C2211yescharacteristic
80C2×#391C2212yes—
81C2×#391C2212yes—
82C2×#391C2212yes—
83C2×#391C2211yescharacteristic
84C2×#391C2211yescharacteristic
85C2×#389C2211yescharacteristic
86C2×#389C2211yescharacteristic
87C2×#389C2211yescharacteristic
88C2×#389C2212yes—
89C2×#389C2212yes—
90C2×#389C2211yescharacteristic
91C2×#389C2211yescharacteristic
92C2×#389C2211yescharacteristic
93C2×#389C2211yescharacteristic
94C2×#389C2211yescharacteristic
95C2×#389C2212yes—
96C2×#389C2211yescharacteristic
97C2×#389C2211yescharacteristic
98C2×#389C2211yescharacteristic
99C2×#389C2211yescharacteristic
100C2×#387C2212yes—
101C2×#387C2212yes—
102C2×#387C2212yes—
103C2×#387C2212yes—
104C2×#387C2212yes—
105C2×#387C2212yes—
106C2×#387C2212yes—
107C2×#387C2212yes—
108C2×#387C2212yes—
109C2×#387C2212yes—
110C2×#387C2212yes—
111C2×#387C2211yescharacteristic
112C2×#387C2212yes—
113C2×#387C2212yes—
114C2×#387C2212yes—
115C2×#387C2212yes—
116C2×#387C2211yescharacteristic
117C2×#387C2211yescharacteristic
118C2×#387C2212yes—
119C2×#387C2211yescharacteristic
120C2×#384C2212yes—
121C2×#383C2212yes—
122C2×#382C2212yes—
123C2×#382C2211yescharacteristic
124C2×#382C2211yescharacteristic
125C2×#382C2212yes—
126C2×#382C2211yescharacteristic
127#2276C22116yes—
128C2×C4×C4⋊C4C2211yescharacteristic
129C2×C4×C4⋊C4C2212yes—
130C2×C4×C4⋊C4C2212yes—
131C2×C4×C4⋊C4C2212yes—
132C2×C4×C4⋊C4C2211yescharacteristic
133C2×C4×C4⋊C4C2211yescharacteristic
134C2×C4×C4⋊C4C2212yes—
135C2×C4×C4⋊C4C2212yes—
136C2×C4×C4⋊C4C2211yescharacteristic
137C2×C4×C4⋊C4C2211yescharacteristic
138C2×C4×C4⋊C4C2211yescharacteristic
139C2×C4×C4⋊C4C2211yescharacteristic
140C2×C4×C4⋊C4C2211yescharacteristic
141C2×C4×C4⋊C4C2212yes—
142C2×#376C2211yescharacteristic
143C2×#376C2211yescharacteristic
144C2×#376C2212yes—
145C2×#376C2212yes—
146C2×C43C2211yescharacteristic
147C23×Q8C2311yescharacteristic
148C23×Q8C2311yescharacteristic
149C23×Q8C2312yes—
150C23×Q8C2312yes—
151C2×C4⋊Q8—28no—
152C2×C4⋊Q8—28no—
153C2×C4⋊Q8C2318yes—
154C2×C4⋊Q8C2318yes—
155C2×#125—28no—
156C2×#125C2318yes—
157C2×C4×Q8—28no—
158C2×C4×Q8—28no—
159C2×C4×Q8—28no—
160C2×C4×Q8Q8116yescomplemented
161C2×C4×Q8C2318yes—
162C2×C4×Q8C2318yes—
163C2×C4×Q8C2318yes—
164C2×C4×Q8C2318yes—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C42C2311yescharacteristic
199C22×C42C2311yescharacteristic
200C22×C42C2312yes—
201C22×C42C2312yes—
202C22×C42C2311yescharacteristic
203C22×C42C2311yescharacteristic
204C22×C42C2311yescharacteristic
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2311yescharacteristic
209C22×C42C2312yes—
210C22×C42C2312yes—
211C22×C42C2312yes—
212C22×C42C2312yes—
213C22×C42C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2312yes—
216C22×C42C2311yescharacteristic
217#400C23116yes—
218#400C23116yes—
219#400C23116yes—
220#400C23116yes—
221#400C23116yes—
222#400C23116yes—
223#400C23116yes—
224#398C23116yes—
225#398C23116yes—
226#398C23116yes—
227#398C23116yes—
228#395C23116yes—
229#395C23116yes—
230#395C23116yes—
231#395C23116yes—
232#395C23116yes—
233#391C23116yes—
234#391C2318yes—
235#391C23116yes—
236#391C23116yes—
237#391C2318yes—
238#391C2318yes—
239#391C2318yes—
240#391C23116yes—
241#391C23116yes—
242#391C23116yes—
243#391C23116yes—
244#391C2318yes—
245#391C2318yes—
246#391C23116yes—
247#391C23116yes—
248#389C2318yes—
249#389C2318yes—
250#389C2318yes—
251#389C2318yes—
252#389C2318yes—
253#389C23116yes—
254#389C23116yes—
255#389C2318yes—
256#389C2318yes—
257#389C2318yes—
258#389C2318yes—
259#389C2318yes—
260#389C2318yes—
261#389C23116yes—
262#389C2318yes—
263#387C23116yes—
264#387C23116yes—
265#387C2318yes—
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#387C2318yes—
279#387C23116yes—
280#387C2318yes—
281#387C23116yes—
282#387C2318yes—
283#384C23116yes—
284#383C23116yes—
285#382C2318yes—
286#382C2318yes—
287#382C23116yes—
288#382C23116yes—
289#382C2318yes—
290C4×C4⋊C4C2318yes—
291C4×C4⋊C4C23116yes—
292C4×C4⋊C4C2318yes—
293C4×C4⋊C4C23116yes—
294C4×C4⋊C4C2318yes—
295C4×C4⋊C4C2318yes—
296C4×C4⋊C4C23116yes—
297C4×C4⋊C4C23116yes—
298C4×C4⋊C4C23116yes—
299C4×C4⋊C4C2318yes—
300C4×C4⋊C4C23116yes—
301C4×C4⋊C4C2318yes—
302C4×C4⋊C4C2318yes—
303C4×C4⋊C4C2318yes—
304#376C2318yes—
305#376C2318yes—
306#376C23116yes—
307#376C23116yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C2×#95C2311yescharacteristic
320C2×#95C2312yes—
321C2×#95C2312yes—
322C2×#95C2312yes—
323C2×#95C2312yes—
324C2×#95C2312yes—
325C2×#95C2312yes—
326C2×#95C2312yes—
327C2×#95C2312yes—
328C2×#95C2312yes—
329C2×#95C2312yes—
330C2×#95C2312yes—
331C2×#95C2312yes—
332C2×#95C2311yescharacteristic
333C2×#95C2311yescharacteristic
334C2×#95C2311yescharacteristic
335C2×#95C2311yescharacteristic
336C2×#95C2311yescharacteristic
337C2×#95C2312yes—
338C2×#95C2312yes—
339C2×#95C2312yes—
340C2×#95C2311yescharacteristic
341C2×#95C2311yescharacteristic
342C2×#95C2311yescharacteristic
343C2×#95C2312yes—
344C2×#95C2311yescharacteristic
345C2×#95C2311yescharacteristic
346C2×#95C2311yescharacteristic
347C2×#95C2311yescharacteristic
348C2×#95C2311yescharacteristic
349C2×#95C2312yes—
350C2×#95C2312yes—
351C43C2318yes—
352C22×Q8—24no—
353C22×Q8—24no—
354C22×Q8—24no—
355C22×Q8—28no—
356C22×Q8—28no—
357C22×Q8—24no—
358C22×Q8—42no—
359C22×Q8—44no—
360C22×Q8—44no—
361C22×Q8—44no—
362C22×Q8—44no—
363C22×Q8C2×Q818yes—
364C22×Q8C2414yes—
365C22×Q8C2414yes—
366C22×Q8C2418yes—
367C22×Q8C2418yes—
368C23×C4C2411yescharacteristic
369C23×C4C2411yescharacteristic
370C23×C4C2412yes—
371C23×C4C2411yescharacteristic
372C23×C4C2411yescharacteristic
373C23×C4C2411yescharacteristic
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2412yes—
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386C23×C4C2412yes—
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C4⋊Q8—232no—
392C4⋊Q8—232no—
393#125—232no—
394C4×Q8—232no—
395C4×Q8—232no—
396C4×Q8—232no—
397C4×Q8C2×Q8164yescomplemented
398C2×C4⋊C4—24no—
399C2×C4⋊C4—28no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—28no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—28no—
408C2×C4⋊C4—28no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—28no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—44no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4—44no—
417C2×C4⋊C4—44no—
418C2×C4⋊C4—44no—
419C2×C4⋊C4—44no—
420C2×C4⋊C4—44no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—44no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—44no—
427C2×C4⋊C4—44no—
428C2×C4⋊C4C2×Q8116yes—
429C2×C4⋊C4C2×Q818yes—
430C2×C4⋊C4#4118yes—
431C2×C4⋊C4C2414yes—
432C2×C4⋊C4C2418yes—
433C2×C4⋊C4C2418yes—
434C2×C4⋊C4C2414yes—
435C2×C4⋊C4C2414yes—
436C2×C4⋊C4C2414yes—
437C2×C4⋊C4C2414yes—
438C2×C4⋊C4C2418yes—
439C2×C4⋊C4C2418yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2414yes—
442C2×C4⋊C4C2414yes—
443C2×C4⋊C4C2418yes—
444C2×C4⋊C4C2418yes—
445C2×C4⋊C4C2418yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2418yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C2414yes—
450C2×C4⋊C4C2418yes—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2414yes—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C2418yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2414yes—
464C2×C42—28no—
465C2×C42—28no—
466C2×C42—24no—
467C2×C42—24no—
468C2×C42—24no—
469C2×C42—24no—
470C2×C42—24no—
471C2×C42—24no—
472C2×C42—44no—
473C2×C42—42no—
474C2×C42—42no—
475C2×C42—42no—
476C2×C42—44no—
477C2×C42—44no—
478C2×C42—44no—
479C2×C42—44no—
480C2×C42C2×Q8116yes—
481C2×C42C2×Q818yes—
482C2×C42#4118yes—
483C2×C42C2414yes—
484C2×C42C2414yes—
485C2×C42C2418yes—
486C2×C42C2418yes—
487C2×C42C2414yes—
488C2×C42C2414yes—
489C2×C42C2414yes—
490C2×C42C2414yes—
491C2×C42C2414yes—
492C2×C42C2414yes—
493C2×C42C2414yes—
494C2×C42C2418yes—
495C2×C42C2418yes—
496C2×C42C2418yes—
497C2×C42C2418yes—
498C2×C42C2418yes—
499C2×C42C2414yes—
500C2×C42C2418yes—
501C2×C42C2414yes—
502#95C2414yes—
503#95C2418yes—
504#95C2414yes—
505#95C2414yes—
506#95C2414yes—
507#95C2418yes—
508#95C2418yes—
509#95C2414yes—
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#95C2414yes—
524#95C2414yes—
525#95C2418yes—
526#95C2418yes—
527#95C2418yes—
528#95C2414yes—
529#95C2414yes—
530#95C2414yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C2418yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C2418yes—
545C24C2511yescharacteristic
546C2×Q8—232no—
547C2×Q8—28no—
548C2×Q8—28no—
549C2×Q8—28no—
550C2×Q8—216no—
551C2×Q8—216no—
552C2×Q8—28no—
553C2×Q8—44no—
554C2×Q8—48no—
555C2×Q8—48no—
556C2×Q8—48no—
557C2×Q8—48no—
558C2×Q8—416no—
559C2×Q8—816no—
560C2×Q8—816no—
561C2×Q8C22×Q8116yes—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—24no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4C22×Q814yes—
621C22×C4C22×Q818yes—
622C22×C4C22×Q814yes—
623C22×C4C22×Q818yes—
624C22×C4C22×Q814yes—
625C22×C4C2×#4114yes—
626C22×C4C2×#4118yes—
627C22×C4C2×#4114yes—
628C22×C4C2×#4114yes—
629C22×C4C2×#4114yes—
630C22×C42−1+414yes—
631C22×C4C2512yes—
632C22×C4C2512yes—
633C22×C4C2512yes—
634C22×C4C2512yes—
635C22×C4C2514yes—
636C22×C4C2512yes—
637C22×C4C2514yes—
638C22×C4C2514yes—
639C22×C4C2514yes—
640C22×C4C2514yes—
641C22×C4C2512yes—
642C22×C4C2512yes—
643C22×C4C2512yes—
644C22×C4C2512yes—
645C22×C4C2512yes—
646C22×C4C2514yes—
647C22×C4C2512yes—
648C22×C4C2514yes—
649C22×C4C2512yes—
650C22×C4C2512yes—
651C22×C4C2514yes—
652C22×C4C2512yes—
653C22×C4C2512yes—
654C4⋊C4—28no—
655C4⋊C4—216no—
656C4⋊C4—216no—
657C4⋊C4—28no—
658C4⋊C4—28no—
659C4⋊C4—28no—
660C4⋊C4—216no—
661C4⋊C4—216no—
662C4⋊C4—28no—
663C4⋊C4—216no—
664C4⋊C4—216no—
665C4⋊C4—28no—
666C4⋊C4—28no—
667C4⋊C4—28no—
668C4⋊C4—216no—
669C4⋊C4—28no—
670C4⋊C4—48no—
671C4⋊C4—44no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—48no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—48no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C4⋊C4—48no—
683C4⋊C4—48no—
684C4⋊C4C22×Q8132yes—
685C4⋊C4C22×Q8116yes—
686C4⋊C4C2×#41116yes—
687C42—216no—
688C42—216no—
689C42—28no—
690C42—28no—
691C42—28no—
692C42—28no—
693C42—28no—
694C42—28no—
695C42—48no—
696C42—44no—
697C42—44no—
698C42—44no—
699C42—48no—
700C42—48no—
701C42—48no—
702C42—48no—
703C42C22×Q8132yes—
704C42C22×Q8116yes—
705C42C2×#41116yes—
706C23C23×Q812yes—
707C23C22×#4112yes—
708C23C22×#4112yes—
709C23C2×2−1+412yes—
710C23#58512yes—
711C23#58512yes—
712C23#58512yes—
713C23C2611yescharacteristic
714Q8—232no—
715Q8—416no—
716Q8—816no—
717Q8—816no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—216no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—28no—
739C2×C4—216no—
740C2×C4—28no—
741C2×C4—216no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—48no—
789C2×C4—48no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—48no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—48no—
797C2×C4—44no—
798C2×C4#533116yes—
799C2×C4C23×Q814yes—
800C2×C4C23×Q814yes—
801C2×C4C23×Q818yes—
802C2×C4C23×Q818yes—
803C2×C4C23×Q814yes—
804C2×C4C22×#4114yes—
805C2×C4C22×#4118yes—
806C2×C4C22×#4114yes—
807C2×C4C22×#4114yes—
808C2×C4C22×#4114yes—
809C2×C4C2×2−1+414yes—
810C22C2×#53314yes—
811C22#349514yes—
812C22#350214yes—
813C22#350414yes—
814C22#351014yes—
815C22#351814yes—
816C22#352114yes—
817C22C24×Q811yescharacteristic
818C22C23×#4111yescharacteristic
819C22C23×#4111yescharacteristic
820C22C22×2−1+411yescharacteristic
821C22C2×#58511yescharacteristic
822C22C2×#58511yescharacteristic
823C22C2×#58511yescharacteristic
824C4—28no—
825C4—24no—
826C4—24no—
827C4—24no—
828C4—24no—
829C4—28no—
830C4—24no—
831C4—28no—
832C4—42no—
833C4—42no—
834C4—44no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—44no—
840C4—44no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—44no—
845C4—44no—
846C4C2×#53318yes—
847C2#3564318yesdirect product factor
848C2C22×#53311yescharacteristic
849C2C2×#352111yescharacteristic
850C2C2×#350211yescharacteristic
851C2C2×#351811yescharacteristic
852C2C2×#349511yescharacteristic
853C2C2×#350411yescharacteristic
854C2C2×#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. #35643C2direct (N × H)
160. C2×C4×Q8Q8semidirect
397. C4×Q8C2×Q8semidirect
847. C2#35643direct (N × H)

Maximal subgroups

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

subgroupindex
#356432
C2×#25682
C2×#25672
C2×#25812
C2×#25702
C2×#25502
C2×#26122
C2×#26052
C2×#25882
C2×#25862
C2×#25092
C2×#25082
C2×#25112
C2×#25202
C2×#24532
C2×#24512
C2×#23312
C2×#23202
C2×C4×#1252
C2×#22952
C2×#22762