Finite Group Databasebeta

← C2×#35221 #7628450

Subgroups — C2×#35221 #7628450

Order 512.

5014 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2864C212yesmaximal
2C2×#2863C212yesmaximal
3#35221C2132yesmaximal, direct product factor
4C2×#2581C211yesmaximal, characteristic
5C2×#2565C211yesmaximal, characteristic
6C2×#2584C211yesmaximal, characteristic
7C2×#2550C211yesmaximal, characteristic
8C2×#2590C212yesmaximal
9C2×#2588C212yesmaximal
10C2×#2586C212yesmaximal
11C2×#2585C212yesmaximal
12C2×#2509C211yesmaximal, characteristic
13C2×#2507C211yesmaximal, characteristic
14C2×#2453C211yesmaximal, characteristic
15C2×#2451C211yesmaximal, characteristic
16C2×#2666C212yesmaximal
17C2×#2666C212yesmaximal
18C2×#2331C211yesmaximal, characteristic
19C2×#2330C211yesmaximal, characteristic
20C2×#2320C211yesmaximal, characteristic
21C2×#2320C211yesmaximal, characteristic
22C2×C4×#125C211yesmaximal, characteristic
23C2×#2295C211yesmaximal, characteristic
24C2×C42×Q8C211yesmaximal, characteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×#125C2211yescharacteristic
27C22×#125C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32#2864C22132yes—
33#2863C22132yes—
34#2666C22132yes—
35#2666C22132yes—
36#2590C22132yes—
37#2588C22132yes—
38#2586C22132yes—
39#2585C22132yes—
40#2584C22116yes—
41#2581C22116yes—
42#2565C22116yes—
43#2550C22116yes—
44#2509C22116yes—
45#2507C22116yes—
46#2453C22116yes—
47#2451C22116yes—
48C2×#400C2212yes—
49C2×#400C2212yes—
50C2×#400C2212yes—
51C2×#400C2212yes—
52C2×#398C2212yes—
53C2×#398C2212yes—
54C2×#398C2212yes—
55C2×#398C2212yes—
56C2×#398C2212yes—
57C2×#398C2212yes—
58C2×#398C2212yes—
59C2×#398C2212yes—
60C2×#395C2212yes—
61C2×#395C2212yes—
62C2×#395C2212yes—
63C2×#395C2212yes—
64#2331C22116yes—
65#2330C22116yes—
66#2320C22116yes—
67#2320C22116yes—
68C4×#125C22116yes—
69#2295C22116yes—
70C2×#391C2211yescharacteristic
71C2×#391C2211yescharacteristic
72C2×#391C2211yescharacteristic
73C2×#391C2211yescharacteristic
74C2×#391C2211yescharacteristic
75C2×#391C2212yes—
76C2×#391C2212yes—
77C2×#391C2212yes—
78C2×#391C2212yes—
79C2×#391C2211yescharacteristic
80C2×#389C2211yescharacteristic
81C2×#389C2211yescharacteristic
82C2×#389C2211yescharacteristic
83C2×#389C2211yescharacteristic
84C2×#389C2211yescharacteristic
85C2×#389C2212yes—
86C2×#389C2212yes—
87C2×#389C2212yes—
88C2×#389C2212yes—
89C2×#389C2212yes—
90C2×#389C2212yes—
91C2×#389C2212yes—
92C2×#389C2212yes—
93C2×#389C2211yescharacteristic
94C2×#389C2211yescharacteristic
95C2×#389C2211yescharacteristic
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×#387C2211yescharacteristic
111C2×#387C2212yes—
112C2×#387C2212yes—
113C2×#387C2211yescharacteristic
114C2×#387C2212yes—
115C2×#387C2212yes—
116C2×#387C2212yes—
117C2×#387C2212yes—
118C2×#387C2211yescharacteristic
119C2×#387C2212yes—
120C2×#387C2211yescharacteristic
121C2×#387C2212yes—
122C2×#384C2211yescharacteristic
123C2×#383C2212yes—
124C2×#383C2212yes—
125C2×#382C2212yes—
126C2×#382C2212yes—
127C2×#382C2211yescharacteristic
128C2×#382C2211yescharacteristic
129C42×Q8C22116yes—
130C2×C4×C4⋊C4C2211yescharacteristic
131C2×C4×C4⋊C4C2211yescharacteristic
132C2×C4×C4⋊C4C2212yes—
133C2×C4×C4⋊C4C2212yes—
134C2×C4×C4⋊C4C2212yes—
135C2×C4×C4⋊C4C2212yes—
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⋊C4C2211yescharacteristic
143C2×#376C2211yescharacteristic
144C2×#376C2211yescharacteristic
145C2×C43C2212yes—
146C2×C43C2211yescharacteristic
147C23×Q8C2311yescharacteristic
148C23×Q8C2311yescharacteristic
149C23×Q8C2312yes—
150C2×C4⋊Q8—28no—
151C2×C4⋊Q8C2318yes—
152C2×#125—28no—
153C2×#125—28no—
154C2×#125C2318yes—
155C2×#125C2318yes—
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—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
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⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2312yes—
202C22×C42C2312yes—
203C22×C42C2311yescharacteristic
204C22×C42C2311yescharacteristic
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2312yes—
211C22×C42C2312yes—
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2312yes—
216C22×C42C2311yescharacteristic
217C22×C42C2312yes—
218C22×C42C2311yescharacteristic
219#400C23116yes—
220#400C23116yes—
221#400C23116yes—
222#400C23116yes—
223#398C23116yes—
224#398C23116yes—
225#398C23116yes—
226#398C23116yes—
227#398C23116yes—
228#398C23116yes—
229#398C23116yes—
230#398C23116yes—
231#395C23116yes—
232#395C23116yes—
233#395C23116yes—
234#395C23116yes—
235#391C2318yes—
236#391C2318yes—
237#391C2318yes—
238#391C2318yes—
239#391C2318yes—
240#391C23116yes—
241#391C23116yes—
242#391C23116yes—
243#391C23116yes—
244#391C2318yes—
245#389C2318yes—
246#389C2318yes—
247#389C2318yes—
248#389C2318yes—
249#389C2318yes—
250#389C2318yes—
251#389C2318yes—
252#389C2318yes—
253#389C2318yes—
254#389C2318yes—
255#389C23116yes—
256#389C23116yes—
257#389C2318yes—
258#389C23116yes—
259#389C23116yes—
260#389C23116yes—
261#389C23116yes—
262#389C23116yes—
263#389C23116yes—
264#389C2318yes—
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#387C23116yes—
279#387C23116yes—
280#387C23116yes—
281#387C23116yes—
282#387C23116yes—
283#387C2318yes—
284#387C2318yes—
285#387C2318yes—
286#387C2318yes—
287#384C2318yes—
288#383C23116yes—
289#383C23116yes—
290#382C2318yes—
291#382C2318yes—
292#382C23116yes—
293#382C23116yes—
294C4×C4⋊C4C2318yes—
295C4×C4⋊C4C2318yes—
296C4×C4⋊C4C23116yes—
297C4×C4⋊C4C23116yes—
298C4×C4⋊C4C2318yes—
299C4×C4⋊C4C2318yes—
300C4×C4⋊C4C23116yes—
301C4×C4⋊C4C2318yes—
302C4×C4⋊C4C23116yes—
303C4×C4⋊C4C23116yes—
304C4×C4⋊C4C2318yes—
305C4×C4⋊C4C2318yes—
306C4×C4⋊C4C2318yes—
307#376C2318yes—
308#376C2318yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C2×#95C2312yes—
320C2×#95C2311yescharacteristic
321C2×#95C2311yescharacteristic
322C2×#95C2312yes—
323C2×#95C2312yes—
324C2×#95C2312yes—
325C2×#95C2312yes—
326C2×#95C2312yes—
327C2×#95C2312yes—
328C2×#95C2312yes—
329C2×#95C2312yes—
330C2×#95C2312yes—
331C2×#95C2312yes—
332C2×#95C2312yes—
333C2×#95C2311yescharacteristic
334C2×#95C2311yescharacteristic
335C2×#95C2311yescharacteristic
336C2×#95C2311yescharacteristic
337C2×#95C2311yescharacteristic
338C2×#95C2311yescharacteristic
339C2×#95C2311yescharacteristic
340C2×#95C2311yescharacteristic
341C2×#95C2312yes—
342C2×#95C2312yes—
343C2×#95C2312yes—
344C2×#95C2312yes—
345C2×#95C2311yescharacteristic
346C2×#95C2311yescharacteristic
347C2×#95C2312yes—
348C2×#95C2311yescharacteristic
349C2×#95C2311yescharacteristic
350C43C2318yes—
351C43C23116yes—
352C22×Q8—24no—
353C22×Q8—24no—
354C22×Q8—24no—
355C22×Q8—28no—
356C22×Q8—42no—
357C22×Q8—42no—
358C22×Q8—44no—
359C22×Q8—44no—
360C22×Q8C2×Q818yes—
361C22×Q8C2414yes—
362C22×Q8C2414yes—
363C22×Q8C2418yes—
364C23×C4C2411yescharacteristic
365C23×C4C2412yes—
366C23×C4C2411yescharacteristic
367C23×C4C2411yescharacteristic
368C23×C4C2411yescharacteristic
369C23×C4C2411yescharacteristic
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2411yescharacteristic
373C23×C4C2412yes—
374C23×C4C2411yescharacteristic
375C23×C4C2411yescharacteristic
376C23×C4C2412yes—
377C23×C4C2411yescharacteristic
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C23×C4C2412yes—
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387C4⋊Q8—232no—
388#125—232no—
389#125—232no—
390C4×Q8—232no—
391C4×Q8—232no—
392C4×Q8—232no—
393C4×Q8C2×Q8164yescomplemented
394C2×C4⋊C4—28no—
395C2×C4⋊C4—28no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—28no—
402C2×C4⋊C4—28no—
403C2×C4⋊C4—28no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—28no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—28no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—44no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4—44no—
415C2×C4⋊C4—44no—
416C2×C4⋊C4—44no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—44no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—44no—
421C2×C4⋊C4—44no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—44no—
424C2×C4⋊C4—44no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—44no—
427C2×C4⋊C4C2×Q8116yes—
428C2×C4⋊C4C2×Q818yes—
429C2×C4⋊C4#4118yes—
430C2×C4⋊C4C2414yes—
431C2×C4⋊C4C2418yes—
432C2×C4⋊C4C2418yes—
433C2×C4⋊C4C2414yes—
434C2×C4⋊C4C2414yes—
435C2×C4⋊C4C2414yes—
436C2×C4⋊C4C2414yes—
437C2×C4⋊C4C2414yes—
438C2×C4⋊C4C2414yes—
439C2×C4⋊C4C2418yes—
440C2×C4⋊C4C2418yes—
441C2×C4⋊C4C2418yes—
442C2×C4⋊C4C2418yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C2418yes—
445C2×C4⋊C4C2418yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2414yes—
448C2×C4⋊C4C2414yes—
449C2×C4⋊C4C2418yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2418yes—
454C2×C4⋊C4C2418yes—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C2418yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2418yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2414yes—
466C2×C42—28no—
467C2×C42—24no—
468C2×C42—28no—
469C2×C42—24no—
470C2×C42—24no—
471C2×C42—24no—
472C2×C42—24no—
473C2×C42—24no—
474C2×C42—42no—
475C2×C42—42no—
476C2×C42—44no—
477C2×C42—44no—
478C2×C42—42no—
479C2×C42—44no—
480C2×C42—44no—
481C2×C42—44no—
482C2×C42C2×Q8116yes—
483C2×C42C2×Q818yes—
484C2×C42#4118yes—
485C2×C42C2414yes—
486C2×C42C2418yes—
487C2×C42C2418yes—
488C2×C42C2414yes—
489C2×C42C2414yes—
490C2×C42C2414yes—
491C2×C42C2414yes—
492C2×C42C2414yes—
493C2×C42C2414yes—
494C2×C42C2414yes—
495C2×C42C2418yes—
496C2×C42C2414yes—
497C2×C42C2418yes—
498C2×C42C2418yes—
499C2×C42C2418yes—
500C2×C42C2418yes—
501C2×C42C2414yes—
502C2×C42C2418yes—
503C2×C42C2414yes—
504#95C2414yes—
505#95C2414yes—
506#95C2414yes—
507#95C2414yes—
508#95C2414yes—
509#95C2414yes—
510#95C2414yes—
511#95C2414yes—
512#95C2418yes—
513#95C2418yes—
514#95C2418yes—
515#95C2418yes—
516#95C2418yes—
517#95C2418yes—
518#95C2418yes—
519#95C2414yes—
520#95C2414yes—
521#95C2418yes—
522#95C2414yes—
523#95C2414yes—
524#95C2418yes—
525#95C2414yes—
526#95C2414yes—
527#95C2418yes—
528#95C2418yes—
529#95C2418yes—
530#95C2418yes—
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—44no—
552C2×Q8—44no—
553C2×Q8—48no—
554C2×Q8—48no—
555C2×Q8—416no—
556C2×Q8—816no—
557C2×Q8C22×Q8116yes—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
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—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4C22×Q814yes—
617C22×C4C22×Q818yes—
618C22×C4C22×Q814yes—
619C22×C4C22×Q818yes—
620C22×C4C22×Q814yes—
621C22×C4C2×#4114yes—
622C22×C4C2×#4118yes—
623C22×C4C2×#4114yes—
624C22×C4C2×#4114yes—
625C22×C4C2×#4114yes—
626C22×C42−1+414yes—
627C22×C4C2512yes—
628C22×C4C2512yes—
629C22×C4C2512yes—
630C22×C4C2512yes—
631C22×C4C2512yes—
632C22×C4C2514yes—
633C22×C4C2514yes—
634C22×C4C2512yes—
635C22×C4C2512yes—
636C22×C4C2514yes—
637C22×C4C2514yes—
638C22×C4C2512yes—
639C22×C4C2512yes—
640C22×C4C2514yes—
641C22×C4C2512yes—
642C22×C4C2514yes—
643C22×C4C2512yes—
644C22×C4C2514yes—
645C22×C4C2512yes—
646C22×C4C2514yes—
647C22×C4C2512yes—
648C22×C4C2512yes—
649C22×C4C2512yes—
650C4⋊C4—216no—
651C4⋊C4—216no—
652C4⋊C4—28no—
653C4⋊C4—28no—
654C4⋊C4—28no—
655C4⋊C4—28no—
656C4⋊C4—216no—
657C4⋊C4—216no—
658C4⋊C4—216no—
659C4⋊C4—216no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—216no—
664C4⋊C4—28no—
665C4⋊C4—216no—
666C4⋊C4—28no—
667C4⋊C4—28no—
668C4⋊C4—48no—
669C4⋊C4—48no—
670C4⋊C4—48no—
671C4⋊C4—48no—
672C4⋊C4—48no—
673C4⋊C4—44no—
674C4⋊C4—48no—
675C4⋊C4—44no—
676C4⋊C4—48no—
677C4⋊C4—48no—
678C4⋊C4—44no—
679C4⋊C4—48no—
680C4⋊C4—48no—
681C4⋊C4—44no—
682C4⋊C4—48no—
683C4⋊C4C22×Q8132yes—
684C4⋊C4C22×Q8116yes—
685C4⋊C4C2×#41116yes—
686C42—216no—
687C42—28no—
688C42—216no—
689C42—28no—
690C42—28no—
691C42—28no—
692C42—28no—
693C42—28no—
694C42—44no—
695C42—44no—
696C42—48no—
697C42—48no—
698C42—48no—
699C42—44no—
700C42—48no—
701C42—48no—
702C42C22×Q8132yes—
703C42C22×Q8116yes—
704C42C2×#41116yes—
705C23C23×Q812yes—
706C23C22×#4112yes—
707C23C22×#4112yes—
708C23C2×2−1+412yes—
709C23#58512yes—
710C23#58512yes—
711C23#58512yes—
712C23C2611yescharacteristic
713Q8—232no—
714Q8—416no—
715Q8—816no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—216no—
733C2×C4—28no—
734C2×C4—28no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—216no—
738C2×C4—28no—
739C2×C4—216no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—48no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—48no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—48no—
795C2×C4—44no—
796C2×C4#533116yes—
797C2×C4C23×Q814yes—
798C2×C4C23×Q814yes—
799C2×C4C23×Q818yes—
800C2×C4C23×Q818yes—
801C2×C4C23×Q814yes—
802C2×C4C22×#4114yes—
803C2×C4C22×#4118yes—
804C2×C4C22×#4114yes—
805C2×C4C22×#4114yes—
806C2×C4C22×#4114yes—
807C2×C4C2×2−1+414yes—
808C22C2×#53314yes—
809C22#345514yes—
810C22#346114yes—
811C22#350214yes—
812C22#350414yes—
813C22#351614yes—
814C22#352114yes—
815C22C24×Q811yescharacteristic
816C22C23×#4111yescharacteristic
817C22C23×#4111yescharacteristic
818C22C22×2−1+411yescharacteristic
819C22C2×#58511yescharacteristic
820C22C2×#58511yescharacteristic
821C22C2×#58511yescharacteristic
822C4—28no—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—28no—
827C4—28no—
828C4—24no—
829C4—24no—
830C4—42no—
831C4—42no—
832C4—44no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—44no—
837C4—42no—
838C4—42no—
839C4—44no—
840C4—44no—
841C4—44no—
842C4—42no—
843C4—42no—
844C4C2×#53318yes—
845C2#3522118yesdirect product factor
846C2C22×#53311yescharacteristic
847C2C2×#346111yescharacteristic
848C2C2×#345511yescharacteristic
849C2C2×#352111yescharacteristic
850C2C2×#350211yescharacteristic
851C2C2×#351611yescharacteristic
852C2C2×#350411yescharacteristic
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
3. #35221C2direct (N × H)
159. C2×C4×Q8Q8semidirect
393. C4×Q8C2×Q8semidirect
845. C2#35221direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28642
C2×#28632
#352212
C2×#25812
C2×#25652
C2×#25842
C2×#25502
C2×#25902
C2×#25882
C2×#25862
C2×#25852
C2×#25092
C2×#25072
C2×#24532
C2×#24512
C2×#26662
C2×#23312
C2×#23302
C2×#23202
C2×C4×#1252
C2×#22952
C2×C42×Q82