Finite Group Databasebeta

← C2×#42820 #7641423

Subgroups — C2×#42820 #7641423

Order 512.

5022 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2791C212yesmaximal
2C2×#2755C212yesmaximal
3C2×#2734C212yesmaximal
4C2×#2713C212yesmaximal
5#42820C2132yesmaximal, direct product factor
6C2×#2843C212yesmaximal
7C2×#2582C211yesmaximal, characteristic
8C2×#2567C211yesmaximal, characteristic
9C2×#2546C211yesmaximal, characteristic
10C2×#2551C211yesmaximal, characteristic
11C2×#2581C211yesmaximal, characteristic
12C2×#2570C211yesmaximal, characteristic
13C2×#2605C212yesmaximal
14C2×#2508C211yesmaximal, characteristic
15C2×#2506C211yesmaximal, characteristic
16C2×#2451C211yesmaximal, characteristic
17C2×#2451C211yesmaximal, characteristic
18C2×#2660C212yesmaximal
19C2×#2647C211yesmaximal, characteristic
20C2×#2666C212yesmaximal
21C2×#2399C211yesmaximal, characteristic
22C2×#2356C211yesmaximal, characteristic
23C2×Q8×C4⋊C4C211yesmaximal, characteristic
24C2×#2320C211yesmaximal, characteristic
25C22×C4⋊Q8C2212yes—
26C22×C4⋊Q8C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28C22×C4⋊Q8C2212yes—
29C22×#125C2212yes—
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2843C22132yes—
36#2791C22132yes—
37#2755C22132yes—
38#2734C22132yes—
39#2713C22132yes—
40#2666C22132yes—
41#2660C22132yes—
42#2647C22116yes—
43#2605C22132yes—
44#2582C22116yes—
45#2581C22116yes—
46#2570C22116yes—
47#2567C22116yes—
48#2551C22116yes—
49#2546C22116yes—
50#2508C22116yes—
51#2506C22116yes—
52#2451C22116yes—
53#2451C22116yes—
54#2399C22116yes—
55C2×#400C2212yes—
56C2×#400C2212yes—
57C2×#400C2212yes—
58C2×#400C2212yes—
59C2×#400C2212yes—
60C2×#400C2212yes—
61C2×#398C2211yescharacteristic
62C2×#398C2212yes—
63C2×#398C2212yes—
64C2×#398C2212yes—
65C2×#398C2212yes—
66C2×#398C2211yescharacteristic
67C2×#398C2212yes—
68C2×#398C2212yes—
69C2×#398C2212yes—
70C2×#398C2212yes—
71C2×#398C2211yescharacteristic
72C2×#398C2212yes—
73C2×#398C2212yes—
74C2×#398C2212yes—
75C2×#398C2211yescharacteristic
76C2×#395C2212yes—
77C2×#395C2212yes—
78C2×#395C2211yescharacteristic
79C2×#395C2212yes—
80C2×#395C2211yescharacteristic
81C2×#395C2212yes—
82C2×#395C2212yes—
83C2×#395C2212yes—
84C2×#395C2212yes—
85C2×#395C2211yescharacteristic
86C2×#395C2211yescharacteristic
87#2356C22116yes—
88Q8×C4⋊C4C22116yes—
89#2320C22116yes—
90C2×#391C2211yescharacteristic
91C2×#391C2211yescharacteristic
92C2×#391C2212yes—
93C2×#391C2212yes—
94C2×#391C2212yes—
95C2×#391C2212yes—
96C2×#391C2212yes—
97C2×#391C2211yescharacteristic
98C2×#391C2211yescharacteristic
99C2×#389C2211yescharacteristic
100C2×#389C2211yescharacteristic
101C2×#389C2212yes—
102C2×#389C2212yes—
103C2×#389C2212yes—
104C2×#389C2211yescharacteristic
105C2×#389C2211yescharacteristic
106C2×#389C2211yescharacteristic
107C2×#389C2211yescharacteristic
108C2×#389C2211yescharacteristic
109C2×#389C2211yescharacteristic
110C2×#389C2212yes—
111C2×#389C2211yescharacteristic
112C2×#389C2211yescharacteristic
113C2×#389C2211yescharacteristic
114C2×#389C2211yescharacteristic
115C2×#387C2212yes—
116C2×#387C2212yes—
117C2×#387C2212yes—
118C2×#387C2212yes—
119C2×#387C2212yes—
120C2×#387C2212yes—
121C2×#387C2212yes—
122C2×#387C2212yes—
123C2×#387C2212yes—
124C2×#387C2212yes—
125C2×#387C2212yes—
126C2×#387C2212yes—
127C2×#384C2212yes—
128C2×#384C2211yescharacteristic
129C2×#384C2212yes—
130C2×#384C2211yescharacteristic
131C2×#383C2212yes—
132C2×#383C2212yes—
133C2×#382C2212yes—
134C2×#382C2211yescharacteristic
135C2×#382C2212yes—
136C2×#382C2211yescharacteristic
137C2×C4×C4⋊C4C2211yescharacteristic
138C2×C4×C4⋊C4C2212yes—
139C2×C4×C4⋊C4C2211yescharacteristic
140C2×C4×C4⋊C4C2211yescharacteristic
141C2×C4×C4⋊C4C2211yescharacteristic
142C2×C4×C4⋊C4C2211yescharacteristic
143C2×C4×C4⋊C4C2211yescharacteristic
144C2×C4×C4⋊C4C2211yescharacteristic
145C2×#376C2211yescharacteristic
146C2×#376C2212yes—
147C23×Q8C2311yescharacteristic
148C23×Q8C2311yescharacteristic
149C23×Q8C2311yescharacteristic
150C23×Q8C2312yes—
151C23×Q8C2312yes—
152C2×C4⋊Q8—44no—
153C2×C4⋊Q8—44no—
154C2×C4⋊Q8—48no—
155C2×C4⋊Q8—48no—
156C2×C4⋊Q8C2318yes—
157C2×C4⋊Q8C23116yes—
158C2×C4⋊Q8C2318yes—
159C2×C4⋊Q8C23116yes—
160C2×#125—48no—
161C2×#125C23116yes—
162C2×C4×Q8—44no—
163C2×C4×Q8—44no—
164C2×C4×Q8—44no—
165C2×C4×Q8—44no—
166C2×C4×Q8Q8116yescomplemented
167C2×C4×Q8C2318yes—
168C2×C4×Q8C2318yes—
169C2×C4×Q8C2318yes—
170C2×C4×Q8C2318yes—
171C2×C4×Q8C2318yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2312yes—
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2312yes—
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2312yes—
224C22×C42C2312yes—
225C22×C42C2311yescharacteristic
226C22×C42C2312yes—
227#400C23116yes—
228#400C23116yes—
229#400C23116yes—
230#400C23116yes—
231#400C23116yes—
232#400C23116yes—
233#398C23116yes—
234#398C23116yes—
235#398C23116yes—
236#398C2318yes—
237#398C23116yes—
238#398C23116yes—
239#398C23116yes—
240#398C23116yes—
241#398C23116yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C23116yes—
246#398C23116yes—
247#398C23116yes—
248#395C23116yes—
249#395C23116yes—
250#395C23116yes—
251#395C23116yes—
252#395C23116yes—
253#395C2318yes—
254#395C23116yes—
255#395C2318yes—
256#395C2318yes—
257#395C2318yes—
258#395C23116yes—
259#391C23116yes—
260#391C2318yes—
261#391C2318yes—
262#391C2318yes—
263#391C23116yes—
264#391C2318yes—
265#391C23116yes—
266#391C23116yes—
267#391C23116yes—
268#389C2318yes—
269#389C2318yes—
270#389C2318yes—
271#389C2318yes—
272#389C2318yes—
273#389C2318yes—
274#389C2318yes—
275#389C2318yes—
276#389C23116yes—
277#389C2318yes—
278#389C23116yes—
279#389C23116yes—
280#389C2318yes—
281#389C2318yes—
282#389C2318yes—
283#389C23116yes—
284#387C23116yes—
285#387C23116yes—
286#387C23116yes—
287#387C23116yes—
288#387C23116yes—
289#387C23116yes—
290#387C23116yes—
291#387C23116yes—
292#387C23116yes—
293#387C23116yes—
294#387C23116yes—
295#387C23116yes—
296#384C23116yes—
297#384C2318yes—
298#384C23116yes—
299#384C2318yes—
300#383C23116yes—
301#383C23116yes—
302#382C2318yes—
303#382C2318yes—
304#382C23116yes—
305#382C23116yes—
306C4×C4⋊C4C2318yes—
307C4×C4⋊C4C2318yes—
308C4×C4⋊C4C2318yes—
309C4×C4⋊C4C23116yes—
310C4×C4⋊C4C2318yes—
311C4×C4⋊C4C2318yes—
312C4×C4⋊C4C2318yes—
313C4×C4⋊C4C2318yes—
314#376C2318yes—
315#376C23116yes—
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2312yes—
320C2×#95C2312yes—
321C2×#95C2312yes—
322C2×#95C2311yescharacteristic
323C2×#95C2311yescharacteristic
324C2×#95C2311yescharacteristic
325C2×#95C2311yescharacteristic
326C2×#95C2312yes—
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×#95C2311yescharacteristic
342C2×#95C2312yes—
343C2×#95C2312yes—
344C2×#95C2311yescharacteristic
345C2×#95C2312yes—
346C2×#95C2312yes—
347C2×#95C2311yescharacteristic
348C2×#95C2312yes—
349C2×#95C2312yes—
350C2×#95C2312yes—
351C2×#95C2312yes—
352C2×#95C2312yes—
353C2×#95C2312yes—
354C2×#95C2312yes—
355C22×Q8—24no—
356C22×Q8—24no—
357C22×Q8—28no—
358C22×Q8—24no—
359C22×Q8—24no—
360C22×Q8—24no—
361C22×Q8—42no—
362C22×Q8—42no—
363C22×Q8—42no—
364C22×Q8—44no—
365C22×Q8—44no—
366C22×Q8—44no—
367C22×Q8—44no—
368C22×Q8—44no—
369C22×Q8C2×Q818yes—
370C22×Q8C2414yes—
371C22×Q8C2414yes—
372C22×Q8C2414yes—
373C22×Q8C2418yes—
374C22×Q8C2418yes—
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2411yescharacteristic
381C23×C4C2412yes—
382C23×C4C2411yescharacteristic
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387C23×C4C2412yes—
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2412yes—
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2412yes—
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C4⋊Q8—416no—
399C4⋊Q8—416no—
400C4⋊Q8—432no—
401C4⋊Q8—432no—
402#125—432no—
403C4×Q8—416no—
404C4×Q8—416no—
405C4×Q8—416no—
406C4×Q8—416no—
407C4×Q8C2×Q8164yescomplemented
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—28no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—28no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—44no—
424C2×C4⋊C4—44no—
425C2×C4⋊C4—44no—
426C2×C4⋊C4—44no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—44no—
432C2×C4⋊C4—44no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—44no—
437C2×C4⋊C4—44no—
438C2×C4⋊C4—44no—
439C2×C4⋊C4—44no—
440C2×C4⋊C4—44no—
441C2×C4⋊C4—44no—
442C2×C4⋊C4—44no—
443C2×C4⋊C4—44no—
444C2×C4⋊C4—44no—
445C2×C4⋊C4—44no—
446C2×C4⋊C4—44no—
447C2×C4⋊C4—44no—
448C2×C4⋊C4C2×Q8116yes—
449C2×C4⋊C4C2×Q818yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2418yes—
454C2×C4⋊C4C2414yes—
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C2414yes—
457C2×C4⋊C4C2414yes—
458C2×C4⋊C4C2414yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2418yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2418yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2414yes—
469C2×C4⋊C4C2414yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C2418yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2418yes—
480C2×C4⋊C4C2418yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2418yes—
484C2×C4⋊C4C2418yes—
485C2×C4⋊C4C2414yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2418yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2418yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2418yes—
492C2×C42—24no—
493C2×C42—24no—
494C2×C42—24no—
495C2×C42—24no—
496C2×C42—24no—
497C2×C42—28no—
498C2×C42—28no—
499C2×C42—24no—
500C2×C42—44no—
501C2×C42—44no—
502C2×C42—44no—
503C2×C42C2×Q8116yes—
504C2×C42C2×Q818yes—
505C2×C42C2414yes—
506C2×C42C2414yes—
507C2×C42C2414yes—
508C2×C42C2414yes—
509C2×C42C2414yes—
510C2×C42C2418yes—
511C2×C42C2414yes—
512C2×C42C2418yes—
513C2×C42C2418yes—
514C2×C42C2418yes—
515C2×C42C2418yes—
516C2×C42C2414yes—
517C2×C42C2418yes—
518#95C2414yes—
519#95C2414yes—
520#95C2418yes—
521#95C2414yes—
522#95C2418yes—
523#95C2418yes—
524#95C2414yes—
525#95C2414yes—
526#95C2414yes—
527#95C2418yes—
528#95C2414yes—
529#95C2418yes—
530#95C2418yes—
531#95C2414yes—
532#95C2414yes—
533#95C2414yes—
534#95C2418yes—
535#95C2418yes—
536#95C2414yes—
537#95C2414yes—
538#95C2418yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C2418yes—
545#95C2418yes—
546#95C2418yes—
547#95C2418yes—
548#95C2418yes—
549#95C2418yes—
550#95C2418yes—
551#95C2418yes—
552#95C2418yes—
553#95C2418yes—
554#95C2418yes—
555#95C2418yes—
556#95C2418yes—
557C24C2511yescharacteristic
558C2×Q8—232no—
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—216no—
562C2×Q8—28no—
563C2×Q8—28no—
564C2×Q8—28no—
565C2×Q8—44no—
566C2×Q8—44no—
567C2×Q8—44no—
568C2×Q8—48no—
569C2×Q8—48no—
570C2×Q8—48no—
571C2×Q8—48no—
572C2×Q8—48no—
573C2×Q8—416no—
574C2×Q8—416no—
575C2×Q8—816no—
576C2×Q8—816no—
577C2×Q8C22×Q8116yes—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—24no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—22no—
624C22×C4—24no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—24no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—22no—
636C22×C4—24no—
637C22×C4C22×Q814yes—
638C22×C4C22×Q818yes—
639C22×C4C22×Q814yes—
640C22×C4C22×Q818yes—
641C22×C4C22×Q814yes—
642C22×C4H(5,𝔽2)14yes—
643C22×C4H(5,𝔽2)14yes—
644C22×C42−1+414yes—
645C22×C42−1+414yes—
646C22×C42−1+414yes—
647C22×C4C2514yes—
648C22×C4C2512yes—
649C22×C4C2512yes—
650C22×C4C2512yes—
651C22×C4C2514yes—
652C22×C4C2512yes—
653C22×C4C2514yes—
654C22×C4C2512yes—
655C22×C4C2512yes—
656C22×C4C2514yes—
657C22×C4C2512yes—
658C22×C4C2512yes—
659C22×C4C2514yes—
660C22×C4C2514yes—
661C22×C4C2512yes—
662C22×C4C2512yes—
663C22×C4C2514yes—
664C22×C4C2514yes—
665C22×C4C2512yes—
666C22×C4C2512yes—
667C22×C4C2512yes—
668C22×C4C2512yes—
669C22×C4C2512yes—
670C4⋊C4—28no—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—216no—
674C4⋊C4—28no—
675C4⋊C4—28no—
676C4⋊C4—28no—
677C4⋊C4—28no—
678C4⋊C4—28no—
679C4⋊C4—28no—
680C4⋊C4—216no—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—44no—
685C4⋊C4—48no—
686C4⋊C4—48no—
687C4⋊C4—48no—
688C4⋊C4—48no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—48no—
694C4⋊C4—48no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—44no—
698C4⋊C4—48no—
699C4⋊C4—48no—
700C4⋊C4—48no—
701C4⋊C4—48no—
702C4⋊C4—48no—
703C4⋊C4—48no—
704C4⋊C4—48no—
705C4⋊C4—48no—
706C4⋊C4—48no—
707C4⋊C4—48no—
708C4⋊C4—48no—
709C4⋊C4—48no—
710C4⋊C4C22×Q8132yes—
711C4⋊C4C22×Q8116yes—
712C42—28no—
713C42—28no—
714C42—28no—
715C42—28no—
716C42—28no—
717C42—216no—
718C42—216no—
719C42—28no—
720C42—48no—
721C42—48no—
722C42—48no—
723C42C22×Q8132yes—
724C42C22×Q8116yes—
725C23C23×Q812yes—
726C23C2×H(5,𝔽2)12yes—
727C23C2×H(5,𝔽2)12yes—
728C23C2×2−1+412yes—
729C23C2×2−1+412yes—
730C23C2×2−1+412yes—
731C23#58512yes—
732C23C2611yescharacteristic
733Q8—232no—
734Q8—416no—
735Q8—416no—
736Q8—816no—
737Q8—816no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—216no—
753C2×C4—28no—
754C2×C4—216no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—28no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—48no—
811C2×C4—48no—
812C2×C4—44no—
813C2×C4—48no—
814C2×C4—48no—
815C2×C4—48no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—48no—
819C2×C4#544116yes—
820C2×C4C23×Q814yes—
821C2×C4C23×Q818yes—
822C2×C4C23×Q814yes—
823C2×C4C23×Q818yes—
824C2×C4C23×Q814yes—
825C2×C4C2×H(5,𝔽2)14yes—
826C2×C4C2×H(5,𝔽2)14yes—
827C2×C4C2×2−1+414yes—
828C2×C4C2×2−1+414yes—
829C2×C4C2×2−1+414yes—
830C22C2×#54414yes—
831C22#350214yes—
832C22#350314yes—
833C22#353814yes—
834C22#354214yes—
835C22#355014yes—
836C22#355514yes—
837C22C24×Q811yescharacteristic
838C22C22×H(5,𝔽2)11yescharacteristic
839C22C22×H(5,𝔽2)11yescharacteristic
840C22C22×2−1+411yescharacteristic
841C22C22×2−1+411yescharacteristic
842C22C22×2−1+411yescharacteristic
843C22C2×#58511yescharacteristic
844C4—24no—
845C4—24no—
846C4—24no—
847C4—28no—
848C4—24no—
849C4—28no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—44no—
855C4—42no—
856C4—44no—
857C4—44no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—44no—
863C4—44no—
864C4—42no—
865C4—44no—
866C4C2×#54418yes—
867C2#4282018yesdirect product factor
868C2C22×#54411yescharacteristic
869C2C2×#354211yescharacteristic
870C2C2×#353811yescharacteristic
871C2C2×#355511yescharacteristic
872C2C2×#355011yescharacteristic
873C2C2×#350211yescharacteristic
874C2C2×#350311yescharacteristic
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
5. #42820C2direct (N × H)
166. C2×C4×Q8Q8semidirect
407. C4×Q8C2×Q8semidirect
867. C2#42820direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#27912
C2×#27552
C2×#27342
C2×#27132
#428202
C2×#28432
C2×#25822
C2×#25672
C2×#25462
C2×#25512
C2×#25812
C2×#25702
C2×#26052
C2×#25082
C2×#25062
C2×#24512
C2×#26602
C2×#26472
C2×#26662
C2×#23992
C2×#23562
C2×Q8×C4⋊C42
C2×#23202