Finite Group Databasebeta

← C2×#37404 #7634795

Subgroups — C2×#37404 #7634795

Order 512.

4414 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2794C212yesmaximal
2C2×#2794C212yesmaximal
3C2×#2789C212yesmaximal
4C2×#2762C212yesmaximal
5C2×#2762C212yesmaximal
6C2×#2758C212yesmaximal
7C2×#2758C212yesmaximal
8C2×#2755C212yesmaximal
9#37404C2132yesmaximal, direct product factor
10C2×#2864C211yesmaximal, characteristic
11C2×#2863C211yesmaximal, characteristic
12C2×#2568C211yesmaximal, characteristic
13C2×#2567C211yesmaximal, characteristic
14C2×#2581C211yesmaximal, characteristic
15C2×#2570C211yesmaximal, characteristic
16C2×#2509C211yesmaximal, characteristic
17C2×#2514C211yesmaximal, characteristic
18C2×#2508C211yesmaximal, characteristic
19C2×#2511C211yesmaximal, characteristic
20C2×#2645C211yesmaximal, characteristic
21C2×#2647C211yesmaximal, characteristic
22C2×#2331C211yesmaximal, characteristic
23C2×#2320C211yesmaximal, characteristic
24C2×#2295C211yesmaximal, characteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28#2864C22116yes—
29#2863C22116yes—
30#2794C22132yes—
31#2794C22132yes—
32#2789C22132yes—
33#2762C22132yes—
34#2762C22132yes—
35#2758C22132yes—
36#2758C22132yes—
37#2755C22132yes—
38#2647C22116yes—
39#2645C22116yes—
40#2581C22116yes—
41#2570C22116yes—
42#2568C22116yes—
43#2567C22116yes—
44#2514C22116yes—
45#2511C22116yes—
46#2509C22116yes—
47#2508C22116yes—
48C2×#401C2212yes—
49C2×#401C2212yes—
50C2×#400C2212yes—
51C2×#400C2212yes—
52C2×#400C2212yes—
53C2×#400C2212yes—
54C2×#400C2212yes—
55C2×#400C2212yes—
56C2×#400C2212yes—
57C2×#400C2212yes—
58C2×#400C2212yes—
59C2×#400C2212yes—
60C2×#400C2212yes—
61C2×#400C2212yes—
62C2×#400C2212yes—
63C2×#400C2212yes—
64C2×#400C2212yes—
65C2×#398C2212yes—
66C2×#398C2212yes—
67C2×#398C2212yes—
68C2×#398C2212yes—
69C2×#395C2212yes—
70C2×#395C2212yes—
71C2×#395C2212yes—
72#2331C22116yes—
73#2320C22116yes—
74#2295C22116yes—
75C2×#391C2211yescharacteristic
76C2×#391C2211yescharacteristic
77C2×#391C2211yescharacteristic
78C2×#391C2212yes—
79C2×#391C2212yes—
80C2×#391C2212yes—
81C2×#391C2211yescharacteristic
82C2×#391C2211yescharacteristic
83C2×#391C2211yescharacteristic
84C2×#391C2211yescharacteristic
85C2×#391C2212yes—
86C2×#391C2212yes—
87C2×#391C2211yescharacteristic
88C2×#389C2211yescharacteristic
89C2×#389C2211yescharacteristic
90C2×#389C2211yescharacteristic
91C2×#389C2211yescharacteristic
92C2×#389C2211yescharacteristic
93C2×#389C2211yescharacteristic
94C2×#389C2211yescharacteristic
95C2×#389C2211yescharacteristic
96C2×#389C2211yescharacteristic
97C2×#389C2211yescharacteristic
98C2×#389C2211yescharacteristic
99C2×#389C2211yescharacteristic
100C2×#389C2211yescharacteristic
101C2×#389C2212yes—
102C2×#389C2211yescharacteristic
103C2×#387C2212yes—
104C2×#387C2212yes—
105C2×#387C2212yes—
106C2×#387C2212yes—
107C2×#387C2212yes—
108C2×#387C2212yes—
109C2×#387C2212yes—
110C2×#387C2211yescharacteristic
111C2×#387C2211yescharacteristic
112C2×#387C2212yes—
113C2×#387C2212yes—
114C2×#387C2212yes—
115C2×#387C2212yes—
116C2×#387C2212yes—
117C2×#387C2212yes—
118C2×#387C2212yes—
119C2×#387C2212yes—
120C2×#387C2212yes—
121C2×#387C2212yes—
122C2×#387C2212yes—
123C2×#387C2212yes—
124C2×#387C2212yes—
125C2×#387C2211yescharacteristic
126C2×#387C2211yescharacteristic
127C2×#384C2212yes—
128C2×#384C2211yescharacteristic
129C2×#383C2212yes—
130C2×#383C2212yes—
131C2×#383C2212yes—
132C2×#382C2212yes—
133C2×#382C2212yes—
134C2×#382C2211yescharacteristic
135C2×#382C2211yescharacteristic
136C2×#382C2211yescharacteristic
137C2×#382C2211yescharacteristic
138C2×C4×C4⋊C4C2211yescharacteristic
139C2×C4×C4⋊C4C2211yescharacteristic
140C2×C4×C4⋊C4C2211yescharacteristic
141C2×C4×C4⋊C4C2211yescharacteristic
142C2×C4×C4⋊C4C2211yescharacteristic
143C2×C4×C4⋊C4C2211yescharacteristic
144C2×#376C2211yescharacteristic
145C2×#376C2211yescharacteristic
146C2×C43C2211yescharacteristic
147C23×Q8C2311yescharacteristic
148C23×Q8C2311yescharacteristic
149C23×Q8C2312yes—
150C2×C4⋊Q8—28no—
151C2×C4⋊Q8C2318yes—
152C2×C4×Q8—28no—
153C2×C4×Q8—28no—
154C2×C4×Q8C2318yes—
155C2×C4×Q8C2318yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2312yes—
188C22×C42C2311yescharacteristic
189C22×C42C2311yescharacteristic
190C22×C42C2312yes—
191C22×C42C2311yescharacteristic
192C22×C42C2311yescharacteristic
193C22×C42C2311yescharacteristic
194C22×C42C2311yescharacteristic
195C22×C42C2311yescharacteristic
196C22×C42C2311yescharacteristic
197C22×C42C2311yescharacteristic
198C22×C42C2311yescharacteristic
199C22×C42C2312yes—
200C22×C42C2312yes—
201C22×C42C2312yes—
202C22×C42C2311yescharacteristic
203#401C23116yes—
204#401C23116yes—
205#400C23116yes—
206#400C23116yes—
207#400C23116yes—
208#400C23116yes—
209#400C23116yes—
210#400C23116yes—
211#400C23116yes—
212#400C23116yes—
213#400C23116yes—
214#400C23116yes—
215#400C23116yes—
216#400C23116yes—
217#400C23116yes—
218#400C23116yes—
219#400C23116yes—
220#398C23116yes—
221#398C23116yes—
222#398C23116yes—
223#398C23116yes—
224#395C23116yes—
225#395C23116yes—
226#395C23116yes—
227#391C23116yes—
228#391C2318yes—
229#391C2318yes—
230#391C23116yes—
231#391C23116yes—
232#391C2318yes—
233#391C2318yes—
234#391C2318yes—
235#391C2318yes—
236#391C23116yes—
237#391C23116yes—
238#391C2318yes—
239#391C2318yes—
240#389C2318yes—
241#389C2318yes—
242#389C2318yes—
243#389C2318yes—
244#389C2318yes—
245#389C2318yes—
246#389C2318yes—
247#389C2318yes—
248#389C2318yes—
249#389C2318yes—
250#389C2318yes—
251#389C2318yes—
252#389C2318yes—
253#389C23116yes—
254#389C2318yes—
255#387C23116yes—
256#387C23116yes—
257#387C23116yes—
258#387C23116yes—
259#387C23116yes—
260#387C23116yes—
261#387C23116yes—
262#387C23116yes—
263#387C23116yes—
264#387C23116yes—
265#387C23116yes—
266#387C23116yes—
267#387C23116yes—
268#387C23116yes—
269#387C23116yes—
270#387C23116yes—
271#387C23116yes—
272#387C23116yes—
273#387C2318yes—
274#387C2318yes—
275#387C23116yes—
276#387C23116yes—
277#387C2318yes—
278#387C2318yes—
279#384C23116yes—
280#384C2318yes—
281#383C23116yes—
282#383C23116yes—
283#383C23116yes—
284#382C2318yes—
285#382C2318yes—
286#382C2318yes—
287#382C2318yes—
288#382C23116yes—
289#382C23116yes—
290C4×C4⋊C4C2318yes—
291C4×C4⋊C4C2318yes—
292C4×C4⋊C4C2318yes—
293C4×C4⋊C4C2318yes—
294C4×C4⋊C4C2318yes—
295C4×C4⋊C4C2318yes—
296#376C2318yes—
297#376C2318yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2311yescharacteristic
307C2×#95C2312yes—
308C2×#95C2311yescharacteristic
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C2×#95C2312yes—
318C2×#95C2312yes—
319C2×#95C2312yes—
320C2×#95C2312yes—
321C2×#95C2312yes—
322C2×#95C2311yescharacteristic
323C2×#95C2311yescharacteristic
324C2×#95C2311yescharacteristic
325C2×#95C2311yescharacteristic
326C2×#95C2311yescharacteristic
327C2×#95C2312yes—
328C2×#95C2312yes—
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×#95C2311yescharacteristic
343C2×#95C2311yescharacteristic
344C2×#95C2311yescharacteristic
345C2×#95C2311yescharacteristic
346C2×#95C2311yescharacteristic
347C43C2318yes—
348C22×Q8—24no—
349C22×Q8—24no—
350C22×Q8—28no—
351C22×Q8—24no—
352C22×Q8—24no—
353C22×Q8—24no—
354C22×Q8—42no—
355C22×Q8—44no—
356C22×Q8—44no—
357C22×Q8C2414yes—
358C22×Q8C2414yes—
359C22×Q8C2418yes—
360C23×C4C2411yescharacteristic
361C23×C4C2412yes—
362C23×C4C2411yescharacteristic
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2411yescharacteristic
367C23×C4C2412yes—
368C23×C4C2412yes—
369C23×C4C2411yescharacteristic
370C23×C4C2412yes—
371C23×C4C2411yescharacteristic
372C23×C4C2411yescharacteristic
373C23×C4C2411yescharacteristic
374C23×C4C2411yescharacteristic
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2412yes—
379C23×C4C2411yescharacteristic
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C23×C4C2411yescharacteristic
383C4⋊Q8—232no—
384C4×Q8—232no—
385C4×Q8—232no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—28no—
391C2×C4⋊C4—28no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—28no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4—44no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4—44no—
411C2×C4⋊C4—44no—
412C2×C4⋊C4—44no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4—44no—
415C2×C4⋊C4—44no—
416C2×C4⋊C4—44no—
417C2×C4⋊C4—44no—
418C2×C4⋊C4C2414yes—
419C2×C4⋊C4C2414yes—
420C2×C4⋊C4C2414yes—
421C2×C4⋊C4C2414yes—
422C2×C4⋊C4C2418yes—
423C2×C4⋊C4C2414yes—
424C2×C4⋊C4C2414yes—
425C2×C4⋊C4C2418yes—
426C2×C4⋊C4C2414yes—
427C2×C4⋊C4C2414yes—
428C2×C4⋊C4C2414yes—
429C2×C4⋊C4C2414yes—
430C2×C4⋊C4C2414yes—
431C2×C4⋊C4C2418yes—
432C2×C4⋊C4C2414yes—
433C2×C4⋊C4C2414yes—
434C2×C4⋊C4C2414yes—
435C2×C4⋊C4C2414yes—
436C2×C4⋊C4C2414yes—
437C2×C4⋊C4C2418yes—
438C2×C4⋊C4C2418yes—
439C2×C4⋊C4C2418yes—
440C2×C4⋊C4C2418yes—
441C2×C4⋊C4C2418yes—
442C2×C4⋊C4C2418yes—
443C2×C4⋊C4C2418yes—
444C2×C4⋊C4C2418yes—
445C2×C4⋊C4C2418yes—
446C2×C4⋊C4C2418yes—
447C2×C4⋊C4C2418yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C2418yes—
450C2×C42—24no—
451C2×C42—28no—
452C2×C42—24no—
453C2×C42—24no—
454C2×C42—24no—
455C2×C42—24no—
456C2×C42—24no—
457C2×C42—24no—
458C2×C42—44no—
459C2×C42—42no—
460C2×C42—44no—
461C2×C42—44no—
462C2×C42—42no—
463C2×C42—42no—
464C2×C42#4118yes—
465C2×C42C2414yes—
466C2×C42C2414yes—
467C2×C42C2418yes—
468C2×C42C2414yes—
469C2×C42C2414yes—
470C2×C42C2414yes—
471C2×C42C2414yes—
472C2×C42C2414yes—
473C2×C42C2414yes—
474C2×C42C2414yes—
475C2×C42C2414yes—
476C2×C42C2418yes—
477C2×C42C2418yes—
478C2×C42C2418yes—
479C2×C42C2414yes—
480#95C2414yes—
481#95C2414yes—
482#95C2414yes—
483#95C2414yes—
484#95C2414yes—
485#95C2414yes—
486#95C2414yes—
487#95C2414yes—
488#95C2414yes—
489#95C2418yes—
490#95C2414yes—
491#95C2414yes—
492#95C2414yes—
493#95C2414yes—
494#95C2414yes—
495#95C2418yes—
496#95C2418yes—
497#95C2418yes—
498#95C2418yes—
499#95C2418yes—
500#95C2418yes—
501#95C2418yes—
502#95C2418yes—
503#95C2418yes—
504#95C2418yes—
505#95C2418yes—
506#95C2418yes—
507#95C2418yes—
508#95C2418yes—
509#95C2418yes—
510#95C2418yes—
511#95C2418yes—
512#95C2418yes—
513#95C2418yes—
514#95C2418yes—
515#95C2418yes—
516#95C2418yes—
517#95C2418yes—
518#95C2418yes—
519#95C2418yes—
520#95C2418yes—
521#95C2418yes—
522#95C2418yes—
523#95C2418yes—
524#95C2418yes—
525#95C2418yes—
526#95C2418yes—
527#95C2418yes—
528#95C2418yes—
529C24C2511yescharacteristic
530C2×Q8—28no—
531C2×Q8—28no—
532C2×Q8—216no—
533C2×Q8—28no—
534C2×Q8—28no—
535C2×Q8—28no—
536C2×Q8—44no—
537C2×Q8—48no—
538C2×Q8—48no—
539C2×Q8—416no—
540C2×Q8—416no—
541C2×Q8—816no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—24no—
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—24no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4C2×#4114yes—
606C22×C4C2×#4114yes—
607C22×C4C2×#4114yes—
608C22×C42−1+414yes—
609C22×C42−1+414yes—
610C22×C42−1+414yes—
611C22×C4C2514yes—
612C22×C4C2512yes—
613C22×C4C2512yes—
614C22×C4C2512yes—
615C22×C4C2512yes—
616C22×C4C2514yes—
617C22×C4C2512yes—
618C22×C4C2512yes—
619C22×C4C2512yes—
620C22×C4C2512yes—
621C22×C4C2514yes—
622C22×C4C2512yes—
623C22×C4C2514yes—
624C22×C4C2514yes—
625C22×C4C2514yes—
626C22×C4C2514yes—
627C22×C4C2514yes—
628C22×C4C2512yes—
629C22×C4C2512yes—
630C22×C4C2512yes—
631C22×C4C2512yes—
632C22×C4C2512yes—
633C22×C4C2512yes—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C4⋊C4—28no—
638C4⋊C4—216no—
639C4⋊C4—216no—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—28no—
643C4⋊C4—216no—
644C4⋊C4—28no—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—48no—
658C4⋊C4—48no—
659C4⋊C4—48no—
660C4⋊C4—48no—
661C4⋊C4—48no—
662C4⋊C4—48no—
663C4⋊C4—48no—
664C4⋊C4—48no—
665C4⋊C4—48no—
666C42—28no—
667C42—216no—
668C42—28no—
669C42—28no—
670C42—28no—
671C42—28no—
672C42—28no—
673C42—28no—
674C42—48no—
675C42—44no—
676C42—48no—
677C42—48no—
678C42—44no—
679C42—44no—
680C42C2×#41116yes—
681C23C22×#4112yes—
682C23C2×2−1+412yes—
683C23C2×2−1+412yes—
684C23C2×2−1+412yes—
685C23#58512yes—
686C23#58512yes—
687C23#58512yes—
688C23C2611yescharacteristic
689Q8—416no—
690Q8—416no—
691Q8—816no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—48no—
759C2×C4—48no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—48no—
764C2×C4—48no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—48no—
770C2×C4—44no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—48no—
777C2×C4#541116yes—
778C2×C4C22×#4114yes—
779C2×C4C22×#4114yes—
780C2×C4C22×#4114yes—
781C2×C4C2×2−1+414yes—
782C2×C4C2×2−1+414yes—
783C2×C4C2×2−1+414yes—
784C22C2×#54114yes—
785C22#349514yes—
786C22#351014yes—
787C22#355514yes—
788C22#355514yes—
789C22#355714yes—
790C22#356514yes—
791C22C23×#4111yescharacteristic
792C22C22×2−1+411yescharacteristic
793C22C22×2−1+411yescharacteristic
794C22C22×2−1+411yescharacteristic
795C22C2×#58511yescharacteristic
796C22C2×#58511yescharacteristic
797C22C2×#58511yescharacteristic
798C4—24no—
799C4—24no—
800C4—24no—
801C4—42no—
802C4—44no—
803C4—44no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—44no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—44no—
813C4—44no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—44no—
818C4—44no—
819C4—44no—
820C4C2×#54118yes—
821C2#3740418yesdirect product factor
822C2C22×#54111yescharacteristic
823C2C2×#355711yescharacteristic
824C2C2×#356511yescharacteristic
825C2C2×#355511yescharacteristic
826C2C2×#355511yescharacteristic
827C2C2×#349511yescharacteristic
828C2C2×#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
9. #37404C2direct (N × H)
821. C2#37404direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#27942
C2×#27892
C2×#27622
C2×#27582
C2×#27552
#374042
C2×#28642
C2×#28632
C2×#25682
C2×#25672
C2×#25812
C2×#25702
C2×#25092
C2×#25142
C2×#25082
C2×#25112
C2×#26452
C2×#26472
C2×#23312
C2×#23202
C2×#22952