Finite Group Databasebeta

← C2×#37344 #7634698

Subgroups — C2×#37344 #7634698

Order 512.

4654 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2802C212yesmaximal
2C2×#2776C212yesmaximal
3C2×#2769C212yesmaximal
4C2×#2762C212yesmaximal
5C2×#2755C212yesmaximal
6C2×#2719C212yesmaximal
7C2×#2719C212yesmaximal
8C2×#2719C212yesmaximal
9#37344C2132yesmaximal, direct product factor
10C2×#2863C211yesmaximal, characteristic
11C2×#2859C211yesmaximal, characteristic
12C2×#2582C211yesmaximal, characteristic
13C2×#2552C211yesmaximal, characteristic
14C2×#2565C211yesmaximal, characteristic
15C2×#2584C211yesmaximal, characteristic
16C2×#2508C211yesmaximal, characteristic
17C2×#2511C211yesmaximal, characteristic
18C2×#2511C211yesmaximal, characteristic
19C2×#2506C211yesmaximal, characteristic
20C2×#2645C211yesmaximal, characteristic
21C2×#2647C211yesmaximal, characteristic
22C2×#2330C211yesmaximal, characteristic
23C2×#2320C211yesmaximal, characteristic
24C2×#2295C211yesmaximal, characteristic
25C22×#125C2211yescharacteristic
26C22×#125C2212yes—
27C22×#125C2212yes—
28C22×#125C2212yes—
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31#2863C22116yes—
32#2859C22116yes—
33#2802C22132yes—
34#2776C22132yes—
35#2769C22132yes—
36#2762C22132yes—
37#2755C22132yes—
38#2719C22132yes—
39#2719C22132yes—
40#2719C22132yes—
41#2647C22116yes—
42#2645C22116yes—
43#2584C22116yes—
44#2582C22116yes—
45#2565C22116yes—
46#2552C22116yes—
47#2511C22116yes—
48#2511C22116yes—
49#2508C22116yes—
50#2506C22116yes—
51C2×#401C2212yes—
52C2×#400C2212yes—
53C2×#400C2212yes—
54C2×#400C2212yes—
55C2×#400C2212yes—
56C2×#400C2212yes—
57C2×#400C2212yes—
58C2×#400C2212yes—
59C2×#400C2212yes—
60C2×#400C2212yes—
61C2×#400C2212yes—
62C2×#400C2212yes—
63C2×#398C2212yes—
64C2×#398C2212yes—
65C2×#398C2212yes—
66C2×#398C2212yes—
67C2×#398C2212yes—
68C2×#398C2212yes—
69C2×#398C2212yes—
70C2×#398C2212yes—
71C2×#398C2212yes—
72C2×#398C2212yes—
73C2×#398C2212yes—
74C2×#395C2212yes—
75#2330C22116yes—
76#2320C22116yes—
77#2295C22116yes—
78C2×#391C2211yescharacteristic
79C2×#391C2211yescharacteristic
80C2×#391C2211yescharacteristic
81C2×#391C2211yescharacteristic
82C2×#391C2211yescharacteristic
83C2×#391C2211yescharacteristic
84C2×#391C2212yes—
85C2×#391C2211yescharacteristic
86C2×#391C2211yescharacteristic
87C2×#389C2211yescharacteristic
88C2×#389C2211yescharacteristic
89C2×#389C2211yescharacteristic
90C2×#389C2212yes—
91C2×#389C2211yescharacteristic
92C2×#389C2211yescharacteristic
93C2×#389C2212yes—
94C2×#389C2211yescharacteristic
95C2×#389C2212yes—
96C2×#389C2212yes—
97C2×#389C2211yescharacteristic
98C2×#389C2211yescharacteristic
99C2×#389C2211yescharacteristic
100C2×#389C2212yes—
101C2×#389C2212yes—
102C2×#389C2211yescharacteristic
103C2×#389C2211yescharacteristic
104C2×#389C2211yescharacteristic
105C2×#389C2211yescharacteristic
106C2×#389C2212yes—
107C2×#389C2212yes—
108C2×#389C2211yescharacteristic
109C2×#387C2212yes—
110C2×#387C2212yes—
111C2×#387C2212yes—
112C2×#387C2212yes—
113C2×#387C2212yes—
114C2×#387C2212yes—
115C2×#387C2212yes—
116C2×#387C2212yes—
117C2×#387C2212yes—
118C2×#387C2212yes—
119C2×#387C2212yes—
120C2×#387C2211yescharacteristic
121C2×#387C2211yescharacteristic
122C2×#387C2212yes—
123C2×#387C2212yes—
124C2×#387C2212yes—
125C2×#387C2212yes—
126C2×#387C2211yescharacteristic
127C2×#387C2211yescharacteristic
128C2×#384C2211yescharacteristic
129C2×#384C2211yescharacteristic
130C2×#384C2211yescharacteristic
131C2×#384C2211yescharacteristic
132C2×#383C2212yes—
133C2×#383C2212yes—
134C2×#382C2212yes—
135C2×#382C2212yes—
136C2×#382C2211yescharacteristic
137C2×#382C2212yes—
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
149C2×#125—28no—
150C2×#125—48no—
151C2×#125—48no—
152C2×#125—48no—
153C2×#125C2318yes—
154C2×#125C23116yes—
155C2×#125C23116yes—
156C2×#125C23116yes—
157C2×C4×Q8—28no—
158C2×C4×Q8—28no—
159C2×C4×Q8C2318yes—
160C2×C4×Q8C2318yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
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⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
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×C42C2311yescharacteristic
215#401C23116yes—
216#400C23116yes—
217#400C23116yes—
218#400C23116yes—
219#400C23116yes—
220#400C23116yes—
221#400C23116yes—
222#400C23116yes—
223#400C23116yes—
224#400C23116yes—
225#400C23116yes—
226#400C23116yes—
227#398C23116yes—
228#398C23116yes—
229#398C23116yes—
230#398C23116yes—
231#398C23116yes—
232#398C23116yes—
233#398C23116yes—
234#398C23116yes—
235#398C23116yes—
236#398C23116yes—
237#398C23116yes—
238#395C23116yes—
239#391C2318yes—
240#391C2318yes—
241#391C2318yes—
242#391C2318yes—
243#391C2318yes—
244#391C2318yes—
245#391C23116yes—
246#391C2318yes—
247#391C2318yes—
248#389C2318yes—
249#389C2318yes—
250#389C2318yes—
251#389C2318yes—
252#389C23116yes—
253#389C2318yes—
254#389C2318yes—
255#389C2318yes—
256#389C2318yes—
257#389C23116yes—
258#389C23116yes—
259#389C2318yes—
260#389C2318yes—
261#389C23116yes—
262#389C23116yes—
263#389C23116yes—
264#389C23116yes—
265#389C2318yes—
266#389C2318yes—
267#389C2318yes—
268#389C23116yes—
269#389C2318yes—
270#387C23116yes—
271#387C23116yes—
272#387C23116yes—
273#387C23116yes—
274#387C23116yes—
275#387C23116yes—
276#387C23116yes—
277#387C23116yes—
278#387C23116yes—
279#387C2318yes—
280#387C2318yes—
281#387C23116yes—
282#387C23116yes—
283#387C23116yes—
284#387C23116yes—
285#387C23116yes—
286#387C23116yes—
287#387C2318yes—
288#387C2318yes—
289#384C2318yes—
290#384C2318yes—
291#384C2318yes—
292#384C2318yes—
293#383C23116yes—
294#383C23116yes—
295#382C2318yes—
296#382C23116yes—
297#382C23116yes—
298#382C23116yes—
299C4×C4⋊C4C2318yes—
300C4×C4⋊C4C2318yes—
301C4×C4⋊C4C2318yes—
302C4×C4⋊C4C2318yes—
303C4×C4⋊C4C2318yes—
304C4×C4⋊C4C2318yes—
305#376C2318yes—
306#376C2318yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2312yes—
319C2×#95C2312yes—
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×#95C2312yes—
333C2×#95C2311yescharacteristic
334C2×#95C2311yescharacteristic
335C2×#95C2311yescharacteristic
336C2×#95C2311yescharacteristic
337C2×#95C2311yescharacteristic
338C2×#95C2311yescharacteristic
339C2×#95C2312yes—
340C2×#95C2312yes—
341C2×#95C2312yes—
342C2×#95C2312yes—
343C2×#95C2312yes—
344C2×#95C2312yes—
345C2×#95C2312yes—
346C2×#95C2311yescharacteristic
347C2×#95C2311yescharacteristic
348C2×#95C2311yescharacteristic
349C2×#95C2311yescharacteristic
350C43C2318yes—
351C22×Q8—24no—
352C22×Q8—24no—
353C22×Q8—24no—
354C22×Q8—24no—
355C22×Q8—24no—
356C22×Q8—42no—
357C22×Q8C2414yes—
358C22×Q8C2414yes—
359C23×C4C2412yes—
360C23×C4C2411yescharacteristic
361C23×C4C2412yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2411yescharacteristic
368C23×C4C2411yescharacteristic
369C23×C4C2411yescharacteristic
370C23×C4C2411yescharacteristic
371C23×C4C2411yescharacteristic
372C23×C4C2411yescharacteristic
373C23×C4C2411yescharacteristic
374C23×C4C2412yes—
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382#125—232no—
383#125—432no—
384#125—432no—
385#125—432no—
386C4×Q8—232no—
387C4×Q8—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—28no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—28no—
394C2×C4⋊C4—28no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—28no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—28no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—28no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—44no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4—44no—
415C2×C4⋊C4—44no—
416C2×C4⋊C4—44no—
417C2×C4⋊C4—44no—
418C2×C4⋊C4—44no—
419C2×C4⋊C4—44no—
420C2×C4⋊C4—44no—
421C2×C4⋊C4—44no—
422C2×C4⋊C4—44no—
423C2×C4⋊C4—44no—
424C2×C4⋊C4—44no—
425C2×C4⋊C4—44no—
426C2×C4⋊C4—44no—
427C2×C4⋊C4C2414yes—
428C2×C4⋊C4C2414yes—
429C2×C4⋊C4C2414yes—
430C2×C4⋊C4C2418yes—
431C2×C4⋊C4C2414yes—
432C2×C4⋊C4C2414yes—
433C2×C4⋊C4C2414yes—
434C2×C4⋊C4C2418yes—
435C2×C4⋊C4C2418yes—
436C2×C4⋊C4C2418yes—
437C2×C4⋊C4C2414yes—
438C2×C4⋊C4C2414yes—
439C2×C4⋊C4C2418yes—
440C2×C4⋊C4C2418yes—
441C2×C4⋊C4C2414yes—
442C2×C4⋊C4C2414yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C2414yes—
445C2×C4⋊C4C2414yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2414yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C2418yes—
450C2×C4⋊C4C2418yes—
451C2×C4⋊C4C2418yes—
452C2×C4⋊C4C2418yes—
453C2×C4⋊C4C2418yes—
454C2×C4⋊C4C2418yes—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C2418yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2418yes—
464C2×C4⋊C4C2418yes—
465C2×C4⋊C4C2418yes—
466C2×C42—24no—
467C2×C42—28no—
468C2×C42—24no—
469C2×C42—24no—
470C2×C42—24no—
471C2×C42—24no—
472C2×C42—24no—
473C2×C42—24no—
474C2×C42—24no—
475C2×C42—24no—
476C2×C42—44no—
477C2×C42—44no—
478C2×C42—42no—
479C2×C42—44no—
480C2×C42#4118yes—
481C2×C42C2414yes—
482C2×C42C2414yes—
483C2×C42C2418yes—
484C2×C42C2414yes—
485C2×C42C2414yes—
486C2×C42C2414yes—
487C2×C42C2414yes—
488C2×C42C2414yes—
489C2×C42C2414yes—
490C2×C42C2414yes—
491C2×C42C2418yes—
492C2×C42C2418yes—
493C2×C42C2414yes—
494C2×C42C2418yes—
495C2×C42C2414yes—
496#95C2414yes—
497#95C2414yes—
498#95C2414yes—
499#95C2414yes—
500#95C2414yes—
501#95C2414yes—
502#95C2414yes—
503#95C2414yes—
504#95C2414yes—
505#95C2418yes—
506#95C2414yes—
507#95C2414yes—
508#95C2414yes—
509#95C2414yes—
510#95C2414yes—
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—
529#95C2418yes—
530#95C2418yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C2418yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539C24C2511yescharacteristic
540C2×Q8—28no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—28no—
544C2×Q8—28no—
545C2×Q8—44no—
546C2×Q8—416no—
547C2×Q8—416no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—24no—
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—22no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4C2×#4114yes—
610C22×C4C2×#4114yes—
611C22×C4C2×#4114yes—
612C22×C4H(5,𝔽2)14yes—
613C22×C42−1+414yes—
614C22×C42−1+414yes—
615C22×C42−1+414yes—
616C22×C42−1+414yes—
617C22×C4C2512yes—
618C22×C4C2514yes—
619C22×C4C2512yes—
620C22×C4C2512yes—
621C22×C4C2512yes—
622C22×C4C2512yes—
623C22×C4C2514yes—
624C22×C4C2514yes—
625C22×C4C2512yes—
626C22×C4C2512yes—
627C22×C4C2512yes—
628C22×C4C2512yes—
629C22×C4C2514yes—
630C22×C4C2514yes—
631C22×C4C2514yes—
632C22×C4C2514yes—
633C22×C4C2514yes—
634C22×C4C2512yes—
635C22×C4C2512yes—
636C22×C4C2512yes—
637C22×C4C2512yes—
638C22×C4C2512yes—
639C22×C4C2512yes—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—216no—
645C4⋊C4—216no—
646C4⋊C4—216no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—216no—
652C4⋊C4—216no—
653C4⋊C4—216no—
654C4⋊C4—28no—
655C4⋊C4—28no—
656C4⋊C4—216no—
657C4⋊C4—28no—
658C4⋊C4—216no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—48no—
664C4⋊C4—44no—
665C4⋊C4—48no—
666C4⋊C4—48no—
667C4⋊C4—48no—
668C4⋊C4—48no—
669C4⋊C4—48no—
670C4⋊C4—48no—
671C4⋊C4—48no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—48no—
677C4⋊C4—48no—
678C4⋊C4—48no—
679C42—28no—
680C42—216no—
681C42—28no—
682C42—28no—
683C42—28no—
684C42—28no—
685C42—28no—
686C42—28no—
687C42—28no—
688C42—28no—
689C42—44no—
690C42—48no—
691C42—48no—
692C42—48no—
693C42C2×#41116yes—
694C23C22×#4112yes—
695C23C2×H(5,𝔽2)12yes—
696C23C2×2−1+412yes—
697C23C2×2−1+412yes—
698C23C2×2−1+412yes—
699C23C2×2−1+412yes—
700C23#58512yes—
701C23C2611yescharacteristic
702Q8—416no—
703Q8—416no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—48no—
771C2×C4—48no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—48no—
775C2×C4—44no—
776C2×C4—48no—
777C2×C4—44no—
778C2×C4—48no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4#541116yes—
788C2×C4C22×#4114yes—
789C2×C4C22×#4114yes—
790C2×C4C22×#4114yes—
791C2×C4C2×H(5,𝔽2)14yes—
792C2×C4C2×2−1+414yes—
793C2×C4C2×2−1+414yes—
794C2×C4C2×2−1+414yes—
795C2×C4C2×2−1+414yes—
796C22C2×#54114yes—
797C22#349514yes—
798C22#351114yes—
799C22#354414yes—
800C22#355414yes—
801C22#355614yes—
802C22#356314yes—
803C22C23×#4111yescharacteristic
804C22C22×H(5,𝔽2)11yescharacteristic
805C22C22×2−1+411yescharacteristic
806C22C22×2−1+411yescharacteristic
807C22C22×2−1+411yescharacteristic
808C22C22×2−1+411yescharacteristic
809C22C2×#58511yescharacteristic
810C4—24no—
811C4—24no—
812C4—24no—
813C4—24no—
814C4—24no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—44no—
819C4—44no—
820C4—44no—
821C4—42no—
822C4—44no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—44no—
827C4—42no—
828C4—44no—
829C4—44no—
830C4—42no—
831C4—44no—
832C4C2×#54118yes—
833C2#3734418yesdirect product factor
834C2C22×#54111yescharacteristic
835C2C2×#356311yescharacteristic
836C2C2×#355411yescharacteristic
837C2C2×#354411yescharacteristic
838C2C2×#355611yescharacteristic
839C2C2×#351111yescharacteristic
840C2C2×#349511yescharacteristic
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. #37344C2direct (N × H)
833. C2#37344direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28022
C2×#27762
C2×#27692
C2×#27622
C2×#27552
C2×#27192
#373442
C2×#28632
C2×#28592
C2×#25822
C2×#25522
C2×#25652
C2×#25842
C2×#25082
C2×#25112
C2×#25062
C2×#26452
C2×#26472
C2×#23302
C2×#23202
C2×#22952