Finite Group Databasebeta

← #7712680

Subgroups — #7712680

Order 512.

7468 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3536C212yesmaximal, complemented
2#59803C218yesmaximal, complemented
3#45489C218yesmaximal, complemented
4#39422C218yesmaximal, complemented
5#39415C218yesmaximal, complemented
6#38083C214yesmaximal, complemented
7#38082C214yesmaximal, complemented
8#37453C211yesmaximal, characteristic, complemented
9#37450C211yesmaximal, characteristic, complemented
10#37421C212yesmaximal, complemented
11#37418C212yesmaximal, complemented
12C2×#2850C212yesmaximal, complemented
13#36164C214yesmaximal, complemented
14#36124C214yesmaximal, complemented
15#35331C212yesmaximal, complemented
16#35328C212yesmaximal, complemented
17C4×#525C211yesmaximal, characteristic, complemented
18#3536—232no—
19C2×#562C2218yescomplemented
20C2×#554C2214yescomplemented
21C2×#548C2214yes—
22C2×#547C2214yes—
23C2×#546C2218yes—
24C2×#546C2214yescomplemented
25C2×#543C2214yescomplemented
26C2×#542C2214yescomplemented
27C2×#539C2214yes—
28C2×#538C2214yescomplemented
29C2×#537C2214yes—
30C2×#537C2214yescomplemented
31C2×#532C2212yescomplemented
32C22×#124C2212yescomplemented
33C2×#525C2211yescharacteristic
34C22×C22⋊Q8C2212yes—
35C22×#121C2212yes—
36C2×C4×#41C2211yescharacteristic, complemented
37C23×C42C2211yescharacteristic
38#2862C2212yescomplemented
39#2858C2212yescomplemented
40#2850C2214yes—
41#2850C2214yes—
42#2850C2218yes—
43#2850C2214yescomplemented
44#2850C2214yescomplemented
45#2850C2214yescomplemented
46#2850C2218yescomplemented
47#2817C2214yescomplemented
48#2815C2214yes—
49#2728C2218yescomplemented
50#2712C2218yescomplemented
51#2703C22116yescomplemented
52#2702C22116yescomplemented
53#2700C22116yescomplemented
54#2699C2218yescomplemented
55#2696C22116yescomplemented
56#2693C2218yescomplemented
57#2690C22116yescomplemented
58#2688C22116yescomplemented
59#2640C2214yescomplemented
60#2627C2218yescomplemented
61#2621C2212yescomplemented
62#2621C2212yescomplemented
63#2621C2212yescomplemented
64#2619C2212yes—
65#2619C2212yes—
66#2619C2212yescomplemented
67#2617C2218yes—
68#2568C2214yescomplemented
69#2563C2214yescomplemented
70#2560C22116yescomplemented
71#2557C22116yescomplemented
72#2555C22116yescomplemented
73#2545C2214yescomplemented
74#2544C2214yescomplemented
75#2543C2218yescomplemented
76#2543C2218yescomplemented
77#2536C2218yescomplemented
78#2535C2218yescomplemented
79#2504C2214yes—
80#2504C2214yescomplemented
81#2503C2214yescomplemented
82#2503C2214yescomplemented
83#2489C22116yescomplemented
84#2488C22116yescomplemented
85#2488C22116yescomplemented
86#2483C2214yes—
87#2461C22116yescomplemented
88#2450C22116yescomplemented
89#2444C22116yescomplemented
90#2434C2214yescomplemented
91#2433C2214yes—
92#2432C2214yescomplemented
93#2431C2214yescomplemented
94#2424C22116yescomplemented
95#2412C22116yescomplemented
96#2404C22116yescomplemented
97#2403C2214yes—
98#2358C22116yescomplemented
99#2339C22116yescomplemented
100#2328C2212yescomplemented
101#2327C2212yescomplemented
102#2311C2214yescomplemented
103C4×#124C2214yescomplemented
104C4×C22⋊Q8C2214yescomplemented
105C4×#123C2214yescomplemented
106C4×#121C2214yescomplemented
107C4×#120C2214yes—
108#2297C2211yescharacteristic, complemented
109#2296C2211yescharacteristic, complemented
110C2×#391C2212yescomplemented
111C2×#390C2212yescomplemented
112#2290C2214yescomplemented
113C2×#388C2218yescomplemented
114C2×#386C2218yes—
115C2×#382C2212yescomplemented
116C2×#382C2212yescomplemented
117#2280C2211yescharacteristic
118C42×D4C2214yescomplemented
119C4×#117C2211yescharacteristic, complemented
120C22×#41C2314yes—
121C22×#41C2318yes—
122C22×#41C2311yescharacteristic
123C23×Q8C2312yes—
124C23×D4C2314yes—
125C23×D4C2312yes—
126C24×C4C2312yes—
127C24×C4C2311yescharacteristic
128#562—264no—
129#554—232no—
130#548—232no—
131#547—232no—
132#546—264no—
133#546—232no—
134#543—232no—
135#542—232no—
136#539—232no—
137#538—232no—
138#537—232no—
139#537—232no—
140#532—48no—
141C2×C4⋊Q8C2314yes—
142C2×C4⋊Q8C2312yes—
143C2×C4⋊Q8C2312yes—
144C2×#127C2312yes—
145C2×#127C2312yes—
146C2×#126C2318yes—
147C2×#125C2318yes—
148C2×#124—48no—
149C2×#124C2314yes—
150C2×#124C2314yes—
151C2×#124C2318yes—
152C2×#124C2318yes—
153C2×#124C2314yes—
154C2×#124C2318yes—
155#525D4116yescomplemented
156C2×#123C2318yes—
157C2×#123C2318yes—
158C2×#123C2318yes—
159C2×#123C2318yes—
160C2×#123C2312yes—
161C2×C22⋊Q8—216no—
162C2×C22⋊Q8C2318yes—
163C2×C22⋊Q8C2314yes—
164C2×C22⋊Q8C2314yes—
165C2×C22⋊Q8C2314yes—
166C2×C22⋊Q8C2314yes—
167C2×C22⋊Q8C2314yes—
168C2×C22⋊Q8C2318yes—
169C2×C22⋊Q8C2318yes—
170C2×C22⋊Q8C2318yes—
171C2×C22⋊Q8C2318yes—
172C2×C22⋊Q8C2318yes—
173C2×C22⋊Q8C2312yes—
174C2×#121—216no—
175C2×#121C2314yes—
176C2×#121C2314yes—
177C2×#121C2314yes—
178C2×#121C2314yes—
179C2×#121C2314yes—
180C2×#121C2318yes—
181C2×#121C2318yes—
182C2×#121C2318yes—
183C2×#121C2318yes—
184C2×#121C2318yes—
185C2×#121C2318yes—
186C2×#121C2312yes—
187C2×#120C2318yes—
188C2×#120C23116yes—
189C2×#120C2312yes—
190C4×#41—44no—
191C2×C4×Q8C2314yes—
192C2×C4×Q8C2312yes—
193C2×C4×D4C2314yes—
194C2×C4×D4C2318yes—
195C2×C4×D4C2318yes—
196C2×C4×D4C2318yes—
197C2×C4×D4C2318yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2312yes—
200C2×C4×D4C2314yes—
201C2×#117C2312yes—
202C2×#117C2311yescharacteristic
203C2×#117C2311yescharacteristic
204C2×#117C2311yescharacteristic
205C22×C4⋊C4C2314yes—
206C22×C4⋊C4C2314yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2312yes—
209C22×C22⋊C4C2318yes—
210C22×C22⋊C4C2314yes—
211C22×C22⋊C4C2314yes—
212C22×C22⋊C4C2318yes—
213C22×C22⋊C4C2318yes—
214C22×C42—44no—
215C22×C42C2312yes—
216C22×C42C2311yescharacteristic
217C22×C42C2312yes—
218C22×C42C2314yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222#400C23116yes—
223#400C23116yes—
224#400C23116yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
228#397C23116yes—
229#397C2318yes—
230#397C2318yes—
231#397C23116yes—
232#397C2318yes—
233#397C23116yes—
234#396C23116yes—
235#395C23116yes—
236#394C2318yes—
237#394C2318yes—
238#394C2318yes—
239#394C23116yes—
240#394C23116yes—
241#393C23116yes—
242#393C23116yes—
243#392C23116yes—
244#392C2318yes—
245#392C2318yes—
246#392C2318yes—
247#392C23116yes—
248#391C23116yes—
249#391C2314yes—
250#391C2314yes—
251#391C2314yes—
252#391C23116yes—
253#391C2318yes—
254#391C2314yes—
255#391C2312yes—
256#390C23116yes—
257#390C2314yes—
258#390C2314yes—
259#390C2314yes—
260#390C2318yes—
261#390C2314yes—
262#390C2312yes—
263#389C2314yes—
264#388C23116yes—
265#388C23116yes—
266#388C23116yes—
267#388C23116yes—
268#388C23116yes—
269#388C23116yes—
270#388C23116yes—
271#388C2318yes—
272#387C23116yes—
273#387C2318yes—
274#386C23116yes—
275#386C23116yes—
276#386C23116yes—
277#386C23116yes—
278#386C23116yes—
279#386C23116yes—
280#386C23116yes—
281#386C23116yes—
282#386C23116yes—
283#386C23116yes—
284#386C23116yes—
285#386C2318yes—
286#386C2314yes—
287#385C23116yes—
288#385C23116yes—
289#385C2318yes—
290#385C2314yes—
291#382C2312yes—
292#382C2314yes—
293#382C2312yes—
294#382C2312yes—
295#382C2312yes—
296#382C2314yes—
297#382C2318yes—
298#382C2318yes—
299#381C2312yes—
300#381C23116yes—
301#381C23116yes—
302#380C23116yes—
303#380C23116yes—
304#380C2314yes—
305#379C2312yes—
306C4×C4⋊C4C2314yes—
307C4×C4⋊C4C2314yes—
308C4×C4⋊C4C2318yes—
309C4×C22⋊C4C23116yes—
310C4×C22⋊C4C2318yes—
311C4×C22⋊C4C2314yes—
312C4×C22⋊C4C2314yes—
313C4×C22⋊C4C2318yes—
314C4×C22⋊C4C2314yes—
315#376C2312yes—
316C2×#95C2318yes—
317C2×#95C2318yes—
318C2×#95C2318yes—
319C43C2312yes—
320C25C2411yescharacteristic
321C25C2414yes—
322C2×#41—232no—
323C2×#41—216no—
324C2×#41—42no—
325C2×#41—42no—
326C2×#41—432no—
327C2×#41—48no—
328C2×#41—48no—
329C2×#41C2×D418yes—
330C22×Q8—28no—
331C22×Q8—44no—
332C22×Q8—44no—
333C22×Q8C2414yes—
334C22×Q8C2414yes—
335C22×Q8C2418yes—
336C22×Q8C2411yescharacteristic
337C22×D4—216no—
338C22×D4—28no—
339C22×D4—44no—
340C22×D4—44no—
341C22×D4—416no—
342C22×D4C2418yes—
343C22×D4C2414yes—
344C22×D4C2414yes—
345C22×D4C2418yes—
346C22×D4C2418yes—
347C22×D4C2414yes—
348C22×D4C2418yes—
349C22×D4C2418yes—
350C22×D4C2418yes—
351C22×D4C2412yes—
352C22×D4C2411yescharacteristic
353C23×C4—42no—
354C23×C4—42no—
355C23×C4—44no—
356C23×C4—48no—
357C23×C4C2×D418yes—
358C23×C4C2414yes—
359C23×C4C2414yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362C23×C4C2411yescharacteristic
363C23×C4C2414yes—
364C23×C4C2414yes—
365C23×C4C2414yes—
366C23×C4C2418yes—
367C23×C4C2418yes—
368C23×C4C2418yes—
369C23×C4C2414yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2412yes—
373C23×C4C2411yescharacteristic
374C4⋊Q8—216no—
375C4⋊Q8—44no—
376C4⋊Q8—44no—
377#127—44no—
378#127—44no—
379#126—232no—
380#125—232no—
381#124—232no—
382#124—232no—
383#124—216no—
384#124—216no—
385#124—416no—
386#124—48no—
387#123—232no—
388#123—232no—
389#123—232no—
390#123—232no—
391#123C2×D4116yes—
392C22⋊Q8—232no—
393C22⋊Q8—216no—
394C22⋊Q8—216no—
395C22⋊Q8—216no—
396C22⋊Q8—216no—
397C22⋊Q8—216no—
398C22⋊Q8—232no—
399C22⋊Q8—232no—
400C22⋊Q8—232no—
401C22⋊Q8—232no—
402C22⋊Q8—232no—
403C22⋊Q8C2×D4116yes—
404#121—232no—
405#121—232no—
406#121—232no—
407#121—232no—
408#121—216no—
409#121—216no—
410#121—216no—
411#121—216no—
412#121—216no—
413#121—232no—
414#121—416no—
415#121C2×D4116yes—
416#120—232no—
417#120—432no—
418#120C2×D4116yes—
419C4×Q8—216no—
420C4×Q8—44no—
421C4×D4—232no—
422C4×D4—232no—
423C4×D4—216no—
424C4×D4—416no—
425C4×D4—44no—
426C4×D4—48no—
427C4×D4—416no—
428C4×D4C2×D4132yes—
429#117—42no—
430#117—44no—
431#117—42no—
432#117C2×D418yes—
433C2×C4⋊C4—28no—
434C2×C4⋊C4—216no—
435C2×C4⋊C4—28no—
436C2×C4⋊C4—216no—
437C2×C4⋊C4C2414yes—
438C2×C4⋊C4C2414yes—
439C2×C4⋊C4C2414yes—
440C2×C4⋊C4C2418yes—
441C2×C4⋊C4C2418yes—
442C2×C4⋊C4C2418yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C2418yes—
445C2×C4⋊C4C2418yes—
446C2×C4⋊C4C2418yes—
447C2×C4⋊C4C2414yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2418yes—
451C2×C4⋊C4C2418yes—
452C2×C4⋊C4C2418yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2414yes—
455C2×C22⋊C4—216no—
456C2×C22⋊C4—216no—
457C2×C22⋊C4—232no—
458C2×C22⋊C4—416no—
459C2×C22⋊C4—416no—
460C2×C22⋊C4C2418yes—
461C2×C22⋊C4C24116yes—
462C2×C22⋊C4C2418yes—
463C2×C22⋊C4C2418yes—
464C2×C22⋊C4C2418yes—
465C2×C22⋊C4C2418yes—
466C2×C22⋊C4C2418yes—
467C2×C22⋊C4C2418yes—
468C2×C22⋊C4C2418yes—
469C2×C22⋊C4C2418yes—
470C2×C22⋊C4C2418yes—
471C2×C22⋊C4C24116yes—
472C2×C22⋊C4C24116yes—
473C2×C22⋊C4C24116yes—
474C2×C22⋊C4C2412yes—
475C2×C22⋊C4C2414yes—
476C2×C22⋊C4C2412yes—
477C2×C22⋊C4C2418yes—
478C2×C22⋊C4C24116yes—
479C2×C22⋊C4C24116yes—
480C2×C22⋊C4C2414yes—
481C2×C22⋊C4C2412yes—
482C2×C22⋊C4C2414yes—
483C2×C42—28no—
484C2×C42—24no—
485C2×C42—28no—
486C2×C42—44no—
487C2×C42—48no—
488C2×C42—42no—
489C2×C42—44no—
490C2×C42C2412yes—
491C2×C42C2411yescharacteristic
492C2×C42C2412yes—
493C2×C42C2414yes—
494C2×C42C2418yes—
495C2×C42C2412yes—
496C2×C42C2414yes—
497C2×C42C2412yes—
498C2×C42C2418yes—
499C2×C42C2414yes—
500C2×C42C2412yes—
501C2×C42C2412yes—
502C2×C42C2411yescharacteristic
503#95C24116yes—
504#95C2418yes—
505#95C24116yes—
506#95C24116yes—
507#95C24116yes—
508#95C2418yes—
509#95C2418yes—
510#95C2418yes—
511#95C2418yes—
512#95C2418yes—
513#95C24116yes—
514#95C24116yes—
515#95C2418yes—
516#95C2418yes—
517C24—28no—
518C24—28no—
519C24—216no—
520C24—41no—
521C24—41no—
522C24—44no—
523C24—44no—
524C24—48no—
525C24C22×D414yes—
526C24C2518yes—
527C24C2511yescharacteristic
528C24C2512yes—
529C24C2512yes—
530#41—416no—
531#41—832no—
532#41—864no—
533C2×Q8—28no—
534C2×Q8—28no—
535C2×Q8—216no—
536C2×Q8—28no—
537C2×Q8—28no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—44no—
541C2×Q8—44no—
542C2×Q8—416no—
543C2×Q8—816no—
544C2×Q8C22×D414yes—
545C2×D4—216no—
546C2×D4—216no—
547C2×D4—232no—
548C2×D4—216no—
549C2×D4—216no—
550C2×D4—216no—
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—41no—
556C2×D4—42no—
557C2×D4—41no—
558C2×D4—42no—
559C2×D4—48no—
560C2×D4—416no—
561C2×D4—48no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—416no—
565C2×D4—416no—
566C2×D4—48no—
567C2×D4—416no—
568C2×D4—48no—
569C2×D4—816no—
570C2×D4—832no—
571C2×D4C22×D4116yes—
572C2×D4C22×D418yes—
573C2×D4C22×D414yes—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—216no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—216no—
587C22×C4—28no—
588C22×C4—24no—
589C22×C4—216no—
590C22×C4—216no—
591C22×C4—28no—
592C22×C4—416no—
593C22×C4—42no—
594C22×C4—41no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—42no—
600C22×C4—41no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—44no—
608C22×C4—416no—
609C22×C4—48no—
610C22×C4—416no—
611C22×C4—432no—
612C22×C4C22×D418yes—
613C22×C4C22×D418yes—
614C22×C4C22×D414yes—
615C22×C4C22×D418yes—
616C22×C4C22×D414yes—
617C22×C4C2514yes—
618C22×C4C2514yes—
619C22×C4C2512yes—
620C22×C4C2514yes—
621C22×C4C2518yes—
622C22×C4C2518yes—
623C22×C4C2518yes—
624C22×C4C2514yes—
625C22×C4C2512yes—
626C22×C4C2512yes—
627C22×C4C2511yescharacteristic
628C22×C4C2512yes—
629C22×C4C2511yescharacteristic
630C4⋊C4—28no—
631C4⋊C4—28no—
632C4⋊C4—28no—
633C4⋊C4—216no—
634C4⋊C4—216no—
635C4⋊C4—216no—
636C4⋊C4—28no—
637C4⋊C4—216no—
638C4⋊C4—216no—
639C4⋊C4—216no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—44no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4C22×D418yes—
647C4⋊C4C22×D4116yes—
648C22⋊C4—216no—
649C22⋊C4—216no—
650C22⋊C4—216no—
651C22⋊C4—216no—
652C22⋊C4—216no—
653C22⋊C4—216no—
654C22⋊C4—216no—
655C22⋊C4—216no—
656C22⋊C4—216no—
657C22⋊C4—216no—
658C22⋊C4—232no—
659C22⋊C4—416no—
660C22⋊C4—416no—
661C22⋊C4—416no—
662C22⋊C4—42no—
663C22⋊C4—44no—
664C22⋊C4—42no—
665C22⋊C4—48no—
666C22⋊C4—416no—
667C22⋊C4—416no—
668C22⋊C4C22×D4116yes—
669C22⋊C4C22×D418yes—
670C22⋊C4C22×D4116yes—
671C42—216no—
672C42—22no—
673C42—24no—
674C42—28no—
675C42—24no—
676C42—24no—
677C42—28no—
678C42—24no—
679C42—42no—
680C42—44no—
681C42—48no—
682C42C22×D418yes—
683C42H(5,𝔽2)14yes—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—28no—
691C23—22no—
692C23—24no—
693C23—216no—
694C23—28no—
695C23—28no—
696C23—216no—
697C23—216no—
698C23—28no—
699C23—44no—
700C23—48no—
701C23—48no—
702C23—416no—
703C23—88no—
704C23—88no—
705C23—816no—
706C23—816no—
707C23C23×D412yes—
708C23C23×D414yes—
709C23C23×D414yes—
710C23#58518yes—
711C23C2611yescharacteristic
712Q8—44no—
713Q8—416no—
714Q8—88no—
715Q8—816no—
716D4—232no—
717D4—44no—
718D4—48no—
719D4—432no—
720D4—416no—
721D4—88no—
722D4—816no—
723D4—816no—
724D4—816no—
725D4—816no—
726D4—168no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—28no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—216no—
736C2×C4—28no—
737C2×C4—216no—
738C2×C4—28no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—216no—
752C2×C4—216no—
753C2×C4—28no—
754C2×C4—48no—
755C2×C4—44no—
756C2×C4—416no—
757C2×C4—48no—
758C2×C4—416no—
759C2×C4—48no—
760C2×C4—416no—
761C2×C4—88no—
762C2×C4—816no—
763C2×C4—816no—
764C2×C4—88no—
765C2×C4—88no—
766C2×C4—816no—
767C2×C4C23×D418yes—
768C2×C4C23×D412yes—
769C2×C4C23×D414yes—
770C2×C4C23×D414yes—
771C2×C4C23×D412yes—
772C2×C4C2×H(5,𝔽2)14yes—
773C2×C4C2×H(5,𝔽2)12yes—
774C2×C4#58512yes—
775C22—28no—
776C22—24no—
777C22—24no—
778C22—28no—
779C22—22no—
780C22—24no—
781C22—28no—
782C22—24no—
783C22—416no—
784C22—42no—
785C22—44no—
786C22—44no—
787C22—42no—
788C22—416no—
789C22—48no—
790C22—48no—
791C22—48no—
792C22—416no—
793C22—1616no—
794C22#350018yes—
795C22C24×D411yescharacteristic
796C22C22×H(5,𝔽2)11yescharacteristic
797C22C2×#58514yes—
798C22C2×#58511yescharacteristic
799C4—24no—
800C4—22no—
801C4—24no—
802C4—24no—
803C4—28no—
804C4—44no—
805C4—42no—
806C4—44no—
807C4—48no—
808C4—48no—
809C4—48no—
810C4—44no—
811C4#349614yes—
812C2—28no—
813C2—44no—
814C2—42no—
815C2—88no—
816C2#6272912yes—
817C2C2×#349611yescharacteristic
818C2C2×#350012yes—
819C2#6282912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3536C2semidirect
2. #59803C2semidirect
3. #45489C2semidirect
4. #39422C2semidirect
5. #39415C2semidirect
6. #38083C2semidirect
7. #38082C2semidirect
8. #37453C2semidirect
9. #37450C2semidirect
10. #37421C2semidirect
11. #37418C2semidirect
12. C2×#2850C2semidirect
13. #36164C2semidirect
14. #36124C2semidirect
15. #35331C2semidirect
16. #35328C2semidirect
17. C4×#525C2semidirect
19. C2×#562C22semidirect
20. C2×#554C22semidirect
24. C2×#546C22semidirect
25. C2×#543C22semidirect
26. C2×#542C22semidirect
28. C2×#538C22semidirect
30. C2×#537C22semidirect
31. C2×#532C22semidirect
32. C22×#124C22semidirect
36. C2×C4×#41C22semidirect
38. #2862C22semidirect
39. #2858C22semidirect
43. #2850C22semidirect
44. #2850C22semidirect
45. #2850C22semidirect
46. #2850C22semidirect
47. #2817C22semidirect
49. #2728C22semidirect
50. #2712C22semidirect
51. #2703C22semidirect
52. #2702C22semidirect
53. #2700C22semidirect
54. #2699C22semidirect
55. #2696C22semidirect
56. #2693C22semidirect
57. #2690C22semidirect
58. #2688C22semidirect
59. #2640C22semidirect
60. #2627C22semidirect
61. #2621C22semidirect
62. #2621C22semidirect
63. #2621C22semidirect
66. #2619C22semidirect
68. #2568C22semidirect
69. #2563C22semidirect
70. #2560C22semidirect
71. #2557C22semidirect
72. #2555C22semidirect
73. #2545C22semidirect
74. #2544C22semidirect
75. #2543C22semidirect
76. #2543C22semidirect
77. #2536C22semidirect
78. #2535C22semidirect
80. #2504C22semidirect
81. #2503C22semidirect
82. #2503C22semidirect
83. #2489C22semidirect
84. #2488C22semidirect
85. #2488C22semidirect
87. #2461C22semidirect
88. #2450C22semidirect
89. #2444C22semidirect
90. #2434C22semidirect
92. #2432C22semidirect
93. #2431C22semidirect
94. #2424C22semidirect
95. #2412C22semidirect
96. #2404C22semidirect
98. #2358C22semidirect
99. #2339C22semidirect
100. #2328C22semidirect
101. #2327C22semidirect
102. #2311C22semidirect
103. C4×#124C22semidirect
104. C4×C22⋊Q8C22semidirect
105. C4×#123C22semidirect
106. C4×#121C22semidirect
108. #2297C22semidirect
109. #2296C22semidirect
110. C2×#391C22semidirect
111. C2×#390C22semidirect
112. #2290C22semidirect
113. C2×#388C22semidirect
115. C2×#382C22semidirect
116. C2×#382C22semidirect
118. C42×D4C22semidirect
119. C4×#117C22semidirect
155. #525D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35362
#598032
#454892
#394222
#394152
#380832
#380822
#374532
#374502
#374212
#374182
C2×#28502
#361642
#361242
#353312
#353282
C4×#5252