Finite Group Databasebeta

← #7634904

Subgroups — #7634904

Order 512.

8278 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3455C211yesmaximal, characteristic, complemented
2C2×#3449C211yesmaximal, characteristic, complemented
3#52164C2116yesmaximal, complemented
4#37424C212yesmaximal, complemented
5#37422C212yesmaximal, complemented
6#37391C214yesmaximal, complemented
7#37390C212yesmaximal, complemented
8#37305C214yesmaximal, complemented
9#37302C212yesmaximal, complemented
10#36741C218yesmaximal, complemented
11#36739C218yesmaximal, complemented
12#36644C211yesmaximal, characteristic, complemented
13#36639C211yesmaximal, characteristic, complemented
14#34937C214yesmaximal, complemented
15#34738C214yesmaximal, complemented
16#34641C211yesmaximal, characteristic, complemented
17#34637C211yesmaximal, characteristic, complemented
18C2×#2298C211yesmaximal, characteristic, complemented
19C23×#41C2212yes—
20#3455—216no—
21C2×#542C2214yescomplemented
22C2×#541C2212yescomplemented
23C2×#540C2212yescomplemented
24C2×#539C2214yescomplemented
25C2×#538C2214yes—
26#3449—216no—
27C2×#537C2214yes—
28C2×#536C2212yes—
29C2×#536C2212yes—
30C2×#535C2212yes—
31C2×#535C2212yes—
32C2×#534C2214yes—
33C2×#533C2211yescharacteristic, complemented
34C2×#532C2211yescharacteristic
35C2×#532C2211yescharacteristic
36C2×#532C2212yes—
37C2×#532C2211yescharacteristic, complemented
38C2×#532C2214yescomplemented
39C2×#532C2214yescomplemented
40C2×#529C2218yescomplemented
41C2×#525C2212yes—
42C2×#525C2218yes—
43C2×C4×#41C2212yescomplemented
44C22×#117C2211yescharacteristic
45#2868C2211yescharacteristic, complemented
46#2867C2211yescharacteristic, complemented
47#2862C2212yescomplemented
48#2861C2212yescomplemented
49#2861C2212yescomplemented
50#2858C2214yescomplemented
51#2858C2212yescomplemented
52#2858C2211yescharacteristic, complemented
53#2858C2211yescharacteristic, complemented
54#2856C2218yescomplemented
55#2850C2218yescomplemented
56#2723C22116yescomplemented
57#2720C22116yescomplemented
58#2718C22116yescomplemented
59#2714C22116yescomplemented
60#2711C22116yescomplemented
61#2710C22116yescomplemented
62#2706C22116yescomplemented
63#2703C22116yescomplemented
64#2696C22116yescomplemented
65#2692C22116yescomplemented
66#2685C22116yescomplemented
67#2678C22116yescomplemented
68#2676C22116yescomplemented
69#2673C22116yescomplemented
70#2670C22116yescomplemented
71#2669C22116yescomplemented
72#2658C2212yescomplemented
73#2658C2212yescomplemented
74#2657C2212yescomplemented
75#2657C2212yescomplemented
76#2656C2218yescomplemented
77#2642C2212yescomplemented
78#2641C2212yescomplemented
79#2640C2214yescomplemented
80#2639C2218yescomplemented
81#2548C2214yescomplemented
82#2547C2214yescomplemented
83#2546C2214yescomplemented
84#2545C2214yescomplemented
85#2545C2214yescomplemented
86#2544C2214yescomplemented
87#2544C2214yescomplemented
88#2543C22116yescomplemented
89#2541C2214yescomplemented
90#2436C2214yescomplemented
91#2435C2214yescomplemented
92#2434C2214yescomplemented
93#2433C2214yescomplemented
94#2432C2214yes—
95#2432C2214yes—
96#2431C2214yes—
97#2431C2214yes—
98#2430C22116yescomplemented
99#2416C22116yescomplemented
100#2410C22116yes—
101#2398C2218yescomplemented
102#2397C2218yescomplemented
103#2392C22116yescomplemented
104#2388C22116yes—
105C4×#127C2218yescomplemented
106C4×#124C2218yescomplemented
107C4×#121C22116yescomplemented
108C4×#120C22116yescomplemented
109#2298C2212yescomplemented
110#2298C2214yescomplemented
111#2298C2212yescomplemented
112#2298C2218yescomplemented
113#2297C2214yescomplemented
114#2297C2214yescomplemented
115C2×#388C2214yes—
116C2×#387C2214yescomplemented
117C2×C4×C4⋊C4C2212yescomplemented
118C2×C4×C22⋊C4C2212yes—
119C2×#376C2211yescharacteristic, complemented
120C2×C43C2211yescharacteristic, complemented
121C22×#41—216no—
122C22×#41—416no—
123C22×#41C2312yes—
124C22×#41C2312yes—
125C22×#41C2312yes—
126C22×#41C2314yes—
127C22×#41C2312yes—
128C22×#41C2312yes—
129C22×#41C2314yes—
130C23×Q8C2312yes—
131C23×D4C2314yes—
132C23×D4C2312yes—
133C24×C4C2311yescharacteristic
134C24×C4C2314yes—
135#542—232no—
136#541—216no—
137#540—216no—
138#539—232no—
139#538—232no—
140#537—232no—
141#536—216no—
142#536—216no—
143#535—216no—
144#535—216no—
145#534—232no—
146#533—28no—
147#532—216no—
148#532—28no—
149#532—28no—
150#532—28no—
151#532—416no—
152#532—416no—
153C2×C4⋊Q8C2312yes—
154C2×C4⋊Q8C2311yescharacteristic
155C2×C4⋊Q8C2311yescharacteristic
156C2×C4⋊Q8C2311yescharacteristic
157C2×C4⋊Q8C2312yes—
158C2×C4⋊Q8C2314yes—
159C2×C4⋊Q8C2314yes—
160C2×#127C2311yescharacteristic
161C2×#127C2311yescharacteristic
162C2×#127C2311yescharacteristic
163C2×#127C2312yes—
164C2×#127C2318yes—
165C2×#127C2314yes—
166C2×#127C2314yes—
167#529—264no—
168C2×#126C2318yes—
169C2×#126C2318yes—
170C2×#125C2312yes—
171C2×#125C2318yes—
172C2×#124C2312yes—
173C2×#124C2312yes—
174C2×#124C2312yes—
175C2×#124C2318yes—
176C2×#124C2312yes—
177C2×#124C2312yes—
178C2×#124C2318yes—
179C2×#124C2314yes—
180C2×#124C2314yes—
181C2×#124C2314yes—
182C2×#124C2314yes—
183#525—216no—
184#525—264no—
185C2×#123C2318yes—
186C2×#123C2318yes—
187C2×#123C2314yes—
188C2×#123C2318yes—
189C2×#123C2318yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2318yes—
192C2×C22⋊Q8C2318yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2318yes—
195C2×#121C2314yes—
196C2×#121C2314yes—
197C2×#121C2314yes—
198C2×#121C2318yes—
199C2×#121C2318yes—
200C2×#121C2314yes—
201C2×#121C2318yes—
202C2×#121C2318yes—
203C2×#121C23116yes—
204C2×#121C23116yes—
205C2×#121C23116yes—
206C2×#120C2314yes—
207C2×#120C2318yes—
208C2×#120C2318yes—
209C2×#120C23116yes—
210C4×#41—216no—
211C2×C4×Q8C2314yes—
212C2×C4×Q8C2314yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2318yes—
216C2×C4×D4C2318yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C23116yes—
221C2×C4×D4C23116yes—
222C2×#117D4116yescomplemented
223C2×#117C2314yes—
224C2×#117C2312yes—
225C2×#117C2314yes—
226C2×#117C2312yes—
227C2×#117C2312yes—
228C22×C4⋊C4C2314yes—
229C22×C4⋊C4C2312yes—
230C22×C22⋊C4C2314yes—
231C22×C22⋊C4C2312yes—
232C22×C42C2314yes—
233C22×C42C2312yes—
234C22×C42C2312yes—
235C22×C42C2314yes—
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238#400C23116yes—
239#399C23116yes—
240#399C23116yes—
241#398C23116yes—
242#397C23116yes—
243#397C23116yes—
244#396C23116yes—
245#396C23116yes—
246#395C23116yes—
247#394C23116yes—
248#394C23116yes—
249#394C23116yes—
250#394C23116yes—
251#394C23116yes—
252#394C23116yes—
253#394C23116yes—
254#393C23116yes—
255#393C23116yes—
256#392C23116yes—
257#392C23116yes—
258#392C23116yes—
259#392C23116yes—
260#392C23116yes—
261#392C23116yes—
262#391C2318yes—
263#391C2314yes—
264#391C2314yes—
265#391C2314yes—
266#391C2314yes—
267#390C23116yes—
268#390C23116yes—
269#390C2318yes—
270#390C2318yes—
271#390C2318yes—
272#390C2314yes—
273#390C2314yes—
274#390C2314yes—
275#390C2314yes—
276#390C23116yes—
277#389C23116yes—
278#388C23116yes—
279#388C23116yes—
280#388C2318yes—
281#388C2318yes—
282#388C23116yes—
283#388C2318yes—
284#388C2318yes—
285#388C23116yes—
286#387C2318yes—
287#387C2318yes—
288#387C2318yes—
289#387C2318yes—
290#386C23116yes—
291#386C23116yes—
292#386C23116yes—
293#386C23116yes—
294#386C23116yes—
295#386C23116yes—
296#386C23116yes—
297#385C23116yes—
298#385C23116yes—
299#385C23116yes—
300#384C2318yes—
301#382C2318yes—
302#380C23116yes—
303#379C23116yes—
304C4×C4⋊C4C2318yes—
305C4×C4⋊C4C2314yes—
306C4×C4⋊C4C2314yes—
307C4×C22⋊C4C2318yes—
308C4×C22⋊C4C23116yes—
309C4×C22⋊C4C23116yes—
310C4×C22⋊C4C2314yes—
311C4×C22⋊C4C2314yes—
312#376C2312yes—
313#376C2312yes—
314#376C2314yes—
315C2×#95C2314yes—
316C2×#95C2314yes—
317C2×#95C2314yes—
318C43C2314yes—
319C43C2312yes—
320C43C2311yescharacteristic
321C43C2311yescharacteristic
322C25C2411yescharacteristic
323C25C2414yes—
324C2×#41—28no—
325C2×#41—216no—
326C2×#41—28no—
327C2×#41—28no—
328C2×#41—28no—
329C2×#41—28no—
330C2×#41—216no—
331C2×#41—216no—
332C2×#41—216no—
333C2×#41—216no—
334C2×#41—416no—
335C2×#41—416no—
336C2×#41—48no—
337C2×#41—48no—
338C2×#41—4128no—
339C22×Q8—28no—
340C22×Q8—48no—
341C22×Q8C2412yes—
342C22×Q8C2412yes—
343C22×Q8C2412yes—
344C22×Q8C2414yes—
345C22×Q8C2414yes—
346C22×D4—216no—
347C22×D4—28no—
348C22×D4—48no—
349C22×D4—416no—
350C22×D4C2414yes—
351C22×D4C2412yes—
352C22×D4C2414yes—
353C22×D4C2414yes—
354C22×D4C2412yes—
355C22×D4C2412yes—
356C22×D4C2418yes—
357C22×D4C2418yes—
358C22×D4C2414yes—
359C22×D4C2414yes—
360C22×D4C24116yes—
361C22×D4C2414yes—
362C22×D4C2414yes—
363C22×D4C2414yes—
364C22×D4C2414yes—
365C22×D4C24116yes—
366C23×C4—28no—
367C23×C4—216no—
368C23×C4—416no—
369C23×C4C2×D418yes—
370C23×C4C2414yes—
371C23×C4C2414yes—
372C23×C4C2414yes—
373C23×C4C2414yes—
374C23×C4C2411yescharacteristic
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2414yes—
378C23×C4C2418yes—
379C23×C4C2414yes—
380C23×C4C2414yes—
381C23×C4C2414yes—
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2411yescharacteristic
385C4⋊Q8—28no—
386C4⋊Q8—24no—
387C4⋊Q8—24no—
388C4⋊Q8—24no—
389C4⋊Q8—28no—
390C4⋊Q8—48no—
391C4⋊Q8—48no—
392#127—28no—
393#127—24no—
394#127—24no—
395#127—24no—
396#127—416no—
397#127—48no—
398#127—48no—
399#126—232no—
400#126—232no—
401#125—232no—
402#125—28no—
403#124—232no—
404#124—28no—
405#124—28no—
406#124—28no—
407#124—28no—
408#124—28no—
409#124—416no—
410#124—48no—
411#124—48no—
412#124—48no—
413#124—48no—
414#123—216no—
415#123—232no—
416#123—232no—
417#123—232no—
418#123—232no—
419C22⋊Q8—216no—
420C22⋊Q8—216no—
421C22⋊Q8—232no—
422C22⋊Q8—232no—
423C22⋊Q8—232no—
424#121—216no—
425#121—232no—
426#121—216no—
427#121—216no—
428#121—216no—
429#121—232no—
430#121—232no—
431#121—232no—
432#121—432no—
433#121—432no—
434#121—432no—
435#120—216no—
436#120—232no—
437#120—232no—
438#120—432no—
439C4×Q8—216no—
440C4×Q8—216no—
441C4×D4—232no—
442C4×D4—232no—
443C4×D4—216no—
444C4×D4—232no—
445C4×D4—216no—
446C4×D4—216no—
447C4×D4—216no—
448C4×D4—432no—
449C4×D4—432no—
450#117—28no—
451#117—216no—
452#117C2×D4132yes—
453#117C2×D4116yes—
454#117C2×D4116yes—
455C2×C4⋊C4—48no—
456C2×C4⋊C4C2×D4116yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2414yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2418yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2418yes—
468C2×C4⋊C4C24116yes—
469C2×C4⋊C4C24116yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2414yes—
472C2×C22⋊C4—48no—
473C2×C22⋊C4C2×D4116yes—
474C2×C22⋊C4C2418yes—
475C2×C22⋊C4C2414yes—
476C2×C22⋊C4C2418yes—
477C2×C22⋊C4C2418yes—
478C2×C22⋊C4C2418yes—
479C2×C22⋊C4C2418yes—
480C2×C22⋊C4C2418yes—
481C2×C22⋊C4C2418yes—
482C2×C22⋊C4C2418yes—
483C2×C22⋊C4C2418yes—
484C2×C22⋊C4C24116yes—
485C2×C22⋊C4C2418yes—
486C2×C22⋊C4C24116yes—
487C2×C22⋊C4C24116yes—
488C2×C22⋊C4C24116yes—
489C2×C22⋊C4C24116yes—
490C2×C22⋊C4C24116yes—
491C2×C22⋊C4C24116yes—
492C2×C22⋊C4C24116yes—
493C2×C22⋊C4C2414yes—
494C2×C22⋊C4C2414yes—
495C2×C42—28no—
496C2×C42—28no—
497C2×C42—216no—
498C2×C42—48no—
499C2×C42C2×D418yes—
500C2×C42C2×D418yes—
501C2×C42C2418yes—
502C2×C42C2412yes—
503C2×C42C2414yes—
504C2×C42C2414yes—
505C2×C42C2412yes—
506C2×C42C2414yes—
507C2×C42C2414yes—
508C2×C42C2414yes—
509C2×C42C2414yes—
510C2×C42C2414yes—
511C2×C42C2414yes—
512C2×C42C2412yes—
513C2×C42C2411yescharacteristic
514C2×C42C2411yescharacteristic
515C2×C42C2412yes—
516C2×C42C2412yes—
517#95C2418yes—
518#95C2418yes—
519#95C2418yes—
520#95C2418yes—
521#95C2418yes—
522#95C2418yes—
523#95C24116yes—
524#95C24116yes—
525#95C24116yes—
526#95C24116yes—
527C24—24no—
528C24—28no—
529C24—44no—
530C24—48no—
531C24—416no—
532C24C22×D414yes—
533C24C2514yes—
534C24C2514yes—
535C24C2514yes—
536C24C2512yes—
537C24C2511yescharacteristic
538#41—464no—
539#41—464no—
540#41—432no—
541#41—432no—
542#41—432no—
543#41—432no—
544#41—432no—
545C2×Q8—24no—
546C2×Q8—28no—
547C2×Q8—24no—
548C2×Q8—24no—
549C2×Q8—28no—
550C2×Q8—28no—
551C2×Q8—28no—
552C2×Q8—28no—
553C2×Q8—48no—
554C2×Q8—48no—
555C2×Q8—432no—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—216no—
562C2×D4—216no—
563C2×D4—216no—
564C2×D4—216no—
565C2×D4—24no—
566C2×D4—28no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—216no—
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—232no—
577C2×D4—48no—
578C2×D4—48no—
579C2×D4—48no—
580C2×D4—432no—
581C2×D4—416no—
582C2×D4—416no—
583C2×D4—416no—
584C2×D4—416no—
585C2×D4—416no—
586C2×D4—416no—
587C2×D4—48no—
588C2×D4—48no—
589C2×D4—416no—
590C2×D4—48no—
591C2×D4—464no—
592C22×C4—24no—
593C22×C4—232no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—216no—
605C22×C4—216no—
606C22×C4—216no—
607C22×C4—28no—
608C22×C4—216no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—416no—
618C22×C4—464no—
619C22×C4C22×D414yes—
620C22×C4C22×D418yes—
621C22×C4C22×D418yes—
622C22×C4C22×D418yes—
623C22×C4C22×D418yes—
624C22×C4C22×D414yes—
625C22×C4H(5,𝔽2)18yes—
626C22×C4C2518yes—
627C22×C4C2514yes—
628C22×C4C2518yes—
629C22×C4C2514yes—
630C22×C4C2514yes—
631C22×C4C2514yes—
632C22×C4C2512yes—
633C22×C4C2512yes—
634C22×C4C2512yes—
635C22×C4C2514yes—
636C22×C4C2514yes—
637C22×C4C2511yescharacteristic
638C22×C4C2511yescharacteristic
639C4⋊C4—28no—
640C4⋊C4—216no—
641C4⋊C4—216no—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—28no—
645C4⋊C4—216no—
646C4⋊C4—216no—
647C4⋊C4—28no—
648C4⋊C4—216no—
649C4⋊C4—48no—
650C4⋊C4—416no—
651C4⋊C4—416no—
652C4⋊C4C22×D4116yes—
653C4⋊C4C22×D4116yes—
654C22⋊C4—28no—
655C22⋊C4—216no—
656C22⋊C4—216no—
657C22⋊C4—216no—
658C22⋊C4—216no—
659C22⋊C4—216no—
660C22⋊C4—216no—
661C22⋊C4—216no—
662C22⋊C4—216no—
663C22⋊C4—216no—
664C22⋊C4—232no—
665C22⋊C4—48no—
666C22⋊C4—416no—
667C22⋊C4—416no—
668C22⋊C4—416no—
669C22⋊C4—416no—
670C22⋊C4—416no—
671C22⋊C4—416no—
672C22⋊C4—416no—
673C22⋊C4C22×D4116yes—
674C22⋊C4C22×D4116yes—
675C42—28no—
676C42—216no—
677C42—28no—
678C42—28no—
679C42—24no—
680C42—28no—
681C42—24no—
682C42—28no—
683C42—28no—
684C42—44no—
685C42—44no—
686C42C22×D418yes—
687C42C22×D418yes—
688C42C22×D418yes—
689C42C22×D414yes—
690C42C22×D414yes—
691C23—24no—
692C23—24no—
693C23—28no—
694C23—28no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—28no—
699C23—28no—
700C23—28no—
701C23—216no—
702C23—216no—
703C23—216no—
704C23—48no—
705C23—416no—
706C23—88no—
707C23—816no—
708C23—832no—
709C23C23×D414yes—
710C23C23×D412yes—
711C23C2×H(5,𝔽2)14yes—
712C23C2611yescharacteristic
713Q8—416no—
714Q8—48no—
715Q8—48no—
716Q8—48no—
717Q8—88no—
718D4—416no—
719D4—416no—
720D4—416no—
721D4—416no—
722D4—416no—
723D4—416no—
724D4—48no—
725D4—48no—
726D4—48no—
727D4—832no—
728D4—816no—
729D4—88no—
730D4—88no—
731D4—88no—
732D4—816no—
733D4—832no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—216no—
742C2×C4—216no—
743C2×C4—28no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—28no—
755C2×C4—216no—
756C2×C4—28no—
757C2×C4—48no—
758C2×C4—48no—
759C2×C4—416no—
760C2×C4—416no—
761C2×C4—416no—
762C2×C4—416no—
763C2×C4—416no—
764C2×C4—416no—
765C2×C4—416no—
766C2×C4—816no—
767C2×C4—88no—
768C2×C4#535116yes—
769C2×C4C23×D418yes—
770C2×C4C23×D414yes—
771C2×C4C23×D414yes—
772C2×C4C23×D414yes—
773C2×C4C23×D412yes—
774C2×C4C23×D412yes—
775C2×C4C2×H(5,𝔽2)14yes—
776C2×C4C2×H(5,𝔽2)14yes—
777C2×C4#58518yes—
778C22—28no—
779C22—24no—
780C22—28no—
781C22—24no—
782C22—48no—
783C22—416no—
784C22—416no—
785C22—416no—
786C22—48no—
787C22—48no—
788C22—48no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—88no—
793C22—832no—
794C22C2×#53514yes—
795C22C24×D411yescharacteristic
796C22C22×H(5,𝔽2)12yes—
797C22C2×#58514yes—
798C4—28no—
799C4—28no—
800C4—24no—
801C4—24no—
802C4—24no—
803C4—44no—
804C4—48no—
805C4—48no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4C2×#53514yes—
810C4C2×#53514yes—
811C2—24no—
812C2—44no—
813C2—84no—
814C2—84no—
815C2—84no—
816C2C22×#53511yescharacteristic
817C2#6274814yes—
818C2#6281212yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3455C2semidirect
2. C2×#3449C2semidirect
3. #52164C2semidirect
4. #37424C2semidirect
5. #37422C2semidirect
6. #37391C2semidirect
7. #37390C2semidirect
8. #37305C2semidirect
9. #37302C2semidirect
10. #36741C2semidirect
11. #36739C2semidirect
12. #36644C2semidirect
13. #36639C2semidirect
14. #34937C2semidirect
15. #34738C2semidirect
16. #34641C2semidirect
17. #34637C2semidirect
18. C2×#2298C2semidirect
21. C2×#542C22semidirect
22. C2×#541C22semidirect
23. C2×#540C22semidirect
24. C2×#539C22semidirect
33. C2×#533C22semidirect
37. C2×#532C22semidirect
38. C2×#532C22semidirect
39. C2×#532C22semidirect
40. C2×#529C22semidirect
43. C2×C4×#41C22semidirect
45. #2868C22semidirect
46. #2867C22semidirect
47. #2862C22semidirect
48. #2861C22semidirect
49. #2861C22semidirect
50. #2858C22semidirect
51. #2858C22semidirect
52. #2858C22semidirect
53. #2858C22semidirect
54. #2856C22semidirect
55. #2850C22semidirect
56. #2723C22semidirect
57. #2720C22semidirect
58. #2718C22semidirect
59. #2714C22semidirect
60. #2711C22semidirect
61. #2710C22semidirect
62. #2706C22semidirect
63. #2703C22semidirect
64. #2696C22semidirect
65. #2692C22semidirect
66. #2685C22semidirect
67. #2678C22semidirect
68. #2676C22semidirect
69. #2673C22semidirect
70. #2670C22semidirect
71. #2669C22semidirect
72. #2658C22semidirect
73. #2658C22semidirect
74. #2657C22semidirect
75. #2657C22semidirect
76. #2656C22semidirect
77. #2642C22semidirect
78. #2641C22semidirect
79. #2640C22semidirect
80. #2639C22semidirect
81. #2548C22semidirect
82. #2547C22semidirect
83. #2546C22semidirect
84. #2545C22semidirect
85. #2545C22semidirect
86. #2544C22semidirect
87. #2544C22semidirect
88. #2543C22semidirect
89. #2541C22semidirect
90. #2436C22semidirect
91. #2435C22semidirect
92. #2434C22semidirect
93. #2433C22semidirect
98. #2430C22semidirect
99. #2416C22semidirect
101. #2398C22semidirect
102. #2397C22semidirect
103. #2392C22semidirect
105. C4×#127C22semidirect
106. C4×#124C22semidirect
107. C4×#121C22semidirect
108. C4×#120C22semidirect
109. #2298C22semidirect
110. #2298C22semidirect
111. #2298C22semidirect
112. #2298C22semidirect
113. #2297C22semidirect
114. #2297C22semidirect
116. C2×#387C22semidirect
117. C2×C4×C4⋊C4C22semidirect
119. C2×#376C22semidirect
120. C2×C43C22semidirect
222. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34552
C2×#34492
#521642
#374242
#374222
#373912
#373902
#373052
#373022
#367412
#367392
#366442
#366392
#349372
#347382
#346412
#346372
C2×#22982