Finite Group Databasebeta

← #7702996

Subgroups — #7702996

Order 512.

7216 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3529C212yesmaximal, complemented
2#52165C214yesmaximal, complemented
3#52152C214yesmaximal, complemented
4#52103C214yesmaximal, complemented
5#46281C214yesmaximal, complemented
6#46280C214yesmaximal, complemented
7#46149C214yesmaximal, complemented
8#45999C214yesmaximal, complemented
9#45785C214yesmaximal, complemented
10#45784C214yesmaximal, complemented
11#45480C218yesmaximal, complemented
12#36684C212yesmaximal, complemented
13#36631C212yesmaximal, complemented
14#34829C218yesmaximal, complemented
15#34743C214yesmaximal, complemented
16C4×#532C211yesmaximal, characteristic, complemented
17#3529—232no—
18C2×#563C2212yescomplemented
19C2×#563C2214yescomplemented
20C2×#562C2214yes—
21C2×#562C2218yescomplemented
22C2×H(3,𝔽4)C2212yescomplemented
23C2×#560C2214yes—
24C2×#560C2218yescomplemented
25C2×#532C2214yes—
26C2×#532C2211yescharacteristic
27C2×#529C2218yescomplemented
28C2×#529C2214yescomplemented
29C2×#525C2218yescomplemented
30C2×#525C2214yescomplemented
31C2×#525C2214yescomplemented
32C2×C4×#41C2212yescomplemented
33#2861C2214yescomplemented
34#2860C2214yescomplemented
35#2860C2214yescomplemented
36#2859C2212yescomplemented
37#2858C2212yes—
38#2857C2212yescomplemented
39#2856C2212yes—
40#2854C2214yescomplemented
41#2854C2214yescomplemented
42#2850C2214yescomplemented
43#2823C2218yescomplemented
44#2822C2212yescomplemented
45#2820C2214yescomplemented
46#2819C2212yes—
47#2814C2218yescomplemented
48#2813C2218yescomplemented
49#2730C2218yescomplemented
50#2729C2218yescomplemented
51#2727C2214yescomplemented
52#2726C2214yescomplemented
53#2725C2218yescomplemented
54#2724C2214yescomplemented
55#2718C2218yescomplemented
56#2717C2214yescomplemented
57#2710C2218yescomplemented
58#2709C2214yescomplemented
59#2701C2218yescomplemented
60#2701C2218yescomplemented
61#2689C2218yescomplemented
62#2688C2218yescomplemented
63#2684C2214yescomplemented
64#2683C2214yescomplemented
65#2682C2214yes—
66#2682C2214yes—
67#2682C2214yes—
68#2681C2218yescomplemented
69#2681C2218yescomplemented
70#2680C2218yescomplemented
71#2679C2214yescomplemented
72#2678C2218yescomplemented
73#2678C2218yescomplemented
74#2678C2218yescomplemented
75#2674C2218yescomplemented
76#2671C2218yescomplemented
77#2669C2218yes—
78#2669C2214yescomplemented
79#2560C2218yescomplemented
80#2559C2218yescomplemented
81#2558C2218yescomplemented
82#2557C2218yescomplemented
83#2556C2218yescomplemented
84#2555C2218yes—
85#2554C2218yescomplemented
86#2553C2218yescomplemented
87#2549C2218yescomplemented
88#2543C2218yes—
89#2539C2218yescomplemented
90#2534C2218yescomplemented
91#2488C2218yescomplemented
92#2472C2218yescomplemented
93#2429C2218yescomplemented
94#2428C2218yes—
95#2427C2218yescomplemented
96#2426C2218yescomplemented
97#2425C2218yescomplemented
98#2425C2218yescomplemented
99#2425C2218yescomplemented
100#2424C2218yescomplemented
101#2424C2218yescomplemented
102#2424C2218yescomplemented
103#2396C2218yescomplemented
104#2395C2218yescomplemented
105#2392C2218yescomplemented
106#2392C2218yescomplemented
107#2392C2218yescomplemented
108#2388C2218yes—
109C4×C4⋊Q8C2212yescomplemented
110C4×C4⋊Q8C2212yescomplemented
111C4×#127C2212yes—
112C4×#127C2212yes—
113C4×#124C2214yescomplemented
114C4×#124C2214yescomplemented
115C4×#123C2218yescomplemented
116C4×#121C2218yescomplemented
117C4×#121C2214yescomplemented
118C4×#121C2214yescomplemented
119C4×#121C2214yescomplemented
120C4×#121C2214yescomplemented
121C4×#120C2218yescomplemented
122#2297C2214yescomplemented
123#2297C2212yescomplemented
124#2296C2214yescomplemented
125#2293C2214yescomplemented
126#2293C2214yescomplemented
127#2293C2214yescomplemented
128#2285C2211yescharacteristic, complemented
129C42×D4C2214yescomplemented
130C2×C4×C22⋊C4C2214yescomplemented
131C2×C43C2211yescharacteristic, complemented
132C22×#41C2314yes—
133C22×#41C2312yes—
134C24×C4C2314yes—
135#563—232no—
136#563—216no—
137#562—232no—
138#562—264no—
139H(3,𝔽4)—216no—
140#560—232no—
141#560—264no—
142#532—232no—
143#532D4116yescomplemented
144C2×C4⋊Q8C2314yes—
145C2×C4⋊Q8C2312yes—
146C2×C4⋊Q8C2311yescharacteristic
147C2×#127C2314yes—
148C2×#127C2312yes—
149C2×#127C2311yescharacteristic
150#529—264no—
151#529—232no—
152C2×#126C2318yes—
153C2×#126C2318yes—
154C2×#126C2318yes—
155C2×#125C2314yes—
156C2×#125C2318yes—
157C2×#124C2314yes—
158C2×#124C2318yes—
159C2×#124C2314yes—
160C2×#124C2314yes—
161C2×#124C2314yes—
162C2×#124C2312yes—
163#525—232no—
164#525—264no—
165#525—416no—
166C2×#123C2318yes—
167C2×#123C2318yes—
168C2×#123C2314yes—
169C2×#123C2314yes—
170C2×#123C2318yes—
171C2×#123C2318yes—
172C2×#123C2318yes—
173C2×#123C2318yes—
174C2×#123C2318yes—
175C2×C22⋊Q8C2318yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2318yes—
178C2×C22⋊Q8C2318yes—
179C2×C22⋊Q8C2318yes—
180C2×C22⋊Q8C2318yes—
181C2×#121C2314yes—
182C2×#121C2318yes—
183C2×#121C2318yes—
184C2×#121C2318yes—
185C2×#121C2318yes—
186C2×#121C2318yes—
187C2×#121C2318yes—
188C2×#121C2314yes—
189C2×#121C2314yes—
190C2×#121C2318yes—
191C2×#121C2318yes—
192C2×#121C2314yes—
193C2×#120C2318yes—
194C2×#120C2314yes—
195C2×#120C2314yes—
196C2×#120C2318yes—
197C2×#120C2318yes—
198C2×#120C2318yes—
199C4×#41—48no—
200C2×C4×Q8C2314yes—
201C2×C4×Q8C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2318yes—
206C2×C4×D4C2318yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2318yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2314yes—
214C2×#117C2314yes—
215C2×#117C2318yes—
216C2×#117C2314yes—
217C2×#117C2312yes—
218C22×C22⋊C4C2318yes—
219C22×C42C2311yescharacteristic
220C22×C42C2314yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2314yes—
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226#400C2318yes—
227#400C2318yes—
228#399C2318yes—
229#399C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#397C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#396C2318yes—
243#396C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2318yes—
250#395C2318yes—
251#395C2318yes—
252#394C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2318yes—
263#394C2318yes—
264#394C2318yes—
265#394C2318yes—
266#393C2318yes—
267#393C2318yes—
268#392C2318yes—
269#392C2318yes—
270#392C2318yes—
271#392C2318yes—
272#392C2318yes—
273#392C2318yes—
274#391C2318yes—
275#391C2314yes—
276#391C2314yes—
277#391C2314yes—
278#390C2318yes—
279#390C2314yes—
280#390C2314yes—
281#390C2314yes—
282#390C2314yes—
283#390C2314yes—
284#390C2314yes—
285#390C2314yes—
286#390C2314yes—
287#390C2314yes—
288#390C2314yes—
289#390C2314yes—
290#390C2314yes—
291#390C2314yes—
292#390C2318yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2318yes—
304#389C2318yes—
305#389C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#387C2318yes—
321#387C2318yes—
322#386C2318yes—
323#386C2318yes—
324#386C2318yes—
325#386C2318yes—
326#386C2314yes—
327#386C2318yes—
328#386C2318yes—
329#386C2318yes—
330#386C2318yes—
331#386C2318yes—
332#386C2318yes—
333#386C2314yes—
334#385C2318yes—
335#385C2318yes—
336#385C2318yes—
337#385C2318yes—
338#385C2318yes—
339#385C2318yes—
340#384C2312yes—
341#384C2312yes—
342#384C2312yes—
343#382C2312yes—
344#382C2314yes—
345#381C2318yes—
346#380C2314yes—
347#380C2314yes—
348#380C2318yes—
349#380C2314yes—
350#379C2318yes—
351C4×C4⋊C4C2314yes—
352C4×C4⋊C4C2314yes—
353C4×C4⋊C4C2314yes—
354C4×C4⋊C4C2314yes—
355C4×C4⋊C4C2314yes—
356C4×C4⋊C4C2318yes—
357C4×C22⋊C4C2318yes—
358C4×C22⋊C4C2318yes—
359C4×C22⋊C4C2318yes—
360C4×C22⋊C4C2318yes—
361C4×C22⋊C4C2318yes—
362C4×C22⋊C4C2318yes—
363C4×C22⋊C4C2318yes—
364C4×C22⋊C4C2318yes—
365C4×C22⋊C4C2318yes—
366C2×#95C2318yes—
367C43C2312yes—
368C43C2312yes—
369C43C2312yes—
370C43C2312yes—
371C25C2414yes—
372C2×#41—216no—
373C2×#41—44no—
374C2×#41—44no—
375C2×#41—48no—
376C2×#41—48no—
377C2×#41C2×D4116yes—
378C22×Q8C2414yes—
379C22×Q8C2414yes—
380C22×Q8C2412yes—
381C22×D4C2418yes—
382C22×D4C2418yes—
383C22×D4C2414yes—
384C22×D4C2414yes—
385C22×D4C2414yes—
386C22×D4C2418yes—
387C22×D4C2418yes—
388C22×D4C2414yes—
389C22×D4C2418yes—
390C22×D4C2414yes—
391C22×D4C2412yes—
392C22×D4C2414yes—
393C23×C4—216no—
394C23×C4—48no—
395C23×C4—48no—
396C23×C4C2418yes—
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2414yes—
401C23×C4C2418yes—
402C23×C4C2418yes—
403C23×C4C2418yes—
404C23×C4C2414yes—
405C23×C4C2411yescharacteristic
406C23×C4C2412yes—
407C4⋊Q8—216no—
408C4⋊Q8—44no—
409C4⋊Q8C2×D418yes—
410#127—216no—
411#127—44no—
412#127C2×D418yes—
413#126—232no—
414#126—232no—
415#126—232no—
416#125—232no—
417#125—216no—
418#124—216no—
419#124—216no—
420#124—232no—
421#124—216no—
422#124—48no—
423#124C2×D4116yes—
424#123—216no—
425#123—216no—
426#123—232no—
427#123—232no—
428#123—232no—
429#123—232no—
430#123—232no—
431#123—416no—
432#123—416no—
433C22⋊Q8—232no—
434C22⋊Q8—216no—
435C22⋊Q8—232no—
436C22⋊Q8—232no—
437C22⋊Q8—232no—
438C22⋊Q8—416no—
439#121—232no—
440#121—232no—
441#121—232no—
442#121—232no—
443#121—232no—
444#121—216no—
445#121—232no—
446#121—48no—
447#121—416no—
448#121—48no—
449#121—416no—
450#121C2×D4132yes—
451#120—216no—
452#120—232no—
453#120—216no—
454#120—232no—
455#120—416no—
456#120—416no—
457C4×Q8—216no—
458C4×Q8—48no—
459C4×D4—232no—
460C4×D4—232no—
461C4×D4—232no—
462C4×D4—216no—
463C4×D4—216no—
464C4×D4—48no—
465C4×D4—48no—
466C4×D4—48no—
467C4×D4—48no—
468C4×D4—416no—
469C4×D4—416no—
470C4×D4C2×D4132yes—
471#117—216no—
472#117—232no—
473#117—216no—
474#117—44no—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2418yes—
480C2×C4⋊C4C2418yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2418yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2418yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2414yes—
498C2×C22⋊C4—416no—
499C2×C22⋊C4C2418yes—
500C2×C22⋊C4C2418yes—
501C2×C22⋊C4C2418yes—
502C2×C22⋊C4C2414yes—
503C2×C22⋊C4C2418yes—
504C2×C22⋊C4C2414yes—
505C2×C22⋊C4C2418yes—
506C2×C22⋊C4C2418yes—
507C2×C22⋊C4C2418yes—
508C2×C22⋊C4C2418yes—
509C2×C22⋊C4C2418yes—
510C2×C22⋊C4C2418yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2418yes—
514C2×C22⋊C4C2418yes—
515C2×C22⋊C4C2418yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2414yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C2418yes—
527C2×C42—216no—
528C2×C42—24no—
529C2×C42—48no—
530C2×C42—42no—
531C2×C42—44no—
532C2×C42—44no—
533C2×C42C2×D418yes—
534C2×C42C2412yes—
535C2×C42C2412yes—
536C2×C42C2412yes—
537C2×C42C2414yes—
538C2×C42C2412yes—
539C2×C42C2414yes—
540C2×C42C2412yes—
541C2×C42C2418yes—
542C2×C42C2414yes—
543C2×C42C2412yes—
544C2×C42C2411yescharacteristic
545C2×C42C2418yes—
546C2×C42C2412yes—
547C2×C42C2412yes—
548C2×C42C2412yes—
549C2×C42C2412yes—
550C2×C42C2412yes—
551C2×C42C2411yescharacteristic
552C2×C42C2411yescharacteristic
553C2×C42C2412yes—
554C2×C42C2411yescharacteristic
555#95C2418yes—
556#95C2418yes—
557#95C2418yes—
558#95C2418yes—
559#95C2418yes—
560#95C2418yes—
561#95C2418yes—
562#95C2418yes—
563#95C2418yes—
564#95C2418yes—
565#95C2418yes—
566#95C2418yes—
567#95C2418yes—
568#95C2418yes—
569#95C2418yes—
570C24—28no—
571C24—48no—
572C24—44no—
573C24—44no—
574C24—48no—
575C24C2518yes—
576C24C2514yes—
577C24C2511yescharacteristic
578#41—432no—
579#41—832no—
580C2×Q8—28no—
581C2×Q8—28no—
582C2×Q8—42no—
583C2×Q8—42no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—44no—
588C2×Q8C22×D418yes—
589C2×D4—216no—
590C2×D4—216no—
591C2×D4—216no—
592C2×D4—216no—
593C2×D4—28no—
594C2×D4—28no—
595C2×D4—28no—
596C2×D4—28no—
597C2×D4—42no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—42no—
602C2×D4—44no—
603C2×D4—48no—
604C2×D4—44no—
605C2×D4—48no—
606C2×D4—48no—
607C2×D4—48no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—44no—
611C2×D4—48no—
612C2×D4—48no—
613C2×D4—48no—
614C2×D4—48no—
615C2×D4—48no—
616C2×D4—48no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—48no—
622C2×D4C22×D4116yes—
623C2×D4C22×D418yes—
624C2×D4C22×D4116yes—
625C22×C4—22no—
626C22×C4—28no—
627C22×C4—22no—
628C22×C4—28no—
629C22×C4—216no—
630C22×C4—28no—
631C22×C4—216no—
632C22×C4—24no—
633C22×C4—216no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—216no—
637C22×C4—216no—
638C22×C4—216no—
639C22×C4—41no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—41no—
645C22×C4—48no—
646C22×C4—48no—
647C22×C4—48no—
648C22×C4—48no—
649C22×C4—44no—
650C22×C4—48no—
651C22×C4—48no—
652C22×C4—44no—
653C22×C4—832no—
654C22×C4C22×D4116yes—
655C22×C4C22×D414yes—
656C22×C4C22×D418yes—
657C22×C4C2512yes—
658C22×C4C2518yes—
659C22×C4C2518yes—
660C22×C4C2518yes—
661C22×C4C2518yes—
662C22×C4C2512yes—
663C22×C4C2514yes—
664C22×C4C2512yes—
665C22×C4C2511yescharacteristic
666C22×C4C2512yes—
667C22×C4C2512yes—
668C22×C4C2512yes—
669C22×C4C2511yescharacteristic
670C4⋊C4—216no—
671C4⋊C4—216no—
672C4⋊C4—216no—
673C4⋊C4—216no—
674C4⋊C4—216no—
675C4⋊C4—216no—
676C4⋊C4—28no—
677C4⋊C4—216no—
678C4⋊C4—28no—
679C4⋊C4—216no—
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—48no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—48no—
690C4⋊C4—48no—
691C4⋊C4—44no—
692C4⋊C4C22×D4116yes—
693C22⋊C4—28no—
694C22⋊C4—28no—
695C22⋊C4—216no—
696C22⋊C4—216no—
697C22⋊C4—216no—
698C22⋊C4—216no—
699C22⋊C4—216no—
700C22⋊C4—216no—
701C22⋊C4—216no—
702C22⋊C4—216no—
703C22⋊C4—216no—
704C22⋊C4—216no—
705C22⋊C4—216no—
706C22⋊C4—216no—
707C22⋊C4—216no—
708C22⋊C4—216no—
709C22⋊C4—216no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—44no—
713C22⋊C4—48no—
714C22⋊C4—48no—
715C22⋊C4—48no—
716C22⋊C4—48no—
717C22⋊C4—48no—
718C22⋊C4—48no—
719C22⋊C4—48no—
720C22⋊C4C22×D4132yes—
721C42—216no—
722C42—28no—
723C42—28no—
724C42—22no—
725C42—24no—
726C42—28no—
727C42—24no—
728C42—24no—
729C42—24no—
730C42—24no—
731C42—24no—
732C42—42no—
733C42—42no—
734C42—42no—
735C42—42no—
736C42—42no—
737C42—48no—
738C42C22×D418yes—
739C42C22×D414yes—
740C42C22×D414yes—
741C42H(5,𝔽2)14yes—
742C23—24no—
743C23—21no—
744C23—28no—
745C23—28no—
746C23—21no—
747C23—22no—
748C23—22no—
749C23—24no—
750C23—28no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—28no—
755C23—28no—
756C23—28no—
757C23—416no—
758C23—88no—
759C23—816no—
760C23—816no—
761C23—88no—
762C23C23×D412yes—
763C23C23×D418yes—
764C23C2611yescharacteristic
765Q8—48no—
766Q8—88no—
767Q8—88no—
768D4—416no—
769D4—416no—
770D4—48no—
771D4—88no—
772D4—88no—
773D4—88no—
774D4—88no—
775D4—816no—
776D4—816no—
777D4—816no—
778D4—816no—
779D4—816no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—24no—
794C2×C4—232no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—28no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—28no—
805C2×C4—28no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—48no—
812C2×C4—48no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—432no—
816C2×C4—816no—
817C2×C4—816no—
818C2×C4—816no—
819C2×C4—88no—
820C2×C4C23×D418yes—
821C2×C4C23×D414yes—
822C2×C4C23×D412yes—
823C2×C4C23×D414yes—
824C2×C4C23×D412yes—
825C2×C4C2×H(5,𝔽2)14yes—
826C2×C4C2×H(5,𝔽2)12yes—
827C2×C4#58514yes—
828C2×C4#58514yes—
829C2×C4#58512yes—
830C22—28no—
831C22—22no—
832C22—24no—
833C22—216no—
834C22—42no—
835C22—48no—
836C22—41no—
837C22—44no—
838C22—41no—
839C22—44no—
840C22—48no—
841C22—48no—
842C22—48no—
843C22—48no—
844C22—48no—
845C22—48no—
846C22—48no—
847C22—832no—
848C22C24×D411yescharacteristic
849C22C22×H(5,𝔽2)11yescharacteristic
850C22C2×#58512yes—
851C22C2×#58512yes—
852C22C2×#58511yescharacteristic
853C4—24no—
854C4—24no—
855C4—24no—
856C4—28no—
857C4—22no—
858C4—24no—
859C4—24no—
860C4—48no—
861C4—48no—
862C4—48no—
863C4—48no—
864C4—42no—
865C4#349614yes—
866C2—42no—
867C2—48no—
868C2—88no—
869C2#6269411yescharacteristic
870C2#6274812yes—
871C2#6275511yescharacteristic
872C2C2×#349611yescharacteristic
873C2#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×#3529C2semidirect
2. #52165C2semidirect
3. #52152C2semidirect
4. #52103C2semidirect
5. #46281C2semidirect
6. #46280C2semidirect
7. #46149C2semidirect
8. #45999C2semidirect
9. #45785C2semidirect
10. #45784C2semidirect
11. #45480C2semidirect
12. #36684C2semidirect
13. #36631C2semidirect
14. #34829C2semidirect
15. #34743C2semidirect
16. C4×#532C2semidirect
18. C2×#563C22semidirect
19. C2×#563C22semidirect
21. C2×#562C22semidirect
22. C2×H(3,𝔽4)C22semidirect
24. C2×#560C22semidirect
27. C2×#529C22semidirect
28. C2×#529C22semidirect
29. C2×#525C22semidirect
30. C2×#525C22semidirect
31. C2×#525C22semidirect
32. C2×C4×#41C22semidirect
33. #2861C22semidirect
34. #2860C22semidirect
35. #2860C22semidirect
36. #2859C22semidirect
38. #2857C22semidirect
40. #2854C22semidirect
41. #2854C22semidirect
42. #2850C22semidirect
43. #2823C22semidirect
44. #2822C22semidirect
45. #2820C22semidirect
47. #2814C22semidirect
48. #2813C22semidirect
49. #2730C22semidirect
50. #2729C22semidirect
51. #2727C22semidirect
52. #2726C22semidirect
53. #2725C22semidirect
54. #2724C22semidirect
55. #2718C22semidirect
56. #2717C22semidirect
57. #2710C22semidirect
58. #2709C22semidirect
59. #2701C22semidirect
60. #2701C22semidirect
61. #2689C22semidirect
62. #2688C22semidirect
63. #2684C22semidirect
64. #2683C22semidirect
68. #2681C22semidirect
69. #2681C22semidirect
70. #2680C22semidirect
71. #2679C22semidirect
72. #2678C22semidirect
73. #2678C22semidirect
74. #2678C22semidirect
75. #2674C22semidirect
76. #2671C22semidirect
78. #2669C22semidirect
79. #2560C22semidirect
80. #2559C22semidirect
81. #2558C22semidirect
82. #2557C22semidirect
83. #2556C22semidirect
85. #2554C22semidirect
86. #2553C22semidirect
87. #2549C22semidirect
89. #2539C22semidirect
90. #2534C22semidirect
91. #2488C22semidirect
92. #2472C22semidirect
93. #2429C22semidirect
95. #2427C22semidirect
96. #2426C22semidirect
97. #2425C22semidirect
98. #2425C22semidirect
99. #2425C22semidirect
100. #2424C22semidirect
101. #2424C22semidirect
102. #2424C22semidirect
103. #2396C22semidirect
104. #2395C22semidirect
105. #2392C22semidirect
106. #2392C22semidirect
107. #2392C22semidirect
109. C4×C4⋊Q8C22semidirect
110. C4×C4⋊Q8C22semidirect
113. C4×#124C22semidirect
114. C4×#124C22semidirect
115. C4×#123C22semidirect
116. C4×#121C22semidirect
117. C4×#121C22semidirect
118. C4×#121C22semidirect
119. C4×#121C22semidirect
120. C4×#121C22semidirect
121. C4×#120C22semidirect
122. #2297C22semidirect
123. #2297C22semidirect
124. #2296C22semidirect
125. #2293C22semidirect
126. #2293C22semidirect
127. #2293C22semidirect
128. #2285C22semidirect
129. C42×D4C22semidirect
130. C2×C4×C22⋊C4C22semidirect
131. C2×C43C22semidirect
143. #532D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35292
#521652
#521522
#521032
#462812
#462802
#461492
#459992
#457852
#457842
#454802
#366842
#366312
#348292
#347432
C4×#5322