Finite Group Databasebeta

← #8092887

Subgroups — #8092887

Order 512.

5511 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53103C212yesmaximal, complemented
2#53102C214yesmaximal, complemented
3#53101C214yesmaximal, complemented
4#53099C212yesmaximal, complemented
5#53076C212yesmaximal, complemented
6#53031C211yesmaximal, characteristic, complemented
7#52986C211yesmaximal, characteristic, complemented
8#52904C214yesmaximal, complemented
9#52748C214yesmaximal, complemented
10#52696C214yesmaximal, complemented
11#52405C214yesmaximal, complemented
12#52245C214yesmaximal, complemented
13#52103C214yesmaximal, complemented
14#36696C214yesmaximal, complemented
15#36652C214yesmaximal, complemented
16#34977C212yesmaximal, complemented
17#34935C212yesmaximal, complemented
18#34797C214yesmaximal, complemented
19#34681C214yesmaximal, complemented
20#34621C212yesmaximal, complemented
21#34547C211yesmaximal, characteristic, complemented
22C2×#532C2212yes—
23C2×#525C2214yes—
24C2×#525C2218yescomplemented
25C2×C4×#41C2211yescharacteristic
26C2×C4×#41C2211yescharacteristic, complemented
27C22×C4×D4C2212yescomplemented
28#2843C2214yescomplemented
29#2830C2218yescomplemented
30#2830C2214yescomplemented
31#2829C2218yescomplemented
32#2829C2218yescomplemented
33#2829C2218yescomplemented
34#2828C2214yes—
35#2828C2218yescomplemented
36#2823C2214yescomplemented
37#2818C2218yescomplemented
38#2817C2214yescomplemented
39#2816C2218yescomplemented
40#2815C2214yes—
41#2814C2218yescomplemented
42#2814C2218yescomplemented
43#2813C2218yescomplemented
44#2813C2218yescomplemented
45#2812C2214yes—
46#2812C2218yescomplemented
47#2812C2214yescomplemented
48#2779C2218yescomplemented
49#2768C2218yescomplemented
50#2764C2214yescomplemented
51#2761C2218yescomplemented
52#2756C2218yescomplemented
53#2752C2214yes—
54#2735C2214yescomplemented
55#2715C2218yescomplemented
56#2685C2218yescomplemented
57#2683C2214yescomplemented
58#2682C2218yescomplemented
59#2681C2218yescomplemented
60#2681C2218yescomplemented
61#2680C2214yes—
62#2680C2214yescomplemented
63#2679C2214yes—
64#2678C2218yes—
65#2678C2218yescomplemented
66#2670C2214yes—
67#2669C2218yescomplemented
68#2651C2218yescomplemented
69#2648C2218yescomplemented
70#2647C2212yescomplemented
71#2644C2214yescomplemented
72#2641C2212yes—
73#2629C2212yescomplemented
74#2624C2214yescomplemented
75#2619C2212yes—
76#2610C2214yescomplemented
77#2610C2214yescomplemented
78#2567C2212yescomplemented
79#2563C2212yescomplemented
80#2548C2212yes—
81#2541C2212yes—
82#2538C2214yescomplemented
83#2537C2214yes—
84#2536C2214yescomplemented
85#2535C2214yes—
86#2534C2214yes—
87#2534C2214yescomplemented
88#2531C2218yescomplemented
89#2529C2218yescomplemented
90#2518C2218yescomplemented
91#2512C2214yescomplemented
92#2507C2214yescomplemented
93#2500C2214yescomplemented
94#2500C2214yescomplemented
95#2495C2214yescomplemented
96#2490C2214yes—
97#2486C2212yes—
98#2486C2212yescomplemented
99#2485C2214yescomplemented
100#2472C2218yescomplemented
101#2467C2218yescomplemented
102#2464C2218yescomplemented
103#2461C2218yescomplemented
104#2452C2214yescomplemented
105#2445C2214yes—
106#2441C2214yescomplemented
107#2440C2214yescomplemented
108#2433C2214yes—
109#2431C2214yescomplemented
110#2428C2214yes—
111#2424C2218yescomplemented
112#2422C2214yescomplemented
113#2416C2214yes—
114#2414C2214yes—
115#2414C2214yescomplemented
116#2414C2214yescomplemented
117#2408C2212yes—
118#2408C2212yescomplemented
119#2408C2214yescomplemented
120#2399C2211yescharacteristic, complemented
121#2398C2211yescharacteristic
122#2398C2211yescharacteristic, complemented
123#2397C2211yescharacteristic
124#2396C2212yescomplemented
125#2396C2212yescomplemented
126#2395C2212yescomplemented
127#2395C2218yescomplemented
128#2395C2218yescomplemented
129#2395C2212yescomplemented
130#2392C2214yes—
131#2392C2212yes—
132#2392C2218yescomplemented
133#2392C2212yescomplemented
134#2392C2218yescomplemented
135#2392C2218yescomplemented
136#2392C2214yescomplemented
137#2392C2214yescomplemented
138#2388C2212yes—
139#2388C2214yescomplemented
140#2388C2218yescomplemented
141#2388C2214yescomplemented
142#2388C2212yescomplemented
143C4×#127C2212yes—
144C4×#127C2214yescomplemented
145C4×#125C2212yescomplemented
146C4×#126C2218yescomplemented
147C4×#124C2214yescomplemented
148C4×#121C2214yes—
149C4×#121C2214yescomplemented
150C4×#121C2214yescomplemented
151C4×#120C2218yescomplemented
152#2293C2218yescomplemented
153#2293C2214yescomplemented
154#2285C2212yescomplemented
155#2280C2214yescomplemented
156C42×D4C2214yescomplemented
157C4×#117C2211yescharacteristic, complemented
158C4×#117C2212yescomplemented
159C22×#41C2311yescharacteristic
160C22×#41C2314yes—
161C22×#41C2311yescharacteristic
162C23×D4C2312yes—
163C24×C4C2314yes—
164#532—48no—
165C2×C4⋊Q8C2312yes—
166C2×#127C2312yes—
167C2×#127C2314yes—
168C2×#127C2312yes—
169C2×#126C2318yes—
170C2×#125C2312yes—
171C2×#124C2314yes—
172C2×#124C2314yes—
173#525—432no—
174#525—416no—
175C2×#123C2314yes—
176C2×#123C2314yes—
177C2×#123C2318yes—
178C2×#123C2318yes—
179C2×C22⋊Q8C2318yes—
180C2×C22⋊Q8C2318yes—
181C2×C22⋊Q8C2318yes—
182C2×#121C2318yes—
183C2×#121C2314yes—
184C2×#121C2314yes—
185C2×#121C2314yes—
186C2×#121C2314yes—
187C2×#121C2318yes—
188C2×#121C2318yes—
189C2×#121C2314yes—
190C2×#120C2314yes—
191C2×#120C2314yes—
192C2×#120C2318yes—
193C2×#120C2318yes—
194C2×#120C2318yes—
195C4×#41—44no—
196C4×#41—44no—
197C2×C4×Q8C2311yescharacteristic
198C2×C4×Q8C2311yescharacteristic
199C2×C4×Q8C2311yescharacteristic
200C2×C4×Q8C2311yescharacteristic
201C2×C4×D4—48no—
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2318yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2318yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2312yes—
211C2×C4×D4C2311yescharacteristic
212C2×C4×D4C2314yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2311yescharacteristic
216C2×C4×D4C2312yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×#117C2311yescharacteristic
223C2×#117C2312yes—
224C2×#117C2312yes—
225C2×#117C2312yes—
226C2×#117C2311yescharacteristic
227C2×#117C2318yes—
228C2×#117C2314yes—
229C2×#117C2314yes—
230C22×C4⋊C4C2312yes—
231C22×C22⋊C4C2314yes—
232C22×C42C2312yes—
233C22×C42C2311yescharacteristic
234C22×C42C2312yes—
235#400C2318yes—
236#400C2318yes—
237#400C2312yes—
238#400C2312yes—
239#399C2318yes—
240#399C2318yes—
241#399C2312yes—
242#399C2312yes—
243#398C2318yes—
244#398C2318yes—
245#398C2312yes—
246#398C2314yes—
247#398C2318yes—
248#398C2318yes—
249#398C2314yes—
250#398C2312yes—
251#398C2314yes—
252#398C2318yes—
253#397C2312yes—
254#397C2314yes—
255#397C2318yes—
256#397C2318yes—
257#397C2314yes—
258#397C2318yes—
259#397C2312yes—
260#397C2314yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#396C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#396C2314yes—
273#396C2318yes—
274#396C2314yes—
275#396C2318yes—
276#396C2318yes—
277#395C2314yes—
278#395C2318yes—
279#395C2314yes—
280#395C2312yes—
281#395C2312yes—
282#394C2314yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2314yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2314yes—
295#394C2318yes—
296#394C2314yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2314yes—
304#394C2318yes—
305#394C2318yes—
306#394C2312yes—
307#394C2314yes—
308#394C2312yes—
309#394C2314yes—
310#394C2318yes—
311#393C2314yes—
312#393C2318yes—
313#393C2314yes—
314#393C2312yes—
315#393C2312yes—
316#392C2314yes—
317#392C2318yes—
318#392C2318yes—
319#392C2318yes—
320#392C2318yes—
321#392C2318yes—
322#392C2318yes—
323#392C2314yes—
324#392C2314yes—
325#392C2314yes—
326#392C2312yes—
327#392C2312yes—
328#392C2318yes—
329#392C2314yes—
330#392C2318yes—
331#391C2314yes—
332#390C2314yes—
333#390C2318yes—
334#390C2314yes—
335#390C2314yes—
336#390C2318yes—
337#390C2318yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2318yes—
343#390C2314yes—
344#390C2318yes—
345#390C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#384C2312yes—
382#384C2314yes—
383#384C2314yes—
384#383C2318yes—
385#382C2312yes—
386#382C2314yes—
387#382C2314yes—
388#381C2314yes—
389#381C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2312yes—
393#380C2312yes—
394#380C2314yes—
395#380C2318yes—
396#380C2314yes—
397#380C2318yes—
398#379C2314yes—
399#379C2318yes—
400#379C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2318yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C22⋊C4C2318yes—
412C4×C22⋊C4C2318yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2312yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425#376C2314yes—
426#376C2311yescharacteristic
427#376C2311yescharacteristic
428C43C2314yes—
429C43C2312yes—
430C25C2414yes—
431C2×#41—28no—
432C2×#41—42no—
433C2×#41—42no—
434C2×#41—416no—
435C2×#41—48no—
436C2×#41—44no—
437C22×Q8C2411yescharacteristic
438C22×Q8C2411yescharacteristic
439C22×Q8C2414yes—
440C22×D4—44no—
441C22×D4—48no—
442C22×D4C2414yes—
443C22×D4C2411yescharacteristic
444C22×D4C2412yes—
445C22×D4C2414yes—
446C22×D4C2412yes—
447C22×D4C2418yes—
448C22×D4C2414yes—
449C22×D4C2414yes—
450C22×D4C2411yescharacteristic
451C22×D4C2418yes—
452C22×D4C2418yes—
453C22×D4C2418yes—
454C22×D4C2414yes—
455C22×D4C2418yes—
456C23×C4—216no—
457C23×C4—48no—
458C23×C4—48no—
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2418yes—
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2414yes—
469C23×C4C2411yescharacteristic
470C23×C4C2418yes—
471C4⋊Q8—44no—
472#127—44no—
473#127—48no—
474#127—44no—
475#126—416no—
476#125—44no—
477#124—48no—
478#124—48no—
479#123—48no—
480#123—416no—
481#123—416no—
482#123—48no—
483C22⋊Q8—416no—
484C22⋊Q8—416no—
485C22⋊Q8—416no—
486#121—416no—
487#121—48no—
488#121—416no—
489#121—48no—
490#121—48no—
491#121—48no—
492#121—48no—
493#121—416no—
494#120—416no—
495#120—48no—
496#120—416no—
497#120—416no—
498#120—48no—
499C4×Q8—42no—
500C4×Q8—42no—
501C4×Q8—42no—
502C4×Q8—42no—
503C4×D4—216no—
504C4×D4—232no—
505C4×D4—216no—
506C4×D4—48no—
507C4×D4—48no—
508C4×D4—48no—
509C4×D4—48no—
510C4×D4—42no—
511C4×D4—42no—
512C4×D4—44no—
513C4×D4—44no—
514C4×D4—44no—
515C4×D4—42no—
516C4×D4—42no—
517C4×D4—44no—
518C4×D4—416no—
519C4×D4—416no—
520C4×D4—416no—
521C4×D4—48no—
522C4×D4—48no—
523#117—44no—
524#117—42no—
525#117—44no—
526#117—44no—
527#117—42no—
528#117—48no—
529#117—416no—
530#117—48no—
531C2×C4⋊C4—44no—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2411yescharacteristic
544C2×C4⋊C4C2411yescharacteristic
545C2×C4⋊C4C2411yescharacteristic
546C2×C4⋊C4C2411yescharacteristic
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C22⋊C4—48no—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2412yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C42—28no—
598C2×C42—24no—
599C2×C42—28no—
600C2×C42C2411yescharacteristic
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2412yes—
604C2×C42C2412yes—
605C2×C42C2412yes—
606C2×C42C2411yescharacteristic
607C2×C42C2412yes—
608C2×C42C2414yes—
609C2×C42C2414yes—
610C2×C42C2418yes—
611C2×C42C2412yes—
612C2×C42C2411yescharacteristic
613C2×C42C2412yes—
614C2×C42C2418yes—
615C2×C42C2414yes—
616C2×C42C2414yes—
617C2×C42C2411yescharacteristic
618#95C2418yes—
619#95C2414yes—
620#95C2412yes—
621#95C2412yes—
622#95C2414yes—
623#95C2412yes—
624#95C2412yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2414yes—
640#95C2414yes—
641#95C2418yes—
642#95C2418yes—
643C24—28no—
644C24—44no—
645C24—48no—
646C24—44no—
647C24—48no—
648C24C2518yes—
649C24C2512yes—
650C24C2511yescharacteristic
651C24C2512yes—
652#41—416no—
653#41—416no—
654#41—832no—
655C2×Q8—24no—
656C2×Q8—24no—
657C2×Q8—41no—
658C2×Q8—41no—
659C2×Q8—48no—
660C2×Q8—44no—
661C2×D4—28no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—216no—
665C2×D4—28no—
666C2×D4—24no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—24no—
670C2×D4—28no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—41no—
675C2×D4—41no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—48no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—44no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—432no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—28no—
703C22×C4—24no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—24no—
707C22×C4—22no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—216no—
711C22×C4—216no—
712C22×C4—216no—
713C22×C4—28no—
714C22×C4—24no—
715C22×C4—28no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—28no—
719C22×C4—24no—
720C22×C4—216no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—44no—
724C22×C4—48no—
725C22×C4—44no—
726C22×C4—48no—
727C22×C4—44no—
728C22×C4—832no—
729C22×C4H(5,𝔽2)18yes—
730C22×C4C2511yescharacteristic
731C22×C4C2512yes—
732C22×C4C2518yes—
733C22×C4C2514yes—
734C22×C4C2512yes—
735C22×C4C2514yes—
736C22×C4C2518yes—
737C22×C4C2512yes—
738C22×C4C2511yescharacteristic
739C22×C4C2512yes—
740C22×C4C2518yes—
741C22×C4C2511yescharacteristic
742C22×C4C2511yescharacteristic
743C22×C4C2512yes—
744C22×C4C2512yes—
745C22×C4C2511yescharacteristic
746C22×C4C2511yescharacteristic
747C4⋊C4—28no—
748C4⋊C4—216no—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—42no—
756C4⋊C4—42no—
757C4⋊C4—42no—
758C4⋊C4—42no—
759C4⋊C4—41no—
760C4⋊C4—41no—
761C4⋊C4—41no—
762C4⋊C4—41no—
763C4⋊C4—48no—
764C4⋊C4—48no—
765C4⋊C4—48no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C4⋊C4—48no—
771C4⋊C4—48no—
772C4⋊C4—48no—
773C4⋊C4—48no—
774C22⋊C4—28no—
775C22⋊C4—216no—
776C22⋊C4—216no—
777C22⋊C4—216no—
778C22⋊C4—28no—
779C22⋊C4—28no—
780C22⋊C4—216no—
781C22⋊C4—48no—
782C22⋊C4—44no—
783C22⋊C4—48no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C22⋊C4—42no—
789C22⋊C4—42no—
790C22⋊C4—44no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—48no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—48no—
808C22⋊C4—48no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C42—24no—
812C42—22no—
813C42—22no—
814C42—24no—
815C42—24no—
816C42—24no—
817C42—24no—
818C42—22no—
819C42—24no—
820C42—28no—
821C42—216no—
822C42—24no—
823C42—24no—
824C42—28no—
825C42—48no—
826C42—44no—
827C42—44no—
828C42H(5,𝔽2)14yes—
829C23—22no—
830C23—22no—
831C23—24no—
832C23—24no—
833C23—28no—
834C23—28no—
835C23—24no—
836C23—21no—
837C23—28no—
838C23—22no—
839C23—22no—
840C23—28no—
841C23—24no—
842C23—22no—
843C23—22no—
844C23—28no—
845C23—28no—
846C23—28no—
847C23—22no—
848C23—22no—
849C23—416no—
850C23—88no—
851C23—816no—
852C23—88no—
853C23—816no—
854C23C2×H(5,𝔽2)14yes—
855C23C2611yescharacteristic
856Q8—44no—
857Q8—44no—
858Q8—88no—
859D4—48no—
860D4—48no—
861D4—44no—
862D4—416no—
863D4—416no—
864D4—44no—
865D4—416no—
866D4—88no—
867D4—816no—
868D4—816no—
869D4—816no—
870D4—816no—
871D4—816no—
872D4—88no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—216no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—22no—
886C2×C4—24no—
887C2×C4—28no—
888C2×C4—24no—
889C2×C4—28no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—24no—
893C2×C4—22no—
894C2×C4—28no—
895C2×C4—24no—
896C2×C4—28no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—28no—
901C2×C4—28no—
902C2×C4—24no—
903C2×C4—28no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—48no—
909C2×C4—44no—
910C2×C4—44no—
911C2×C4—48no—
912C2×C4—48no—
913C2×C4—432no—
914C2×C4—44no—
915C2×C4—48no—
916C2×C4—84no—
917C2×C4—816no—
918C2×C4—88no—
919C2×C4C2×H(5,𝔽2)12yes—
920C2×C4C2×H(5,𝔽2)14yes—
921C2×C4C2×H(5,𝔽2)12yes—
922C2×C4C2×H(5,𝔽2)14yes—
923C2×C4C2×H(5,𝔽2)12yes—
924C2×C4#58514yes—
925C2×C4#58514yes—
926C22—24no—
927C22—28no—
928C22—42no—
929C22—44no—
930C22—42no—
931C22—48no—
932C22—41no—
933C22—42no—
934C22—42no—
935C22—41no—
936C22—48no—
937C22—44no—
938C22—44no—
939C22—44no—
940C22—48no—
941C22—48no—
942C22—48no—
943C22—48no—
944C22—41no—
945C22—42no—
946C22—48no—
947C22—832no—
948C22C22×H(5,𝔽2)11yescharacteristic
949C22C22×H(5,𝔽2)12yes—
950C22C2×#58512yes—
951C22C2×#58512yes—
952C4—24no—
953C4—22no—
954C4—24no—
955C4—48no—
956C4—41no—
957C4—42no—
958C4—41no—
959C4—42no—
960C4—44no—
961C4—48no—
962C4—48no—
963C4—44no—
964C4—42no—
965C4—41no—
966C4—42no—
967C4#352914yes—
968C4#353714yes—
969C2—44no—
970C2—81no—
971C2—82no—
972C2—88no—
973C2C2×#352911yescharacteristic
974C2C2×#353711yescharacteristic
975C2#6272911yescharacteristic
976C2#6275914yes—
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. #53103C2semidirect
2. #53102C2semidirect
3. #53101C2semidirect
4. #53099C2semidirect
5. #53076C2semidirect
6. #53031C2semidirect
7. #52986C2semidirect
8. #52904C2semidirect
9. #52748C2semidirect
10. #52696C2semidirect
11. #52405C2semidirect
12. #52245C2semidirect
13. #52103C2semidirect
14. #36696C2semidirect
15. #36652C2semidirect
16. #34977C2semidirect
17. #34935C2semidirect
18. #34797C2semidirect
19. #34681C2semidirect
20. #34621C2semidirect
21. #34547C2semidirect
24. C2×#525C22semidirect
26. C2×C4×#41C22semidirect
27. C22×C4×D4C22semidirect
28. #2843C22semidirect
29. #2830C22semidirect
30. #2830C22semidirect
31. #2829C22semidirect
32. #2829C22semidirect
33. #2829C22semidirect
35. #2828C22semidirect
36. #2823C22semidirect
37. #2818C22semidirect
38. #2817C22semidirect
39. #2816C22semidirect
41. #2814C22semidirect
42. #2814C22semidirect
43. #2813C22semidirect
44. #2813C22semidirect
46. #2812C22semidirect
47. #2812C22semidirect
48. #2779C22semidirect
49. #2768C22semidirect
50. #2764C22semidirect
51. #2761C22semidirect
52. #2756C22semidirect
54. #2735C22semidirect
55. #2715C22semidirect
56. #2685C22semidirect
57. #2683C22semidirect
58. #2682C22semidirect
59. #2681C22semidirect
60. #2681C22semidirect
62. #2680C22semidirect
65. #2678C22semidirect
67. #2669C22semidirect
68. #2651C22semidirect
69. #2648C22semidirect
70. #2647C22semidirect
71. #2644C22semidirect
73. #2629C22semidirect
74. #2624C22semidirect
76. #2610C22semidirect
77. #2610C22semidirect
78. #2567C22semidirect
79. #2563C22semidirect
82. #2538C22semidirect
84. #2536C22semidirect
87. #2534C22semidirect
88. #2531C22semidirect
89. #2529C22semidirect
90. #2518C22semidirect
91. #2512C22semidirect
92. #2507C22semidirect
93. #2500C22semidirect
94. #2500C22semidirect
95. #2495C22semidirect
98. #2486C22semidirect
99. #2485C22semidirect
100. #2472C22semidirect
101. #2467C22semidirect
102. #2464C22semidirect
103. #2461C22semidirect
104. #2452C22semidirect
106. #2441C22semidirect
107. #2440C22semidirect
109. #2431C22semidirect
111. #2424C22semidirect
112. #2422C22semidirect
115. #2414C22semidirect
116. #2414C22semidirect
118. #2408C22semidirect
119. #2408C22semidirect
120. #2399C22semidirect
122. #2398C22semidirect
124. #2396C22semidirect
125. #2396C22semidirect
126. #2395C22semidirect
127. #2395C22semidirect
128. #2395C22semidirect
129. #2395C22semidirect
132. #2392C22semidirect
133. #2392C22semidirect
134. #2392C22semidirect
135. #2392C22semidirect
136. #2392C22semidirect
137. #2392C22semidirect
139. #2388C22semidirect
140. #2388C22semidirect
141. #2388C22semidirect
142. #2388C22semidirect
144. C4×#127C22semidirect
145. C4×#125C22semidirect
146. C4×#126C22semidirect
147. C4×#124C22semidirect
149. C4×#121C22semidirect
150. C4×#121C22semidirect
151. C4×#120C22semidirect
152. #2293C22semidirect
153. #2293C22semidirect
154. #2285C22semidirect
155. #2280C22semidirect
156. C42×D4C22semidirect
157. C4×#117C22semidirect
158. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#531032
#531022
#531012
#530992
#530762
#530312
#529862
#529042
#527482
#526962
#524052
#522452
#521032
#366962
#366522
#349772
#349352
#347972
#346812
#346212
#345472