Finite Group Databasebeta

← #7643526

Subgroups — #7643526

Order 512.

5380 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40026C218yesmaximal, complemented
2#40025C218yesmaximal, complemented
3#38460C2116yesmaximal, complemented
4#37329C218yesmaximal, complemented
5#36640C211yesmaximal, characteristic, complemented
6C2×#2858C211yesmaximal, characteristic, complemented
7#35679C211yesmaximal, characteristic, complemented
8#35677C211yesmaximal, characteristic, complemented
9#35674C211yesmaximal, characteristic, complemented
10#35667C211yesmaximal, characteristic, complemented
11#35626C211yesmaximal, characteristic, complemented
12#35617C211yesmaximal, characteristic, complemented
13#35554C211yesmaximal, characteristic, complemented
14#35528C211yesmaximal, characteristic
15#35327C211yesmaximal, characteristic, complemented
16#35327C211yesmaximal, characteristic, complemented
17#35136C218yesmaximal, complemented
18#34211C211yesmaximal, characteristic, complemented
19#34211C211yesmaximal, characteristic, complemented
20#34026C211yesmaximal, characteristic, complemented
21C2×#536C2211yescharacteristic
22C2×#536C2211yescharacteristic
23C2×#535C2211yescharacteristic
24C2×#535C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×#127C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C22×#124C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36#2864C2214yescomplemented
37#2859C2214yescomplemented
38#2858C2214yes—
39#2858C2218yes—
40#2858C2214yes—
41#2851C2218yes—
42#2850C2214yescomplemented
43#2850C2214yescomplemented
44#2803C22116yescomplemented
45#2800C22116yescomplemented
46#2780C22116yescomplemented
47#2761C22116yescomplemented
48#2753C22116yescomplemented
49#2711C22116yescomplemented
50#2707C22116yescomplemented
51#2701C22116yescomplemented
52#2651C22116yescomplemented
53#2648C22116yescomplemented
54#2620C2214yescomplemented
55#2620C2214yescomplemented
56#2548C2214yescomplemented
57#2547C2214yescomplemented
58#2546C2214yescomplemented
59#2545C2214yescomplemented
60#2545C2214yescomplemented
61#2545C2214yescomplemented
62#2545C2214yescomplemented
63#2544C2214yes—
64#2544C2214yescomplemented
65#2544C2214yescomplemented
66#2544C2214yescomplemented
67#2541C2214yes—
68#2534C2218yes—
69#2534C2218yes—
70#2531C22116yescomplemented
71#2526C22116yescomplemented
72#2484C2218yes—
73#2483C2218yes—
74#2482C2218yes—
75#2476C22116yescomplemented
76#2471C22116yescomplemented
77#2448C2218yescomplemented
78#2448C2218yescomplemented
79#2447C2218yescomplemented
80#2447C2218yescomplemented
81#2446C2218yescomplemented
82#2446C2218yescomplemented
83#2445C2218yes—
84#2445C2218yes—
85#2429C2218yescomplemented
86#2428C2218yes—
87#2427C2218yescomplemented
88#2426C2218yescomplemented
89#2413C2218yes—
90#2412C2218yes—
91#2411C2218yes—
92#2410C2218yes—
93#2405C2218yes—
94#2367C2218yescomplemented
95#2367C2218yescomplemented
96#2342C2218yes—
97#2342C2218yes—
98#2335C22116yescomplemented
99#2333C22116yescomplemented
100#2326C2214yescomplemented
101#2326C2214yescomplemented
102#2310C2211yescharacteristic
103#2310C2211yescharacteristic
104#2310C2211yescharacteristic
105#2310C2211yescharacteristic
106#2309C2211yescharacteristic
107#2309C2211yescharacteristic
108#2309C2211yescharacteristic
109#2309C2211yescharacteristic
110C4×#125C2218yescomplemented
111C4×#124C2214yescomplemented
112C4×#124C2214yescomplemented
113#2298C2214yescomplemented
114#2297C2211yescharacteristic
115#2297C2211yescharacteristic
116#2296C2211yescharacteristic
117#2296C2211yescharacteristic
118#2296C2211yescharacteristic
119#2296C2211yescharacteristic
120#2296C2211yescharacteristic
121#2296C2211yescharacteristic
122#2295C2214yescomplemented
123#2293C2214yescomplemented
124C2×#390C2218yes—
125#2290C2218yes—
126#2285C2211yescharacteristic
127#2285C2211yescharacteristic
128C4×#117C2211yescharacteristic
129C4×#117C2214yescomplemented
130C2×C43C2211yescharacteristic
131C22×#41C2311yescharacteristic
132C23×Q8C2311yescharacteristic
133C23×Q8C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2314yes—
137#536—44no—
138#536—44no—
139#535—44no—
140#535—44no—
141C2×C4⋊Q8—44no—
142C2×C4⋊Q8C2314yes—
143C2×C4⋊Q8C2314yes—
144C2×C4⋊Q8C2312yes—
145C2×C4⋊Q8C2312yes—
146C2×#127—44no—
147C2×#127C2314yes—
148C2×#127C2314yes—
149C2×#127C2312yes—
150C2×#127C2312yes—
151C2×#125C2318yes—
152C2×#124—28no—
153C2×#124—28no—
154C2×#124—44no—
155C2×#124—44no—
156C2×#124C2312yes—
157C2×#124C2312yes—
158C2×#124C2312yes—
159C2×#124C2312yes—
160C2×#124C2314yes—
161C2×#124C2314yes—
162C2×#124C2314yes—
163C2×#124C2314yes—
164C2×#124C2314yes—
165C2×#124C2314yes—
166C2×#124C2312yes—
167C2×#124C2312yes—
168C2×#124C2312yes—
169C2×#124C2312yes—
170C2×#123C23116yes—
171C2×#123C2314yes—
172C2×#123C2314yes—
173C2×C22⋊Q8C2314yes—
174C2×C22⋊Q8C2314yes—
175C2×#121C23116yes—
176C2×#121C2314yes—
177C2×#121C2314yes—
178C2×#120C2314yes—
179C2×#120C2314yes—
180#519—44no—
181#519—44no—
182#518—44no—
183#518—44no—
184C4×#41—28no—
185C2×C4×Q8C2312yes—
186C2×C4×Q8C2314yes—
187C2×C4×Q8C2314yes—
188C2×C4×Q8C2314yes—
189C2×C4×Q8C2314yes—
190C2×C4×D4C2314yes—
191C2×C4×D4C2312yes—
192C2×C4×D4C2314yes—
193C2×C4×D4C2314yes—
194C2×C4×D4C2314yes—
195C2×C4×D4C2314yes—
196C2×#117C2311yescharacteristic
197C2×#117C2311yescharacteristic
198C2×#117C2311yescharacteristic
199C2×#117C2311yescharacteristic
200C2×#117C2311yescharacteristic
201C2×#117C2311yescharacteristic
202C2×#117C2311yescharacteristic
203C2×#117C2312yes—
204C2×#117C2314yes—
205C2×#117C2314yes—
206C2×#117C2318yes—
207C22×C4⋊C4C2314yes—
208C22×C22⋊C4C2314yes—
209C22×C22⋊C4C2314yes—
210C22×C22⋊C4C2314yes—
211C22×C22⋊C4C2314yes—
212C22×C22⋊C4C2314yes—
213C22×C22⋊C4C2314yes—
214C22×C42C2312yes—
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2314yes—
218C22×C42C2311yescharacteristic
219#400C23116yes—
220#399C23116yes—
221#398C23116yes—
222#398C23116yes—
223#397C23116yes—
224#397C23116yes—
225#397C23116yes—
226#397C23116yes—
227#396C23116yes—
228#396C23116yes—
229#396C23116yes—
230#396C23116yes—
231#394C23116yes—
232#394C23116yes—
233#394C23116yes—
234#394C23116yes—
235#394C23116yes—
236#394C23116yes—
237#394C23116yes—
238#392C23116yes—
239#391C2314yes—
240#391C2314yes—
241#391C2314yes—
242#391C2314yes—
243#391C2314yes—
244#391C2314yes—
245#391C2314yes—
246#391C2314yes—
247#391C2312yes—
248#391C2312yes—
249#390C2314yes—
250#390C2314yes—
251#390C2314yes—
252#390C2314yes—
253#390C2314yes—
254#390C2314yes—
255#390C2314yes—
256#390C2314yes—
257#390C23116yes—
258#390C23116yes—
259#390C23116yes—
260#390C23116yes—
261#390C23116yes—
262#390C2312yes—
263#390C2312yes—
264#389C2318yes—
265#389C2318yes—
266#389C23116yes—
267#389C2314yes—
268#389C2314yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2314yes—
273#388C23116yes—
274#388C23116yes—
275#388C23116yes—
276#388C23116yes—
277#388C23116yes—
278#388C23116yes—
279#388C23116yes—
280#388C23116yes—
281#388C23116yes—
282#388C23116yes—
283#388C2318yes—
284#388C2318yes—
285#387C2318yes—
286#387C2318yes—
287#387C2318yes—
288#387C2318yes—
289#387C23116yes—
290#387C23116yes—
291#387C2318yes—
292#387C2318yes—
293#386C23116yes—
294#386C23116yes—
295#386C23116yes—
296#386C23116yes—
297#386C23116yes—
298#386C2314yes—
299#386C2314yes—
300#385C23116yes—
301#385C23116yes—
302#385C23116yes—
303#385C2314yes—
304#385C2314yes—
305#385C2314yes—
306#385C2314yes—
307#385C2314yes—
308#385C2314yes—
309#384C2312yes—
310#384C2312yes—
311#382C2318yes—
312#382C2312yes—
313#382C2312yes—
314#381C2314yes—
315#381C2314yes—
316#381C2314yes—
317#381C2314yes—
318#381C23116yes—
319#380C23116yes—
320#380C2314yes—
321#380C2314yes—
322#379C2314yes—
323#379C2314yes—
324#379C2314yes—
325#379C2314yes—
326C4×C4⋊C4C2314yes—
327C4×C4⋊C4C2314yes—
328C4×C4⋊C4C2314yes—
329C4×C4⋊C4C2314yes—
330C4×C4⋊C4C2314yes—
331C4×C4⋊C4C2314yes—
332C4×C4⋊C4C2318yes—
333C4×C4⋊C4C2314yes—
334C4×C4⋊C4C2314yes—
335C4×C4⋊C4C2314yes—
336C4×C22⋊C4C2318yes—
337C4×C22⋊C4C23116yes—
338C4×C22⋊C4C23116yes—
339C4×C22⋊C4C2314yes—
340C4×C22⋊C4C2314yes—
341C4×C22⋊C4C2314yes—
342#376C2312yes—
343#376C2318yes—
344C43C2314yes—
345C43C2312yes—
346C43C2312yes—
347C43C2312yes—
348C25C2412yes—
349C25C2412yes—
350C2×#41—24no—
351C2×#41—24no—
352C2×#41—24no—
353C22×Q8—24no—
354C22×Q8—24no—
355C22×Q8—24no—
356C22×Q8—24no—
357C22×Q8—24no—
358C22×Q8—24no—
359C22×Q8C2412yes—
360C22×Q8C2412yes—
361C22×Q8C2412yes—
362C22×Q8C2412yes—
363C22×Q8C2411yescharacteristic
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—24no—
370C22×D4—416no—
371C22×D4—48no—
372C22×D4C2412yes—
373C22×D4C2412yes—
374C22×D4C2412yes—
375C22×D4C2412yes—
376C22×D4C2412yes—
377C22×D4C2411yescharacteristic
378C22×D4C24116yes—
379C22×D4C2418yes—
380C22×D4C2418yes—
381C23×C4C2412yes—
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2414yes—
387C23×C4C2418yes—
388C23×C4C2418yes—
389C23×C4C2412yes—
390C23×C4C2411yescharacteristic
391C4⋊Q8—48no—
392C4⋊Q8—48no—
393C4⋊Q8—44no—
394C4⋊Q8—44no—
395#127—48no—
396#127—48no—
397#127—44no—
398#127—44no—
399#125—416no—
400#124—28no—
401#124—28no—
402#124—28no—
403#124—28no—
404#124—216no—
405#124—216no—
406#124—48no—
407#124—48no—
408#124—48no—
409#124—48no—
410#124—44no—
411#124—44no—
412#124—44no—
413#124—44no—
414#123—48no—
415#123—48no—
416#123—432no—
417C22⋊Q8—48no—
418C22⋊Q8—48no—
419#121—432no—
420#121—48no—
421#121—48no—
422#120—48no—
423#120—48no—
424C4×Q8—28no—
425C4×Q8—48no—
426C4×Q8—48no—
427C4×Q8—48no—
428C4×Q8—48no—
429C4×D4—216no—
430C4×D4—28no—
431C4×D4—48no—
432C4×D4—48no—
433C4×D4—48no—
434C4×D4—48no—
435#117—24no—
436#117—24no—
437#117—24no—
438#117—24no—
439#117—24no—
440#117—24no—
441#117—24no—
442#117—28no—
443#117—416no—
444#117—48no—
445#117—48no—
446C2×C4⋊C4—48no—
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C2412yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C2418yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C24116yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2418yes—
464C2×C4⋊C4C2418yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2418yes—
467C2×C4⋊C4C2418yes—
468C2×C22⋊C4—216no—
469C2×C22⋊C4—216no—
470C2×C22⋊C4—48no—
471C2×C22⋊C4—48no—
472C2×C22⋊C4—48no—
473C2×C22⋊C4—48no—
474C2×C22⋊C4C2412yes—
475C2×C22⋊C4C2412yes—
476C2×C22⋊C4C2412yes—
477C2×C22⋊C4C2412yes—
478C2×C22⋊C4C2418yes—
479C2×C22⋊C4C2418yes—
480C2×C22⋊C4C2418yes—
481C2×C22⋊C4C2418yes—
482C2×C22⋊C4C2412yes—
483C2×C22⋊C4C2412yes—
484C2×C22⋊C4C2412yes—
485C2×C22⋊C4C2414yes—
486C2×C22⋊C4C2418yes—
487C2×C22⋊C4C2418yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C24116yes—
490C2×C22⋊C4C24116yes—
491C2×C22⋊C4C2418yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C2418yes—
494C2×C22⋊C4C24116yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C24116yes—
498C2×C22⋊C4C24116yes—
499C2×C22⋊C4C24116yes—
500C2×C42—24no—
501C2×C42—24no—
502C2×C42—28no—
503C2×C42—48no—
504C2×C42#4118yes—
505C2×C42C2414yes—
506C2×C42C2412yes—
507C2×C42C2412yes—
508C2×C42C2412yes—
509C2×C42C2412yes—
510C2×C42C2412yes—
511C2×C42C2412yes—
512C2×C42C2412yes—
513C2×C42C2414yes—
514C2×C42C2412yes—
515C2×C42C2412yes—
516C2×C42C2414yes—
517C2×C42C2412yes—
518C2×C42C2412yes—
519C2×C42C2418yes—
520C2×C42C2418yes—
521C2×C42C2418yes—
522C2×C42C2414yes—
523C2×C42C2414yes—
524C2×C42C2411yescharacteristic
525C2×C42C2412yes—
526C2×C42C2411yescharacteristic
527#95C2418yes—
528#95C2418yes—
529#95C2418yes—
530#95C2418yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C24116yes—
535#95C24116yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C2418yes—
540#95C24116yes—
541#95C24116yes—
542C24—24no—
543C24—24no—
544C24—24no—
545C24—24no—
546C24—24no—
547C24—24no—
548C24—48no—
549C24—48no—
550C24C2514yes—
551C24C2514yes—
552C24C2512yes—
553C24C2511yescharacteristic
554#41—416no—
555C2×Q8—22no—
556C2×Q8—24no—
557C2×Q8—24no—
558C2×Q8—24no—
559C2×Q8—24no—
560C2×Q8—24no—
561C2×Q8—24no—
562C2×Q8—24no—
563C2×Q8—24no—
564C2×Q8—24no—
565C2×Q8—24no—
566C2×Q8—24no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—24no—
570C2×Q8—416no—
571C2×Q8—416no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—22no—
576C2×D4—24no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—24no—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—24no—
586C2×D4—24no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—24no—
590C2×D4—232no—
591C2×D4—416no—
592C2×D4—416no—
593C2×D4—48no—
594C2×D4—48no—
595C2×D4—416no—
596C2×D4—416no—
597C2×D4—416no—
598C2×D4—416no—
599C2×D4—832no—
600C22×C4—24no—
601C22×C4—28no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—28no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—416no—
619C22×C4—416no—
620C22×C4C2×#4118yes—
621C22×C4C2×#4114yes—
622C22×C4H(5,𝔽2)14yes—
623C22×C4H(5,𝔽2)14yes—
624C22×C4C2514yes—
625C22×C4C2514yes—
626C22×C4C2514yes—
627C22×C4C2514yes—
628C22×C4C2514yes—
629C22×C4C2514yes—
630C22×C4C2514yes—
631C22×C4C2514yes—
632C22×C4C2514yes—
633C22×C4C2512yes—
634C22×C4C2514yes—
635C22×C4C2512yes—
636C22×C4C2512yes—
637C22×C4C2514yes—
638C22×C4C2511yescharacteristic
639C22×C4C2511yescharacteristic
640C4⋊C4—24no—
641C4⋊C4—28no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—216no—
649C4⋊C4—216no—
650C4⋊C4—216no—
651C4⋊C4—416no—
652C4⋊C4—48no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—48no—
658C4⋊C4—48no—
659C4⋊C4—48no—
660C4⋊C4—48no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—216no—
669C22⋊C4—216no—
670C22⋊C4—216no—
671C22⋊C4—216no—
672C22⋊C4—28no—
673C22⋊C4—216no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—416no—
677C22⋊C4—416no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—48no—
681C22⋊C4—416no—
682C22⋊C4—48no—
683C22⋊C4—48no—
684C22⋊C4—416no—
685C22⋊C4—416no—
686C22⋊C4—416no—
687C42—24no—
688C42—28no—
689C42—24no—
690C42—24no—
691C42—24no—
692C42—24no—
693C42—24no—
694C42—24no—
695C42—24no—
696C42—24no—
697C42—24no—
698C42—24no—
699C42—28no—
700C42—28no—
701C42—44no—
702C42—44no—
703C42—48no—
704C42—48no—
705C42—48no—
706C42C2×#4114yes—
707C42C2×#4114yes—
708C42C2×#4118yes—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—22no—
713C23—24no—
714C23—24no—
715C23—22no—
716C23—22no—
717C23—24no—
718C23—24no—
719C23—28no—
720C23—216no—
721C23—216no—
722C23—48no—
723C23—48no—
724C23—88no—
725C23—88no—
726C23—88no—
727C23—88no—
728C23—88no—
729C23—88no—
730C23C22×#4112yes—
731C23C2×H(5,𝔽2)12yes—
732C23C2×H(5,𝔽2)12yes—
733C23C2611yescharacteristic
734Q8—48no—
735Q8—48no—
736Q8—48no—
737Q8—48no—
738Q8—44no—
739D4—48no—
740D4—48no—
741D4—48no—
742D4—48no—
743D4—48no—
744D4—44no—
745D4—832no—
746D4—168no—
747D4—168no—
748C2×C4—216no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—28no—
773C2×C4—28no—
774C2×C4—28no—
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—28no—
779C2×C4—48no—
780C2×C4—416no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—168no—
786C2×C4—168no—
787C2×C4#540116yes—
788C2×C4C22×#4114yes—
789C2×C4C22×#4114yes—
790C2×C4C22×#4112yes—
791C2×C4C22×#4112yes—
792C2×C4C2×H(5,𝔽2)12yes—
793C2×C4C2×H(5,𝔽2)12yes—
794C2×C4C2×H(5,𝔽2)12yes—
795C2×C4C2×H(5,𝔽2)12yes—
796C2×C4#58518yes—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—44no—
801C22—48no—
802C22—48no—
803C22—48no—
804C22—48no—
805C22—44no—
806C22—48no—
807C22—44no—
808C22—48no—
809C22—42no—
810C22—44no—
811C22—44no—
812C22—168no—
813C22—168no—
814C22C2×#54014yes—
815C22C23×#4111yescharacteristic
816C22C22×H(5,𝔽2)11yescharacteristic
817C22C22×H(5,𝔽2)11yescharacteristic
818C22C2×#58514yes—
819C4—24no—
820C4—24no—
821C4—28no—
822C4—44no—
823C4—44no—
824C4—44no—
825C4—44no—
826C4—44no—
827C4—44no—
828C4—44no—
829C4—44no—
830C4—42no—
831C4—44no—
832C4—44no—
833C4C2×#54014yes—
834C4C2×#54014yes—
835C2—24no—
836C2—82no—
837C2—84no—
838C2—84no—
839C2C22×#54011yescharacteristic
840C2#6281512yes—
841C2#6282412yes—
842C2#6283612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35528C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40026C2semidirect
2. #40025C2semidirect
3. #38460C2semidirect
4. #37329C2semidirect
5. #36640C2semidirect
6. C2×#2858C2semidirect
7. #35679C2semidirect
8. #35677C2semidirect
9. #35674C2semidirect
10. #35667C2semidirect
11. #35626C2semidirect
12. #35617C2semidirect
13. #35554C2semidirect
15. #35327C2semidirect
16. #35327C2semidirect
17. #35136C2semidirect
18. #34211C2semidirect
19. #34211C2semidirect
20. #34026C2semidirect
36. #2864C22semidirect
37. #2859C22semidirect
42. #2850C22semidirect
43. #2850C22semidirect
44. #2803C22semidirect
45. #2800C22semidirect
46. #2780C22semidirect
47. #2761C22semidirect
48. #2753C22semidirect
49. #2711C22semidirect
50. #2707C22semidirect
51. #2701C22semidirect
52. #2651C22semidirect
53. #2648C22semidirect
54. #2620C22semidirect
55. #2620C22semidirect
56. #2548C22semidirect
57. #2547C22semidirect
58. #2546C22semidirect
59. #2545C22semidirect
60. #2545C22semidirect
61. #2545C22semidirect
62. #2545C22semidirect
64. #2544C22semidirect
65. #2544C22semidirect
66. #2544C22semidirect
70. #2531C22semidirect
71. #2526C22semidirect
75. #2476C22semidirect
76. #2471C22semidirect
77. #2448C22semidirect
78. #2448C22semidirect
79. #2447C22semidirect
80. #2447C22semidirect
81. #2446C22semidirect
82. #2446C22semidirect
85. #2429C22semidirect
87. #2427C22semidirect
88. #2426C22semidirect
94. #2367C22semidirect
95. #2367C22semidirect
98. #2335C22semidirect
99. #2333C22semidirect
100. #2326C22semidirect
101. #2326C22semidirect
110. C4×#125C22semidirect
111. C4×#124C22semidirect
112. C4×#124C22semidirect
113. #2298C22semidirect
122. #2295C22semidirect
123. #2293C22semidirect
129. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#400262
#400252
#384602
#373292
#366402
C2×#28582
#356792
#356772
#356742
#356672
#356262
#356172
#355542
#355282
#353272
#351362
#342112
#340262