Finite Group Databasebeta

← #7646893

Subgroups — #7646893

Order 512.

6952 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#556C211yesmaximal, characteristic, complemented
2C2×#3461C211yesmaximal, characteristic, complemented
3#42802C218yesmaximal, complemented
4#42799C218yesmaximal, complemented
5#39882C218yesmaximal, complemented
6#39879C218yesmaximal, complemented
7#37538C214yesmaximal, complemented
8#36971C214yesmaximal, complemented
9#36719C214yesmaximal, complemented
10#35677C212yesmaximal, complemented
11#35667C212yesmaximal, complemented
12#35327C212yesmaximal, complemented
13#35302C214yesmaximal, complemented
14#35174C211yesmaximal, characteristic, complemented
15#35168C211yesmaximal, characteristic
16#35154C211yesmaximal, characteristic, complemented
17#35153C211yesmaximal, characteristic, complemented
18#34952C212yesmaximal, complemented
19#34182C211yesmaximal, characteristic, complemented
20C2×#556—216no—
21C2×#556C2218yes—
22C2×#556C2218yes—
23#3461—216no—
24C2×#544C2211yescharacteristic
25C2×#542C2214yescomplemented
26C2×#541C2214yescomplemented
27C2×#539C2214yes—
28C2×#537C2211yescharacteristic
29C2×#536C2212yes—
30C2×#536C2212yes—
31C2×#535C2212yes—
32C2×#533C2214yescomplemented
33C22×C4⋊Q8C2211yescharacteristic
34C2×#529C2214yes—
35C2×#529C2214yescomplemented
36C22×#126C2212yes—
37C22×#126C2212yes—
38C22×#124C2211yescharacteristic
39C22×#124C2211yescharacteristic
40C22×C22⋊Q8C2212yes—
41C2×#519C2212yes—
42C2×C4×#41C2212yes—
43C22×C4×Q8C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45C22×C4×Q8C2211yescharacteristic
46C22×C4×D4C2211yescharacteristic
47C22×#117C2212yes—
48#2855C2214yes—
49#2854C2214yes—
50#2850C2218yes—
51#2848C2214yes—
52#2847C2214yes—
53#2823C22116yescomplemented
54#2727C22116yescomplemented
55#2725C22116yescomplemented
56#2705C22116yescomplemented
57#2704C22116yescomplemented
58#2702C22116yescomplemented
59#2702C22116yescomplemented
60#2683C22116yescomplemented
61#2681C22116yescomplemented
62#2664C2218yescomplemented
63#2662C2218yescomplemented
64#2637C2218yescomplemented
65#2636C2218yescomplemented
66#2629C2218yescomplemented
67#2627C2214yes—
68#2626C2214yes—
69#2620C2218yes—
70#2620C2218yescomplemented
71#2618C2214yes—
72#2617C2214yes—
73#2609C22116yescomplemented
74#2601C22116yescomplemented
75#2601C22116yescomplemented
76#2582C2214yescomplemented
77#2581C2214yescomplemented
78#2580C2214yescomplemented
79#2579C2214yes—
80#2579C2214yes—
81#2548C2218yes—
82#2546C2218yescomplemented
83#2545C2214yes—
84#2545C2218yes—
85#2545C2214yes—
86#2545C2218yescomplemented
87#2544C2214yes—
88#2544C2214yes—
89#2538C2214yescomplemented
90#2534C2218yes—
91#2534C2218yes—
92#2487C2214yes—
93#2454C2218yes—
94#2453C2218yescomplemented
95#2452C2218yes—
96#2451C2218yescomplemented
97#2429C2218yescomplemented
98#2429C2218yescomplemented
99#2429C2218yescomplemented
100#2428C2218yes—
101#2427C2218yes—
102#2426C2218yes—
103#2426C2218yes—
104#2426C2218yescomplemented
105#2413C2218yes—
106#2413C2218yes—
107#2411C2218yes—
108#2411C2218yes—
109#2409C2214yes—
110#2396C2218yescomplemented
111#2351C2218yescomplemented
112Q8×C4⋊C4C2218yescomplemented
113#2324C2218yescomplemented
114#2323C2218yescomplemented
115#2316C2211yescharacteristic
116#2316C2211yescharacteristic
117#2316C2214yes—
118#2310C2212yes—
119#2309C2212yes—
120C4×C22⋊Q8C2218yescomplemented
121#2297C2212yes—
122#2297C2212yes—
123#2296C2212yes—
124#2296C2212yes—
125#2285C2212yes—
126#2285C2214yes—
127C22×#41C2312yes—
128C23×Q8C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×Q8C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C24×C4C2312yes—
133#556—264no—
134#556—264no—
135#544—28no—
136#542—232no—
137#541—232no—
138#539—232no—
139#537—28no—
140#536—216no—
141#536—48no—
142#535—48no—
143#533—232no—
144C2×C4⋊Q8—28no—
145C2×C4⋊Q8C2318yes—
146C2×C4⋊Q8C2314yes—
147C2×C4⋊Q8C2314yes—
148C2×C4⋊Q8C2314yes—
149C2×#127C2314yes—
150#529—232no—
151#529—232no—
152C2×#126—216no—
153C2×#126—216no—
154C2×#126C2318yes—
155C2×#126C2318yes—
156C2×#126C2318yes—
157C2×#126C23116yes—
158C2×#126C2318yes—
159C2×#125C2314yes—
160C2×#125C2314yes—
161C2×#125C2318yes—
162C2×#124—28no—
163C2×#124—28no—
164C2×#124C2314yes—
165C2×#124C2314yes—
166C2×#124C2314yes—
167C2×#124C2318yes—
168C2×#124C2314yes—
169C2×#124C2314yes—
170C2×#124C2314yes—
171C2×#123C2318yes—
172C2×#123C2318yes—
173C2×#123C2318yes—
174C2×C22⋊Q8—216no—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C23116yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2318yes—
181C2×C22⋊Q8C2318yes—
182C2×C22⋊Q8C2318yes—
183C2×C22⋊Q8C2318yes—
184C2×#121C2314yes—
185C2×#121C2314yes—
186C2×#121C2318yes—
187C2×#121C2318yes—
188C2×#120C2318yes—
189#519—48no—
190C4×#41—216no—
191C2×C4×Q8—28no—
192C2×C4×Q8—28no—
193C2×C4×Q8D4116yescomplemented
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2312yes—
197C2×C4×Q8C2312yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2318yes—
200C2×C4×Q8C2318yes—
201C2×C4×Q8C2318yes—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2314yes—
204C2×C4×D4—28no—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2312yes—
211C2×#117—216no—
212C2×#117C2312yes—
213C2×#117C2312yes—
214C2×#117C2312yes—
215C2×#117C2318yes—
216C2×#117C2318yes—
217C2×#117C2318yes—
218C2×#117C2314yes—
219C2×#117C2318yes—
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C42C2314yes—
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2312yes—
238C22×C42C2311yescharacteristic
239#400C2318yes—
240#400C2318yes—
241#399C2318yes—
242#399C2318yes—
243#398C2318yes—
244#398C23116yes—
245#398C23116yes—
246#398C2318yes—
247#398C23116yes—
248#398C2318yes—
249#397C2318yes—
250#396C2318yes—
251#396C23116yes—
252#396C23116yes—
253#396C23116yes—
254#396C23116yes—
255#396C23116yes—
256#396C2318yes—
257#396C23116yes—
258#396C23116yes—
259#396C23116yes—
260#395C2318yes—
261#395C2318yes—
262#394C23116yes—
263#394C23116yes—
264#394C23116yes—
265#394C23116yes—
266#394C2318yes—
267#394C23116yes—
268#393C2318yes—
269#393C2318yes—
270#392C2318yes—
271#391C2318yes—
272#391C2314yes—
273#391C2314yes—
274#391C2318yes—
275#391C2314yes—
276#391C2314yes—
277#391C2318yes—
278#390C2318yes—
279#390C2314yes—
280#390C2314yes—
281#390C2318yes—
282#390C23116yes—
283#390C2314yes—
284#390C2314yes—
285#390C23116yes—
286#389C23116yes—
287#389C2318yes—
288#389C2318yes—
289#389C23116yes—
290#389C2318yes—
291#389C23116yes—
292#389C2318yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2318yes—
298#389C23116yes—
299#388C23116yes—
300#388C23116yes—
301#388C23116yes—
302#388C23116yes—
303#388C23116yes—
304#388C23116yes—
305#388C23116yes—
306#387C2318yes—
307#387C2318yes—
308#387C23116yes—
309#386C2314yes—
310#386C2314yes—
311#386C2314yes—
312#386C2314yes—
313#386C23116yes—
314#386C23116yes—
315#386C23116yes—
316#385C2318yes—
317#385C2318yes—
318#385C2314yes—
319#385C2314yes—
320#385C2314yes—
321#385C2314yes—
322#385C23116yes—
323#384C2318yes—
324#384C2314yes—
325#382C2314yes—
326#382C2318yes—
327#381C2318yes—
328#380C2314yes—
329#380C2314yes—
330#380C2314yes—
331#380C2318yes—
332#380C2314yes—
333#380C2318yes—
334#380C2318yes—
335#379C2318yes—
336C4×C4⋊C4C2318yes—
337C4×C4⋊C4C2318yes—
338C4×C4⋊C4C2314yes—
339C4×C4⋊C4C2314yes—
340C4×C4⋊C4C2318yes—
341C4×C4⋊C4C2318yes—
342C4×C22⋊C4C2318yes—
343C4×C22⋊C4C2318yes—
344C25C2412yes—
345C2×#41—28no—
346C2×#41—28no—
347C2×#41—28no—
348C22×Q8—24no—
349C22×Q8—24no—
350C22×Q8—24no—
351C22×Q8—24no—
352C22×Q8—24no—
353C22×Q8—24no—
354C22×Q8—44no—
355C22×Q8C2×D418yes—
356C22×Q8C2414yes—
357C22×Q8C2412yes—
358C22×Q8C2414yes—
359C22×Q8C2414yes—
360C22×Q8C2414yes—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4C2414yes—
365C22×D4C2414yes—
366C22×D4C2412yes—
367C22×D4C2414yes—
368C22×D4C24116yes—
369C23×C4—28no—
370C23×C4—48no—
371C23×C4C2412yes—
372C23×C4C2411yescharacteristic
373C23×C4C2414yes—
374C23×C4C2418yes—
375C23×C4C2412yes—
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2414yes—
380C23×C4C2414yes—
381C23×C4C2411yescharacteristic
382C23×C4C2411yescharacteristic
383C23×C4C2412yes—
384C23×C4C2411yescharacteristic
385C4⋊Q8—232no—
386C4⋊Q8—216no—
387C4⋊Q8—216no—
388C4⋊Q8—48no—
389#127—48no—
390#126—264no—
391#126—232no—
392#126—232no—
393#126—232no—
394#126—232no—
395#125—216no—
396#125—232no—
397#125—216no—
398#124—232no—
399#124—216no—
400#124—216no—
401#124—216no—
402#124—216no—
403#124—48no—
404#124—48no—
405#123—232no—
406#123—232no—
407#123—416no—
408C22⋊Q8—216no—
409C22⋊Q8—216no—
410C22⋊Q8—216no—
411C22⋊Q8—264no—
412C22⋊Q8—216no—
413C22⋊Q8—232no—
414C22⋊Q8—416no—
415C22⋊Q8—416no—
416C22⋊Q8—416no—
417#121—216no—
418#121—216no—
419#121—416no—
420#121—416no—
421#120—416no—
422C4×Q8—232no—
423C4×Q8—216no—
424C4×Q8—216no—
425C4×Q8—28no—
426C4×Q8—28no—
427C4×Q8—216no—
428C4×Q8—416no—
429C4×Q8—416no—
430C4×Q8C2×D4132yes—
431C4×Q8C2×D4132yes—
432C4×D4—216no—
433C4×D4—216no—
434C4×D4—232no—
435C4×D4—28no—
436C4×D4—28no—
437C4×D4—216no—
438#117—28no—
439#117—28no—
440#117—28no—
441#117—232no—
442#117—232no—
443#117—216no—
444#117—232no—
445#117—416no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—28no—
448C2×C4⋊C4—28no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—28no—
452C2×C4⋊C4C2×D418yes—
453C2×C4⋊C4C2×D4116yes—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2412yes—
456C2×C4⋊C4C2418yes—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2414yes—
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2412yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2418yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C24116yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C24116yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2418yes—
480C2×C4⋊C4C2418yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2418yes—
485C2×C22⋊C4—28no—
486C2×C22⋊C4—28no—
487C2×C22⋊C4—28no—
488C2×C22⋊C4—28no—
489C2×C22⋊C4—28no—
490C2×C22⋊C4C2414yes—
491C2×C22⋊C4C2418yes—
492C2×C22⋊C4C2414yes—
493C2×C22⋊C4C2418yes—
494C2×C22⋊C4C2418yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C2414yes—
497C2×C22⋊C4C2414yes—
498C2×C22⋊C4C2414yes—
499C2×C22⋊C4C2414yes—
500C2×C22⋊C4C2414yes—
501C2×C22⋊C4C2418yes—
502C2×C22⋊C4C2418yes—
503C2×C22⋊C4C2418yes—
504C2×C22⋊C4C2418yes—
505C2×C22⋊C4C24116yes—
506C2×C22⋊C4C24116yes—
507C2×C22⋊C4C2418yes—
508C2×C22⋊C4C24116yes—
509C2×C22⋊C4C2418yes—
510C2×C22⋊C4C2418yes—
511C2×C22⋊C4C24116yes—
512C2×C42—28no—
513C2×C42—24no—
514C2×C42—24no—
515C2×C42—216no—
516C2×C42C2×D4116yes—
517C2×C42C2×D418yes—
518C2×C42C2414yes—
519C2×C42C2418yes—
520C2×C42C2414yes—
521C2×C42C2414yes—
522C2×C42C2414yes—
523C2×C42C2414yes—
524C2×C42C2414yes—
525C2×C42C2414yes—
526C2×C42C24116yes—
527C2×C42C2414yes—
528C2×C42C2412yes—
529C2×C42C2414yes—
530C2×C42C2412yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C2418yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C24116yes—
544#95C24116yes—
545C24—24no—
546C24—24no—
547C24—24no—
548C24—44no—
549C24—44no—
550C24C2514yes—
551C24C2514yes—
552C24C2511yescharacteristic
553#41—432no—
554C2×Q8—232no—
555C2×Q8—28no—
556C2×Q8—24no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—24no—
562C2×Q8—28no—
563C2×Q8—28no—
564C2×Q8—24no—
565C2×Q8—28no—
566C2×Q8—44no—
567C2×Q8—48no—
568C2×Q8—416no—
569C2×Q8—416no—
570C2×Q8C22×D4116yes—
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—24no—
575C2×D4—28no—
576C2×D4—28no—
577C2×D4—28no—
578C2×D4—24no—
579C2×D4—28no—
580C2×D4—24no—
581C2×D4—48no—
582C2×D4—416no—
583C2×D4—416no—
584C2×D4—416no—
585C2×D4—416no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—216no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—216no—
602C22×C4—28no—
603C22×C4—44no—
604C22×C4—48no—
605C22×C4—42no—
606C22×C4—48no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—48no—
612C22×C4—432no—
613C22×C4C22×D418yes—
614C22×C4C22×D418yes—
615C22×C4C22×D414yes—
616C22×C4C22×D414yes—
617C22×C4C22×D414yes—
618C22×C4H(5,𝔽2)14yes—
619C22×C42−1+414yes—
620C22×C4C2518yes—
621C22×C4C2512yes—
622C22×C4C2518yes—
623C22×C4C2512yes—
624C22×C4C2514yes—
625C22×C4C2514yes—
626C22×C4C2514yes—
627C22×C4C2512yes—
628C22×C4C2514yes—
629C22×C4C2511yescharacteristic
630C22×C4C2512yes—
631C22×C4C2514yes—
632C22×C4C2511yescharacteristic
633C22×C4C2514yes—
634C22×C4C2512yes—
635C22×C4C2512yes—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—216no—
639C4⋊C4—216no—
640C4⋊C4—28no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—216no—
644C4⋊C4—24no—
645C4⋊C4—28no—
646C4⋊C4—24no—
647C4⋊C4—28no—
648C4⋊C4—216no—
649C4⋊C4—216no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—216no—
653C4⋊C4—28no—
654C4⋊C4—28no—
655C4⋊C4—216no—
656C4⋊C4—48no—
657C4⋊C4—48no—
658C4⋊C4—48no—
659C4⋊C4—416no—
660C4⋊C4—48no—
661C4⋊C4—48no—
662C4⋊C4—48no—
663C4⋊C4—48no—
664C4⋊C4—416no—
665C4⋊C4C22×D4116yes—
666C4⋊C4C22×D4132yes—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—216no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—216no—
674C22⋊C4—216no—
675C22⋊C4—216no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—216no—
679C22⋊C4—216no—
680C22⋊C4—216no—
681C22⋊C4—216no—
682C22⋊C4—48no—
683C22⋊C4—416no—
684C22⋊C4—48no—
685C22⋊C4—416no—
686C22⋊C4—416no—
687C22⋊C4—48no—
688C22⋊C4—416no—
689C42—28no—
690C42—216no—
691C42—28no—
692C42—28no—
693C42—28no—
694C42—28no—
695C42—28no—
696C42—28no—
697C42—416no—
698C42C22×D418yes—
699C42C22×D4116yes—
700C42C22×D418yes—
701C42C22×D4116yes—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—48no—
715C23—48no—
716C23—48no—
717C23—88no—
718C23—88no—
719C23C23×D412yes—
720C23C2×H(5,𝔽2)12yes—
721C23C2×2−1+412yes—
722C23C2611yescharacteristic
723Q8—232no—
724Q8—416no—
725Q8—416no—
726Q8—48no—
727Q8—88no—
728D4—416no—
729D4—416no—
730D4—48no—
731D4—88no—
732D4—1616no—
733C2×C4—28no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—28no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—216no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—28no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—24no—
764C2×C4—28no—
765C2×C4—22no—
766C2×C4—48no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—432no—
770C2×C4—416no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—48no—
775C2×C4—416no—
776C2×C4—88no—
777C2×C4#537116yes—
778C2×C4C23×D412yes—
779C2×C4C23×D414yes—
780C2×C4C23×D418yes—
781C2×C4C23×D412yes—
782C2×C4C23×D418yes—
783C2×C4C23×D414yes—
784C2×C4C2×H(5,𝔽2)14yes—
785C2×C4C2×2−1+414yes—
786C2×C4#58514yes—
787C22—22no—
788C22—22no—
789C22—24no—
790C22—24no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—48no—
798C22—48no—
799C22—48no—
800C22—48no—
801C22—816no—
802C22C2×#53714yes—
803C22C24×D411yescharacteristic
804C22C22×H(5,𝔽2)11yescharacteristic
805C22C22×2−1+411yescharacteristic
806C22C2×#58512yes—
807C222−1+612yes—
808C4—24no—
809C4—28no—
810C4—24no—
811C4—22no—
812C4—22no—
813C4—28no—
814C4—42no—
815C4—44no—
816C4—42no—
817C4—44no—
818C4—42no—
819C4—44no—
820C4—44no—
821C4—48no—
822C4—48no—
823C4C2×#53718yes—
824C2—24no—
825C2—84no—
826C2—84no—
827C2C22×#53711yescharacteristic
828C2#6281111yescharacteristic
829C2#6284811yescharacteristic
830C2#6293112yes—
831C2#6293212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35168C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#556C2semidirect
2. C2×#3461C2semidirect
3. #42802C2semidirect
4. #42799C2semidirect
5. #39882C2semidirect
6. #39879C2semidirect
7. #37538C2semidirect
8. #36971C2semidirect
9. #36719C2semidirect
10. #35677C2semidirect
11. #35667C2semidirect
12. #35327C2semidirect
13. #35302C2semidirect
14. #35174C2semidirect
16. #35154C2semidirect
17. #35153C2semidirect
18. #34952C2semidirect
19. #34182C2semidirect
25. C2×#542C22semidirect
26. C2×#541C22semidirect
32. C2×#533C22semidirect
35. C2×#529C22semidirect
53. #2823C22semidirect
54. #2727C22semidirect
55. #2725C22semidirect
56. #2705C22semidirect
57. #2704C22semidirect
58. #2702C22semidirect
59. #2702C22semidirect
60. #2683C22semidirect
61. #2681C22semidirect
62. #2664C22semidirect
63. #2662C22semidirect
64. #2637C22semidirect
65. #2636C22semidirect
66. #2629C22semidirect
70. #2620C22semidirect
73. #2609C22semidirect
74. #2601C22semidirect
75. #2601C22semidirect
76. #2582C22semidirect
77. #2581C22semidirect
78. #2580C22semidirect
82. #2546C22semidirect
86. #2545C22semidirect
89. #2538C22semidirect
94. #2453C22semidirect
96. #2451C22semidirect
97. #2429C22semidirect
98. #2429C22semidirect
99. #2429C22semidirect
104. #2426C22semidirect
110. #2396C22semidirect
111. #2351C22semidirect
112. Q8×C4⋊C4C22semidirect
113. #2324C22semidirect
114. #2323C22semidirect
120. C4×C22⋊Q8C22semidirect
193. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5562
C2×#34612
#428022
#427992
#398822
#398792
#375382
#369712
#367192
#356772
#356672
#353272
#353022
#351742
#351682
#351542
#351532
#349522
#341822