Finite Group Databasebeta

← #7654966

Subgroups — #7654966

Order 512.

5706 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42983C213yesmaximal, complemented
2#42982C213yesmaximal, complemented
3#42919C216yesmaximal, complemented
4#40056C216yesmaximal, complemented
5#40044C216yesmaximal, complemented
6#39034C216yesmaximal, complemented
7#39020C216yesmaximal, complemented
8#37514C213yesmaximal, complemented
9#36585C212yesmaximal, complemented
10#36578C212yesmaximal, complemented
11#36467C212yesmaximal, complemented
12#36434C212yesmaximal, complemented
13#36082C212yesmaximal, complemented
14#36040C211yesmaximal, characteristic, complemented
15#35737C211yesmaximal, characteristic, complemented
16#35025C216yesmaximal, complemented
17#34962C213yesmaximal, complemented
18#34258C211yesmaximal, characteristic, complemented
19C4×#548C212yesmaximal, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×#557C2211yescharacteristic, complemented
22C2×D4×Q8C2211yescharacteristic, complemented
23C2×#548C2212yes—
24C2×#548C2212yes—
25C2×#548C2212yes—
26C2×#520C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28C22×C4×Q8C2212yescomplemented
29#2861C2216yescomplemented
30#2860C2216yescomplemented
31#2854C2216yescomplemented
32#2850C2216yescomplemented
33#2833C2216yescomplemented
34#2830C2216yescomplemented
35#2781C22112yescomplemented
36#2778C22112yescomplemented
37#2778C22112yescomplemented
38#2741C22112yescomplemented
39#2736C2216yescomplemented
40#2735C22112yescomplemented
41#2735C2216yescomplemented
42#2735C2216yescomplemented
43#2684C22112yescomplemented
44#2668C2216yescomplemented
45#2653C22112yescomplemented
46#2651C22112yescomplemented
47#2649C22112yescomplemented
48#2648C22112yescomplemented
49#2628C2213yescomplemented
50#2621C2213yescomplemented
51#2616C2216yes—
52#2593C2216yescomplemented
53#2593C2213yescomplemented
54#2592C2216yescomplemented
55#2586C2213yescomplemented
56#2580C2213yescomplemented
57#2574C2216yescomplemented
58#2572C2211yescharacteristic, complemented
59#2563C2213yescomplemented
60#2562C2216yescomplemented
61#2555C2213yescomplemented
62#2554C2216yescomplemented
63#2547C2213yescomplemented
64#2545C2216yescomplemented
65#2536C2216yescomplemented
66#2535C2213yescomplemented
67#2518C2216yescomplemented
68#2513C2216yescomplemented
69#2513C2216yescomplemented
70#2513C2216yescomplemented
71#2504C2216yescomplemented
72#2494C2216yescomplemented
73#2494C2216yescomplemented
74#2494C2216yescomplemented
75#2492C2216yescomplemented
76#2491C2216yescomplemented
77#2490C2216yescomplemented
78#2489C2216yescomplemented
79#2487C2216yescomplemented
80#2480C22112yescomplemented
81#2467C2216yescomplemented
82#2459C2216yescomplemented
83#2456C2216yescomplemented
84#2454C2216yescomplemented
85#2448C2216yescomplemented
86#2448C2216yescomplemented
87#2442C2216yescomplemented
88#2435C2216yes—
89#2435C2216yes—
90#2435C2216yes—
91#2429C2216yescomplemented
92#2427C2216yescomplemented
93#2426C2216yescomplemented
94#2421C2216yescomplemented
95#2421C2216yescomplemented
96#2418C22112yescomplemented
97#2417C2216yescomplemented
98#2417C2216yescomplemented
99#2416C2216yescomplemented
100#2408C2216yes—
101#2408C2216yes—
102#2408C2216yes—
103#2396C2213yescomplemented
104#2392C2213yescomplemented
105#2388C2216yes—
106#2367C2216yescomplemented
107#2362C2216yescomplemented
108#2361C2216yescomplemented
109#2352C2216yescomplemented
110#2351C2212yescomplemented
111#2351C2212yescomplemented
112#2351C2211yescharacteristic, complemented
113#2351C2211yescharacteristic, complemented
114#2341C2212yes—
115#2341C2212yes—
116#2341C2212yes—
117#2341C2212yes—
118#2341C2212yes—
119Q8×C22⋊C4C2212yescomplemented
120Q8×C22⋊C4C2212yescomplemented
121D4×C22⋊C4C2216yes—
122D4×C22⋊C4C2216yes—
123#2321C22112yescomplemented
124#2312C22112yescomplemented
125#2311C2213yes—
126#2309C2213yes—
127C4×#126C2216yescomplemented
128C4×#124C2216yescomplemented
129C4×#124C2216yescomplemented
130C4×C22⋊Q8C2216yescomplemented
131C4×#123C2216yescomplemented
132C4×#121C2216yescomplemented
133C4×#121C2216yescomplemented
134#2297C2213yes—
135C2×#390C2213yes—
136C42×Q8C2212yescomplemented
137C42×D4C2216yescomplemented
138C2×H(5,𝔽2)—28no—
139C2×H(5,𝔽2)—44no—
140C2×H(5,𝔽2)—44no—
141C22×#41C2312yes—
142C22×#41C2311yescharacteristic
143C22×#41C2313yes—
144C23×Q8C2312yes—
145C23×D4C2313yes—
146C23×D4C2316yes—
147#557—44no—
148D4×Q8—44no—
149#548—216no—
150#548—48no—
151#548—48no—
152C2×C4⋊Q8C2313yes—
153C2×C4⋊Q8C2313yes—
154C2×#126C2316yes—
155C2×#125C2316yes—
156C2×#124C2316yes—
157C2×#124C2316yes—
158C2×#124C2316yes—
159C2×#124C2316yes—
160C2×#123C2316yes—
161C2×C22⋊Q8C2316yes—
162C2×C22⋊Q8C2316yes—
163C2×C22⋊Q8C2316yes—
164C2×C22⋊Q8C2316yes—
165C2×#121C2316yes—
166C2×#121C2316yes—
167C2×#121C2316yes—
168C2×#121C2316yes—
169C2×#120C23112yes—
170#520—44no—
171C4×#41—44no—
172C2×C4×Q8—48no—
173C2×C4×Q8C2311yescharacteristic
174C2×C4×Q8C2312yes—
175C2×C4×Q8C2312yes—
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2312yes—
178C2×C4×Q8C2311yescharacteristic
179C2×C4×Q8C2313yes—
180C2×C4×Q8C2316yes—
181C2×C4×Q8C2316yes—
182C2×C4×D4C2316yes—
183C2×C4×D4C2316yes—
184C2×C4×D4C2313yes—
185C2×C4×D4C2316yes—
186C2×C4×D4C2316yes—
187C2×C4×D4C2313yes—
188C2×C4×D4C2316yes—
189C2×C4×D4C2313yes—
190C2×C4×D4C2316yes—
191C2×#117C2313yes—
192C2×#117C2313yes—
193C22×C4⋊C4C2313yes—
194C22×C4⋊C4C2316yes—
195C22×C22⋊C4C23112yes—
196C22×C42C2316yes—
197C22×C42C2313yes—
198#401C23112yes—
199#400C23112yes—
200#400C2311yescharacteristic
201#400C2316yes—
202#400C23112yes—
203#399C2313yes—
204#399C2316yes—
205#399C23112yes—
206#398C2316yes—
207#398C2313yes—
208#398C2316yes—
209#398C23112yes—
210#397C23112yes—
211#397C23112yes—
212#397C23112yes—
213#397C2316yes—
214#397C2316yes—
215#397C2313yes—
216#397C23112yes—
217#397C23112yes—
218#397C23112yes—
219#396C2316yes—
220#396C23112yes—
221#396C23112yes—
222#396C2316yes—
223#395C2316yes—
224#395C2313yes—
225#394C23112yes—
226#394C2311yescharacteristic
227#394C23112yes—
228#394C2316yes—
229#394C23112yes—
230#394C23112yes—
231#394C2316yes—
232#394C2316yes—
233#394C2316yes—
234#394C23112yes—
235#393C2313yes—
236#393C2316yes—
237#393C2312yes—
238#393C23112yes—
239#392C2316yes—
240#392C2316yes—
241#392C2316yes—
242#392C2313yes—
243#391C2313yes—
244#391C2311yescharacteristic
245#391C2316yes—
246#391C2316yes—
247#391C2316yes—
248#391C2316yes—
249#391C2316yes—
250#390C2316yes—
251#390C2313yes—
252#390C2316yes—
253#390C2316yes—
254#390C2316yes—
255#390C2316yes—
256#390C2316yes—
257#390C2316yes—
258#390C2316yes—
259#390C2313yes—
260#390C2316yes—
261#390C2316yes—
262#390C2316yes—
263#390C2316yes—
264#390C2316yes—
265#389C2316yes—
266#389C2316yes—
267#389C2316yes—
268#389C2316yes—
269#389C2316yes—
270#389C2316yes—
271#389C2316yes—
272#388C2316yes—
273#388C2316yes—
274#388C2316yes—
275#388C2316yes—
276#388C23112yes—
277#388C2316yes—
278#388C23112yes—
279#388C23112yes—
280#388C23112yes—
281#388C23112yes—
282#388C23112yes—
283#388C23112yes—
284#388C2312yes—
285#388C2316yes—
286#388C23112yes—
287#388C23112yes—
288#388C23112yes—
289#388C2316yes—
290#388C2316yes—
291#388C2316yes—
292#388C2316yes—
293#388C23112yes—
294#388C23112yes—
295#388C23112yes—
296#387C2316yes—
297#387C2316yes—
298#387C2316yes—
299#387C2316yes—
300#387C23112yes—
301#387C2316yes—
302#386C23112yes—
303#386C2312yes—
304#386C23112yes—
305#386C23112yes—
306#386C23112yes—
307#386C2316yes—
308#386C2316yes—
309#386C2316yes—
310#386C23112yes—
311#386C2316yes—
312#385C2316yes—
313#385C23112yes—
314#385C23112yes—
315#383C2312yes—
316#382C2316yes—
317#382C2316yes—
318#382C2313yes—
319#382C2316yes—
320#382C2313yes—
321#381C2312yes—
322#380C2316yes—
323#380C2316yes—
324#380C2316yes—
325#380C2316yes—
326#380C23112yes—
327#380C2316yes—
328#380C23112yes—
329#380C2316yes—
330#380C2316yes—
331#380C2316yes—
332#379C2316yes—
333#379C2316yes—
334#379C23112yes—
335#379C23112yes—
336#379C23112yes—
337C4×C4⋊C4C2313yes—
338C4×C4⋊C4C2316yes—
339C4×C4⋊C4C2316yes—
340C4×C4⋊C4C2316yes—
341C4×C4⋊C4C2313yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C2316yes—
344C4×C4⋊C4C2316yes—
345C4×C4⋊C4C2316yes—
346C4×C22⋊C4C2316yes—
347C4×C22⋊C4C2316yes—
348C4×C22⋊C4C2316yes—
349C4×C22⋊C4C2316yes—
350C4×C22⋊C4C23112yes—
351C4×C22⋊C4C2312yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356C4×C22⋊C4C2316yes—
357C4×C22⋊C4C2316yes—
358C43C2316yes—
359C25C2416yes—
360H(5,𝔽2)—464no—
361C2×#41—28no—
362C2×#41—24no—
363C2×#41—24no—
364C2×#41—28no—
365C2×#41—28no—
366C2×#41—212no—
367C2×#41—46no—
368C2×#41—46no—
369C2×#41#4118yes—
370C22×Q8—28no—
371C22×Q8—28no—
372C22×Q8—28no—
373C22×Q8C2416yes—
374C22×Q8C2411yescharacteristic
375C22×Q8C2413yes—
376C22×Q8C2411yescharacteristic
377C22×D4—224no—
378C22×D4—212no—
379C22×D4—46no—
380C22×D4—46no—
381C22×D4—412no—
382C22×D4—412no—
383C22×D4C2416yes—
384C22×D4C2416yes—
385C22×D4C2411yescharacteristic
386C22×D4C2413yes—
387C22×D4C2416yes—
388C22×D4C2416yes—
389C22×D4C2416yes—
390C22×D4C2413yes—
391C23×C4C2416yes—
392C23×C4C2416yes—
393C23×C4C2412yes—
394C23×C4C2413yes—
395C23×C4C2416yes—
396C23×C4C2416yes—
397C23×C4C2416yes—
398C4⋊Q8—46no—
399C4⋊Q8—46no—
400#126—412no—
401#125—412no—
402#124—224no—
403#124—412no—
404#124—412no—
405#124—412no—
406#123—412no—
407C22⋊Q8—224no—
408C22⋊Q8—412no—
409C22⋊Q8—412no—
410C22⋊Q8—412no—
411#121—224no—
412#121—412no—
413#121—412no—
414#121—412no—
415#120—424no—
416C4×Q8—28no—
417C4×Q8—28no—
418C4×Q8—28no—
419C4×Q8—24no—
420C4×Q8—24no—
421C4×Q8—28no—
422C4×Q8—46no—
423C4×Q8—412no—
424C4×Q8—412no—
425C4×D4—224no—
426C4×D4—412no—
427C4×D4—46no—
428C4×D4—46no—
429C4×D4—412no—
430C4×D4—412no—
431C4×D4—46no—
432C4×D4—412no—
433C4×D4—412no—
434#117—46no—
435#117—46no—
436C2×C4⋊C4—412no—
437C2×C4⋊C4—46no—
438C2×C4⋊C4C2416yes—
439C2×C4⋊C4C2413yes—
440C2×C4⋊C4C2413yes—
441C2×C4⋊C4C2416yes—
442C2×C4⋊C4C2416yes—
443C2×C4⋊C4C2416yes—
444C2×C4⋊C4C2416yes—
445C2×C4⋊C4C2416yes—
446C2×C4⋊C4C2413yes—
447C2×C4⋊C4C24112yes—
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2416yes—
450C2×C4⋊C4C2416yes—
451C2×C4⋊C4C2413yes—
452C2×C4⋊C4C2416yes—
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2416yes—
455C2×C4⋊C4C2416yes—
456C2×C4⋊C4C2416yes—
457C2×C4⋊C4C2416yes—
458C2×C4⋊C4C2416yes—
459C2×C4⋊C4C2416yes—
460C2×C4⋊C4C2416yes—
461C2×C22⋊C4—424no—
462C2×C22⋊C4C2416yes—
463C2×C22⋊C4C2416yes—
464C2×C22⋊C4C2412yes—
465C2×C22⋊C4C2412yes—
466C2×C22⋊C4C2416yes—
467C2×C22⋊C4C2416yes—
468C2×C22⋊C4C24112yes—
469C2×C22⋊C4C2412yes—
470C2×C22⋊C4C24112yes—
471C2×C22⋊C4C24112yes—
472C2×C22⋊C4C2416yes—
473C2×C22⋊C4C2413yes—
474C2×C22⋊C4C2413yes—
475C2×C22⋊C4C2412yes—
476C2×C22⋊C4C2412yes—
477C2×C22⋊C4C2416yes—
478C2×C22⋊C4C2416yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C2416yes—
481C2×C22⋊C4C2416yes—
482C2×C22⋊C4C24112yes—
483C2×C22⋊C4C24112yes—
484C2×C22⋊C4C24112yes—
485C2×C22⋊C4C24112yes—
486C2×C22⋊C4C24112yes—
487C2×C22⋊C4C2416yes—
488C2×C22⋊C4C2416yes—
489C2×C22⋊C4C2416yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C2416yes—
492C2×C22⋊C4C2416yes—
493C2×C22⋊C4C2416yes—
494C2×C42—412no—
495C2×C42—46no—
496C2×C42C2413yes—
497C2×C42C2413yes—
498C2×C42C2416yes—
499C2×C42C2416yes—
500C2×C42C2416yes—
501C2×C42C2416yes—
502C2×C42C2412yes—
503C2×C42C2413yes—
504C2×C42C2416yes—
505C2×C42C2416yes—
506C2×C42C2416yes—
507C2×C42C2416yes—
508C2×C42C2416yes—
509C2×C42C2411yescharacteristic
510#95C2412yes—
511#95C2412yes—
512#95C2412yes—
513#95C2412yes—
514#95C2412yes—
515#95C2412yes—
516#95C2416yes—
517#95C2416yes—
518#95C2416yes—
519#95C2416yes—
520#95C2416yes—
521#95C2416yes—
522#95C2416yes—
523#95C2416yes—
524#95C2416yes—
525#95C24112yes—
526#95C24112yes—
527#95C2416yes—
528#95C2411yescharacteristic
529#95C2411yescharacteristic
530#95C2412yes—
531#95C24112yes—
532#95C2416yes—
533#95C2413yes—
534#95C2413yes—
535#95C24112yes—
536#95C24112yes—
537#95C2416yes—
538#95C2416yes—
539C24—212no—
540C24—46no—
541C24—46no—
542C24—412no—
543C24—412no—
544C24C2516yes—
545C24C2513yes—
546C24C2512yes—
547#41—232no—
548#41—448no—
549#41—432no—
550C2×Q8—212no—
551C2×Q8—22no—
552C2×Q8—212no—
553C2×Q8—212no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—43no—
557C2×Q8—46no—
558C2×Q8—432no—
559C2×Q8C2×#4114yes—
560C2×Q8H(5,𝔽2)14yes—
561C2×Q8H(5,𝔽2)14yes—
562C2×D4—212no—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—24no—
566C2×D4—212no—
567C2×D4—212no—
568C2×D4—26no—
569C2×D4—212no—
570C2×D4—26no—
571C2×D4—26no—
572C2×D4—212no—
573C2×D4—212no—
574C2×D4—41no—
575C2×D4—46no—
576C2×D4—43no—
577C2×D4—43no—
578C2×D4—46no—
579C2×D4—46no—
580C2×D4—448no—
581C2×D4—46no—
582C2×D4—46no—
583C2×D4—46no—
584C2×D4—46no—
585C2×D4—496no—
586C2×D4C2×#41112yes—
587C22×C4—26no—
588C22×C4—26no—
589C22×C4—24no—
590C22×C4—212no—
591C22×C4—212no—
592C22×C4—212no—
593C22×C4—212no—
594C22×C4—212no—
595C22×C4—212no—
596C22×C4—24no—
597C22×C4—212no—
598C22×C4—42no—
599C22×C4—46no—
600C22×C4—46no—
601C22×C4—46no—
602C22×C4—46no—
603C22×C4—46no—
604C22×C4—412no—
605C22×C4—46no—
606C22×C4C2×#41112yes—
607C22×C4C2512yes—
608C22×C4C2511yescharacteristic
609C22×C4C2516yes—
610C22×C4C2512yes—
611C22×C4C2516yes—
612C22×C4C2516yes—
613C22×C4C2516yes—
614C22×C4C2513yes—
615C22×C4C2513yes—
616C22×C4C2512yes—
617C22×C4C2511yescharacteristic
618C22×C4C2516yes—
619C22×C4C2512yes—
620C22×C4C2511yescharacteristic
621C22×C4C2512yes—
622C22×C4C2513yes—
623C4⋊C4—212no—
624C4⋊C4—212no—
625C4⋊C4—212no—
626C4⋊C4—26no—
627C4⋊C4—26no—
628C4⋊C4—212no—
629C4⋊C4—212no—
630C4⋊C4—212no—
631C4⋊C4—43no—
632C4⋊C4—412no—
633C4⋊C4—41no—
634C4⋊C4—46no—
635C4⋊C4—46no—
636C4⋊C4—46no—
637C4⋊C4—43no—
638C4⋊C4—41no—
639C4⋊C4—46no—
640C4⋊C4—46no—
641C4⋊C4—46no—
642C4⋊C4—46no—
643C4⋊C4—46no—
644C4⋊C4—46no—
645C4⋊C4—46no—
646C22⋊C4—212no—
647C22⋊C4—224no—
648C22⋊C4—212no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—212no—
652C22⋊C4—212no—
653C22⋊C4—24no—
654C22⋊C4—412no—
655C22⋊C4—412no—
656C22⋊C4—43no—
657C22⋊C4—43no—
658C22⋊C4—46no—
659C22⋊C4—46no—
660C22⋊C4—46no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—46no—
664C22⋊C4—46no—
665C22⋊C4—46no—
666C22⋊C4—412no—
667C22⋊C4—412no—
668C22⋊C4—412no—
669C22⋊C4—46no—
670C22⋊C4—412no—
671C22⋊C4—412no—
672C22⋊C4—46no—
673C22⋊C4—46no—
674C22⋊C4—46no—
675C22⋊C4—46no—
676C22⋊C4—46no—
677C22⋊C4—46no—
678C42—212no—
679C42—212no—
680C42—212no—
681C42—26no—
682C42—26no—
683C42—212no—
684C42—24no—
685C42—41no—
686C42—43no—
687C42—46no—
688C42—46no—
689C42—46no—
690C42—46no—
691C42—46no—
692C23—22no—
693C23—22no—
694C23—23no—
695C23—23no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—26no—
700C23—26no—
701C23—22no—
702C23—26no—
703C23—26no—
704C23—26no—
705C23—26no—
706C23—26no—
707C23—26no—
708C23—26no—
709C23—424no—
710C23—824no—
711C23—1612no—
712C23—166no—
713C23—166no—
714C23C22×#4116yes—
715C23#58514yes—
716C23C2611yescharacteristic
717Q8—44no—
718Q8—424no—
719Q8—86no—
720Q8#538116yes—
721D4—224no—
722D4—412no—
723D4—44no—
724D4—424no—
725D4—424no—
726D4—424no—
727D4—812no—
728D4—812no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—224no—
734C2×C4—22no—
735C2×C4—26no—
736C2×C4—26no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—26no—
743C2×C4—26no—
744C2×C4—23no—
745C2×C4—26no—
746C2×C4—23no—
747C2×C4—26no—
748C2×C4—26no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—26no—
756C2×C4—26no—
757C2×C4—26no—
758C2×C4—26no—
759C2×C4—26no—
760C2×C4—26no—
761C2×C4—26no—
762C2×C4—22no—
763C2×C4—26no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—26no—
769C2×C4—48no—
770C2×C4—424no—
771C2×C4—424no—
772C2×C4—812no—
773C2×C4—812no—
774C2×C4—166no—
775C2×C4C22×#4112yes—
776C2×C4C22×#4116yes—
777C2×C4C2×H(5,𝔽2)16yes—
778C2×C4C2×H(5,𝔽2)16yes—
779C2×C4#58514yes—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—212no—
784C22—26no—
785C22—42no—
786C22—46no—
787C22—43no—
788C22—43no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—46no—
793C22—46no—
794C22—46no—
795C22—46no—
796C22—46no—
797C22—46no—
798C22—46no—
799C22—1624no—
800C22C23×#4111yescharacteristic
801C22C22×H(5,𝔽2)11yescharacteristic
802C22C22×H(5,𝔽2)11yescharacteristic
803C22C2×#58512yes—
804C22C2×#58512yes—
805C4—24no—
806C4—22no—
807C4—42no—
808C4—46no—
809C4—46no—
810C4—41no—
811C4—46no—
812C4—41no—
813C4—42no—
814C4—43no—
815C4—43no—
816C4—42no—
817C4—46no—
818C4—42no—
819C4—46no—
820C4C2×#538112yes—
821C2—44no—
822C2—46no—
823C2—86no—
824C2C22×#53811yescharacteristic
825C2#6281012yes—
826C2#6302012yes—
827C2#6302011yescharacteristic
828C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42983C2semidirect
2. #42982C2semidirect
3. #42919C2semidirect
4. #40056C2semidirect
5. #40044C2semidirect
6. #39034C2semidirect
7. #39020C2semidirect
8. #37514C2semidirect
9. #36585C2semidirect
10. #36578C2semidirect
11. #36467C2semidirect
12. #36434C2semidirect
13. #36082C2semidirect
14. #36040C2semidirect
15. #35737C2semidirect
16. #35025C2semidirect
17. #34962C2semidirect
18. #34258C2semidirect
19. C4×#548C2semidirect
21. C2×#557C22semidirect
22. C2×D4×Q8C22semidirect
28. C22×C4×Q8C22semidirect
29. #2861C22semidirect
30. #2860C22semidirect
31. #2854C22semidirect
32. #2850C22semidirect
33. #2833C22semidirect
34. #2830C22semidirect
35. #2781C22semidirect
36. #2778C22semidirect
37. #2778C22semidirect
38. #2741C22semidirect
39. #2736C22semidirect
40. #2735C22semidirect
41. #2735C22semidirect
42. #2735C22semidirect
43. #2684C22semidirect
44. #2668C22semidirect
45. #2653C22semidirect
46. #2651C22semidirect
47. #2649C22semidirect
48. #2648C22semidirect
49. #2628C22semidirect
50. #2621C22semidirect
52. #2593C22semidirect
53. #2593C22semidirect
54. #2592C22semidirect
55. #2586C22semidirect
56. #2580C22semidirect
57. #2574C22semidirect
58. #2572C22semidirect
59. #2563C22semidirect
60. #2562C22semidirect
61. #2555C22semidirect
62. #2554C22semidirect
63. #2547C22semidirect
64. #2545C22semidirect
65. #2536C22semidirect
66. #2535C22semidirect
67. #2518C22semidirect
68. #2513C22semidirect
69. #2513C22semidirect
70. #2513C22semidirect
71. #2504C22semidirect
72. #2494C22semidirect
73. #2494C22semidirect
74. #2494C22semidirect
75. #2492C22semidirect
76. #2491C22semidirect
77. #2490C22semidirect
78. #2489C22semidirect
79. #2487C22semidirect
80. #2480C22semidirect
81. #2467C22semidirect
82. #2459C22semidirect
83. #2456C22semidirect
84. #2454C22semidirect
85. #2448C22semidirect
86. #2448C22semidirect
87. #2442C22semidirect
91. #2429C22semidirect
92. #2427C22semidirect
93. #2426C22semidirect
94. #2421C22semidirect
95. #2421C22semidirect
96. #2418C22semidirect
97. #2417C22semidirect
98. #2417C22semidirect
99. #2416C22semidirect
103. #2396C22semidirect
104. #2392C22semidirect
106. #2367C22semidirect
107. #2362C22semidirect
108. #2361C22semidirect
109. #2352C22semidirect
110. #2351C22semidirect
111. #2351C22semidirect
112. #2351C22semidirect
113. #2351C22semidirect
119. Q8×C22⋊C4C22semidirect
120. Q8×C22⋊C4C22semidirect
123. #2321C22semidirect
124. #2312C22semidirect
127. C4×#126C22semidirect
128. C4×#124C22semidirect
129. C4×#124C22semidirect
130. C4×C22⋊Q8C22semidirect
131. C4×#123C22semidirect
132. C4×#121C22semidirect
133. C4×#121C22semidirect
136. C42×Q8C22semidirect
137. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#429832
#429822
#429192
#400562
#400442
#390342
#390202
#375142
#365852
#365782
#364672
#364342
#360822
#360402
#357372
#350252
#349622
#342582
C4×#5482