Finite Group Databasebeta

← #8095861

Subgroups — #8095861

Order 512.

5547 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53095C216yesmaximal, complemented
2#53051C216yesmaximal, complemented
3#53018C216yesmaximal, complemented
4#52293C213yesmaximal, complemented
5#46338C213yesmaximal, complemented
6#46020C216yesmaximal, complemented
7#45721C216yesmaximal, complemented
8#45697C213yesmaximal, complemented
9#45624C216yesmaximal, complemented
10#45493C213yesmaximal, complemented
11Q8×#127C211yesmaximal, characteristic, complemented
12Q8×#123C211yesmaximal, characteristic, complemented
13#36458C212yesmaximal, complemented
14#36434C212yesmaximal, complemented
15#36428C211yesmaximal, characteristic, complemented
16#36428C212yesmaximal, complemented
17#35771C212yesmaximal, complemented
18#35771C212yesmaximal, complemented
19#35723C212yesmaximal, complemented
20C23×#41C2211yescharacteristic
21C2×D4×Q8C2212yes—
22C2×D4×Q8C2211yescharacteristic
23C2×D4×Q8C2212yescomplemented
24C2×D4×Q8C2211yescharacteristic, complemented
25C2×#548C2212yes—
26C2×#548C2212yes—
27C2×#548C2212yes—
28C2×#519C2212yescomplemented
29C22×C4×Q8C2211yescharacteristic, complemented
30#2868C2213yescomplemented
31#2860C2216yescomplemented
32#2855C2213yescomplemented
33#2850C2216yescomplemented
34#2848C2213yes—
35#2848C2216yes—
36#2842C2216yes—
37#2829C22112yescomplemented
38#2829C22112yescomplemented
39#2828C2216yescomplemented
40#2827C22112yescomplemented
41#2826C2216yescomplemented
42#2823C22112yescomplemented
43#2807C2216yes—
44#2797C2216yescomplemented
45#2796C22112yescomplemented
46#2795C2216yescomplemented
47#2795C22112yescomplemented
48#2795C22112yescomplemented
49#2790C22112yescomplemented
50#2790C22112yescomplemented
51#2790C2216yescomplemented
52#2780C22112yescomplemented
53#2757C2216yes—
54#2752C2216yescomplemented
55#2749C2216yescomplemented
56#2748C2213yes—
57#2735C22112yes—
58#2714C22112yescomplemented
59#2709C2211yescharacteristic
60#2697C2213yes—
61#2691C2216yescomplemented
62#2685C22112yes—
63#2685C2216yes—
64#2669C2213yes—
65#2625C2216yescomplemented
66#2620C2216yescomplemented
67#2620C2216yescomplemented
68#2545C2216yescomplemented
69#2545C2216yescomplemented
70#2545C2216yescomplemented
71#2542C2216yes—
72#2542C2213yes—
73#2542C2213yescomplemented
74#2542C2216yescomplemented
75#2538C2216yescomplemented
76#2538C2216yescomplemented
77#2536C2216yescomplemented
78#2513C2216yescomplemented
79#2512C2216yescomplemented
80#2512C2216yescomplemented
81#2502C2213yescomplemented
82#2499C2216yescomplemented
83#2497C2216yescomplemented
84#2496C2216yescomplemented
85#2495C2216yescomplemented
86#2487C2213yes—
87#2485C2216yes—
88#2446C2216yescomplemented
89#2446C2216yescomplemented
90#2446C2216yescomplemented
91#2435C2213yes—
92#2435C2216yes—
93#2432C2216yes—
94#2432C2216yes—
95#2432C2216yes—
96#2429C2216yescomplemented
97#2429C2216yescomplemented
98#2429C2216yescomplemented
99#2426C2216yescomplemented
100#2426C2216yescomplemented
101#2426C2216yescomplemented
102#2423C2216yes—
103#2423C2216yes—
104#2421C2216yes—
105#2417C2216yescomplemented
106#2416C2216yescomplemented
107#2415C2216yescomplemented
108#2415C2216yescomplemented
109#2414C2216yescomplemented
110#2414C2216yescomplemented
111#2408C2216yes—
112#2408C2213yes—
113#2407C2216yes—
114#2407C2216yes—
115#2407C2216yes—
116#2395C2216yes—
117#2392C2216yescomplemented
118#2392C2216yescomplemented
119#2383C22112yescomplemented
120#2375C2216yes—
121#2351C2212yescomplemented
122Q8×C4⋊C4C2212yescomplemented
123Q8×C4⋊C4C2212yescomplemented
124#2341C2212yes—
125#2341C2212yes—
126#2341C2212yes—
127Q8×C22⋊C4C2211yescharacteristic
128Q8×C22⋊C4C2212yes—
129Q8×C22⋊C4C2212yescomplemented
130Q8×C22⋊C4C2211yescharacteristic, complemented
131C4×#127C2213yes—
132C4×#126C2216yescomplemented
133C4×#123C2213yes—
134C4×#121C2216yescomplemented
135C4×#120C2216yes—
136C4×#120C2213yes—
137C42×Q8C2211yescharacteristic, complemented
138C22×#41—44no—
139C22×#41—48no—
140C22×#41C2312yes—
141C22×#41C2316yes—
142C23×Q8C2311yescharacteristic
143C23×Q8C2311yescharacteristic
144C23×Q8C2312yes—
145C23×D4C2313yes—
146C24×C4C2313yes—
147D4×Q8—44no—
148D4×Q8—48no—
149D4×Q8—48no—
150D4×Q8—44no—
151#548—48no—
152#548—48no—
153#548—48no—
154C2×C4⋊Q8C2313yes—
155C2×C4⋊Q8C2316yes—
156C2×C4⋊Q8C2316yes—
157C2×C4⋊Q8C2313yes—
158C2×#127C2311yescharacteristic
159C2×#126C2316yes—
160C2×#126C23112yes—
161C2×#124C2316yes—
162C2×#124C2316yes—
163C2×#124C2316yes—
164C2×#123C2311yescharacteristic
165C2×C22⋊Q8C2316yes—
166C2×C22⋊Q8C2316yes—
167C2×C22⋊Q8C2316yes—
168C2×C22⋊Q8C2316yes—
169C2×C22⋊Q8C2313yes—
170C2×C22⋊Q8C2316yes—
171C2×C22⋊Q8C2313yes—
172C2×C22⋊Q8C2316yes—
173C2×C22⋊Q8C2316yes—
174C2×C22⋊Q8C2316yes—
175C2×#121C2316yes—
176C2×#121C2316yes—
177C2×#121C2316yes—
178C2×#121C2316yes—
179C2×#120C2313yes—
180C2×#120C2316yes—
181#519—48no—
182C2×C4×Q8—44no—
183C2×C4×Q8C2312yes—
184C2×C4×Q8C2312yes—
185C2×C4×Q8C2312yes—
186C2×C4×Q8C2311yescharacteristic
187C2×C4×Q8C2312yes—
188C2×C4×Q8C2316yes—
189C2×C4×Q8C2316yes—
190C2×C4×Q8C2316yes—
191C2×C4×D4C2313yes—
192C2×C4×D4C2316yes—
193C2×C4×D4C2316yes—
194C2×C4×D4C2313yes—
195C2×C4×D4C2316yes—
196C2×C4×D4C2316yes—
197C2×C4×D4C2316yes—
198C2×#117C2316yes—
199C2×#117C2316yes—
200C22×C4⋊C4C2313yes—
201C22×C42C2313yes—
202#400C23112yes—
203#400C23112yes—
204#400C2316yes—
205#400C2316yes—
206#399C2316yes—
207#399C23112yes—
208#399C2316yes—
209#399C2316yes—
210#399C2316yes—
211#398C2316yes—
212#398C23112yes—
213#398C23112yes—
214#398C23112yes—
215#398C2316yes—
216#398C2316yes—
217#397C23112yes—
218#397C2316yes—
219#397C23112yes—
220#397C2316yes—
221#397C2316yes—
222#397C23112yes—
223#397C2316yes—
224#397C2316yes—
225#396C2316yes—
226#396C23112yes—
227#396C23112yes—
228#396C23112yes—
229#396C23112yes—
230#396C23112yes—
231#396C2316yes—
232#396C23112yes—
233#396C23112yes—
234#396C2316yes—
235#396C2316yes—
236#394C23112yes—
237#394C23112yes—
238#394C23112yes—
239#394C2316yes—
240#394C23112yes—
241#394C23112yes—
242#394C23112yes—
243#394C2316yes—
244#394C2316yes—
245#394C2316yes—
246#394C2316yes—
247#394C23112yes—
248#394C2312yes—
249#394C2312yes—
250#394C2312yes—
251#394C2316yes—
252#392C2316yes—
253#392C2316yes—
254#392C23112yes—
255#392C2316yes—
256#391C2316yes—
257#391C2316yes—
258#391C2316yes—
259#391C2316yes—
260#391C2316yes—
261#391C2316yes—
262#390C2313yes—
263#390C2313yes—
264#390C2316yes—
265#390C2316yes—
266#390C2316yes—
267#390C23112yes—
268#390C2316yes—
269#390C2316yes—
270#390C2316yes—
271#390C2316yes—
272#390C2316yes—
273#390C2316yes—
274#390C23112yes—
275#389C2316yes—
276#389C2316yes—
277#389C2316yes—
278#389C2316yes—
279#389C2316yes—
280#389C2316yes—
281#389C2316yes—
282#389C23112yes—
283#389C23112yes—
284#388C2316yes—
285#388C2316yes—
286#388C2316yes—
287#388C23112yes—
288#388C23112yes—
289#388C23112yes—
290#388C23112yes—
291#388C23112yes—
292#388C23112yes—
293#388C23112yes—
294#388C23112yes—
295#388C23112yes—
296#388C2316yes—
297#388C2316yes—
298#388C2316yes—
299#387C2312yes—
300#387C2316yes—
301#387C2316yes—
302#387C23112yes—
303#387C23112yes—
304#387C23112yes—
305#387C23112yes—
306#387C2316yes—
307#386C23112yes—
308#386C2316yes—
309#386C2316yes—
310#386C2313yes—
311#386C2316yes—
312#386C2316yes—
313#386C2311yescharacteristic
314#386C2312yes—
315#386C2312yes—
316#385C2313yes—
317#385C23112yes—
318#385C23112yes—
319#385C2316yes—
320#385C2313yes—
321#385C23112yes—
322#385C2316yes—
323#385C2316yes—
324#385C2316yes—
325#385C2316yes—
326#384C2313yes—
327#384C23112yes—
328#384C2316yes—
329#384C2316yes—
330#384C2316yes—
331#383C2316yes—
332#382C2316yes—
333#381C2313yes—
334#380C2313yes—
335#380C2316yes—
336#380C2316yes—
337#380C2316yes—
338#380C2316yes—
339#380C2313yes—
340#380C2316yes—
341#380C2316yes—
342#379C2313yes—
343#379C23112yes—
344#379C2316yes—
345#379C2316yes—
346C4×C4⋊C4C2316yes—
347C4×C4⋊C4C2316yes—
348C4×C4⋊C4C2316yes—
349C4×C4⋊C4C2316yes—
350C4×C4⋊C4C2313yes—
351C4×C22⋊C4C2316yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2313yes—
355C4×C22⋊C4C2316yes—
356C4×C22⋊C4C2313yes—
357C4×C22⋊C4C2316yes—
358C43C2313yes—
359C25C2413yes—
360C2×#41—28no—
361C2×#41—28no—
362C2×#41—28no—
363C2×#41—412no—
364C2×#41—412no—
365C2×#41—412no—
366C2×#41—464no—
367C22×Q8—24no—
368C22×Q8—28no—
369C22×Q8—28no—
370C22×Q8—28no—
371C22×Q8—28no—
372C22×Q8—24no—
373C22×Q8—28no—
374C22×Q8C2413yes—
375C22×Q8C2416yes—
376C22×Q8C2413yes—
377C22×Q8C2411yescharacteristic
378C22×D4—412no—
379C22×D4—46no—
380C22×D4C2416yes—
381C22×D4C2412yes—
382C22×D4C2412yes—
383C22×D4C2411yescharacteristic
384C22×D4C2416yes—
385C22×D4C2416yes—
386C22×D4C2416yes—
387C22×D4C2416yes—
388C22×D4C2411yescharacteristic
389C23×C4—412no—
390C23×C4—46no—
391C23×C4C2413yes—
392C23×C4C2416yes—
393C23×C4C2413yes—
394C23×C4C2416yes—
395C23×C4C2411yescharacteristic
396C23×C4C2413yes—
397C23×C4C2411yescharacteristic
398C23×C4C2416yes—
399C4⋊Q8—412no—
400C4⋊Q8—46no—
401C4⋊Q8—46no—
402C4⋊Q8—412no—
403#127—24no—
404#126—412no—
405#126—424no—
406#124—412no—
407#124—412no—
408#124—412no—
409#123—24no—
410C22⋊Q8—412no—
411C22⋊Q8—412no—
412C22⋊Q8—412no—
413C22⋊Q8—46no—
414C22⋊Q8—412no—
415C22⋊Q8—412no—
416C22⋊Q8—412no—
417C22⋊Q8—412no—
418C22⋊Q8—412no—
419C22⋊Q8—46no—
420#121—412no—
421#121—412no—
422#121—412no—
423#121—412no—
424#120—212no—
425#120—412no—
426C4×Q8—28no—
427C4×Q8—28no—
428C4×Q8—28no—
429C4×Q8—24no—
430C4×Q8—28no—
431C4×Q8—412no—
432C4×Q8—412no—
433C4×Q8—412no—
434C4×D4—412no—
435C4×D4—412no—
436C4×D4—412no—
437C4×D4—46no—
438C4×D4—412no—
439C4×D4—46no—
440C4×D4—412no—
441#117—412no—
442#117—412no—
443C2×C4⋊C4—46no—
444C2×C4⋊C4C2416yes—
445C2×C4⋊C4C2416yes—
446C2×C4⋊C4C2416yes—
447C2×C4⋊C4C2416yes—
448C2×C4⋊C4C2413yes—
449C2×C4⋊C4C2416yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2416yes—
453C2×C4⋊C4C2416yes—
454C2×C4⋊C4C2416yes—
455C2×C4⋊C4C2416yes—
456C2×C4⋊C4C2416yes—
457C2×C4⋊C4C2416yes—
458C2×C4⋊C4C2416yes—
459C2×C4⋊C4C2413yes—
460C2×C4⋊C4C2413yes—
461C2×C4⋊C4C2416yes—
462C2×C4⋊C4C2416yes—
463C2×C4⋊C4C24112yes—
464C2×C4⋊C4C24112yes—
465C2×C4⋊C4C2416yes—
466C2×C4⋊C4C2416yes—
467C2×C4⋊C4C2416yes—
468C2×C4⋊C4C24112yes—
469C2×C4⋊C4C24112yes—
470C2×C4⋊C4C2416yes—
471C2×C22⋊C4C2416yes—
472C2×C22⋊C4C2416yes—
473C2×C22⋊C4C2413yes—
474C2×C22⋊C4C2416yes—
475C2×C22⋊C4C2412yes—
476C2×C22⋊C4C2411yescharacteristic
477C2×C22⋊C4C2416yes—
478C2×C22⋊C4C2412yes—
479C2×C22⋊C4C2412yes—
480C2×C22⋊C4C2412yes—
481C2×C22⋊C4C2412yes—
482C2×C22⋊C4C2416yes—
483C2×C22⋊C4C2413yes—
484C2×C22⋊C4C2416yes—
485C2×C22⋊C4C2413yes—
486C2×C22⋊C4C2416yes—
487C2×C22⋊C4C2416yes—
488C2×C22⋊C4C2416yes—
489C2×C22⋊C4C2416yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C2416yes—
492C2×C22⋊C4C2416yes—
493C2×C22⋊C4C24112yes—
494C2×C22⋊C4C24112yes—
495C2×C22⋊C4C24112yes—
496C2×C22⋊C4C2416yes—
497C2×C22⋊C4C2416yes—
498C2×C22⋊C4C2416yes—
499C2×C22⋊C4C24112yes—
500C2×C22⋊C4C24112yes—
501C2×C22⋊C4C2411yescharacteristic
502C2×C22⋊C4C2412yes—
503C2×C22⋊C4C2416yes—
504C2×C22⋊C4C2413yes—
505C2×C22⋊C4C24112yes—
506C2×C42—46no—
507C2×C42C2416yes—
508C2×C42C2416yes—
509C2×C42C2416yes—
510C2×C42C2413yes—
511C2×C42C2416yes—
512C2×C42C2416yes—
513C2×C42C2411yescharacteristic
514C2×C42C24112yes—
515C2×C42C2416yes—
516C2×C42C2413yes—
517#95C2412yes—
518#95C2412yes—
519#95C2412yes—
520#95C2416yes—
521#95C2416yes—
522#95C2416yes—
523#95C2416yes—
524#95C2416yes—
525#95C2416yes—
526#95C2416yes—
527#95C2416yes—
528#95C2416yes—
529#95C2412yes—
530#95C2416yes—
531#95C2416yes—
532#95C2416yes—
533#95C2416yes—
534#95C2416yes—
535#95C2416yes—
536#95C24112yes—
537#95C2416yes—
538#95C24112yes—
539#95C2416yes—
540#95C24112yes—
541C24—26no—
542C24—46no—
543C24—43no—
544C24—46no—
545C24—43no—
546C24C2516yes—
547C24C2512yes—
548C24C2511yescharacteristic
549C24C2511yescharacteristic
550#41—496no—
551#41—432no—
552C2×Q8—26no—
553C2×Q8—212no—
554C2×Q8—212no—
555C2×Q8—212no—
556C2×Q8—212no—
557C2×Q8—212no—
558C2×Q8—26no—
559C2×Q8—416no—
560C2×Q8—432no—
561C2×Q8—416no—
562C2×Q8H(5,𝔽2)14yes—
563C2×Q8H(5,𝔽2)18yes—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—212no—
567C2×D4—212no—
568C2×D4—212no—
569C2×D4—212no—
570C2×D4—22no—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—41no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—41no—
577C2×D4—412no—
578C2×D4—46no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—46no—
582C2×D4—46no—
583C2×D4—46no—
584C2×D4—46no—
585C2×D4—46no—
586C2×D4—46no—
587C2×D4—46no—
588C2×D4—46no—
589C2×D4—448no—
590C2×D42−1+414yes—
591C22×C4—22no—
592C22×C4—26no—
593C22×C4—212no—
594C22×C4—212no—
595C22×C4—212no—
596C22×C4—212no—
597C22×C4—212no—
598C22×C4—26no—
599C22×C4—212no—
600C22×C4—212no—
601C22×C4—212no—
602C22×C4—41no—
603C22×C4—42no—
604C22×C4—41no—
605C22×C4—46no—
606C22×C4—46no—
607C22×C4—46no—
608C22×C4—41no—
609C22×C4—43no—
610C22×C4—46no—
611C22×C4—448no—
612C22×C4C2512yes—
613C22×C4C2516yes—
614C22×C4C2512yes—
615C22×C4C2513yes—
616C22×C4C2512yes—
617C22×C4C2516yes—
618C22×C4C2516yes—
619C22×C4C2512yes—
620C22×C4C2516yes—
621C22×C4C2513yes—
622C22×C4C2516yes—
623C22×C4C2513yes—
624C22×C4C2511yescharacteristic
625C22×C4C2512yes—
626C22×C4C2513yes—
627C4⋊C4—212no—
628C4⋊C4—212no—
629C4⋊C4—212no—
630C4⋊C4—212no—
631C4⋊C4—26no—
632C4⋊C4—24no—
633C4⋊C4—212no—
634C4⋊C4—24no—
635C4⋊C4—46no—
636C4⋊C4—46no—
637C4⋊C4—46no—
638C4⋊C4—46no—
639C4⋊C4—46no—
640C4⋊C4—46no—
641C4⋊C4—46no—
642C4⋊C4—46no—
643C4⋊C4—43no—
644C4⋊C4—43no—
645C4⋊C4—46no—
646C4⋊C4—46no—
647C4⋊C4—412no—
648C4⋊C4—412no—
649C4⋊C4—46no—
650C4⋊C4—46no—
651C4⋊C4—46no—
652C4⋊C4—412no—
653C4⋊C4—412no—
654C22⋊C4—26no—
655C22⋊C4—22no—
656C22⋊C4—24no—
657C22⋊C4—212no—
658C22⋊C4—212no—
659C22⋊C4—212no—
660C22⋊C4—46no—
661C22⋊C4—412no—
662C22⋊C4—42no—
663C22⋊C4—43no—
664C22⋊C4—41no—
665C22⋊C4—42no—
666C22⋊C4—46no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—46no—
671C22⋊C4—43no—
672C22⋊C4—46no—
673C22⋊C4—46no—
674C22⋊C4—46no—
675C22⋊C4—43no—
676C22⋊C4—46no—
677C22⋊C4—46no—
678C22⋊C4—46no—
679C22⋊C4—46no—
680C22⋊C4—46no—
681C22⋊C4—46no—
682C22⋊C4—412no—
683C22⋊C4—412no—
684C22⋊C4—412no—
685C22⋊C4—46no—
686C22⋊C4—46no—
687C22⋊C4—412no—
688C22⋊C4—412no—
689C42—212no—
690C42—212no—
691C42—212no—
692C42—212no—
693C42—26no—
694C42—22no—
695C42—212no—
696C42—46no—
697C42—43no—
698C42—412no—
699C23—22no—
700C23—21no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—26no—
711C23—26no—
712C23—26no—
713C23—26no—
714C23—22no—
715C23—26no—
716C23—26no—
717C23—22no—
718C23—22no—
719C23—26no—
720C23—22no—
721C23—412no—
722C23—812no—
723C23—86no—
724C23—86no—
725C23—812no—
726C23C2×2−1+412yes—
727C23C2×2−1+412yes—
728C23C2611yescharacteristic
729Q8—412no—
730Q8—424no—
731Q8—412no—
732Q8#560116yes—
733D4—44no—
734D4—48no—
735D4—48no—
736D4—44no—
737D4—424no—
738D4—424no—
739D4—812no—
740D4—812no—
741D4—812no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—26no—
750C2×C4—26no—
751C2×C4—26no—
752C2×C4—23no—
753C2×C4—26no—
754C2×C4—26no—
755C2×C4—23no—
756C2×C4—26no—
757C2×C4—26no—
758C2×C4—26no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—26no—
763C2×C4—23no—
764C2×C4—22no—
765C2×C4—26no—
766C2×C4—22no—
767C2×C4—26no—
768C2×C4—26no—
769C2×C4—26no—
770C2×C4—26no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—26no—
774C2×C4—26no—
775C2×C4—26no—
776C2×C4—22no—
777C2×C4—26no—
778C2×C4—22no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—424no—
782C2×C4—412no—
783C2×C4—424no—
784C2×C4—412no—
785C2×C4—424no—
786C2×C4—86no—
787C2×C4C2×H(5,𝔽2)112yes—
788C2×C4C2×H(5,𝔽2)16yes—
789C2×C4C2×2−1+412yes—
790C2×C4#58514yes—
791C22—24no—
792C22—24no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—42no—
799C22—41no—
800C22—41no—
801C22—42no—
802C22—42no—
803C22—46no—
804C22—46no—
805C22—42no—
806C22—46no—
807C22—42no—
808C22—46no—
809C22—42no—
810C22—46no—
811C22—42no—
812C22—46no—
813C22—42no—
814C22—46no—
815C22—824no—
816C22C22×H(5,𝔽2)12yes—
817C22C22×H(5,𝔽2)11yescharacteristic
818C22C22×2−1+411yescharacteristic
819C22C2×#58512yes—
820C222−1+611yescharacteristic
821C4—24no—
822C4—22no—
823C4—42no—
824C4—46no—
825C4—43no—
826C4—46no—
827C4—42no—
828C4—42no—
829C4—46no—
830C4—46no—
831C4—42no—
832C4—43no—
833C4—46no—
834C4—43no—
835C4C2×#560112yes—
836C2—42no—
837C2—42no—
838C2—82no—
839C2—86no—
840C2C22×#56011yescharacteristic
841C2#6289311yescharacteristic
842C2#6292212yes—
843C2#6301512yes—
844C2#6302211yescharacteristic
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. #53095C2semidirect
2. #53051C2semidirect
3. #53018C2semidirect
4. #52293C2semidirect
5. #46338C2semidirect
6. #46020C2semidirect
7. #45721C2semidirect
8. #45697C2semidirect
9. #45624C2semidirect
10. #45493C2semidirect
11. Q8×#127C2semidirect
12. Q8×#123C2semidirect
13. #36458C2semidirect
14. #36434C2semidirect
15. #36428C2semidirect
16. #36428C2semidirect
17. #35771C2semidirect
18. #35771C2semidirect
19. #35723C2semidirect
23. C2×D4×Q8C22semidirect
24. C2×D4×Q8C22semidirect
28. C2×#519C22semidirect
29. C22×C4×Q8C22semidirect
30. #2868C22semidirect
31. #2860C22semidirect
32. #2855C22semidirect
33. #2850C22semidirect
37. #2829C22semidirect
38. #2829C22semidirect
39. #2828C22semidirect
40. #2827C22semidirect
41. #2826C22semidirect
42. #2823C22semidirect
44. #2797C22semidirect
45. #2796C22semidirect
46. #2795C22semidirect
47. #2795C22semidirect
48. #2795C22semidirect
49. #2790C22semidirect
50. #2790C22semidirect
51. #2790C22semidirect
52. #2780C22semidirect
54. #2752C22semidirect
55. #2749C22semidirect
58. #2714C22semidirect
61. #2691C22semidirect
65. #2625C22semidirect
66. #2620C22semidirect
67. #2620C22semidirect
68. #2545C22semidirect
69. #2545C22semidirect
70. #2545C22semidirect
73. #2542C22semidirect
74. #2542C22semidirect
75. #2538C22semidirect
76. #2538C22semidirect
77. #2536C22semidirect
78. #2513C22semidirect
79. #2512C22semidirect
80. #2512C22semidirect
81. #2502C22semidirect
82. #2499C22semidirect
83. #2497C22semidirect
84. #2496C22semidirect
85. #2495C22semidirect
88. #2446C22semidirect
89. #2446C22semidirect
90. #2446C22semidirect
96. #2429C22semidirect
97. #2429C22semidirect
98. #2429C22semidirect
99. #2426C22semidirect
100. #2426C22semidirect
101. #2426C22semidirect
105. #2417C22semidirect
106. #2416C22semidirect
107. #2415C22semidirect
108. #2415C22semidirect
109. #2414C22semidirect
110. #2414C22semidirect
117. #2392C22semidirect
118. #2392C22semidirect
119. #2383C22semidirect
121. #2351C22semidirect
122. Q8×C4⋊C4C22semidirect
123. Q8×C4⋊C4C22semidirect
129. Q8×C22⋊C4C22semidirect
130. Q8×C22⋊C4C22semidirect
132. C4×#126C22semidirect
134. C4×#121C22semidirect
137. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#530952
#530512
#530182
#522932
#463382
#460202
#457212
#456972
#456242
#454932
Q8×#1272
Q8×#1232
#364582
#364342
#364282
#357712
#357232