Finite Group Databasebeta

← #7658110

Subgroups — #7658110

Order 512.

8937 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3498C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#42987C216yesmaximal, complemented
4#42986C216yesmaximal, complemented
5#42484C216yesmaximal, complemented
6#42480C216yesmaximal, complemented
7#39342C216yesmaximal, complemented
8#38910C216yesmaximal, complemented
9#37621C213yesmaximal, complemented
10#37614C213yesmaximal, complemented
11#36576C212yesmaximal, complemented
12#36455C212yesmaximal, complemented
13#36091C212yesmaximal, complemented
14#36082C212yesmaximal, complemented
15#36066C212yesmaximal, complemented
16#36049C212yesmaximal, complemented
17#35272C213yesmaximal, complemented
18#34609C213yesmaximal, complemented
19#34193C211yesmaximal, characteristic, complemented
20C22×H(5,𝔽2)C2212yes—
21#3498—216no—
22#3480—216no—
23C2×#559C2213yescomplemented
24C2×#557C2211yescharacteristic, complemented
25C2×#556C2213yescomplemented
26C2×#553C2213yescomplemented
27C2×#553C2213yescomplemented
28C2×#550C2212yes—
29C2×#550C2212yes—
30C2×#550C2211yescharacteristic
31C2×#550C2214yescomplemented
32C2×#548C2211yescharacteristic
33C2×#548C2211yescharacteristic, complemented
34C2×#548C2214yescomplemented
35C2×D42C2216yes—
36C2×D42C2216yes—
37C2×#535C2216yes—
38C2×#535C2216yescomplemented
39C2×#532C2213yes—
40C2×#532C2213yescomplemented
41C22×#127C2213yes—
42C2×#529C2213yescomplemented
43C2×#529C2213yescomplemented
44C2×C4×#41C2211yescharacteristic
45C2×C4×#41C2213yescomplemented
46C2×C4×#41C2211yescharacteristic, complemented
47C22×C4×Q8C2211yescharacteristic, complemented
48#2856C2216yescomplemented
49#2856C2216yescomplemented
50#2818C22112yescomplemented
51#2813C22112yescomplemented
52#2685C22124yescomplemented
53#2678C22124yescomplemented
54#2670C22124yescomplemented
55#2669C22124yescomplemented
56#2662C22112yescomplemented
57#2657C2216yescomplemented
58#2641C2216yescomplemented
59#2635C2216yescomplemented
60#2635C2216yescomplemented
61#2632C2216yescomplemented
62#2631C2216yescomplemented
63#2628C2211yescharacteristic, complemented
64#2628C2213yescomplemented
65#2624C2216yescomplemented
66#2619C2213yescomplemented
67#2619C2213yescomplemented
68#2619C2216yescomplemented
69#2616C2216yescomplemented
70#2615C2216yescomplemented
71#2615C2216yescomplemented
72#2613C22112yescomplemented
73#2562C2216yescomplemented
74#2548C2216yescomplemented
75#2548C2216yescomplemented
76#2548C2216yescomplemented
77#2541C2216yescomplemented
78#2541C22112yescomplemented
79#2541C2216yescomplemented
80#2541C2216yescomplemented
81#2540C22112yescomplemented
82#2540C2216yescomplemented
83#2538C2216yescomplemented
84#2537C2216yescomplemented
85#2491C22112yescomplemented
86#2490C22112yescomplemented
87#2435C2216yescomplemented
88#2435C22112yescomplemented
89#2433C22112yescomplemented
90#2433C2216yescomplemented
91#2428C22112yescomplemented
92#2426C22112yescomplemented
93#2416C22112yescomplemented
94#2414C22112yescomplemented
95#2414C22112yescomplemented
96#2408C22112yescomplemented
97#2408C22112yescomplemented
98#2408C2216yescomplemented
99#2408C2216yescomplemented
100#2408C2216yescomplemented
101#2408C2216yescomplemented
102#2408C22112yescomplemented
103#2398C2216yescomplemented
104#2397C2216yescomplemented
105#2388C2216yescomplemented
106#2388C2216yescomplemented
107#2354C2216yescomplemented
108Q8×C4⋊C4C2212yescomplemented
109#2347C2216yescomplemented
110#2341C2212yes—
111#2341C2214yescomplemented
112#2341C2214yescomplemented
113#2319C2216yescomplemented
114#2309C2216yescomplemented
115C4×#121C2216yescomplemented
116C4×#121C2216yescomplemented
117#2285C2213yescomplemented
118#2283C2213yescomplemented
119#2276C2212yescomplemented
120C2×H(5,𝔽2)—216no—
121C2×H(5,𝔽2)—416no—
122C22×#41C2314yes—
123C22×#41C2311yescharacteristic
124C22×#41C2313yes—
125C22×#41C2311yescharacteristic
126C22×#41C2316yes—
127C23×Q8C2311yescharacteristic
128C23×D4C2316yes—
129C23×D4C2316yes—
130C23×D4C23112yes—
131C23×D4C2316yes—
132#559—224no—
133#557—28no—
134#556—224no—
135#553—224no—
136#553—224no—
137#550—28no—
138#550—216no—
139#550—216no—
140#550—416no—
141#548—28no—
142#548—28no—
143#548—416no—
144D42—248no—
145D42—248no—
146#535—248no—
147#535—424no—
148#532—224no—
149#532—224no—
150C2×C4⋊Q8C2311yescharacteristic
151C2×C4⋊Q8C2313yes—
152C2×#127—224no—
153C2×#127C2316yes—
154C2×#127C2316yes—
155C2×#127C2313yes—
156C2×#127C2316yes—
157C2×#127C2313yes—
158C2×#127C23112yes—
159C2×#127C23112yes—
160#529—224no—
161#529—224no—
162C2×#126C2316yes—
163C2×#126C2316yes—
164C2×#125C2313yes—
165C2×#125C2313yes—
166C2×#124C2316yes—
167C2×#124C2313yes—
168C2×#124C2316yes—
169C2×#124C2313yes—
170C2×#124C23112yes—
171C2×#124C23112yes—
172C2×#123C2316yes—
173C2×#123C2316yes—
174C2×C22⋊Q8C2313yes—
175C2×C22⋊Q8C2313yes—
176C2×C22⋊Q8C23112yes—
177C2×#121C2316yes—
178C2×#121C2313yes—
179C2×#121C2316yes—
180C2×#121C2316yes—
181C2×#121C2313yes—
182C2×#121C2313yes—
183C2×#121C2316yes—
184C2×#121C23112yes—
185C2×#121C2313yes—
186C2×#121C23112yes—
187C2×#121C23112yes—
188C2×#121C23112yes—
189C2×#121C23112yes—
190C2×#121C2316yes—
191C2×#121C23112yes—
192C2×#121C23112yes—
193C2×#121C23112yes—
194C2×#120C23124yes—
195C2×#120C23112yes—
196C2×#120C23112yes—
197C2×#120C23124yes—
198C4×#41—28no—
199C4×#41—224no—
200C4×#41D4116yescomplemented
201C2×C4×Q8—28no—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2311yescharacteristic
204C2×C4×Q8C2311yescharacteristic
205C2×C4×Q8C2313yes—
206C2×C4×Q8C2313yes—
207C2×C4×Q8C2313yes—
208C2×C4×Q8C2313yes—
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2311yescharacteristic
211C2×C4×D4C2316yes—
212C2×C4×D4C2313yes—
213C2×C4×D4C2313yes—
214C2×C4×D4C2313yes—
215C2×C4×D4C2313yes—
216C2×C4×D4C2313yes—
217C2×C4×D4C2313yes—
218C2×C4×D4C2313yes—
219C2×C4×D4C2313yes—
220C2×C4×D4C2316yes—
221C2×C4×D4C2316yes—
222C2×C4×D4C23112yes—
223C2×C4×D4C23112yes—
224C2×C4×D4C2313yes—
225C2×C4×D4C2313yes—
226C2×#117C2313yes—
227C2×#117C2311yescharacteristic
228C2×#117C2313yes—
229C2×#117C2313yes—
230C2×#117C2316yes—
231C2×#117C2313yes—
232C22×C4⋊C4C2313yes—
233C22×C42C2313yes—
234C22×C42C2313yes—
235C22×C42C2313yes—
236#400C2316yes—
237#400C2312yes—
238#399C23112yes—
239#399C2312yes—
240#399C2316yes—
241#397C23112yes—
242#396C23124yes—
243#395C2316yes—
244#395C2312yes—
245#394C23112yes—
246#394C2316yes—
247#394C23124yes—
248#394C23112yes—
249#394C23124yes—
250#394C2316yes—
251#394C23124yes—
252#394C2316yes—
253#394C2316yes—
254#394C23112yes—
255#394C23112yes—
256#394C23124yes—
257#393C2316yes—
258#393C23112yes—
259#393C2312yes—
260#392C2316yes—
261#392C23124yes—
262#392C23112yes—
263#392C23124yes—
264#392C2316yes—
265#392C23112yes—
266#392C23112yes—
267#392C23112yes—
268#392C23112yes—
269#392C23124yes—
270#392C2316yes—
271#392C2316yes—
272#390C2316yes—
273#390C23112yes—
274#390C23112yes—
275#390C23112yes—
276#390C23112yes—
277#390C23112yes—
278#390C23112yes—
279#390C23112yes—
280#390C23112yes—
281#390C23112yes—
282#390C23112yes—
283#390C2316yes—
284#390C23124yes—
285#389C23112yes—
286#389C2312yes—
287#389C2316yes—
288#388C23124yes—
289#388C23124yes—
290#388C23112yes—
291#388C23112yes—
292#386C23112yes—
293#386C23112yes—
294#384C2316yes—
295#383C2316yes—
296#382C2311yescharacteristic
297#382C2313yes—
298#381C2316yes—
299#380C23112yes—
300#380C23112yes—
301#380C2316yes—
302#380C2316yes—
303#380C2316yes—
304#380C2312yes—
305#380C2316yes—
306#379C23112yes—
307#379C23112yes—
308#379C23124yes—
309C4×C4⋊C4C2316yes—
310C4×C4⋊C4C2316yes—
311C4×C4⋊C4C23112yes—
312C4×C4⋊C4C2316yes—
313C4×C22⋊C4C2316yes—
314C4×C22⋊C4C23112yes—
315C4×C22⋊C4C23112yes—
316#376C2316yes—
317C25C24112yes—
318H(5,𝔽2)—4128no—
319C2×#41—24no—
320C2×#41—216no—
321C2×#41—28no—
322C2×#41—216no—
323C2×#41—28no—
324C2×#41—216no—
325C2×#41—212no—
326C2×#41—224no—
327C2×#41—212no—
328C2×#41—46no—
329C2×#41—424no—
330C2×#41C2×D418yes—
331C22×Q8—24no—
332C22×Q8—28no—
333C22×Q8C2413yes—
334C22×Q8C2413yes—
335C22×Q8C2412yes—
336C22×Q8C2411yescharacteristic
337C22×D4—248no—
338C22×D4—224no—
339C22×D4—224no—
340C22×D4—224no—
341C22×D4—424no—
342C22×D4—424no—
343C22×D4—424no—
344C22×D4—412no—
345C22×D4—412no—
346C22×D4—812no—
347C22×D4C2413yes—
348C22×D4C2416yes—
349C22×D4C24112yes—
350C22×D4C2413yes—
351C22×D4C2413yes—
352C22×D4C2413yes—
353C22×D4C2413yes—
354C22×D4C2416yes—
355C22×D4C24112yes—
356C22×D4C2416yes—
357C22×D4C24112yes—
358C22×D4C24112yes—
359C22×D4C24112yes—
360C22×D4C2416yes—
361C22×D4C24112yes—
362C22×D4C24124yes—
363C23×C4C2413yes—
364C23×C4C2413yes—
365C23×C4C2413yes—
366C23×C4C24112yes—
367C23×C4C2413yes—
368C23×C4C2413yes—
369C23×C4C2411yescharacteristic
370C23×C4C2413yes—
371C23×C4C2413yes—
372C23×C4C2413yes—
373C4⋊Q8—212no—
374C4⋊Q8—24no—
375#127—212no—
376#127—212no—
377#127—224no—
378#127—224no—
379#127—224no—
380#127—424no—
381#127—424no—
382#126—224no—
383#126—224no—
384#125—212no—
385#125—212no—
386#124—212no—
387#124—224no—
388#124—212no—
389#124—224no—
390#124—424no—
391#124—424no—
392#123—224no—
393#123—224no—
394C22⋊Q8—212no—
395C22⋊Q8—212no—
396C22⋊Q8—424no—
397#121—212no—
398#121—212no—
399#121—212no—
400#121—224no—
401#121—224no—
402#121—224no—
403#121—212no—
404#121—248no—
405#121—248no—
406#121—224no—
407#121—412no—
408#121—424no—
409#121—424no—
410#121—424no—
411#121—424no—
412#121—812no—
413#121—812no—
414#120—296no—
415#120—424no—
416#120—424no—
417#120—824no—
418C4×Q8—24no—
419C4×Q8—24no—
420C4×Q8—216no—
421C4×Q8—212no—
422C4×Q8—212no—
423C4×Q8—212no—
424C4×Q8—212no—
425C4×Q8C2×D418yes—
426C4×Q8C2×D418yes—
427C4×D4—212no—
428C4×D4—212no—
429C4×D4—212no—
430C4×D4—212no—
431C4×D4—224no—
432C4×D4—212no—
433C4×D4—212no—
434C4×D4—212no—
435C4×D4—212no—
436C4×D4—224no—
437C4×D4—224no—
438C4×D4—424no—
439C4×D4—424no—
440C4×D4C2×D4124yes—
441C4×D4C2×D4124yes—
442#117—212no—
443#117—212no—
444#117—24no—
445#117—212no—
446#117—412no—
447#117C2×D4124yes—
448C2×C4⋊C4—212no—
449C2×C4⋊C4C2413yes—
450C2×C4⋊C4C2416yes—
451C2×C4⋊C4C2416yes—
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2413yes—
455C2×C4⋊C4C2413yes—
456C2×C4⋊C4C2413yes—
457C2×C4⋊C4C2413yes—
458C2×C4⋊C4C2413yes—
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2412yes—
461C2×C4⋊C4C2416yes—
462C2×C4⋊C4C24112yes—
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C24112yes—
466C2×C4⋊C4C24112yes—
467C2×C4⋊C4C2413yes—
468C2×C4⋊C4C2413yes—
469C2×C22⋊C4C2411yescharacteristic
470C2×C22⋊C4C2411yescharacteristic
471C2×C22⋊C4C2413yes—
472C2×C22⋊C4C2413yes—
473C2×C22⋊C4C2416yes—
474C2×C22⋊C4C2413yes—
475C2×C22⋊C4C2413yes—
476C2×C22⋊C4C24112yes—
477C2×C22⋊C4C24112yes—
478C2×C22⋊C4C2416yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C24112yes—
481C2×C22⋊C4C24112yes—
482C2×C22⋊C4C2414yes—
483C2×C22⋊C4C24112yes—
484C2×C22⋊C4C24112yes—
485C2×C22⋊C4C24112yes—
486C2×C22⋊C4C24112yes—
487C2×C22⋊C4C24112yes—
488C2×C22⋊C4C24124yes—
489C2×C22⋊C4C24124yes—
490C2×C22⋊C4C24112yes—
491C2×C22⋊C4C24124yes—
492C2×C22⋊C4C24112yes—
493C2×C22⋊C4C2416yes—
494C2×C42—212no—
495C2×C42—212no—
496C2×C42C2×D4124yes—
497C2×C42C2411yescharacteristic
498C2×C42C2413yes—
499C2×C42C2413yes—
500C2×C42C2413yes—
501C2×C42C24112yes—
502C2×C42C2413yes—
503C2×C42C2413yes—
504C2×C42C24112yes—
505C2×C42C2411yescharacteristic
506C2×C42C2413yes—
507C2×C42C2413yes—
508C2×C42C2413yes—
509#95C2412yes—
510#95C2416yes—
511#95C24112yes—
512#95C2414yes—
513#95C2412yes—
514#95C2414yes—
515#95C2416yes—
516#95C24112yes—
517#95C24112yes—
518#95C24112yes—
519C24—224no—
520C24—424no—
521C24—412no—
522C24—424no—
523C24—412no—
524C24C25112yes—
525C24C2513yes—
526C24C2513yes—
527C24C2511yescharacteristic
528#41—232no—
529#41—448no—
530#41—496no—
531#41—416no—
532#41—464no—
533C2×Q8—26no—
534C2×Q8—26no—
535C2×Q8—24no—
536C2×Q8—212no—
537C2×Q8—26no—
538C2×Q8—43no—
539C2×Q8—44no—
540C2×Q8—416no—
541C2×Q8C22×D414yes—
542C2×Q8H(5,𝔽2)18yes—
543C2×D4—26no—
544C2×D4—26no—
545C2×D4—224no—
546C2×D4—26no—
547C2×D4—26no—
548C2×D4—212no—
549C2×D4—224no—
550C2×D4—26no—
551C2×D4—26no—
552C2×D4—212no—
553C2×D4—212no—
554C2×D4—224no—
555C2×D4—212no—
556C2×D4—224no—
557C2×D4—224no—
558C2×D4—212no—
559C2×D4—26no—
560C2×D4—212no—
561C2×D4—212no—
562C2×D4—224no—
563C2×D4—224no—
564C2×D4—212no—
565C2×D4—412no—
566C2×D4—412no—
567C2×D4—412no—
568C2×D4—412no—
569C2×D4—43no—
570C2×D4—43no—
571C2×D4—43no—
572C2×D4—496no—
573C2×D4—412no—
574C2×D4—412no—
575C2×D4—412no—
576C2×D4—412no—
577C2×D4—412no—
578C2×D4—412no—
579C2×D4—412no—
580C2×D4—412no—
581C2×D4—412no—
582C2×D4—412no—
583C2×D4—424no—
584C2×D4—424no—
585C2×D4—424no—
586C2×D4—4192no—
587C2×D4—848no—
588C2×D4—848no—
589C2×D4C22×D4112yes—
590C22×C4—22no—
591C22×C4—26no—
592C22×C4—212no—
593C22×C4—26no—
594C22×C4—22no—
595C22×C4—26no—
596C22×C4—26no—
597C22×C4—26no—
598C22×C4—224no—
599C22×C4—212no—
600C22×C4—212no—
601C22×C4—224no—
602C22×C4—224no—
603C22×C4—26no—
604C22×C4—26no—
605C22×C4—26no—
606C22×C4—26no—
607C22×C4—46no—
608C22×C4—46no—
609C22×C4—46no—
610C22×C4C22×D4112yes—
611C22×C4C22×D4112yes—
612C22×C4C22×D4112yes—
613C22×C4H(5,𝔽2)14yescomplemented
614C22×C4C2514yes—
615C22×C4C2514yes—
616C22×C4C25112yes—
617C22×C4C2511yescharacteristic
618C22×C4C2513yes—
619C22×C4C2513yes—
620C22×C4C2511yescharacteristic
621C22×C4C2513yes—
622C22×C4C2511yescharacteristic
623C22×C4C2511yescharacteristic
624C22×C4C2513yes—
625C22×C4C2513yes—
626C22×C4C2511yescharacteristic
627C22×C4C2513yes—
628C22×C4C2511yescharacteristic
629C4⋊C4—26no—
630C4⋊C4—212no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—26no—
634C4⋊C4—26no—
635C4⋊C4—26no—
636C4⋊C4—26no—
637C4⋊C4—26no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—212no—
641C4⋊C4—212no—
642C4⋊C4—224no—
643C4⋊C4—24no—
644C4⋊C4—44no—
645C4⋊C4—412no—
646C4⋊C4—412no—
647C4⋊C4C22×D4112yes—
648C4⋊C4C22×D4112yes—
649C22⋊C4—26no—
650C22⋊C4—26no—
651C22⋊C4—212no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—26no—
655C22⋊C4—212no—
656C22⋊C4—26no—
657C22⋊C4—224no—
658C22⋊C4—224no—
659C22⋊C4—212no—
660C22⋊C4—224no—
661C22⋊C4—412no—
662C22⋊C4—44no—
663C22⋊C4—412no—
664C22⋊C4—412no—
665C22⋊C4—412no—
666C22⋊C4—424no—
667C22⋊C4—412no—
668C22⋊C4—412no—
669C22⋊C4—424no—
670C22⋊C4—412no—
671C22⋊C4—424no—
672C22⋊C4—412no—
673C22⋊C4C22×D4124yes—
674C42—22no—
675C42—26no—
676C42—26no—
677C42—26no—
678C42—26no—
679C42—26no—
680C42—224no—
681C42—412no—
682C42C22×D4112yes—
683C42C22×D414yes—
684C42C22×D4112yes—
685C42C22×D4112yes—
686C23—21no—
687C23—23no—
688C23—22no—
689C23—26no—
690C23—21no—
691C23—23no—
692C23—26no—
693C23—22no—
694C23—23no—
695C23—212no—
696C23—212no—
697C23—212no—
698C23—26no—
699C23—212no—
700C23—23no—
701C23—212no—
702C23—23no—
703C23—212no—
704C23—212no—
705C23—26no—
706C23—448no—
707C23—824no—
708C23—824no—
709C23—1624no—
710C23—1624no—
711C23C23×D416yes—
712C23C2×H(5,𝔽2)12yes—
713C23C2611yescharacteristic
714Q8—412no—
715Q8—48no—
716Q8—412no—
717Q8#535116yescomplemented
718D4—224no—
719D4—412no—
720D4—412no—
721D4—424no—
722D4—424no—
723D4—412no—
724D4—448no—
725D4—448no—
726D4—412no—
727D4—424no—
728D4—824no—
729D4—824no—
730D4—812no—
731D4—824no—
732D4—824no—
733D4—1624no—
734C2×C4—21no—
735C2×C4—23no—
736C2×C4—22no—
737C2×C4—23no—
738C2×C4—21no—
739C2×C4—26no—
740C2×C4—22no—
741C2×C4—224no—
742C2×C4—224no—
743C2×C4—28no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—23no—
747C2×C4—23no—
748C2×C4—23no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—212no—
752C2×C4—212no—
753C2×C4—23no—
754C2×C4—22no—
755C2×C4—26no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—23no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—26no—
762C2×C4—24no—
763C2×C4—212no—
764C2×C4—412no—
765C2×C4—448no—
766C2×C4—412no—
767C2×C4—412no—
768C2×C4—412no—
769C2×C4—86no—
770C2×C4—86no—
771C2×C4C23×D416yes—
772C2×C4C23×D412yes—
773C2×C4C23×D412yes—
774C2×C4C23×D416yes—
775C2×C4C23×D416yes—
776C2×C4C23×D412yes—
777C2×C4C2×H(5,𝔽2)12yes—
778C2×C4C2×H(5,𝔽2)112yes—
779C2×C4C2×H(5,𝔽2)12yes—
780C2×C4#58512yes—
781C22—22no—
782C22—26no—
783C22—26no—
784C22—24no—
785C22—26no—
786C22—41no—
787C22—46no—
788C22—42no—
789C22—46no—
790C22—41no—
791C22—43no—
792C22—412no—
793C22—43no—
794C22—412no—
795C22—412no—
796C22—46no—
797C22—412no—
798C22—46no—
799C22—412no—
800C22—412no—
801C22—412no—
802C22—43no—
803C22—1648no—
804C22C24×D411yescharacteristic
805C22C22×H(5,𝔽2)11yescharacteristic
806C22C22×H(5,𝔽2)12yes—
807C22C2×#58511yescharacteristic
808C22H(7,𝔽2)12yes—
809C4—26no—
810C4—22no—
811C4—22no—
812C4—26no—
813C4—22no—
814C4—43no—
815C4—41no—
816C4—43no—
817C4—412no—
818C4—44no—
819C4—41no—
820C4—44no—
821C4—43no—
822C4C2×#535112yes—
823C4#348814yes—
824C2—42no—
825C2—46no—
826C2—83no—
827C2—812no—
828C2C22×#53511yescharacteristic
829C2C2×#348811yescharacteristic
830C2#6285211yescharacteristic
831C2#6291612yes—
832C2#6292312yes—
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. C2×#3498C2semidirect
2. C2×#3480C2semidirect
3. #42987C2semidirect
4. #42986C2semidirect
5. #42484C2semidirect
6. #42480C2semidirect
7. #39342C2semidirect
8. #38910C2semidirect
9. #37621C2semidirect
10. #37614C2semidirect
11. #36576C2semidirect
12. #36455C2semidirect
13. #36091C2semidirect
14. #36082C2semidirect
15. #36066C2semidirect
16. #36049C2semidirect
17. #35272C2semidirect
18. #34609C2semidirect
19. #34193C2semidirect
23. C2×#559C22semidirect
24. C2×#557C22semidirect
25. C2×#556C22semidirect
26. C2×#553C22semidirect
27. C2×#553C22semidirect
31. C2×#550C22semidirect
33. C2×#548C22semidirect
34. C2×#548C22semidirect
38. C2×#535C22semidirect
40. C2×#532C22semidirect
42. C2×#529C22semidirect
43. C2×#529C22semidirect
45. C2×C4×#41C22semidirect
46. C2×C4×#41C22semidirect
47. C22×C4×Q8C22semidirect
48. #2856C22semidirect
49. #2856C22semidirect
50. #2818C22semidirect
51. #2813C22semidirect
52. #2685C22semidirect
53. #2678C22semidirect
54. #2670C22semidirect
55. #2669C22semidirect
56. #2662C22semidirect
57. #2657C22semidirect
58. #2641C22semidirect
59. #2635C22semidirect
60. #2635C22semidirect
61. #2632C22semidirect
62. #2631C22semidirect
63. #2628C22semidirect
64. #2628C22semidirect
65. #2624C22semidirect
66. #2619C22semidirect
67. #2619C22semidirect
68. #2619C22semidirect
69. #2616C22semidirect
70. #2615C22semidirect
71. #2615C22semidirect
72. #2613C22semidirect
73. #2562C22semidirect
74. #2548C22semidirect
75. #2548C22semidirect
76. #2548C22semidirect
77. #2541C22semidirect
78. #2541C22semidirect
79. #2541C22semidirect
80. #2541C22semidirect
81. #2540C22semidirect
82. #2540C22semidirect
83. #2538C22semidirect
84. #2537C22semidirect
85. #2491C22semidirect
86. #2490C22semidirect
87. #2435C22semidirect
88. #2435C22semidirect
89. #2433C22semidirect
90. #2433C22semidirect
91. #2428C22semidirect
92. #2426C22semidirect
93. #2416C22semidirect
94. #2414C22semidirect
95. #2414C22semidirect
96. #2408C22semidirect
97. #2408C22semidirect
98. #2408C22semidirect
99. #2408C22semidirect
100. #2408C22semidirect
101. #2408C22semidirect
102. #2408C22semidirect
103. #2398C22semidirect
104. #2397C22semidirect
105. #2388C22semidirect
106. #2388C22semidirect
107. #2354C22semidirect
108. Q8×C4⋊C4C22semidirect
109. #2347C22semidirect
111. #2341C22semidirect
112. #2341C22semidirect
113. #2319C22semidirect
114. #2309C22semidirect
115. C4×#121C22semidirect
116. C4×#121C22semidirect
117. #2285C22semidirect
118. #2283C22semidirect
119. #2276C22semidirect
200. C4×#41D4semidirect
613. C22×C4H(5,𝔽2)semidirect
717. Q8#535semidirect

Maximal subgroups

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

subgroupindex
C2×#34982
C2×#34802
#429872
#429862
#424842
#424802
#393422
#389102
#376212
#376142
#365762
#364552
#360912
#360822
#360662
#360492
#352722
#346092
#341932