Finite Group Databasebeta

← #7711153

Subgroups — #7711153

Order 512.

5888 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C212yesmaximal, complemented
2#59817C211yesmaximal, characteristic, complemented
3#59816C211yesmaximal, characteristic, complemented
4#59233C212yesmaximal, complemented
5#59041C212yesmaximal, complemented
6#46287C214yesmaximal, complemented
7#46073C214yesmaximal, complemented
8#40173C218yesmaximal, complemented
9#39124C214yesmaximal, complemented
10#38910C214yesmaximal, complemented
11#38206C218yesmaximal, complemented
12#37636C212yesmaximal, complemented
13#37150C214yesmaximal, complemented
14#36631C212yesmaximal, complemented
15#36174C214yesmaximal, complemented
16D4×#124C214yesmaximal, complemented
17#35129C214yesmaximal, complemented
18#34493C212yesmaximal, complemented
19C4×#532C211yesmaximal, characteristic, complemented
20C2×D4×Q8C2214yescomplemented
21C2×D42C2212yes—
22C2×D42C2214yes—
23C2×#532C2211yescharacteristic
24C2×#529C2214yescomplemented
25C22×#124C2214yescomplemented
26C2×C4×#41C2212yescomplemented
27#2861C2214yescomplemented
28#2860C2214yescomplemented
29#2860C2214yescomplemented
30#2859C2212yescomplemented
31#2858C2212yes—
32#2857C2212yescomplemented
33#2856C2212yes—
34#2854C2214yescomplemented
35#2854C2214yescomplemented
36#2850C2218yescomplemented
37#2850C2214yescomplemented
38#2832C2218yescomplemented
39#2808C2218yescomplemented
40#2785C2218yescomplemented
41#2753C22116yescomplemented
42#2736C22116yescomplemented
43#2723C22116yescomplemented
44#2696C22116yescomplemented
45#2685C22116yescomplemented
46#2684C2218yescomplemented
47#2683C2214yescomplemented
48#2679C2214yes—
49#2678C22116yescomplemented
50#2632C2218yescomplemented
51#2631C2218yescomplemented
52#2628C2218yescomplemented
53#2624C2218yescomplemented
54#2610C2218yescomplemented
55#2610C2218yescomplemented
56#2592C2218yescomplemented
57#2563C2214yescomplemented
58#2563C2218yescomplemented
59#2551C2212yescomplemented
60#2548C2214yes—
61#2547C2214yescomplemented
62#2540C2218yescomplemented
63#2538C2214yescomplemented
64#2537C2212yes—
65#2537C2214yes—
66#2535C2218yescomplemented
67#2526C22116yescomplemented
68#2518C22116yescomplemented
69#2513C2218yescomplemented
70#2495C2218yescomplemented
71#2491C2218yescomplemented
72#2491C2218yescomplemented
73#2490C2218yescomplemented
74#2489C2218yescomplemented
75#2485C2218yescomplemented
76#2482C2218yescomplemented
77#2472C22116yescomplemented
78#2472C22116yescomplemented
79#2452C2218yescomplemented
80#2436C2218yescomplemented
81#2435C2218yescomplemented
82#2420C2218yescomplemented
83#2414C2218yescomplemented
84#2409C2214yescomplemented
85#2409C2214yescomplemented
86#2408C2214yes—
87#2408C2218yes—
88#2408C2214yescomplemented
89#2408C2218yescomplemented
90#2404C2218yescomplemented
91#2375C2218yescomplemented
92#2366C2212yes—
93#2363C2218yescomplemented
94#2355C2214yescomplemented
95#2354C2214yescomplemented
96#2354C2214yescomplemented
97#2346C2218yescomplemented
98D4×C22⋊C4C2218yescomplemented
99D4×C22⋊C4C2218yescomplemented
100#2324C2218yescomplemented
101#2321C2218yescomplemented
102#2321C2218yescomplemented
103#2309C2218yescomplemented
104C4×C4⋊Q8C2211yescharacteristic, complemented
105C4×C4⋊Q8C2212yescomplemented
106C4×C4⋊Q8C2211yescharacteristic, complemented
107C4×#127C2212yes—
108C4×#127C2211yescharacteristic
109C4×#127C2211yescharacteristic
110C4×#124C2214yescomplemented
111C4×#124C2212yescomplemented
112C4×#124C2212yescomplemented
113C4×#121C2214yescomplemented
114C4×#121C2214yescomplemented
115C4×#121C2214yescomplemented
116C4×#121C2214yescomplemented
117#2297C2212yescomplemented
118#2293C2214yescomplemented
119#2293C2214yescomplemented
120#2293C2214yescomplemented
121#2285C2211yescharacteristic, complemented
122#2283C2214yescomplemented
123C42×D4C2214yescomplemented
124C2×C43C2211yescharacteristic, complemented
125C22×#41C2312yes—
126C23×Q8C2314yes—
127C23×D4C2318yes—
128C23×D4C2314yes—
129D4×Q8—416no—
130D42—216no—
131D42—416no—
132#532—28no—
133C2×C4⋊Q8C2311yescharacteristic
134C2×C4⋊Q8C2312yes—
135C2×C4⋊Q8C2318yes—
136C2×#127C2312yes—
137C2×#127C2311yescharacteristic
138#529—416no—
139C2×#126C2318yes—
140C2×#125C2314yes—
141C2×#124—416no—
142C2×#124C2314yes—
143C2×#124C2312yes—
144C2×#124C2318yes—
145C2×#124C2314yes—
146C2×#124C2318yes—
147C2×#124C2318yes—
148C2×#123C2318yes—
149C2×C22⋊Q8C2314yes—
150C2×C22⋊Q8C2318yes—
151C2×C22⋊Q8C23116yes—
152C2×#121C2318yes—
153C2×#121C2314yes—
154C2×#121C2314yes—
155C2×#121C2318yes—
156C2×#121C2314yes—
157C2×#121C2314yes—
158C2×#121C2318yes—
159C2×#120C2318yes—
160C2×#120C2318yes—
161C2×#120C23116yes—
162C4×#41—48no—
163C2×C4×Q8C2314yes—
164C2×C4×Q8C2312yes—
165C2×C4×Q8C2312yes—
166C2×C4×D4C2314yes—
167C2×C4×D4C2314yes—
168C2×C4×D4C2314yes—
169C2×C4×D4C2314yes—
170C2×C4×D4C2312yes—
171C2×C4×D4C2314yes—
172C2×C4×D4C2312yes—
173C2×C4×D4C2314yes—
174C2×C4×D4C2318yes—
175C2×C4×D4C2314yes—
176C2×C4×D4C2318yes—
177C2×C4×D4C2314yes—
178C2×#117C2318yes—
179C2×#117C2318yes—
180C2×#117C2312yes—
181C2×#117C2314yes—
182C22×C22⋊C4C2318yes—
183C22×C22⋊C4C2318yes—
184C22×C42C2311yescharacteristic
185C22×C42C2314yes—
186C22×C42C2312yes—
187C22×C42C2311yescharacteristic
188C22×C42C2311yescharacteristic
189C22×C42C2312yes—
190#400C23116yes—
191#399C23116yes—
192#397C23116yes—
193#397C23116yes—
194#397C23116yes—
195#397C23116yes—
196#396C23116yes—
197#395C2318yes—
198#395C2318yes—
199#394C2318yes—
200#394C23116yes—
201#394C2318yes—
202#394C23116yes—
203#394C23116yes—
204#394C23116yes—
205#394C23116yes—
206#393C2318yes—
207#393C23116yes—
208#393C23116yes—
209#393C23116yes—
210#393C2318yes—
211#392C2318yes—
212#392C2318yes—
213#392C23116yes—
214#391C2312yes—
215#391C2314yes—
216#391C2312yes—
217#391C2318yes—
218#391C2314yes—
219#390C2314yes—
220#390C2314yes—
221#390C2314yes—
222#390C2314yes—
223#390C2312yes—
224#390C2314yes—
225#390C2312yes—
226#390C23116yes—
227#390C2318yes—
228#390C2314yes—
229#390C23116yes—
230#390C2318yes—
231#390C2318yes—
232#390C23116yes—
233#390C2318yes—
234#390C2314yes—
235#390C2314yes—
236#390C2314yes—
237#390C2314yes—
238#390C2314yes—
239#390C2314yes—
240#389C2314yes—
241#389C2314yes—
242#389C2314yes—
243#389C2314yes—
244#389C2314yes—
245#389C2314yes—
246#389C2314yes—
247#389C2314yes—
248#389C2314yes—
249#389C2318yes—
250#389C2314yes—
251#388C2318yes—
252#388C2318yes—
253#388C23116yes—
254#388C23116yes—
255#388C23116yes—
256#388C23116yes—
257#388C23116yes—
258#388C2318yes—
259#388C2318yes—
260#388C2318yes—
261#388C2318yes—
262#388C23116yes—
263#388C2318yes—
264#388C2318yes—
265#388C23116yes—
266#388C2318yes—
267#388C2318yes—
268#387C23116yes—
269#386C2318yes—
270#386C23116yes—
271#386C2318yes—
272#386C2318yes—
273#386C23116yes—
274#386C23116yes—
275#386C23116yes—
276#386C2318yes—
277#386C2318yes—
278#385C2318yes—
279#385C2318yes—
280#384C2311yescharacteristic
281#384C2311yescharacteristic
282#384C2312yes—
283#384C2312yes—
284#383C2318yes—
285#382C23116yes—
286#382C2318yes—
287#382C2314yes—
288#382C2312yes—
289#381C2318yes—
290#380C2314yes—
291#380C2314yes—
292#380C2318yes—
293#380C2318yes—
294#380C2318yes—
295#380C2318yes—
296#380C2314yes—
297#380C2314yes—
298#380C2314yes—
299#379C2318yes—
300#379C23116yes—
301#379C2318yes—
302#379C23116yes—
303C4×C4⋊C4C2314yes—
304C4×C4⋊C4C2314yes—
305C4×C4⋊C4C2314yes—
306C4×C4⋊C4C2314yes—
307C4×C4⋊C4C2318yes—
308C4×C4⋊C4C2318yes—
309C4×C4⋊C4C2314yes—
310C4×C22⋊C4C2318yes—
311C4×C22⋊C4C2318yes—
312C4×C22⋊C4C2318yes—
313C4×C22⋊C4C2318yes—
314C4×C22⋊C4C2318yes—
315C4×C22⋊C4C2318yes—
316#376C2318yes—
317C43C2311yescharacteristic
318C43C2311yescharacteristic
319C43C2312yes—
320C43C2311yescharacteristic
321C43C2312yes—
322C43C2311yescharacteristic
323C25C2418yes—
324C2×#41—28no—
325C2×#41—44no—
326C2×#41—44no—
327C22×Q8—48no—
328C22×Q8—416no—
329C22×Q8C2414yes—
330C22×Q8C2412yes—
331C22×Q8C2418yes—
332C22×D4—232no—
333C22×D4—48no—
334C22×D4—416no—
335C22×D4—416no—
336C22×D4—416no—
337C22×D4C2414yes—
338C22×D4C2414yes—
339C22×D4C2414yes—
340C22×D4C2414yes—
341C22×D4C2414yes—
342C22×D4C2418yes—
343C22×D4C24116yes—
344C22×D4C2418yes—
345C22×D4C2412yes—
346C23×C4C2418yes—
347C23×C4C2411yescharacteristic
348C23×C4C2411yescharacteristic
349C23×C4C2412yes—
350C23×C4C2414yes—
351C23×C4C2414yes—
352C23×C4C2412yes—
353C23×C4C2414yes—
354C23×C4C2411yescharacteristic
355C23×C4C2418yes—
356C4⋊Q8—24no—
357C4⋊Q8—28no—
358C4⋊Q8—416no—
359#127—28no—
360#127#4118yes—
361#126—416no—
362#125—48no—
363#124—28no—
364#124—216no—
365#124—416no—
366#124—416no—
367#124—416no—
368#124—48no—
369#123—416no—
370C22⋊Q8—432no—
371C22⋊Q8—48no—
372C22⋊Q8—416no—
373#121—216no—
374#121—232no—
375#121—48no—
376#121—48no—
377#121—416no—
378#121—416no—
379#121—48no—
380#120—232no—
381#120—432no—
382#120—416no—
383C4×Q8—216no—
384C4×Q8—44no—
385C4×Q8—44no—
386C4×D4—216no—
387C4×D4—216no—
388C4×D4—216no—
389C4×D4—216no—
390C4×D4—48no—
391C4×D4—416no—
392C4×D4—48no—
393C4×D4—44no—
394C4×D4—44no—
395C4×D4—48no—
396C4×D4—48no—
397C4×D4—416no—
398#117—48no—
399#117—44no—
400#117—416no—
401#117—416no—
402C2×C4⋊C4C2414yes—
403C2×C4⋊C4C2414yes—
404C2×C4⋊C4C2414yes—
405C2×C4⋊C4C2414yes—
406C2×C4⋊C4C2414yes—
407C2×C4⋊C4C2414yes—
408C2×C4⋊C4C2414yes—
409C2×C4⋊C4C2414yes—
410C2×C4⋊C4C2418yes—
411C2×C4⋊C4C2414yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2414yes—
415C2×C4⋊C4C2414yes—
416C2×C4⋊C4C2418yes—
417C2×C4⋊C4C2418yes—
418C2×C4⋊C4C2418yes—
419C2×C4⋊C4C2414yes—
420C2×C4⋊C4C2414yes—
421C2×C4⋊C4C24116yes—
422C2×C22⋊C4—416no—
423C2×C22⋊C4—416no—
424C2×C22⋊C4C2418yes—
425C2×C22⋊C4C2418yes—
426C2×C22⋊C4C2418yes—
427C2×C22⋊C4C2418yes—
428C2×C22⋊C4C2418yes—
429C2×C22⋊C4C2418yes—
430C2×C22⋊C4C2418yes—
431C2×C22⋊C4C24116yes—
432C2×C22⋊C4C24116yes—
433C2×C22⋊C4C2414yes—
434C2×C22⋊C4C2414yes—
435C2×C22⋊C4C2414yes—
436C2×C22⋊C4C2418yes—
437C2×C22⋊C4C2418yes—
438C2×C22⋊C4C24116yes—
439C2×C22⋊C4C24116yes—
440C2×C22⋊C4C2418yes—
441C2×C22⋊C4C2418yes—
442C2×C22⋊C4C2418yes—
443C2×C22⋊C4C2418yes—
444C2×C22⋊C4C24116yes—
445C2×C22⋊C4C2418yes—
446C2×C22⋊C4C24116yes—
447C2×C22⋊C4C2418yes—
448C2×C22⋊C4C2418yes—
449C2×C42—24no—
450C2×C42—24no—
451C2×C42—216no—
452C2×C42—28no—
453C2×C42—44no—
454C2×C42—42no—
455C2×C42C2411yescharacteristic
456C2×C42C2412yes—
457C2×C42C2414yes—
458C2×C42C2418yes—
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2412yes—
462C2×C42C2412yes—
463C2×C42C2412yes—
464C2×C42C2414yes—
465C2×C42C2414yes—
466C2×C42C2412yes—
467C2×C42C2411yescharacteristic
468C2×C42C2412yes—
469C2×C42C24116yes—
470C2×C42C2412yes—
471C2×C42C2412yes—
472C2×C42C2412yes—
473C2×C42C2411yescharacteristic
474C2×C42C2411yescharacteristic
475C2×C42C2411yescharacteristic
476C2×C42C2412yes—
477C2×C42C2411yescharacteristic
478#95C2418yes—
479#95C2418yes—
480#95C2418yes—
481#95C2418yes—
482#95C2418yes—
483#95C2418yes—
484#95C2418yes—
485#95C2418yes—
486#95C2418yes—
487#95C24116yes—
488#95C24116yes—
489#95C2418yes—
490#95C2418yes—
491#95C24116yes—
492C24—216no—
493C24—48no—
494C24—416no—
495C24—416no—
496C24—48no—
497C24C2518yes—
498C24C2514yes—
499C24C2511yescharacteristic
500#41—432no—
501C2×Q8—24no—
502C2×Q8—28no—
503C2×Q8—28no—
504C2×Q8—28no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—416no—
508C2×Q8—48no—
509C2×Q8—832no—
510C2×D4—28no—
511C2×D4—28no—
512C2×D4—232no—
513C2×D4—216no—
514C2×D4—28no—
515C2×D4—28no—
516C2×D4—28no—
517C2×D4—28no—
518C2×D4—28no—
519C2×D4—28no—
520C2×D4—28no—
521C2×D4—28no—
522C2×D4—28no—
523C2×D4—42no—
524C2×D4—44no—
525C2×D4—42no—
526C2×D4—48no—
527C2×D4—44no—
528C2×D4—416no—
529C2×D4—416no—
530C2×D4—44no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—416no—
534C2×D4—864no—
535C2×D4—832no—
536C2×D4C2×#41116yes—
537C2×D4C2×#4118yes—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—28no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—216no—
545C22×C4—28no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—216no—
553C22×C4—216no—
554C22×C4—24no—
555C22×C4—216no—
556C22×C4—28no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—44no—
560C22×C4—48no—
561C22×C4—416no—
562C22×C4—48no—
563C22×C4C2514yes—
564C22×C4C2518yes—
565C22×C4C2512yes—
566C22×C4C2514yes—
567C22×C4C2511yescharacteristic
568C22×C4C2512yes—
569C22×C4C2518yes—
570C22×C4C2514yes—
571C22×C4C2518yes—
572C22×C4C2511yescharacteristic
573C22×C4C2511yescharacteristic
574C22×C4C2511yescharacteristic
575C22×C4C2511yescharacteristic
576C22×C4C2512yes—
577C22×C4C2512yes—
578C22×C4C2511yescharacteristic
579C4⋊C4—28no—
580C4⋊C4—28no—
581C4⋊C4—28no—
582C4⋊C4—28no—
583C4⋊C4—28no—
584C4⋊C4—28no—
585C4⋊C4—216no—
586C4⋊C4—28no—
587C4⋊C4—28no—
588C4⋊C4—28no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—44no—
596C4⋊C4—48no—
597C4⋊C4—44no—
598C4⋊C4—416no—
599C22⋊C4—216no—
600C22⋊C4—216no—
601C22⋊C4—216no—
602C22⋊C4—216no—
603C22⋊C4—216no—
604C22⋊C4—216no—
605C22⋊C4—216no—
606C22⋊C4—416no—
607C22⋊C4—416no—
608C22⋊C4—416no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—416no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—416no—
621C22⋊C4—416no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C42—24no—
625C42—22no—
626C42—22no—
627C42—24no—
628C42—28no—
629C42—22no—
630C42—22no—
631C42—28no—
632C42—28no—
633C42—24no—
634C42—24no—
635C42—216no—
636C42—24no—
637C42—24no—
638C42—42no—
639C42—41no—
640C42—42no—
641C42—41no—
642C42—42no—
643C42—416no—
644C42C2×#4114yes—
645C42H(5,𝔽2)14yes—
646C42H(5,𝔽2)18yes—
647C23—21no—
648C23—28no—
649C23—21no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—28no—
654C23—22no—
655C23—28no—
656C23—28no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—28no—
662C23—832no—
663C23—816no—
664C23—816no—
665C23—816no—
666C23—1616no—
667C23C22×#4118yes—
668C23#58512yes—
669C23C2611yescharacteristic
670Q8—48no—
671Q8—416no—
672Q8—816no—
673D4—232no—
674D4—48no—
675D4—416no—
676D4—416no—
677D4—416no—
678D4—88no—
679D4—816no—
680D4—832no—
681D4—816no—
682C2×C4—28no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—28no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—24no—
716C2×C4—48no—
717C2×C4—416no—
718C2×C4—44no—
719C2×C4—48no—
720C2×C4—432no—
721C2×C4—44no—
722C2×C4—416no—
723C2×C4—88no—
724C2×C4—816no—
725C2×C4C22×#4112yes—
726C2×C4C22×#4114yes—
727C2×C4C2×H(5,𝔽2)12yes—
728C2×C4C2×H(5,𝔽2)12yes—
729C2×C4C2×H(5,𝔽2)14yes—
730C2×C4C2×H(5,𝔽2)14yes—
731C2×C4C2×H(5,𝔽2)12yes—
732C2×C4C2×H(5,𝔽2)14yes—
733C2×C4#58514yes—
734C22—22no—
735C22—28no—
736C22—216no—
737C22—24no—
738C22—44no—
739C22—41no—
740C22—41no—
741C22—44no—
742C22—42no—
743C22—48no—
744C22—48no—
745C22—48no—
746C22—48no—
747C22—48no—
748C22—48no—
749C22—48no—
750C22—48no—
751C22—1632no—
752C22C23×#4111yescharacteristic
753C22C22×H(5,𝔽2)11yescharacteristic
754C22C22×H(5,𝔽2)12yes—
755C22C2×#58512yes—
756C22C2×#58511yescharacteristic
757C4—22no—
758C4—22no—
759C4—22no—
760C4—24no—
761C4—41no—
762C4—44no—
763C4—48no—
764C4—41no—
765C4—44no—
766C4—44no—
767C4—42no—
768C4—48no—
769C4—42no—
770C4—48no—
771C4#351418yes—
772C4#354914yes—
773C2—42no—
774C2—48no—
775C2—88no—
776C2C2×#354911yescharacteristic
777C2#6275911yescharacteristic
778C2#6277311yescharacteristic
779C2C2×#351412yes—
780C2#6283012yes—
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. #59863C2semidirect
2. #59817C2semidirect
3. #59816C2semidirect
4. #59233C2semidirect
5. #59041C2semidirect
6. #46287C2semidirect
7. #46073C2semidirect
8. #40173C2semidirect
9. #39124C2semidirect
10. #38910C2semidirect
11. #38206C2semidirect
12. #37636C2semidirect
13. #37150C2semidirect
14. #36631C2semidirect
15. #36174C2semidirect
16. D4×#124C2semidirect
17. #35129C2semidirect
18. #34493C2semidirect
19. C4×#532C2semidirect
20. C2×D4×Q8C22semidirect
24. C2×#529C22semidirect
25. C22×#124C22semidirect
26. C2×C4×#41C22semidirect
27. #2861C22semidirect
28. #2860C22semidirect
29. #2860C22semidirect
30. #2859C22semidirect
32. #2857C22semidirect
34. #2854C22semidirect
35. #2854C22semidirect
36. #2850C22semidirect
37. #2850C22semidirect
38. #2832C22semidirect
39. #2808C22semidirect
40. #2785C22semidirect
41. #2753C22semidirect
42. #2736C22semidirect
43. #2723C22semidirect
44. #2696C22semidirect
45. #2685C22semidirect
46. #2684C22semidirect
47. #2683C22semidirect
49. #2678C22semidirect
50. #2632C22semidirect
51. #2631C22semidirect
52. #2628C22semidirect
53. #2624C22semidirect
54. #2610C22semidirect
55. #2610C22semidirect
56. #2592C22semidirect
57. #2563C22semidirect
58. #2563C22semidirect
59. #2551C22semidirect
61. #2547C22semidirect
62. #2540C22semidirect
63. #2538C22semidirect
66. #2535C22semidirect
67. #2526C22semidirect
68. #2518C22semidirect
69. #2513C22semidirect
70. #2495C22semidirect
71. #2491C22semidirect
72. #2491C22semidirect
73. #2490C22semidirect
74. #2489C22semidirect
75. #2485C22semidirect
76. #2482C22semidirect
77. #2472C22semidirect
78. #2472C22semidirect
79. #2452C22semidirect
80. #2436C22semidirect
81. #2435C22semidirect
82. #2420C22semidirect
83. #2414C22semidirect
84. #2409C22semidirect
85. #2409C22semidirect
88. #2408C22semidirect
89. #2408C22semidirect
90. #2404C22semidirect
91. #2375C22semidirect
93. #2363C22semidirect
94. #2355C22semidirect
95. #2354C22semidirect
96. #2354C22semidirect
97. #2346C22semidirect
98. D4×C22⋊C4C22semidirect
99. D4×C22⋊C4C22semidirect
100. #2324C22semidirect
101. #2321C22semidirect
102. #2321C22semidirect
103. #2309C22semidirect
104. C4×C4⋊Q8C22semidirect
105. C4×C4⋊Q8C22semidirect
106. C4×C4⋊Q8C22semidirect
110. C4×#124C22semidirect
111. C4×#124C22semidirect
112. C4×#124C22semidirect
113. C4×#121C22semidirect
114. C4×#121C22semidirect
115. C4×#121C22semidirect
116. C4×#121C22semidirect
117. #2297C22semidirect
118. #2293C22semidirect
119. #2293C22semidirect
120. #2293C22semidirect
121. #2285C22semidirect
122. #2283C22semidirect
123. C42×D4C22semidirect
124. C2×C43C22semidirect

Maximal subgroups

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

subgroupindex
#598632
#598172
#598162
#592332
#590412
#462872
#460732
#401732
#391242
#389102
#382062
#376362
#371502
#366312
#361742
D4×#1242
#351292
#344932
C4×#5322