Finite Group Databasebeta

← #62857

Subgroups — #62857

Order 256.

3541 conjugacy classes of subgroups.

The subgroup lattice has 673 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3524C212yesmaximal, complemented
2#3522C212yesmaximal, complemented
3#3521C216yesmaximal, complemented
4#3520C216yesmaximal, complemented
5#3518C212yesmaximal, complemented
6#3516C212yesmaximal, complemented
7#3514C216yesmaximal, complemented
8#3513C216yesmaximal, complemented
9#3511C213yesmaximal, complemented
10#3510C213yesmaximal, complemented
11#3503C211yesmaximal, characteristic, complemented
12#3500C211yesmaximal, characteristic, complemented
13#3495C213yesmaximal, complemented
14#3494C213yesmaximal, complemented
15#3489C211yesmaximal, characteristic, complemented
16#3488C211yesmaximal, characteristic, complemented
17#3461C213yesmaximal, complemented
18#3460C213yesmaximal, complemented
19#3455C213yesmaximal, complemented
20C2×#542C213yesmaximal, complemented
21C4×2−1+4C211yesmaximal, characteristic, complemented
22C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
23#3428C211yesmaximal, characteristic, complemented
24C2×2−1+4C2211yescharacteristic
25C2×H(5,𝔽2)C2211yescharacteristic
26C22×#41C2211yescharacteristic
27#559C2216yescomplemented
28#559C2216yescomplemented
29Q82C2212yescomplemented
30#557C2212yescomplemented
31#556C2216yescomplemented
32#556C2216yescomplemented
33#556C2216yescomplemented
34#556C2216yescomplemented
35#555C2216yescomplemented
36#555C2216yescomplemented
37#554C2216yescomplemented
38#554C2216yescomplemented
39#554C2216yescomplemented
40#553C2216yescomplemented
41#553C2216yescomplemented
42#553C22112yescomplemented
43#552C2216yescomplemented
44#552C22112yescomplemented
45#552C2216yescomplemented
46#551C22112yescomplemented
47#551C22112yescomplemented
48#551C22112yescomplemented
49#551C22112yescomplemented
50#550C2212yes—
51D4×Q8C2212yescomplemented
52D4×Q8C2216yescomplemented
53#548C2212yes—
54#548C2212yescomplemented
55#548C2212yescomplemented
56#548C2212yescomplemented
57#548C22112yescomplemented
58#547C2216yescomplemented
59#547C2216yescomplemented
60#547C2216yescomplemented
61#546C2216yes—
62#546C2216yescomplemented
63#546C22112yescomplemented
64#546C2216yescomplemented
65#546C2216yescomplemented
66D42C2216yes—
67#544C2213yescomplemented
68#544C2213yescomplemented
69#542C2213yescomplemented
70#542C2216yescomplemented
71#542C2216yescomplemented
72#542C2216yescomplemented
73#542C2216yescomplemented
74#542C2216yescomplemented
75#542C2216yescomplemented
76#542C2216yescomplemented
77#542C2211yescharacteristic, complemented
78#542C2213yescomplemented
79#542C2213yescomplemented
80#542C2216yescomplemented
81#542C2216yescomplemented
82#541C2213yescomplemented
83#541C2213yescomplemented
84#541C2216yescomplemented
85#540C2213yescomplemented
86#540C2213yescomplemented
87#540C2216yescomplemented
88#539C2216yescomplemented
89#539C2216yescomplemented
90#539C22112yescomplemented
91#538C2216yescomplemented
92#538C2216yescomplemented
93#538C22112yescomplemented
94#537C2213yes—
95#537C2213yescomplemented
96#536C2213yescomplemented
97#536C2213yescomplemented
98#535C2213yes—
99#535C2213yescomplemented
100#533C2213yescomplemented
101#533C2216yescomplemented
102#533C2216yescomplemented
103#532C2213yescomplemented
104#532C2216yescomplemented
105#532C2216yescomplemented
106C2×C4⋊Q8C2213yescomplemented
107#529C2216yescomplemented
108#529C2216yescomplemented
109#529C2216yescomplemented
110#529C2216yescomplemented
111#529C2216yescomplemented
112#529C2216yescomplemented
113#529C2216yescomplemented
114#529C2216yescomplemented
115#529C22112yescomplemented
116C2×#126C2216yescomplemented
117C2×#124C2213yescomplemented
118C2×#124C2216yescomplemented
119#525C2213yes—
120#525C2213yescomplemented
121#525C22112yescomplemented
122C2×#123C2216yescomplemented
123C2×C22⋊Q8C2213yescomplemented
124C2×C22⋊Q8C2216yescomplemented
125C2×#121C2213yes—
126#520C2211yescharacteristic
127#520C2211yescharacteristic
128#520C2213yescomplemented
129#520C2213yescomplemented
130#520C2211yescharacteristic, complemented
131#520C2211yescharacteristic, complemented
132#520C2213yescomplemented
133#520C2212yescomplemented
134#520C2213yescomplemented
135#520C2216yescomplemented
136#519C2211yescharacteristic, complemented
137#519C2211yescharacteristic, complemented
138#519C2213yescomplemented
139#519C2212yescomplemented
140#518C2213yescomplemented
141#518C2213yescomplemented
142#518C2213yescomplemented
143#518C2216yescomplemented
144C4×#41C2211yescharacteristic
145C4×#41C2211yescharacteristic
146C4×#41C2213yescomplemented
147C4×#41C2213yescomplemented
148C4×#41C2213yescomplemented
149C4×#41C2212yescomplemented
150C4×#41C2213yescomplemented
151C4×#41C2216yescomplemented
152C2×C4×Q8C2213yescomplemented
153C2×C4×Q8C2212yescomplemented
154C2×C4×D4C2213yescomplemented
155C2×C4×D4C2216yescomplemented
156C2×#117C2213yescomplemented
157C2×#117C2213yescomplemented
1582−1+4—28no—
159H(5,𝔽2)—28no—
160C2×#41—28no—
161C2×#41C2313yes—
162C2×#41C2313yes—
163C2×#41C2313yes—
164C2×#41C2316yes—
165C2×#41C2312yes—
166C2×#41C2313yes—
167C2×#41C2311yescharacteristic
168C2×#41C23112yes—
169C2×#41C2311yescharacteristic
170C22×Q8C2313yes—
171C22×Q8C2312yes—
172C22×Q8C2311yescharacteristic
173C22×Q8C2316yes—
174C22×D4C2313yes—
175C22×D4C2316yes—
176C22×D4C2313yes—
177C22×D4C2316yes—
178C23×C4C2313yes—
179C23×C4C2316yes—
180C4⋊Q8C2313yes—
181C4⋊Q8C2316yes—
182C4⋊Q8C2316yes—
183C4⋊Q8C2316yes—
184C4⋊Q8C2313yes—
185C4⋊Q8C2316yes—
186C4⋊Q8C2311yescharacteristic
187C4⋊Q8C2316yes—
188C4⋊Q8C2316yes—
189#127C2313yes—
190#127C2316yes—
191#126C2316yes—
192#126C23112yes—
193#126C23112yes—
194#126C23112yes—
195#126C2316yes—
196#126C2316yes—
197#126C2312yes—
198#126C2316yes—
199#126C2316yes—
200#126C23112yes—
201#126C23112yes—
202#126C2316yes—
203#126C2316yes—
204#125C2316yes—
205#125C2313yes—
206#125C2313yes—
207#125C2316yes—
208#125C2316yes—
209#125C2316yes—
210#125C2316yes—
211#125C2316yes—
212#125C23112yes—
213#124C2316yes—
214#124C2313yes—
215#124C2316yes—
216#124C23112yes—
217#124C2316yes—
218#124C2316yes—
219#124C23112yes—
220#124C23112yes—
221#124C2312yes—
222#124C2316yes—
223#124C2316yes—
224#124C2316yes—
225#124C2316yes—
226#124C2311yescharacteristic
227#124C23112yes—
228#123C2316yes—
229#123C23112yes—
230#123C23112yes—
231#123C23112yes—
232#123C2316yes—
233#123C2316yes—
234#123C2316yes—
235#123C2312yes—
236#123C2316yes—
237#123C23112yes—
238#123C23112yes—
239#123C23112yes—
240#123C2316yes—
241#123C2316yes—
242#123C2316yes—
243#123C2316yes—
244#123C23112yes—
245C22⋊Q8C2313yes—
246C22⋊Q8C2316yes—
247C22⋊Q8C23112yes—
248C22⋊Q8C2316yes—
249C22⋊Q8C2316yes—
250C22⋊Q8C2316yes—
251C22⋊Q8C23112yes—
252C22⋊Q8C23112yes—
253C22⋊Q8C2311yescharacteristic
254C22⋊Q8C2313yes—
255C22⋊Q8C2313yes—
256C22⋊Q8C23112yes—
257C22⋊Q8C2312yes—
258C22⋊Q8C2316yes—
259C22⋊Q8C2316yes—
260C22⋊Q8C2316yes—
261C22⋊Q8C2316yes—
262C22⋊Q8C23112yes—
263C22⋊Q8C2316yes—
264C22⋊Q8C2316yes—
265C22⋊Q8C2316yes—
266C22⋊Q8C2316yes—
267C22⋊Q8C23112yes—
268#121C2313yes—
269#121C2316yes—
270#121C2316yes—
271#121C2316yes—
272#121C2313yes—
273#121C2311yescharacteristic
274#121C2316yes—
275#121C2313yes—
276#121C23112yes—
277#121C2316yes—
278#121C2316yes—
279#121C23112yes—
280#121C2316yes—
281#121C2316yes—
282#121C2316yes—
283#121C2316yes—
284#121C2316yes—
285#121C2316yes—
286#121C2316yes—
287#121C23112yes—
288#120C2316yes—
289#120C23112yes—
290#120C23112yes—
291#120C2316yes—
292C4×Q8C2311yescharacteristic
293C4×Q8C2313yes—
294C4×Q8C2316yes—
295C4×Q8C2312yes—
296C4×Q8C2316yes—
297C4×Q8C2316yes—
298C4×Q8C2316yes—
299C4×Q8C2311yescharacteristic
300C4×Q8C2311yescharacteristic
301C4×Q8C2311yescharacteristic
302C4×Q8C2311yescharacteristic
303C4×Q8C2313yes—
304C4×Q8C2316yes—
305C4×Q8C2313yes—
306C4×Q8C2313yes—
307C4×Q8C2313yes—
308C4×Q8C2313yes—
309C4×Q8C2312yes—
310C4×Q8C2313yes—
311C4×Q8C2316yes—
312C4×Q8C2316yes—
313C4×Q8C23112yes—
314C4×D4C2313yes—
315C4×D4C2316yes—
316C4×D4C2313yes—
317C4×D4C2316yes—
318C4×D4C2316yes—
319C4×D4C2316yes—
320C4×D4C2316yes—
321C4×D4C2316yes—
322C4×D4C23112yes—
323C4×D4C2313yes—
324C4×D4C2313yes—
325C4×D4C2313yes—
326C4×D4C2316yes—
327C4×D4C2311yescharacteristic
328C4×D4C2316yes—
329C4×D4C2313yes—
330C4×D4C2316yes—
331C4×D4C2316yes—
332C4×D4C2316yes—
333C4×D4C2313yes—
334C4×D4C2313yes—
335C4×D4C2313yes—
336C4×D4C2316yes—
337C4×D4C2316yes—
338C4×D4C2313yes—
339C4×D4C2316yes—
340C4×D4C2316yes—
341C4×D4C2313yes—
342C4×D4C23112yes—
343C4×D4C2316yes—
344C4×D4C2316yes—
345C4×D4C2316yes—
346C4×D4C2316yes—
347C4×D4C23112yes—
348C4×D4C23112yes—
349C4×D4C23112yes—
350C4×D4C2316yes—
351C4×D4C2316yes—
352#117C2313yes—
353#117C2311yescharacteristic
354#117C2313yes—
355#117C2313yes—
356#117C2313yes—
357#117C2313yes—
358#117C2313yes—
359#117C2313yes—
360#117C2313yes—
361#117C2313yes—
362#117C2313yes—
363#117C2313yes—
364#117C2316yes—
365#117C2313yes—
366#117C2316yes—
367#117C2316yes—
368#117C2313yes—
369#117C2316yes—
370#117C23112yes—
371#117C2316yes—
372#117C23112yes—
373#117C23112yes—
374#117C23112yes—
375C2×C4⋊C4C2313yes—
376C2×C4⋊C4C2313yes—
377C2×C4⋊C4C2313yes—
378C2×C4⋊C4C2313yes—
379C2×C4⋊C4C2313yes—
380C2×C4⋊C4C2316yes—
381C2×C4⋊C4C2313yes—
382C2×C4⋊C4C2316yes—
383C2×C4⋊C4C2316yes—
384C2×C4⋊C4C2316yes—
385C2×C4⋊C4C2316yes—
386C2×C22⋊C4C2313yes—
387C2×C22⋊C4C2313yes—
388C2×C22⋊C4C2316yes—
389C2×C22⋊C4C2316yes—
390C2×C22⋊C4C23112yes—
391C2×C22⋊C4C2316yes—
392C2×C22⋊C4C2316yes—
393C2×C22⋊C4C2316yes—
394C2×C22⋊C4C2316yes—
395C2×C42C2313yes—
396C2×C42C2313yes—
397C2×C42C2316yes—
398C2×C42C2316yes—
399C2×C42C2316yes—
400C2×C42C2316yes—
401C24C2413yes—
402C24C2416yes—
403#41—24no—
404#41—28no—
405#41—212no—
406#41—224no—
407#41—212no—
408#41—212no—
409#41—212no—
410#41—812no—
411#41#4118yescomplemented
412C2×Q8—24no—
413C2×Q8—28no—
414C2×Q8—212no—
415C2×Q8—86no—
416C2×Q8C2413yes—
417C2×Q8C2416yes—
418C2×Q8C2413yes—
419C2×Q8C2411yescharacteristic
420C2×Q8C2412yes—
421C2×Q8C2416yes—
422C2×Q8C24112yes—
423C2×Q8C2411yescharacteristic
424C2×D4—212no—
425C2×D4—224no—
426C2×D4—212no—
427C2×D4—86no—
428C2×D4C2416yes—
429C2×D4C2416yes—
430C2×D4C2416yes—
431C2×D4C2413yes—
432C2×D4C2416yes—
433C2×D4C2413yes—
434C2×D4C2411yescharacteristic
435C2×D4C2412yes—
436C2×D4C2416yes—
437C2×D4C2416yes—
438C2×D4C2416yes—
439C2×D4C2416yes—
440C2×D4C2416yes—
441C2×D4C24112yes—
442C2×D4C2413yes—
443C22×C4—212no—
444C22×C4—86no—
445C22×C4C2413yes—
446C22×C4C2416yes—
447C22×C4C2416yes—
448C22×C4C2416yes—
449C22×C4C2413yes—
450C22×C4C2413yes—
451C22×C4C2413yes—
452C22×C4C2411yescharacteristic
453C22×C4C2413yes—
454C22×C4C2412yes—
455C22×C4C2413yes—
456C22×C4C2413yes—
457C22×C4C2416yes—
458C22×C4C2413yes—
459C22×C4C2416yes—
460C22×C4C2416yes—
461C22×C4C2416yes—
462C22×C4C2416yes—
463C22×C4C2416yes—
464C22×C4C2416yes—
465C22×C4C24112yes—
466C22×C4C2413yes—
467C4⋊C4C2413yes—
468C4⋊C4C2411yescharacteristic
469C4⋊C4C2413yes—
470C4⋊C4C2411yescharacteristic
471C4⋊C4C2413yes—
472C4⋊C4C2413yes—
473C4⋊C4C2416yes—
474C4⋊C4C2416yes—
475C4⋊C4C2413yes—
476C4⋊C4C2416yes—
477C4⋊C4C2416yes—
478C4⋊C4C24112yes—
479C4⋊C4C2416yes—
480C4⋊C4C2416yes—
481C4⋊C4C2413yes—
482C4⋊C4C2413yes—
483C4⋊C4C2413yes—
484C4⋊C4C2413yes—
485C4⋊C4C2413yes—
486C4⋊C4C2413yes—
487C4⋊C4C2413yes—
488C4⋊C4C24112yes—
489C4⋊C4C24112yes—
490C4⋊C4C2411yescharacteristic
491C4⋊C4C2412yes—
492C4⋊C4C2411yescharacteristic
493C4⋊C4C2416yes—
494C4⋊C4C2416yes—
495C4⋊C4C2416yes—
496C4⋊C4C2416yes—
497C4⋊C4C2416yes—
498C4⋊C4C2412yes—
499C4⋊C4C2416yes—
500C4⋊C4C2416yes—
501C4⋊C4C2416yes—
502C4⋊C4C2416yes—
503C4⋊C4C2412yes—
504C22⋊C4C2416yes—
505C22⋊C4C2413yes—
506C22⋊C4C2413yes—
507C22⋊C4C2411yescharacteristic
508C22⋊C4C2411yescharacteristic
509C22⋊C4C2416yes—
510C22⋊C4C2416yes—
511C22⋊C4C2416yes—
512C22⋊C4C24112yes—
513C22⋊C4C2416yes—
514C22⋊C4C2416yes—
515C22⋊C4C2416yes—
516C22⋊C4C2416yes—
517C22⋊C4C2416yes—
518C22⋊C4C2413yes—
519C22⋊C4C2413yes—
520C22⋊C4C2413yes—
521C22⋊C4C2413yes—
522C22⋊C4C24112yes—
523C22⋊C4C24112yes—
524C22⋊C4C24112yes—
525C22⋊C4C24112yes—
526C22⋊C4C2416yes—
527C22⋊C4C2412yes—
528C22⋊C4C2416yes—
529C22⋊C4C2416yes—
530C22⋊C4C2416yes—
531C22⋊C4C2412yes—
532C22⋊C4C2416yes—
533C22⋊C4C2416yes—
534C22⋊C4C2412yes—
535C22⋊C4C2412yes—
536C22⋊C4C2412yes—
537C42C2411yescharacteristic
538C42C2413yes—
539C42C2413yes—
540C42C2413yes—
541C42C2411yescharacteristic
542C42C2413yes—
543C42C2412yes—
544C42C2416yes—
545C42C2416yes—
546C42C2416yes—
547C42C2416yes—
548C42C24112yes—
549C42C2416yes—
550C42C2416yes—
551C42C2413yes—
552C42C2413yes—
553C42C2416yes—
554C23—26no—
555C23—212no—
556C23—46no—
557C23—43no—
558C23—43no—
559C23—46no—
560C23C2511yescharacteristic
561C23C2516yes—
562C23C2513yes—
563C23C2512yes—
564C23C2513yes—
565Q8—212no—
566Q8—26no—
567Q8—26no—
568Q8—22no—
569Q8—46no—
570Q8—412no—
571Q8—42no—
572Q8C2×#4114yes—
573D4—212no—
574D4—212no—
575D4—212no—
576D4—212no—
577D4—26no—
578D4—26no—
579D4—22no—
580D4—46no—
581D4—412no—
582D4—46no—
583D4—42no—
584D4—46no—
585D4—46no—
586D4—46no—
587D4C2×#41112yes—
588C2×C4—26no—
589C2×C4—212no—
590C2×C4—22no—
591C2×C4—26no—
592C2×C4—26no—
593C2×C4—26no—
594C2×C4—212no—
595C2×C4—212no—
596C2×C4—43no—
597C2×C4—46no—
598C2×C4—46no—
599C2×C4—412no—
600C2×C4—43no—
601C2×C4—46no—
602C2×C4—46no—
603C2×C4—42no—
604C2×C4—43no—
605C2×C4—46no—
606C2×C4—43no—
607C2×C4—46no—
608C2×C4—46no—
609C2×C4C2×#41112yes—
610C2×C4C2511yescharacteristic
611C2×C4C2513yes—
612C2×C4C2512yes—
613C2×C4C2511yescharacteristic
614C2×C4C2513yes—
615C2×C4C2511yescharacteristic
616C2×C4C2511yescharacteristic
617C2×C4C2512yes—
618C2×C4C2516yes—
619C2×C4C2513yes—
620C2×C4C2513yes—
621C2×C4C2513yes—
622C2×C4C2512yes—
623C2×C4C2516yes—
624C2×C4C2516yes—
625C2×C4C2511yescharacteristic
626C2×C4C2513yes—
627C2×C4C2511yescharacteristic
628C22—23no—
629C22—23no—
630C22—21no—
631C22—22no—
632C22—23no—
633C22—26no—
634C22—22no—
635C22—26no—
636C22—23no—
637C22—21no—
638C22—23no—
639C22—22no—
640C22—26no—
641C22—21no—
642C22—86no—
643C22—812no—
644C22C22×#4116yes—
645C22C2611yescharacteristic
646C4—21no—
647C4—22no—
648C4—23no—
649C4—26no—
650C4—21no—
651C4—23no—
652C4—26no—
653C4—26no—
654C4—23no—
655C4—21no—
656C4—21no—
657C4—23no—
658C4—23no—
659C4—22no—
660C4—21no—
661C4—22no—
662C4C22×#4116yes—
663C4C22×#4112yes—
664C2—26no—
665C2—42no—
666C2—43no—
667C2—46no—
668C2—41no—
669C2C23×#4111yescharacteristic
670C2H(7,𝔽2)11yescharacteristic
671C22−1+611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC22C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3524C2semidirect
2. #3522C2semidirect
3. #3521C2semidirect
4. #3520C2semidirect
5. #3518C2semidirect
6. #3516C2semidirect
7. #3514C2semidirect
8. #3513C2semidirect
9. #3511C2semidirect
10. #3510C2semidirect
11. #3503C2semidirect
12. #3500C2semidirect
13. #3495C2semidirect
14. #3494C2semidirect
15. #3489C2semidirect
16. #3488C2semidirect
17. #3461C2semidirect
18. #3460C2semidirect
19. #3455C2semidirect
20. C2×#542C2semidirect
21. C4×2−1+4C2semidirect
22. C4×H(5,𝔽2)C2semidirect
23. #3428C2semidirect
27. #559C22semidirect
28. #559C22semidirect
29. Q82C22semidirect
30. #557C22semidirect
31. #556C22semidirect
32. #556C22semidirect
33. #556C22semidirect
34. #556C22semidirect
35. #555C22semidirect
36. #555C22semidirect
37. #554C22semidirect
38. #554C22semidirect
39. #554C22semidirect
40. #553C22semidirect
41. #553C22semidirect
42. #553C22semidirect
43. #552C22semidirect
44. #552C22semidirect
45. #552C22semidirect
46. #551C22semidirect
47. #551C22semidirect
48. #551C22semidirect
49. #551C22semidirect
51. D4×Q8C22semidirect
52. D4×Q8C22semidirect
54. #548C22semidirect
55. #548C22semidirect
56. #548C22semidirect
57. #548C22semidirect
58. #547C22semidirect
59. #547C22semidirect
60. #547C22semidirect
62. #546C22semidirect
63. #546C22semidirect
64. #546C22semidirect
65. #546C22semidirect
67. #544C22semidirect
68. #544C22semidirect
69. #542C22semidirect
70. #542C22semidirect
71. #542C22semidirect
72. #542C22semidirect
73. #542C22semidirect
74. #542C22semidirect
75. #542C22semidirect
76. #542C22semidirect
77. #542C22semidirect
78. #542C22semidirect
79. #542C22semidirect
80. #542C22semidirect
81. #542C22semidirect
82. #541C22semidirect
83. #541C22semidirect
84. #541C22semidirect
85. #540C22semidirect
86. #540C22semidirect
87. #540C22semidirect
88. #539C22semidirect
89. #539C22semidirect
90. #539C22semidirect
91. #538C22semidirect
92. #538C22semidirect
93. #538C22semidirect
95. #537C22semidirect
96. #536C22semidirect
97. #536C22semidirect
99. #535C22semidirect
100. #533C22semidirect
101. #533C22semidirect
102. #533C22semidirect
103. #532C22semidirect
104. #532C22semidirect
105. #532C22semidirect
106. C2×C4⋊Q8C22semidirect
107. #529C22semidirect
108. #529C22semidirect
109. #529C22semidirect
110. #529C22semidirect
111. #529C22semidirect
112. #529C22semidirect
113. #529C22semidirect
114. #529C22semidirect
115. #529C22semidirect
116. C2×#126C22semidirect
117. C2×#124C22semidirect
118. C2×#124C22semidirect
120. #525C22semidirect
121. #525C22semidirect
122. C2×#123C22semidirect
123. C2×C22⋊Q8C22semidirect
124. C2×C22⋊Q8C22semidirect
128. #520C22semidirect
129. #520C22semidirect
130. #520C22semidirect
131. #520C22semidirect
132. #520C22semidirect
133. #520C22semidirect
134. #520C22semidirect
135. #520C22semidirect
136. #519C22semidirect
137. #519C22semidirect
138. #519C22semidirect
139. #519C22semidirect
140. #518C22semidirect
141. #518C22semidirect
142. #518C22semidirect
143. #518C22semidirect
146. C4×#41C22semidirect
147. C4×#41C22semidirect
148. C4×#41C22semidirect
149. C4×#41C22semidirect
150. C4×#41C22semidirect
151. C4×#41C22semidirect
152. C2×C4×Q8C22semidirect
153. C2×C4×Q8C22semidirect
154. C2×C4×D4C22semidirect
155. C2×C4×D4C22semidirect
156. C2×#117C22semidirect
157. C2×#117C22semidirect
411. #41#41semidirect

Maximal subgroups

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

subgroupindex
#35242
#35222
#35212
#35202
#35182
#35162
#35142
#35132
#35112
#35102
#35032
#35002
#34952
#34942
#34892
#34882
#34612
#34602
#34552
C2×#5422
C4×2−1+42
C4×H(5,𝔽2)2
#34282