Finite Group Databasebeta

← #11864356

Subgroups — #11864356

Order 1152.

1583 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic
2#10594805C211yesmaximal, characteristic, complemented
3C2×#63811C211yesmaximal, characteristic, complemented
4C2×#63796C211yesmaximal, characteristic, complemented
5#10592426C211yesmaximal, characteristic, complemented
6C3×#4733C211yesmaximal, characteristic, complemented
7C3×#4731C211yesmaximal, characteristic, complemented
8#10591170C211yesmaximal, characteristic, complemented
9#10591169C211yesmaximal, characteristic, complemented
10#10590965C211yesmaximal, characteristic, complemented
11#10590961C211yesmaximal, characteristic, complemented
12#10590956C211yesmaximal, characteristic, complemented
13#10590943C211yesmaximal, characteristic, complemented
14#10590943C211yesmaximal, characteristic, complemented
15#10590941C211yesmaximal, characteristic, complemented
16#80229—31nomaximal
17#80148—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C2×D3×#67—21no—
22C2×D3×#67—21no—
23#64307—24no—
24#64307—24no—
25C2×#3802C2211yescharacteristic
26C2×#3802C2211yescharacteristic
27C2×D3×D12—21no—
28C2×#3797C2211yescharacteristic, complemented
29C2×#3796C2211yescharacteristic
30C2×#3796C2211yescharacteristic
31C2×#3795—21no—
32C2×#3743C2211yescharacteristic, complemented
33C2×C8×C3⋊D3C2211yescharacteristic, complemented
34C3×#924C2211yescharacteristic, complemented
35C3×#924C2211yescharacteristic, complemented
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×#204C2211yescharacteristic, complemented
39C2×C3×#204C2211yescharacteristic, complemented
40#63975—21no—
41#63953—21no—
42#63897—21no—
43#63871C2211yescharacteristic, complemented
44#63871C2211yescharacteristic, complemented
45#63849C2211yescharacteristic, complemented
46#63840—21no—
47C2×#3718C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51#63811—24no—
52#63796—24no—
53C32×C22⋊C8C2211yescharacteristic, complemented
54#63657C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56#63647C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×#821C2211yescharacteristic, complemented
59C3×#821C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63562C2211yescharacteristic, complemented
64#63562C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1004—31no—
67C2×#918—31no—
68C2×#915—31no—
69C2×D3×SD16—31no—
70C2×D3×SD16—31no—
71#5628—31no—
72#5628—31no—
73C3×#452—31no—
74C3×#450—31no—
75#5239—31no—
76#5218—31no—
77#5187—31no—
78#5173—31no—
79#5169—31no—
80#5169—31no—
81#5047—31no—
82#5046—31no—
83#4808—31no—
84#4804—31no—
85#4783—31no—
86#4776—31no—
87#4776—31no—
88#4772—31no—
89#4770—31no—
90#4770—31no—
91#4733D311yescharacteristic, complemented
92#4731D311yescharacteristic, complemented
93#4727—31no—
94#4727—31no—
95#4727—61no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C22×D32—21no—
99C22×C32×C4C2311yescharacteristic
100C2×#638D411yescharacteristic
101C2×#638D411yescharacteristic
102#3828—22no—
103#3828—22no—
104C2×C4⋊(C3⋊D3)D411yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634D411yescharacteristic
108C2×C3×#67—21no—
109C3×#235—22no—
110C3×#235—22no—
111C2×C3×D12—21no—
112C2×C3×D12—22no—
113C2×C3×D12—22no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121D3×#67—28no—
122D3×#67—28no—
123C2×#627—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#625—21no—
127C2×#625—21no—
128C2×#624—21no—
129C2×D3×Dic3—21no—
130C2×D3×Dic3—21no—
131#3802—22no—
132#3802—22no—
133#3802—22no—
134#3802D414yes—
135D3×D12—28no—
136#3797—22no—
137#3797—22no—
138#3796—22no—
139#3796—22no—
140#3796—22no—
141#3796D414yes—
142#3795—28no—
143C2×C32×C8C2311yescharacteristic
144C2×C32×C8C2311yescharacteristic
145C2×C3⋊(C3⋊C8)C2311yescharacteristic
146C2×C3⋊(C3⋊C8)C2311yescharacteristic
147#3743—22no—
148C8×C3⋊D3—22no—
149C3×#217—21no—
150C3×#217—21no—
151C3×C4⋊Dic3C2311yescharacteristic
152C3×C4⋊Dic3C2311yescharacteristic
153C3×Dic3⋊C4—21no—
154C3×Dic3⋊C4—21no—
155C3×Dic12—22no—
156C3×#204—22no—
157C3×#204—22no—
158C3×#204—22no—
159Dic3⋊Dic3—21no—
160Dic3⋊Dic3—21no—
161#3722—21no—
162#3722—21no—
163#3722—21no—
164Dic32—21no—
165#3718—22no—
166#3715—22no—
167#3715—22no—
168#3715—22no—
169#3009—91noSylow
170C2×C3×#41—31no—
171C22×C3×D4—31no—
172C22×#67—61no—
173C22×#67—61no—
174#1009—64no—
175#1009—64no—
176C2×#239—31no—
177C2×#239—31no—
178C2×D3×Q8—31no—
179C2×D3×Q8—31no—
180#1004—64no—
181#1004—64no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—61no—
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×D3×D4—31no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×D3×D4—61no—
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—61no—
195C2×#235—61no—
196C2×#235C2×D311yescharacteristic
197C22×D12—61no—
198C22×D12C2×D311yescharacteristic
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C2×C3×SD16—31no—
202C2×C3×SD16—31no—
203C3×C22⋊Q8—31no—
204C3×C22⋊Q8—31no—
205#946—31no—
206#946—31no—
207C2×#216—31no—
208C2×#216—31no—
209C2×#215—31no—
210C2×#215—31no—
211C2×#215—31no—
212C2×#214—31no—
213C2×#214—31no—
214C2×#214—31no—
215#924C2×D311yescharacteristic, complemented
216#924C2×D311yescharacteristic, complemented
217#918—64no—
218#915—64no—
219D3×SD16—64no—
220D3×SD16—64no—
221C2×Dic12C2×D311yescharacteristic, complemented
222C2×#204C2×D311yescharacteristic, complemented
223C2×#204C2×D311yescharacteristic, complemented
224C2×#204C2×D311yescharacteristic, complemented
225C2×ΓL(1,𝔽25)—31no—
226C2×ΓL(1,𝔽25)—31no—
227C2×ΓL(1,𝔽25)—61no—
228C2×D3×C8—31no—
229C2×D3×C8—31no—
230C2×D3×C8—61no—
231#897—31no—
232#897—31no—
233#894—61no—
234#894—61no—
235#892—31no—
236#892—31no—
237#888—61no—
238#888—61no—
239#885—61no—
240#885—61no—
241#883—61no—
242#883—61no—
243C3×#103—31no—
244C3×#102—31no—
245C3×#102—31no—
246C3×#102—31no—
247C3×C22⋊C8—21no—
248C3×C22⋊C8C2×D311yescharacteristic, complemented
249C3×C22⋊C8C2×D311yescharacteristic, complemented
250#835—31no—
251#832—31no—
252#832—31no—
253#832—31no—
254#830—31no—
255#830—31no—
256#830—61no—
257#821C2×D311yescharacteristic, complemented
258#821C2×D311yescharacteristic, complemented
259#821C2×D311yescharacteristic, complemented
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—61no—
265(C2×D3)⋊C8—61no—
266#816C2×D311yescharacteristic, complemented
267#810—31no—
268#809—31no—
269#809—31no—
270#809—31no—
271C23×C32C2×D411yescharacteristic
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3—24no—
278C22×C3×D3—81no—
279C22×C3×D3—81no—
280C2×D32—24no—
281C2×D32—24no—
282C2×D32—81no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4C2×D411yescharacteristic
289C2×C32×C4C2411yescharacteristic
290#638—22no—
291#638—22no—
292C2×C3⋊Dic3C2×D411yescharacteristic
293C2×C3⋊Dic3C2×D411yescharacteristic
294C4⋊(C3⋊D3)—22no—
295C4×C3⋊D3—21no—
296C4×C3⋊D3—21no—
297C4×C3⋊D3C2×D412yes—
298C4×C3⋊D3C2×D412yes—
299#634—22no—
300C3×#67—24no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C3×D12—24no—
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12C2×D412yes—
311C3×D12C2×D412yes—
312C3×D12C2×D412yes—
313C3×C4×D3—24no—
314C3×Dic6—21no—
315C3×Dic6—21no—
316C3×Dic6—21no—
317C3×Dic6—21no—
318C3×Dic6—21no—
319C3×Dic6C2×D412yes—
320#627—42no—
321#626—24no—
322#626—24no—
323#625—24no—
324#625—24no—
325#624—42no—
326D3×Dic3—24no—
327D3×Dic3—24no—
328C32×C8—21no—
329C32×C8—21no—
330C3⋊(C3⋊C8)—21no—
331C3⋊(C3⋊C8)—21no—
332C2×H(5,𝔽2)—91no—
333C2×#137—91no—
334C22×SD16—91no—
335#536—91no—
336#452—31no—
337#452—91no—
338#452—91no—
339#452—91no—
340#450—31no—
341#450—91no—
342#450—91no—
343#450—91no—
344#418—91no—
345#416—91no—
346#408—91no—
347C24×C3—61no—
348C23×D3—21no—
349C23×D3—61no—
350C23×D3—61no—
351C23×D3—61no—
352C23×D3—61no—
353C3×#41—62no—
354C3×#41—62no—
355C2×C3×Q8—31no—
356C2×C3×Q8—31no—
357C2×C3×Q8—31no—
358C2×C3×D4—31no—
359C2×C3×D4—31no—
360C2×C3×D4—31no—
361C2×C3×D4—62no—
362C2×C3×D4—62no—
363C2×C3×D4—61no—
364C2×C3×D4—61no—
365C22×C3×C4—21no—
366C22×C3×C4—61no—
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C2×#67—21no—
370C2×#67—31no—
371C2×#67—31no—
372C2×#67—31no—
373C2×#67—31no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—68no—
383C2×#67—68no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386#239—34no—
387#239—62no—
388#239—62no—
389#239—62no—
390D3×Q8—62no—
391D3×Q8—62no—
392D3×Q8—62no—
393D3×Q8—62no—
394#237—34no—
395#237—62no—
396#237—62no—
397#237—68no—
398#237—62no—
399D3×D4—34no—
400D3×D4—34no—
401D3×D4—68no—
402D3×D4—62no—
403D3×D4—62no—
404D3×D4—62no—
405D3×D4—62no—
406D3×D4—68no—
407D3×D4—68no—
408D3×D4—62no—
409D3×D4—62no—
410#235—22no—
411#235—22no—
412#235—62no—
413#235—62no—
414#235—62no—
415#235—62no—
416#235—68no—
417#235—122no—
418#235—122no—
419C2×D12—21no—
420C2×D12—22no—
421C2×D12—22no—
422C2×D12—31no—
423C2×D12—31no—
424C2×D12—61no—
425C2×D12—68no—
426C2×D12—61no—
427C2×D12—61no—
428C2×D12C22×D311yescharacteristic
429C2×D12C22×D311yescharacteristic
430C2×D12C22×D311yescharacteristic
431C2×C4×D3—21no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—61no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×Dic6—31no—
443C2×Dic6—31no—
444C2×Dic6—61no—
445C2×Dic6—61no—
446C2×Dic6—61no—
447C2×Dic6C22×D311yescharacteristic
448C2×Dic6C22×D311yescharacteristic
449C2×Dic6C22×D311yescharacteristic
450C3×Q16—62no—
451C3×SD16—62no—
452C3×SD16—62no—
453C3×SD16—62no—
454C2×C3×C8—21no—
455C2×C3×C8—21no—
456C2×C3×C8C22×D311yescharacteristic
457C2×C3×C8C22×D311yescharacteristic
458C2×C3×C8C22×D311yescharacteristic
459C2×C3×C8C22×D311yescharacteristic
460C3×C4⋊C4—31no—
461C3×C4⋊C4—31no—
462C3×C4⋊C4—61no—
463C3×C4⋊C4—61no—
464C3×C22⋊C4—61no—
465C3×C22⋊C4—61no—
466#217—21no—
467#217—21no—
468#216—62no—
469#216—62no—
470#215—62no—
471#215—62no—
472#215—62no—
473#214—62no—
474#214—62no—
475#214—62no—
476(C2×D3)⋊C4—61no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—61no—
482C4⋊Dic3—61no—
483C4⋊Dic3—61no—
484C4⋊Dic3C22×D311yescharacteristic
485C4⋊Dic3C22×D311yescharacteristic
486Dic3⋊C4—21no—
487Dic3⋊C4—21no—
488Dic3⋊C4—61no—
489Dic3⋊C4—61no—
490C4×Dic3—61no—
491C4×Dic3—61no—
492C2×C3⋊C8—31no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—61no—
497C2×C3⋊C8—61no—
498Dic12—22no—
499#204—22no—
500#204—22no—
501#204—22no—
502ΓL(1,𝔽25)—62no—
503ΓL(1,𝔽25)—62no—
504ΓL(1,𝔽25)—122no—
505D3×C8—62no—
506D3×C8—62no—
507D3×C8—122no—
508C22×C32—21no—
509C22×C32—21no—
510C22×C32—21no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—21no—
517C2×C3⋊D3#12012yes—
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3—84no—
528D32—84no—
529D32—84no—
530C32×C4—21no—
531C32×C4C22×D411yescharacteristic
532C32×C4C22×D411yescharacteristic
533C3⋊Dic3—21no—
534C3⋊Dic3#12012yes—
535C3×Dic3—22no—
536C3×Dic3—41no—
537C3×Dic3—41no—
538C3×Dic3—41no—
539C3×Dic3—41no—
540H(5,𝔽2)—184no—
541H(5,𝔽2)—184no—
542C2×#41—31no—
543C2×#41—91no—
544C2×#41—91no—
545C2×#41—91no—
546C2×#41—181no—
547C22×Q8—91no—
548C22×D4—31no—
549C22×D4—91no—
550C22×D4—91no—
551C22×D4—181no—
552C22×D4—181no—
553C22×D4—181no—
554#137—184no—
555C2×Q16—31no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—31no—
559C2×SD16—31no—
560C2×SD16—91no—
561C2×SD16—91no—
562C2×SD16—91no—
563C2×SD16—184no—
564C2×M16—91no—
565C22×C8—91no—
566C4⋊Q8—181no—
567#124—181no—
568#123—181no—
569#123—181no—
570C22⋊Q8—31no—
571C22⋊Q8—31no—
572C22⋊Q8—91no—
573C22⋊Q8—91no—
574#117—91no—
575#103—31no—
576#103—91no—
577#102—31no—
578#102—31no—
579#102—31no—
580#102—91no—
581#102—91no—
582#102—91no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C22⋊C8D3211yescharacteristic, complemented
587C23×C3—21no—
588C23×C3—64no—
589C23×C3—61no—
590C23×C3—61no—
591C23×C3—61no—
592C23×C3—241no—
593C23×C3—241no—
594C23×C3D3×D411yescharacteristic
595C23×C3D3×D411yescharacteristic
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—24no—
600C22×D3—31no—
601C22×D3—31no—
602C22×D3—31no—
603C22×D3—31no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—64no—
607C22×D3—64no—
608C22×D3—64no—
609C22×D3—64no—
610C22×D3—81no—
611C22×D3—81no—
612C22×D3—241no—
613C22×D3—241no—
614C22×D3—241no—
615C22×D3—241no—
616C22×D3—241no—
617C22×D3—241no—
618C22×D3—241no—
619C22×D3—241no—
620C3×Q8—32no—
621C3×Q8—61no—
622C3×Q8—61no—
623C3×Q8—61no—
624C3×Q8—61no—
625C3×Q8—61no—
626C3×D4—32no—
627C3×D4—32no—
628C3×D4—32no—
629C3×D4—64no—
630C3×D4—64no—
631C3×D4—61no—
632C3×D4—61no—
633C3×D4—61no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—64no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4D3×D411yescharacteristic
649C2×C3×C4D3×D411yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652#67—24no—
653#67—64no—
654#67—64no—
655#67—64no—
656#67—64no—
657#67—62no—
658#67—62no—
659#67—64no—
660#67—64no—
661#67—62no—
662#67—62no—
663#67—122no—
664#67—122no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—31no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—64no—
677C2×Dic3—64no—
678D12—24no—
679D12—21no—
680D12—21no—
681D12—21no—
682D12—62no—
683D12—62no—
684D12—64no—
685D12—64no—
686D12—122no—
687D12D3×D412yes—
688D12D3×D412yes—
689D12D3×D412yes—
690C4×D3—24no—
691C4×D3—32no—
692C4×D3—32no—
693C4×D3—32no—
694C4×D3—32no—
695C4×D3—62no—
696C4×D3—62no—
697C4×D3—64no—
698C4×D3—64no—
699C4×D3—61no—
700C4×D3—61no—
701C4×D3—61no—
702C4×D3—61no—
703C4×D3—121no—
704C4×D3—121no—
705C4×D3—122no—
706C4×D3—122no—
707Dic6—21no—
708Dic6—21no—
709Dic6—21no—
710Dic6—21no—
711Dic6—21no—
712Dic6—62no—
713Dic6—62no—
714Dic6—122no—
715Dic6—122no—
716Dic6—122no—
717Dic6D3×D412yes—
718C3×C8—21no—
719C3×C8—21no—
720C3×C8—21no—
721C3×C8—21no—
722C3×C8—41no—
723C3×C8—41no—
724C3⋊C8—61no—
725C3⋊C8—61no—
726C3⋊C8—61no—
727C3⋊C8—61no—
728C3⋊C8—121no—
729C3⋊C8—121no—
730C2×C32—41no—
731C2×C32C2×#12011yescharacteristic
732C2×C32#57711yescharacteristic
733C2×C32#57711yescharacteristic
734C3⋊D3—22no—
735C3⋊D3—41no—
736C3×D3—42no—
737C3×D3—42no—
738C3×D3—42no—
739C24—61no—
740C24—181no—
741C24—181no—
742#41—62no—
743#41—62no—
744#41—94no—
745#41—182no—
746#41—182no—
747#41—188no—
748#41—182no—
749#41—182no—
750#41—182no—
751C2×Q8—31no—
752C2×Q8—31no—
753C2×Q8—31no—
754C2×Q8—91no—
755C2×Q8—181no—
756C2×Q8—182no—
757C2×Q8—182no—
758C2×D4—31no—
759C2×D4—31no—
760C2×D4—31no—
761C2×D4—62no—
762C2×D4—62no—
763C2×D4—61no—
764C2×D4—61no—
765C2×D4—94no—
766C2×D4—91no—
767C2×D4—91no—
768C2×D4—91no—
769C2×D4—188no—
770C2×D4—181no—
771C2×D4—181no—
772C2×D4—182no—
773C2×D4—181no—
774C2×D4—181no—
775C2×D4—182no—
776C2×D4—182no—
777C2×D4—188no—
778C2×D4—188no—
779C22×C4—61no—
780C22×C4—91no—
781C22×C4—91no—
782C22×C4—181no—
783C22×C4—181no—
784C22×C4—181no—
785C22×C4C2×D3211yescharacteristic
786Q16—62no—
787Q16—182no—
788SD16—62no—
789SD16—62no—
790SD16—62no—
791SD16—182no—
792SD16—182no—
793SD16—182no—
794M16—182no—
795C2×C8—91no—
796C2×C8—91no—
797C2×C8—182no—
798C2×C8C2×D3211yescharacteristic
799C2×C8C2×D3211yescharacteristic
800C4⋊C4—31no—
801C4⋊C4—31no—
802C4⋊C4—61no—
803C4⋊C4—61no—
804C4⋊C4—181no—
805C4⋊C4—181no—
806C22⋊C4—61no—
807C22⋊C4—61no—
808C22⋊C4—181no—
809C22⋊C4—181no—
810C22⋊C4—181no—
811C42—181no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—121no—
826C22×C3—121no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—244no—
832C22×C3C2×D3×D411yescharacteristic
833C22×C3C2×D3×D411yescharacteristic
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—32no—
838C2×D3—32no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—62no—
846C2×D3—61no—
847C2×D3—61no—
848C2×D3—61no—
849C2×D3—61no—
850C2×D3—61no—
851C2×D3—61no—
852C2×D3—61no—
853C2×D3—61no—
854C2×D3—61no—
855C2×D3—61no—
856C2×D3—84no—
857C2×D3—121no—
858C2×D3—121no—
859C2×D3—121no—
860C2×D3—121no—
861C2×D3—121no—
862C2×D3—244no—
863C2×D3—244no—
864C2×D3—244no—
865C2×D3—244no—
866C3×C4—21no—
867C3×C4—21no—
868C3×C4—21no—
869C3×C4—21no—
870C3×C4—41no—
871C3×C4—62no—
872C3×C4—121no—
873C3×C4—121no—
874C3×C4—121no—
875C3×C4—121no—
876C3×C4C2×D3×D411yescharacteristic
877C3×C4C2×D3×D411yescharacteristic
878C3×C4C2×D3×D411yescharacteristic
879C3×C4C2×D3×D411yescharacteristic
880Dic3—22no—
881Dic3—32no—
882Dic3—32no—
883Dic3—41no—
884Dic3—41no—
885Dic3—41no—
886Dic3—41no—
887Dic3—62no—
888Dic3—61no—
889Dic3—61no—
890Dic3—121no—
891C32#300911yescharacteristic, complemented, Sylow
892C23—64no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—91no—
897C23—91no—
898C23—184no—
899C23—184no—
900C23—241no—
901C23—241no—
902C23—721no—
903C23—721no—
904C23—721no—
905C23—721no—
906C23#380211yescharacteristic
907Q8—32no—
908Q8—61no—
909Q8—61no—
910Q8—61no—
911Q8—61no—
912Q8—61no—
913Q8—182no—
914Q8—362no—
915D4—32no—
916D4—32no—
917D4—32no—
918D4—64no—
919D4—64no—
920D4—61no—
921D4—61no—
922D4—61no—
923D4—182no—
924D4—184no—
925D4—184no—
926D4—182no—
927D4—184no—
928D4—182no—
929D4—184no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—64no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—91no—
939C2×C4—92no—
940C2×C4—92no—
941C2×C4—91no—
942C2×C4—184no—
943C2×C4—184no—
944C2×C4—181no—
945C2×C4—181no—
946C2×C4—362no—
947C2×C4#380211yescharacteristic
948C2×C4C22×D3211yescharacteristic
949C8—21no—
950C8—21no—
951C8—181no—
952C8—181no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—41no—
957C2×C3—41no—
958C2×C3—81no—
959C2×C3—122no—
960C2×C3—122no—
961C2×C3—122no—
962C2×C3D3×#12011yescharacteristic
963C2×C3D3×#12011yescharacteristic
964C2×C3#576211yescharacteristic
965C2×C3#577011yescharacteristic
966C2×C3#577511yescharacteristic
967C2×C3#577811yescharacteristic
968D3—42no—
969D3—42no—
970D3—42no—
971D3—62no—
972D3—62no—
973D3—122no—
974D3—121no—
975D3—121no—
976D3—241no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—92no—
984C22—121no—
985C22—121no—
986C22—121no—
987C22—121no—
988C22—121no—
989C22—121no—
990C22—181no—
991C22—181no—
992C22—181no—
993C22—181no—
994C22—181no—
995C22—244no—
996C22—724no—
997C22—724no—
998C22C2×#380211yescharacteristic
999C4—21no—
1000C4—62no—
1001C4—92no—
1002C4—121no—
1003C4—121no—
1004C4—121no—
1005C4—121no—
1006C4—181no—
1007C4D32×D411yescharacteristic
1008C4D32×D411yescharacteristic
1009C3—21no—
1010C3#8014811yescharacteristic, complemented
1011C3#8022911yescharacteristic, complemented
1012C2—41no—
1013C2—122no—
1014C2—122no—
1015C2—122no—
1016C2—182no—
1017C2—361no—
1018C2#1059425811yescharacteristic
1019C2#1059468611yescharacteristic
1020C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#64307C2
hypercenterC22⋊C8D32
hypocenterC32#3009
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594805C2semidirect
3. C2×#63811C2semidirect
4. C2×#63796C2semidirect
5. #10592426C2semidirect
6. C3×#4733C2semidirect
7. C3×#4731C2semidirect
8. #10591170C2semidirect
9. #10591169C2semidirect
10. #10590965C2semidirect
11. #10590961C2semidirect
12. #10590956C2semidirect
13. #10590943C2semidirect
14. #10590943C2semidirect
15. #10590941C2semidirect
28. C2×#3797C22semidirect
32. C2×#3743C22semidirect
33. C2×C8×C3⋊D3C22semidirect
34. C3×#924C22semidirect
35. C3×#924C22semidirect
36. C2×C3×Dic12C22semidirect
37. C2×C3×#204C22semidirect
38. C2×C3×#204C22semidirect
39. C2×C3×#204C22semidirect
43. #63871C22semidirect
44. #63871C22semidirect
45. #63849C22semidirect
47. C2×#3718C22semidirect
48. C2×#3715C22semidirect
49. C2×#3715C22semidirect
50. C2×#3715C22semidirect
53. C32×C22⋊C8C22semidirect
54. #63657C22semidirect
55. #63647C22semidirect
56. #63647C22semidirect
57. C3×#821C22semidirect
58. C3×#821C22semidirect
59. C3×#821C22semidirect
60. C3×#816C22semidirect
61. #63565C22semidirect
62. #63562C22semidirect
63. #63562C22semidirect
64. #63562C22semidirect
91. #4733D3semidirect
92. #4731D3semidirect
215. #924C2×D3semidirect
216. #924C2×D3semidirect
221. C2×Dic12C2×D3semidirect
222. C2×#204C2×D3semidirect
223. C2×#204C2×D3semidirect
224. C2×#204C2×D3semidirect
248. C3×C22⋊C8C2×D3semidirect
249. C3×C22⋊C8C2×D3semidirect
257. #821C2×D3semidirect
258. #821C2×D3semidirect
259. #821C2×D3semidirect
266. #816C2×D3semidirect
586. C22⋊C8D32semidirect
891. C32#3009semidirect
1010. C3#80148semidirect
1011. C3#80229semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
#105948052
C2×#638112
C2×#637962
#105924262
C3×#47332
C3×#47312
#105911702
#105911692
#105909652
#105909612
#105909562
#105909432
#105909412
#802293
#801483