Finite Group Databasebeta

← #11864053

Subgroups — #11864053

Order 1152.

1611 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64312C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic, complemented
3C2×#63811C211yesmaximal, characteristic, complemented
4#10594632C211yesmaximal, characteristic, complemented
5#10592469C211yesmaximal, characteristic, complemented
6C3×#4783C211yesmaximal, characteristic, complemented
7C3×#4781C211yesmaximal, characteristic, complemented
8#10591461C211yesmaximal, characteristic, complemented
9#10591450C211yesmaximal, characteristic, complemented
10#10590966C211yesmaximal, characteristic, complemented
11#10590937C211yesmaximal, characteristic, complemented
12#10590823C211yesmaximal, characteristic, complemented
13#10590616C211yesmaximal, characteristic, complemented
14#10590615C211yesmaximal, characteristic, complemented
15#10590602C211yesmaximal, characteristic, complemented
16#80227—31nomaximal
17#80083—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×#3811—21no—
22C22×#624—21no—
23C2×#3804—21no—
24C2×#3804—21no—
25#64312—24no—
26#64312—24no—
27C2×C4×D32C2211yescharacteristic
28C2×#3799C2211yescharacteristic
29C2×#3799C2211yescharacteristic
30C2×#3797C2211yescharacteristic
31C2×#3796C2211yescharacteristic
32C2×#3743C2211yescharacteristic
33#64101C2211yescharacteristic
34C2×C3×#214C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic, complemented
40#63937—24no—
41#63922—21no—
42#63908C2211yescharacteristic, complemented
43#63902—21no—
44#63898—21no—
45#63856C2211yescharacteristic, complemented
46#63854—21no—
47C2×#3718C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3712C2211yescharacteristic
52#63811—24no—
53C32×#102C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63636C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#810C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63566C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C2×D3×#41—31no—
67C2×#918—31no—
68C2×#915—31no—
69C2×#914—31no—
70C2×#911—31no—
71#5627—31no—
72#5606—31no—
73C3×#452—31no—
74C3×#449—31no—
75#5239—31no—
76#5238—31no—
77#5187—31no—
78#5173—31no—
79#5172—31no—
80#5158—31no—
81#5047—31no—
82#5037—31no—
83#4810—31no—
84#4808—31no—
85#4802—31no—
86#4802—31no—
87#4783D311yescharacteristic, complemented
88#4781D311yescharacteristic, complemented
89#4770—31no—
90#4770—31no—
91#4770—61no—
92#4734—31no—
93#4733—31no—
94#4726—31no—
95#4726—31no—
96C23×C3⋊D3—21no—
97C22×D32D411yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C2×#638—21no—
100D4×C3⋊D3—22no—
101D4×C3⋊D3D414yescomplemented
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C3×#237—22no—
109C3×#237—22no—
110C3×#237—22no—
111C3×#237—22no—
112C2×C3×D12—21no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119#3811—28no—
120C2×#627—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#625—21no—
125C2×#624—28no—
126C2×#624—21no—
127C2×#624—21no—
128C2×#624—21no—
129C2×#624D411yescharacteristic
130#3804—28no—
131#3804—28no—
132C2×D3×Dic3—21no—
133C2×D3×Dic3D411yescharacteristic
134C2×D3×Dic3D411yescharacteristic
135C4×D32—22no—
136C4×D32—22no—
137#3799—22no—
138#3799—22no—
139#3799—22no—
140#3799—22no—
141#3797—22no—
142#3797D414yescomplemented
143#3796—22no—
144#3796—22no—
145C2×C32×C8C2311yescharacteristic
146C32×C4⋊C4C2311yescharacteristic
147#3752—21no—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149C4×C3⋊Dic3—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151#3743—22no—
152C3×#214—22no—
153C3×#213—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×Dic12—22no—
160C3×#204—22no—
161#3724—21no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164#3718—22no—
165#3717—22no—
166#3715—22no—
167#3714—22no—
168#3712—22no—
169#3005—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172D3×#41—64no—
173D3×#41—64no—
174D3×#41—64no—
175D3×#41—64no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×#237—31no—
182C2×#237—61no—
183C2×#237—61no—
184C2×#237C2×D311yescharacteristic
185C2×#237C2×D311yescharacteristic
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—61no—
194C2×#235—61no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×C4×D3—61no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C2×C3×SD16—31no—
202C2×C3×D8—31no—
203C3×C22⋊Q8—31no—
204C3×#121—31no—
205#946—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#215—31no—
209C2×#215—31no—
210#938—31no—
211#937—61no—
212D4×Dic3—61no—
213C2×#214—31no—
214C2×#214C2×D311yescharacteristic, complemented
215C2×#213—31no—
216C2×#213C2×D311yescharacteristic, complemented
217#930—31no—
218#924—31no—
219#918—64no—
220#915—64no—
221#914—64no—
222#911—64no—
223C2×Dic12C2×D311yescharacteristic, complemented
224C2×D24—31no—
225C2×#204—31no—
226C2×#204C2×D311yescharacteristic, complemented
227C2×ΓL(1,𝔽25)—31no—
228C2×ΓL(1,𝔽25)—31no—
229C2×ΓL(1,𝔽25)—31no—
230C2×ΓL(1,𝔽25)—31no—
231C2×ΓL(1,𝔽25)—61no—
232#897C2×D311yescharacteristic, complemented
233#895C2×D311yescharacteristic, complemented
234#894—61no—
235#893—61no—
236#892—31no—
237#892—31no—
238#892—61no—
239#883—61no—
240#882—61no—
241#67⋊C4—61no—
242#67⋊C4—61no—
243C3×#103—31no—
244C3×#103—31no—
245C3×#102—21no—
246C3×#102C2×D311yescharacteristic, complemented
247C3×#102C2×D311yescharacteristic, complemented
248C3×C22⋊C8—31no—
249C3×C22⋊C8—31no—
250#835—31no—
251#835—31no—
252#832—31no—
253#832—31no—
254#832—61no—
255#830—31no—
256#830—31no—
257#821—31no—
258#821—31no—
259#821—61no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263(C2×D3)⋊C8C2×D311yescharacteristic, complemented
264#816—31no—
265#816—31no—
266#810C2×D311yescharacteristic, complemented
267#810C2×D311yescharacteristic, complemented
268#809—31no—
269#809—31no—
270#809—61no—
271C23×C32—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3—24no—
274C22×C3⋊D3—42no—
275C22×C3⋊D3—42no—
276C22×C3⋊D3C2×D411yescharacteristic
277C22×C3×D3—21no—
278C22×C3×D3C2×D411yescharacteristic
279C22×C3×D3C2×D411yescharacteristic
280C2×D32—22no—
281C2×D32—41no—
282C2×D32—41no—
283C32×D4—21no—
284C32×D4C2×D412yes—
285C2×C32×C4—21no—
286C2×C32×C4C2411yescharacteristic
287#638—24no—
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3C2×D411yescharacteristic
290C4⋊(C3⋊D3)—21no—
291C4⋊(C3⋊D3)C2×D412yes—
292C4×C3⋊D3C2×D412yes—
293C4×C3⋊D3C2×D412yes—
294C3×#67—24no—
295C3×#67—24no—
296C2×C3×Dic3—24no—
297C2×C3×Dic3—24no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3C2×D411yescharacteristic
302C2×C3×Dic3C2×D411yescharacteristic
303C3×D12—21no—
304C3×D12—21no—
305C3×D12—42no—
306C3×C4×D3—21no—
307C3×C4×D3—21no—
308C3×C4×D3—21no—
309C3×C4×D3—21no—
310C3×Dic6—21no—
311C3×Dic6—21no—
312C3×Dic6—21no—
313C3×Dic6—21no—
314C3×Dic6C2×D412yes—
315C3×Dic6C2×D412yes—
316#627—24no—
317#626—24no—
318#626—24no—
319#626—42no—
320#625—42no—
321#624—24no—
322#624—24no—
323#624—24no—
324#624—22no—
325D3×Dic3—22no—
326D3×Dic3—22no—
327D3×Dic3—42no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C22×#41—91no—
333C2×#137—91no—
334C2×AGL(1,ℤ/8)—91no—
335#525—91no—
336#452—31no—
337#452—91no—
338#452—91no—
339#452—91no—
340#449—31no—
341#449—91no—
342#449—91no—
343#449—91no—
344#419—91no—
345#418—91no—
346#407—91no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—61no—
350C23×D3—61no—
351C23×D3—121no—
352C3×#41—62no—
353C3×#41—62no—
354C3×#41—62no—
355C3×#41—62no—
356C2×C3×Q8—31no—
357C2×C3×Q8—31no—
358C2×C3×Q8—31no—
359C2×C3×D4—21no—
360C2×C3×D4—31no—
361C2×C3×D4—61no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C2×C3×D4C22×D311yescharacteristic
365C2×C3×D4C22×D311yescharacteristic
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—61no—
369C22×C3×C4—61no—
370C2×#67—21no—
371C2×#67—21no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—121no—
380C22×Dic3—21no—
381C22×Dic3—21no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—61no—
385#239—62no—
386#239—62no—
387#239—62no—
388#239—62no—
389#239—62no—
390#239—62no—
391D3×Q8—34no—
392D3×Q8—34no—
393D3×Q8—62no—
394D3×Q8—62no—
395#237—22no—
396#237—22no—
397#237—22no—
398#237—22no—
399#237—62no—
400#237—62no—
401#237—68no—
402#237—68no—
403D3×D4—34no—
404D3×D4—34no—
405D3×D4—64no—
406D3×D4—62no—
407D3×D4—62no—
408D3×D4—68no—
409D3×D4—68no—
410D3×D4—122no—
411#235—62no—
412#235—62no—
413#235—68no—
414#235—68no—
415#235—62no—
416#235—62no—
417C2×D12—21no—
418C2×D12—31no—
419C2×D12—31no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12—61no—
423C2×D12—61no—
424C2×D12C22×D311yescharacteristic
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—61no—
432C2×C4×D3—62no—
433C2×C4×D3—62no—
434C2×C4×D3—62no—
435C2×C4×D3—62no—
436C2×C4×D3—61no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—68no—
441C2×C4×D3—68no—
442C2×C4×D3—61no—
443C2×C4×D3—61no—
444C2×C4×D3—61no—
445C2×C4×D3C22×D311yescharacteristic
446C2×C4×D3C22×D311yescharacteristic
447C2×Dic6—61no—
448C2×Dic6—61no—
449C2×Dic6C22×D311yescharacteristic
450C2×Dic6C22×D311yescharacteristic
451C2×Dic6C22×D311yescharacteristic
452C3×Q16—62no—
453C3×SD16—62no—
454C3×SD16—62no—
455C3×D8—62no—
456C2×C3×C8—21no—
457C2×C3×C8—31no—
458C2×C3×C8—31no—
459C2×C3×C8C22×D311yescharacteristic
460C2×C3×C8C22×D311yescharacteristic
461C3×C4⋊C4—21no—
462C3×C4⋊C4—61no—
463C3×C4⋊C4C22×D311yescharacteristic
464C3×C4⋊C4C22×D311yescharacteristic
465C3×C22⋊C4—61no—
466C3×C22⋊C4—61no—
467#217—61no—
468#217—61no—
469#216—62no—
470#216—62no—
471#215—62no—
472#215—62no—
473#214—22no—
474#214—62no—
475#213—22no—
476#213—62no—
477(C2×D3)⋊C4—21no—
478(C2×D3)⋊C4—21no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—121no—
484C4⋊Dic3—21no—
485C4⋊Dic3—31no—
486C4⋊Dic3—31no—
487C4⋊Dic3—61no—
488Dic3⋊C4—61no—
489Dic3⋊C4—61no—
490C4×Dic3—61no—
491C4×Dic3—61no—
492C4×Dic3—121no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—61no—
496C2×C3⋊C8C22×D311yescharacteristic
497C2×C3⋊C8C22×D311yescharacteristic
498Dic12—22no—
499D24—62no—
500#204—22no—
501#204—62no—
502ΓL(1,𝔽25)—62no—
503ΓL(1,𝔽25)—62no—
504ΓL(1,𝔽25)—62no—
505ΓL(1,𝔽25)—62no—
506ΓL(1,𝔽25)—122no—
507C22×C32—22no—
508C22×C32—41no—
509C22×C32—41no—
510C22×C32C22×D411yescharacteristic
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—48no—
515C2×C3⋊D3—41no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3#12012yes—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527D32—44no—
528C32×C4—41no—
529C32×C4C22×D411yescharacteristic
530C32×C4C22×D411yescharacteristic
531C3⋊Dic3—41no—
532C3⋊Dic3#12012yes—
533C3×Dic3—21no—
534C3×Dic3—21no—
535C3×Dic3—22no—
536C3×Dic3—22no—
537C3×Dic3—41no—
538C2×#41—31no—
539C2×#41—31no—
540C2×#41—91no—
541C2×#41—91no—
542C2×#41—91no—
543C2×#41—181no—
544C2×#41—181no—
545C2×#41—184no—
546C2×#41—184no—
547C22×Q8—91no—
548C22×D4—91no—
549C22×D4—181no—
550C23×C4—91no—
551C23×C4—181no—
552#137—184no—
553AGL(1,ℤ/8)—184no—
554C2×Q16—31no—
555C2×Q16—91no—
556C2×SD16—31no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×D8—31no—
561C2×D8—91no—
562C2×M16—91no—
563C2×M16—91no—
564#123—181no—
565C22⋊Q8—31no—
566C22⋊Q8—91no—
567#121—31no—
568#121—91no—
569#120—181no—
570C4×D4—181no—
571C4×D4—181no—
572#117—91no—
573#103—31no—
574#103—31no—
575#103—91no—
576#103—91no—
577#102—91no—
578#102—91no—
579#102—91no—
580#102D3211yescharacteristic, complemented
581C22⋊C8—31no—
582C22⋊C8—31no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C23×C3—21no—
586C23×C3—21no—
587C23×C3—31no—
588C23×C3—31no—
589C23×C3—41no—
590C23×C3—61no—
591C22×D3—21no—
592C22×D3—31no—
593C22×D3—31no—
594C22×D3—61no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—64no—
598C22×D3—64no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—124no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3—122no—
611C22×D3—242no—
612C22×D3—242no—
613C22×D3D3×D411yescharacteristic
614C22×D3D3×D411yescharacteristic
615C3×Q8—32no—
616C3×Q8—32no—
617C3×Q8—61no—
618C3×Q8—61no—
619C3×Q8—61no—
620C3×Q8—61no—
621C3×D4—21no—
622C3×D4—21no—
623C3×D4—22no—
624C3×D4—41no—
625C3×D4—64no—
626C3×D4—64no—
627C3×D4—61no—
628C3×D4—61no—
629C3×D4—122no—
630C3×D4D3×D412yes—
631C3×D4D3×D412yes—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—31no—
636C2×C3×C4—31no—
637C2×C3×C4—41no—
638C2×C3×C4—64no—
639C2×C3×C4—64no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D311yescharacteristic
649#67—24no—
650#67—24no—
651#67—64no—
652#67—64no—
653#67—64no—
654#67—64no—
655#67—124no—
656#67—122no—
657#67—122no—
658#67—122no—
659C2×Dic3—24no—
660C2×Dic3—24no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—31no—
665C2×Dic3—31no—
666C2×Dic3—61no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—121no—
672C2×Dic3—122no—
673C2×Dic3D3×D411yescharacteristic
674C2×Dic3D3×D411yescharacteristic
675D12—21no—
676D12—21no—
677D12—32no—
678D12—32no—
679D12—42no—
680D12—62no—
681D12—64no—
682D12—64no—
683D12—61no—
684D12—61no—
685D12—121no—
686D12—122no—
687C4×D3—21no—
688C4×D3—21no—
689C4×D3—21no—
690C4×D3—21no—
691C4×D3—32no—
692C4×D3—32no—
693C4×D3—32no—
694C4×D3—32no—
695C4×D3—62no—
696C4×D3—62no—
697C4×D3—62no—
698C4×D3—62no—
699C4×D3—64no—
700C4×D3—64no—
701C4×D3—64no—
702C4×D3—64no—
703C4×D3—64no—
704C4×D3—64no—
705C4×D3—62no—
706C4×D3—62no—
707C4×D3—122no—
708Dic6—21no—
709Dic6—21no—
710Dic6—21no—
711Dic6—21no—
712Dic6—64no—
713Dic6—64no—
714Dic6D3×D412yes—
715Dic6D3×D412yes—
716C3×C8—21no—
717C3×C8—21no—
718C3×C8—41no—
719C3×C8—61no—
720C3×C8—61no—
721C3⋊C8—21no—
722C3⋊C8—21no—
723C3⋊C8—61no—
724C3⋊C8—61no—
725C3⋊C8—121no—
726C2×C32—42no—
727C2×C32C2×#12011yescharacteristic
728C2×C32#57511yescharacteristic
729C2×C32#57511yescharacteristic
730C3⋊D3—22no—
731C3⋊D3—42no—
732C3×D3—41no—
733C3×D3—41no—
734C3×D3—81no—
735C24—91no—
736C24—181no—
737#41—62no—
738#41—62no—
739#41—62no—
740#41—62no—
741#41—188no—
742#41—188no—
743#41—182no—
744#41—182no—
745#41—182no—
746#41—182no—
747#41—182no—
748#41—182no—
749C2×Q8—31no—
750C2×Q8—31no—
751C2×Q8—31no—
752C2×Q8—94no—
753C2×Q8—181no—
754C2×Q8—182no—
755C2×D4—31no—
756C2×D4—61no—
757C2×D4—61no—
758C2×D4—61no—
759C2×D4—94no—
760C2×D4—91no—
761C2×D4—181no—
762C2×D4—181no—
763C2×D4—181no—
764C2×D4—182no—
765C2×D4—181no—
766C2×D4—188no—
767C2×D4—181no—
768C2×D4C2×D3211yescharacteristic
769C22×C4—31no—
770C22×C4—31no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—91no—
774C22×C4—91no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—181no—
778C22×C4—181no—
779C22×C4—182no—
780C22×C4—182no—
781C22×C4—181no—
782C22×C4—188no—
783C22×C4—181no—
784Q16—62no—
785Q16—182no—
786SD16—62no—
787SD16—62no—
788SD16—182no—
789SD16—182no—
790D8—62no—
791D8—182no—
792M16—182no—
793M16—182no—
794C2×C8—31no—
795C2×C8—31no—
796C2×C8—91no—
797C2×C8C2×D3211yescharacteristic
798C4⋊C4—61no—
799C4⋊C4—91no—
800C4⋊C4—181no—
801C4⋊C4C2×D3211yescharacteristic
802C22⋊C4—61no—
803C22⋊C4—61no—
804C22⋊C4—181no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C42—181no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—21no—
811C22×C3—42no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—81no—
823C22×C3—81no—
824C22×C3—121no—
825C22×C3—121no—
826C22×C3—121no—
827C22×C3C2×D3×D411yescharacteristic
828C22×C3C2×D3×D411yescharacteristic
829C2×D3—21no—
830C2×D3—21no—
831C2×D3—21no—
832C2×D3—21no—
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—32no—
836C2×D3—32no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—62no—
841C2×D3—61no—
842C2×D3—61no—
843C2×D3—61no—
844C2×D3—61no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—122no—
850C2×D3—124no—
851C2×D3—124no—
852C2×D3—128no—
853C2×D3—128no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3—121no—
857C2×D3—121no—
858C2×D3—248no—
859C2×D3—241no—
860C2×D3—241no—
861C3×C4—21no—
862C3×C4—21no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—62no—
866C3×C4—62no—
867C3×C4—61no—
868C3×C4—61no—
869C3×C4—81no—
870C3×C4—121no—
871C3×C4C2×D3×D411yescharacteristic
872C3×C4C2×D3×D411yescharacteristic
873C3×C4C2×D3×D411yescharacteristic
874C3×C4C2×D3×D411yescharacteristic
875Dic3—22no—
876Dic3—22no—
877Dic3—21no—
878Dic3—21no—
879Dic3—32no—
880Dic3—32no—
881Dic3—41no—
882Dic3—62no—
883Dic3—121no—
884Dic3—121no—
885Dic3—241no—
886C32#300511yescharacteristic, complemented, Sylow
887C23—21no—
888C23—31no—
889C23—31no—
890C23—61no—
891C23—91no—
892C23—184no—
893C23—182no—
894C23—181no—
895C23—362no—
896C23—362no—
897C23—361no—
898C23—361no—
899Q8—32no—
900Q8—32no—
901Q8—61no—
902Q8—61no—
903Q8—61no—
904Q8—61no—
905Q8—184no—
906D4—21no—
907D4—64no—
908D4—64no—
909D4—61no—
910D4—61no—
911D4—92no—
912D4—122no—
913D4—184no—
914D4—184no—
915D4—184no—
916D4—181no—
917D4—362no—
918D4—362no—
919D4#380212yes—
920C2×C4—21no—
921C2×C4—31no—
922C2×C4—31no—
923C2×C4—64no—
924C2×C4—64no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—91no—
933C2×C4—92no—
934C2×C4—92no—
935C2×C4—182no—
936C2×C4—184no—
937C2×C4—184no—
938C2×C4—184no—
939C2×C4—182no—
940C2×C4—182no—
941C2×C4—181no—
942C2×C4—362no—
943C2×C4C22×D3211yescharacteristic
944C8—21no—
945C8—61no—
946C8—61no—
947C8—181no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—42no—
952C2×C3—42no—
953C2×C3—82no—
954C2×C3—121no—
955C2×C3—121no—
956C2×C3—241no—
957C2×C3D3×#12011yescharacteristic
958C2×C3D3×#12011yescharacteristic
959C2×C3#576811yescharacteristic
960C2×C3#576811yescharacteristic
961C2×C3#577311yescharacteristic
962C2×C3#577711yescharacteristic
963D3—41no—
964D3—41no—
965D3—62no—
966D3—62no—
967D3—81no—
968D3—122no—
969D3—122no—
970D3—122no—
971D3—242no—
972C22—22no—
973C22—41no—
974C22—41no—
975C22—61no—
976C22—61no—
977C22—61no—
978C22—61no—
979C22—61no—
980C22—61no—
981C22—92no—
982C22—121no—
983C22—121no—
984C22—121no—
985C22—181no—
986C22—181no—
987C22—182no—
988C22—368no—
989C22—364no—
990C22—361no—
991C22—361no—
992C22D32×D411yescharacteristic
993C4—41no—
994C4—61no—
995C4—61no—
996C4—62no—
997C4—62no—
998C4—92no—
999C4—121no—
1000C4—361no—
1001C4C2×#380211yescharacteristic
1002C4D32×D411yescharacteristic
1003C3—21no—
1004C3#8008311yescharacteristic, complemented
1005C3#8022711yescharacteristic, complemented
1006C2—42no—
1007C2—121no—
1008C2—121no—
1009C2—182no—
1010C2—241no—
1011C2—362no—
1012C2#1059425811yescharacteristic
1013C2#1059472911yescharacteristic
1014C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×#64312C2semidirect
2. C2×#63937C2semidirect
3. C2×#63811C2semidirect
4. #10594632C2semidirect
5. #10592469C2semidirect
6. C3×#4783C2semidirect
7. C3×#4781C2semidirect
8. #10591461C2semidirect
9. #10591450C2semidirect
10. #10590966C2semidirect
11. #10590937C2semidirect
12. #10590823C2semidirect
13. #10590616C2semidirect
14. #10590615C2semidirect
15. #10590602C2semidirect
34. C2×C3×#214C22semidirect
35. C2×C3×#213C22semidirect
36. C2×C3×Dic12C22semidirect
37. C2×C3×#204C22semidirect
38. C3×#897C22semidirect
39. C3×#895C22semidirect
42. #63908C22semidirect
45. #63856C22semidirect
47. C2×#3718C22semidirect
48. C2×#3717C22semidirect
49. C2×#3715C22semidirect
50. C2×#3714C22semidirect
53. C32×#102C22semidirect
54. #63659C22semidirect
55. #63648C22semidirect
56. #63636C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#810C22semidirect
60. C3×#810C22semidirect
61. #63566C22semidirect
62. #63566C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
87. #4783D3semidirect
88. #4781D3semidirect
101. D4×C3⋊D3D4semidirect
142. #3797D4semidirect
214. C2×#214C2×D3semidirect
216. C2×#213C2×D3semidirect
223. C2×Dic12C2×D3semidirect
226. C2×#204C2×D3semidirect
232. #897C2×D3semidirect
233. #895C2×D3semidirect
246. C3×#102C2×D3semidirect
247. C3×#102C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
263. (C2×D3)⋊C8C2×D3semidirect
266. #810C2×D3semidirect
267. #810C2×D3semidirect
580. #102D32semidirect
886. C32#3005semidirect
1004. C3#80083semidirect
1005. C3#80227semidirect

Maximal subgroups

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

subgroupindex
C2×#643122
C2×#639372
C2×#638112
#105946322
#105924692
C3×#47832
C3×#47812
#105914612
#105914502
#105909662
#105909372
#105908232
#105906162
#105906152
#105906022
#802273
#800833