Finite Group Databasebeta

← #11863890

Subgroups — #11863890

Order 1152.

1607 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×#63950C211yesmaximal, characteristic, complemented
3C2×#63809C211yesmaximal, characteristic, complemented
4#10594632C211yesmaximal, characteristic, complemented
5#10592503C211yesmaximal, characteristic, complemented
6C3×#4808C211yesmaximal, characteristic, complemented
7C3×#4806C211yesmaximal, characteristic, complemented
8#10591594C211yesmaximal, characteristic, complemented
9#10591586C211yesmaximal, characteristic, complemented
10#10590942C211yesmaximal, characteristic, complemented
11#10590935C211yesmaximal, characteristic, complemented
12#10590823C211yesmaximal, characteristic, complemented
13#10590616C211yesmaximal, characteristic, complemented
14#10590611C211yesmaximal, characteristic, complemented
15#10590595C211yesmaximal, characteristic, complemented
16#80226—31nomaximal
17#80038—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21D3×#239—24no—
22D3×#239—24no—
23C2×D3×D12—21no—
24C2×D3×D12C2211yescharacteristic
25C2×C4×D32—21no—
26C2×C4×D32C2211yescharacteristic
27C2×#3799—21no—
28C2×#3799C2211yescharacteristic
29C2×#3796—21no—
30C2×#3796C2211yescharacteristic
31C2×#3796C2211yescharacteristic, complemented
32C2×C8×C3⋊D3C2211yescharacteristic, complemented
33#64101C2211yescharacteristic, complemented
34C2×C3×#216C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C3×#897C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic
40#63950—24no—
41#63922—21no—
42#63908C2211yescharacteristic, complemented
43#63902—21no—
44#63898—21no—
45#63856C2211yescharacteristic
46#63854—21no—
47C2×#3718C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3710C2211yescharacteristic, complemented
52#63809—24no—
53C32×#103C2211yescharacteristic, complemented
54#63662C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63636C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#239—31no—
67C2×#919—31no—
68C2×#916—31no—
69C2×#916—31no—
70C2×#916—31no—
71#5627—31no—
72#5606—31no—
73C3×#452—31no—
74C3×#448—31no—
75#5238—31no—
76#5228—31no—
77#5186—31no—
78#5172—31no—
79#5172—31no—
80#5169—31no—
81#5047—31no—
82#5036—31no—
83#4808—31no—
84#4808D311yescharacteristic, complemented
85#4806D311yescharacteristic, complemented
86#4804—31no—
87#4804—31no—
88#4804—31no—
89#4804—61no—
90#4773—31no—
91#4772—31no—
92#4734—31no—
93#4731—31no—
94D3×C22⋊C8—31no—
95D3×C22⋊C8—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99#3832—22no—
100#3832D414yescomplemented
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C3×#239—22no—
106C3×#239—22no—
107C3×D3×Q8—22no—
108C3×D3×Q8—22no—
109C2×C3×D12—21no—
110C2×C3×D12—21no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#625—21no—
125C2×#624—21no—
126C2×#624D411yescharacteristic
127C2×D3×Dic3—21no—
128C2×D3×Dic3—21no—
129C2×D3×Dic3D411yescharacteristic
130C2×D3×Dic3D411yescharacteristic
131D3×D12—28no—
132D3×D12—22no—
133D3×D12—22no—
134C4×D32—28no—
135C4×D32—22no—
136C4×D32—22no—
137#3799—28no—
138#3799—22no—
139#3799—22no—
140#3796—28no—
141#3796—22no—
142#3796—22no—
143#3796—22no—
144#3796D414yescomplemented
145C2×C32×C8C2311yescharacteristic
146C32×C4⋊C4C2311yescharacteristic
147#3752—21no—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149C4×C3⋊Dic3—21no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C8×C3⋊D3—22no—
152C3×#216—22no—
153C3×#215—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×#204—22no—
160C3×#204—22no—
161#3724—21no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164#3718—22no—
165#3717—22no—
166#3714—22no—
167#3713—22no—
168#3710—22no—
169#3002—91noSylow
170C2×C3×#41—31no—
171C22×C3×Q8—31no—
172D3×#41—64no—
173D3×#41—64no—
174C2×#239—31no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—61no—
180C2×#239—61no—
181C2×#239—61no—
182C2×#239—64no—
183C2×#239—64no—
184C2×#239C2×D311yescharacteristic
185C2×D3×Q8C2×D311yescharacteristic
186C2×#237—31no—
187C2×#237—31no—
188C2×#237—61no—
189C2×D3×D4—31no—
190C2×D3×D4—61no—
191C2×#235—31no—
192C2×#235—61no—
193C22×D12—31no—
194C22×D12—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×SD16—31no—
203C3×C22⋊Q8—31no—
204C3×#121—31no—
205#946—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#216C2×D311yescharacteristic, complemented
209C2×#215—31no—
210C2×#215C2×D311yescharacteristic, complemented
211#938—31no—
212#937—61no—
213D4×Dic3—61no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213—31no—
217#930—31no—
218#924—31no—
219#919—64no—
220#916—64no—
221#916—64no—
222#916—64no—
223C2×D24—31no—
224C2×#204—31no—
225C2×#204C2×D311yescharacteristic, complemented
226C2×#204C2×D311yescharacteristic, complemented
227C2×D3×C8—31no—
228C2×D3×C8—31no—
229C2×D3×C8—31no—
230C2×D3×C8—31no—
231C2×D3×C8—61no—
232#897C2×D311yescharacteristic, complemented
233#895C2×D311yescharacteristic
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—21no—
244C3×#103—31no—
245C3×#103C2×D311yescharacteristic, complemented
246C3×#103C2×D311yescharacteristic, complemented
247C3×#102—31no—
248C3×C22⋊C8—31no—
249C3×C22⋊C8—31no—
250#835—31no—
251#835—31no—
252#835—31no—
253#835—61no—
254#832—31no—
255#830—31no—
256#830—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—61no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8C2×D311yescharacteristic
264(C2×D3)⋊C8C2×D311yescharacteristic, complemented
265#816—31no—
266#810C2×D311yescharacteristic, complemented
267#809—31no—
268#809—31no—
269#809—61no—
270#809C2×D311yescharacteristic, complemented
271C22×C3⋊D3—21no—
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3C2×D411yescharacteristic
276C22×C3×D3C2×D411yescharacteristic
277C2×D32—24no—
278C2×D32—22no—
279C2×D32—22no—
280C2×D32—41no—
281C2×D32—42no—
282C2×D32—42no—
283C32×Q8—21no—
284C32×Q8C2×D412yes—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4C2411yescharacteristic
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3C2×D411yescharacteristic
290C4⋊(C3⋊D3)—24no—
291C4⋊(C3⋊D3)—21no—
292C4⋊(C3⋊D3)C2×D412yes—
293C4×C3⋊D3—24no—
294C4×C3⋊D3C2×D412yes—
295C4×C3⋊D3C2×D412yes—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3C2×D411yescharacteristic
299C2×C3×Dic3C2×D411yescharacteristic
300C3×D12—24no—
301C3×D12—21no—
302C3×D12—21no—
303C3×D12—21no—
304C3×D12—42no—
305C3×D12C2×D412yes—
306C3×C4×D3—24no—
307C3×C4×D3—24no—
308C3×C4×D3—21no—
309C3×C4×D3—21no—
310C3×C4×D3—21no—
311C3×C4×D3—21no—
312C3×Dic6—24no—
313C3×Dic6—21no—
314C3×Dic6—21no—
315C3×Dic6—21no—
316C3×Dic6C2×D412yes—
317#626—24no—
318#626—24no—
319#626—24no—
320#626—42no—
321#625—42no—
322#624—24no—
323#624—22no—
324D3×Dic3—22no—
325D3×Dic3—24no—
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×#135—91no—
334C2×#135—91no—
335#525—91no—
336#452—31no—
337#452—91no—
338#451—91no—
339#450—91no—
340#449—91no—
341#449—91no—
342#448—31no—
343#447—91no—
344#416—91no—
345#416—91no—
346C2×C22⋊C8—91no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—61no—
350C23×D3—61no—
351C3×#41—62no—
352C3×#41—62no—
353C2×C3×Q8—21no—
354C2×C3×Q8—31no—
355C2×C3×Q8—31no—
356C2×C3×Q8—61no—
357C2×C3×Q8—62no—
358C2×C3×Q8—62no—
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×Q8C22×D311yescharacteristic
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C2×C3×D4—61no—
364C2×C3×D4—61no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—61no—
368C22×C3×C4—61no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—61no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379#239—22no—
380#239—22no—
381#239—34no—
382#239—34no—
383#239—34no—
384#239—64no—
385#239—62no—
386#239—62no—
387#239—68no—
388#239—62no—
389#239—62no—
390#239—62no—
391#239—62no—
392#239—62no—
393#239—68no—
394#239—122no—
395D3×Q8—22no—
396D3×Q8—22no—
397#237—34no—
398#237—62no—
399#237—62no—
400#237—62no—
401#237—68no—
402D3×D4—62no—
403D3×D4—62no—
404D3×D4—68no—
405#235—62no—
406#235—68no—
407#235—62no—
408C2×D12—21no—
409C2×D12—21no—
410C2×D12—31no—
411C2×D12—31no—
412C2×D12—61no—
413C2×D12—62no—
414C2×D12—68no—
415C2×D12—61no—
416C2×D12—61no—
417C2×D12—61no—
418C2×D12—61no—
419C2×D12—61no—
420C2×D12—62no—
421C2×D12—61no—
422C2×D12—121no—
423C2×D12C22×D311yescharacteristic
424C2×D12C22×D311yescharacteristic
425C2×C4×D3—21no—
426C2×C4×D3—21no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—61no—
434C2×C4×D3—62no—
435C2×C4×D3—62no—
436C2×C4×D3—62no—
437C2×C4×D3—62no—
438C2×C4×D3—68no—
439C2×C4×D3—68no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3—61no—
443C2×C4×D3—61no—
444C2×C4×D3—61no—
445C2×C4×D3—61no—
446C2×C4×D3—121no—
447C2×C4×D3C22×D311yescharacteristic
448C2×C4×D3C22×D311yescharacteristic
449C2×Dic6—21no—
450C2×Dic6C22×D311yescharacteristic
451C2×Dic6C22×D311yescharacteristic
452C3×Q16—62no—
453C3×SD16—62no—
454C3×SD16—62no—
455C3×SD16—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—22no—
470#216—62no—
471#216—62no—
472#215—22no—
473#215—62no—
474#213—62no—
475#213—62no—
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
498D24—62no—
499#204—22no—
500#204—22no—
501#204—62no—
502D3×C8—62no—
503D3×C8—62no—
504D3×C8—62no—
505D3×C8—62no—
506D3×C8—122no—
507C22×C32C22×D411yescharacteristic
508C2×C3⋊D3—21no—
509C2×C3⋊D3—21no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—41no—
512C2×C3⋊D3—41no—
513C2×C3⋊D3#12012yes—
514C2×C3×D3—21no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—22no—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—41no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3#13512yescomplemented
526D32—44no—
527D32—48no—
528C32×C4—22no—
529C32×C4—41no—
530C32×C4C22×D411yescharacteristic
531C32×C4C22×D411yescharacteristic
532C3⋊Dic3—41no—
533C3⋊Dic3#12012yes—
534C3×Dic3—21no—
535C3×Dic3—21no—
536C3×Dic3—22no—
537C3×Dic3—41no—
538C2×#41—31no—
539C2×#41—91no—
540C2×#41—91no—
541C2×#41—91no—
542C2×#41—91no—
543C2×#41—181no—
544C2×#41—181no—
545C2×#41—184no—
546C2×#41—184no—
547C22×Q8—31no—
548C22×D4—91no—
549C22×D4—181no—
550C23×C4—91no—
551C23×C4—181no—
552#135—184no—
553#135—184no—
554C2×Q16—31no—
555C2×Q16—91no—
556C2×SD16—31no—
557C2×SD16—31no—
558C2×SD16—31no—
559C2×SD16—91no—
560C2×D8—91no—
561C2×D8—91no—
562C22×C8—91no—
563C22×C8—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—91no—
575#103—91no—
576#103D3211yescharacteristic, complemented
577#102—31no—
578#102—91no—
579#102—91no—
580#102—91no—
581C22⋊C8—31no—
582C22⋊C8—31no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C23×C3—31no—
586C23×C3—31no—
587C23×C3—61no—
588C23×C3—61no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—31no—
592C22×D3—31no—
593C22×D3—61no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—64no—
598C22×D3—64no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—62no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—122no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3D3×D411yescharacteristic
610C22×D3D3×D411yescharacteristic
611C3×Q8—21no—
612C3×Q8—21no—
613C3×Q8—22no—
614C3×Q8—32no—
615C3×Q8—41no—
616C3×Q8—64no—
617C3×Q8—61no—
618C3×Q8—61no—
619C3×Q8—61no—
620C3×Q8D3×D412yes—
621C3×Q8D3×D412yes—
622C3×D4—32no—
623C3×D4—64no—
624C3×D4—61no—
625C3×D4—61no—
626C3×D4—61no—
627C3×D4—122no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—31no—
634C2×C3×C4—31no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—64no—
638C2×C3×C4—64no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647#67—64no—
648#67—64no—
649#67—64no—
650#67—122no—
651#67—122no—
652#67—122no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—31no—
656C2×Dic3—31no—
657C2×Dic3—61no—
658C2×Dic3—62no—
659C2×Dic3—64no—
660C2×Dic3—62no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—121no—
664C2×Dic3—122no—
665C2×Dic3D3×D411yescharacteristic
666C2×Dic3D3×D411yescharacteristic
667D12—24no—
668D12—21no—
669D12—21no—
670D12—21no—
671D12—32no—
672D12—32no—
673D12—42no—
674D12—62no—
675D12—64no—
676D12—64no—
677D12—64no—
678D12—64no—
679D12—64no—
680D12—61no—
681D12—61no—
682D12—121no—
683D12—124no—
684D12—122no—
685D12D3×D412yes—
686C4×D3—24no—
687C4×D3—24no—
688C4×D3—21no—
689C4×D3—21no—
690C4×D3—21no—
691C4×D3—21no—
692C4×D3—32no—
693C4×D3—32no—
694C4×D3—32no—
695C4×D3—32no—
696C4×D3—62no—
697C4×D3—62no—
698C4×D3—62no—
699C4×D3—62no—
700C4×D3—64no—
701C4×D3—64no—
702C4×D3—64no—
703C4×D3—64no—
704C4×D3—62no—
705C4×D3—62no—
706C4×D3—64no—
707C4×D3—124no—
708C4×D3—122no—
709Dic6—24no—
710Dic6—21no—
711Dic6—21no—
712Dic6—21no—
713Dic6D3×D412yes—
714C3×C8—21no—
715C3×C8—21no—
716C3×C8—41no—
717C3×C8—61no—
718C3×C8—61no—
719C3⋊C8—21no—
720C3⋊C8—21no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—121no—
724C2×C32C2×#12011yescharacteristic
725C2×C32C2×#13511yescharacteristic
726C2×C32#57511yescharacteristic
727C3⋊D3—22no—
728C3⋊D3—42no—
729C3×D3—22no—
730C3×D3—41no—
731C3×D3—42no—
732C3×D3—81no—
733C24—91no—
734C24—181no—
735#41—62no—
736#41—62no—
737#41—94no—
738#41—94no—
739#41—182no—
740#41—182no—
741#41—188no—
742#41—182no—
743#41—182no—
744#41—182no—
745#41—182no—
746#41—188no—
747C2×Q8—31no—
748C2×Q8—31no—
749C2×Q8—61no—
750C2×Q8—62no—
751C2×Q8—62no—
752C2×Q8C2×D3211yescharacteristic
753C2×D4—31no—
754C2×D4—31no—
755C2×D4—61no—
756C2×D4—61no—
757C2×D4—91no—
758C2×D4—181no—
759C2×D4—181no—
760C2×D4—182no—
761C2×D4—182no—
762C2×D4—188no—
763C2×D4—181no—
764C2×D4—181no—
765C2×D4—181no—
766C2×D4—181no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—91no—
774C22×C4—91no—
775C22×C4—181no—
776C22×C4—181no—
777C22×C4—182no—
778C22×C4—182no—
779C22×C4—188no—
780C22×C4—181no—
781C22×C4—181no—
782Q16—62no—
783Q16—182no—
784SD16—62no—
785SD16—62no—
786SD16—62no—
787SD16—182no—
788D8—182no—
789D8—182no—
790C2×C8—31no—
791C2×C8—31no—
792C2×C8—91no—
793C2×C8—182no—
794C2×C8—182no—
795C2×C8C2×D3211yescharacteristic
796C4⋊C4—61no—
797C4⋊C4—91no—
798C4⋊C4—181no—
799C4⋊C4C2×D3211yescharacteristic
800C22⋊C4—61no—
801C22⋊C4—61no—
802C22⋊C4—181no—
803C22⋊C4—181no—
804C22⋊C4—181no—
805C42—181no—
806C22×C3—21no—
807C22×C3—32no—
808C22×C3—61no—
809C22×C3—61no—
810C22×C3—61no—
811C22×C3—61no—
812C22×C3—62no—
813C22×C3—61no—
814C22×C3—121no—
815C22×C3—121no—
816C22×C3—121no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3C2×D3×D411yescharacteristic
820C22×C3C2×D3×D411yescharacteristic
821C2×D3—21no—
822C2×D3—21no—
823C2×D3—21no—
824C2×D3—21no—
825C2×D3—21no—
826C2×D3—22no—
827C2×D3—32no—
828C2×D3—32no—
829C2×D3—41no—
830C2×D3—41no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—62no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—121no—
842C2×D3—121no—
843C2×D3—122no—
844C2×D3—124no—
845C2×D3—128no—
846C2×D3—124no—
847C2×D3—128no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—241no—
853C2×D3—241no—
854C2×D3#91612yescomplemented
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—21no—
858C3×C4—21no—
859C3×C4—42no—
860C3×C4—41no—
861C3×C4—41no—
862C3×C4—61no—
863C3×C4—61no—
864C3×C4—62no—
865C3×C4—81no—
866C3×C4—121no—
867C3×C4C2×D3×D411yescharacteristic
868C3×C4C2×D3×D411yescharacteristic
869C3×C4C2×D3×D411yescharacteristic
870C3×C4C2×D3×D411yescharacteristic
871Dic3—21no—
872Dic3—22no—
873Dic3—21no—
874Dic3—32no—
875Dic3—32no—
876Dic3—41no—
877Dic3—62no—
878Dic3—121no—
879Dic3—121no—
880Dic3—241no—
881C32#300211yescharacteristic, complemented, Sylow
882C23—31no—
883C23—31no—
884C23—61no—
885C23—61no—
886C23—91no—
887C23—182no—
888C23—182no—
889C23—184no—
890C23—181no—
891C23—362no—
892C23—361no—
893C23—362no—
894Q8—21no—
895Q8—32no—
896Q8—64no—
897Q8—61no—
898Q8—61no—
899Q8—61no—
900Q8#380212yes—
901D4—32no—
902D4—64no—
903D4—61no—
904D4—61no—
905D4—61no—
906D4—92no—
907D4—122no—
908D4—184no—
909D4—184no—
910D4—184no—
911D4—184no—
912D4—181no—
913D4—362no—
914D4—362no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—31no—
918C2×C4—31no—
919C2×C4—64no—
920C2×C4—64no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—91no—
928C2×C4—92no—
929C2×C4—92no—
930C2×C4—184no—
931C2×C4—182no—
932C2×C4—184no—
933C2×C4—182no—
934C2×C4—182no—
935C2×C4—184no—
936C2×C4—181no—
937C2×C4—362no—
938C2×C4C22×D3211yescharacteristic
939C8—21no—
940C8—61no—
941C8—61no—
942C8—181no—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—62no—
947C2×C3—121no—
948C2×C3—122no—
949C2×C3—241no—
950C2×C3D3×#12011yescharacteristic
951C2×C3D3×#12011yescharacteristic
952C2×C3C2×#91611yescharacteristic
953C2×C3D3×#13511yescharacteristic
954C2×C3#577711yescharacteristic
955C2×C3#577711yescharacteristic
956D3—22no—
957D3—41no—
958D3—42no—
959D3—62no—
960D3—62no—
961D3—81no—
962D3—122no—
963D3—122no—
964D3—122no—
965D3—242no—
966C22—32no—
967C22—61no—
968C22—61no—
969C22—61no—
970C22—61no—
971C22—62no—
972C22—61no—
973C22—92no—
974C22—121no—
975C22—121no—
976C22—121no—
977C22—121no—
978C22—121no—
979C22—181no—
980C22—181no—
981C22—182no—
982C22—364no—
983C22—368no—
984C22—361no—
985C22—361no—
986C22D32×D411yescharacteristic
987C4—22no—
988C4—41no—
989C4—61no—
990C4—61no—
991C4—62no—
992C4—92no—
993C4—121no—
994C4—361no—
995C4C2×#380211yescharacteristic
996C4D32×D411yescharacteristic
997C3—21no—
998C3#8003811yescharacteristic, complemented
999C3#8022611yescharacteristic, complemented
1000C2—62no—
1001C2—121no—
1002C2—122no—
1003C2—182no—
1004C2—241no—
1005C2—362no—
1006C2#1059425811yescharacteristic
1007C2D3×#91611yescharacteristic
1008C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3002
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. C2×#63950C2semidirect
3. C2×#63809C2semidirect
4. #10594632C2semidirect
5. #10592503C2semidirect
6. C3×#4808C2semidirect
7. C3×#4806C2semidirect
8. #10591594C2semidirect
9. #10591586C2semidirect
10. #10590942C2semidirect
11. #10590935C2semidirect
12. #10590823C2semidirect
13. #10590616C2semidirect
14. #10590611C2semidirect
15. #10590595C2semidirect
31. C2×#3796C22semidirect
32. C2×C8×C3⋊D3C22semidirect
33. #64101C22semidirect
34. C2×C3×#216C22semidirect
35. C2×C3×#215C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×#204C22semidirect
38. C3×#897C22semidirect
42. #63908C22semidirect
47. C2×#3718C22semidirect
48. C2×#3717C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3710C22semidirect
53. C32×#103C22semidirect
54. #63662C22semidirect
55. #63648C22semidirect
56. #63636C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63566C22semidirect
62. #63563C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4808D3semidirect
85. #4806D3semidirect
100. #3832D4semidirect
144. #3796D4semidirect
208. C2×#216C2×D3semidirect
210. C2×#215C2×D3semidirect
225. C2×#204C2×D3semidirect
226. C2×#204C2×D3semidirect
232. #897C2×D3semidirect
245. C3×#103C2×D3semidirect
246. C3×#103C2×D3semidirect
264. (C2×D3)⋊C8C2×D3semidirect
266. #810C2×D3semidirect
270. #809C2×D3semidirect
525. C2×C3×D3#135semidirect
576. #103D32semidirect
854. C2×D3#916semidirect
881. C32#3002semidirect
998. C3#80038semidirect
999. C3#80226semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×#639502
C2×#638092
#105946322
#105925032
C3×#48082
C3×#48062
#105915942
#105915862
#105909422
#105909352
#105908232
#105906162
#105906112
#105905952
#802263
#800383