Finite Group Databasebeta

← #11863893

Subgroups — #11863893

Order 1152.

1661 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×#64128C211yesmaximal, characteristic, complemented
3#10595430C211yesmaximal, characteristic, complemented
4C2×#63950C211yesmaximal, characteristic, complemented
5C3×#5187C211yesmaximal, characteristic, complemented
6C3×#5186C211yesmaximal, characteristic, complemented
7#10591657C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591588C211yesmaximal, characteristic, complemented
10#10591584C211yesmaximal, characteristic, complemented
11#10591560C211yesmaximal, characteristic, complemented
12#10590967C211yesmaximal, characteristic, complemented
13#10590956C211yesmaximal, characteristic, complemented
14#10590947C211yesmaximal, characteristic, complemented
15#10590935C211yesmaximal, characteristic, complemented
16#80226—31nomaximal
17#80182—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3832C2211yescharacteristic, complemented
20C2×C3×#239C2211yescharacteristic
21C2×C3×D3×Q8C2211yescharacteristic
22D3×#239—24no—
23D3×#239—24no—
24C2×D3×D12—21no—
25C2×D3×D12C2211yescharacteristic
26C2×C4×D32—21no—
27C2×C4×D32C2211yescharacteristic
28C2×#3799—21no—
29C2×#3799C2211yescharacteristic
30C2×#3796—21no—
31C2×#3796C2211yescharacteristic
32C2×C32×Q16C2211yescharacteristic, complemented
33C2×#3755C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35#64128—24no—
36C2×#3745C2211yescharacteristic, complemented
37C2×C8×C3⋊D3C2211yescharacteristic, complemented
38C3×#946C2211yescharacteristic
39C3×#946C2211yescharacteristic, complemented
40C2×C3×#216C2211yescharacteristic, complemented
41C2×C3×#215C2211yescharacteristic, complemented
42#63950—24no—
43#63923—21no—
44#63909C2211yescharacteristic
45#63909C2211yescharacteristic, complemented
46#63897—21no—
47#63881—21no—
48#63881—21no—
49#63849C2211yescharacteristic, complemented
50C2×#3717C2211yescharacteristic, complemented
51C2×#3714C2211yescharacteristic, complemented
52C2×#3710C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, 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×#919—31no—
69C2×#919—31no—
70C2×#919—61no—
71C2×#916—31no—
72#5627—31no—
73#5627—31no—
74C3×#452—31no—
75C3×#451—31no—
76#5238—31no—
77#5227—31no—
78#5187—31no—
79#5187D311yescharacteristic, complemented
80#5186D311yescharacteristic, complemented
81#5169—31no—
82#5047—31no—
83#5046—31no—
84#4810—31no—
85#4810—31no—
86#4806—31no—
87#4804—31no—
88#4804—31no—
89#4804—31no—
90#4773—31no—
91#4772—31no—
92#4734—31no—
93#4732—31no—
94D3×C22⋊C8—31no—
95D3×C22⋊C8—31no—
96C22×D32—21no—
97C22×D32D411yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100#3832—22no—
101#3832—22no—
102#3832—22no—
103#3832D414yescomplemented
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)—21no—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C4×C3⋊D3—21no—
109C2×C4×C3⋊D3—21no—
110C2×C4×C3⋊D3C2311yescharacteristic
111C3×#239—22no—
112C3×#239—22no—
113C3×D3×Q8—22no—
114C3×D3×Q8—22no—
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6—21no—
122C2×C3×Dic6C2311yescharacteristic
123C2×#626—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#624—21no—
129C2×#624D411yescharacteristic
130C2×D3×Dic3—21no—
131C2×D3×Dic3D411yescharacteristic
132C2×D3×Dic3D411yescharacteristic
133D3×D12—28no—
134D3×D12—22no—
135D3×D12—22no—
136C4×D32—28no—
137C4×D32—22no—
138C4×D32—22no—
139#3799—28no—
140#3799—22no—
141#3799—22no—
142#3796—28no—
143#3796—22no—
144#3796D414yescomplemented
145C32×Q16—22no—
146C2×C32×C8C2311yescharacteristic
147#3755—22no—
148#3755—22no—
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150#3745—22no—
151C8×C3⋊D3—22no—
152C3×#216—22no—
153C3×#215—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3C2311yescharacteristic
157C3×C4⋊Dic3C2311yescharacteristic
158C3×Dic3⋊C4—21no—
159C3×Dic3⋊C4—21no—
160C2×C3×C3⋊C8C2311yescharacteristic
161C2×C3×C3⋊C8C2311yescharacteristic
162#3722—21no—
163#3722—21no—
164#3722—21no—
165Dic32—21no—
166#3717—22no—
167#3714—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—31no—
180C2×#239—61no—
181C2×#239—61no—
182C2×#239—61no—
183C2×#239—61no—
184C2×#239—64no—
185C2×#239—64no—
186C2×#239C2×D311yescharacteristic
187C2×D3×Q8C2×D311yescharacteristic
188C2×#237—31no—
189C2×#237—61no—
190C2×D3×D4—31no—
191C2×D3×D4—61no—
192C2×#235—31no—
193C2×#235—61no—
194C22×D12—31no—
195C22×D12—61no—
196C22×C4×D3—31no—
197C22×C4×D3—31no—
198C22×C4×D3—61no—
199C22×C4×D3—61no—
200C2×C3×Q16—21no—
201C2×C3×Q16—31no—
202C2×C3×Q16C2×D311yescharacteristic, complemented
203C2×C3×Q16C2×D311yescharacteristic, complemented
204C2×C3×SD16—31no—
205C3×C22⋊Q8—31no—
206C3×C22⋊Q8—31no—
207#946C2×D311yescharacteristic
208#946C2×D311yescharacteristic, complemented
209C2×#216C2×D311yescharacteristic, complemented
210C2×#215—31no—
211C2×#215—31no—
212C2×#215—31no—
213C2×#215—31no—
214C2×#215—31no—
215C2×#215—61no—
216C2×#215—61no—
217C2×#215C2×D311yescharacteristic, complemented
218C2×#213—31no—
219#930—31no—
220#930—31no—
221#919—64no—
222#919—64no—
223#919—64no—
224#919—68no—
225#916—64no—
226C2×D24—31no—
227C2×D24—31no—
228C2×D24—31no—
229C2×D24—61no—
230C2×#204—31no—
231C2×D3×C8—31no—
232C2×D3×C8—31no—
233C2×D3×C8—31no—
234C2×D3×C8—31no—
235C2×D3×C8—61no—
236#895—31no—
237#895—31no—
238#894—61no—
239#894—61no—
240#893—61no—
241#893—61no—
242#892—31no—
243#892—31no—
244#882—61no—
245#882—61no—
246#67⋊C4—61no—
247#67⋊C4—61no—
248C3×#103—31no—
249C3×#103—31no—
250C3×#103—31no—
251C3×#102—31no—
252C3×C22⋊C8—31no—
253C3×C22⋊C8—31no—
254#835—31no—
255#835C2×D311yescharacteristic, complemented
256#835C2×D311yescharacteristic, complemented
257#832—31no—
258#830—31no—
259#830—31no—
260#821—31no—
261#821—31no—
262#821C2×D311yescharacteristic, complemented
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8C2×D311yescharacteristic
266(C2×D3)⋊C8C2×D311yescharacteristic, complemented
267#816C2×D311yescharacteristic, complemented
268#810—31no—
269#809—31no—
270#809—31no—
271#809—31no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3—21no—
274C22×C3⋊D3C2×D411yescharacteristic
275C22×C3×D3—21no—
276C22×C3×D3C2×D411yescharacteristic
277C22×C3×D3C2×D411yescharacteristic
278C2×D32—24no—
279C2×D32—22no—
280C2×D32—22no—
281C2×D32—41no—
282C2×D32—42no—
283C2×D32—42no—
284C32×Q8—21no—
285C32×Q8—21no—
286C32×Q8—21no—
287C32×Q8C2×D412yes—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4C2411yescharacteristic
291C2×C3⋊Dic3C2×D411yescharacteristic
292C4⋊(C3⋊D3)—21no—
293C4⋊(C3⋊D3)—24no—
294C4⋊(C3⋊D3)—21no—
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)—42no—
297C4⋊(C3⋊D3)C2×D412yes—
298C4×C3⋊D3—24no—
299C4×C3⋊D3—42no—
300C4×C3⋊D3C2×D412yes—
301C4×C3⋊D3C2×D412yes—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3C2×D411yescharacteristic
306C2×C3×Dic3C2×D411yescharacteristic
307C3×D12—24no—
308C3×D12—21no—
309C3×D12C2×D412yes—
310C3×C4×D3—24no—
311C3×C4×D3—24no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×Dic6—24no—
317C3×Dic6—21no—
318C3×Dic6C2×D412yes—
319#626—24no—
320#626—24no—
321#626—24no—
322#626—42no—
323#626—42no—
324#624—24no—
325#624—22no—
326D3×Dic3—22no—
327D3×Dic3—24no—
328D3×Dic3—22no—
329C32×C8—21no—
330C3⋊(C3⋊C8)—21no—
331C3×C3⋊C8—21no—
332C3×C3⋊C8—21no—
333C22×#41—91no—
334C2×#135—91no—
335C2×#135—91no—
336#525—91no—
337#452—31no—
338#452—91no—
339#451—31no—
340#450—91no—
341#449—91no—
342#449—91no—
343#448—91no—
344#447—91no—
345#416—91no—
346#416—91no—
347C2×C22⋊C8—91no—
348C23×D3—31no—
349C23×D3—31no—
350C23×D3—61no—
351C23×D3—61no—
352C3×#41—62no—
353C3×#41—62no—
354C2×C3×Q8—21no—
355C2×C3×Q8—21no—
356C2×C3×Q8—31no—
357C2×C3×Q8—61no—
358C2×C3×Q8—62no—
359C2×C3×Q8—62no—
360C2×C3×Q8C22×D311yescharacteristic
361C2×C3×Q8C22×D311yescharacteristic
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×Q8C22×D311yescharacteristic
364C2×C3×D4—31no—
365C2×C3×D4—61no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—61no—
369C22×C3×C4—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—
378#239—22no—
379#239—22no—
380#239—34no—
381#239—34no—
382#239—34no—
383#239—64no—
384#239—62no—
385#239—62no—
386#239—68no—
387#239—62no—
388#239—62no—
389#239—62no—
390#239—62no—
391#239—62no—
392#239—62no—
393#239—62no—
394#239—68no—
395#239—64no—
396#239—122no—
397#239—122no—
398D3×Q8—22no—
399D3×Q8—22no—
400#237—34no—
401#237—62no—
402#237—68no—
403D3×D4—62no—
404D3×D4—62no—
405D3×D4—68no—
406#235—62no—
407#235—68no—
408#235—62no—
409C2×D12—21no—
410C2×D12—31no—
411C2×D12—31no—
412C2×D12—31no—
413C2×D12—31no—
414C2×D12—61no—
415C2×D12—61no—
416C2×D12—62no—
417C2×D12—68no—
418C2×D12—61no—
419C2×D12—61no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12—61no—
423C2×D12—62no—
424C2×D12—61no—
425C2×D12—61no—
426C2×D12—61no—
427C2×D12—61no—
428C2×D12—121no—
429C2×D12—121no—
430C2×D12C22×D311yescharacteristic
431C2×C4×D3—21no—
432C2×C4×D3—21no—
433C2×C4×D3—31no—
434C2×C4×D3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—31no—
437C2×C4×D3—31no—
438C2×C4×D3—31no—
439C2×C4×D3—61no—
440C2×C4×D3—62no—
441C2×C4×D3—62no—
442C2×C4×D3—62no—
443C2×C4×D3—62no—
444C2×C4×D3—68no—
445C2×C4×D3—68no—
446C2×C4×D3—61no—
447C2×C4×D3—61no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3—121no—
454C2×C4×D3—121no—
455C2×C4×D3C22×D311yescharacteristic
456C2×C4×D3C22×D311yescharacteristic
457C2×Dic6—21no—
458C2×Dic6C22×D311yescharacteristic
459C3×Q16—24no—
460C3×Q16—22no—
461C3×Q16—22no—
462C3×Q16—62no—
463C3×SD16—62no—
464C2×C3×C8—21no—
465C2×C3×C8—31no—
466C2×C3×C8—31no—
467C2×C3×C8C22×D311yescharacteristic
468C2×C3×C8C22×D311yescharacteristic
469C3×C4⋊C4—31no—
470C3×C4⋊C4—31no—
471C3×C4⋊C4—61no—
472C3×C4⋊C4—61no—
473C3×C22⋊C4—61no—
474C3×C22⋊C4—61no—
475#216—22no—
476#215—22no—
477#215—62no—
478#215—62no—
479#215—62no—
480#215—64no—
481#215—64no—
482#215—62no—
483#215—62no—
484#213—62no—
485(C2×D3)⋊C4—21no—
486(C2×D3)⋊C4—21no—
487(C2×D3)⋊C4—61no—
488(C2×D3)⋊C4—61no—
489(C2×D3)⋊C4—61no—
490(C2×D3)⋊C4—61no—
491(C2×D3)⋊C4—61no—
492(C2×D3)⋊C4—61no—
493C4⋊Dic3C22×D311yescharacteristic
494C4⋊Dic3C22×D311yescharacteristic
495Dic3⋊C4—21no—
496Dic3⋊C4—21no—
497C4×Dic3—61no—
498C4×Dic3—61no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—61no—
502C2×C3⋊C8C22×D311yescharacteristic
503C2×C3⋊C8C22×D311yescharacteristic
504D24—62no—
505D24—62no—
506D24—64no—
507D24—62no—
508#204—62no—
509D3×C8—62no—
510D3×C8—62no—
511D3×C8—62no—
512D3×C8—62no—
513D3×C8—64no—
514C22×C32C22×D411yescharacteristic
515C2×C3⋊D3—21no—
516C2×C3⋊D3—21no—
517C2×C3⋊D3—22no—
518C2×C3⋊D3—41no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3⋊D3—41no—
522C2×C3⋊D3—41no—
523C2×C3⋊D3#12012yes—
524C2×C3×D3—21no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—22no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3#13512yescomplemented
533D32—44no—
534D32—48no—
535C32×C4—22no—
536C32×C4—41no—
537C32×C4C22×D411yescharacteristic
538C32×C4C22×D411yescharacteristic
539C3⋊Dic3#12012yes—
540C3×Dic3—21no—
541C3×Dic3—21no—
542C3×Dic3—22no—
543C3×Dic3—41no—
544C3×Dic3—41no—
545C2×#41—31no—
546C2×#41—91no—
547C2×#41—91no—
548C2×#41—91no—
549C2×#41—91no—
550C2×#41—181no—
551C2×#41—181no—
552C2×#41—184no—
553C2×#41—184no—
554C22×Q8—31no—
555C22×D4—91no—
556C22×D4—181no—
557C23×C4—91no—
558C23×C4—181no—
559#135—184no—
560#135—184no—
561C2×Q16—31no—
562C2×Q16D3211yescharacteristic, complemented
563C2×SD16—31no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×SD16—91no—
567C2×D8—91no—
568C2×D8—91no—
569C22×C8—91no—
570C22×C8—91no—
571#123—181no—
572C22⋊Q8—31no—
573C22⋊Q8—31no—
574#121—91no—
575#121—91no—
576#120—181no—
577C4×D4—181no—
578C4×D4—181no—
579#117—91no—
580#103—31no—
581#103—31no—
582#103—31no—
583#103—91no—
584#102—31no—
585#102—91no—
586#102—91no—
587#102—91no—
588C22⋊C8—31no—
589C22⋊C8—31no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—31no—
593C23×C3—31no—
594C23×C3—61no—
595C22×D3—21no—
596C22×D3—31no—
597C22×D3—31no—
598C22×D3—61no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—62no—
602C22×D3—64no—
603C22×D3—64no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—62no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—122no—
614C22×D3—122no—
615C22×D3—122no—
616C22×D3—122no—
617C22×D3D3×D411yescharacteristic
618C22×D3D3×D411yescharacteristic
619C3×Q8—21no—
620C3×Q8—21no—
621C3×Q8—22no—
622C3×Q8—21no—
623C3×Q8—21no—
624C3×Q8—21no—
625C3×Q8—21no—
626C3×Q8—22no—
627C3×Q8—32no—
628C3×Q8—41no—
629C3×Q8—41no—
630C3×Q8—64no—
631C3×Q8—61no—
632C3×Q8D3×D412yes—
633C3×Q8D3×D412yes—
634C3×D4—32no—
635C3×D4—64no—
636C3×D4—61no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—31no—
643C2×C3×C4—31no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—64no—
647C2×C3×C4—64no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657#67—64no—
658#67—64no—
659#67—64no—
660#67—122no—
661#67—122no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—31no—
666C2×Dic3—31no—
667C2×Dic3—61no—
668C2×Dic3—62no—
669C2×Dic3—64no—
670C2×Dic3—62no—
671C2×Dic3D3×D411yescharacteristic
672C2×Dic3D3×D411yescharacteristic
673D12—24no—
674D12—21no—
675D12—32no—
676D12—32no—
677D12—62no—
678D12—64no—
679D12—64no—
680D12—62no—
681D12—64no—
682D12—64no—
683D12—64no—
684D12—61no—
685D12—61no—
686D12—61no—
687D12—61no—
688D12—61no—
689D12—61no—
690D12—121no—
691D12—121no—
692D12—124no—
693D12—122no—
694D12—122no—
695D12—124no—
696D12—122no—
697D12—122no—
698D12D3×D412yes—
699C4×D3—24no—
700C4×D3—24no—
701C4×D3—21no—
702C4×D3—21no—
703C4×D3—21no—
704C4×D3—21no—
705C4×D3—32no—
706C4×D3—32no—
707C4×D3—32no—
708C4×D3—32no—
709C4×D3—62no—
710C4×D3—62no—
711C4×D3—62no—
712C4×D3—62no—
713C4×D3—64no—
714C4×D3—64no—
715C4×D3—64no—
716C4×D3—64no—
717C4×D3—62no—
718C4×D3—62no—
719C4×D3—64no—
720C4×D3—124no—
721C4×D3—122no—
722C4×D3—122no—
723C4×D3—124no—
724Dic6—24no—
725Dic6—21no—
726Dic6D3×D412yes—
727C3×C8—22no—
728C3×C8—21no—
729C3×C8—21no—
730C3×C8—61no—
731C3×C8—61no—
732C3⋊C8—21no—
733C3⋊C8—21no—
734C3⋊C8—62no—
735C3⋊C8—61no—
736C3⋊C8—61no—
737C2×C32C2×#12011yescharacteristic
738C2×C32C2×#13511yescharacteristic
739C2×C32#57511yescharacteristic
740C3⋊D3—22no—
741C3⋊D3—42no—
742C3⋊D3—81no—
743C3×D3—22no—
744C3×D3—41no—
745C3×D3—42no—
746C24—91no—
747C24—181no—
748#41—62no—
749#41—62no—
750#41—94no—
751#41—94no—
752#41—182no—
753#41—182no—
754#41—188no—
755#41—182no—
756#41—182no—
757#41—182no—
758#41—182no—
759#41—188no—
760C2×Q8—31no—
761C2×Q8—61no—
762C2×Q8—62no—
763C2×Q8—62no—
764C2×Q8C2×D3211yescharacteristic
765C2×Q8C2×D3211yescharacteristic
766C2×D4—31no—
767C2×D4—61no—
768C2×D4—91no—
769C2×D4—91no—
770C2×D4—181no—
771C2×D4—181no—
772C2×D4—181no—
773C2×D4—182no—
774C2×D4—182no—
775C2×D4—188no—
776C2×D4—181no—
777C2×D4—181no—
778C2×D4—181no—
779C2×D4—181no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—91no—
785C22×C4—91no—
786C22×C4—91no—
787C22×C4—91no—
788C22×C4—181no—
789C22×C4—181no—
790C22×C4—181no—
791C22×C4—182no—
792C22×C4—182no—
793C22×C4—188no—
794C22×C4—181no—
795Q16—22no—
796Q16—62no—
797SD16—62no—
798SD16—182no—
799SD16—182no—
800SD16—182no—
801D8—182no—
802D8—182no—
803C2×C8—31no—
804C2×C8—31no—
805C2×C8—91no—
806C2×C8—182no—
807C2×C8—182no—
808C2×C8C2×D3211yescharacteristic
809C4⋊C4—31no—
810C4⋊C4—31no—
811C4⋊C4—61no—
812C4⋊C4—61no—
813C22⋊C4—61no—
814C22⋊C4—61no—
815C22⋊C4—181no—
816C22⋊C4—181no—
817C22⋊C4—181no—
818C42—181no—
819C22×C3—21no—
820C22×C3—32no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—62no—
826C22×C3—61no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3C2×D3×D411yescharacteristic
830C22×C3C2×D3×D411yescharacteristic
831C2×D3—21no—
832C2×D3—21no—
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—22no—
837C2×D3—32no—
838C2×D3—32no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—62no—
842C2×D3—61no—
843C2×D3—61no—
844C2×D3—61no—
845C2×D3—61no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—122no—
851C2×D3—124no—
852C2×D3—128no—
853C2×D3—124no—
854C2×D3—128no—
855C2×D3—121no—
856C2×D3—121no—
857C2×D3—121no—
858C2×D3—121no—
859C2×D3—122no—
860C2×D3—121no—
861C2×D3—121no—
862C2×D3—121no—
863C2×D3—121no—
864C2×D3—121no—
865C2×D3—121no—
866C2×D3—241no—
867C2×D3—241no—
868C2×D3—241no—
869C2×D3—241no—
870C2×D3#91912yescomplemented
871C3×C4—22no—
872C3×C4—22no—
873C3×C4—21no—
874C3×C4—21no—
875C3×C4—42no—
876C3×C4—42no—
877C3×C4—41no—
878C3×C4—41no—
879C3×C4—61no—
880C3×C4—61no—
881C3×C4—62no—
882C3×C4—121no—
883C3×C4—121no—
884C3×C4C2×D3×D411yescharacteristic
885C3×C4C2×D3×D411yescharacteristic
886C3×C4C2×D3×D411yescharacteristic
887C3×C4C2×D3×D411yescharacteristic
888Dic3—21no—
889Dic3—22no—
890Dic3—21no—
891Dic3—32no—
892Dic3—32no—
893Dic3—41no—
894Dic3—41no—
895Dic3—62no—
896C32#300211yescharacteristic, complemented, Sylow
897C23—31no—
898C23—31no—
899C23—61no—
900C23—91no—
901C23—182no—
902C23—182no—
903C23—184no—
904C23—181no—
905C23—181no—
906C23—362no—
907C23—361no—
908C23—362no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—32no—
913Q8—64no—
914Q8—61no—
915Q8#381112yes—
916D4—32no—
917D4—64no—
918D4—61no—
919D4—92no—
920D4—184no—
921D4—184no—
922D4—184no—
923D4—184no—
924D4—181no—
925D4—181no—
926D4—181no—
927D4—362no—
928D4—362no—
929D4—362no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—31no—
933C2×C4—31no—
934C2×C4—64no—
935C2×C4—64no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—61no—
940C2×C4—61no—
941C2×C4—61no—
942C2×C4—61no—
943C2×C4—91no—
944C2×C4—92no—
945C2×C4—92no—
946C2×C4—184no—
947C2×C4—182no—
948C2×C4—184no—
949C2×C4—182no—
950C2×C4—182no—
951C2×C4—184no—
952C2×C4—362no—
953C2×C4C22×D3211yescharacteristic
954C8—21no—
955C8—61no—
956C8—61no—
957C8—181no—
958C2×C3—21no—
959C2×C3—21no—
960C2×C3—21no—
961C2×C3—62no—
962C2×C3—121no—
963C2×C3—122no—
964C2×C3D3×#12011yescharacteristic
965C2×C3D3×#12011yescharacteristic
966C2×C3C2×#91911yescharacteristic
967C2×C3D3×#13511yescharacteristic
968C2×C3#577711yescharacteristic
969C2×C3#577711yescharacteristic
970D3—22no—
971D3—41no—
972D3—42no—
973D3—62no—
974D3—62no—
975D3—122no—
976D3—122no—
977D3—122no—
978D3—242no—
979D3—242no—
980D3—241no—
981D3—241no—
982C22—32no—
983C22—61no—
984C22—61no—
985C22—61no—
986C22—61no—
987C22—62no—
988C22—61no—
989C22—92no—
990C22—121no—
991C22—121no—
992C22—181no—
993C22—181no—
994C22—182no—
995C22—364no—
996C22—368no—
997C22—361no—
998C22—361no—
999C22—361no—
1000C22—361no—
1001C22—361no—
1002C22D32×D411yescharacteristic
1003C4—22no—
1004C4—41no—
1005C4—61no—
1006C4—61no—
1007C4—62no—
1008C4—92no—
1009C4—121no—
1010C4—121no—
1011C4D32×D411yescharacteristic
1012C4C2×#381111yescharacteristic
1013C3—21no—
1014C3#8018211yescharacteristic, complemented
1015C3#8022611yescharacteristic, complemented
1016C2—62no—
1017C2—121no—
1018C2—122no—
1019C2—182no—
1020C2—362no—
1021C2—721no—
1022C2D3×#91911yescharacteristic
1023C2#1059476211yescharacteristic
1024C2#1059527811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
hypercenterC2×Q16D32
hypocenterC32#3002
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. C2×#64128C2semidirect
3. #10595430C2semidirect
4. C2×#63950C2semidirect
5. C3×#5187C2semidirect
6. C3×#5186C2semidirect
7. #10591657C2semidirect
8. #10591651C2semidirect
9. #10591588C2semidirect
10. #10591584C2semidirect
11. #10591560C2semidirect
12. #10590967C2semidirect
13. #10590956C2semidirect
14. #10590947C2semidirect
15. #10590935C2semidirect
19. C2×#3832C22semidirect
32. C2×C32×Q16C22semidirect
33. C2×#3755C22semidirect
34. C2×#3755C22semidirect
36. C2×#3745C22semidirect
37. C2×C8×C3⋊D3C22semidirect
39. C3×#946C22semidirect
40. C2×C3×#216C22semidirect
41. C2×C3×#215C22semidirect
45. #63909C22semidirect
49. #63849C22semidirect
50. C2×#3717C22semidirect
51. C2×#3714C22semidirect
52. C2×#3710C22semidirect
53. C3×#835C22semidirect
54. C3×#835C22semidirect
55. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
79. #5187D3semidirect
80. #5186D3semidirect
103. #3832D4semidirect
144. #3796D4semidirect
202. C2×C3×Q16C2×D3semidirect
203. C2×C3×Q16C2×D3semidirect
208. #946C2×D3semidirect
209. C2×#216C2×D3semidirect
217. C2×#215C2×D3semidirect
255. #835C2×D3semidirect
256. #835C2×D3semidirect
262. #821C2×D3semidirect
266. (C2×D3)⋊C8C2×D3semidirect
267. #816C2×D3semidirect
532. C2×C3×D3#135semidirect
562. C2×Q16D32semidirect
870. C2×D3#919semidirect
896. C32#3002semidirect
1014. C3#80182semidirect
1015. 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×#641282
#105954302
C2×#639502
C3×#51872
C3×#51862
#105916572
#105916512
#105915882
#105915842
#105915602
#105909672
#105909562
#105909472
#105909352
#802263
#801823