Finite Group Databasebeta

← #11863906

Subgroups — #11863906

Order 1152.

1604 conjugacy classes of subgroups.

The subgroup lattice has 1013 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2C3×#5627C211yesmaximal, characteristic, complemented
3C2×#63949C211yesmaximal, characteristic, complemented
4C2×#63947C211yesmaximal, characteristic, complemented
5#10592746C211yesmaximal, characteristic, complemented
6C3×#5047C211yesmaximal, characteristic, complemented
7#10591653C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591182C211yesmaximal, characteristic, complemented
10#10591161C211yesmaximal, characteristic, complemented
11D3×#830C211yesmaximal, characteristic, complemented
12#10590610C211yesmaximal, characteristic, complemented
13#10590608C211yesmaximal, characteristic, complemented
14#10590603C211yesmaximal, characteristic, complemented
15#10590595C211yesmaximal, characteristic, complemented
16#82926—31nomaximal
17#80226—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C2×D3×#67—21no—
23C2×#3804—21no—
24D3×#235—24no—
25D3×#235—24no—
26C2×D3×D12C2211yescharacteristic
27C2×C4×D32—21no—
28C2×#3799C2211yescharacteristic
29C2×#3798—21no—
30C2×#3795C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C32×C22⋊Q8C2211yescharacteristic, complemented
33C2×#3756C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C3×#930C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic
40C3×#894—21no—
41C3×#893—21no—
42C3×#892C2211yescharacteristic, complemented
43C3×#882—21no—
44C3×#67⋊C4—21no—
45#63949—24no—
46#63947—24no—
47C2×#3716C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63657C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
65C2×D3×#41—31no—
66C22×#235—31no—
67C3×#525—31no—
68C2×#950—31no—
69C2×#950—31no—
70C2×#919—31no—
71C2×#916—31no—
72#5627D311yescharacteristic, complemented
73C3×#452—31no—
74#5238—31no—
75C2×#830—31no—
76#5186—31no—
77#5169—31no—
78#5050—31no—
79#5047—31no—
80#5047—31no—
81#5047—61no—
82#5047D311yescharacteristic, complemented
83#5046—31no—
84#5040—31no—
85#5037—31no—
86#5037—31no—
87#5036—31no—
88#5002—31no—
89#5002—31no—
90#4806—31no—
91#4804—31no—
92#4773—31no—
93#4772—31no—
94#4734—31no—
95D3×C22⋊C8—31no—
96C23×C3×D3D411yescharacteristic
97C22×D32—21no—
98C2×C32×Q8C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×#638—21no—
101#3828—22no—
102#3828—22no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C22×C3×Dic3D411yescharacteristic
109C3×#239—22no—
110C3×#239—22no—
111C3×#235—22no—
112C3×#235—22no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3D411yescharacteristic
122C2×C3×C4×D3D411yescharacteristic
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×Dic6C2311yescharacteristic
126D3×#67—28no—
127C2×#627—21no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#625—21no—
131C2×#624—21no—
132#3804—28no—
133C2×D3×Dic3—21no—
134C2×D3×Dic3—21no—
135D3×D12—22no—
136D3×D12—22no—
137C4×D32—28no—
138#3799—22no—
139#3799D414yescomplemented
140#3798—28no—
141#3795—22no—
142#3795D414yescomplemented
143D3×Dic6—22no—
144D3×Dic6—22no—
145C32×C4⋊C4—21no—
146C32×C4⋊C4C2311yescharacteristic
147C32×C22⋊C4—21no—
148#3756—22no—
149#3755—22no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C3×#216—22no—
153C3×#215—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×(C2×D3)⋊C4—21no—
156C3×(C2×D3)⋊C4—21no—
157C3×(C2×D3)⋊C4—21no—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×Dic3⋊C4—21no—
160C3×C4×Dic3—21no—
161C2×C3×C3⋊C8C2311yescharacteristic
162C2×C3×C3⋊C8C2311yescharacteristic
163#3716—22no—
164#3715—22no—
165#3714—22no—
166#3713—22no—
167D3×C3⋊C8—22no—
168D3×C3⋊C8—22no—
169#3002—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C23×C3×C4—31no—
173C22×#67—61no—
174D3×#41—64no—
175D3×#41—64no—
176C2×#239—31no—
177C2×#239C2×D311yescharacteristic, complemented
178C2×D3×Q8—31no—
179C2×#237—31no—
180C2×#237—61no—
181C2×D3×D4—31no—
182C2×D3×D4—61no—
183C2×#235—31no—
184C2×#235—31no—
185C2×#235—31no—
186C2×#235—31no—
187C2×#235—61no—
188C2×#235—61no—
189C2×#235—64no—
190C2×#235—64no—
191C2×#235—61no—
192C2×#235—61no—
193C2×#235C2×D311yescharacteristic
194C22×D12—31no—
195C22×C4×D3—61no—
196C22×C4×D3—61no—
197C22×C4×D3C2×D311yescharacteristic
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C3×#123—61no—
202C3×C22⋊Q8—21no—
203C3×C22⋊Q8—31no—
204C3×C22⋊Q8C2×D311yescharacteristic, complemented
205C3×C22⋊Q8C2×D311yescharacteristic, complemented
206C3×#121—31no—
207C3×#121—31no—
208C3×#120—61no—
209C3×C4×D4—61no—
210C3×C4×D4—61no—
211C3×#117—31no—
212#950—64no—
213#950—64no—
214#946C2×D311yescharacteristic
215C2×#216—31no—
216C2×#216—31no—
217C2×#216—61no—
218C2×#216C2×D311yescharacteristic, complemented
219C2×#215—31no—
220C2×#215—31no—
221C2×#215—31no—
222C2×#215—61no—
223C2×#215C2×D311yescharacteristic, complemented
224C2×#214—31no—
225C2×#214—31no—
226C2×#213—31no—
227C2×#213—31no—
228C2×#213—31no—
229#930C2×D311yescharacteristic, complemented
230C22×C3⋊C8—31no—
231C22×C3⋊C8—31no—
232#919—64no—
233#916—64no—
234C2×D24—31no—
235C2×#204—31no—
236C2×D3×C8—31no—
237C2×D3×C8—31no—
238#895C2×D311yescharacteristic
239#894—21no—
240#893—21no—
241#892C2×D311yescharacteristic, complemented
242#882—21no—
243#67⋊C4—21no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#832—31no—
249#830—31no—
250#830—31no—
251#830—31no—
252#830—31no—
253#830—61no—
254#830C2×D311yescharacteristic, complemented
255#821—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258#816—31no—
259#810—31no—
260#810—31no—
261#810—31no—
262#810—31no—
263#810—61no—
264#810C2×D311yescharacteristic, complemented
265#809—31no—
266#809—31no—
267#809—31no—
268#809—31no—
269#809—61no—
270#809C2×D311yescharacteristic, complemented
271C23×C32C2×D411yescharacteristic
272C22×C3⋊D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—22no—
275C22×C3×D3—22no—
276C22×C3×D3—21no—
277C22×C3×D3—41no—
278C22×C3×D3C2×D411yescharacteristic
279C22×C3×D3C2×D411yescharacteristic
280C2×D32—24no—
281C2×D32—42no—
282C2×D32—42no—
283C32×Q8—21no—
284C32×Q8—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4C2×D411yescharacteristic
290C2×C32×C4C2411yescharacteristic
291#638—24no—
292C2×C3⋊Dic3—21no—
293C4⋊(C3⋊D3)—21no—
294C4⋊(C3⋊D3)C2×D412yes—
295C4×C3⋊D3—24no—
296#634—21no—
297#634C2×D412yes—
298C3×#67—24no—
299C3×#67—42no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C2×D411yescharacteristic
304C2×C3×Dic3C2×D411yescharacteristic
305C3×D12—21no—
306C3×D12—21no—
307C3×D12—21no—
308C3×D12—42no—
309C3×D12—42no—
310C3×D12C2×D412yes—
311C3×C4×D3—24no—
312C3×C4×D3—22no—
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×C4×D3—22no—
316C3×C4×D3—42no—
317C3×C4×D3C2×D412yes—
318C3×C4×D3C2×D412yes—
319C3×Dic6—21no—
320C3×Dic6C2×D412yes—
321#627—24no—
322#626—24no—
323#626—24no—
324#625—24no—
325#624—24no—
326D3×Dic3—24no—
327D3×Dic3—24no—
328C3⋊(C3⋊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—31no—
336#452—31no—
337#452—91no—
338#451—91no—
339#450—91no—
340#449—91no—
341#449—91no—
342#448—91no—
343#447—91no—
344#416—91no—
345#416—91no—
346C2×C22⋊C8—91no—
347C24×C3—31no—
348C23×D3—61no—
349C23×D3—61no—
350C23×D3#6711yescharacteristic
351C3×#41—62no—
352C3×#41—62no—
353C3×#41—62no—
354C3×#41—62no—
355C2×C3×Q8—21no—
356C2×C3×Q8—31no—
357C2×C3×Q8C22×D311yescharacteristic
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×D4—31no—
360C2×C3×D4—31no—
361C2×C3×D4—61no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C2×C3×D4—61no—
365C22×C3×C4—21no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—62no—
372C22×C3×C4—62no—
373C22×C3×C4—61no—
374C22×C3×C4—61no—
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C2×#67—21no—
378C2×#67—21no—
379C2×#67—61no—
380C2×#67—68no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—121no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3#6711yescharacteristic
390#239—22no—
391#239—22no—
392#239—34no—
393#239—62no—
394D3×Q8—62no—
395D3×Q8—62no—
396#237—34no—
397#237—68no—
398#237—62no—
399D3×D4—62no—
400D3×D4—62no—
401D3×D4—68no—
402#235—22no—
403#235—22no—
404#235—34no—
405#235—34no—
406#235—62no—
407#235—62no—
408#235—62no—
409#235—68no—
410#235—68no—
411#235—62no—
412#235—62no—
413#235—62no—
414#235—68no—
415#235—122no—
416#235—122no—
417C2×D12—21no—
418C2×D12—21no—
419C2×D12—31no—
420C2×D12—31no—
421C2×D12—61no—
422C2×D12—62no—
423C2×D12—61no—
424C2×D12—61no—
425C2×D12—62no—
426C2×D12C22×D311yescharacteristic
427C2×D12C22×D311yescharacteristic
428C2×C4×D3—21no—
429C2×C4×D3—22no—
430C2×C4×D3—22no—
431C2×C4×D3—21no—
432C2×C4×D3—68no—
433C2×C4×D3—68no—
434C2×C4×D3—61no—
435C2×C4×D3—61no—
436C2×C4×D3—61no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—121no—
441C2×C4×D3#6711yescharacteristic
442C2×C4×D3#6711yescharacteristic
443C2×C4×D3C22×D311yescharacteristic
444C2×C4×D3C22×D311yescharacteristic
445C2×Dic6—31no—
446C2×Dic6—31no—
447C2×Dic6—61no—
448C2×Dic6—62no—
449C2×Dic6—61no—
450C2×Dic6—61no—
451C2×Dic6—62no—
452C2×Dic6C22×D311yescharacteristic
453C3×Q16—62no—
454C3×SD16—62no—
455C2×C3×C8—31no—
456C2×C3×C8—31no—
457C3×C4⋊C4—21no—
458C3×C4⋊C4—21no—
459C3×C4⋊C4—21no—
460C3×C4⋊C4—31no—
461C3×C4⋊C4—41no—
462C3×C4⋊C4—61no—
463C3×C4⋊C4C22×D311yescharacteristic
464C3×C4⋊C4C22×D311yescharacteristic
465C3×C22⋊C4—21no—
466C3×C22⋊C4—21no—
467C3×C22⋊C4—41no—
468C3×C22⋊C4—61no—
469C3×C22⋊C4—61no—
470C3×C22⋊C4—61no—
471C3×C22⋊C4—61no—
472C3×C42—61no—
473#216—22no—
474#216—62no—
475#216—62no—
476#216—122no—
477#215—22no—
478#215—62no—
479#215—62no—
480#215—62no—
481#215—122no—
482#214—62no—
483#214—62no—
484#213—62no—
485#213—62no—
486#213—62no—
487(C2×D3)⋊C4—21no—
488(C2×D3)⋊C4—21no—
489(C2×D3)⋊C4—21no—
490(C2×D3)⋊C4—21no—
491C4⋊Dic3C22×D311yescharacteristic
492Dic3⋊C4—21no—
493C4×Dic3—21no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—31no—
497C2×C3⋊C8—31no—
498C2×C3⋊C8—61no—
499C2×C3⋊C8—61no—
500C2×C3⋊C8—62no—
501C2×C3⋊C8—62no—
502C2×C3⋊C8C22×D311yescharacteristic
503C2×C3⋊C8C22×D311yescharacteristic
504D24—62no—
505#204—62no—
506D3×C8—62no—
507D3×C8—62no—
508C22×C32—21no—
509C22×C32—21no—
510C22×C32—21no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—22no—
513C2×C3⋊D3—41no—
514C2×C3⋊D3—41no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—21no—
519C2×C3×D3—22no—
520C2×C3×D3—44no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3#12012yes—
527C2×C3×D3#13512yescomplemented
528D32—48no—
529C32×C4—21no—
530C32×C4—41no—
531C32×C4—41no—
532C32×C4C22×D411yescharacteristic
533C32×C4C22×D411yescharacteristic
534C3⋊Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—21no—
537C3×Dic3—41no—
538C3×Dic3#12012yes—
539C2×#41—31no—
540C2×#41—31no—
541C2×#41—91no—
542C2×#41—91no—
543C2×#41—91no—
544C2×#41—181no—
545C2×#41—181no—
546C2×#41—184no—
547C2×#41—184no—
548C22×Q8—91no—
549C22×D4—91no—
550C22×D4—181no—
551C23×C4—31no—
552C23×C4—181no—
553#135—184no—
554#135—184no—
555C2×Q16—31no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×D8—91no—
562C2×D8—91no—
563C22×C8—91no—
564C22×C8—91no—
565#123—61no—
566C22⋊Q8—31no—
567C22⋊Q8D3211yescharacteristic, complemented
568#121—31no—
569#121—31no—
570#120—61no—
571C4×D4—61no—
572C4×D4—61no—
573#117—31no—
574#103—31no—
575#103—91no—
576#103—91no—
577#103—91no—
578#102—31no—
579#102—91no—
580#102—91no—
581#102—91no—
582C22⋊C8—31no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C23×C3—21no—
587C23×C3—31no—
588C23×C3—31no—
589C23×C3—62no—
590C23×C3—62no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—121no—
594C23×C3D3×D411yescharacteristic
595C23×C3C2×#6711yescharacteristic
596C22×D3—21no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—21no—
600C22×D3—41no—
601C22×D3—64no—
602C22×D3—64no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—121no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3C2×#6711yescharacteristic
611C22×D3C2×#6711yescharacteristic
612C3×Q8—21no—
613C3×Q8—21no—
614C3×Q8—21no—
615C3×Q8—21no—
616C3×Q8—32no—
617C3×Q8—41no—
618C3×Q8—41no—
619C3×Q8—61no—
620C3×D4—32no—
621C3×D4—64no—
622C3×D4—61no—
623C3×D4—61no—
624C3×D4—61no—
625C3×D4—122no—
626C3×D4—122no—
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—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—31no—
639C2×C3×C4—32no—
640C2×C3×C4—32no—
641C2×C3×C4—31no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—62no—
647C2×C3×C4—62no—
648C2×C3×C4—64no—
649C2×C3×C4—62no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—122no—
655C2×C3×C4D3×D411yescharacteristic
656C2×C3×C4C2×#6711yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659#67—24no—
660#67—42no—
661#67—64no—
662#67—64no—
663#67—64no—
664#67—64no—
665#67—64no—
666#67—64no—
667#67—124no—
668C2×Dic3—21no—
669C2×Dic3—22no—
670C2×Dic3—21no—
671C2×Dic3—64no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—64no—
675C2×Dic3—121no—
676C2×Dic3C2×#6711yescharacteristic
677C2×Dic3C2×#6711yescharacteristic
678D12—21no—
679D12—21no—
680D12—21no—
681D12—32no—
682D12—32no—
683D12—42no—
684D12—42no—
685D12—62no—
686D12—64no—
687D12—64no—
688D12—61no—
689D12—61no—
690D12—121no—
691D12D3×D412yes—
692C4×D3—24no—
693C4×D3—22no—
694C4×D3—21no—
695C4×D3—21no—
696C4×D3—22no—
697C4×D3—42no—
698C4×D3—64no—
699C4×D3—64no—
700C4×D3—64no—
701C4×D3—64no—
702C4×D3—64no—
703C4×D3—64no—
704C4×D3—124no—
705C4×D3D3×D412yes—
706C4×D3D3×D412yes—
707Dic6—21no—
708Dic6—32no—
709Dic6—32no—
710Dic6—62no—
711Dic6—64no—
712Dic6—64no—
713Dic6—61no—
714Dic6—61no—
715Dic6—121no—
716Dic6D3×D412yes—
717C3×C8—61no—
718C3×C8—61no—
719C3⋊C8—21no—
720C3⋊C8—21no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—61no—
724C3⋊C8—61no—
725C3⋊C8—121no—
726C3⋊C8—121no—
727C2×C32—41no—
728C2×C32C2×#12011yescharacteristic
729C2×C32C2×#13511yescharacteristic
730C2×C32#57511yescharacteristic
731C3⋊D3—42no—
732C3×D3—22no—
733C3×D3—22no—
734C3×D3—42no—
735C3×D3—81no—
736C24—31no—
737C24—181no—
738#41—62no—
739#41—62no—
740#41—62no—
741#41—62no—
742#41—94no—
743#41—94no—
744#41—182no—
745#41—182no—
746#41—182no—
747#41—182no—
748#41—188no—
749#41—188no—
750C2×Q8—31no—
751C2×Q8—91no—
752C2×Q8—181no—
753C2×Q8—182no—
754C2×Q8—182no—
755C2×Q8C2×D3211yescharacteristic
756C2×D4—31no—
757C2×D4—31no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—61no—
761C2×D4—61no—
762C2×D4—91no—
763C2×D4—181no—
764C2×D4—182no—
765C2×D4—182no—
766C2×D4—181no—
767C2×D4—188no—
768C2×D4—181no—
769C2×D4—181no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—31no—
775C22×C4—62no—
776C22×C4—62no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—181no—
780C22×C4—181no—
781C22×C4—188no—
782C22×C4—181no—
783C22×C4—181no—
784C22×C4C2×D3211yescharacteristic
785Q16—62no—
786Q16—182no—
787SD16—62no—
788SD16—182no—
789SD16—182no—
790SD16—182no—
791D8—182no—
792D8—182no—
793C2×C8—31no—
794C2×C8—31no—
795C2×C8—91no—
796C2×C8—91no—
797C2×C8—182no—
798C2×C8—182no—
799C4⋊C4—21no—
800C4⋊C4—31no—
801C4⋊C4—61no—
802C4⋊C4C2×D3211yescharacteristic
803C22⋊C4—21no—
804C22⋊C4—61no—
805C22⋊C4—61no—
806C22⋊C4—61no—
807C22⋊C4—61no—
808C42—61no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—32no—
817C22×C3—32no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—62no—
826C22×C3—124no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3C2×D3×D411yescharacteristic
833C22×C3C22×#6711yescharacteristic
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—22no—
839C2×D3—44no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—122no—
848C2×D3—128no—
849C2×D3—128no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—241no—
855C2×D3—241no—
856C2×D3#93712yes—
857C2×D3#95012yescomplemented
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—21no—
862C3×C4—32no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—41no—
866C3×C4—41no—
867C3×C4—41no—
868C3×C4—62no—
869C3×C4—61no—
870C3×C4—81no—
871C3×C4—81no—
872C3×C4—121no—
873C3×C4C2×D3×D411yescharacteristic
874C3×C4C2×D3×D411yescharacteristic
875C3×C4C2×D3×D411yescharacteristic
876C3×C4C2×D3×D411yescharacteristic
877Dic3—21no—
878Dic3—22no—
879Dic3—41no—
880Dic3—62no—
881Dic3—62no—
882Dic3—122no—
883Dic3#93712yes—
884C32#300211yescharacteristic, complemented, Sylow
885C23—31no—
886C23—31no—
887C23—62no—
888C23—62no—
889C23—61no—
890C23—61no—
891C23—121no—
892C23—184no—
893C23—181no—
894C23—362no—
895C23—362no—
896C23D3×#6711yescharacteristic
897Q8—21no—
898Q8—21no—
899Q8—32no—
900Q8—61no—
901Q8—92no—
902Q8—184no—
903Q8—181no—
904D4—32no—
905D4—64no—
906D4—61no—
907D4—61no—
908D4—61no—
909D4—92no—
910D4—122no—
911D4—122no—
912D4—122no—
913D4—184no—
914D4—184no—
915D4—184no—
916D4—184no—
917D4—181no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—31no—
923C2×C4—32no—
924C2×C4—32no—
925C2×C4—31no—
926C2×C4—62no—
927C2×C4—62no—
928C2×C4—64no—
929C2×C4—62no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—122no—
935C2×C4—184no—
936C2×C4—184no—
937C2×C4—184no—
938C2×C4—184no—
939C2×C4—181no—
940C2×C4D3×#6711yescharacteristic
941C2×C4C22×D3211yescharacteristic
942C8—61no—
943C8—61no—
944C8—181no—
945C8—181no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—41no—
950C2×C3—41no—
951C2×C3—62no—
952C2×C3—62no—
953C2×C3—81no—
954C2×C3—122no—
955C2×C3—241no—
956C2×C3D3×#12011yescharacteristic
957C2×C3D3×#13511yescharacteristic
958C2×C3#577711yescharacteristic
959C2×C3C2×#93711yescharacteristic
960C2×C3C2×#95011yescharacteristic
961C2×C3#582211yescharacteristic
962D3—22no—
963D3—22no—
964D3—42no—
965D3—81no—
966D3—122no—
967D3—122no—
968D3—242no—
969C22—21no—
970C22—21no—
971C22—21no—
972C22—32no—
973C22—32no—
974C22—61no—
975C22—61no—
976C22—61no—
977C22—61no—
978C22—62no—
979C22—124no—
980C22—121no—
981C22—121no—
982C22—121no—
983C22—121no—
984C22—121no—
985C22—182no—
986C22—368no—
987C22—361no—
988C22—361no—
989C22C2×D3×#6711yescharacteristic
990C4—21no—
991C4—32no—
992C4—41no—
993C4—41no—
994C4—61no—
995C4—62no—
996C4—121no—
997C4—182no—
998C4D32×D411yescharacteristic
999C4D32×D411yescharacteristic
1000C3—21no—
1001C3#8022611yescharacteristic, complemented
1002C3#8292611yescharacteristic, complemented
1003C2—41no—
1004C2—62no—
1005C2—62no—
1006C2—122no—
1007C2—241no—
1008C2—362no—
1009C2D3×#93711yescharacteristic
1010C2#1059531711yescharacteristic
1011C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3002
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×D3×#235C2semidirect
2. C3×#5627C2semidirect
3. C2×#63949C2semidirect
4. C2×#63947C2semidirect
5. #10592746C2semidirect
6. C3×#5047C2semidirect
7. #10591653C2semidirect
8. #10591651C2semidirect
9. #10591182C2semidirect
10. #10591161C2semidirect
11. D3×#830C2semidirect
12. #10590610C2semidirect
13. #10590608C2semidirect
14. #10590603C2semidirect
15. #10590595C2semidirect
19. C2×C3×#239C22semidirect
32. C32×C22⋊Q8C22semidirect
33. C2×#3756C22semidirect
34. C2×#3755C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#215C22semidirect
38. C3×#930C22semidirect
42. C3×#892C22semidirect
47. C2×#3716C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63657C22semidirect
54. #63637C22semidirect
55. #63636C22semidirect
56. C3×#830C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. #63567C22semidirect
60. #63565C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
72. #5627D3semidirect
82. #5047D3semidirect
139. #3799D4semidirect
142. #3795D4semidirect
177. C2×#239C2×D3semidirect
204. C3×C22⋊Q8C2×D3semidirect
205. C3×C22⋊Q8C2×D3semidirect
218. C2×#216C2×D3semidirect
223. C2×#215C2×D3semidirect
229. #930C2×D3semidirect
241. #892C2×D3semidirect
254. #830C2×D3semidirect
264. #810C2×D3semidirect
270. #809C2×D3semidirect
527. C2×C3×D3#135semidirect
567. C22⋊Q8D32semidirect
857. C2×D3#950semidirect
884. C32#3002semidirect
1001. C3#80226semidirect
1002. C3#82926semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C3×#56272
C2×#639492
C2×#639472
#105927462
C3×#50472
#105916532
#105916512
#105911822
#105911612
D3×#8302
#105906102
#105906082
#105906032
#105905952
#829263
#802263