Finite Group Databasebeta

← #11860625

Subgroups — #11860625

Order 1152.

1069 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64151C211yesmaximal, characteristic
2C3×#5812C211yesmaximal, characteristic, complemented
3#10594990C211yesmaximal, characteristic
4C2×C3×#835C211yesmaximal, characteristic, complemented
5#10591541C212yesmaximal, complemented
6#10591540C212yesmaximal, complemented
7#10591537C212yesmaximal, complemented
8#10591536C212yesmaximal, complemented
9#10591139C211yesmaximal, characteristic, complemented
10#10591105C211yesmaximal, characteristic
11#10591055C211yesmaximal, characteristic, complemented
12#82547—31nomaximal
13#78774—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16C2×#3756C2212yes—
17#64151C418yescomplemented
18C2×#3755C2212yes—
19C2×#3748C2211yescharacteristic
20C3×Q8×Dic3—21no—
21C3×Q8×Dic3—21no—
22C3×Q8×Dic3C2212yes—
23C3×Q8×Dic3C2212yes—
24C3×#926—22no—
25C3×#926C2211yescharacteristic
26C3×#926C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29#63952—22no—
30#63900—21no—
31#63894C2212yes—
32#63849—21no—
33#63844C2212yes—
34C3×#835C2212yes—
35C3×#835C2212yes—
36#63576C2212yes—
37#63574C2212yes—
38#63567C2211yescharacteristic
39#63567C2211yescharacteristic
40#63564C2211yescharacteristic
41#63564C2211yescharacteristic
42#63554C2212yes—
43Dic3×C3⋊C8C2212yes—
44C3×#519—31no—
45#5812D311yescharacteristic, complemented
46C2×#942—31no—
47C2×#942—31no—
48C2×#942—61no—
49#5523—31no—
50#5504—31no—
51C2×C3×#103—31no—
52C2×#835D311yescharacteristic, complemented
53#5113—31no—
54#5101—31no—
55#5030—32no—
56C4×#216—32no—
57#5026—32no—
58C4×#215—32no—
59#5002—31no—
60#4997—31no—
61#4995—31no—
62#4964—31no—
63#4817—32no—
64#4790—32no—
65#4789—32no—
66#4788—32no—
67C2×C32×Q8—21no—
68C2×C32×Q8—22no—
69C2×C32×Q8C2×C414yescomplemented
70C2×C32×Q8C2312yes—
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C2×#638—21no—
74#3828—22no—
75#3828C2×C414yes—
76C2×C4⋊(C3⋊D3)C2311yescharacteristic
77C2×C4×C3⋊D3—21no—
78C2×#634C2311yescharacteristic
79C22×C3×Dic3—21no—
80C2×#624—22no—
81#3756C2×C418yescomplemented
82#3755C2×C418yescomplemented
83#3748C2×C414yescomplemented
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#217—21no—
86C3×#217D412yes—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3—21no—
96C3×C4×Dic3—22no—
97C3×C4×Dic3—22no—
98C3×C4×Dic3C2312yes—
99C2×C3×C3⋊C8—22no—
100C2×C3×C3⋊C8C2311yescharacteristic
101C2×C3×C3⋊C8C2311yescharacteristic
102#3724—22no—
103#3722—22no—
104Dic32—22no—
105#2947—91noSylow
106C22×C3×Q8—21no—
107C22×C3×Q8C2×D311yescharacteristic
108C22×C3×Q8C2×D311yescharacteristic
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C22×C3×C8—31no—
113C3×C4×Q8—32no—
114C3×C4×Q8—32no—
115C3×C4×Q8—61no—
116C3×C4×Q8—61no—
117C3×#117—31no—
118C3×#117—31no—
119C3×#117—62no—
120C2×C3×C4⋊C4—31no—
121Q8×Dic3—21no—
122Q8×Dic3—21no—
123Q8×Dic3C2×D312yes—
124Q8×Dic3C2×D312yes—
125C2×#216—32no—
126C2×#216—32no—
127C2×#216—62no—
128#942—38no—
129#942—38no—
130#942—68no—
131C2×#215—32no—
132C2×#215—32no—
133C2×#215—62no—
134C4×#67—62no—
135#926—22no—
136#926C2×D311yescharacteristic
137#926C2×D311yescharacteristic
138C2×C4⋊Dic3C2×D311yescharacteristic
139C2×#208—31no—
140C2×#208—31no—
141C2×#208—61no—
142C22×C3⋊C8C2×D311yescharacteristic
143#893—32no—
144#892—61no—
145#892—61no—
146D3×C4⋊C4—61no—
147D3×C4⋊C4—61no—
148#887—32no—
149#67⋊C4—62no—
150C4×D12—32no—
151C4×Dic6—32no—
152C3×#103—32no—
153C3×#103—32no—
154#835C2×D312yes—
155#835C2×D312yes—
156#821—31no—
157#821—31no—
158#816—31no—
159#816—31no—
160#815—32no—
161C8×Dic3—32no—
162#810—31no—
163#810—31no—
164#809—31no—
165#809—31no—
166#808—32no—
167#808—32no—
168#807—32no—
169#807—32no—
170#803—32no—
171C4×C3⋊C8—32no—
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3—21no—
174C32×Q8—24no—
175C32×Q8—22no—
176C32×Q8C22×C414yes—
177C2×C32×C4—24no—
178C2×C32×C4—22no—
179C2×C32×C4C22×C412yes—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4#4112yes—
182C2×C32×C4C2411yescharacteristic
183#638—24no—
184C2×C3⋊Dic3—21no—
185C4⋊(C3⋊D3)—21no—
186C4⋊(C3⋊D3)C22×C412yes—
187C4×C3⋊D3—24no—
188#634—21no—
189#634C22×C412yes—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—81no—
194C2×C3×Dic3C2×D412yes—
195C2×C3×Dic3C2×D412yes—
196#624—82no—
197C3⋊(C3⋊C8)C22×C414yes—
198C3×C3⋊C8—21no—
199C3×C3⋊C8—21no—
200C2×#137—91no—
201#520—91no—
202#519—31no—
203#441—92no—
204#440—92no—
205C4×Q16—92no—
206C4×SD16—92no—
207#428—91no—
208#416—91no—
209C2×#103—31no—
210#405—91no—
211C2×C3×Q8—22no—
212C2×C3×Q8—21no—
213C2×C3×Q8—22no—
214C2×C3×Q8—21no—
215C2×C3×Q8—24no—
216C2×C3×Q8—22no—
217C2×C3×Q8—42no—
218C2×C3×Q8—41no—
219C2×C3×Q8C4×D314yescomplemented
220C2×C3×Q8C4×D314yescomplemented
221C2×C3×Q8C22×D312yes—
222C2×C3×Q8C22×D312yes—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—41no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—61no—
231C2×#67—61no—
232C2×#67—121no—
233C22×Dic3—21no—
234#235—34no—
235#235—34no—
236#235—64no—
237#235—62no—
238#235—62no—
239#235—122no—
240C2×D12—31no—
241C2×D12—31no—
242C2×D12—61no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×C4×D3—121no—
248C2×Dic6—31no—
249C2×Dic6—31no—
250C2×Dic6—61no—
251C2×C3×C8—31no—
252C2×C3×C8—31no—
253C2×C3×C8—62no—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—32no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—62no—
260C3×C4⋊C4—62no—
261C3×C4⋊C4—61no—
262C3×C22⋊C4—32no—
263C3×C22⋊C4—61no—
264C3×C42—32no—
265C3×C42—62no—
266C3×C42—62no—
267C3×C42—61no—
268#217—21no—
269#217#6712yes—
270#216—38no—
271#216—38no—
272#216—68no—
273#215—38no—
274#215—38no—
275#215—68no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—62no—
278C4⋊Dic3—21no—
279C4⋊Dic3—22no—
280C4⋊Dic3—22no—
281C4⋊Dic3#6711yescharacteristic
282C4⋊Dic3#6711yescharacteristic
283C4⋊Dic3C22×D311yescharacteristic
284C4⋊Dic3C22×D312yes—
285C4⋊Dic3C22×D311yescharacteristic
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288C4×Dic3—21no—
289C4×Dic3—22no—
290C4×Dic3—22no—
291C4×Dic3—62no—
292C4×Dic3—62no—
293C4×Dic3C22×D312yes—
294#208—34no—
295#208—34no—
296#208—64no—
297C2×C3⋊C8—22no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—62no—
301C2×C3⋊C8C22×D311yescharacteristic
302C2×C3⋊C8C22×D311yescharacteristic
303C22×C32—21no—
304C22×C32—21no—
305C22×C32C4×D412yes—
306C22×C32C22×D411yescharacteristic
307C2×C3⋊D3—22no—
308C2×C3⋊D3—41no—
309C2×C3⋊D3—41no—
310C32×C4—24no—
311C32×C4C4×D412yes—
312C32×C4C23×C411yescharacteristic
313C32×C4C2×#4111yescharacteristic
314C3⋊Dic3—22no—
315C3×Dic3—22no—
316C3×Dic3—22no—
317C3×Dic3—42no—
318C3×Dic3—41no—
319C3×Dic3—41no—
320C2×#41—91no—
321C22×Q8D3211yescharacteristic
322#137—98no—
323C2×Q16—92no—
324C2×SD16—92no—
325C2×M16—91no—
326C22×C8—31no—
327C4×Q8—32no—
328C4×Q8—32no—
329C4×Q8—61no—
330C4×Q8—61no—
331C4×Q8—92no—
332C4×D4—92no—
333C4×D4—182no—
334#117—31no—
335#117—31no—
336#117—62no—
337#117—181no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—181no—
340#107—92no—
341#106—92no—
342#103—32no—
343#103—32no—
344#103—91no—
345#103—91no—
346#102—91no—
347#102—91no—
348#97—92no—
349C4×C8—92no—
350C23×C3—21no—
351C23×C3D3×D411yescharacteristic
352C23×C3C2×#6711yescharacteristic
353C22×D3—61no—
354C22×D3—61no—
355C22×D3—121no—
356C3×Q8—24no—
357C3×Q8—24no—
358C3×Q8—22no—
359C3×Q8—22no—
360C3×Q8—24no—
361C3×Q8—42no—
362C3×Q8—44no—
363C3×Q8C2×C4×D314yes—
364C3×Q8C2×C4×D314yes—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—21no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—21no—
373C2×C3×C4—32no—
374C2×C3×C4—32no—
375C2×C3×C4—42no—
376C2×C3×C4—44no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—241no—
381C2×C3×C4C2×C4×D312yes—
382C2×C3×C4C2×C4×D312yes—
383C2×C3×C4#23512yes—
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4#23712yes—
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389#67—64no—
390#67—64no—
391#67—124no—
392C2×Dic3—22no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—81no—
398C2×Dic3—121no—
399C2×Dic3C2×#6712yes—
400C2×Dic3C2×#6712yes—
401D12—32no—
402D12—32no—
403D12—62no—
404D12—61no—
405D12—61no—
406D12—121no—
407C4×D3—64no—
408C4×D3—64no—
409C4×D3—124no—
410C4×D3—242no—
411C4×D3—242no—
412Dic6—32no—
413Dic6—32no—
414Dic6—62no—
415Dic6—61no—
416Dic6—61no—
417Dic6—121no—
418C3×C8—61no—
419C3×C8—61no—
420C3⋊C8—21no—
421C3⋊C8—21no—
422C3⋊C8—34no—
423C3⋊C8—34no—
424C3⋊C8—64no—
425C2×C32—22no—
426C2×C32C2×C4×D411yescharacteristic
427C2×C32#57711yescharacteristic
428C2×C32#57811yescharacteristic
429C3⋊D3—42no—
430#41—94no—
431#41—182no—
432C2×Q8—22no—
433C2×Q8—21no—
434C2×Q8—91no—
435C2×Q8#62414yescomplemented
436C2×Q8C2×D3212yes—
437C2×D4—91no—
438C2×D4—181no—
439C22×C4—21no—
440C22×C4—61no—
441C22×C4—182no—
442C22×C4—181no—
443C22×C4C2×D3211yescharacteristic
444Q16—98no—
445SD16—98no—
446M16—94no—
447C2×C8—31no—
448C2×C8—31no—
449C2×C8—62no—
450C2×C8—92no—
451C4⋊C4—31no—
452C4⋊C4—31no—
453C4⋊C4—31no—
454C4⋊C4—31no—
455C4⋊C4—32no—
456C4⋊C4—62no—
457C4⋊C4—62no—
458C4⋊C4—61no—
459C4⋊C4—182no—
460C22⋊C4—32no—
461C22⋊C4—61no—
462C22⋊C4—182no—
463C42—32no—
464C42—62no—
465C42—62no—
466C42—61no—
467C42—182no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—22no—
474C22×C3—41no—
475C22×C3—41no—
476C22×C3#67⋊C412yes—
477C22×C3C4×#6712yes—
478C22×C3C2×D3×D411yescharacteristic
479C22×C3C22×#6711yescharacteristic
480C2×D3—62no—
481C2×D3—62no—
482C2×D3—122no—
483C2×D3—121no—
484C2×D3—121no—
485C2×D3—121no—
486C2×D3—121no—
487C2×D3—241no—
488C2×D3—241no—
489C3×C4—24no—
490C3×C4—24no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—22no—
494C3×C4—44no—
495C3×C4—62no—
496C3×C4—62no—
497C3×C4—121no—
498C3×C4—121no—
499C3×C4—122no—
500C3×C4#67⋊C412yes—
501C3×C4C4×#6712yes—
502C3×C4C22×C4×D311yescharacteristic
503C3×C4C22×C4×D311yescharacteristic
504C3×C4C2×#23511yescharacteristic
505C3×C4C2×#23711yescharacteristic
506Dic3—22no—
507Dic3—22no—
508Dic3—42no—
509Dic3—41no—
510Dic3—41no—
511Dic3—62no—
512Dic3—62no—
513Dic3—122no—
514C32#294711yescharacteristic, complemented, Sylow
515C23—181no—
516C23D3×#6711yescharacteristic
517Q8—22no—
518Q8—24no—
519Q8—92no—
520Q8—181no—
521Q8C2×#62414yes—
522D4—92no—
523D4—184no—
524D4—181no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—32no—
528C2×C4—32no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—62no—
532C2×C4—181no—
533C2×C4—184no—
534C2×C4—241no—
535C2×C4—722no—
536C2×C4#380412yes—
537C2×C4C2×#62412yes—
538C2×C4D3×#6711yescharacteristic
539C2×C4C22×D3211yescharacteristic
540C8—61no—
541C8—61no—
542C8—94no—
543C2×C3—22no—
544C2×C3—22no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—42no—
549C2×C3C2×#67⋊C411yescharacteristic
550C2×C3#576211yescharacteristic
551C2×C3#576611yescharacteristic
552C2×C3C2×C4×#6711yescharacteristic
553C2×C3#583711yescharacteristic
554C2×C3#583811yescharacteristic
555D3—122no—
556D3—122no—
557D3—242no—
558C22—21no—
559C22—21no—
560C22—182no—
561C22—361no—
562C22—361no—
563C22#6395212yes—
564C22C2×D3×#6711yescharacteristic
565C4—24no—
566C4—62no—
567C4—62no—
568C4—122no—
569C4—121no—
570C4—121no—
571C4—182no—
572C4#6395212yes—
573C4C2×#380411yescharacteristic
574C4C22×#62411yescharacteristic
575C3—21no—
576C3#7877411yescharacteristic, complemented
577C3#8254711yescharacteristic, complemented
578C2—22no—
579C2—362no—
580C2#1059531811yescharacteristic
581C2#1059532711yescharacteristic
582C2C2×#6395211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32#2947
LCSG ▷ 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
2. C3×#5812C2semidirect
4. C2×C3×#835C2semidirect
5. #10591541C2semidirect
6. #10591540C2semidirect
7. #10591537C2semidirect
8. #10591536C2semidirect
9. #10591139C2semidirect
11. #10591055C2semidirect
17. #64151C4semidirect
45. #5812D3semidirect
52. C2×#835D3semidirect
69. C2×C32×Q8C2×C4semidirect
81. #3756C2×C4semidirect
82. #3755C2×C4semidirect
83. #3748C2×C4semidirect
219. C2×C3×Q8C4×D3semidirect
220. C2×C3×Q8C4×D3semidirect
435. C2×Q8#624semidirect
514. C32#2947semidirect
576. C3#78774semidirect
577. C3#82547semidirect

Maximal subgroups

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

subgroupindex
C2×#641512
C3×#58122
#105949902
C2×C3×#8352
#105915412
#105915402
#105915372
#105915362
#105911392
#105911052
#105910552
#825473
#787743