Finite Group Databasebeta

← #11860630

Subgroups — #11860630

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594986C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic
4#10592800C211yesmaximal, characteristic, complemented
5C3×#5113C211yesmaximal, characteristic
6C2×C3×#816C211yesmaximal, characteristic, complemented
7#10591139C211yesmaximal, characteristic, complemented
8#10590791C212yesmaximal, complemented
9#10590790C212yesmaximal, complemented
10#10590743C212yesmaximal, complemented
11#10590742C212yesmaximal, complemented
12#78821—31nomaximal
13#78774—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×C32×C8C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21Dic3×#67—22no—
22#63955—22no—
23#63898C2212yes—
24D3×C4⋊Dic3—21no—
25#63843C2212yes—
26#63843C2212yes—
27#63843C2212yes—
28Dic3×Dic6—21no—
29Dic3×Dic6—21no—
30#63841—21no—
31C2×#3718C2212yes—
32#63827C418yescomplemented
33C2×#3715C2212yes—
34#63642C2212yes—
35C8×C3⋊Dic3C2212yes—
36C3×#821C2211yescharacteristic
37C3×#821C2211yescharacteristic
38C3×#816C2212yes—
39C3×#816C2212yes—
40C3×#816C2211yescharacteristic
41C3×#816C2211yescharacteristic
42#63576C2212yes—
43#63574C2212yes—
44#5827—31no—
45C2×#951—31no—
46#5812—31no—
47C2×#942—31no—
48#5516—31no—
49#5504—31no—
50C3×#416—31no—
51C2×C3×#103—31no—
52#5113D311yescharacteristic
53C2×#816D311yescharacteristic, complemented
54#5101—31no—
55#5101—31no—
56#5101—61no—
57#4995—31no—
58#4964—31no—
59#4817—32no—
60#4790—32no—
61#4790—32no—
62#4789—32no—
63#4789—32no—
64#4788—32no—
65#4758—32no—
66#4757—32no—
67C22×C32×C4C2311yescharacteristic
68C2×C3×#67—21no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3—21no—
71C3×#235—22no—
72C3×#235C2×C414yes—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6C2×C414yescomplemented
78C2×C3×Dic6C2312yes—
79C2×C3×Dic6C2311yescharacteristic
80C2×D3×Dic3—22no—
81C2×C32×C8—22no—
82C2×C32×C8C2311yescharacteristic
83C2×C32×C8C2311yescharacteristic
84#3757D412yes—
85C4⋊(C3⋊Dic3)D411yescharacteristic
86C4⋊(C3⋊Dic3)D411yescharacteristic
87C4×C3⋊Dic3C2312yes—
88#3748C2×C414yescomplemented
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3—21no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98Dic3⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100Dic32—22no—
101Dic32—22no—
102Dic32—22no—
103#3718C2×C418yescomplemented
104#3715C2×C418yescomplemented
105#2947—91noSylow
106C2×C3×#41—31no—
107C22×C3×Q8—31no—
108C2×#235C2×D311yescharacteristic
109C22×Dic6C2×D311yescharacteristic
110C22×C3×C8—21no—
111C22×C3×C8C2×D311yescharacteristic
112C22×C3×C8C2×D311yescharacteristic
113C3×#117—31no—
114C2×C3×C4⋊C4—31no—
115#951—38no—
116Q8×Dic3—32no—
117Q8×Dic3—32no—
118Q8×Dic3—32no—
119Q8×Dic3—61no—
120Q8×Dic3—61no—
121C2×#216—32no—
122C2×#216—32no—
123#942—38no—
124C2×#215—32no—
125D4×Dic3—32no—
126D4×Dic3—62no—
127C2×#214—32no—
128C4×#67—62no—
129#926—31no—
130#926—31no—
131#926—61no—
132#926—61no—
133#926—62no—
134#926C2×D311yescharacteristic
135C2×C4⋊Dic3—61no—
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×#208—31no—
138C2×#208—31no—
139C2×#208—61no—
140#893—32no—
141#892—61no—
142D3×C4⋊C4—61no—
143#887—32no—
144#887—32no—
145#887—32no—
146#877—62no—
147C4×Dic6—61no—
148C4×Dic6—61no—
149C3×#103—32no—
150C3×#103—32no—
151C3×#103—31no—
152C3×#103—31no—
153C3×#102—31no—
154C3×#102—31no—
155#821C2×D311yescharacteristic
156#821C2×D311yescharacteristic
157#816C2×D312yes—
158#816C2×D312yes—
159#816C2×D311yescharacteristic
160#816C2×D311yescharacteristic
161#815—32no—
162#815—32no—
163#815—62no—
164C8×Dic3—32no—
165C8×Dic3—32no—
166C8×Dic3—62no—
167#808—32no—
168#808—32no—
169#807—32no—
170#807—32no—
171C23×C32C2×D411yescharacteristic
172C22×C3×D3—21no—
173C2×C32×C4C22×C412yes—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4#4112yes—
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3C2×D412yes—
178C2×C3⋊Dic3C2×D412yes—
179C3×#67—24no—
180C2×C3×Dic3—24no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—81no—
187C3×D12—21no—
188C3×D12C22×C412yes—
189C3×C4×D3—24no—
190C3×Dic6—24no—
191C3×Dic6—22no—
192C3×Dic6—21no—
193C3×Dic6C22×C414yes—
194C3×Dic6C22×C412yes—
195D3×Dic3—82no—
196C32×C8—21no—
197C32×C8—21no—
198C3⋊(C3⋊C8)C22×C414yes—
199C2×#137—91no—
200#520—91no—
201#519—91no—
202#441—92no—
203#440—92no—
204C4×Q16—92no—
205C4×SD16—92no—
206#428—91no—
207#416—31no—
208C2×#103—31no—
209#405—91no—
210C3×#41—34no—
211C3×#41—62no—
212C2×C3×Q8—34no—
213C2×C3×Q8—32no—
214C2×C3×Q8—31no—
215C2×C3×Q8—61no—
216C2×C3×Q8—62no—
217C2×C3×D4—31no—
218C2×C3×D4—61no—
219C22×C3×C4—21no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C22×C3×C4—61no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—21no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—62no—
229#235—22no—
230#235C4×D314yes—
231C2×D12C22×D311yescharacteristic
232C2×C4×D3—21no—
233C2×C4×D3—62no—
234C2×Dic6—21no—
235C2×Dic6—22no—
236C2×Dic6C4×D314yescomplemented
237C2×Dic6C22×D312yes—
238C2×Dic6C22×D311yescharacteristic
239C2×C3×C8—24no—
240C2×C3×C8—22no—
241C2×C3×C8—22no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8C22×D311yescharacteristic
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C2×C3×C8C22×D311yescharacteristic
248C3×C4⋊C4—31no—
249C3×C4⋊C4—32no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—61no—
252C3×C22⋊C4—61no—
253C3×C42—61no—
254#217—21no—
255#217—32no—
256#217—32no—
257#217—62no—
258#217—62no—
259#216—38no—
260#216—38no—
261#215—38no—
262#214—38no—
263(C2×D3)⋊C4—62no—
264C4⋊Dic3—21no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—31no—
268C4⋊Dic3—31no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3—62no—
272C4⋊Dic3—62no—
273C4⋊Dic3—62no—
274C4⋊Dic3C22×D311yescharacteristic
275C4⋊Dic3C22×D312yes—
276C4⋊Dic3C22×D311yescharacteristic
277Dic3⋊C4—62no—
278Dic3⋊C4—62no—
279Dic3⋊C4—62no—
280C4×Dic3—21no—
281C4×Dic3—32no—
282C4×Dic3—32no—
283C4×Dic3—62no—
284C4×Dic3—62no—
285C4×Dic3—62no—
286C4×Dic3—62no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C4×Dic3—62no—
290#208—34no—
291#208—34no—
292#208—64no—
293C2×C3⋊C8—32no—
294C2×C3⋊C8—32no—
295C2×C3⋊C8—62no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32C4×D412yes—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—22no—
301C2×C3×D3—41no—
302C2×C3×D3—41no—
303C32×C4C4×D412yes—
304C32×C4C23×C411yescharacteristic
305C32×C4C2×#4111yescharacteristic
306C3⋊Dic3—22no—
307C3⋊Dic3—22no—
308C3×Dic3—24no—
309C3×Dic3—22no—
310C3×Dic3—42no—
311C3×Dic3—41no—
312C3×Dic3—41no—
313C2×#41—31no—
314C22×Q8—31no—
315#137—98no—
316C2×Q16—92no—
317C2×SD16—92no—
318C2×M16—91no—
319C22×C8D3211yescharacteristic
320C4×Q8—92no—
321C4×Q8—92no—
322C4×Q8—92no—
323C4×Q8—181no—
324C4×Q8—181no—
325C4×D4—92no—
326C4×D4—182no—
327#117—31no—
328#117—91no—
329#117—182no—
330#117—181no—
331C2×C4⋊C4—31no—
332C2×C4⋊C4—181no—
333#107—92no—
334#106—92no—
335#103—32no—
336#103—32no—
337#103—31no—
338#103—31no—
339#102—31no—
340#102—31no—
341#97—92no—
342C4×C8—92no—
343C23×C3—21no—
344C23×C3—61no—
345C23×C3D3×D411yescharacteristic
346C23×C3D3×D411yescharacteristic
347C22×D3—21no—
348C3×Q8—34no—
349C3×Q8—32no—
350C3×Q8—64no—
351C3×Q8—62no—
352C3×Q8—61no—
353C3×D4—32no—
354C3×D4—64no—
355C3×D4—61no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—64no—
361C2×C3×C4—61no—
362C2×C3×C4—62no—
363C2×C3×C4—64no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—62no—
367C2×C3×C4—241no—
368C2×C3×C4C2×C4×D312yes—
369C2×C3×C4C2×C4×D312yes—
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4#23712yes—
373C2×C3×C4#23712yes—
374C2×C3×C4C23×D311yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376#67—24no—
377C2×Dic3—24no—
378C2×Dic3—22no—
379C2×Dic3—21no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—22no—
383C2×Dic3—32no—
384C2×Dic3—32no—
385C2×Dic3—32no—
386C2×Dic3—32no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—81no—
390C2×Dic3—242no—
391D12—21no—
392D12C2×C4×D312yes—
393C4×D3—24no—
394C4×D3—242no—
395Dic6—24no—
396Dic6—22no—
397Dic6—21no—
398Dic6C2×C4×D314yes—
399Dic6C2×C4×D312yes—
400C3×C8—22no—
401C3×C8—22no—
402C3×C8—21no—
403C3×C8—21no—
404C3×C8—21no—
405C3×C8—21no—
406C3⋊C8—34no—
407C3⋊C8—34no—
408C3⋊C8—64no—
409C2×C32—22no—
410C2×C32C2×C4×D411yescharacteristic
411C2×C32#57711yescharacteristic
412C2×C32#57811yescharacteristic
413C3×D3—42no—
414#41—34no—
415#41—62no—
416C2×Q8—32no—
417C2×Q8—31no—
418C2×Q8—34no—
419C2×Q8—61no—
420C2×Q8—62no—
421C2×D4—31no—
422C2×D4—61no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—182no—
427C22×C4C2×D3211yescharacteristic
428Q16—98no—
429SD16—98no—
430M16—94no—
431C2×C8—22no—
432C2×C8—92no—
433C2×C8C2×D3211yescharacteristic
434C2×C8C2×D3211yescharacteristic
435C4⋊C4—31no—
436C4⋊C4—31no—
437C4⋊C4—32no—
438C4⋊C4—61no—
439C4⋊C4—91no—
440C4⋊C4—91no—
441C4⋊C4—182no—
442C4⋊C4—182no—
443C4⋊C4—182no—
444C22⋊C4—61no—
445C22⋊C4—92no—
446C22⋊C4—182no—
447C42—61no—
448C42—92no—
449C42—182no—
450C42—182no—
451C42—182no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—22no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—62no—
461C22×C3—121no—
462C22×C3—121no—
463C22×C3#67⋊C412yes—
464C22×C3#67⋊C412yes—
465C22×C3C2×D3×D411yescharacteristic
466C22×C3C2×D3×D411yescharacteristic
467C2×D3—22no—
468C2×D3—41no—
469C2×D3—41no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—62no—
474C3×C4—64no—
475C3×C4—121no—
476C3×C4—121no—
477C3×C4—122no—
478C3×C4#67⋊C412yes—
479C3×C4#67⋊C412yes—
480C3×C4C22×C4×D311yescharacteristic
481C3×C4C22×C4×D311yescharacteristic
482C3×C4C2×#23711yescharacteristic
483C3×C4C2×#23711yescharacteristic
484Dic3—24no—
485Dic3—22no—
486Dic3—42no—
487Dic3—41no—
488Dic3—41no—
489Dic3—62no—
490Dic3—62no—
491Dic3—62no—
492Dic3—62no—
493Dic3—122no—
494Dic3—122no—
495C32#294711yescharacteristic, complemented, Sylow
496C23—61no—
497C23#380211yescharacteristic
498Q8—34no—
499Q8—32no—
500Q8—62no—
501Q8—61no—
502Q8—64no—
503D4—32no—
504D4—64no—
505D4—61no—
506C2×C4—61no—
507C2×C4—62no—
508C2×C4—64no—
509C2×C4—64no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—62no—
513C2×C4—92no—
514C2×C4—92no—
515C2×C4—241no—
516C2×C4—722no—
517C2×C4C4×D3212yes—
518C2×C4#380211yescharacteristic
519C2×C4#380512yes—
520C2×C4C22×D3211yescharacteristic
521C8—21no—
522C8—21no—
523C8—94no—
524C2×C3—22no—
525C2×C3—22no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—42no—
530C2×C3—122no—
531C2×C3C2×#67⋊C411yescharacteristic
532C2×C3C2×#67⋊C411yescharacteristic
533C2×C3#576211yescharacteristic
534C2×C3#576611yescharacteristic
535C2×C3#577011yescharacteristic
536C2×C3#577111yescharacteristic
537D3—42no—
538C22—21no—
539C22—21no—
540C22—62no—
541C22—121no—
542C22—121no—
543C22#6390212yes—
544C22C2×#380211yescharacteristic
545C4—62no—
546C4—64no—
547C4—122no—
548C4—121no—
549C4—121no—
550C4—182no—
551C4—182no—
552C4#6390212yes—
553C4C2×C4×D3211yescharacteristic
554C4C2×#380511yescharacteristic
555C3—21no—
556C3#7877411yescharacteristic, complemented
557C3#7882111yescharacteristic, complemented
558C2—22no—
559C2—122no—
560C2#1059468611yescharacteristic
561C2#1059470311yescharacteristic
562C2C2×#6390211yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594818C2semidirect
4. #10592800C2semidirect
6. C2×C3×#816C2semidirect
7. #10591139C2semidirect
8. #10590791C2semidirect
9. #10590790C2semidirect
10. #10590743C2semidirect
11. #10590742C2semidirect
32. #63827C4semidirect
53. C2×#816D3semidirect
77. C2×C3×Dic6C2×C4semidirect
88. #3748C2×C4semidirect
103. #3718C2×C4semidirect
104. #3715C2×C4semidirect
236. C2×Dic6C4×D3semidirect
495. C32#2947semidirect
556. C3#78774semidirect
557. C3#78821semidirect

Maximal subgroups

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

subgroupindex
#105949862
#105948182
C2×#638272
#105928002
C3×#51132
C2×C3×#8162
#105911392
#105907912
#105907902
#105907432
#105907422
#788213
#787743