Finite Group Databasebeta

← #11901759

Subgroups — #11901759

Order 1152.

3120 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#533C211yesmaximal, characteristic, complemented
2#10596204C214yesmaximal, complemented
3#10596169C212yesmaximal, complemented
4#10596168C212yesmaximal, complemented
5#10596116C214yesmaximal, complemented
6#10596115C214yesmaximal, complemented
7#10596051C218yesmaximal, complemented
8#10595995C212yesmaximal, complemented
9#10595993C212yesmaximal, complemented
10#10595948C211yesmaximal, characteristic, complemented
11C2×#64081C211yesmaximal, characteristic, complemented
12#86273—34nomaximal
13C2×#3828C2212yes—
14C22×C4×C3⋊D3C2211yescharacteristic
15C32×C4⋊Q8C2212yescomplemented
16C32×#125C2212yescomplemented
17C32×C22⋊Q8C2214yes—
18C32×C4×Q8C2214yescomplemented
19C32×#117C2212yes—
20C2×C32×C42C2211yescharacteristic
21#64156C2218yes—
22#64155C2218yescomplemented
23#64139C2214yes—
24C2×#3752C2212yes—
25C2×#3750C2212yes—
26C2×C4×C3⋊Dic3C2211yescharacteristic
27#64107C2218yes—
28#64107C2218yescomplemented
29#64106C2214yes—
30#64104C2218yes—
31#64104C2214yes—
32#64103C2218yes—
33#64103C2218yescomplemented
34#64102C2214yescomplemented
35#64099C2218yescomplemented
36#64096C2214yescomplemented
37#64095C2214yes—
38#64091C2214yes—
39#64090C2218yes—
40#64084C2212yescomplemented
41#64083C2211yescharacteristic, complemented
42C4×C4⋊(C3⋊D3)C2218yes—
43C4×C4⋊(C3⋊D3)C2214yescomplemented
44#64081C2212yes—
45#64081C2212yes—
46#64081C2214yes—
47#64081C2214yescomplemented
48C42×C3⋊D3C2214yescomplemented
49#64078C2211yescharacteristic, complemented
50C3×#533D314yescomplemented
51#5733—316no—
52#5698—38no—
53#5697—38no—
54#5645—316no—
55#5644—316no—
56#5580—332no—
57#5524—38no—
58#5522—38no—
59#5477—34no—
60C2×#872—34no—
61C23×C3⋊D3C2311yescharacteristic
62C2×C32×Q8C2314yes—
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C2×#638C2314yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68#3828—28no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C4⋊(C3⋊D3)C2318yes—
71C2×C4⋊(C3⋊D3)C2314yes—
72C2×C4×C3⋊D3—24no—
73C2×C4×C3⋊D3C2314yes—
74C2×C4×C3⋊D3C2312yes—
75C2×C4×C3⋊D3C2312yes—
76C2×C4×C3⋊D3C2318yes—
77C2×#634C2312yes—
78C32×C4⋊C4C2314yes—
79C32×C4⋊C4C2318yes—
80C32×C4⋊C4C2314yes—
81C32×C22⋊C4C2314yes—
82C32×C42C2311yescharacteristic
83C32×C42C2314yes—
84C32×C42C2312yes—
85C32×C42C2311yescharacteristic
86#3752C2314yes—
87#3752C2314yes—
88#3752C2318yes—
89#3752C2318yes—
90#3752C2318yes—
91#3752C2318yes—
92C4⋊(C3⋊Dic3)C2314yes—
93C4⋊(C3⋊Dic3)C2318yes—
94#3750C2314yes—
95#3750C2314yes—
96#3750C2318yes—
97C4×C3⋊Dic3C2312yes—
98C4×C3⋊Dic3C2318yes—
99C4×C3⋊Dic3C2312yes—
100#3455—91noSylow
101C2×#235—38no—
102C22×C4×D3—34no—
103C3×C4⋊Q8C2×D318yescomplemented
104C3×#125C2×D318yescomplemented
105C3×C22⋊Q8C2×D3116yes—
106C3×C4×Q8C2×D3116yescomplemented
107C3×#117C2×D318yes—
108C2×C3×C42C2×D314yes—
109#947—332no—
110#946—332no—
111#930—316no—
112C2×(C2×D3)⋊C4—38no—
113C2×Dic3⋊C4—38no—
114C2×C4×Dic3—34no—
115#898—332no—
116#898—332no—
117#897—316no—
118#895—332no—
119#895—316no—
120#894—332no—
121#894—332no—
122#893—316no—
123#890—332no—
124#887—316no—
125#886—316no—
126#882—316no—
127#67⋊C4—332no—
128#875—38no—
129#874—34no—
130C4×D12—332no—
131C4×D12—316no—
132#872—38no—
133#872—38no—
134#872—316no—
135#872—316no—
136C42×D3—316no—
137#869—34no—
138C23×C32C2411yescharacteristic
139C22×C3⋊D3—22no—
140C22×C3⋊D3—42no—
141C22×C3⋊D3C2412yes—
142C22×C3⋊D3C2414yes—
143C32×Q8—44no—
144C2×C32×C4—42no—
145C2×C32×C4#4114yes—
146C2×C32×C4C2418yes—
147C2×C32×C4C2412yes—
148C2×C32×C4C2412yes—
149C2×C32×C4C2411yescharacteristic
150C2×C32×C4C2411yescharacteristic
151#638—28no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—42no—
154C2×C3⋊Dic3C2414yes—
155C2×C3⋊Dic3C2414yes—
156C2×C3⋊Dic3C2412yes—
157C4⋊(C3⋊D3)—24no—
158C4⋊(C3⋊D3)—48no—
159C4⋊(C3⋊D3)—44no—
160C4×C3⋊D3—24no—
161C4×C3⋊D3—24no—
162C4×C3⋊D3—28no—
163C4×C3⋊D3—48no—
164#634—24no—
165#542—94no—
166#541—92no—
167#540—92no—
168#539—94no—
169#538—94no—
170#533C3⋊D311yescharacteristic, complemented
171#532—91no—
172#529—98no—
173#525—92no—
174C4×#41—92no—
175C2×#117—91no—
176C23×D3—34no—
177C2×C3×Q8C22×D3116yes—
178C22×C3×C4C22×D318yes—
179C22×C3×C4C22×D314yes—
180C2×#67—316no—
181C22×Dic3—34no—
182C22×Dic3—38no—
183#235—632no—
184C2×D12—38no—
185C2×D12—316no—
186C2×D12—332no—
187C2×C4×D3—316no—
188C2×C4×D3—38no—
189C2×C4×D3—38no—
190C2×C4×D3—332no—
191C2×C4×D3—616no—
192C2×Dic6—38no—
193C3×C4⋊C4C22×D3116yes—
194C3×C4⋊C4C22×D3132yes—
195C3×C4⋊C4C22×D3116yes—
196C3×C22⋊C4C22×D3116yes—
197C3×C42C22×D314yes—
198C3×C42C22×D3116yes—
199C3×C42C22×D318yes—
200C3×C42C22×D314yes—
201(C2×D3)⋊C4—316no—
202(C2×D3)⋊C4—316no—
203(C2×D3)⋊C4—332no—
204(C2×D3)⋊C4—332no—
205(C2×D3)⋊C4—332no—
206(C2×D3)⋊C4—332no—
207C4⋊Dic3—316no—
208C4⋊Dic3—332no—
209Dic3⋊C4—316no—
210Dic3⋊C4—316no—
211Dic3⋊C4—332no—
212C4×Dic3—38no—
213C4×Dic3—332no—
214C4×Dic3—38no—
215C22×C32—22no—
216C22×C32C2×#4112yes—
217C22×C32C2511yescharacteristic
218C2×C3⋊D3—22no—
219C2×C3⋊D3—24no—
220C2×C3⋊D3—28no—
221C2×C3⋊D3—24no—
222C2×C3⋊D3—44no—
223C32×C4—28no—
224C32×C4—22no—
225C32×C4—22no—
226C32×C4C2×#4112yes—
227C32×C4C2×#4112yes—
228C3⋊Dic3—24no—
229C3⋊Dic3—22no—
230C3⋊Dic3—24no—
231C2×#41—92no—
232C23×C4—91no—
233C4⋊Q8—91no—
234C4⋊Q8C2×C3⋊D312yescomplemented
235#127—91no—
236#126—98no—
237#126—98no—
238#125—98no—
239#125C2×C3⋊D312yescomplemented
240#124—98no—
241#124—92no—
242#123—98no—
243#123—98no—
244#123—94no—
245C22⋊Q8—98no—
246C22⋊Q8—94no—
247C22⋊Q8C2×C3⋊D314yes—
248#121—94no—
249#121—94no—
250#121—98no—
251#120—94no—
252C4×Q8—94no—
253C4×Q8C2×C3⋊D314yescomplemented
254C4×D4—94no—
255C4×D4—98no—
256C4×D4—98no—
257C4×D4—94no—
258#117—94no—
259#117—92no—
260#117—92no—
261#117—94no—
262#117C2×C3⋊D312yes—
263C2×C4⋊C4—92no—
264C2×C22⋊C4—92no—
265C2×C42—91no—
266C2×C42—94no—
267C2×C42C2×C3⋊D311yescharacteristic
268C23×C3C23×D314yes—
269C22×D3—38no—
270C22×D3—316no—
271C22×D3—68no—
272C22×D3—128no—
273C3×Q8—416no—
274C2×C3×C4—48no—
275C2×C3×C4#239116yes—
276C2×C3×C4C23×D3132yes—
277C2×C3×C4C23×D318yes—
278C2×C3×C4C23×D318yes—
279C2×C3×C4C23×D314yes—
280C2×C3×C4C23×D314yes—
281#67—632no—
282C2×Dic3—316no—
283C2×Dic3—316no—
284C2×Dic3—38no—
285C2×Dic3—68no—
286C2×Dic3—128no—
287D12—616no—
288D12—1232no—
289D12—1216no—
290C4×D3—616no—
291C4×D3—616no—
292C4×D3—632no—
293C4×D3—1232no—
294Dic6—616no—
295C2×C32—22no—
296C2×C32C22×#4111yescharacteristic
297C2×C32#58512yes—
298C3⋊D3—44no—
299C3⋊D3—42no—
300C24—91no—
301#41—188no—
302C2×Q8—92no—
303C2×Q8C22×C3⋊D314yes—
304C2×D4—94no—
305C2×D4—92no—
306C2×D4—98no—
307C2×D4—94no—
308C22×C4—91no—
309C22×C4—92no—
310C22×C4—92no—
311C22×C4—94no—
312C22×C4—92no—
313C22×C4—98no—
314C22×C4—184no—
315C22×C4C22×C3⋊D312yes—
316C22×C4C22×C3⋊D311yescharacteristic
317C4⋊C4—94no—
318C4⋊C4—94no—
319C4⋊C4—98no—
320C4⋊C4—94no—
321C4⋊C4—98no—
322C4⋊C4C22×C3⋊D314yes—
323C4⋊C4C22×C3⋊D318yes—
324C4⋊C4C22×C3⋊D314yes—
325C22⋊C4—94no—
326C22⋊C4—94no—
327C22⋊C4—98no—
328C22⋊C4—98no—
329C22⋊C4—98no—
330C22⋊C4—98no—
331C22⋊C4C22×C3⋊D314yes—
332C42—92no—
333C42—98no—
334C42—92no—
335C42C22×C3⋊D311yescharacteristic
336C42C22×C3⋊D311yescharacteristic
337C42C22×C3⋊D314yes—
338C42C22×C3⋊D312yes—
339C22×C3—28no—
340C22×C3C2×#23918yes—
341C22×C3C24×D314yes—
342C2×D3—68no—
343C2×D3—616no—
344C2×D3—632no—
345C2×D3—616no—
346C2×D3—1216no—
347C3×C4—232no—
348C3×C4—28no—
349C3×C4—28no—
350C3×C4C2×#23918yes—
351C3×C4C2×#23918yes—
352Dic3—616no—
353Dic3—68no—
354Dic3—616no—
355C32#345511yescharacteristic, complemented, Sylow
356C23—92no—
357C23—94no—
358C23—182no—
359C23—362no—
360C23C23×C3⋊D311yescharacteristic
361Q8—44no—
362Q8—184no—
363D4—188no—
364D4—184no—
365D4—364no—
366D4—368no—
367C2×C4—42no—
368C2×C4—94no—
369C2×C4—94no—
370C2×C4—92no—
371C2×C4—182no—
372C2×C4—184no—
373C2×C4—184no—
374C2×C4—188no—
375C2×C4—368no—
376C2×C4—362no—
377C2×C4#383214yes—
378C2×C4C23×C3⋊D318yes—
379C2×C4C23×C3⋊D312yes—
380C2×C4C23×C3⋊D312yes—
381C2×C4C23×C3⋊D311yescharacteristic
382C2×C4C23×C3⋊D311yescharacteristic
383C2×C3—28no—
384C2×C3C22×#23914yes—
385C2×C3#596418yes—
386D3—128no—
387D3—1216no—
388C22—22no—
389C22—182no—
390C22—184no—
391C22—188no—
392C22—184no—
393C22—364no—
394C22C2×#383212yes—
395C22C24×C3⋊D311yescharacteristic
396C4—22no—
397C4—22no—
398C4—28no—
399C4—182no—
400C4—184no—
401C4—184no—
402C4C2×#383212yes—
403C4C2×#383212yes—
404C3#8627314yescomplemented
405C2—22no—
406C2—362no—
407C2—364no—
408C2C22×#383211yescharacteristic
409C2#1059675612yes—
subgroupG/H
centerC2×C4C23×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC32×#533C2
hypercenter#533C3⋊D3
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C32×#533C2semidirect
2. #10596204C2semidirect
3. #10596169C2semidirect
4. #10596168C2semidirect
5. #10596116C2semidirect
6. #10596115C2semidirect
7. #10596051C2semidirect
8. #10595995C2semidirect
9. #10595993C2semidirect
10. #10595948C2semidirect
11. C2×#64081C2semidirect
15. C32×C4⋊Q8C22semidirect
16. C32×#125C22semidirect
18. C32×C4×Q8C22semidirect
22. #64155C22semidirect
28. #64107C22semidirect
33. #64103C22semidirect
34. #64102C22semidirect
35. #64099C22semidirect
36. #64096C22semidirect
40. #64084C22semidirect
41. #64083C22semidirect
43. C4×C4⋊(C3⋊D3)C22semidirect
47. #64081C22semidirect
48. C42×C3⋊D3C22semidirect
49. #64078C22semidirect
50. C3×#533D3semidirect
103. C3×C4⋊Q8C2×D3semidirect
104. C3×#125C2×D3semidirect
106. C3×C4×Q8C2×D3semidirect
170. #533C3⋊D3semidirect
234. C4⋊Q8C2×C3⋊D3semidirect
239. #125C2×C3⋊D3semidirect
253. C4×Q8C2×C3⋊D3semidirect
355. C32#3455semidirect
404. C3#86273semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
#105962042
#105961692
#105961682
#105961162
#105961152
#105960512
#105959952
#105959932
#105959482
C2×#640812
#862733