Finite Group Databasebeta

← #11860158

Subgroups — #11860158

Order 1152.

1385 conjugacy classes of subgroups; only the 240 normal subgroups are shown.

normal subgroups only

This group has 1385 conjugacy classes of subgroups — too many to draw. Only its 240 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×C3⋊D3C211yesmaximal, characteristic
2D4×#624C212yesmaximal, complemented
3C3×#5152C212yesmaximal, complemented
4#10591416C212yesmaximal, complemented
5#10591404C214yesmaximal, complemented
6#10590768C212yesmaximal, complemented
7#10590685C211yesmaximal, characteristic, complemented
8#10590668C211yesmaximal, characteristic, complemented
9D3×#442—32nomaximal
10C2×D4×C3⋊D3C2212yes—
11C22×#624—22no—
12C2×C32×D8C2211yescharacteristic
13C2×#3753C2212yes—
14D8×C3⋊D3C418yescomplemented
15C2×#3745C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C3×D4×Dic3C2214yescomplemented
18#63974—22no—
19#63952—24no—
20#63900C2212yes—
21#63894C2214yescomplemented
22C4×#624C2211yescharacteristic
23C2×#3710C2211yescharacteristic
24C3×#832C2214yescomplemented
25C3×#817C2212yescomplemented
26C3×#815C2212yescomplemented
27#63574C2212yescomplemented
28#63564C2214yescomplemented
29#63554C2212yescomplemented
30C2×D3×D8—32no—
31C2×D3×D8—61no—
32C4×D3×D4—34no—
33C3×#442—32no—
34#5152D312yescomplemented
35#5014—34no—
36#4869—32no—
37D3×#106—32no—
38#4785—34no—
39D3×#102—34no—
40#4711—32no—
41D3×#97—32no—
42C23×C3⋊D3—22no—
43C2×C32×D4C2312yes—
44C2×#638—22no—
45D4×C3⋊D3—24no—
46D4×C3⋊D3C2×C418yescomplemented
47C2×C4⋊(C3⋊D3)C2312yes—
48C2×C4×C3⋊D3C2311yescharacteristic
49C22×C3×Dic3—24no—
50C2×#624—22no—
51C2×#624—24no—
52C2×#624—48no—
53C2×#624D412yes—
54C32×D8C2×C414yescomplemented
55C2×C32×C8C2311yescharacteristic
56#3753C2×C418yescomplemented
57C2×C3⋊(C3⋊C8)C2311yescharacteristic
58#3745C2×C414yescomplemented
59C8×C3⋊D3C2×C414yescomplemented
60C3×#217—24no—
61C3×C4⋊Dic3C2314yes—
62C3×C4×Dic3C2312yes—
63C2×C3×C3⋊C8C2312yes—
64#3724—22no—
65#3722—24no—
66Dic32D412yes—
67#3710—22no—
68C2×#442—91noSylow
69C2×D3×D4—34no—
70C2×D3×D4—62no—
71C22×C4×D3—64no—
72C2×C3×D8—21no—
73C2×C3×D8C2×D312yes—
74C3×C4×D4—34no—
75D4×Dic3C2×D314yescomplemented
76C2×#213—34no—
77C2×#213—62no—
78C4×#67—64no—
79D3×D8—316no—
80D3×D8—68no—
81C2×D24—32no—
82C2×D24—61no—
83C2×D3×C8—32no—
84C2×D3×C8—32no—
85C2×D3×C8—61no—
86#893—34no—
87D3×C4⋊C4—34no—
88#67⋊C4—64no—
89D3×C22⋊C4—64no—
90C4×D12—34no—
91C42×D3—32no—
92C3×#106—32no—
93C3×#102—34no—
94C3×#97—32no—
95#832C2×D314yescomplemented
96#821—34no—
97#817C2×D312yescomplemented
98#815—32no—
99#815C2×D312yescomplemented
100#809—34no—
101#808—34no—
102#803—32no—
103C23×C32—22no—
104C22×C3⋊D3—22no—
105C22×C3⋊D3—28no—
106C22×C3⋊D3—44no—
107C22×C3⋊D3—44no—
108C22×C3⋊D3C2×D411yescharacteristic
109C32×D4—22no—
110C32×D4C22×C414yescomplemented
111C2×C32×C4C2411yescharacteristic
112#638—28no—
113C2×C3⋊Dic3C2×D411yescharacteristic
114C4⋊(C3⋊D3)—22no—
115C4⋊(C3⋊D3)C22×C414yescomplemented
116C4×C3⋊D3C22×C412yes—
117C4×C3⋊D3#4112yes—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—48no—
120C2×C3×Dic3C2×D414yes—
121#624—24no—
122#624—48no—
123#624—44no—
124C32×C8C22×C412yescomplemented
125C3⋊(C3⋊C8)C22×C412yescomplemented
126C3×C3⋊C8—22no—
127C22×D8—91no—
128C2×C4×D4—92no—
129#442—32no—
130#442—92no—
131#442—94no—
132C2×#106—91no—
133C2×#102—92no—
134C2×#97—91no—
135C23×D3—64no—
136C23×D3—122no—
137C2×C3×D4—22no—
138C2×C3×D4C22×D314yes—
139C22×C3×C4—64no—
140C2×#67—64no—
141C2×#67—122no—
142C22×Dic3—24no—
143D3×D4—316no—
144D3×D4—68no—
145D3×D4—68no—
146D3×D4—124no—
147C2×D12—34no—
148C2×D12—62no—
149C2×C4×D3—32no—
150C2×C4×D3—34no—
151C2×C4×D3—61no—
152C2×C4×D3—64no—
153C2×C4×D3—64no—
154C2×C4×D3—64no—
155C2×C4×D3—1216no—
156C3×D8—24no—
157C3×D8C4×D318yescomplemented
158C2×C3×C8—21no—
159C2×C3×C8—32no—
160C2×C3×C8C22×D312yes—
161C3×C4⋊C4—34no—
162C3×C22⋊C4—64no—
163C3×C42—32no—
164#217—24no—
165#213—316no—
166#213—68no—
167(C2×D3)⋊C4—64no—
168(C2×D3)⋊C4—64no—
169C4⋊Dic3C22×D314yes—
170Dic3⋊C4—64no—
171C4×Dic3—34no—
172C4×Dic3C22×D312yes—
173C2×C3⋊C8—32no—
174C2×C3⋊C8—61no—
175C2×C3⋊C8C22×D312yes—
176D24—38no—
177D24—64no—
178D3×C8—38no—
179D3×C8—64no—
180D3×C8—64no—
181C22×C32—24no—
182C22×C32—42no—
183C22×C32—42no—
184C22×C32C22×D411yescharacteristic
185C2×C3⋊D3—24no—
186C2×C3⋊D3—42no—
187C2×C3⋊D3—42no—
188C2×C3⋊D3—416no—
189C2×C3⋊D3C4×D412yes—
190C2×C3⋊D3AGL(1,ℤ/8)14yes—
191C32×C4C23×C411yescharacteristic
192C32×C4C2×#4111yescharacteristic
193C3⋊Dic3C4×D412yes—
194C3×Dic3—24no—
195C3×Dic3—44no—
196C22×D4—92no—
197C23×C4—182no—
198C2×D8—92no—
199C2×D8—98no—
200C2×D8—91no—
201C2×D8D3211yescharacteristic
202C22×C8—91no—
203C22×C8—91no—
204C4×D4—34no—
205C4×D4—94no—
206C4×D4—184no—
207C2×C4⋊C4—92no—
208C2×C22⋊C4—182no—
209C2×C42—91no—
210#106—32no—
211#106—92no—
212#102—34no—
213#102—94no—
214#97—32no—
215#97—92no—
216C23×C3—24no—
217C23×C3—42no—
218C22×D3—32no—
219C22×D3—61no—
220C22×D3—616no—
221C22×D3—64no—
222C22×D3—128no—
223C22×D3—122no—
224C22×D3—128no—
225C22×D3—128no—
226C22×D3—244no—
227C22×D3—244no—
228C3×D4—24no—
229C3×D4—24no—
230C3×D4—42no—
231C3×D4C2×C4×D318yescomplemented
232C2×C3×C4—21no—
233C2×C3×C4—34no—
234C2×C3×C4—64no—
235C2×C3×C4—128no—
236C2×C3×C4C23×D312yes—
237#67—616no—
238#67—128no—
239C2×Dic3—24no—
240C2×Dic3—32no—
241C2×Dic3—48no—
242C2×Dic3—61no—
243C2×Dic3D3×D414yes—
244D12—38no—
245D12—64no—
246D12—64no—
247D12—122no—
248C4×D3—34no—
249C4×D3—34no—
250C4×D3—62no—
251C4×D3—62no—
252C4×D3—68no—
253C4×D3—128no—
254C4×D3—128no—
255C4×D3—128no—
256C3×C8—22no—
257C3×C8—62no—
258C3×C8C2×C4×D314yescomplemented
259C3⋊C8—22no—
260C3⋊C8—34no—
261C3⋊C8—62no—
262C2×C32—44no—
263C2×C32C2×C4×D411yescharacteristic
264C2×C32C2×AGL(1,ℤ/8)12yes—
265C3⋊D3—44no—
266C3⋊D3#44214yescomplemented
267C24—182no—
268C2×D4—98no—
269C2×D4—92no—
270C2×D4—184no—
271C2×D4—182no—
272C2×D4C2×D3212yes—
273C22×C4—64no—
274C22×C4—92no—
275C22×C4—91no—
276C22×C4—184no—
277C22×C4—182no—
278C22×C4—368no—
279D8—98no—
280D8—94no—
281D8#62414yescomplemented
282C2×C8—32no—
283C2×C8—91no—
284C2×C8—94no—
285C2×C8—182no—
286C2×C8C2×D3211yescharacteristic
287C4⋊C4—34no—
288C4⋊C4—182no—
289C22⋊C4—64no—
290C22⋊C4—184no—
291C42—32no—
292C42—92no—
293C22×C3—28no—
294C22×C3—21no—
295C22×C3—44no—
296C22×C3—44no—
297C22×C3—44no—
298C22×C3—82no—
299C22×C3—82no—
300C22×C3C2×D3×D412yes—
301C2×D3—38no—
302C2×D3—34no—
303C2×D3—62no—
304C2×D3—64no—
305C2×D3—68no—
306C2×D3—124no—
307C2×D3—1232no—
308C2×D3—124no—
309C2×D3—124no—
310C2×D3—2416no—
311C2×D3—242no—
312C2×D3—242no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—64no—
316C3×C4—124no—
317C3×C4C22×C4×D312yes—
318C3×C4D3×#4112yes—
319Dic3—24no—
320Dic3—34no—
321Dic3—44no—
322Dic3—62no—
323C32C2×#44211yescharacteristic, complemented, Sylow
324C23—22no—
325C23—91no—
326C23—188no—
327C23—182no—
328C23—364no—
329C23—364no—
330D4—22no—
331D4—94no—
332D4—188no—
333D4—182no—
334D4C2×#62414yescomplemented
335C2×C4—34no—
336C2×C4—64no—
337C2×C4—91no—
338C2×C4—92no—
339C2×C4—92no—
340C2×C4—128no—
341C2×C4—184no—
342C2×C4—368no—
343C2×C4—364no—
344C2×C4C22×D3211yescharacteristic
345C8—62no—
346C8—92no—
347C8C2×#62412yescomplemented
348C2×C3—21no—
349C2×C3—22no—
350C2×C3—48no—
351C2×C3—84no—
352C2×C3C4×D3×D412yes—
353C2×C3D3×AGL(1,ℤ/8)14yes—
354D3—38no—
355D3—64no—
356D3—128no—
357D3—244no—
358C22—24no—
359C22—42no—
360C22—42no—
361C22—92no—
362C22—94no—
363C22—184no—
364C22—3616no—
365C22—362no—
366C22—362no—
367C22D32×D411yescharacteristic
368C4—64no—
369C4—92no—
370C4—124no—
371C4#6431211yescharacteristic
372C4C22×#62411yescharacteristic
373C3—21no—
374C3D3×#44212yescomplemented
375C2—44no—
376C2—94no—
377C2—364no—
378C2#1059472612yes—
379C2D4×#62411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC2×D8×C3⋊D3C2
cosocleC2×C32×C4C24
hypercenterC2×D8D32
hypocenterC32C2×#442
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. D4×#624C2semidirect
3. C3×#5152C2semidirect
4. #10591416C2semidirect
5. #10591404C2semidirect
6. #10590768C2semidirect
7. #10590685C2semidirect
8. #10590668C2semidirect
14. D8×C3⋊D3C4semidirect
17. C3×D4×Dic3C22semidirect
21. #63894C22semidirect
24. C3×#832C22semidirect
25. C3×#817C22semidirect
26. C3×#815C22semidirect
27. #63574C22semidirect
28. #63564C22semidirect
29. #63554C22semidirect
34. #5152D3semidirect
46. D4×C3⋊D3C2×C4semidirect
54. C32×D8C2×C4semidirect
56. #3753C2×C4semidirect
58. #3745C2×C4semidirect
59. C8×C3⋊D3C2×C4semidirect
75. D4×Dic3C2×D3semidirect
95. #832C2×D3semidirect
97. #817C2×D3semidirect
99. #815C2×D3semidirect
110. C32×D4C22×C4semidirect
115. C4⋊(C3⋊D3)C22×C4semidirect
124. C32×C8C22×C4semidirect
125. C3⋊(C3⋊C8)C22×C4semidirect
157. C3×D8C4×D3semidirect
231. C3×D4C2×C4×D3semidirect
258. C3×C8C2×C4×D3semidirect
266. C3⋊D3#442semidirect
281. D8#624semidirect
323. C32C2×#442semidirect
334. D4C2×#624semidirect
347. C8C2×#624semidirect
374. C3D3×#442semidirect

Maximal subgroups

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

subgroupindex
C2×D8×C3⋊D32
D4×#6242
C3×#51522
#105914162
#105914042
#105907682
#105906852
#105906682
D3×#4423