Finite Group Databasebeta

← #11777536

Subgroups — #11777536

Order 1152.

331 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 331 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C3×#4831C211yesmaximal, characteristic
2C4×#3718C211yesmaximal, characteristic
3C3⋊C8×Dic6C211yesmaximal, characteristic
4#10589345C211yesmaximal, characteristic
5C3×#4484C211yesmaximal, characteristic
6#10589084C211yesmaximal, characteristic
7#10589078C211yesmaximal, characteristic
8#70956—31nomaximal
9#68218—31nomaximal
10C3×C4×Dic6C2211yescharacteristic
11C3×C4×Dic6C2211yescharacteristic
12C2×#3718C411yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#815—21no—
17C3×Dic3⋊C8—21no—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63576C411yescharacteristic
21Dic3⋊(C3⋊C8)—21no—
22#63565C411yescharacteristic
23#63565C411yescharacteristic
24Dic3×C3⋊C8—21no—
25C3×#446—31no—
26C4×#216—31no—
27C4×#216—31no—
28Q8×C3⋊C8—31no—
29#4831D311yescharacteristic
30C8×Dic6—31no—
31C3×Q8⋊C8—31no—
32#4535—31no—
33#4484D311yescharacteristic
34#4479—31no—
35#4479—31no—
36#4479—61no—
37#4456—31no—
38#4455—31no—
39#4454—31no—
40C2×C3×Dic6C2×C411yescharacteristic
41C2×C3×Dic6C2×C411yescharacteristic
42C2×C32×C8—21no—
43C32×C42C2311yescharacteristic
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
46C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
47C3×C4⋊Dic3C2×C411yescharacteristic
48C3×C4⋊Dic3C2×C411yescharacteristic
49C3×Dic3⋊C4—21no—
50C3×Dic3⋊C4—21no—
51C3×C4×Dic3—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3718—22no—
57#1584—91noSylow
58C3×C4×Q8—31no—
59C3×C4×Q8—31no—
60C2×#216—31no—
61C2×#216—31no—
62C4×Dic6C2×D311yescharacteristic
63C4×Dic6C2×D311yescharacteristic
64C3×C4⋊C8—21no—
65C3×C4⋊C8—61no—
66C3×C4⋊C8C2×D311yescharacteristic
67C3×C4⋊C8C2×D311yescharacteristic
68C3×#97—61no—
69C3×C4×C8—31no—
70C3×C4×C8—31no—
71#835—31no—
72#835—31no—
73#815—21no—
74Dic3⋊C8—21no—
75Dic3⋊C8—61no—
76C8×Dic3—61no—
77#810—31no—
78#810—31no—
79#807—31no—
80#807—31no—
81C4⋊(C3⋊C8)—31no—
82C4⋊(C3⋊C8)—31no—
83C4⋊(C3⋊C8)—61no—
84C4⋊(C3⋊C8)—61no—
85C4×C3⋊C8—31no—
86C4×C3⋊C8—31no—
87C4×C3⋊C8—61no—
88C4×C3⋊C8—61no—
89C4×C3⋊C8C2×D311yescharacteristic
90C4×C3⋊C8C2×D311yescharacteristic
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3×Dic3—21no—
95C2×C3×Dic3—21no—
96C2×C3×Dic3—21no—
97C2×C3×Dic3—21no—
98C3×Dic6—21no—
99C3×Dic6—21no—
100C3×Dic6—21no—
101C3×Dic6M1612yes—
102C32×C8—41no—
103C3⋊(C3⋊C8)—21no—
104C3⋊(C3⋊C8)—21no—
105C3⋊(C3⋊C8)—41no—
106C3×C3⋊C8—21no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8Q1612yescomplemented
109#446—31no—
110C8×Q8—91no—
111C4×Q16—91no—
112#335—91no—
113Q8⋊C8—31no—
114Q8⋊C8—91no—
115#322—91no—
116C2×C3×Q8—31no—
117C2×C3×Q8—31no—
118C2×Dic6C4×D311yescharacteristic
119C2×Dic6C4×D311yescharacteristic
120C2×C3×C8—21no—
121C2×C3×C8—21no—
122C2×C3×C8—31no—
123C2×C3×C8—31no—
124C2×C3×C8—41no—
125C2×C3×C8—61no—
126C3×C4⋊C4—31no—
127C3×C4⋊C4—31no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C42—21no—
131C3×C42—61no—
132C3×C42—61no—
133C3×C42C22×D311yescharacteristic
134C3×C42C22×D311yescharacteristic
135#216—62no—
136#216—62no—
137C4⋊Dic3C4×D311yescharacteristic
138C4⋊Dic3C4×D311yescharacteristic
139Dic3⋊C4—21no—
140Dic3⋊C4—21no—
141C4×Dic3—21no—
142C4×Dic3—21no—
143C2×C3⋊C8—21no—
144C2×C3⋊C8—31no—
145C2×C3⋊C8—31no—
146C2×C3⋊C8—31no—
147C2×C3⋊C8—31no—
148C2×C3⋊C8—61no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—121no—
153C2×C3⋊C8#6711yescharacteristic
154C2×C3⋊C8#6711yescharacteristic
155C22×C32C4×D411yescharacteristic
156C32×C4—21no—
157C32×C4C2×M1611yescharacteristic
158C32×C4#13111yescharacteristic
159C32×C4C2×Q1611yescharacteristic
160C32×C4#13511yescharacteristic
161C3×Dic3—22no—
162C3×Dic3—41no—
163C3×Dic3—41no—
164C3×Dic3—41no—
165C2×Q16—91no—
166C4×Q8—31no—
167C4×Q8—31no—
168#107—91no—
169C4⋊C8—61no—
170C4⋊C8—91no—
171C4⋊C8—181no—
172C4⋊C8D3211yescharacteristic
173#103—91no—
174#103—91no—
175#97—61no—
176C4×C8—31no—
177C4×C8—31no—
178C4×C8—91no—
179C4×C8—181no—
180C3×Q8—32no—
181C3×Q8—61no—
182C3×Q8—61no—
183C3×Q8—61no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—61no—
188C2×C3×C4—61no—
189C2×C3×C4—61no—
190C2×C3×C4—61no—
191C2×C3×C4C2×C4×D311yescharacteristic
192C2×C3×C4C2×C4×D311yescharacteristic
193C2×C3×C4#23511yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4#23711yescharacteristic
196C2×C3×C4C2×#6711yescharacteristic
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201Dic6—21no—
202Dic6—21no—
203Dic6—21no—
204Dic6ΓL(1,𝔽25)12yes—
205C3×C8—32no—
206C3×C8—41no—
207C3×C8—41no—
208C3×C8—61no—
209C3×C8—81no—
210C3×C8—121no—
211C3⋊C8—21no—
212C3⋊C8—41no—
213C3⋊C8—62no—
214C3⋊C8—61no—
215C3⋊C8—61no—
216C3⋊C8—61no—
217C3⋊C8—61no—
218C3⋊C8—121no—
219C3⋊C8—121no—
220C3⋊C8—121no—
221C3⋊C8—241no—
222C3⋊C8#21612yescomplemented
223C2×C32#43511yescharacteristic
224C2×C32C4×Q1611yescharacteristic
225C2×C32#44411yescharacteristic
226C2×Q8—31no—
227C2×Q8—31no—
228Q16—182no—
229C2×C8—21no—
230C2×C8—31no—
231C2×C8—31no—
232C2×C8—61no—
233C2×C8—91no—
234C2×C8—91no—
235C2×C8—181no—
236C4⋊C4—31no—
237C4⋊C4—31no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C42—61no—
241C42—61no—
242C42C2×D3211yescharacteristic
243C22×C3—21no—
244C22×C3#67⋊C411yescharacteristic
245C22×C3C4×#6711yescharacteristic
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—41no—
253C3×C4—62no—
254C3×C4—121no—
255C3×C4—121no—
256C3×C4—121no—
257C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
258C3×C4D3×M1611yescharacteristic
259C3×C4#90711yescharacteristic
260C3×C4#90711yescharacteristic
261C3×C4#91611yescharacteristic
262C3×C4D3×Q1611yescharacteristic
263C3×C4C2×#21611yescharacteristic
264C3×C4#95011yescharacteristic
265Dic3—22no—
266Dic3—41no—
267Dic3—41no—
268Dic3—41no—
269C32#158411yescharacteristic, complemented, Sylow
270Q8—32no—
271Q8—61no—
272Q8—61no—
273Q8—61no—
274C2×C4—61no—
275C2×C4—61no—
276C2×C4—61no—
277C2×C4—61no—
278C2×C4#379511yescharacteristic
279C2×C4C4×D3211yescharacteristic
280C2×C4D3×#6711yescharacteristic
281C8—32no—
282C8—41no—
283C8—61no—
284C8—121no—
285C8—181no—
286C8—181no—
287C8—361no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3#473011yescharacteristic
292C2×C3#479011yescharacteristic
293C2×C3#482311yescharacteristic
294C2×C3C4×#21611yescharacteristic
295C2×C3#512711yescharacteristic
296C2×C3#514511yescharacteristic
297C22#6387911yescharacteristic
298C4—21no—
299C4—62no—
300C4—121no—
301C4—121no—
302C4—121no—
303C4D3×ΓL(1,𝔽25)11yescharacteristic
304C4#6380511yescharacteristic
305C4#6393511yescharacteristic
306C4D3×#21611yescharacteristic
307C3—21no—
308C3#6821811yescharacteristic, complemented
309C3#7095611yescharacteristic, complemented
310C2#1059047611yescharacteristic
311C2#1059072411yescharacteristic
312C2#1059097611yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32C4×D4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1584
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
108. C3×C3⋊C8Q16semidirect
222. C3⋊C8#216semidirect
269. C32#1584semidirect
308. C3#68218semidirect
309. C3#70956semidirect

Maximal subgroups

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

subgroupindex
C3×#48312
C4×#37182
C3⋊C8×Dic62
#105893452
C3×#44842
#105890842
#105890782
#709563
#682183