Finite Group Databasebeta

← #11796922

Subgroups — #11796922

Order 1152.

477 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 477 conjugacy classes of subgroups — too many to draw. Only its 92 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×#63802C211yesmaximal, characteristic
2C3⋊D3×M32C211yesmaximal, characteristic
3#10590913C211yesmaximal, characteristic
4C3×#4517C212yesmaximal, complemented
5#10589129C212yesmaximal, complemented
6D3×#362—32nomaximal
7C2×#3797—21no—
8C2×C8×C3⋊D3C2211yescharacteristic
9C2×C3×Dic12C2212yes—
10C2×#3718—21no—
11#63818—21no—
12#63802—21no—
13#63802—21no—
14#63802C412yes—
15#63802C412yes—
16C32×M32C2211yescharacteristic
17#63639C2211yescharacteristic
18#63625—21no—
19C16×C3⋊D3—21no—
20C3×#819C2212yes—
21#63578—21no—
22C2×D3×Q16—32no—
23D3×M32—32no—
24D3×M32—61no—
25D3×#108—32no—
26C3×#362—32no—
27#4565—32no—
28#4517D312yescomplemented
29#4496—32no—
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C3×Dic6—22no—
32C2×#627—41no—
33C2×#624—41no—
34#3797—22no—
35#3797—22no—
36#3797—41no—
37#3797—41no—
38C2×C32×C8C2311yescharacteristic
39C2×C3⋊(C3⋊C8)D411yescharacteristic
40C8×C3⋊D3C2×C411yescharacteristic
41C8×C3⋊D3C2×C411yescharacteristic
42C8×C3⋊D3D411yescharacteristic
43C8×C3⋊D3D411yescharacteristic
44C3×#208—22no—
45C3×Dic12—22no—
46C3×Dic12C2×C414yes—
47#3718—22no—
48#3718—22no—
49#3712—41no—
50#3710—41no—
51C32×C16—21no—
52C3⋊(C3⋊C16)—21no—
53C2×#362—91noSylow
54C2×D3×Q8—62no—
55C2×C3×Q16—32no—
56C2×#216—62no—
57D3×Q16—34no—
58D3×Q16—34no—
59D3×Q16—62no—
60D3×Q16—62no—
61D3×M16—62no—
62C2×Dic12C2×D312yes—
63C2×D3×C8—32no—
64C2×D3×C8—61no—
65C3×M32—21no—
66C3×M32C2×D312yes—
67C3×#108—32no—
68#822—62no—
69#819C2×D312yes—
70#812—32no—
71#812—61no—
72#798—62no—
73#798—62no—
74D3×C16—62no—
75D3×C16—62no—
76C22×C3⋊D3SD1611yescharacteristic
77C2×C32×C4C2×D411yescharacteristic
78C2×C3⋊Dic3SD1611yescharacteristic
79C4×C3⋊D3C22⋊C411yescharacteristic
80C4×C3⋊D3C22⋊C411yescharacteristic
81C4×C3⋊D3D811yescharacteristic
82C4×C3⋊D3D811yescharacteristic
83C2×C3×Dic3—42no—
84C3×Dic6—24no—
85C3×Dic6—42no—
86#627—42no—
87#627—42no—
88#624—42no—
89#624—42no—
90C32×C8C22×C411yescharacteristic
91C32×C8C2×D411yescharacteristic
92C3⋊(C3⋊C8)C22⋊C411yescharacteristic
93C3⋊(C3⋊C8)C22⋊C411yescharacteristic
94C3×C3⋊C8—42no—
95C22×Q16—91no—
96C2×M32—91no—
97C2×#108—91no—
98#362—32no—
99#362—92no—
100C2×C3×Q8—62no—
101D3×Q8—64no—
102D3×Q8—64no—
103D3×Q8—122no—
104D3×Q8—122no—
105C2×C4×D3—32no—
106C2×C4×D3—61no—
107C2×C4×D3—122no—
108C2×Dic6—22no—
109C2×Dic6—122no—
110C3×Q16—34no—
111C3×Q16—62no—
112C3×M16—62no—
113C2×C3×C8—21no—
114C2×C3×C8C22×D312yes—
115#216—64no—
116#216—64no—
117#208—22no—
118C2×C3⋊C8—32no—
119C2×C3⋊C8—61no—
120Dic12—22no—
121Dic12C4×D314yes—
122ΓL(1,𝔽25)—122no—
123D3×C8—32no—
124D3×C8—32no—
125D3×C8—32no—
126D3×C8—32no—
127D3×C8—61no—
128D3×C8—61no—
129D3×C8—61no—
130D3×C8—61no—
131D3×C8—122no—
132C3×C16—22no—
133C3×C16—22no—
134C3⋊C16—62no—
135C3⋊C16—62no—
136C22×C32C2×SD1611yescharacteristic
137C2×C3⋊D3—22no—
138C2×C3⋊D3#10211yescharacteristic
139C2×C3⋊D3#10211yescharacteristic
140C32×C4C2×C22⋊C411yescharacteristic
141C32×C4C2×D811yescharacteristic
142C3⋊Dic3#10211yescharacteristic
143C3⋊Dic3#10211yescharacteristic
144C3×Dic3—44no—
145C22×Q8—181no—
146C2×Q16—32no—
147C2×Q16—92no—
148C2×Q16—92no—
149C2×Q16—181no—
150C2×Q16—181no—
151C2×Q16—181no—
152C2×M16—181no—
153C22×C8—91no—
154M32—91no—
155M32—181no—
156M32D3211yescharacteristic
157C2×C16—181no—
158#108—32no—
159#108—181no—
160C22×D3—32no—
161C22×D3—61no—
162C3×Q8—64no—
163C3×Q8—122no—
164C2×C3×C4—21no—
165C2×C3×C4—122no—
166C2×C3×C4D3×D412yes—
167C2×Dic3—32no—
168C2×Dic3—42no—
169C2×Dic3—61no—
170C4×D3—32no—
171C4×D3—32no—
172C4×D3—32no—
173C4×D3—32no—
174C4×D3—61no—
175C4×D3—61no—
176C4×D3—61no—
177C4×D3—61no—
178C4×D3—124no—
179C4×D3—124no—
180Dic6—24no—
181Dic6—42no—
182Dic6—124no—
183Dic6—124no—
184C3×C8—21no—
185C3×C8—21no—
186C3×C8—122no—
187C3×C8C2×C4×D312yes—
188C3×C8D3×D412yes—
189C3⋊C8—32no—
190C3⋊C8—32no—
191C3⋊C8—42no—
192C3⋊C8—61no—
193C3⋊C8—61no—
194C2×C32—21no—
195C2×C32C2×#10211yescharacteristic
196C3⋊D3—21no—
197C3⋊D3#36212yescomplemented
198C2×Q8—62no—
199C2×Q8—182no—
200C2×Q8—182no—
201C2×Q8—361no—
202C2×Q8—361no—
203C2×Q8—361no—
204C22×C4—91no—
205C22×C4—361no—
206Q16—34no—
207Q16—62no—
208Q16—182no—
209Q16—182no—
210M16—62no—
211M16—361no—
212C2×C8—91no—
213C2×C8—91no—
214C2×C8—91no—
215C2×C8—91no—
216C2×C8—91no—
217C2×C8—361no—
218C2×C8C2×D3211yescharacteristic
219C16—21no—
220C16—181no—
221C22×C3—21no—
222C22×C3D3×SD1612yes—
223C2×D3—32no—
224C2×D3—32no—
225C2×D3—61no—
226C2×D3—61no—
227C2×D3—64no—
228C2×D3—122no—
229C3×C4—21no—
230C3×C4—21no—
231C3×C4—124no—
232C3×C4D3×C22⋊C412yes—
233C3×C4D3×D812yes—
234Dic3—32no—
235Dic3—32no—
236Dic3—44no—
237Dic3—61no—
238Dic3—61no—
239C32C2×#36211yescharacteristic, complemented, Sylow
240C23—91no—
241Q8—64no—
242Q8—122no—
243Q8—362no—
244Q8—362no—
245C2×C4—91no—
246C2×C4—91no—
247C2×C4—91no—
248C2×C4—91no—
249C2×C4—91no—
250C2×C4—122no—
251C2×C4—362no—
252C2×C4—362no—
253C2×C4#380211yescharacteristic
254C8—91no—
255C8—91no—
256C8—122no—
257C8C4×D3211yescharacteristic
258C8#381111yescharacteristic
259C2×C3—22no—
260C2×C3—21no—
261C2×C3—41no—
262C2×C3D3×#10212yes—
263D3—34no—
264D3—62no—
265D3—62no—
266D3—121no—
267C22—91no—
268C22—91no—
269C22—182no—
270C22#6379611yescharacteristic
271C4—91no—
272C4—91no—
273C4—124no—
274C4#6379711yescharacteristic
275C4#6392111yescharacteristic
276C3—21no—
277C3D3×#36212yescomplemented
278C2—21no—
279C2—92no—
280C2—181no—
281C2#1059094011yescharacteristic
subgroupG/H
centerC2#10590940
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32C2×#102
prime radicalC22×C3⋊D3SD16
cosocleC2×C32×C8C23
hypercenterM32D32
hypocenterC32C2×#362
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
4. C3×#4517C2semidirect
5. #10589129C2semidirect
28. #4517D3semidirect
197. C3⋊D3#362semidirect
239. C32C2×#362semidirect
277. C3D3×#362semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
C3⋊D3×M322
#105909132
C3×#45172
#105891292
D3×#3623