Finite Group Databasebeta

← #11790544

Subgroups — #11790544

Order 1152.

302 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 63 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
1#10593771C211yesmaximal, characteristic
2#10593330C212yesmaximal
3#10590913C211yesmaximal, characteristic
4#10590700C211yesmaximal, characteristic
5#10590054C212yesmaximal
6#64283C2212yes—
7C2×C8×C3⋊D3C2211yescharacteristic
8#63874C2211yescharacteristic
9C2×#3712C2211yescharacteristic
10#63818C2212yes—
11#63771C412yescomplemented
12#63770C412yescomplemented
13#63733—24no—
14C3×#819—21no—
15C3×C8×Dic3—21no—
16#63578—21no—
17#63554—21no—
18D3×#108—61no—
19#4689—61no—
20C2×C4×C3⋊D3C2311yescharacteristic
21#3792—22no—
22#3788C2×C414yes—
23#3787—22no—
24C2×C32×C8D411yescharacteristic
25C2×C3⋊(C3⋊C8)D411yescharacteristic
26C8×C3⋊D3C2×C411yescharacteristic
27C8×C3⋊D3C2×C411yescharacteristic
28C8×C3⋊D3Q811yescharacteristic
29C8×C3⋊D3Q811yescharacteristic
30C3×C4×Dic3—21no—
31C3×#208—22no—
32C2×C3×C3⋊C8—21no—
33#3724—21no—
34#3722Q812yes—
35#3712—21no—
36#3712—22no—
37#3712D412yes—
38#3710—22no—
39#1953—91nomaximal, Sylow
40D3×M16—62no—
41C2×ΓL(1,𝔽25)—61no—
42C2×D3×C8—61no—
43C2×D3×C8—61no—
44#872—61no—
45C3×#108—61no—
46C3×C4×C8—61no—
47#822—62no—
48#819—21no—
49#815—61no—
50C8×Dic3—21no—
51#803—61no—
52C22×C3⋊D3C2×Q811yescharacteristic
53C2×C32×C4C2×D411yescharacteristic
54C2×C3⋊Dic3#4111yescharacteristic
55C4×C3⋊D3C22×C411yescharacteristic
56C4×C3⋊D3C2×D411yescharacteristic
57C4×C3⋊D3C2×Q811yescharacteristic
58C4×C3⋊D3#4111yescharacteristic
59C2×C3×Dic3—22no—
60#622—24no—
61C32×C8C4⋊C411yescharacteristic
62C32×C8C4⋊C411yescharacteristic
63C3⋊(C3⋊C8)C4⋊C411yescharacteristic
64C3⋊(C3⋊C8)C4⋊C411yescharacteristic
65C3×C3⋊C8—22no—
66C3×C3⋊C8—42no—
67#430—92no—
68C2×#108—91no—
69C2×#108—91no—
70#405—91no—
71#344—92no—
72C2×C4×D3—61no—
73C2×C4×D3—61no—
74C3×M16—62no—
75C2×C3×C8—21no—
76C2×C3×C8—21no—
77C2×C3×C8—61no—
78C3×C42—61no—
79(C2×D3)⋊C4—62no—
80Dic3⋊C4—62no—
81C4×Dic3—21no—
82#208—22no—
83C2×C3⋊C8—21no—
84C2×C3⋊C8—61no—
85C2×C3⋊C8—61no—
86ΓL(1,𝔽25)—62no—
87ΓL(1,𝔽25)—62no—
88ΓL(1,𝔽25)—122no—
89D3×C8—61no—
90D3×C8—61no—
91D3×C8—61no—
92D3×C8—61no—
93D3×C8—61no—
94D3×C8—61no—
95D3×C8—61no—
96D3×C8—61no—
97D3×C8—122no—
98C22×C32C22⋊Q811yescharacteristic
99C2×C3⋊D3—41no—
100C2×C3⋊D3C4×Q811yescharacteristic
101C2×C3⋊D3C4⋊Q811yescharacteristic
102C32×C4C2×C4⋊C411yescharacteristic
103C32×C4#12111yescharacteristic
104C3⋊Dic3C4×D411yescharacteristic
105C3⋊Dic3#12511yescharacteristic
106C3×Dic3—42no—
107C2×M16—91no—
108C2×M16—92no—
109C2×M16—92no—
110C22×C8—91no—
111#117—91no—
112#108—61no—
113#108—92no—
114#108—92no—
115#108—181no—
116#108—184no—
117#97—181no—
118C4×C8—61no—
119C22×D3—61no—
120C22×D3—61no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—62no—
124C2×Dic3—22no—
125C2×Dic3—61no—
126C2×Dic3—61no—
127C4×D3—61no—
128C4×D3—61no—
129C4×D3—61no—
130C4×D3—61no—
131C4×D3—61no—
132C4×D3—61no—
133C4×D3—61no—
134C4×D3—61no—
135C3×C8—21no—
136C3×C8—21no—
137C3×C8—21no—
138C3×C8—21no—
139C3×C8—62no—
140C3×C8—122no—
141C3⋊C8—22no—
142C3⋊C8—42no—
143C3⋊C8—61no—
144C3⋊C8—61no—
145C3⋊C8—61no—
146C3⋊C8—61no—
147C2×C32—21no—
148C2×C32#38911yescharacteristic
149C3⋊D3—21no—
150C3⋊D3—21no—
151C22×C4—91no—
152M16—62no—
153M16—92no—
154M16—94no—
155M16—181no—
156M16—182no—
157M16—182no—
158C2×C8—61no—
159C2×C8—91no—
160C2×C8—91no—
161C2×C8—91no—
162C2×C8—91no—
163C2×C8—91no—
164C2×C8—182no—
165C2×C8—182no—
166C2×C8GO+(4,𝔽2)11yescharacteristic
167C4⋊C4—181no—
168C22⋊C4—92no—
169C42—61no—
170C22×C3—21no—
171C22×C3—21no—
172C2×D3—61no—
173C2×D3—61no—
174C2×D3—61no—
175C2×D3—61no—
176C2×D3—122no—
177C2×D3—122no—
178C3×C4—21no—
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—122no—
183Dic3—42no—
184Dic3—61no—
185Dic3—61no—
186Dic3—61no—
187Dic3—61no—
188C32#195311yescharacteristic, complemented, Sylow
189C23—91no—
190C2×C4—62no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—91no—
196C2×C4C2×GO+(4,𝔽2)11yescharacteristic
197C8—62no—
198C8—91no—
199C8—91no—
200C8—122no—
201C8—184no—
202C8#377311yescharacteristic
203C8#377311yescharacteristic
204C2×C3—22no—
205C2×C3—21no—
206C2×C3—21no—
207C2×C3—41no—
208D3—62no—
209D3—121no—
210D3—121no—
211D3—121no—
212C22—91no—
213C22—91no—
214C22—361no—
215C22D32⋊Q811yescharacteristic
216C4—91no—
217C4—91no—
218C4—122no—
219C4#6423011yescharacteristic
220C4C2×#377311yescharacteristic
221C3—21no—
222C3—21no—
223C2—21no—
224C2—181no—
225C2—181no—
226C2#1059341211yescharacteristic
subgroupG/H
centerC4#64230
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#389
prime radicalC22×C3⋊D3C2×Q8
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1953
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
11. #63771C4semidirect
12. #63770C4semidirect
188. C32#1953semidirect

Maximal subgroups

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

subgroupindex
#105937712
#105933302
#105909132
#105907002
#105900542
#19539