Finite Group Databasebeta

← #11781095

Subgroups — #11781095

Order 1152.

252 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 47 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
1Q8×#622C211yesmaximal, characteristic
2#10593384C211yesmaximal, characteristic
3#10591633C211yesmaximal, characteristic
4#10591631C211yesmaximal, characteristic
5#10590041C211yesmaximal, characteristic
6#10590040C211yesmaximal, characteristic
7#10590038C211yesmaximal, characteristic
8Q8×C3⋊Dic3C2211yescharacteristic
9C2×C3×#216—21no—
10#63919C2211yescharacteristic
11#63873C2211yescharacteristic
12C4⋊#622—21no—
13C4⋊#622C2211yescharacteristic
14C4×#622—21no—
15C4×#622C2211yescharacteristic
16#63742—21no—
17#63742—21no—
18C3×#835—21no—
19#63575—21no—
20#63572C2211yescharacteristic
21#63572C2211yescharacteristic
22#63566—21no—
23#5182—61no—
24#4793—61no—
25C2×C32×Q8D411yescharacteristic
26C2×C3×Dic6—21no—
27C2×#627—21no—
28C2×#622—21no—
29C2×#622D411yescharacteristic
30C2×#622D411yescharacteristic
31C4⋊(C3⋊Dic3)—21no—
32C4⋊(C3⋊Dic3)D411yescharacteristic
33C4×C3⋊Dic3—21no—
34C4×C3⋊Dic3C2311yescharacteristic
35C3×#216—42no—
36C3×C4⋊Dic3—21no—
37C2×C3×C3⋊C8—21no—
38C2×C3×C3⋊C8—21no—
39#3724—21no—
40#3724—21no—
41#3724—21no—
42#1672—91nomaximal, Sylow
43C2×C3×Q16—61no—
44Q8×Dic3—61no—
45Q8×Dic3—61no—
46#944—61no—
47C2×#216—21no—
48#888—61no—
49C3×#103—61no—
50#835—21no—
51#835—61no—
52#818—61no—
53#816—61no—
54Dic3⋊C8—61no—
55Dic3⋊C8—61no—
56#807—61no—
57C32×Q8—21no—
58C32×Q8SD1612yes—
59C2×C32×C4—21no—
60C2×C32×C4C2×D411yescharacteristic
61C2×C3⋊Dic3—21no—
62C2×C3⋊Dic3C2×D411yescharacteristic
63C2×C3⋊Dic3#4111yescharacteristic
64C2×C3×Dic3—41no—
65C2×C3×Dic3—41no—
66C3×Dic6—41no—
67C3×Dic6—41no—
68#627—81no—
69#622—21no—
70#622—41no—
71#622Q1612yescomplemented
72C3×C3⋊C8—41no—
73C3×C3⋊C8—41no—
74#498—91no—
75#477—91no—
76#462—91no—
77C8×Q8—91no—
78#334—91no—
79#333—91no—
80#332—91no—
81C2×C3×Q8—21no—
82C2×C3×Q8—21no—
83C2×C3×Q8—61no—
84C2×Dic6—21no—
85C2×Dic6—121no—
86C3×Q16—122no—
87C2×C3×C8—61no—
88C2×C3×C8—61no—
89C3×C4⋊C4—61no—
90#216—42no—
91C4⋊Dic3—21no—
92C4⋊Dic3—61no—
93C4⋊Dic3—61no—
94C4⋊Dic3—121no—
95C4⋊Dic3—121no—
96Dic3⋊C4—121no—
97Dic3⋊C4—121no—
98Dic3⋊C4—121no—
99C4×Dic3—61no—
100C4×Dic3—61no—
101C4×Dic3—121no—
102C4×Dic3—121no—
103C2×C3⋊C8—21no—
104C2×C3⋊C8—21no—
105C22×C32#12111yescharacteristic
106C32×C4—22no—
107C32×C4C2×SD1611yescharacteristic
108C32×C4#13511yescharacteristic
109C3⋊Dic3—21no—
110C3⋊Dic3—41no—
111C3⋊Dic3C2×Q1611yescharacteristic
112C3⋊Dic3#13711yescharacteristic
113C3×Dic3—81no—
114C3×Dic3—81no—
115C2×Q16—61no—
116C4⋊Q8—91no—
117C4⋊Q8—91no—
118C4×Q8—91no—
119#107—181no—
120#106—181no—
121#106—181no—
122C4⋊C8—91no—
123C4⋊C8—91no—
124C4⋊C8—91no—
125C4⋊C8—181no—
126#103—61no—
127#103—181no—
128C4×C8—91no—
129C4×C8—181no—
130C3×Q8—22no—
131C3×Q8—22no—
132C3×Q8—41no—
133C3×Q8—41no—
134C3×Q8—121no—
135C3×Q8—121no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—41no—
139C2×C3×C4—41no—
140C2×C3×C4—121no—
141C2×C3×C4—121no—
142C2×Dic3—41no—
143C2×Dic3—41no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147C2×Dic3—61no—
148C2×Dic3—121no—
149C2×Dic3—121no—
150Dic6—41no—
151Dic6—41no—
152Dic6—242no—
153C3×C8—121no—
154C3×C8—121no—
155C3⋊C8—41no—
156C3⋊C8—41no—
157C2×C32#46211yescharacteristic
158C2×C32#46511yescharacteristic
159C2×C32#47111yescharacteristic
160C2×Q8—61no—
161C2×Q8—181no—
162C2×Q8GO+(4,𝔽2)11yescharacteristic
163Q16—122no—
164C2×C8—61no—
165C2×C8—61no—
166C2×C8—91no—
167C2×C8—91no—
168C2×C8—181no—
169C4⋊C4—61no—
170C4⋊C4—91no—
171C4⋊C4—181no—
172C4⋊C4—181no—
173C4⋊C4—181no—
174C4⋊C4—181no—
175C42—91no—
176C42—181no—
177C22×C3—21no—
178C22×C3—21no—
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—21no—
183C3×C4—42no—
184C3×C4—42no—
185C3×C4—241no—
186C3×C4—241no—
187Dic3—61no—
188Dic3—61no—
189Dic3—61no—
190Dic3—61no—
191Dic3—81no—
192Dic3—81no—
193Dic3—121no—
194Dic3—121no—
195Dic3—241no—
196Dic3—241no—
197C32#167211yescharacteristic, complemented, Sylow
198Q8—21no—
199Q8—121no—
200Q8—121no—
201Q8—721no—
202Q8#377512yes—
203C2×C4—21no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4—121no—
207C2×C4—121no—
208C2×C4—181no—
209C2×C4C2×GO+(4,𝔽2)11yescharacteristic
210C8—92no—
211C8—121no—
212C8—121no—
213C8—181no—
214C8—361no—
215C2×C3—21no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—21no—
221C22#6424211yescharacteristic
222C4—22no—
223C4—91no—
224C4—91no—
225C4—181no—
226C4—241no—
227C4—241no—
228C4—361no—
229C4#6423711yescharacteristic
230C4C2×#377511yescharacteristic
231C3—21no—
232C3—21no—
233C2#1059347711yescharacteristic
234C2#1059348111yescharacteristic
235C2#1059352611yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×Q8D4
socle, prime radicalC22×C32#121
hypercenterC2×Q8GO+(4,𝔽2)
hypocenterC32#1672
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
71. #622Q16semidirect
197. C32#1672semidirect

Maximal subgroups

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

subgroupindex
Q8×#6222
#105933842
#105916332
#105916312
#105900412
#105900402
#105900382
#16729