Finite Group Databasebeta

← #11781888

Subgroups — #11781888

Order 1152.

219 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 219 conjugacy classes of subgroups — too many to draw. Only its 68 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#10588764C211yesmaximal, characteristic
2#10588760C211yesmaximal, characteristic
3#10588513C211yesmaximal, characteristic
4#10588509C211yesmaximal, characteristic
5C9×#333C211yesmaximal, characteristic
6#10588161C211yesmaximal, characteristic
7#10588156C211yesmaximal, characteristic
8#68512—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C2×Dic36—21no—
11#63431C2211yescharacteristic
12C4×Dic18C2211yescharacteristic
13C9×C4⋊C8C2211yescharacteristic
14C9×C4⋊C8C2211yescharacteristic
15#63376—21no—
16#63375—21no—
17Dic9⋊C8—21no—
18#63368—21no—
19#63367—21no—
20#63367—21no—
21#63366—21no—
22C4⋊(C9⋊C8)C2211yescharacteristic
23C4×C9⋊C8C2211yescharacteristic
24#5091—31no—
25#5080—31no—
26#4849—31no—
27#4831—31no—
28C3×#333D311yescharacteristic
29#4486—31no—
30#4479—31no—
31C2×Q8×C9—21no—
32C2×Dic18—21no—
33C2×Dic18D411yescharacteristic
34C2×C8×C9—21no—
35C2×C8×C9—21no—
36C9×C4⋊C4—21no—
37C9×C4⋊C4—21no—
38C42×C9C2311yescharacteristic
39C4⋊Dic9—21no—
40C4⋊Dic9—21no—
41C4⋊Dic9D411yescharacteristic
42Dic9⋊C4—21no—
43C4×Dic9—21no—
44C2×C9⋊C8—21no—
45C2×C9⋊C8D411yescharacteristic
46C2×C9⋊C8D411yescharacteristic
47Dic36—42no—
48#1692—91noSylow
49C3×C4⋊Q8C2×D311yescharacteristic
50C2×Dic12—61no—
51#869—31no—
52C4×Dic6—31no—
53C3×C4⋊C8C2×D311yescharacteristic
54C3×C4⋊C8C2×D311yescharacteristic
55#816—61no—
56#815—61no—
57Dic3⋊C8—61no—
58#810—61no—
59#808—61no—
60#808—61no—
61#807—61no—
62C4⋊(C3⋊C8)—31no—
63C4×C3⋊C8—31no—
64Q8×C9—81no—
65C2×C4×C9—41no—
66C2×C4×C9C2×D411yescharacteristic
67C2×C4×C9C2×D411yescharacteristic
68C2×C4×C9#4111yescharacteristic
69C2×Dic9—21no—
70C2×Dic9—21no—
71C2×Dic9—41no—
72Dic18—21no—
73Dic18—21no—
74Dic18—41no—
75Dic18—41no—
76C8×C9—41no—
77C8×C9—41no—
78C9⋊C8—21no—
79C9⋊C8—41no—
80C9⋊C8Q1612yescomplemented
81#498—91no—
82#477—91no—
83#462—91no—
84#446—91no—
85#335—91no—
86#333D911yescharacteristic
87#332—91no—
88C2×C3×Q8—21no—
89C2×Dic6—31no—
90C2×Dic6—61no—
91C2×C3×C8—21no—
92C2×C3×C8—21no—
93C3×C4⋊C4—21no—
94C3×C4⋊C4—21no—
95C3×C42C22×D311yescharacteristic
96C4⋊Dic3—31no—
97C4⋊Dic3—61no—
98C4⋊Dic3—61no—
99Dic3⋊C4—61no—
100C4×Dic3—61no—
101C2×C3⋊C8—31no—
102C2×C3⋊C8—31no—
103C2×C3⋊C8—61no—
104Dic12—122no—
105C22×C9#12111yescharacteristic
106C4×C9—21no—
107C4×C9—81no—
108C4×C9C2×Q1611yescharacteristic
109C4×C9AGL(1,ℤ/8)11yescharacteristic
110C4×C9#13711yescharacteristic
111C4×C9#13711yescharacteristic
112Dic9—41no—
113Dic9—41no—
114Dic9—81no—
115C2×Q16—181no—
116C4⋊Q8—91no—
117C4⋊Q8C2×D911yescharacteristic
118C4×Q8—91no—
119#107—181no—
120#106—181no—
121#106—181no—
122C4⋊C8—91no—
123C4⋊C8—181no—
124C4⋊C8C2×D911yescharacteristic
125C4⋊C8C2×D911yescharacteristic
126#103—181no—
127#103—181no—
128#97—181no—
129C4×C8—91no—
130C3×Q8—81no—
131C2×C3×C4—41no—
132C2×C3×C4#23511yescharacteristic
133C2×C3×C4D3×D411yescharacteristic
134C2×C3×C4D3×D411yescharacteristic
135C2×Dic3—61no—
136C2×Dic3—61no—
137C2×Dic3—121no—
138Dic6—61no—
139Dic6—61no—
140Dic6—121no—
141Dic6—121no—
142C3×C8—41no—
143C3×C8—41no—
144C3⋊C8—32no—
145C3⋊C8—61no—
146C3⋊C8—121no—
147C2×C9#46211yescharacteristic
148C2×C9#46811yescharacteristic
149C2×C9#47111yescharacteristic
150C2×Q8—21no—
151C2×Q8—91no—
152C2×Q8—181no—
153Q16—362no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—91no—
157C2×C8—91no—
158C2×C8—181no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—91no—
162C4⋊C4—181no—
163C4⋊C4—181no—
164C4⋊C4—181no—
165C42—181no—
166C42C22×D911yescharacteristic
167C22×C3#88411yescharacteristic
168C3×C4—21no—
169C3×C4—81no—
170C3×C4#91411yescharacteristic
171C3×C4#91511yescharacteristic
172C3×C4D3×Q1611yescharacteristic
173C3×C4#91811yescharacteristic
174Dic3—121no—
175Dic3—121no—
176Dic3—241no—
177C9#169211yescharacteristic, complemented, Sylow
178Q8—81no—
179Q8—181no—
180Q8—181no—
181Q8—361no—
182Q8—361no—
183C2×C4—41no—
184C2×C4—181no—
185C2×C4—181no—
186C2×C4—361no—
187C2×C4#369711yescharacteristic
188C2×C4D4×D911yescharacteristic
189C2×C4D4×D911yescharacteristic
190C8—41no—
191C8—41no—
192C8—92no—
193C8—181no—
194C8—361no—
195C2×C3#474811yescharacteristic
196C2×C3#479511yescharacteristic
197C2×C3#481211yescharacteristic
198C22#6344611yescharacteristic
199C4—21no—
200C4—81no—
201C4—361no—
202C4—361no—
203C4—721no—
204C4#6347611yescharacteristic
205C4#6347711yescharacteristic
206C4Q16×D911yescharacteristic
207C4#6348011yescharacteristic
208C3#6851211yescharacteristic
209C2#1058842811yescharacteristic
210C2#1058847511yescharacteristic
211C2#1058849211yescharacteristic
subgroupG/H
centerC22#63446
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#333C2
socle, prime radicalC22×C3#884
hypercenter#333D9
hypocenterC9#1692
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
80. C9⋊C8Q16semidirect
177. C9#1692semidirect

Maximal subgroups

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

subgroupindex
#105887642
#105887602
#105885132
#105885092
C9×#3332
#105881612
#105881562
#685123