Finite Group Databasebeta

← #3358⋊C9 #11919597

Subgroups — #3358⋊C9 #11919597

Order 1152.

226 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 49 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
1C4⋊(#41⋊C9)C211yesmaximal, characteristic, complemented
2D4×Q8⋊C9C211yesmaximal, characteristic, complemented
3C8×Q8⋊C9C211yesmaximal, characteristic, complemented
4C3×#3358C311yesmaximal, characteristic
5C2×#41⋊C9—21no—
6C22×Q8⋊C9—21no—
7C4×Q8⋊C9C2211yescharacteristic
8C9×#102—41nomaximal
9C3×#550C2×C311yescharacteristic
10C3×D4×Q8C2×C311yescharacteristic
11C3×#486—31no—
12C3×#474—31no—
13C3×#459—31no—
14C3×C8×Q8C2×C311yescharacteristic
15C3×C4×D8—31no—
16C2×D4×C9—41no—
17#41⋊C9—41no—
18C2×Q8⋊C9—41no—
19C2×Q8⋊C9D411yescharacteristic
20C2×C8×C9—41no—
21C9×C4⋊C4—41no—
22#3358C911yescharacteristic, complemented, Sylow
23C2×C3×#41—21no—
24C22×C3×Q8—21no—
25C2×C3×D8—31no—
26C3×C4⋊Q8—31no—
27C3×#127—31no—
28C3×C22⋊Q8—61no—
29C3×#121—61no—
30C3×C4×Q8C22×C311yescharacteristic
31C3×C4×D4—31no—
32C3×C4×D4—31no—
33C3×#107—31no—
34C3×C4⋊C8—31no—
35C3×#102—32no—
36C3×#102—31no—
37C3×#102A411yescharacteristic
38C3×C4×C8—31no—
39C23×C9—81no—
40D4×C9—42no—
41D4×C9—81no—
42C2×C4×C9—41no—
43C2×C4×C9—81no—
44Q8⋊C9D811yescharacteristic, complemented
45C8×C9—81no—
46#550C2×C911yescharacteristic, complemented
47D4×Q8C2×C911yescharacteristic
48#486—31no—
49#474—31no—
50#459—31no—
51C8×Q8C2×C911yescharacteristic, complemented
52C4×D8—31no—
53C3×#41—41no—
54C3×#41—121no—
55C2×C3×Q8—41no—
56C2×C3×Q8—61no—
57C2×C3×Q8—121no—
58C2×C3×Q8C3×D411yescharacteristic
59C2×C3×D4—31no—
60C2×C3×D4—61no—
61C2×C3×D4—61no—
62C2×C3×D4C2×A411yescharacteristic
63C22×C3×C4—61no—
64C22×C3×C4—61no—
65C3×D8—62no—
66C2×C3×C8—31no—
67C2×C3×C8C2×A411yescharacteristic
68C3×C4⋊C4—31no—
69C3×C4⋊C4—31no—
70C3×C4⋊C4—61no—
71C3×C4⋊C4C2×A411yescharacteristic
72C3×C22⋊C4—61no—
73C3×C22⋊C4—61no—
74C3×C42—31no—
75C22×C9—41no—
76C22×C9—82no—
77C22×C9—161no—
78C22×C9—161no—
79C4×C9—41no—
80C4×C9—41no—
81C4×C9—161no—
82C2×#41—21no—
83C22×Q8—21no—
84C2×D8—31no—
85C4⋊Q8—31no—
86#127—31no—
87C22⋊Q8—61no—
88#121—61no—
89C4×Q8C22×C911yescharacteristic
90C4×D4—31no—
91C4×D4—31no—
92#107—31no—
93C4⋊C8—31no—
94#102—32no—
95#102—31no—
96#102C22⋊C911yescharacteristic
97C4×C8—31no—
98C23×C3—21no—
99C23×C3—61no—
100C3×Q8—31no—
101C3×Q8—121no—
102C3×Q8—121no—
103C3×Q8C3×D811yescharacteristic
104C3×D4—21no—
105C3×D4—61no—
106C3×D4—61no—
107C3×D4—121no—
108C3×D4—121no—
109C3×D4—241no—
110C3×D4#41⋊C312yes—
111C2×C3×C4—21no—
112C2×C3×C4—31no—
113C2×C3×C4—31no—
114C2×C3×C4—61no—
115C2×C3×C4—121no—
116C2×C3×C4—121no—
117C2×C3×C4—121no—
118C2×C3×C4—121no—
119C2×C3×C4C22×A411yescharacteristic
120C3×C8—21no—
121C3×C8—61no—
122C2×C9—41no—
123C2×C9—41no—
124C2×C9—41no—
125C2×C9—162no—
126#41—41no—
127#41—121no—
128C2×Q8—41no—
129C2×Q8—61no—
130C2×Q8—121no—
131C2×Q8D4×C911yescharacteristic
132C2×D4—31no—
133C2×D4—61no—
134C2×D4—61no—
135C2×D4C2×C22⋊C911yescharacteristic
136C22×C4—61no—
137C22×C4—61no—
138D8—62no—
139C2×C8—31no—
140C2×C8C2×C22⋊C911yescharacteristic
141C4⋊C4—31no—
142C4⋊C4—31no—
143C4⋊C4—61no—
144C4⋊C4C2×C22⋊C911yescharacteristic
145C22⋊C4—61no—
146C22⋊C4—61no—
147C42—31no—
148C22×C3—22no—
149C22×C3—41no—
150C22×C3—41no—
151C22×C3—121no—
152C22×C3—121no—
153C22×C3—121no—
154C22×C3D4×A411yescharacteristic
155C3×C4—31no—
156C3×C4—31no—
157C3×C4—41no—
158C3×C4—61no—
159C3×C4—121no—
160C3×C4C2×#41⋊C311yescharacteristic
161C3×C42−1+4⋊C311yescharacteristic
162C9—41noSylow
163C23—21no—
164C23—61no—
165Q8—31no—
166Q8—121no—
167Q8—121no—
168Q8C9×D811yescharacteristic
169D4—21no—
170D4—61no—
171D4—61no—
172D4—121no—
173D4—121no—
174D4—241no—
175D4#41⋊C912yescomplemented
176C2×C4—21no—
177C2×C4—31no—
178C2×C4—31no—
179C2×C4—61no—
180C2×C4—121no—
181C2×C4—121no—
182C2×C4—121no—
183C2×C4—121no—
184C2×C4C22×C22⋊C911yescharacteristic
185C8—21no—
186C8—61no—
187C2×C3—42no—
188C2×C3—241no—
189C2×C3#548⋊C311yescharacteristic
190C2×C3A4×D811yescharacteristic
191C2×C3#577⋊C311yescharacteristic
192C22—22no—
193C22—41no—
194C22—41no—
195C22—121no—
196C22—121no—
197C22—121no—
198C22D4×C22⋊C911yescharacteristic
199C4—31no—
200C4—31no—
201C4—41no—
202C4—61no—
203C4—121no—
204C4C2×#41⋊C911yescharacteristic
205C42−1+4⋊C911yescharacteristic
206C3#3358⋊C311yescharacteristic
207C2—42no—
208C2—241no—
209C2#548⋊C911yescharacteristic
210C2D8×C22⋊C911yescharacteristic
211C2#577⋊C911yescharacteristic
subgroupG/H
center, socleC22×C3D4×A4
commutatorC4×Q8C22×C9
FrattiniC2×C3×C4C22×A4
Fitting, prime radicalC3×#3358C3
cosocleC3×C4×Q8C22×C3
hypercenterC3×#102A4
hypocenterQ8C9×D8
LCSG ▷ C4×Q8 ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#102

Complements

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

NH ≅ G/Ntype
1. C4⋊(#41⋊C9)C2semidirect
2. D4×Q8⋊C9C2semidirect
3. C8×Q8⋊C9C2semidirect
22. #3358C9semidirect
44. Q8⋊C9D8semidirect
46. #550C2×C9semidirect
51. C8×Q8C2×C9semidirect
175. D4#41⋊C9semidirect

Maximal subgroups

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

subgroupindex
C4⋊(#41⋊C9)2
D4×Q8⋊C92
C8×Q8⋊C92
C3×#33583
C9×#1024