Finite Group Databasebeta

← #11807119

Subgroups — #11807119

Order 1152.

786 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 188 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2#10593837C214yesmaximal
3#10593759C214yesmaximal
4C4⋊C4×#157C214yesmaximal
5C4×C4⋊#157C212yesmaximal
6C2×Q8×C3⋊D3C2212yes—
7C2×C4⋊#157C2212yes—
8C2×C4⋊#157C2214yes—
9C2×C4⋊#157C2212yes—
10C2×C4×#157C2214yes—
11C2×C4×#157C2214yes—
12C32×C4⋊Q8C411yescharacteristic, complemented
13#64153C412yescomplemented
14C4⋊C4×C3⋊D3C2214yes—
15#64097C414yescomplemented
16C42×C3⋊D3C2211yescharacteristic
17#64078C411yescharacteristic, complemented
18#63781C2214yes—
19#63781C2218yes—
20D3×C4⋊Q8—62no—
21C22×#157C2314yes—
22C22×#157C2314yes—
23C2×C32×Q8C2×C412yes—
24Q8×C3⋊D3—42no—
25Q8×C3⋊D3—42no—
26C2×C4×C3⋊D3C2314yes—
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×C4×C3⋊D3C2312yes—
29C2×#634C2×C412yes—
30C2×#634C2×C414yes—
31C4⋊#157—24no—
32C4⋊#157—44no—
33C4⋊#157Q818yescomplemented
34C4×#157—28no—
35C4×#157—44no—
36C32×C4⋊C4C2×C414yes—
37C32×C42C2×C411yescharacteristic
38C4⋊(C3⋊Dic3)C2×C414yes—
39#3750C2×C418yes—
40C4×C3⋊Dic3C2×C412yes—
41C4×C3⋊Dic3C2×C411yescharacteristic
42#2369—91nomaximal, Sylow
43C2×D3×Q8—64no—
44C3×C4⋊Q8—22no—
45#944—64no—
46D3×C4⋊C4—68no—
47#888—68no—
48C42×D3—62no—
49#869—62no—
50C22×C3⋊D3C2411yescharacteristic
51C2×#157—24no—
52C2×#157—24no—
53C2×#157—24no—
54C2×#157—24no—
55C2×#157—24no—
56C2×#157C2×Q818yes—
57C32×Q8—42no—
58C2×C32×C4C22×C411yescharacteristic
59C2×C32×C4C22×C414yes—
60C2×C32×C4C22×C412yes—
61C2×C3⋊Dic3C22×C411yescharacteristic
62C2×C3⋊Dic3C22×C414yes—
63C2×C3⋊Dic3C22×C412yes—
64C4×C3⋊D3—21no—
65C4×C3⋊D3—21no—
66C4×C3⋊D3—24no—
67C4×C3⋊D3—24no—
68C4×C3⋊D3C2×Q814yes—
69C4×C3⋊D3#4114yes—
70#634—44no—
71#634—42no—
72C2×C4⋊Q8—91no—
73#391—94no—
74#389—94no—
75C4×C4⋊C4—92no—
76C4×C4⋊C4—94no—
77C2×C3×Q8—24no—
78D3×Q8—128no—
79D3×Q8—128no—
80C2×C4×D3—64no—
81C2×C4×D3—62no—
82C2×C4×D3—68no—
83C2×Dic6—64no—
84C2×Dic6—68no—
85C3×C4⋊C4—28no—
86C3×C42—22no—
87C4⋊Dic3—68no—
88Dic3⋊C4—616no—
89C4×Dic3—64no—
90C4×Dic3—62no—
91C22×C32C23×C411yescharacteristic
92C2×C3⋊D3C22×Q812yes—
93C2×C3⋊D3C2×#4112yes—
94C2×C3⋊D3H(5,𝔽2)11yescharacteristic
95C2×C3⋊D3H(5,𝔽2)11yescharacteristic
96#157—28no—
97#157—44no—
98C32×C4—21no—
99C32×C4—24no—
100C32×C4C4×Q814yes—
101C3⋊Dic3—21no—
102C3⋊Dic3—24no—
103C3⋊Dic3C4×Q814yes—
104C22×Q8—92no—
105C4⋊Q8—92no—
106C4⋊Q8—94no—
107C4⋊Q8—91no—
108C4⋊Q8#15711yescharacteristic, complemented
109C2×C4⋊C4—92no—
110C2×C4⋊C4—94no—
111C2×C4⋊C4—92no—
112C2×C4⋊C4—94no—
113C2×C42—91no—
114C2×C42—94no—
115C2×C42—94no—
116#95—98no—
117#95—94no—
118C22×D3—62no—
119C3×Q8—48no—
120C2×C3×C4—24no—
121C2×C3×C4—22no—
122C2×C3×C4—28no—
123C2×Dic3—64no—
124C2×Dic3—62no—
125C2×Dic3—68no—
126C4×D3—68no—
127C4×D3—68no—
128C4×D3—64no—
129C4×D3—64no—
130C4×D3—128no—
131C4×D3—128no—
132Dic6—1216no—
133Dic6—128no—
134C2×C32C2×C4×Q812yes—
135C2×C32#51811yescharacteristic
136C3⋊D3#55412yes—
137C3⋊D3#55511yescharacteristic
138C3⋊D3Q8211yescharacteristic
139C2×Q8—94no—
140C2×Q8—92no—
141C2×Q8—362no—
142C2×Q8—362no—
143C2×Q8C2×#15712yes—
144C22×C4—92no—
145C22×C4—94no—
146C22×C4—91no—
147C22×C4—94no—
148C22×C4—94no—
149C4⋊C4—98no—
150C4⋊C4—98no—
151C4⋊C4—94no—
152C4⋊C4—184no—
153C4⋊C4—364no—
154C4⋊C4C2×#15714yes—
155C42—91no—
156C42—92no—
157C42—188no—
158C42—364no—
159C42C2×#15711yescharacteristic
160C22×C3—22no—
161C2×D3—62no—
162C2×D3—62no—
163C2×D3—64no—
164C2×D3—64no—
165C3×C4—24no—
166C3×C4—28no—
167C3×C4—48no—
168Dic3—68no—
169Dic3—64no—
170Dic3—128no—
171C32#236911yescharacteristic, complemented, Sylow
172C23—91no—
173Q8—42no—
174Q8—362no—
175Q8—364no—
176C2×C4—92no—
177C2×C4—94no—
178C2×C4—94no—
179C2×C4—98no—
180C2×C4—91no—
181C2×C4—94no—
182C2×C4—184no—
183C2×C4—184no—
184C2×C4—181no—
185C2×C4—181no—
186C2×C4—184no—
187C2×C4—184no—
188C2×C4—184no—
189C2×C4—184no—
190C2×C4—184no—
191C2×C4C22×#15711yescharacteristic
192C2×C4C22×#15714yes—
193C2×C4C22×#15712yes—
194C2×C3—22no—
195C2×C3—24no—
196D3—64no—
197D3—62no—
198D3—62no—
199C22—91no—
200C22—91no—
201C22—92no—
202C22—92no—
203C22C23×#15711yescharacteristic
204C4—21no—
205C4—24no—
206C4—94no—
207C4—188no—
208C4—181no—
209C4—184no—
210C4—364no—
211C4Q8×#15714yes—
212C3—22no—
213C2—92no—
214C2—91no—
215C2—91no—
216C2#1059664211yescharacteristic
217C2C2×Q8×#15712yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4⋊Q8C4
prime radical, cosocleC22×C3⋊D3C24
hypercenterC4⋊Q8#157
hypocenterC32#2369
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
12. C32×C4⋊Q8C4semidirect
13. #64153C4semidirect
15. #64097C4semidirect
17. #64078C4semidirect
33. C4⋊#157Q8semidirect
108. C4⋊Q8#157semidirect
171. C32#2369semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105938372
#105937592
C4⋊C4×#1572
C4×C4⋊#1572
#23699