Finite Group Databasebeta

← #11861393

Subgroups — #11861393

Order 1152.

570 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 162 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#10596199C211yesmaximal, characteristic
2#10593835C214yesmaximal, complemented
3#10593755C212yesmaximal
4#10593754C214yesmaximal, complemented
5#10593748C212yesmaximal
6#10593729C211yesmaximal, characteristic
7#10593723C211yesmaximal, characteristic
8C2×#3788C2212yes—
9C2×#3787C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11C32×C4⋊Q8C411yescharacteristic
12#64155C412yes—
13Q8×C3⋊Dic3C2212yes—
14#64106C412yes—
15#64101C2212yes—
16#64099C412yes—
17#64096C2212yes—
18C42×C3⋊D3C2211yescharacteristic
19#64078C411yescharacteristic
20#63779C2212yes—
21#63779C2214yes—
22#63779C2212yes—
23#63777C2212yes—
24#63777C2214yes—
25#63777C2212yes—
26C4⋊#622C2214yes—
27C4×#622C2214yes—
28#5728—62no—
29C2×C32×Q8C2×C412yes—
30C2×C4×C3⋊D3C2×C411yescharacteristic
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3C2311yescharacteristic
33C2×#634C2×C412yes—
34C2×#622C2312yes—
35C2×#622C2314yes—
36C2×#622C2312yes—
37#3788—24no—
38#3787—22no—
39#3787Q814yescomplemented
40C32×C4⋊C4C2×C412yes—
41C32×C4⋊C4C2×C412yes—
42C32×C42C2×C411yescharacteristic
43#3752C2×C414yes—
44C4⋊(C3⋊Dic3)C2×C412yes—
45C4⋊(C3⋊Dic3)C2×C412yes—
46C4⋊(C3⋊Dic3)C2×C414yes—
47#3750C2×C414yes—
48C4×C3⋊Dic3C2×C411yescharacteristic
49C4×C3⋊Dic3C2314yes—
50C4×C3⋊Dic3C2311yescharacteristic
51C4×C3⋊Dic3C2311yescharacteristic
52#2961—91nomaximal, Sylow
53C3×C4⋊Q8—22no—
54#946—64no—
55Q8×Dic3—64no—
56#897—64no—
57#892—64no—
58#890—64no—
59#887—64no—
60C42×D3—62no—
61#869—62no—
62C22×C3⋊D3C22×C411yescharacteristic
63C32×Q8—42no—
64C2×C32×C4C22×C414yes—
65C2×C32×C4C22×C411yescharacteristic
66C2×C32×C4C22×C411yescharacteristic
67C2×C32×C4C22×C411yescharacteristic
68C2×C3⋊Dic3C22×C411yescharacteristic
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C22×C414yes—
71C2×C3⋊Dic3C2411yescharacteristic
72C4×C3⋊D3—41no—
73C4×C3⋊D3—41no—
74C4×C3⋊D3C2×Q812yes—
75C4×C3⋊D3#4112yes—
76#634—42no—
77#622—22no—
78#622—24no—
79#622C2×Q814yes—
80#533—91no—
81#446—94no—
82#446—94no—
83#424—92no—
84#423—91no—
85#405—92no—
86C2×#97—91no—
87C2×C3×Q8—24no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×C4×D3—62no—
91C2×Dic6—64no—
92C3×C4⋊C4—24no—
93C3×C4⋊C4—24no—
94C3×C42—22no—
95(C2×D3)⋊C4—68no—
96C4⋊Dic3—64no—
97C4⋊Dic3—64no—
98C4⋊Dic3—68no—
99Dic3⋊C4—68no—
100C4×Dic3—62no—
101C4×Dic3—62no—
102C4×Dic3—62no—
103C4×Dic3—68no—
104C22×C32C23×C411yescharacteristic
105C2×C3⋊D3—21no—
106C2×C3⋊D3—21no—
107C2×C3⋊D3C4×Q812yes—
108C32×C4—21no—
109C32×C4—21no—
110C32×C4—24no—
111C32×C4C4×Q812yes—
112C3⋊Dic3—24no—
113C3⋊Dic3—21no—
114C3⋊Dic3—21no—
115C3⋊Dic3C22×Q811yescharacteristic
116C3⋊Dic3C2×#4111yescharacteristic
117C2×M16—92no—
118C22×C8—91no—
119C22×C8—91no—
120C4⋊Q8—91no—
121C4⋊Q8#15711yescharacteristic
122#125—92no—
123C22⋊Q8—92no—
124C22⋊Q8—92no—
125C4×Q8—92no—
126C4×Q8—92no—
127#117—92no—
128C2×C42—91no—
129C4⋊C8—94no—
130C4⋊C8—92no—
131C4⋊C8—92no—
132C4⋊C8—94no—
133#97—92no—
134#97—92no—
135#97—94no—
136C4×C8—94no—
137C22×D3—62no—
138C3×Q8—48no—
139C2×C3×C4—22no—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—28no—
143C2×Dic3—62no—
144C2×Dic3—62no—
145C2×Dic3—62no—
146C2×Dic3—68no—
147C4×D3—64no—
148C4×D3—64no—
149C4×D3—124no—
150C4×D3—124no—
151Dic6—128no—
152C2×C32C2×C4×Q811yescharacteristic
153C2×C32#56811yescharacteristic
154C2×C32#56811yescharacteristic
155C3⋊D3—22no—
156C2×Q8—92no—
157C2×Q8C2×#15712yes—
158C22×C4—91no—
159C22×C4—91no—
160C22×C4—91no—
161M16—184no—
162C2×C8—92no—
163C2×C8—94no—
164C2×C8—94no—
165C2×C8—92no—
166C2×C8—182no—
167C4⋊C4—92no—
168C4⋊C4—94no—
169C4⋊C4—94no—
170C4⋊C4—92no—
171C4⋊C4C2×#15712yes—
172C4⋊C4C2×#15712yes—
173C22⋊C4—94no—
174C42—94no—
175C42—91no—
176C42—91no—
177C42—91no—
178C42C2×#15711yescharacteristic
179C22×C3—22no—
180C2×D3—64no—
181C2×D3—122no—
182C2×D3—122no—
183C3×C4—24no—
184C3×C4—24no—
185C3×C4—24no—
186C3×C4—48no—
187Dic3—62no—
188Dic3—62no—
189Dic3—128no—
190Dic3—122no—
191Dic3—122no—
192C32#296111yescharacteristic, complemented, Sylow
193C23—91no—
194Q8—42no—
195Q8—362no—
196C2×C4—91no—
197C2×C4—92no—
198C2×C4—92no—
199C2×C4—91no—
200C2×C4—91no—
201C2×C4—94no—
202C2×C4—361no—
203C2×C4—361no—
204C2×C4C22×#15711yescharacteristic
205C2×C4C22×#15711yescharacteristic
206C2×C4C22×#15714yes—
207C2×C4C22×#15711yescharacteristic
208C8—94no—
209C8—182no—
210C8—184no—
211C2×C3—22no—
212C2×C3—22no—
213C2×C3—22no—
214D3—124no—
215C22—92no—
216C22—181no—
217C22—181no—
218C22C23×#15711yescharacteristic
219C4—21no—
220C4—24no—
221C4—21no—
222C4—91no—
223C4—91no—
224C4—181no—
225C4—181no—
226C4—184no—
227C4Q8×#15712yes—
228C3—22no—
229C2—182no—
230C2#1059664011yescharacteristic
231C2#1059664411yescharacteristic
232C2C2×Q8×#15711yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4⋊Q8C4
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C3⋊Dic3C24
hypercenterC4⋊Q8#157
hypocenterC32#2961
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10593835C2semidirect
4. #10593754C2semidirect
39. #3787Q8semidirect
192. C32#2961semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105938352
#105937552
#105937542
#105937482
#105937292
#105937232
#29619