Finite Group Databasebeta

← #11791637

Subgroups — #11791637

Order 1152.

534 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#63873C211yesmaximal, characteristic
2C2×C4⋊#622C211yesmaximal, characteristic
3C4×#3724C211yesmaximal, characteristic
4#10590075C214yesmaximal
5C22×C3×Dic6—21no—
6C22×#622C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×C4×Dic3—21no—
9C2×#3724—21no—
10C2×#3724C2212yes—
11C2×#3724C2212yes—
12#63873—22no—
13#63873C414yescomplemented
14C4⋊#622—22no—
15#63579—21no—
16C2×#944—61no—
17C4×Dic3⋊C4—61no—
18C22×C32×C4D411yescharacteristic
19C22×C3⋊Dic3D411yescharacteristic
20C22×C3⋊Dic3C2311yescharacteristic
21C22×C3×Dic3—22no—
22C22×C3×Dic3—22no—
23C2×C3×Dic6—24no—
24C2×C3×Dic6—42no—
25C2×C3×Dic6—42no—
26C2×#622—22no—
27C2×#622—24no—
28C4×C3⋊Dic3C2×C412yes—
29C4×C3⋊Dic3D412yes—
30C3×C4×Dic3—42no—
31#3724—24no—
32#3724—22no—
33#3724—22no—
34#3724C2×C414yes—
35#3724Q814yescomplemented
36#1988—91nomaximal, Sylow
37C22×C3×Q8—61no—
38C22×Dic6—21no—
39C2×C3×C42—61no—
40#944—64no—
41#944—64no—
42C2×Dic3⋊C4—62no—
43C2×Dic3⋊C4—62no—
44C2×Dic3⋊C4—62no—
45C2×C4×Dic3—21no—
46C2×C4×Dic3—61no—
47C2×C4×Dic3—61no—
48C3⋊#95—62no—
49C23×C32C2×D411yescharacteristic
50C2×C32×C4C22⋊C412yes—
51C2×C32×C4D812yes—
52C2×C32×C4SD1612yes—
53C2×C3⋊Dic3—22no—
54C2×C3⋊Dic3C22⋊C412yes—
55C2×C3⋊Dic3C22×C411yescharacteristic
56C2×C3⋊Dic3C2×D411yescharacteristic
57C2×C3⋊Dic3C2×Q812yes—
58C2×C3⋊Dic3#4112yes—
59C2×C3×Dic3—24no—
60C2×C3×Dic3—24no—
61C2×C3×Dic3—42no—
62C2×C3×Dic3—42no—
63C2×C3×Dic3—42no—
64C2×C3×Dic3—42no—
65C3×Dic6—48no—
66#622—42no—
67C2×C4⋊Q8—91no—
68C2×C4⋊C8—91no—
69C4×C4⋊C4—91no—
70#340—94no—
71C2×C3×Q8—64no—
72C2×C3×Q8—122no—
73C2×C3×Q8—122no—
74C22×C3×C4—21no—
75C22×C3×C4—21no—
76C22×C3×C4—62no—
77C22×C3×C4—62no—
78C22×Dic3—22no—
79C22×Dic3—22no—
80C22×Dic3—61no—
81C22×Dic3—61no—
82C22×Dic3—61no—
83C22×Dic3—61no—
84C2×Dic6—24no—
85C2×Dic6—42no—
86C2×Dic6—42no—
87C3×C42—122no—
88Dic3⋊C4—64no—
89Dic3⋊C4—64no—
90Dic3⋊C4—64no—
91Dic3⋊C4—64no—
92Dic3⋊C4—68no—
93C4×Dic3—42no—
94C4×Dic3—62no—
95C4×Dic3—62no—
96C4×Dic3—62no—
97C4×Dic3—62no—
98C22×C32C2×C22⋊C411yescharacteristic
99C22×C32C22⋊Q812yes—
100C22×C32C2×D811yescharacteristic
101C22×C32C2×SD1611yescharacteristic
102C22×C32#13712yes—
103C32×C4#10214yes—
104C3⋊Dic3—22no—
105C3⋊Dic3C4×Q812yes—
106C3⋊Dic3#12411yescharacteristic
107C3⋊Dic3C4⋊Q811yescharacteristic
108C3×Dic3—44no—
109C3×Dic3—44no—
110C22×Q8—61no—
111C22×C8—92no—
112C4⋊Q8—94no—
113C4⋊Q8—182no—
114C2×C4⋊C4—92no—
115C2×C4⋊C4—92no—
116C2×C4⋊C4—181no—
117C2×C42—61no—
118C2×C42—91no—
119C4⋊C8—182no—
120#95—181no—
121C23×C3—21no—
122C23×C3—21no—
123C3×Q8—128no—
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×C3×C4—22no—
127C2×C3×C4—22no—
128C2×C3×C4—22no—
129C2×C3×C4—22no—
130C2×C3×C4—64no—
131C2×C3×C4—64no—
132C2×C3×C4—122no—
133C2×C3×C4—122no—
134C2×C3×C4—122no—
135C2×C3×C4—122no—
136C2×Dic3—24no—
137C2×Dic3—24no—
138C2×Dic3—42no—
139C2×Dic3—42no—
140C2×Dic3—42no—
141C2×Dic3—42no—
142C2×Dic3—62no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147C2×Dic3—62no—
148C2×Dic3—62no—
149C2×Dic3—62no—
150C2×Dic3—62no—
151C2×Dic3—62no—
152C2×Dic3—64no—
153C2×Dic3—122no—
154Dic6—48no—
155C2×C32#39111yescharacteristic
156C2×C32C2×#10211yescharacteristic
157C2×C32#41911yescharacteristic
158C2×C32#47412yes—
159C2×C32#47512yes—
160C2×Q8—64no—
161C2×Q8—122no—
162C2×Q8—122no—
163C22×C4—62no—
164C22×C4—62no—
165C22×C4—91no—
166C22×C4—91no—
167C22×C4GO+(4,𝔽2)11yescharacteristic
168C2×C8—182no—
169C2×C8—184no—
170C4⋊C4—94no—
171C4⋊C4—94no—
172C4⋊C4—182no—
173C4⋊C4—182no—
174C4⋊C4—184no—
175C42—92no—
176C42—92no—
177C42—122no—
178C22×C3—22no—
179C22×C3—22no—
180C22×C3—22no—
181C22×C3—22no—
182C22×C3—21no—
183C22×C3—21no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—21no—
188C3×C4—24no—
189C3×C4—24no—
190C3×C4—124no—
191C3×C4—124no—
192Dic3—44no—
193Dic3—44no—
194Dic3—62no—
195Dic3—62no—
196Dic3—61no—
197Dic3—61no—
198Dic3—61no—
199Dic3—61no—
200Dic3—64no—
201Dic3—122no—
202C32#198811yescharacteristic, complemented, Sylow
203C23C2×GO+(4,𝔽2)11yescharacteristic
204Q8—128no—
205C2×C4—64no—
206C2×C4—64no—
207C2×C4—92no—
208C2×C4—92no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—92no—
212C2×C4—122no—
213C2×C4—122no—
214C2×C4—122no—
215C2×C4—122no—
216C2×C4—182no—
217C2×C4D32⋊C412yes—
218C2×C4#377412yes—
219C2×C4#377512yes—
220C8—362no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3—22no—
224C2×C3—22no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3—22no—
228C2×C3—22no—
229C2×C3—21no—
230C2×C3—21no—
231C22D32⋊Q812yes—
232C22#6422612yes—
233C22C2×D32⋊C411yescharacteristic
234C22C2×#377411yescharacteristic
235C22C2×#377511yescharacteristic
236C4—91no—
237C4—91no—
238C4—92no—
239C4—124no—
240C4—124no—
241C4—182no—
242C4#6373914yes—
243C3—21no—
244C3—21no—
245C2#1059334111yescharacteristic
246C2#1059334712yes—
247C2#1059337411yescharacteristic
248C2#1059337612yes—
249C2C2×#6373911yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1988
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
13. #63873C4semidirect
35. #3724Q8semidirect
202. C32#1988semidirect

Maximal subgroups

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

subgroupindex
C2×#638732
C2×C4⋊#6222
C4×#37242
#105900752
#19889