Finite Group Databasebeta

← #11785798

Subgroups — #11785798

Order 1152.

670 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C22×#3724C211yesmaximal, characteristic
2C2×C22⋊#622C211yesmaximal, characteristic
3#10591720C211yesmaximal, characteristic
4#10590075C214yesmaximal, complemented
5C23×C3⋊Dic3C2211yescharacteristic
6C23×C3×Dic3—21no—
7C22×#622C2212yes—
8C2×C3×#217—21no—
9C2×#3724—21no—
10C2×#3724—22no—
11C2×#3724C414yescomplemented
12C2×#3724C2212yes—
13C2×#3724C2212yes—
14C22⋊#622—22no—
15#63579—21no—
16C22×Dic3⋊C4—61no—
17#4942—61no—
18C24×C32D411yescharacteristic
19C22×C3⋊Dic3—24no—
20C22×C3⋊Dic3C2×C412yes—
21C22×C3⋊Dic3D411yescharacteristic
22C22×C3⋊Dic3D412yes—
23C22×C3⋊Dic3C2311yescharacteristic
24C22×C3×Dic3—24no—
25C22×C3×Dic3—22no—
26C22×C3×Dic3—22no—
27C22×C3×Dic3—44no—
28C2×#622—22no—
29C2×#622—24no—
30C3×#217—42no—
31#3724—24no—
32#3724—22no—
33#3724—24no—
34#3724C2×C414yes—
35#1824—91nomaximal, Sylow
36C23×C3×C4—61no—
37C23×Dic3—21no—
38C23×Dic3—61no—
39C23×Dic3—61no—
40C2×C3×C22⋊C4—61no—
41C2×#217—21no—
42C2×Dic3⋊C4—64no—
43C2×Dic3⋊C4—62no—
44C2×Dic3⋊C4—62no—
45C2×Dic3⋊C4—62no—
46C2×Dic3⋊C4—64no—
47C3⋊#95—62no—
48C23×C32—22no—
49C23×C32—22no—
50C23×C32C22⋊C412yes—
51C23×C32SD1612yes—
52C23×C32Q1612yes—
53C23×C32C2×D411yescharacteristic
54C2×C3⋊Dic3—22no—
55C2×C3⋊Dic3—24no—
56C2×C3⋊Dic3—24no—
57C2×C3⋊Dic3C22⋊C412yes—
58C2×C3⋊Dic3C22×C411yescharacteristic
59C2×C3⋊Dic3C2×D411yescharacteristic
60C2×C3⋊Dic3#4114yes—
61C2×C3×Dic3—24no—
62C2×C3×Dic3—48no—
63C2×C3×Dic3—44no—
64C2×C3×Dic3—42no—
65C2×C3×Dic3—42no—
66C2×C3×Dic3—42no—
67#622—42no—
68C22×C4⋊C4—91no—
69C2×C22⋊C8—91no—
70#380—91no—
71#340—94no—
72C24×C3—21no—
73C24×C3—21no—
74C22×C3×C4—62no—
75C22×C3×C4—64no—
76C22×C3×C4—62no—
77C22×C3×C4—124no—
78C22×Dic3—22no—
79C22×Dic3—24no—
80C22×Dic3—22no—
81C22×Dic3—44no—
82C22×Dic3—62no—
83C22×Dic3—61no—
84C22×Dic3—62no—
85C22×Dic3—61no—
86C22×Dic3—61no—
87C22×Dic3—61no—
88C22×Dic3—62no—
89C22×Dic3—62no—
90C22×Dic3—68no—
91C22×Dic3—124no—
92C3×C22⋊C4—122no—
93#217—42no—
94Dic3⋊C4—64no—
95Dic3⋊C4—68no—
96Dic3⋊C4—64no—
97Dic3⋊C4—124no—
98C22×C32—22no—
99C22×C32—22no—
100C22×C32—24no—
101C22×C32—24no—
102C22×C32#10314yes—
103C22×C32C2×C22⋊C411yescharacteristic
104C22×C32#12312yes—
105C22×C32C2×SD1611yescharacteristic
106C22×C32C2×Q1611yescharacteristic
107C22×C32AGL(1,ℤ/8)12yes—
108C3⋊Dic3—22no—
109C3⋊Dic3#11712yes—
110C3⋊Dic3#12312yes—
111C3×Dic3—44no—
112C3×Dic3—82no—
113C23×C4—61no—
114C23×C4—91no—
115C22×C8—92no—
116C2×C4⋊C4—92no—
117C2×C4⋊C4—94no—
118C2×C4⋊C4—92no—
119C2×C4⋊C4—181no—
120C2×C4⋊C4—182no—
121C2×C22⋊C4—61no—
122C22⋊C8—182no—
123#95—181no—
124C23×C3—24no—
125C23×C3—24no—
126C23×C3—21no—
127C23×C3—21no—
128C23×C3—22no—
129C23×C3—22no—
130C23×C3—22no—
131C23×C3—22no—
132C23×C3—22no—
133C23×C3—22no—
134C23×C3—42no—
135C23×C3—42no—
136C2×C3×C4—64no—
137C2×C3×C4—128no—
138C2×C3×C4—124no—
139C2×C3×C4—122no—
140C2×C3×C4—122no—
141C2×C3×C4—122no—
142C2×Dic3—24no—
143C2×Dic3—48no—
144C2×Dic3—44no—
145C2×Dic3—42no—
146C2×Dic3—42no—
147C2×Dic3—42no—
148C2×Dic3—62no—
149C2×Dic3—61no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C2×Dic3—64no—
154C2×Dic3—64no—
155C2×Dic3—62no—
156C2×Dic3—68no—
157C2×Dic3—68no—
158C2×Dic3—64no—
159C2×Dic3—124no—
160C2×Dic3—124no—
161C2×Dic3—122no—
162C2×C32—24no—
163C2×C32#38111yescharacteristic
164C2×C32C2×#10311yescharacteristic
165C2×C32#41811yescharacteristic
166C2×C32#48112yes—
167C2×C32#48412yes—
168C24GO+(4,𝔽2)11yescharacteristic
169C22×C4—62no—
170C22×C4—64no—
171C22×C4—62no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—92no—
175C22×C4—92no—
176C22×C4—124no—
177C22×C4—184no—
178C2×C8—182no—
179C2×C8—184no—
180C4⋊C4—94no—
181C4⋊C4—182no—
182C4⋊C4—184no—
183C4⋊C4—184no—
184C22⋊C4—122no—
185C22×C3—24no—
186C22×C3—24no—
187C22×C3—28no—
188C22×C3—28no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—22no—
192C22×C3—22no—
193C22×C3—22no—
194C22×C3—22no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—24no—
200C22×C3—24no—
201C22×C3—42no—
202C22×C3—42no—
203C22×C3—44no—
204C22×C3—44no—
205C3×C4—124no—
206C3×C4—242no—
207Dic3—44no—
208Dic3—62no—
209Dic3—62no—
210Dic3—62no—
211Dic3—62no—
212Dic3—64no—
213Dic3—82no—
214Dic3—122no—
215C32#182411yescharacteristic, complemented, Sylow
216C23—22no—
217C23—22no—
218C23D32⋊C412yes—
219C23#377512yes—
220C23#377612yes—
221C23C2×GO+(4,𝔽2)11yescharacteristic
222C2×C4—64no—
223C2×C4—91no—
224C2×C4—91no—
225C2×C4—94no—
226C2×C4—92no—
227C2×C4—128no—
228C2×C4—124no—
229C2×C4—122no—
230C2×C4—122no—
231C2×C4—122no—
232C2×C4—184no—
233C2×C4—184no—
234C2×C4—182no—
235C8—362no—
236C2×C3—28no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—22no—
242C2×C3—22no—
243C2×C3—22no—
244C2×C3—22no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—44no—
248C22—22no—
249C22—22no—
250C22—24no—
251C22—24no—
252C22#6374014yes—
253C22C2×D32⋊C411yescharacteristic
254C22#6423312yes—
255C22#6423612yes—
256C22C2×#377511yescharacteristic
257C22C2×#377611yescharacteristic
258C4—92no—
259C4—92no—
260C4—124no—
261C4—182no—
262C4—242no—
263C3—21no—
264C3—21no—
265C2—24no—
266C2#1059348811yescharacteristic
267C2#1059349311yescharacteristic
268C2#1059349712yes—
269C2#1059350012yes—
270C2C2×#6374011yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
Fitting, prime radicalC24×C32D4
socleC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32#1824
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
4. #10590075C2semidirect
11. C2×#3724C4semidirect
215. C32#1824semidirect

Maximal subgroups

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

subgroupindex
C22×#37242
C2×C22⋊#6222
#105917202
#105900752
#18249