Finite Group Databasebeta

← #11785772

Subgroups — #11785772

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—42no—
28C22×C3×Dic3—42no—
29C2×#622—22no—
30C2×#622—24no—
31C3×#217—42no—
32#3724—24no—
33#3724—22no—
34#3724—24no—
35#3724C2×C414yes—
36#1823—91nomaximal, Sylow
37C23×C3×C4—61no—
38C23×Dic3—21no—
39C23×Dic3—61no—
40C23×Dic3—61no—
41C2×C3×C22⋊C4—61no—
42C2×#217—21no—
43C2×Dic3⋊C4—64no—
44C2×Dic3⋊C4—62no—
45C2×Dic3⋊C4—62no—
46C2×Dic3⋊C4—62no—
47C2×Dic3⋊C4—64no—
48C3⋊#95—62no—
49C23×C32—22no—
50C23×C32—22no—
51C23×C32C22⋊C412yes—
52C23×C32D812yes—
53C23×C32SD1612yes—
54C23×C32C2×D411yescharacteristic
55C2×C3⋊Dic3—22no—
56C2×C3⋊Dic3—24no—
57C2×C3⋊Dic3—24no—
58C2×C3⋊Dic3C22⋊C412yes—
59C2×C3⋊Dic3C22×C411yescharacteristic
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3#4114yes—
62C2×C3×Dic3—24no—
63C2×C3×Dic3—48no—
64C2×C3×Dic3—42no—
65C2×C3×Dic3—42no—
66C2×C3×Dic3—42no—
67C2×C3×Dic3—42no—
68C2×C3×Dic3—42no—
69#622—42no—
70C22×C4⋊C4—91no—
71C2×C22⋊C8—91no—
72#380—91no—
73#340—94no—
74C24×C3—21no—
75C24×C3—21no—
76C22×C3×C4—62no—
77C22×C3×C4—64no—
78C22×C3×C4—62no—
79C22×C3×C4—122no—
80C22×C3×C4—122no—
81C22×Dic3—22no—
82C22×Dic3—24no—
83C22×Dic3—22no—
84C22×Dic3—42no—
85C22×Dic3—42no—
86C22×Dic3—62no—
87C22×Dic3—61no—
88C22×Dic3—62no—
89C22×Dic3—61no—
90C22×Dic3—61no—
91C22×Dic3—61no—
92C22×Dic3—62no—
93C22×Dic3—62no—
94C22×Dic3—68no—
95C22×Dic3—124no—
96C3×C22⋊C4—122no—
97#217—42no—
98Dic3⋊C4—64no—
99Dic3⋊C4—68no—
100Dic3⋊C4—64no—
101Dic3⋊C4—124no—
102C22×C32—22no—
103C22×C32—22no—
104C22×C32—24no—
105C22×C32—24no—
106C22×C32#10214yes—
107C22×C32C2×C22⋊C411yescharacteristic
108C22×C32#12312yes—
109C22×C32C2×D811yescharacteristic
110C22×C32C2×SD1611yescharacteristic
111C22×C32#13712yes—
112C3⋊Dic3—22no—
113C3⋊Dic3#11712yes—
114C3⋊Dic3#12312yes—
115C3×Dic3—44no—
116C3×Dic3—82no—
117C23×C4—61no—
118C23×C4—91no—
119C22×C8—92no—
120C2×C4⋊C4—92no—
121C2×C4⋊C4—94no—
122C2×C4⋊C4—92no—
123C2×C4⋊C4—181no—
124C2×C4⋊C4—182no—
125C2×C22⋊C4—61no—
126C22⋊C8—182no—
127#95—181no—
128C23×C3—24no—
129C23×C3—24no—
130C23×C3—21no—
131C23×C3—21no—
132C23×C3—22no—
133C23×C3—22no—
134C23×C3—22no—
135C23×C3—22no—
136C23×C3—22no—
137C23×C3—22no—
138C23×C3—42no—
139C23×C3—42no—
140C2×C3×C4—64no—
141C2×C3×C4—122no—
142C2×C3×C4—122no—
143C2×C3×C4—128no—
144C2×C3×C4—122no—
145C2×C3×C4—122no—
146C2×C3×C4—122no—
147C2×Dic3—24no—
148C2×Dic3—42no—
149C2×Dic3—42no—
150C2×Dic3—48no—
151C2×Dic3—42no—
152C2×Dic3—42no—
153C2×Dic3—42no—
154C2×Dic3—62no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—64no—
160C2×Dic3—64no—
161C2×Dic3—62no—
162C2×Dic3—68no—
163C2×Dic3—68no—
164C2×Dic3—64no—
165C2×Dic3—124no—
166C2×Dic3—124no—
167C2×Dic3—122no—
168C2×C32—24no—
169C2×C32#38111yescharacteristic
170C2×C32C2×#10211yescharacteristic
171C2×C32#41911yescharacteristic
172C2×C32#48012yes—
173C2×C32#48312yes—
174C24GO+(4,𝔽2)11yescharacteristic
175C22×C4—62no—
176C22×C4—64no—
177C22×C4—62no—
178C22×C4—91no—
179C22×C4—91no—
180C22×C4—92no—
181C22×C4—92no—
182C22×C4—122no—
183C22×C4—122no—
184C22×C4—184no—
185C2×C8—182no—
186C2×C8—184no—
187C4⋊C4—94no—
188C4⋊C4—182no—
189C4⋊C4—184no—
190C4⋊C4—184no—
191C22⋊C4—122no—
192C22×C3—24no—
193C22×C3—28no—
194C22×C3—24no—
195C22×C3—28no—
196C22×C3—21no—
197C22×C3—21no—
198C22×C3—22no—
199C22×C3—22no—
200C22×C3—21no—
201C22×C3—21no—
202C22×C3—21no—
203C22×C3—21no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—24no—
207C22×C3—24no—
208C22×C3—42no—
209C22×C3—44no—
210C22×C3—42no—
211C22×C3—44no—
212C3×C4—124no—
213C3×C4—242no—
214Dic3—44no—
215Dic3—62no—
216Dic3—62no—
217Dic3—62no—
218Dic3—62no—
219Dic3—64no—
220Dic3—82no—
221Dic3—122no—
222C32#182311yescharacteristic, complemented, Sylow
223C23—22no—
224C23—22no—
225C23D32⋊C412yes—
226C23#377412yes—
227C23#377512yes—
228C23C2×GO+(4,𝔽2)11yescharacteristic
229C2×C4—64no—
230C2×C4—91no—
231C2×C4—91no—
232C2×C4—94no—
233C2×C4—92no—
234C2×C4—122no—
235C2×C4—122no—
236C2×C4—128no—
237C2×C4—122no—
238C2×C4—122no—
239C2×C4—122no—
240C2×C4—184no—
241C2×C4—184no—
242C2×C4—182no—
243C8—362no—
244C2×C3—28no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—22no—
250C2×C3—22no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—22no—
254C2×C3—22no—
255C2×C3—44no—
256C22—22no—
257C22—24no—
258C22—22no—
259C22—24no—
260C22#6373914yes—
261C22C2×D32⋊C411yescharacteristic
262C22#6423312yes—
263C22C2×#377411yescharacteristic
264C22C2×#377511yescharacteristic
265C22#6423912yes—
266C4—92no—
267C4—92no—
268C4—124no—
269C4—182no—
270C4—242no—
271C3—21no—
272C3—21no—
273C2—24no—
274C2#1059348811yescharacteristic
275C2C2×#6373911yescharacteristic
276C2#1059349212yes—
277C2#1059350311yescharacteristic
278C2#1059350412yes—
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#1823
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
222. C32#1823semidirect

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
#18239