Finite Group Databasebeta

← #11790083

Subgroups — #11790083

Order 1152.

390 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C4×C4⋊#157C211yesmaximal, characteristic
2C2×#63732C212yesmaximal
3#10590331C211yesmaximal, characteristic
4#10590322C211yesmaximal, characteristic
5#10590044C212yesmaximal
6C2×C4⋊#157C412yes—
7C2×C4×#157C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C2×#3710C2212yes—
10C2×#3710C2211yescharacteristic
11C2×#3710C2211yescharacteristic
12#63781C411yescharacteristic
13#63781C411yescharacteristic
14#63732—24no—
15C3×C4⋊(C3⋊C8)—21no—
16C3×#803—21no—
17#63572—21no—
18#63555—21no—
19D3×C4⋊C8—61no—
20D3×#97—61no—
21C22×#157C2×C412yes—
22C22×#157C2×C412yes—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C4⋊#157—24no—
27C4×#157—22no—
28C4×#157—22no—
29C32×C42D411yescharacteristic
30C4×C3⋊Dic3D411yescharacteristic
31C4×C3⋊Dic3Q811yescharacteristic
32C4×C3⋊Dic3Q811yescharacteristic
33C2×C3×C3⋊C8—21no—
34C2×C3×C3⋊C8—21no—
35C2×C3×C3⋊C8—22no—
36#3710—21no—
37#3710—21no—
38#3710—22no—
39#3710—22no—
40#3710D412yes—
41#3710Q812yes—
42#1940—91nomaximal, Sylow
43C2×D3×C8—61no—
44C2×D3×C8—61no—
45C2×D3×C8—62no—
46C42×D3—61no—
47C42×D3—61no—
48C3×C4⋊C8—61no—
49C3×#97—61no—
50#815—61no—
51#815—61no—
52Dic3⋊C8—62no—
53C4⋊(C3⋊C8)—21no—
54#803—21no—
55C22×C3⋊D3C22×C411yescharacteristic
56C2×#157—22no—
57C2×#157—22no—
58C2×#157—22no—
59C2×#157—22no—
60C2×#157—22no—
61C2×#157M1614yes—
62C2×C32×C4C4⋊C411yescharacteristic
63C2×C32×C4C4⋊C411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C3⋊Dic3C4⋊C411yescharacteristic
66C2×C3⋊Dic3C4⋊C411yescharacteristic
67C2×C3⋊Dic3C2×Q811yescharacteristic
68C4×C3⋊D3—22no—
69C4×C3⋊D3—22no—
70C4×C3⋊D3C2×D411yescharacteristic
71C4×C3⋊D3C2×Q811yescharacteristic
72C4×C3⋊D3#4111yescharacteristic
73C4×C3⋊D3#4111yescharacteristic
74C3×C3⋊C8—22no—
75C3×C3⋊C8—22no—
76C3×C3⋊C8—42no—
77C2×C4⋊C8—91no—
78C2×C4⋊C8—92no—
79C2×#97—91no—
80C4×C4⋊C4—91no—
81#336—92no—
82C2×C4×D3—61no—
83C2×C4×D3—61no—
84C2×C4×D3—61no—
85C2×C4×D3—61no—
86C2×C4×D3—61no—
87C2×C4×D3—61no—
88C2×C3×C8—61no—
89C2×C3×C8—61no—
90C2×C3×C8—62no—
91C3×C42—21no—
92C3×C42—21no—
93C4×Dic3—61no—
94C4×Dic3—61no—
95C4×Dic3—61no—
96C4×Dic3—61no—
97C4×Dic3—61no—
98C4×Dic3—61no—
99C2×C3⋊C8—21no—
100C2×C3⋊C8—21no—
101C2×C3⋊C8—22no—
102D3×C8—62no—
103D3×C8—62no—
104D3×C8—62no—
105D3×C8—62no—
106D3×C8—122no—
107D3×C8—122no—
108C22×C32C2×C4⋊C411yescharacteristic
109C2×C3⋊D3C4×D411yescharacteristic
110C2×C3⋊D3C4×Q811yescharacteristic
111C2×C3⋊D3C2×M1612yes—
112C2×C3⋊D3#13112yes—
113#157—24no—
114#157—42no—
115C32×C4—21no—
116C32×C4—21no—
117C32×C4#12111yescharacteristic
118C32×C4C22⋊Q811yescharacteristic
119C3⋊Dic3—21no—
120C3⋊Dic3—21no—
121C3⋊Dic3#12511yescharacteristic
122C3⋊Dic3C4⋊Q811yescharacteristic
123C22×C8—91no—
124C22×C8—91no—
125C22×C8—92no—
126C2×C4⋊C4—92no—
127C2×C42—91no—
128C2×C42—92no—
129C4⋊C8—61no—
130C4⋊C8—181no—
131C4⋊C8—184no—
132#97—61no—
133#97—181no—
134#95—91no—
135#95—91no—
136C22×D3—61no—
137C22×D3—61no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—21no—
143C2×C3×C4—21no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147C2×Dic3—61no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150C4×D3—61no—
151C4×D3—61no—
152C4×D3—61no—
153C4×D3—61no—
154C4×D3—61no—
155C4×D3—61no—
156C4×D3—61no—
157C4×D3—61no—
158C4×D3—64no—
159C4×D3—122no—
160C4×D3—122no—
161C4×D3—122no—
162C3×C8—62no—
163C3×C8—62no—
164C3×C8—122no—
165C3⋊C8—22no—
166C3⋊C8—22no—
167C3⋊C8—42no—
168C2×C32#38911yescharacteristic
169C2×C32#42311yescharacteristic
170C2×C32#42411yescharacteristic
171C3⋊D3#43512yes—
172C3⋊D3#44612yes—
173C22×C4—91no—
174C22×C4—92no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—92no—
178C2×C8—61no—
179C2×C8—61no—
180C2×C8—62no—
181C2×C8—92no—
182C2×C8—92no—
183C2×C8—181no—
184C2×C8—181no—
185C2×C8—182no—
186C2×C8—182no—
187C4⋊C4—184no—
188C42—91no—
189C42—91no—
190C42—91no—
191C42—182no—
192C42—182no—
193C42GO+(4,𝔽2)11yescharacteristic
194C22×C3—21no—
195C22×C3—21no—
196C2×D3—61no—
197C2×D3—61no—
198C2×D3—61no—
199C2×D3—61no—
200C2×D3—62no—
201C2×D3—62no—
202C2×D3—62no—
203C2×D3—62no—
204C3×C4—22no—
205C3×C4—21no—
206C3×C4—21no—
207C3×C4—21no—
208C3×C4—21no—
209C3×C4—41no—
210C3×C4—41no—
211C3×C4—41no—
212Dic3—61no—
213Dic3—61no—
214Dic3—61no—
215Dic3—61no—
216Dic3—62no—
217Dic3—121no—
218Dic3—121no—
219Dic3—121no—
220C32#194011yescharacteristic, complemented, Sylow
221C23—91no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—91no—
225C2×C4—91no—
226C2×C4—91no—
227C2×C4—94no—
228C2×C4—91no—
229C2×C4—91no—
230C2×C4—182no—
231C2×C4—182no—
232C2×C4—182no—
233C2×C4—182no—
234C2×C4—182no—
235C2×C4—182no—
236C2×C4—182no—
237C2×C4#377311yescharacteristic
238C2×C4#377311yescharacteristic
239C2×C4C2×GO+(4,𝔽2)11yescharacteristic
240C8—62no—
241C8—62no—
242C8—122no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249D3—62no—
250D3—62no—
251D3—62no—
252D3—62no—
253C22—92no—
254C22—92no—
255C22—91no—
256C22—91no—
257C22C2×#377311yescharacteristic
258C4—21no—
259C4—21no—
260C4—91no—
261C4—91no—
262C4—184no—
263C4—181no—
264C4—181no—
265C4—362no—
266C4D32⋊Q811yescharacteristic
267C4#6423011yescharacteristic
268C3—21no—
269C3—21no—
270C2—92no—
271C2—92no—
272C2#1059332711yescharacteristic
273C2#1059332811yescharacteristic
274C2#1059341211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutator, prime radicalC22×C3⋊D3C22×C4
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1940
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
220. C32#1940semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#1572
C2×#637322
#105903312
#105903222
#105900442
#19409