Finite Group Databasebeta

← #11790151

Subgroups — #11790151

Order 1152.

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

normal subgroups only

This group has 394 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
1C2×#63769C211yesmaximal, characteristic
2#10593412C212yesmaximal
3#10590687C211yesmaximal, characteristic
4C8×#624C211yesmaximal, characteristic
5#10590049C212yesmaximal
6C2×C4⋊#157C2212yes—
7C2×#3773—22no—
8C2×C8×C3⋊D3C2211yescharacteristic
9#63900C2212yes—
10C4×#624C2211yescharacteristic
11C2×#3710C2211yescharacteristic
12#63769C414yescomplemented
13#63737—22no—
14C3×#818—21no—
15C3×C8×Dic3—21no—
16#63576—21no—
17Dic3×C3⋊C8—21no—
18D3×#107—61no—
19C4×D3×C8—61no—
20C22×#157—22no—
21C2×C4×C3⋊D3C2311yescharacteristic
22C2×#624—22no—
23C2×#624D411yescharacteristic
24C2×#624D411yescharacteristic
25C4⋊#157—22no—
26C4⋊#157C2×C414yes—
27#3773—44no—
28C2×C32×C8D411yescharacteristic
29C2×C3⋊(C3⋊C8)D411yescharacteristic
30C8×C3⋊D3C2×C412yes—
31C8×C3⋊D3Q812yes—
32C3×C4⋊Dic3—22no—
33C3×C4×Dic3—21no—
34C2×C3×C3⋊C8—21no—
35#3724—22no—
36Dic32—21no—
37#3710—21no—
38#3710Q812yes—
39#1942—91nomaximal, Sylow
40C2×D3×C8—61no—
41C2×D3×C8—61no—
42C2×D3×C8—61no—
43D3×C4⋊C4—62no—
44C42×D3—61no—
45C3×#107—61no—
46C3×C4×C8—61no—
47#818—21no—
48C8×Dic3—21no—
49C8×Dic3—61no—
50#807—62no—
51C4×C3⋊C8—61no—
52C22×C3⋊D3C2×D411yescharacteristic
53C2×#157—24no—
54C2×#157—42no—
55C2×#157—42no—
56C2×C32×C4C2×D411yescharacteristic
57C2×C3⋊Dic3#4111yescharacteristic
58C4×C3⋊D3C22×C411yescharacteristic
59C4×C3⋊D3C2×Q811yescharacteristic
60C4×C3⋊D3C2×Q811yescharacteristic
61C4×C3⋊D3#4111yescharacteristic
62C2×C3×Dic3—21no—
63C2×C3×Dic3—21no—
64C2×C3×Dic3—42no—
65#624—21no—
66#624—21no—
67#624—42no—
68#624—42no—
69#624D812yes—
70#624Q1612yes—
71C32×C8C4⋊C412yescomplemented
72C3⋊(C3⋊C8)C4⋊C412yescomplemented
73C3×C3⋊C8—22no—
74C2×#107—91no—
75C2×#107—91no—
76C2×C4×C8—91no—
77#389—92no—
78#340—92no—
79C2×C4×D3—61no—
80C2×C4×D3—61no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C4×D3—122no—
84C2×C3×C8—21no—
85C2×C3×C8—21no—
86C2×C3×C8—61no—
87C3×C4⋊C4—62no—
88C3×C42—61no—
89C4⋊Dic3—22no—
90Dic3⋊C4—122no—
91C4×Dic3—21no—
92C4×Dic3—61no—
93C4×Dic3—61no—
94C2×C3⋊C8—21no—
95C2×C3⋊C8—61no—
96C2×C3⋊C8—61no—
97D3×C8—62no—
98D3×C8—62no—
99D3×C8—62no—
100D3×C8—62no—
101D3×C8—62no—
102D3×C8—62no—
103C22×C32#12111yescharacteristic
104C2×C3⋊D3C4×D411yescharacteristic
105C2×C3⋊D3C4⋊Q811yescharacteristic
106C2×C3⋊D3C2×D811yescharacteristic
107C2×C3⋊D3C2×Q1611yescharacteristic
108C2×C3⋊D3#13511yescharacteristic
109C2×C3⋊D3#13511yescharacteristic
110#157—44no—
111C32×C4C2×C4⋊C411yescharacteristic
112C32×C4C22⋊Q811yescharacteristic
113C3⋊Dic3C4×Q811yescharacteristic
114C3⋊Dic3#12511yescharacteristic
115C3×Dic3—22no—
116C3×Dic3—22no—
117C3×Dic3—82no—
118C22×C8—91no—
119C22×C8—91no—
120C2×C4⋊C4—92no—
121C2×C4⋊C4—92no—
122C2×C4⋊C4—182no—
123C2×C42—91no—
124#107—61no—
125#107—94no—
126#107—181no—
127C4×C8—61no—
128C4×C8—181no—
129#95—182no—
130C22×D3—61no—
131C22×D3—61no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—61no—
135C2×C3×C4—61no—
136C2×C3×C4—122no—
137C2×Dic3—21no—
138C2×Dic3—21no—
139C2×Dic3—42no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C4×D3—62no—
143C4×D3—62no—
144C4×D3—61no—
145C4×D3—61no—
146C4×D3—61no—
147C4×D3—61no—
148C4×D3—61no—
149C4×D3—61no—
150C4×D3—61no—
151C4×D3—61no—
152C4×D3—62no—
153C4×D3—62no—
154C4×D3—242no—
155C4×D3—242no—
156C3×C8—22no—
157C3×C8—22no—
158C3×C8—62no—
159C3⋊C8—22no—
160C3⋊C8—62no—
161C3⋊C8—62no—
162C2×C32#38911yescharacteristic
163C2×C32#46611yescharacteristic
164C2×C32#46711yescharacteristic
165C3⋊D3C4×D811yescharacteristic
166C3⋊D3C4×Q1611yescharacteristic
167C3⋊D3#49911yescharacteristic
168C3⋊D3#50011yescharacteristic
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—182no—
173C22×C4—182no—
174C2×C8—61no—
175C2×C8—92no—
176C2×C8—91no—
177C2×C8—92no—
178C2×C8—92no—
179C2×C8—181no—
180C2×C8GO+(4,𝔽2)11yescharacteristic
181C4⋊C4—62no—
182C4⋊C4—94no—
183C4⋊C4—182no—
184C4⋊C4—182no—
185C4⋊C4—364no—
186C42—61no—
187C42—181no—
188C22×C3—21no—
189C22×C3—21no—
190C2×D3—61no—
191C2×D3—61no—
192C2×D3—61no—
193C2×D3—61no—
194C2×D3—61no—
195C2×D3—61no—
196C2×D3—61no—
197C2×D3—61no—
198C2×D3—61no—
199C2×D3—61no—
200C2×D3—61no—
201C2×D3—61no—
202C3×C4—21no—
203C3×C4—21no—
204C3×C4—21no—
205C3×C4—21no—
206C3×C4—62no—
207C3×C4—62no—
208C3×C4—242no—
209Dic3—22no—
210Dic3—22no—
211Dic3—61no—
212Dic3—61no—
213Dic3—61no—
214Dic3—61no—
215Dic3—82no—
216C32#194211yescharacteristic, complemented, Sylow
217C23—91no—
218C2×C4—61no—
219C2×C4—61no—
220C2×C4—92no—
221C2×C4—92no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—91no—
225C2×C4—91no—
226C2×C4—91no—
227C2×C4—122no—
228C2×C4—181no—
229C2×C4—181no—
230C2×C4—184no—
231C2×C4—362no—
232C2×C4—362no—
233C2×C4—362no—
234C2×C4—362no—
235C2×C4C2×GO+(4,𝔽2)11yescharacteristic
236C8—62no—
237C8—92no—
238C8#377312yescomplemented
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245D3—61no—
246D3—61no—
247D3—61no—
248D3—61no—
249D3—61no—
250D3—61no—
251D3—61no—
252D3—61no—
253C22—91no—
254C22—91no—
255C22—91no—
256C22—91no—
257C22—91no—
258C22—91no—
259C22#6423011yescharacteristic
260C4—62no—
261C4—62no—
262C4—91no—
263C4—91no—
264C4—242no—
265C4—364no—
266C4D32⋊Q811yescharacteristic
267C4C2×#377311yescharacteristic
268C3—21no—
269C3—21no—
270C2—91no—
271C2—91no—
272C2—91no—
273C2—91no—
274C2#1059328511yescharacteristic
275C2#1059328811yescharacteristic
276C2#1059341211yescharacteristic
subgroupG/H
centerC22#64230
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1942
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
12. #63769C4semidirect
71. C32×C8C4⋊C4semidirect
72. C3⋊(C3⋊C8)C4⋊C4semidirect
216. C32#1942semidirect
238. C8#3773semidirect

Maximal subgroups

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

subgroupindex
C2×#637692
#105934122
#105906872
C8×#6242
#105900492
#19429