Finite Group Databasebeta

← #11792010

Subgroups — #11792010

Order 1152.

1176 conjugacy classes of subgroups; only the 241 normal subgroups are shown.

normal subgroups only

This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 241 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×#3746C211yesmaximal, characteristic, complemented
2C2×#64106C212yesmaximal
3C2×#63647C211yesmaximal, characteristic
4C2×#63637C212yesmaximal, complemented
5C32×#340C211yesmaximal, characteristic, complemented
6#68888—34nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#634C2212yes—
9C22×C32×C8C2211yescharacteristic
10C2×C32×C4⋊C4C2212yes—
11C2×#3752—22no—
12C2×C4⋊(C3⋊Dic3)—22no—
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×#3746—24no—
15C2×#3746—22no—
16#64106—24no—
17#64106—24no—
18#63647—22no—
19#63637—24no—
20C22×Dic12—34no—
21C2×#897—38no—
22C2×(C2×D3)⋊C8—34no—
23C2×#810—38no—
24C3×#340D314yescomplemented
25C23×C3⋊D3D411yescharacteristic
26C22×C32×C4—22no—
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3—22no—
29C22×C3⋊Dic3D411yescharacteristic
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—21no—
34C2×#634—22no—
35C2×#634—22no—
36C2×#634—22no—
37C2×#634—22no—
38C2×#634—22no—
39C2×#634D414yes—
40C2×C32×C8—22no—
41C2×C32×C8D412yes—
42C32×C4⋊C4—22no—
43C32×C4⋊C4D414yes—
44#3752—28no—
45C4⋊(C3⋊Dic3)—28no—
46C2×C3⋊(C3⋊C8)—22no—
47C2×C3⋊(C3⋊C8)—21no—
48#3746—28no—
49#2001—91noSylow
50C22×C4×D3—34no—
51C22×Dic6—38no—
52C22×C3×C8C2×D314yes—
53C2×C3×C4⋊C4C2×D318yes—
54C2×(C2×D3)⋊C4—68no—
55C2×C4⋊Dic3—68no—
56C22×C3⋊C8—34no—
57C2×Dic12—616no—
58C2×Dic12—68no—
59#897—616no—
60#897—616no—
61(C2×D3)⋊C8—68no—
62#810—616no—
63C23×C32C2×D411yescharacteristic
64C22×C3⋊D3—22no—
65C22×C3⋊D3—21no—
66C22×C3⋊D3—21no—
67C22×C3⋊D3—22no—
68C22×C3⋊D3Q1612yescomplemented
69C2×C32×C4—24no—
70C2×C32×C4—42no—
71C2×C32×C4—42no—
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×D412yes—
74C2×C32×C4C2×D412yes—
75C2×C32×C4#4111yescharacteristic
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—24no—
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—42no—
80C2×C3⋊Dic3—42no—
81C4×C3⋊D3—41no—
82C4×C3⋊D3—42no—
83C4×C3⋊D3—41no—
84#634—24no—
85#634—24no—
86#634—42no—
87#634—42no—
88C32×C8—22no—
89C3⋊(C3⋊C8)—41no—
90C22×Q16—91no—
91C2×C22⋊Q8—92no—
92C2×#103—92no—
93C2×C22⋊C8—91no—
94#340C3⋊D311yescharacteristic, complemented
95C23×D3—34no—
96C22×C3×C4—28no—
97C22×C3×C4C22×D314yes—
98C22×Dic3—34no—
99C22×Dic3—68no—
100C2×C4×D3—64no—
101C2×C4×D3—68no—
102C2×C4×D3—68no—
103C2×C4×D3—64no—
104C2×Dic6—316no—
105C2×Dic6—68no—
106C2×Dic6—68no—
107C2×Dic6—68no—
108C2×Dic6—68no—
109C2×Dic6—68no—
110C2×C3×C8—28no—
111C2×C3×C8D1218yes—
112C3×C4⋊C4—28no—
113C3×C4⋊C4D12116yes—
114(C2×D3)⋊C4—632no—
115C4⋊Dic3—632no—
116C2×C3⋊C8—68no—
117C2×C3⋊C8—64no—
118Dic12—632no—
119C22×C32#12012yes—
120C22×C32#12111yescharacteristic
121C22×C32C2×Q1611yescharacteristic
122C22×C32#13511yescharacteristic
123C22×C32#13712yes—
124C2×C3⋊D3—24no—
125C2×C3⋊D3—22no—
126C2×C3⋊D3—41no—
127C2×C3⋊D3—42no—
128C2×C3⋊D3—41no—
129C32×C4—44no—
130C32×C4#12011yescharacteristic
131C32×C4#12112yes—
132C32×C4#12711yescharacteristic
133C3⋊Dic3—44no—
134C3⋊Dic3—41no—
135C22×Q8—92no—
136C23×C4—91no—
137C2×Q16—184no—
138C2×Q16—182no—
139C22×C8—91no—
140C22×C8C2×C3⋊D311yescharacteristic
141C22⋊Q8—184no—
142C22⋊Q8—184no—
143C2×C4⋊C4—182no—
144C2×C4⋊C4C2×C3⋊D312yes—
145C2×C22⋊C4—182no—
146#103—184no—
147C22⋊C8—182no—
148C23×C3D3×D414yes—
149C22×D3—38no—
150C22×D3—68no—
151C22×D3—64no—
152C22×D3—64no—
153C22×D3—68no—
154C2×C3×C4—216no—
155C2×C3×C4—48no—
156C2×C3×C4—48no—
157C2×C3×C4C2×D1214yes—
158C2×C3×C4C2×D1218yes—
159C2×C3×C4D3×D418yes—
160C2×C3×C4#23914yes—
161C2×Dic3—68no—
162C2×Dic3—616no—
163C2×Dic3—64no—
164C2×Dic3—128no—
165C2×Dic3—128no—
166C4×D3—124no—
167C4×D3—124no—
168C4×D3—128no—
169Dic6—616no—
170Dic6—616no—
171Dic6—128no—
172Dic6—128no—
173C3×C8—28no—
174C3⋊C8—124no—
175C2×C32#39211yescharacteristic
176C2×C32#45112yes—
177C2×C32#45212yes—
178C2×C32#46711yescharacteristic
179C2×C32#47011yescharacteristic
180C3⋊D3—42no—
181C24—91no—
182C2×Q8—94no—
183C2×Q8—182no—
184C2×Q8—182no—
185C2×Q8—182no—
186C2×Q8—182no—
187C2×Q8—182no—
188C22×C4—22no—
189C22×C4—91no—
190C22×C4—182no—
191C22×C4—181no—
192C22×C4—182no—
193C22×C4—182no—
194C22×C4—181no—
195C22×C4C22×C3⋊D311yescharacteristic
196Q16—188no—
197C2×C8—22no—
198C2×C8—181no—
199C2×C8—182no—
200C2×C8C4⋊(C3⋊D3)12yes—
201C4⋊C4—22no—
202C4⋊C4—188no—
203C4⋊C4C4⋊(C3⋊D3)14yes—
204C22⋊C4—188no—
205C22×C3#88218yes—
206C22×C3#89514yes—
207C22×C3#91214yes—
208C22×C3#91518yes—
209C22×C3D3×Q1614yes—
210C2×D3—68no—
211C2×D3—616no—
212C2×D3—124no—
213C2×D3—124no—
214C2×D3—128no—
215C3×C4—416no—
216C3×C4#87414yes—
217C3×C4#88214yes—
218C3×C4#89518yes—
219Dic3—1216no—
220Dic3—124no—
221C32#200111yescharacteristic, complemented, Sylow
222C23—92no—
223C23—182no—
224C23—181no—
225C23—181no—
226C23—182no—
227C23D4×C3⋊D311yescharacteristic
228Q8—184no—
229Q8—184no—
230Q8—362no—
231Q8—362no—
232C2×C4—24no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—184no—
236C2×C4—182no—
237C2×C4—181no—
238C2×C4—362no—
239C2×C4—362no—
240C2×C4—361no—
241C2×C4—361no—
242C2×C4—362no—
243C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
244C2×C4C2×C4⋊(C3⋊D3)12yes—
245C2×C4D4×C3⋊D312yes—
246C2×C4#383211yescharacteristic
247C8—22no—
248C8—361no—
249C2×C3#467114yes—
250C2×C3#478318yes—
251C2×C3#480918yes—
252C2×C3#486714yes—
253C2×C3#488714yes—
254D3—128no—
255C22—182no—
256C22—184no—
257C22—361no—
258C22—361no—
259C22—362no—
260C22#6409112yes—
261C22#6410411yescharacteristic
262C22#6412111yescharacteristic
263C22#6412412yes—
264C22Q16×C3⋊D311yescharacteristic
265C4—44no—
266C4—361no—
267C4—364no—
268C4#6408311yescharacteristic
269C4#6409111yescharacteristic
270C4#6410412yes—
271C3#6888814yescomplemented
272C2—362no—
273C2#1059237011yescharacteristic
274C2#1059248212yes—
275C2#1059250812yes—
276C2#1059256611yescharacteristic
277C2#1059258611yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenter#340C3⋊D3
hypocenterC32#2001
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C22×#3746C2semidirect
4. C2×#63637C2semidirect
5. C32×#340C2semidirect
24. C3×#340D3semidirect
68. C22×C3⋊D3Q16semidirect
94. #340C3⋊D3semidirect
221. C32#2001semidirect
271. C3#68888semidirect

Maximal subgroups

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

subgroupindex
C22×#37462
C2×#641062
C2×#636472
C2×#636372
C32×#3402
#688883