Finite Group Databasebeta

← #11806876

Subgroups — #11806876

Order 1152.

850 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 175 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×#64222C211yesmaximal, characteristic
2#10594363C212yesmaximal
3C4⋊C4×#157C211yesmaximal, characteristic
4#10593410C212yesmaximal
5C4×#3773C212yesmaximal
6C4×#3773C211yesmaximal, characteristic
7#10593341C212yesmaximal
8#10593338C214yesmaximal
9C2×#3797C2212yes—
10C2×C4⋊#157C2211yescharacteristic
11C2×C4×#157C2212yes—
12C2×C4×#157C2211yescharacteristic
13C2×#3773C2211yescharacteristic
14C2×#3773C2212yes—
15C2×#3773C2212yes—
16C2×#3773C2211yescharacteristic
17#64222C418yescomplemented
18C4⋊C4×C3⋊D3C2211yescharacteristic
19C3×#887—22no—
20#63883C2214yes—
21C4×#624C2214yes—
22C4×#624C2212yes—
23Dic3×Dic6—22no—
24#63837—24no—
25#63781C2212yes—
26#63737C2212yes—
27#63737C2214yes—
28#63737C2214yes—
29C4×D3×Q8—62no—
30C22×#157C2312yes—
31C22×#157C2311yescharacteristic
32C22×#157C2311yescharacteristic
33C2×C4×C3⋊D3C2312yes—
34C2×C4×C3⋊D3C2311yescharacteristic
35C2×C3×Dic6—22no—
36C2×#627—22no—
37C2×#624C2312yes—
38C2×#624C2314yes—
39C2×#624C2312yes—
40#3797—24no—
41#3797C2×C418yes—
42C4⋊#157—22no—
43C4×#157—24no—
44C4×#157C2×C414yes—
45#3773—22no—
46#3773C2×C418yes—
47#3773C2×C418yes—
48#3773Q814yescomplemented
49C32×C4⋊C4D411yescharacteristic
50C4⋊(C3⋊Dic3)D411yescharacteristic
51#3750D412yes—
52C3×Dic3⋊C4—24no—
53C3×C4×Dic3—24no—
54C3×C4×Dic3—22no—
55Dic3⋊Dic3—24no—
56Dic32—22no—
57Dic32—24no—
58#2365—91nomaximal, Sylow
59C2×D3×Q8—62no—
60C3×C4×Q8—62no—
61Q8×Dic3—62no—
62D3×C4⋊C4—64no—
63D3×C4⋊C4—62no—
64#887—22no—
65#887—64no—
66C42×D3—64no—
67C42×D3—62no—
68C4×Dic6—64no—
69C4×Dic6—62no—
70C22×C3⋊D3C2411yescharacteristic
71C2×#157—21no—
72C2×#157—21no—
73C2×#157—22no—
74C2×#157—22no—
75C2×#157—22no—
76C2×#157C22×C412yes—
77C2×#157C22×C412yes—
78C2×#157C2×Q812yes—
79C2×#157#4112yes—
80C2×C32×C4C2×D412yes—
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3C2×D412yes—
83C2×C3⋊Dic3C2×D411yescharacteristic
84C4×C3⋊D3—22no—
85C4×C3⋊D3—22no—
86C4×C3⋊D3C22×C412yes—
87C4×C3⋊D3#4112yes—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—22no—
91C3×Dic6—28no—
92#627—28no—
93#624—24no—
94#624—22no—
95#624—22no—
96#624—22no—
97#624C22×C418yes—
98#624C2×Q814yes—
99C2×C4⋊Q8—91no—
100C2×C4×Q8—92no—
101#391—92no—
102#389—92no—
103#387—94no—
104C4×C4⋊C4—91no—
105C4×C4⋊C4—92no—
106C4×C4⋊C4—91no—
107C2×C3×Q8—62no—
108D3×Q8—68no—
109D3×Q8—68no—
110C2×C4×D3—62no—
111C2×C4×D3—64no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—64no—
115C2×Dic6—22no—
116C2×Dic6—64no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4—64no—
119C3×C42—62no—
120C3×C42—64no—
121C4⋊Dic3—62no—
122C4⋊Dic3—64no—
123Dic3⋊C4—24no—
124Dic3⋊C4—64no—
125Dic3⋊C4—64no—
126C4×Dic3—24no—
127C4×Dic3—22no—
128C4×Dic3—64no—
129C4×Dic3—62no—
130C4×Dic3—62no—
131C4×Dic3—64no—
132C22×C32C22×D411yescharacteristic
133C2×C3⋊D3C23×C411yescharacteristic
134C2×C3⋊D3C22×Q811yescharacteristic
135C2×C3⋊D3C2×#4111yescharacteristic
136C2×C3⋊D3C2×#4111yescharacteristic
137C2×C3⋊D32−1+411yescharacteristic
138C2×C3⋊D32−1+411yescharacteristic
139#157—22no—
140#157—42no—
141#157C4×Q814yescomplemented
142C32×C4—22no—
143C32×C4C4×D412yes—
144C3⋊Dic3—22no—
145C3⋊Dic3C4×D412yes—
146C3×Dic3—28no—
147C3×Dic3—24no—
148C3×Dic3—42no—
149C22×Q8—92no—
150C4⋊Q8—98no—
151C4×Q8—62no—
152C4×Q8—184no—
153C4×Q8—182no—
154C2×C4⋊C4—94no—
155C2×C4⋊C4—92no—
156C2×C4⋊C4—92no—
157C2×C4⋊C4—91no—
158C2×C4⋊C4—91no—
159C2×C4⋊C4—91no—
160C2×C4⋊C4—91no—
161C2×C42—94no—
162C2×C42—92no—
163C2×C42—91no—
164C2×C42—92no—
165#95—92no—
166#95—92no—
167#95—94no—
168#95—94no—
169C22×D3—62no—
170C3×Q8—68no—
171C2×C3×C4—22no—
172C2×C3×C4—24no—
173C2×C3×C4—62no—
174C2×C3×C4—64no—
175C2×C3×C4—62no—
176C2×Dic3—22no—
177C2×Dic3—24no—
178C2×Dic3—22no—
179C2×Dic3—62no—
180C2×Dic3—64no—
181C4×D3—68no—
182C4×D3—64no—
183C4×D3—64no—
184C4×D3—64no—
185C4×D3—64no—
186C4×D3—68no—
187C4×D3—122no—
188C4×D3—122no—
189C4×D3—124no—
190C4×D3—124no—
191Dic6—28no—
192Dic6—616no—
193C2×C32C2×C4×D411yescharacteristic
194C2×C32#54711yescharacteristic
195C2×C32D4×Q811yescharacteristic
196C3⋊D3C2×C4×Q811yescharacteristic
197C3⋊D3#51911yescharacteristic
198C3⋊D3#55611yescharacteristic
199C3⋊D3#55711yescharacteristic
200C2×Q8—62no—
201C2×Q8—98no—
202C2×Q8—182no—
203C2×Q8—184no—
204C22×C4—92no—
205C22×C4—94no—
206C22×C4—92no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—91no—
210C22×C4—92no—
211C22×C4—92no—
212C4⋊C4—64no—
213C4⋊C4—98no—
214C4⋊C4—98no—
215C4⋊C4—94no—
216C4⋊C4—92no—
217C4⋊C4—91no—
218C4⋊C4—184no—
219C4⋊C4—182no—
220C4⋊C4—182no—
221C4⋊C4GO+(4,𝔽2)11yescharacteristic
222C42—64no—
223C42—62no—
224C42—94no—
225C42—184no—
226C42—182no—
227C42—184no—
228C22×C3—22no—
229C2×D3—62no—
230C2×D3—62no—
231C2×D3—62no—
232C2×D3—62no—
233C2×D3—62no—
234C2×D3—62no—
235C3×C4—24no—
236C3×C4—44no—
237C3×C4—68no—
238C3×C4—64no—
239C3×C4—122no—
240Dic3—28no—
241Dic3—24no—
242Dic3—42no—
243Dic3—64no—
244Dic3—124no—
245C32#236511yescharacteristic, complemented, Sylow
246C23—91no—
247Q8—68no—
248Q8—188no—
249C2×C4—62no—
250C2×C4—64no—
251C2×C4—62no—
252C2×C4—98no—
253C2×C4—94no—
254C2×C4—92no—
255C2×C4—92no—
256C2×C4—92no—
257C2×C4—91no—
258C2×C4—92no—
259C2×C4—92no—
260C2×C4—92no—
261C2×C4—92no—
262C2×C4—182no—
263C2×C4—182no—
264C2×C4—184no—
265C2×C4—182no—
266C2×C4—182no—
267C2×C4—182no—
268C2×C4—181no—
269C2×C4—181no—
270C2×C4—182no—
271C2×C4—182no—
272C2×C4—182no—
273C2×C4C2×GO+(4,𝔽2)12yes—
274C2×C4C2×GO+(4,𝔽2)11yescharacteristic
275C2×C3—22no—
276C2×C3—22no—
277C2×C3—22no—
278D3—62no—
279D3—62no—
280D3—62no—
281D3—62no—
282C22—91no—
283C22—91no—
284C22—91no—
285C22—91no—
286C22—91no—
287C22—91no—
288C22C22×GO+(4,𝔽2)11yescharacteristic
289C4—22no—
290C4—68no—
291C4—64no—
292C4—94no—
293C4—92no—
294C4—122no—
295C4—182no—
296C4—182no—
297C4—362no—
298C4C4×GO+(4,𝔽2)12yes—
299C3—22no—
300C2—91no—
301C2—91no—
302C2—91no—
303C2—91no—
304C2C2×C4×GO+(4,𝔽2)11yescharacteristic
305C2#1059651911yescharacteristic
306C2Q8×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
prime radical, cosocleC22×C3⋊D3C24
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2365
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
17. #64222C4semidirect
48. #3773Q8semidirect
141. #157C4×Q8semidirect
245. C32#2365semidirect

Maximal subgroups

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

subgroupindex
C2×#642222
#105943632
C4⋊C4×#1572
#105934102
C4×#37732
#105933412
#105933382
#23659