Finite Group Databasebeta

← #11778831

Subgroups — #11778831

Order 1152.

372 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 43 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
1#10594813C211yesmaximal, characteristic
2#10593500C212yesmaximal
3#10591217C211yesmaximal, characteristic
4#10590203C211yesmaximal, characteristic
5#10590072C212yesmaximal
6C2×#3750C2211yescharacteristic
7C3×#924—21no—
8#63982C2212yes—
9C2×#3724C2211yescharacteristic
10#63957—21no—
11#63847—22no—
12#63839—22no—
13C22⋊#622C2212yes—
14#63743—22no—
15#63740—22no—
16C3×C3⋊#95—21no—
17#63579—21no—
18#63579C2211yescharacteristic
19#5623—61no—
20#4658—61no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3C2311yescharacteristic
24C22×C3×Dic3—21no—
25C22×C3×Dic3—21no—
26C2×C3×Dic6—21no—
27C2×#627D412yes—
28C2×#622—22no—
29#3750—22no—
30C3×#217—22no—
31C3×C4⋊Dic3—21no—
32C3×Dic3⋊C4—22no—
33#3724—21no—
34#3724—21no—
35#3724—22no—
36#3724D412yes—
37Dic3⋊Dic3—22no—
38Dic32—22no—
39#1617—91nomaximal, Sylow
40C3×C22⋊Q8—61no—
41#944—62no—
42#924—21no—
43C2×Dic3⋊C4—61no—
44C2×Dic3⋊C4—61no—
45C2×Dic3⋊C4—61no—
46#889—62no—
47#889—62no—
48#888—62no—
49#878—62no—
50#877—62no—
51C3×#95—61no—
52C3⋊#95—21no—
53C3⋊#95—61no—
54C3⋊#95—61no—
55C3⋊#95—61no—
56C23×C32C2×D411yescharacteristic
57C2×C32×C4—21no—
58C2×C32×C4—41no—
59C2×C3⋊Dic3—21no—
60C2×C3⋊Dic3—21no—
61C2×C3⋊Dic3—41no—
62C2×C3⋊Dic3Q1612yes—
63C2×C3⋊Dic3C2×D412yes—
64C2×C3×Dic3—22no—
65C2×C3×Dic3—22no—
66C2×C3×Dic3—41no—
67C2×C3×Dic3—41no—
68C2×C3×Dic3—41no—
69C2×C3×Dic3—41no—
70C2×C3×Dic3—41no—
71C2×C3×Dic3—41no—
72C3×Dic6—81no—
73#627—42no—
74#622—42no—
75#544—91no—
76#484—92no—
77#400—91no—
78#328—92no—
79#324—91no—
80C2×C3×Q8—61no—
81C22×C3×C4—21no—
82C22×C3×C4—21no—
83C22×C3×C4—61no—
84C22×C3×C4—61no—
85C22×Dic3—21no—
86C22×Dic3—21no—
87C22×Dic3—61no—
88C22×Dic3—61no—
89C22×Dic3—61no—
90C22×Dic3—61no—
91C2×Dic6—21no—
92C2×Dic6—62no—
93C3×C4⋊C4—62no—
94C3×C4⋊C4—61no—
95C3×C22⋊C4—62no—
96#217—22no—
97C4⋊Dic3—21no—
98C4⋊Dic3—62no—
99Dic3⋊C4—22no—
100Dic3⋊C4—62no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104Dic3⋊C4—62no—
105Dic3⋊C4—62no—
106Dic3⋊C4—122no—
107Dic3⋊C4—122no—
108C4×Dic3—62no—
109C4×Dic3—62no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32#12011yescharacteristic
113C22×C32C2×Q1611yescharacteristic
114C22×C32#13711yescharacteristic
115C32×C4—41no—
116C3⋊Dic3—22no—
117C3⋊Dic3—22no—
118C3×Dic3—42no—
119C3×Dic3—42no—
120C3×Dic3—81no—
121C3×Dic3—81no—
122C4⋊Q8—182no—
123#125—182no—
124C22⋊Q8—61no—
125C22⋊Q8—92no—
126#117—181no—
127C2×C4⋊C4—91no—
128C2×C4⋊C4—91no—
129#107—182no—
130#103—182no—
131C22⋊C8—92no—
132#95—61no—
133#95—91no—
134#95—181no—
135C23×C3—21no—
136C23×C3—21no—
137C3×Q8—241no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—41no—
141C2×C3×C4—41no—
142C2×C3×C4—41no—
143C2×C3×C4—62no—
144C2×C3×C4—62no—
145C2×C3×C4—81no—
146C2×C3×C4—121no—
147C2×C3×C4—121no—
148C2×C3×C4—121no—
149C2×C3×C4—121no—
150C2×C3×C4—121no—
151C2×C3×C4—121no—
152C2×Dic3—22no—
153C2×Dic3—22no—
154C2×Dic3—41no—
155C2×Dic3—41no—
156C2×Dic3—41no—
157C2×Dic3—41no—
158C2×Dic3—41no—
159C2×Dic3—41no—
160C2×Dic3—62no—
161C2×Dic3—62no—
162C2×Dic3—62no—
163C2×Dic3—62no—
164C2×Dic3—62no—
165C2×Dic3—62no—
166C2×Dic3—121no—
167C2×Dic3—121no—
168C2×Dic3—121no—
169C2×Dic3—121no—
170C2×Dic3—241no—
171Dic6—81no—
172Dic6—242no—
173C2×C32—21no—
174C2×C32—21no—
175C2×C32#45111yescharacteristic
176C2×C32#45411yescharacteristic
177C2×C32#45811yescharacteristic
178C2×Q8—61no—
179C2×Q8—92no—
180C22×C4—61no—
181C22×C4—61no—
182C22×C4—91no—
183C22×C4—91no—
184C22×C4GO+(4,𝔽2)11yescharacteristic
185C2×C8—182no—
186C4⋊C4—61no—
187C4⋊C4—62no—
188C4⋊C4—92no—
189C4⋊C4—182no—
190C4⋊C4—182no—
191C4⋊C4—181no—
192C4⋊C4—181no—
193C4⋊C4—182no—
194C22⋊C4—62no—
195C42—182no—
196C22×C3—21no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3—21no—
201C22×C3—21no—
202C22×C3—21no—
203C22×C3—21no—
204C22×C3—21no—
205C22×C3—21no—
206C22×C3—41no—
207C22×C3—41no—
208C3×C4—41no—
209C3×C4—41no—
210C3×C4—81no—
211C3×C4—122no—
212C3×C4—122no—
213C3×C4—241no—
214C3×C4—241no—
215Dic3—42no—
216Dic3—42no—
217Dic3—64no—
218Dic3—81no—
219Dic3—81no—
220Dic3—122no—
221Dic3—122no—
222Dic3—122no—
223C32#161711yescharacteristic, complemented, Sylow
224C23C2×GO+(4,𝔽2)11yescharacteristic
225Q8—241no—
226Q8—362no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—62no—
230C2×C4—62no—
231C2×C4—92no—
232C2×C4—92no—
233C2×C4—121no—
234C2×C4—121no—
235C2×C4—121no—
236C2×C4—121no—
237C2×C4—121no—
238C2×C4—121no—
239C2×C4—181no—
240C2×C4—181no—
241C2×C4—361no—
242C8—362no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—41no—
254C2×C3—41no—
255C22—21no—
256C22—21no—
257C22#6422611yescharacteristic
258C22#6422811yescharacteristic
259C22#6424111yescharacteristic
260C4—41no—
261C4—122no—
262C4—122no—
263C4—182no—
264C4—182no—
265C4—241no—
266C4—241no—
267C3—21no—
268C3—21no—
269C2—21no—
270C2—21no—
271C2#1059337111yescharacteristic
272C2#1059345111yescharacteristic
273C2#1059351811yescharacteristic
subgroupG/H
centerC22#64241
commutator, cosocleC22×C3⋊Dic3C23
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1617
LCSG ▷ C22×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
223. C32#1617semidirect

Maximal subgroups

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

subgroupindex
#105948132
#105935002
#105912172
#105902032
#105900722
#16179