Finite Group Databasebeta

← #11771946

Subgroups — #11771946

Order 1152.

318 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 31 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#10591715C211yesmaximal, characteristic
2#10590222C211yesmaximal, characteristic
3#10589187C211yesmaximal, characteristic
4C2×#3757C2211yescharacteristic
5C2×C3×#217—21no—
6C2×C3×#217—21no—
7C2×#3724C411yescharacteristic, complemented
8C2×Dic3⋊Dic3—21no—
9C22⋊#622—21no—
10#63579C411yescharacteristic, complemented
11#4949—61no—
12#4527—61no—
13C24×C32D411yescharacteristic
14C22×C3⋊Dic3C2×C411yescharacteristic
15C22×C3⋊Dic3D411yescharacteristic
16C22×C3×Dic3—21no—
17C22×C3×Dic3—21no—
18C22×C3×Dic3—41no—
19C2×#622—41no—
20#3757—41no—
21C3×#217—22no—
22C3×#217—42no—
23C3×#217—41no—
24#3724—41no—
25Dic3⋊Dic3—42no—
26#1352—91nomaximal, Sylow
27C2×C3×C22⋊C4—61no—
28C2×C3×C22⋊C4—61no—
29C2×#217—21no—
30C2×#217—21no—
31C2×#217—61no—
32C2×#217—61no—
33C2×C4⋊Dic3—61no—
34C2×Dic3⋊C4—61no—
35C2×Dic3⋊C4—61no—
36C3⋊#95—61no—
37C23×C32—21no—
38C23×C32—21no—
39C23×C32—41no—
40C23×C32—41no—
41C23×C32C22⋊C411yescharacteristic
42C23×C32SD1611yescharacteristic
43C23×C32Q1611yescharacteristic
44C2×C3⋊Dic3—21no—
45C2×C3⋊Dic3—21no—
46C2×C3⋊Dic3—41no—
47C2×C3⋊Dic3—41no—
48C2×C3×Dic3—22no—
49C2×C3×Dic3—41no—
50C2×C3×Dic3—41no—
51C2×C3×Dic3—41no—
52C2×C3×Dic3—42no—
53C2×C3×Dic3—41no—
54C2×C3×Dic3—41no—
55C2×C3×Dic3—81no—
56C2×C3×Dic3—81no—
57#622—81no—
58#399—91no—
59#342—91no—
60#323—91no—
61C24×C3—21no—
62C24×C3—21no—
63C22×C3×C4—61no—
64C22×C3×C4—61no—
65C22×C3×C4—121no—
66C22×Dic3—21no—
67C22×Dic3—21no—
68C22×Dic3—41no—
69C22×Dic3—61no—
70C22×Dic3—61no—
71C22×Dic3—61no—
72C22×Dic3—61no—
73C3×C22⋊C4—62no—
74C3×C22⋊C4—122no—
75C3×C22⋊C4—121no—
76#217—22no—
77#217—42no—
78#217—41no—
79#217—122no—
80#217—121no—
81#217—121no—
82C4⋊Dic3—122no—
83Dic3⋊C4—122no—
84Dic3⋊C4—122no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32—41no—
90C22×C32—41no—
91C22×C32—41no—
92C22×C32—41no—
93C22×C32—81no—
94C22×C32#9911yescharacteristic
95C22×C32#10311yescharacteristic
96C22×C32#10411yescharacteristic
97C3⋊Dic3—41no—
98C3⋊Dic3—41no—
99C3×Dic3—42no—
100C3×Dic3—82no—
101C3×Dic3—81no—
102C2×C4⋊C4—91no—
103C2×C4⋊C4—181no—
104C2×C22⋊C4—61no—
105C2×C22⋊C4—61no—
106C2×C22⋊C4—91no—
107C22⋊C8—181no—
108#95—91no—
109C23×C3—21no—
110C23×C3—21no—
111C23×C3—21no—
112C23×C3—21no—
113C23×C3—21no—
114C23×C3—21no—
115C23×C3—21no—
116C23×C3—21no—
117C23×C3—21no—
118C23×C3—21no—
119C23×C3—41no—
120C23×C3—41no—
121C23×C3—41no—
122C23×C3—41no—
123C23×C3—41no—
124C23×C3—41no—
125C23×C3—81no—
126C23×C3—81no—
127C2×C3×C4—62no—
128C2×C3×C4—121no—
129C2×C3×C4—121no—
130C2×C3×C4—121no—
131C2×C3×C4—121no—
132C2×C3×C4—122no—
133C2×C3×C4—121no—
134C2×C3×C4—241no—
135C2×C3×C4—241no—
136C2×Dic3—22no—
137C2×Dic3—41no—
138C2×Dic3—41no—
139C2×Dic3—41no—
140C2×Dic3—41no—
141C2×Dic3—42no—
142C2×Dic3—41no—
143C2×Dic3—62no—
144C2×Dic3—81no—
145C2×Dic3—81no—
146C2×Dic3—121no—
147C2×Dic3—121no—
148C2×Dic3—121no—
149C2×Dic3—121no—
150C2×Dic3—121no—
151C2×Dic3—121no—
152C2×Dic3—121no—
153C2×Dic3—241no—
154C2×Dic3—241no—
155C2×C32—21no—
156C2×C32—21no—
157C2×C32—41no—
158C2×C32—41no—
159C2×C32#32811yescharacteristic
160C2×C32#35211yescharacteristic
161C2×C32#35311yescharacteristic
162C24GO+(4,𝔽2)11yescharacteristic
163C22×C4—61no—
164C22×C4—61no—
165C22×C4—91no—
166C22×C4—91no—
167C22×C4—121no—
168C2×C8—361no—
169C4⋊C4—362no—
170C4⋊C4—361no—
171C22⋊C4—62no—
172C22⋊C4—122no—
173C22⋊C4—121no—
174C22⋊C4—361no—
175C22×C3—21no—
176C22×C3—21no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—21no—
180C22×C3—21no—
181C22×C3—21no—
182C22×C3—21no—
183C22×C3—21no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3—21no—
189C22×C3—41no—
190C22×C3—41no—
191C22×C3—41no—
192C22×C3—41no—
193C22×C3—41no—
194C22×C3—41no—
195C22×C3—41no—
196C22×C3—41no—
197C22×C3—41no—
198C22×C3—41no—
199C22×C3—41no—
200C22×C3—41no—
201C22×C3—81no—
202C22×C3—81no—
203C22×C3—81no—
204C22×C3—81no—
205C22×C3—81no—
206C22×C3—81no—
207C22×C3—81no—
208C22×C3—81no—
209C3×C4—122no—
210C3×C4—241no—
211C3×C4—242no—
212Dic3—42no—
213Dic3—81no—
214Dic3—82no—
215Dic3—122no—
216Dic3—241no—
217Dic3—241no—
218Dic3—241no—
219C32#135211yescharacteristic, complemented, Sylow
220C23—21no—
221C23—21no—
222C23—41no—
223C23—41no—
224C23D32⋊C411yescharacteristic
225C23#377511yescharacteristic
226C23#377611yescharacteristic
227C2×C4—62no—
228C2×C4—121no—
229C2×C4—121no—
230C2×C4—122no—
231C2×C4—121no—
232C2×C4—121no—
233C2×C4—121no—
234C2×C4—181no—
235C2×C4—181no—
236C2×C4—241no—
237C2×C4—241no—
238C2×C4—361no—
239C2×C4—361no—
240C8—721no—
241C2×C3—21no—
242C2×C3—21no—
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—41no—
252C2×C3—41no—
253C2×C3—41no—
254C2×C3—41no—
255C2×C3—41no—
256C2×C3—41no—
257C2×C3—81no—
258C2×C3—81no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—41no—
264C22—41no—
265C22—41no—
266C22—41no—
267C22—81no—
268C22#6373811yescharacteristic
269C22#6374011yescharacteristic
270C22#6374111yescharacteristic
271C4—122no—
272C4—242no—
273C4—241no—
274C4—361no—
275C4—361no—
276C3—21no—
277C3—21no—
278C2—21no—
279C2—21no—
280C2—41no—
281C2—41no—
282C2#1059007211yescharacteristic
283C2#1059007911yescharacteristic
284C2#1059008011yescharacteristic
subgroupG/H
centerC22#63738
commutatorC22×C3⋊Dic3C2×C4
Frattini, hypercenterC24GO+(4,𝔽2)
Fitting, prime radicalC24×C32D4
socleC22×C32#99
cosocleC2×#3757C22
hypocenterC32#1352
LCSG ▷ C22×C3⋊Dic3 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
7. C2×#3724C4semidirect
10. #63579C4semidirect
219. C32#1352semidirect

Maximal subgroups

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

subgroupindex
#105917152
#105902222
#105891872
#13529