Finite Group Databasebeta

← #11771929

Subgroups — #11771929

Order 1152.

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

normal subgroups only

This group has 334 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#10591692C211yesmaximal, characteristic
2#10590222C211yesmaximal, characteristic
3#10589187C211yesmaximal, characteristic
4C22×#627C411yescharacteristic, complemented
5C2×#3757C2211yescharacteristic
6C2×C3×#217—21no—
7C2×C3×#217—21no—
8C22⋊#622—21no—
9#63579—21no—
10#63579C411yescharacteristic, complemented
11#4947—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×#627—41no—
20C2×#627—42no—
21C2×#622—41no—
22#3757—41no—
23C3×#217—22no—
24C3×#217—42no—
25C3×#217—41no—
26#1351—91nomaximal, Sylow
27C22×Dic6—61no—
28C2×C3×C22⋊C4—61no—
29C2×C3×C22⋊C4—61no—
30C2×#217—21no—
31C2×#217—21no—
32C2×#217—61no—
33C2×#217—61no—
34C3⋊#95—61no—
35C3⋊#95—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—42no—
52C2×C3×Dic3—41no—
53C2×C3×Dic3—41no—
54C2×C3×Dic3—41no—
55C2×C3×Dic3—81no—
56C2×C3×Dic3—81no—
57#627—42no—
58#627—42no—
59#622—81no—
60#393—91no—
61#342—91no—
62#323—91no—
63C24×C3—21no—
64C24×C3—21no—
65C22×C3×C4—61no—
66C22×C3×C4—61no—
67C22×C3×C4—121no—
68C22×Dic3—21no—
69C22×Dic3—21no—
70C22×Dic3—41no—
71C22×Dic3—61no—
72C22×Dic3—61no—
73C22×Dic3—61no—
74C22×Dic3—61no—
75C2×Dic6—122no—
76C2×Dic6—122no—
77C2×Dic6—122no—
78C3×C22⋊C4—62no—
79C3×C22⋊C4—122no—
80C3×C22⋊C4—121no—
81#217—22no—
82#217—42no—
83#217—41no—
84#217—122no—
85#217—121no—
86#217—121no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32—21no—
90C22×C32—21no—
91C22×C32—41no—
92C22×C32—41no—
93C22×C32—41no—
94C22×C32—41no—
95C22×C32—81no—
96C22×C32#9911yescharacteristic
97C22×C32#10311yescharacteristic
98C22×C32#10411yescharacteristic
99C3⋊Dic3—41no—
100C3⋊Dic3—41no—
101C3×Dic3—42no—
102C3×Dic3—81no—
103C3×Dic3—82no—
104C22×Q8—91no—
105C2×C22⋊C4—61no—
106C2×C22⋊C4—61no—
107C2×C22⋊C4—91no—
108C22⋊C8—181no—
109#95—91no—
110#95—181no—
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—21no—
120C23×C3—21no—
121C23×C3—41no—
122C23×C3—41no—
123C23×C3—41no—
124C23×C3—41no—
125C23×C3—41no—
126C23×C3—41no—
127C23×C3—81no—
128C23×C3—81no—
129C2×C3×C4—62no—
130C2×C3×C4—121no—
131C2×C3×C4—121no—
132C2×C3×C4—122no—
133C2×C3×C4—121no—
134C2×C3×C4—121no—
135C2×C3×C4—121no—
136C2×C3×C4—241no—
137C2×C3×C4—241no—
138C2×Dic3—22no—
139C2×Dic3—41no—
140C2×Dic3—41no—
141C2×Dic3—42no—
142C2×Dic3—41no—
143C2×Dic3—41no—
144C2×Dic3—41no—
145C2×Dic3—62no—
146C2×Dic3—81no—
147C2×Dic3—81no—
148C2×Dic3—121no—
149C2×Dic3—121no—
150C2×Dic3—121no—
151C2×Dic3—121no—
152C2×Dic3—121no—
153C2×Dic3—121no—
154C2×Dic3—121no—
155C2×Dic3—241no—
156C2×Dic3—241no—
157Dic6—124no—
158Dic6—124no—
159C2×C32—21no—
160C2×C32—21no—
161C2×C32—41no—
162C2×C32—41no—
163C2×C32#32811yescharacteristic
164C2×C32AΣL(1,𝔽16)11yescharacteristic
165C2×C32#35411yescharacteristic
166C24GO+(4,𝔽2)11yescharacteristic
167C2×Q8—362no—
168C2×Q8—361no—
169C22×C4—61no—
170C22×C4—61no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—121no—
174C2×C8—361no—
175C22⋊C4—62no—
176C22⋊C4—122no—
177C22⋊C4—121no—
178C22⋊C4—361no—
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—21no—
190C22×C3—21no—
191C22×C3—21no—
192C22×C3—21no—
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—41no—
202C22×C3—41no—
203C22×C3—41no—
204C22×C3—41no—
205C22×C3—81no—
206C22×C3—81no—
207C22×C3—81no—
208C22×C3—81no—
209C22×C3—81no—
210C22×C3—81no—
211C22×C3—81no—
212C22×C3—81no—
213C3×C4—122no—
214C3×C4—241no—
215C3×C4—242no—
216Dic3—42no—
217Dic3—81no—
218Dic3—82no—
219Dic3—122no—
220Dic3—241no—
221Dic3—241no—
222Dic3—241no—
223C32#135111yescharacteristic, complemented, Sylow
224C23—21no—
225C23—21no—
226C23—41no—
227C23—41no—
228C23D32⋊C411yescharacteristic
229C23#377511yescharacteristic
230C23#377611yescharacteristic
231Q8—362no—
232Q8—362no—
233C2×C4—62no—
234C2×C4—121no—
235C2×C4—121no—
236C2×C4—122no—
237C2×C4—121no—
238C2×C4—121no—
239C2×C4—121no—
240C2×C4—181no—
241C2×C4—181no—
242C2×C4—241no—
243C2×C4—241no—
244C2×C4—361no—
245C2×C4—361no—
246C8—721no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—41no—
258C2×C3—41no—
259C2×C3—41no—
260C2×C3—41no—
261C2×C3—41no—
262C2×C3—41no—
263C2×C3—81no—
264C2×C3—81no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—81no—
274C22#6373811yescharacteristic
275C22#6374011yescharacteristic
276C22#6374111yescharacteristic
277C4—122no—
278C4—241no—
279C4—242no—
280C4—361no—
281C4—361no—
282C3—21no—
283C3—21no—
284C2—21no—
285C2—21no—
286C2—41no—
287C2—41no—
288C2#1059007211yescharacteristic
289C2#1059007811yescharacteristic
290C2#1059008111yescharacteristic
subgroupG/H
centerC22#63738
commutatorC22×C3⋊Dic3C2×C4
Frattini, hypercenterC24GO+(4,𝔽2)
Fitting, prime radicalC24×C32D4
socleC22×C32#99
cosocleC2×#3757C22
hypocenterC32#1351
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
4. C22×#627C4semidirect
10. #63579C4semidirect
223. C32#1351semidirect

Maximal subgroups

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

subgroupindex
#105916922
#105902222
#105891872
#13519