Finite Group Databasebeta

← #11771395

Subgroups — #11771395

Order 1152.

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

normal subgroups only

This group has 338 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#10591386C211yesmaximal, characteristic
2#10590203C211yesmaximal, characteristic, complemented
3#10589148C211yesmaximal, characteristic, complemented
4C22×#625C411yescharacteristic
5C2×#3750C2211yescharacteristic
6C2×C3×(C2×D3)⋊C4—21no—
7C2×(C2×D3)⋊Dic3—21no—
8C2×Dic32C411yescharacteristic
9C22⋊#622—21no—
10C3×#830—21no—
11#4957—61no—
12#4469—61no—
13C23×C3×D3—21no—
14C22×C32×C4D411yescharacteristic
15C22×C3⋊Dic3C2×C411yescharacteristic
16C22×C3⋊Dic3D411yescharacteristic
17C22×C3×Dic3—21no—
18C2×#625—21no—
19C2×#625—41no—
20C2×#625—41no—
21C2×#625C812yescomplemented
22C2×#622—41no—
23#3750—41no—
24C3×(C2×D3)⋊C4—42no—
25C2×C3×C3⋊C8—41no—
26(C2×D3)⋊Dic3—42no—
27Dic32—41no—
28#1318—91nomaximal, Sylow
29C22×#67—61no—
30C2×C3×C22⋊C4—61no—
31C2×#217—61no—
32C2×(C2×D3)⋊C4—21no—
33C2×(C2×D3)⋊C4—61no—
34C2×Dic3⋊C4—61no—
35C2×Dic3⋊C4—61no—
36C2×C4×Dic3—61no—
37C3×C22⋊C8—61no—
38#830—21no—
39C23×C32C22⋊C411yescharacteristic
40C22×C3×D3—22no—
41C22×C3×D3—41no—
42C22×C3×D3—41no—
43C22×C3×D3—41no—
44C22×C3×D3—41no—
45C22×C3×D3—41no—
46C22×C3×D3—41no—
47C2×C32×C4—21no—
48C2×C32×C4—41no—
49C2×C3⋊Dic3—21no—
50C2×C3⋊Dic3—21no—
51C2×C3⋊Dic3—21no—
52C2×C3⋊Dic3—41no—
53C2×C3⋊Dic3C2×C811yescharacteristic
54C2×C3⋊Dic3M1611yescharacteristic
55C2×C3×Dic3—22no—
56C2×C3×Dic3—41no—
57C2×C3×Dic3—41no—
58#625—42no—
59#625—42no—
60#622—81no—
61C3×C3⋊C8—81no—
62#390—91no—
63#324—91no—
64#324—91no—
65C24×C3—61no—
66C23×D3—21no—
67C22×C3×C4—21no—
68C22×C3×C4—21no—
69C22×C3×C4—61no—
70C2×#67—62no—
71C2×#67—62no—
72C2×#67—122no—
73C2×#67—122no—
74C22×Dic3—21no—
75C22×Dic3—61no—
76C22×Dic3—61no—
77C22×Dic3—61no—
78C22×Dic3—61no—
79C2×C3×C8—121no—
80C3×C22⋊C4—122no—
81#217—122no—
82(C2×D3)⋊C4—42no—
83(C2×D3)⋊C4—122no—
84Dic3⋊C4—122no—
85Dic3⋊C4—121no—
86Dic3⋊C4—121no—
87C4×Dic3—122no—
88C2×C3⋊C8—41no—
89C22×C32—21no—
90C22×C32—21no—
91C22×C32C22⋊C811yescharacteristic
92C22×C32#9911yescharacteristic
93C22×C32#10011yescharacteristic
94C2×C3×D3—42no—
95C2×C3×D3—42no—
96C2×C3×D3—42no—
97C2×C3×D3—81no—
98C2×C3×D3—81no—
99C2×C3×D3—81no—
100C2×C3×D3—81no—
101C32×C4—41no—
102C3⋊Dic3—21no—
103C3⋊Dic3—21no—
104C3⋊Dic3—41no—
105C3×Dic3—42no—
106C22×D4—91no—
107C2×C4⋊C4—91no—
108C2×C22⋊C4—61no—
109C2×C22⋊C4—181no—
110C2×C42—91no—
111C22⋊C8—61no—
112C22⋊C8—181no—
113C23×C3—21no—
114C23×C3—21no—
115C23×C3—62no—
116C23×C3—121no—
117C23×C3—121no—
118C23×C3—121no—
119C23×C3—121no—
120C23×C3—121no—
121C23×C3—121no—
122C22×D3—22no—
123C22×D3—41no—
124C22×D3—41no—
125C22×D3—41no—
126C22×D3—41no—
127C22×D3—41no—
128C22×D3—41no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—41no—
132C2×C3×C4—41no—
133C2×C3×C4—41no—
134C2×C3×C4—62no—
135C2×C3×C4—81no—
136C2×C3×C4—121no—
137C2×C3×C4—121no—
138#67—124no—
139#67—124no—
140C2×Dic3—22no—
141C2×Dic3—41no—
142C2×Dic3—41no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147C2×Dic3—62no—
148C2×Dic3—62no—
149C2×Dic3—121no—
150C2×Dic3—121no—
151C2×Dic3—121no—
152C2×Dic3—121no—
153C2×Dic3—121no—
154C2×Dic3—121no—
155C2×Dic3—241no—
156C3×C8—241no—
157C3⋊C8—81no—
158C2×C32—21no—
159C2×C32—21no—
160C2×C32#32311yescharacteristic
161C2×C32#35311yescharacteristic
162C2×C32#35511yescharacteristic
163C3×D3—82no—
164C24—61no—
165C2×D4—92no—
166C2×D4—181no—
167C2×D4—361no—
168C2×D4—361no—
169C22×C4—61no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4GO+(4,𝔽2)11yescharacteristic
173C2×C8—121no—
174C2×C8—361no—
175C4⋊C4—361no—
176C22⋊C4—122no—
177C22⋊C4—362no—
178C42—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—41no—
190C22×C3—41no—
191C22×C3—122no—
192C22×C3—122no—
193C22×C3—122no—
194C22×C3—241no—
195C22×C3—241no—
196C22×C3—241no—
197C22×C3—241no—
198C2×D3—42no—
199C2×D3—42no—
200C2×D3—42no—
201C2×D3—81no—
202C2×D3—81no—
203C2×D3—81no—
204C2×D3—81no—
205C3×C4—41no—
206C3×C4—41no—
207C3×C4—81no—
208C3×C4—122no—
209Dic3—42no—
210Dic3—62no—
211Dic3—62no—
212Dic3—121no—
213Dic3—121no—
214Dic3—241no—
215Dic3—241no—
216C32#131811yescharacteristic, complemented, Sylow
217C23—62no—
218C23—121no—
219C23—121no—
220C23—121no—
221C23—121no—
222C23—121no—
223C23—121no—
224C23D32⋊C411yescharacteristic
225D4—362no—
226D4—362no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—62no—
230C2×C4—91no—
231C2×C4—91no—
232C2×C4—121no—
233C2×C4—121no—
234C2×C4—181no—
235C2×C4—181no—
236C2×C4—181no—
237C2×C4—361no—
238C8—241no—
239C8—721no—
240C2×C3—21no—
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—41no—
251C2×C3—41no—
252C2×C3—242no—
253D3—82no—
254C22—21no—
255C22—21no—
256C22—122no—
257C22—122no—
258C22—122no—
259C22—241no—
260C22—241no—
261C22—241no—
262C22—241no—
263C22D32⋊C811yescharacteristic
264C22#6372711yescharacteristic
265C22#6373811yescharacteristic
266C4—41no—
267C4—122no—
268C4—181no—
269C4—181no—
270C4—361no—
271C3—21no—
272C3—21no—
273C2—21no—
274C2—21no—
275C2—242no—
276C2#1059002711yescharacteristic
277C2#1059005911yescharacteristic
278C2#1059008011yescharacteristic
subgroupG/H
centerC22#63738
commutatorC2×C3⋊Dic3C2×C8
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#99
prime radicalC22×#625C4
cosocleC2×#3750C22
hypocenterC32#1318
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10590203C2semidirect
3. #10589148C2semidirect
21. C2×#625C8semidirect
216. C32#1318semidirect

Maximal subgroups

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

subgroupindex
#105913862
#105902032
#105891482
#13189