Finite Group Databasebeta

← #11776250

Subgroups — #11776250

Order 1152.

372 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 61 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#10593882C211yesmaximal, characteristic
2#10593727C211yesmaximal, characteristic
3#10590297C211yesmaximal, characteristic
4#10590039C212yesmaximal, complemented
5#10590038C212yesmaximal, complemented
6C42×C3⋊D3C2211yescharacteristic
7C3×C4×Dic6—21no—
8#63919C2211yescharacteristic
9C4×#627—21no—
10#63874C412yes—
11#63873C2211yescharacteristic
12#63871—21no—
13#63870C412yes—
14#63865—21no—
15#63778—21no—
16C4⋊#622C2212yes—
17C4×#622—21no—
18C3×C4×C3⋊C8—21no—
19#63572C2212yes—
20#63557—21no—
21#5578—61no—
22#4685—61no—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C3×Dic6—21no—
27C2×#627—21no—
28C2×#622—22no—
29C32×C42D411yescharacteristic
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33C3×C4⋊Dic3—21no—
34C3×Dic3⋊C4—22no—
35C3×C4×Dic3—22no—
36C2×C3×C3⋊C8—22no—
37#3724—21no—
38#3724C2×C412yes—
39#3724C2×C412yes—
40Dic3⋊Dic3—22no—
41#3722—22no—
42#1544—91nomaximal, Sylow
43C3×C4×Q8—61no—
44#946—61no—
45#944—61no—
46#897—61no—
47#896—62no—
48#889—62no—
49#888—61no—
50#872—62no—
51C42×D3—61no—
52C42×D3—61no—
53C4×Dic6—21no—
54C4×Dic6—62no—
55C3×C4×C8—61no—
56(C2×D3)⋊C8—62no—
57Dic3⋊C8—62no—
58C4×C3⋊C8—21no—
59C22×C3⋊D3C22⋊C411yescharacteristic
60C2×C32×C4C22⋊C411yescharacteristic
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3C22⋊C411yescharacteristic
64C2×C3⋊Dic3C22×C411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66C4×C3⋊D3—22no—
67C4×C3⋊D3—22no—
68C4×C3⋊D3—22no—
69C2×C3×Dic3—22no—
70C2×C3×Dic3—22no—
71C3×Dic6—42no—
72#627—42no—
73#622—42no—
74C3×C3⋊C8—42no—
75#533—91no—
76#431—91no—
77#431—91no—
78#332—92no—
79#332—92no—
80C2×C3×Q8—61no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C4×D3—61no—
84C2×C4×D3—61no—
85C2×C4×D3—61no—
86C2×C4×D3—61no—
87C2×Dic6—21no—
88C2×Dic6—62no—
89C2×C3×C8—62no—
90C3×C4⋊C4—61no—
91C3×C4⋊C4—62no—
92C3×C42—21no—
93C3×C42—21no—
94C3×C42—62no—
95(C2×D3)⋊C4—62no—
96(C2×D3)⋊C4—62no—
97C4⋊Dic3—21no—
98C4⋊Dic3—62no—
99Dic3⋊C4—22no—
100Dic3⋊C4—62no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104C4×Dic3—22no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C2×C3⋊C8—22no—
112C22×C32C2×C22⋊C411yescharacteristic
113C2×C3⋊D3—21no—
114C2×C3⋊D3—21no—
115C2×C3⋊D3—21no—
116C32×C4—21no—
117C32×C4#10112yes—
118C32×C4#13512yes—
119C3⋊Dic3—21no—
120C3⋊Dic3—21no—
121C3⋊Dic3#13512yes—
122C3×Dic3—42no—
123C3×Dic3—42no—
124C4⋊Q8—91no—
125C4⋊Q8—91no—
126#125—92no—
127C22⋊Q8—181no—
128C22⋊Q8—181no—
129C4×Q8—61no—
130C4×Q8—181no—
131#117—92no—
132C2×C42—91no—
133C4⋊C8—92no—
134C4⋊C8—92no—
135C22⋊C8—181no—
136C22⋊C8—181no—
137C4×C8—61no—
138C4×C8—181no—
139C22×D3—61no—
140C22×D3—61no—
141C3×Q8—122no—
142C2×C3×C4—21no—
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—62no—
149C2×C3×C4—62no—
150C2×Dic3—22no—
151C2×Dic3—22no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C4×D3—64no—
159C4×D3—64no—
160C4×D3—122no—
161C4×D3—122no—
162C4×D3—122no—
163C4×D3—122no—
164Dic6—42no—
165Dic6—124no—
166C3×C8—122no—
167C3⋊C8—42no—
168C2×C32C2×#10111yescharacteristic
169C2×C32#41611yescharacteristic
170C2×C32#41611yescharacteristic
171C3⋊D3—41no—
172C2×Q8—61no—
173C2×Q8—181no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—91no—
177C2×C8—62no—
178C2×C8—182no—
179C4⋊C4—61no—
180C4⋊C4—62no—
181C4⋊C4—92no—
182C4⋊C4—92no—
183C4⋊C4—182no—
184C4⋊C4—181no—
185C22⋊C4—182no—
186C42—62no—
187C42—91no—
188C42—91no—
189C42—91no—
190C42GO+(4,𝔽2)11yescharacteristic
191C22×C3—21no—
192C22×C3—21no—
193C2×D3—62no—
194C2×D3—62no—
195C2×D3—121no—
196C2×D3—121no—
197C2×D3—121no—
198C2×D3—121no—
199C3×C4—22no—
200C3×C4—22no—
201C3×C4—22no—
202C3×C4—22no—
203C3×C4—22no—
204C3×C4—41no—
205C3×C4—122no—
206C3×C4—122no—
207Dic3—42no—
208Dic3—42no—
209Dic3—62no—
210Dic3—62no—
211Dic3—62no—
212Dic3—121no—
213Dic3—121no—
214Dic3—121no—
215C32#154411yescharacteristic, complemented, Sylow
216C23—91no—
217Q8—122no—
218Q8—362no—
219C2×C4—62no—
220C2×C4—62no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—182no—
225C2×C4—182no—
226C2×C4—182no—
227C2×C4D32⋊C411yescharacteristic
228C2×C4D32⋊C411yescharacteristic
229C2×C4C2×GO+(4,𝔽2)11yescharacteristic
230C8—122no—
231C8—362no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238D3—122no—
239D3—122no—
240C22—181no—
241C22—181no—
242C22—181no—
243C22C2×D32⋊C411yescharacteristic
244C4—21no—
245C4—92no—
246C4—122no—
247C4—122no—
248C4—181no—
249C4—181no—
250C4#6372812yes—
251C4#6422312yes—
252C3—21no—
253C3—21no—
254C2—361no—
255C2C2×#6372811yescharacteristic
256C2#1059331711yescharacteristic
257C2#1059334911yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1544
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590039C2semidirect
5. #10590038C2semidirect
215. C32#1544semidirect

Maximal subgroups

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

subgroupindex
#105938822
#105937272
#105902972
#105900392
#105900382
#15449