Finite Group Databasebeta

← #11796458

Subgroups — #11796458

Order 1152.

590 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C3⋊D3×#124C211yesmaximal, characteristic
2#10593836C212yesmaximal, complemented
3#10590212C212yesmaximal, complemented
4#10590145C212yesmaximal, complemented
5C2×Q8×C3⋊D3C2211yescharacteristic
6C2×D4×C3⋊D3C411yescharacteristic
7#64283—22no—
8C32×#124C411yescharacteristic
9#64156C411yescharacteristic
10#64145C2211yescharacteristic
11#64094—22no—
12C22⋊C4×C3⋊D3—22no—
13#64084C2211yescharacteristic
14C42×C3⋊D3C411yescharacteristic
15#63780—22no—
16#63780C2214yescomplemented
17D3×#124—62no—
18C23×C3⋊D3—21no—
19C2×C32×Q8C2×C411yescharacteristic
20C2×C32×D4C2×C411yescharacteristic
21C2×#638—21no—
22Q8×C3⋊D3—41no—
23Q8×C3⋊D3—41no—
24D4×C3⋊D3—41no—
25D4×C3⋊D3—41no—
26C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
27C2×C4×C3⋊D3—21no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D412yes—
30C2×#634D412yes—
31C2×#634C2311yescharacteristic
32#3792—24no—
33#3788—42no—
34#3787—42no—
35C32×C22⋊C4—22no—
36C32×C42C2×C411yescharacteristic
37#3757—22no—
38#3752—22no—
39#3752—22no—
40C4×C3⋊Dic3—21no—
41C4×C3⋊Dic3C2×C411yescharacteristic
42C2×#355—91nomaximal, Sylow
43C2×D3×Q8—62no—
44C2×D3×D4—62no—
45C3×#124—22no—
46#947—62no—
47#936—62no—
48#885—68no—
49D3×C22⋊C4—68no—
50#875—62no—
51C42×D3—62no—
52C23×C32—21no—
53C22×C3⋊D3—21no—
54C22×C3⋊D3—44no—
55C22×C3⋊D3—41no—
56C22×C3⋊D3—41no—
57C22×C3⋊D3C22⋊C411yescharacteristic
58C32×Q8—41no—
59C32×D4—41no—
60C2×C32×C4—21no—
61C2×C32×C4C22⋊C412yes—
62C2×C32×C4C22×C411yescharacteristic
63#638—42no—
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C2×D412yes—
67C4⋊(C3⋊D3)—41no—
68C4×C3⋊D3—21no—
69C4×C3⋊D3—21no—
70C4×C3⋊D3—22no—
71C4×C3⋊D3—22no—
72C4×C3⋊D3—42no—
73#634—42no—
74#634—41no—
75#622—44no—
76C2×#124—91no—
77C2×#101—92no—
78#355—92no—
79#355—92no—
80C23×D3—64no—
81C2×C3×Q8—22no—
82C2×C3×D4—22no—
83C2×#67—64no—
84D3×Q8—124no—
85D3×Q8—124no—
86D3×D4—124no—
87D3×D4—124no—
88C2×D12—62no—
89C2×C4×D3—62no—
90C2×C4×D3—64no—
91C2×C4×D3—64no—
92C2×Dic6—62no—
93C2×Dic6—64no—
94C3×C22⋊C4—28no—
95C3×C42—22no—
96#217—68no—
97(C2×D3)⋊C4—68no—
98(C2×D3)⋊C4—68no—
99C4×Dic3—62no—
100C4×Dic3—64no—
101C22×C32—42no—
102C22×C32—41no—
103C22×C32C2×C22⋊C411yescharacteristic
104C2×C3⋊D3—22no—
105C2×C3⋊D3—42no—
106C2×C3⋊D3—41no—
107C2×C3⋊D3—82no—
108C2×C3⋊D3—82no—
109C2×C3⋊D3#9911yescharacteristic
110C2×C3⋊D3#9911yescharacteristic
111C32×C4—21no—
112C32×C4—22no—
113C32×C4—41no—
114C3⋊Dic3—21no—
115C3⋊Dic3—22no—
116C3⋊Dic3—41no—
117C22×Q8—91no—
118C22×D4—91no—
119C2×M16—182no—
120#124—91no—
121#124—91no—
122#124—91no—
123#124—182no—
124#124#15711yescharacteristic
125C2×C22⋊C4—182no—
126C2×C42—91no—
127#101—94no—
128#101—182no—
129C23×C3—24no—
130C22×D3—62no—
131C22×D3—64no—
132C22×D3—124no—
133C22×D3—124no—
134C22×D3—1216no—
135C3×Q8—44no—
136C3×D4—44no—
137C2×C3×C4—24no—
138C2×C3×C4—22no—
139C2×C3×C4—24no—
140#67—128no—
141C2×Dic3—62no—
142C2×Dic3—64no—
143C2×Dic3—64no—
144D12—124no—
145C4×D3—64no—
146C4×D3—64no—
147C4×D3—124no—
148C4×D3—124no—
149C4×D3—128no—
150Dic6—128no—
151Dic6—124no—
152C2×C32—21no—
153C2×C32—81no—
154C2×C32C2×#9911yescharacteristic
155C3⋊D3—21no—
156C3⋊D3—81no—
157C3⋊D3#35512yescomplemented
158C24—181no—
159C2×Q8—91no—
160C2×Q8—92no—
161C2×Q8—361no—
162C2×Q8—361no—
163C2×Q8C2×#15711yescharacteristic
164C2×D4—91no—
165C2×D4—181no—
166C2×D4—361no—
167C2×D4—361no—
168C2×D4C2×#15711yescharacteristic
169C22×C4—91no—
170C22×C4—92no—
171C22×C4—181no—
172M16—184no—
173M16—362no—
174C2×C8—362no—
175C22⋊C4—22no—
176C22⋊C4—182no—
177C22⋊C4—182no—
178C22⋊C4—182no—
179C42—91no—
180C42—181no—
181C42C2×#15711yescharacteristic
182C22×C3—22no—
183C22×C3—44no—
184C22×C3—48no—
185C2×D3—62no—
186C2×D3—62no—
187C2×D3—68no—
188C2×D3—124no—
189C2×D3—128no—
190C2×D3—248no—
191C2×D3—248no—
192C3×C4—24no—
193C3×C4—44no—
194C3×C4—44no—
195Dic3—64no—
196Dic3—124no—
197Dic3—124no—
198C32C2×#35511yescharacteristic, complemented, Sylow
199C23—21no—
200C23—91no—
201C23—181no—
202C23—361no—
203C23—361no—
204C23—364no—
205Q8—41no—
206Q8—361no—
207Q8—362no—
208D4—41no—
209D4—361no—
210D4—362no—
211C2×C4—21no—
212C2×C4—91no—
213C2×C4—92no—
214C2×C4—182no—
215C2×C4—182no—
216C2×C4—181no—
217C2×C4—181no—
218C2×C4—181no—
219C2×C4—362no—
220C2×C4C22⋊#15712yes—
221C2×C4C22×#15711yescharacteristic
222C8—364no—
223C2×C3—24no—
224C2×C3—22no—
225C2×C3—84no—
226D3—64no—
227D3—64no—
228D3—244no—
229C22—42no—
230C22—41no—
231C22—91no—
232C22—91no—
233C22—182no—
234C22—362no—
235C22—361no—
236C22—722no—
237C22—722no—
238C22C2×C22⋊#15711yescharacteristic
239C4—21no—
240C4—22no—
241C4—41no—
242C4—182no—
243C4—181no—
244C4—361no—
245C3—22no—
246C2—21no—
247C2—81no—
248C2—92no—
249C2—181no—
250C2—721no—
251C2#1059381711yescharacteristic
subgroupG/H
centerC2#10593817
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#124C4
socleC2×C32C2×#99
prime radicalC2×D4×C3⋊D3C4
cosocleC2×#634C23
hypercenter#124#157
hypocenterC32C2×#355
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10593836C2semidirect
3. #10590212C2semidirect
4. #10590145C2semidirect
16. #63780C22semidirect
157. C3⋊D3#355semidirect
198. C32C2×#355semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1242
#105938362
#105902122
#105901452
C2×#3559