Finite Group Databasebeta

← #11786019

Subgroups — #11786019

Order 1152.

282 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 59 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#10593765C211yesmaximal, characteristic
2#10590913C211yesmaximal, characteristic
3#10590712C211yesmaximal, characteristic
4#10590056C212yesmaximal
5#10590045C212yesmaximal
6#64286C2211yescharacteristic
7#64283C2211yescharacteristic
8C2×C8×C3⋊D3C2211yescharacteristic
9#63849C2212yes—
10#63818C2212yes—
11#63767C412yescomplemented
12C8×#157C412yescomplemented
13C3×#819—21no—
14C3×#817—21no—
15#63578—21no—
16#63576—21no—
17D3×#108—61no—
18#4860—61no—
19C2×C4×C3⋊D3C2311yescharacteristic
20C22⋊#157—21no—
21#3792—21no—
22C4⋊#157—21no—
23C4×#157C2×C412yes—
24#3788—21no—
25#3787C2×C412yes—
26C2×C32×C8D411yescharacteristic
27C2×C3⋊(C3⋊C8)D411yescharacteristic
28C8×C3⋊D3C2×C411yescharacteristic
29C8×C3⋊D3C2×C411yescharacteristic
30C8×C3⋊D3Q811yescharacteristic
31C8×C3⋊D3Q811yescharacteristic
32C3×C4⋊Dic3—22no—
33C3×#208—22no—
34#3722—22no—
35Dic32—22no—
36#3712—22no—
37#3710—22no—
38#1833—91nomaximal, Sylow
39D3×M16—62no—
40C2×D3×C8—61no—
41C2×D3×C8—61no—
42#892—62no—
43C3×#108—61no—
44C3×#106—61no—
45#822—62no—
46#819—21no—
47#817—21no—
48#807—62no—
49C22×C3⋊D3#4111yescharacteristic
50C2×#157—22no—
51C2×C32×C4C2×D411yescharacteristic
52C2×C3⋊Dic3#4111yescharacteristic
53C4×C3⋊D3C22×C411yescharacteristic
54C4×C3⋊D3C2×Q811yescharacteristic
55C4×C3⋊D3#4111yescharacteristic
56C4×C3⋊D3#4111yescharacteristic
57C2×C3×Dic3—42no—
58#622—22no—
59C32×C8C4⋊C411yescharacteristic
60C32×C8C4⋊C411yescharacteristic
61C3⋊(C3⋊C8)C4⋊C411yescharacteristic
62C3⋊(C3⋊C8)C4⋊C411yescharacteristic
63C3×C3⋊C8—42no—
64C2×#108—91no—
65#427—91no—
66#405—91no—
67#344—92no—
68H(3,ℤ/4)—92no—
69C2×C4×D3—61no—
70C2×C4×D3—61no—
71C3×M16—62no—
72C2×C3×C8—21no—
73C2×C3×C8—21no—
74C3×C4⋊C4—62no—
75(C2×D3)⋊C4—122no—
76C4⋊Dic3—22no—
77C4×Dic3—122no—
78#208—22no—
79C2×C3⋊C8—61no—
80C2×C3⋊C8—61no—
81ΓL(1,𝔽25)—122no—
82D3×C8—61no—
83D3×C8—61no—
84D3×C8—61no—
85D3×C8—61no—
86D3×C8—61no—
87D3×C8—61no—
88D3×C8—61no—
89D3×C8—61no—
90D3×C8—122no—
91C22×C32#12411yescharacteristic
92C2×C3⋊D3—41no—
93C2×C3⋊D3#11711yescharacteristic
94C2×C3⋊D3#12511yescharacteristic
95#157—42no—
96C32×C4C2×C4⋊C411yescharacteristic
97C32×C4#12411yescharacteristic
98C3⋊Dic3#11711yescharacteristic
99C3⋊Dic3#12511yescharacteristic
100C3×Dic3—82no—
101C2×M16—91no—
102C2×M16—92no—
103C22×C8—91no—
104#117—91no—
105#117—92no—
106#108—61no—
107#108—181no—
108#107—181no—
109#106—61no—
110#97—92no—
111C4×C8—92no—
112C22×D3—61no—
113C22×D3—61no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—122no—
117C2×Dic3—42no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C4×D3—61no—
121C4×D3—61no—
122C4×D3—61no—
123C4×D3—61no—
124C4×D3—61no—
125C4×D3—61no—
126C4×D3—61no—
127C4×D3—61no—
128C3×C8—21no—
129C3×C8—21no—
130C3×C8—21no—
131C3×C8—21no—
132C3×C8—122no—
133C3⋊C8—42no—
134C3⋊C8—61no—
135C3⋊C8—61no—
136C3⋊C8—61no—
137C3⋊C8—61no—
138C2×C32—21no—
139C2×C32#38211yescharacteristic
140C3⋊D3—21no—
141C3⋊D3—21no—
142C22×C4—91no—
143M16—62no—
144M16—182no—
145M16—181no—
146M16—181no—
147C2×C8—91no—
148C2×C8—91no—
149C2×C8—91no—
150C2×C8—91no—
151C2×C8—91no—
152C2×C8—92no—
153C2×C8—182no—
154C2×C8GO+(4,𝔽2)11yescharacteristic
155C4⋊C4—62no—
156C4⋊C4—181no—
157C22⋊C4—182no—
158C22⋊C4—181no—
159C42—92no—
160C42—182no—
161C22×C3—21no—
162C22×C3—21no—
163C2×D3—61no—
164C2×D3—61no—
165C2×D3—61no—
166C2×D3—61no—
167C2×D3—122no—
168C2×D3—122no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—21no—
173C3×C4—242no—
174Dic3—61no—
175Dic3—61no—
176Dic3—61no—
177Dic3—61no—
178Dic3—82no—
179C32#183311yescharacteristic, complemented, Sylow
180C23—91no—
181C2×C4—91no—
182C2×C4—91no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—122no—
187C2×C4—182no—
188C2×C4C2×GO+(4,𝔽2)11yescharacteristic
189C8—91no—
190C8—91no—
191C8—122no—
192C8—182no—
193C8#377311yescharacteristic
194C8#377311yescharacteristic
195C2×C3—22no—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3—41no—
199D3—62no—
200D3—121no—
201D3—121no—
202D3—121no—
203C22—91no—
204C22—91no—
205C22—361no—
206C22#6422111yescharacteristic
207C4—91no—
208C4—91no—
209C4—242no—
210C4—362no—
211C4#6422111yescharacteristic
212C4C2×#377311yescharacteristic
213C3—21no—
214C3—21no—
215C2—21no—
216C2—181no—
217C2—181no—
218C2#1059334411yescharacteristic
subgroupG/H
centerC2#10593344
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#382
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1833
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
11. #63767C4semidirect
12. C8×#157C4semidirect
179. C32#1833semidirect

Maximal subgroups

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

subgroupindex
#105937652
#105909132
#105907122
#105900562
#105900452
#18339