Finite Group Databasebeta

← #11790352

Subgroups — #11790352

Order 1152.

386 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C4⋊C4×#157C211yesmaximal, characteristic
2#10593413C211yesmaximal, characteristic
3C2×#63732C211yesmaximal, characteristic
4#10590575C212yesmaximal
5#10590049C212yesmaximal
6C2×C4⋊#157C2211yescharacteristic
7C2×C4×#157—21no—
8C2×C4×#157C2211yescharacteristic
9C2×#3773—21no—
10C2×#3773—21no—
11C4⋊C4×C3⋊D3C2211yescharacteristic
12#63900C2212yes—
13C2×#3710C2212yes—
14#63781—21no—
15#63732C414yescomplemented
16C3×#808—22no—
17#63573—22no—
18D3×#106—62no—
19C22×#157—21no—
20C22×#157D411yescharacteristic
21C22×#157D411yescharacteristic
22C2×C4×C3⋊D3—21no—
23C2×C4×C3⋊D3C2311yescharacteristic
24C2×#624—22no—
25C4⋊#157—21no—
26C4⋊#157Q812yes—
27C4×#157—42no—
28C4×#157C2×C412yes—
29C4×#157Q812yes—
30#3773—42no—
31#3773—42no—
32C32×C4⋊C4D411yescharacteristic
33C4⋊(C3⋊Dic3)D411yescharacteristic
34#3750—21no—
35C3×C4⋊Dic3—22no—
36C2×C3×C3⋊C8—22no—
37#3724—22no—
38#3710—22no—
39#3710C2×C414yes—
40#1948—91nomaximal, Sylow
41C2×D3×C8—62no—
42D3×C4⋊C4—62no—
43D3×C4⋊C4—62no—
44C3×#106—62no—
45#817—62no—
46#808—22no—
47#808—62no—
48C22×C3⋊D3C2×D411yescharacteristic
49C2×#157—21no—
50C2×#157—21no—
51C2×#157—22no—
52C2×#157—41no—
53C2×#157—41no—
54C2×#157C4⋊C412yes—
55C2×#157C4⋊C412yes—
56C2×#157SD1612yes—
57C2×#157SD1612yes—
58C2×C32×C4—21no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C3⋊Dic3—21no—
61C2×C3⋊Dic3#4111yescharacteristic
62C4×C3⋊D3—41no—
63C4×C3⋊D3—41no—
64C4×C3⋊D3C22×C411yescharacteristic
65C4×C3⋊D3C2×Q811yescharacteristic
66C4×C3⋊D3C2×Q811yescharacteristic
67C4×C3⋊D3#4111yescharacteristic
68C2×C3×Dic3—42no—
69#624—42no—
70#624—42no—
71C3×C3⋊C8—24no—
72C2×#106—92no—
73C2×C4⋊C8—91no—
74#384—91no—
75C4×C4⋊C4—91no—
76#340—92no—
77C2×C4×D3—62no—
78C2×C4×D3—122no—
79C2×C4×D3—122no—
80C2×C3×C8—62no—
81C3×C4⋊C4—22no—
82C3×C4⋊C4—62no—
83C4⋊Dic3—22no—
84C4⋊Dic3—62no—
85Dic3⋊C4—122no—
86Dic3⋊C4—122no—
87C2×C3⋊C8—22no—
88D3×C8—64no—
89D3×C8—64no—
90C22×C32#12111yescharacteristic
91C2×C3⋊D3C2×C4⋊C411yescharacteristic
92C2×C3⋊D3C22⋊Q811yescharacteristic
93C2×C3⋊D3C2×SD1611yescharacteristic
94C2×C3⋊D3C2×SD1611yescharacteristic
95C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
96C2×C3⋊D3#13711yescharacteristic
97#157—22no—
98#157—42no—
99#157#10614yescomplemented
100C32×C4—41no—
101C32×C4C4×D411yescharacteristic
102C32×C4C4⋊Q811yescharacteristic
103C3⋊Dic3—41no—
104C3⋊Dic3C4×Q811yescharacteristic
105C3⋊Dic3#12511yescharacteristic
106C3×Dic3—82no—
107C22×C8—92no—
108C2×C4⋊C4—92no—
109C2×C4⋊C4—91no—
110C2×C4⋊C4—91no—
111C2×C4⋊C4—181no—
112C2×C4⋊C4—181no—
113C2×C42—91no—
114C2×C42—181no—
115#106—62no—
116#106—182no—
117C4⋊C8—94no—
118#95—181no—
119C22×D3—62no—
120C2×C3×C4—22no—
121C2×C3×C4—42no—
122C2×C3×C4—122no—
123C2×Dic3—42no—
124C2×Dic3—62no—
125C2×Dic3—122no—
126C4×D3—62no—
127C4×D3—62no—
128C4×D3—62no—
129C4×D3—62no—
130C4×D3—242no—
131C4×D3—242no—
132C4×D3—242no—
133C4×D3—242no—
134C3×C8—64no—
135C3⋊C8—24no—
136C2×C32#38911yescharacteristic
137C2×C32#46011yescharacteristic
138C2×C32#46111yescharacteristic
139C3⋊D3C2×#10611yescharacteristic
140C3⋊D3#42811yescharacteristic
141C3⋊D3#47511yescharacteristic
142C3⋊D3#47611yescharacteristic
143C22×C4—91no—
144C22×C4—91no—
145C22×C4—91no—
146C22×C4—181no—
147C22×C4—182no—
148C22×C4—181no—
149C2×C8—62no—
150C2×C8—94no—
151C2×C8—182no—
152C4⋊C4—62no—
153C4⋊C4—92no—
154C4⋊C4—91no—
155C4⋊C4—181no—
156C4⋊C4—182no—
157C4⋊C4—181no—
158C4⋊C4—362no—
159C4⋊C4—362no—
160C4⋊C4GO+(4,𝔽2)11yescharacteristic
161C42—92no—
162C42—92no—
163C42—362no—
164C22×C3—22no—
165C2×D3—62no—
166C2×D3—62no—
167C2×D3—62no—
168C2×D3—62no—
169C2×D3—62no—
170C2×D3—62no—
171C3×C4—22no—
172C3×C4—22no—
173C3×C4—82no—
174C3×C4—242no—
175Dic3—62no—
176Dic3—62no—
177Dic3—82no—
178Dic3—242no—
179C32#194811yescharacteristic, complemented, Sylow
180C23—91no—
181C2×C4—21no—
182C2×C4—92no—
183C2×C4—92no—
184C2×C4—92no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—91no—
188C2×C4—91no—
189C2×C4—91no—
190C2×C4—92no—
191C2×C4—122no—
192C2×C4—181no—
193C2×C4—181no—
194C2×C4—182no—
195C2×C4—181no—
196C2×C4—361no—
197C2×C4—361no—
198C2×C4—362no—
199C2×C4—362no—
200C2×C4—361no—
201C2×C4—361no—
202C2×C4C2×GO+(4,𝔽2)11yescharacteristic
203C8—64no—
204C2×C3—22no—
205C2×C3—22no—
206C2×C3—22no—
207D3—62no—
208D3—62no—
209D3—62no—
210D3—62no—
211C22—91no—
212C22—91no—
213C22—91no—
214C22—91no—
215C22—91no—
216C22—91no—
217C22#6424211yescharacteristic
218C4—41no—
219C4—94no—
220C4—91no—
221C4—91no—
222C4—182no—
223C4—242no—
224C4—362no—
225C4—361no—
226C4#6422211yescharacteristic
227C4C4×GO+(4,𝔽2)11yescharacteristic
228C3—22no—
229C2—91no—
230C2—91no—
231C2—91no—
232C2—91no—
233C2#1059341011yescharacteristic
234C2#1059346511yescharacteristic
235C2#1059347611yescharacteristic
subgroupG/H
centerC22#64242
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1948
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
15. #63732C4semidirect
99. #157#106semidirect
179. C32#1948semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×#1572
#105934132
C2×#637322
#105905752
#105900492
#19489