Finite Group Databasebeta

← #11796297

Subgroups — #11796297

Order 1152.

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

normal subgroups only

This group has 504 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
1#10596287C211yesmaximal, characteristic
2#10593808C211yesmaximal, characteristic
3#10593792C211yesmaximal, characteristic
4#10590205C214yesmaximal, complemented
5C22×C32×Q8C411yescharacteristic, complemented
6C2×#3828C2211yescharacteristic
7#64286—21no—
8#64283—21no—
9#64156—21no—
10#64155—21no—
11#64155—21no—
12#64153—21no—
13#64138C412yescomplemented
14#64138C2212yes—
15#64135C411yescharacteristic, complemented
16#63788C2212yes—
17#63786C2212yes—
18#63780—21no—
19#63774—21no—
20#5816—62no—
21C2×C32×Q8—21no—
22C2×C32×Q8—21no—
23C2×C32×Q8—41no—
24C2×C32×Q8—41no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C412yes—
27C2×#638C2×C411yescharacteristic
28C2×#638C2311yescharacteristic
29#3828—41no—
30#3828—41no—
31C2×C4⋊(C3⋊D3)D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×#634D411yescharacteristic
35C22⋊#157—22no—
36#3792—22no—
37C4⋊#157—41no—
38C4×#157—41no—
39#3788—41no—
40#3787—41no—
41#3757C2×C412yes—
42#3752—22no—
43#3752—22no—
44C4⋊(C3⋊Dic3)—21no—
45#3750—22no—
46#3750—22no—
47C4×C3⋊Dic3—21no—
48#2123—91nomaximal, Sylow
49C22×C3×Q8—22no—
50C2×#235—62no—
51#947—64no—
52#946—64no—
53#946—64no—
54#944—64no—
55#929—64no—
56#929—64no—
57#926—62no—
58C23×C32C22×C411yescharacteristic
59C22×C3⋊D3C22⋊C411yescharacteristic
60C22×C3⋊D3C2×D411yescharacteristic
61C2×#157—42no—
62C32×Q8—42no—
63C32×Q8—41no—
64C32×Q8—41no—
65C2×C32×C4—21no—
66C2×C32×C4—21no—
67C2×C32×C4—22no—
68C2×C32×C4—42no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C22⋊C411yescharacteristic
71#638—41no—
72#638—41no—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C4⋊(C3⋊D3)—41no—
77C4×C3⋊D3—21no—
78C4×C3⋊D3—21no—
79C4×C3⋊D3—21no—
80C4×C3⋊D3—21no—
81#634—41no—
82#622—42no—
83#536—91no—
84#413—91no—
85#410—91no—
86#352—94no—
87C2×C3×Q8—24no—
88C2×C3×Q8—24no—
89C2×C3×Q8—44no—
90C2×C3×Q8—44no—
91C22×C3×C4—24no—
92C22×C3×C4—22no—
93C2×#67—62no—
94C2×#67—62no—
95#235—124no—
96#235—124no—
97C2×D12—62no—
98C2×C4×D3—62no—
99C2×C4×D3—62no—
100C2×Dic6—62no—
101#217—64no—
102(C2×D3)⋊C4—68no—
103(C2×D3)⋊C4—68no—
104C4⋊Dic3—64no—
105Dic3⋊C4—68no—
106Dic3⋊C4—68no—
107C4×Dic3—64no—
108C22×C32—21no—
109C22×C32—41no—
110C22×C32C2×C22⋊C411yescharacteristic
111C2×C3⋊D3—21no—
112C2×C3⋊D3—21no—
113C2×C3⋊D3—41no—
114C2×C3⋊D3—41no—
115#157—82no—
116C32×C4—21no—
117C32×C4—42no—
118C32×C4#9911yescharacteristic
119C32×C4#9911yescharacteristic
120C3⋊Dic3—21no—
121C3⋊Dic3—21no—
122C3⋊Dic3—42no—
123C2×#41—91no—
124C22×Q8#15711yescharacteristic, complemented
125C2×M16—181no—
126C4⋊Q8—181no—
127#124—181no—
128#123—92no—
129#123—92no—
130C22⋊Q8—181no—
131C22⋊Q8—181no—
132#117—91no—
133#117—181no—
134#101—181no—
135#100—92no—
136#99—92no—
137#99—181no—
138C23×C3—22no—
139C22×D3—62no—
140C22×D3—62no—
141C3×Q8—48no—
142C3×Q8—44no—
143C3×Q8—44no—
144C2×C3×C4—24no—
145C2×C3×C4—24no—
146C2×C3×C4—28no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—48no—
150#67—124no—
151#67—124no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—68no—
155D12—124no—
156C4×D3—122no—
157C4×D3—122no—
158C4×D3—122no—
159C4×D3—122no—
160Dic6—124no—
161C2×C32—21no—
162C2×C32—41no—
163C2×C32C2×#9911yescharacteristic
164C3⋊D3—41no—
165C3⋊D3—41no—
166#41—361no—
167#41—361no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—41no—
171C2×Q8—41no—
172C2×Q8—91no—
173C2×D4—91no—
174C2×D4—91no—
175C2×D4—91no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4C2×#15712yes—
179C22×C4C2×#15711yescharacteristic
180M16—182no—
181M16—361no—
182C2×C8—361no—
183C4⋊C4—182no—
184C4⋊C4—182no—
185C4⋊C4—181no—
186C4⋊C4—361no—
187C22⋊C4—92no—
188C22⋊C4—182no—
189C22⋊C4—182no—
190C22⋊C4—182no—
191C42—181no—
192C42—361no—
193C22×C3—24no—
194C22×C3—22no—
195C22×C3—44no—
196C2×D3—122no—
197C2×D3—122no—
198C2×D3—124no—
199C2×D3—124no—
200C3×C4—24no—
201C3×C4—22no—
202C3×C4—22no—
203C3×C4—48no—
204Dic3—122no—
205Dic3—122no—
206Dic3—128no—
207C32#212311yescharacteristic, complemented, Sylow
208C23—91no—
209C23—91no—
210C23C22×#15711yescharacteristic
211Q8—42no—
212Q8—41no—
213Q8—41no—
214Q8—361no—
215D4—361no—
216D4—361no—
217D4—361no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—42no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—181no—
225C2×C4—181no—
226C2×C4—181no—
227C2×C4—181no—
228C2×C4—182no—
229C2×C4—362no—
230C2×C4C22⋊#15711yescharacteristic
231C2×C4C22⋊#15711yescharacteristic
232C8—362no—
233C2×C3—24no—
234C2×C3—22no—
235C2×C3—44no—
236D3—242no—
237D3—242no—
238C22—21no—
239C22—41no—
240C22—181no—
241C22—181no—
242C22—361no—
243C22—361no—
244C22C2×C22⋊#15711yescharacteristic
245C4—21no—
246C4—42no—
247C4—181no—
248C4—181no—
249C4—362no—
250C4—722no—
251C4#6378611yescharacteristic
252C4#6378611yescharacteristic
253C3—22no—
254C2—21no—
255C2—41no—
256C2—361no—
257C2—361no—
258C2C2×#6378611yescharacteristic
subgroupG/H
centerC2C2×#63786
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC22×C32×Q8C4
socleC2×C32C2×#99
prime radicalC2×#3828C22
cosocleC2×#638C23
hypercenterC22×Q8#157
hypocenterC32#2123
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10590205C2semidirect
5. C22×C32×Q8C4semidirect
13. #64138C4semidirect
15. #64135C4semidirect
124. C22×Q8#157semidirect
207. C32#2123semidirect

Maximal subgroups

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

subgroupindex
#105962872
#105938082
#105937922
#105902052
#21239