Finite Group Databasebeta

← #11777828

Subgroups — #11777828

Order 1152.

274 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 55 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×#3775C211yesmaximal, characteristic
2#10590787C211yesmaximal, characteristic, complemented
3#10590733C211yesmaximal, characteristic
4C8×#622C211yesmaximal, characteristic, complemented
5#10590041C211yesmaximal, characteristic, complemented
6#10590032C211yesmaximal, characteristic, complemented
7#10590029C211yesmaximal, characteristic
8C2×#3775C411yescharacteristic
9C2×C3×ΓL(1,𝔽25)—21no—
10C4×#627C2211yescharacteristic
11C4×#625C2211yescharacteristic
12C4×#622C2211yescharacteristic
13C4×#622C2211yescharacteristic
14#63742C411yescharacteristic
15#63740C411yescharacteristic
16#63739C411yescharacteristic
17C8×C3⋊Dic3C2211yescharacteristic
18C3×#815—21no—
19#63572C2211yescharacteristic
20#63572C2211yescharacteristic
21Dic3⋊(C3⋊C8)—21no—
22(C2×D3)⋊(C3⋊C8)—21no—
23#5128—61no—
24#4701—61no—
25C2×C3×C4×D3—21no—
26C2×#627C2×C411yescharacteristic
27C2×#625C2×C411yescharacteristic
28C2×#622—21no—
29C2×#622C2×C411yescharacteristic
30C2×#622C2×C411yescharacteristic
31#3775—22no—
32C2×C32×C8D411yescharacteristic
33C4×C3⋊Dic3C2311yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C3×C4×Dic3—21no—
36C2×C3×C3⋊C8—21no—
37C2×C3×C3⋊C8—21no—
38C3×ΓL(1,𝔽25)—42no—
39#3724C2×C411yescharacteristic
40#3724C2×C411yescharacteristic
41Dic3⋊Dic3—21no—
42(C2×D3)⋊Dic3—21no—
43#1590—91nomaximal, Sylow
44C2×C3×M16—61no—
45C4×#67—61no—
46C2×ΓL(1,𝔽25)—21no—
47C4×Dic6—61no—
48C3×#97—61no—
49#830—61no—
50(C2×D3)⋊C8—61no—
51#815—21no—
52Dic3⋊C8—61no—
53Dic3⋊C8—61no—
54Dic3⋊C8—61no—
55C8×Dic3—61no—
56C8×Dic3—61no—
57C4⋊(C3⋊C8)—61no—
58C22×C3×D3—21no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C3⋊Dic3C22×C411yescharacteristic
61C2×C3⋊Dic3#4111yescharacteristic
62C2×C3×Dic3—21no—
63C2×C3×Dic3—21no—
64C2×C3×Dic3—21no—
65C3×C4×D3—41no—
66C3×C4×D3—41no—
67#627—21no—
68#627—21no—
69#625—21no—
70#625—21no—
71#622—22no—
72#622—21no—
73#622M1612yescomplemented
74C32×C8SD1612yescomplemented
75C3⋊(C3⋊C8)—21no—
76C3×C3⋊C8—41no—
77C3×C3⋊C8—41no—
78#446—91no—
79C4×SD16—91no—
80#436—91no—
81#334—91no—
82Q8⋊C8—91no—
83D4⋊C8—91no—
84C82—91no—
85C22×C3×C4—61no—
86C2×#67—61no—
87C2×C4×D3—21no—
88C2×Dic6—61no—
89C3×M16—122no—
90C2×C3×C8—21no—
91C2×C3×C8—21no—
92C2×C3×C8—61no—
93C2×C3×C8—61no—
94C3×C42—61no—
95#217—61no—
96(C2×D3)⋊C4—61no—
97C4⋊Dic3—61no—
98Dic3⋊C4—61no—
99Dic3⋊C4—61no—
100Dic3⋊C4—61no—
101C4×Dic3—21no—
102C4×Dic3—61no—
103C4×Dic3—61no—
104C2×C3⋊C8—21no—
105C2×C3⋊C8—21no—
106C2×C3⋊C8—61no—
107C2×C3⋊C8—61no—
108ΓL(1,𝔽25)—42no—
109C22×C32C4×D411yescharacteristic
110C2×C3×D3—41no—
111C2×C3×D3—41no—
112C2×C3×D3—41no—
113C32×C4C2×SD1611yescharacteristic
114C32×C4#13511yescharacteristic
115C3⋊Dic3—21no—
116C3⋊Dic3C2×M1611yescharacteristic
117C3⋊Dic3#13111yescharacteristic
118C3×Dic3—41no—
119C3×Dic3—41no—
120C3×Dic3—41no—
121C2×SD16—91no—
122C2×M16—61no—
123C4×Q8—91no—
124C4×D4—91no—
125#106—91no—
126C4⋊C8—91no—
127C4⋊C8—91no—
128C4⋊C8—181no—
129#103—91no—
130#102—91no—
131C22⋊C8—181no—
132#97—61no—
133C4×C8—91no—
134C4×C8—91no—
135C4×C8—91no—
136C23×C3—61no—
137C22×D3—21no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—61no—
141C2×C3×C4—61no—
142C2×C3×C4—61no—
143C2×C3×C4—121no—
144C2×C3×C4—121no—
145#67—121no—
146#67—121no—
147C2×Dic3—21no—
148C2×Dic3—21no—
149C2×Dic3—21no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C4×D3—41no—
155C4×D3—41no—
156Dic6—121no—
157Dic6—121no—
158C3×C8—22no—
159C3×C8—22no—
160C3×C8—121no—
161C3×C8—121no—
162C3⋊C8—41no—
163C3⋊C8—41no—
164C3⋊C8—121no—
165C3⋊C8—121no—
166C2×C32#43611yescharacteristic
167C2×C32C4×SD1611yescharacteristic
168C2×C32#44311yescharacteristic
169C3×D3—81no—
170C2×Q8—91no—
171C2×D4—91no—
172C22×C4—61no—
173SD16—182no—
174M16—122no—
175C2×C8—61no—
176C2×C8—61no—
177C2×C8—91no—
178C2×C8—91no—
179C2×C8—91no—
180C2×C8—181no—
181C2×C8GO+(4,𝔽2)11yescharacteristic
182C4⋊C4—91no—
183C4⋊C4—91no—
184C4⋊C4—181no—
185C22⋊C4—181no—
186C42—61no—
187C42—91no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—121no—
191C22×C3—121no—
192C22×C3—121no—
193C2×D3—41no—
194C2×D3—41no—
195C2×D3—41no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—21no—
199C3×C4—21no—
200C3×C4—121no—
201C3×C4—121no—
202C3×C4—121no—
203Dic3—41no—
204Dic3—41no—
205Dic3—41no—
206Dic3—61no—
207Dic3—61no—
208Dic3—61no—
209Dic3—61no—
210Dic3—121no—
211Dic3—121no—
212C32#159011yescharacteristic, complemented, Sylow
213C23—61no—
214Q8—181no—
215Q8—181no—
216D4—181no—
217D4—181no—
218C2×C4—61no—
219C2×C4—61no—
220C2×C4—61no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—121no—
224C2×C4—121no—
225C2×C4C2×GO+(4,𝔽2)11yescharacteristic
226C8—92no—
227C8—121no—
228C8—121no—
229C8—181no—
230C8—182no—
231C8—181no—
232C8#377512yescomplemented
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—241no—
240D3—81no—
241C22—121no—
242C22—121no—
243C22—121no—
244C22C4×GO+(4,𝔽2)11yescharacteristic
245C4—91no—
246C4—91no—
247C4—121no—
248C4—121no—
249C4—121no—
250C4—181no—
251C4#6422311yescharacteristic
252C4C2×#377511yescharacteristic
253C3—21no—
254C3—21no—
255C2—241no—
256C2#1059328311yescharacteristic
257C2#1059329911yescharacteristic
258C2C4×#377511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC2×C32×C8D4
socleC22×C32C4×D4
prime radicalC2×#625C2×C4
cosocleC4×C3⋊Dic3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1590
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10590787C2semidirect
4. C8×#622C2semidirect
5. #10590041C2semidirect
6. #10590032C2semidirect
73. #622M16semidirect
74. C32×C8SD16semidirect
212. C32#1590semidirect
232. C8#3775semidirect

Maximal subgroups

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

subgroupindex
C4×#37752
#105907872
#105907332
C8×#6222
#105900412
#105900322
#105900292
#15909