Finite Group Databasebeta

← #11781865

Subgroups — #11781865

Order 1152.

270 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 45 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#10593437C211yesmaximal, characteristic
2#10593359C211yesmaximal, characteristic
3#10590900C211yesmaximal, characteristic, complemented
4#10590733C211yesmaximal, characteristic
5#10590171C211yesmaximal, characteristic, complemented
6#10590040C211yesmaximal, characteristic, complemented
7#10590039C211yesmaximal, characteristic, complemented
8C2×#3775—21no—
9C2×C3×ΓL(1,𝔽25)—21no—
10#63919C2211yescharacteristic
11#63919C2211yescharacteristic
12C4×#625C2211yescharacteristic
13C4⋊#622C2211yescharacteristic
14C4⋊#622C2211yescharacteristic
15#63742—21no—
16#63740—21no—
17#63739—21no—
18C8×C3⋊Dic3C2211yescharacteristic
19C3×#817—21no—
20#63574—21no—
21#63572C2211yescharacteristic
22(C2×D3)⋊(C3⋊C8)—21no—
23#5128—61no—
24#4855—61no—
25C2×C3×C4×D3—21no—
26C2×#627—21no—
27C2×#627—21no—
28C2×#625D411yescharacteristic
29C2×#622—21no—
30C2×#622—21no—
31#3775—42no—
32C2×C32×C8D411yescharacteristic
33C4×C3⋊Dic3C2311yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C3×C4⋊Dic3—21no—
36C3×C4⋊Dic3—21no—
37C2×C3×C3⋊C8—21no—
38C3×ΓL(1,𝔽25)—42no—
39#3724—21no—
40#3724—21no—
41#3724D411yescharacteristic
42(C2×D3)⋊Dic3—21no—
43#1691—91nomaximal, Sylow
44C2×C3×M16—61no—
45C4×#67—61no—
46C2×ΓL(1,𝔽25)—21no—
47#888—61no—
48#888—61no—
49C3×#106—61no—
50#830—61no—
51(C2×D3)⋊C8—61no—
52#817—21no—
53Dic3⋊C8—61no—
54C8×Dic3—61no—
55C8×Dic3—61no—
56#808—61no—
57#808—61no—
58C22×C3×D3—21no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3#4111yescharacteristic
62C2×C3×Dic3—21no—
63C2×C3×Dic3—41no—
64C2×C3×Dic3—41no—
65C3×C4×D3—41no—
66C3×C4×D3—41no—
67#627—41no—
68#627—41no—
69#627—81no—
70#625—21no—
71#625—21no—
72#622—41no—
73#622—41no—
74C32×C8SD1612yescomplemented
75C3⋊(C3⋊C8)—21no—
76C3×C3⋊C8—41no—
77#498—91no—
78#476—91no—
79#461—91no—
80#436—91no—
81#335—91no—
82#333—91no—
83#332—91no—
84C22×C3×C4—61no—
85C2×#67—61no—
86C2×C4×D3—21no—
87C2×Dic6—121no—
88C2×Dic6—121no—
89C3×M16—122no—
90C2×C3×C8—21no—
91C2×C3×C8—21no—
92C2×C3×C8—61no—
93C3×C4⋊C4—61no—
94C3×C4⋊C4—61no—
95#217—61no—
96(C2×D3)⋊C4—61no—
97C4⋊Dic3—21no—
98C4⋊Dic3—21no—
99Dic3⋊C4—61no—
100Dic3⋊C4—121no—
101Dic3⋊C4—121no—
102C4×Dic3—61no—
103C4×Dic3—61no—
104C2×C3⋊C8—21no—
105C2×C3⋊C8—61no—
106C2×C3⋊C8—61no—
107ΓL(1,𝔽25)—42no—
108C22×C32#12111yescharacteristic
109C2×C3×D3—41no—
110C2×C3×D3—41no—
111C2×C3×D3—41no—
112C32×C4C2×SD1611yescharacteristic
113C32×C4#13711yescharacteristic
114C3⋊Dic3—21no—
115C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
116C3⋊Dic3#13711yescharacteristic
117C3×Dic3—41no—
118C3×Dic3—81no—
119C3×Dic3—81no—
120C2×SD16—181no—
121C2×M16—61no—
122C4⋊Q8—91no—
123C4⋊Q8—91no—
124C4×D4—91no—
125#106—61no—
126#106—181no—
127#106—181no—
128C4⋊C8—91no—
129C4⋊C8—91no—
130C4⋊C8—91no—
131#103—181no—
132#102—181no—
133C22⋊C8—181no—
134C4×C8—91no—
135C23×C3—61no—
136C22×D3—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—61no—
140C2×C3×C4—121no—
141C2×C3×C4—121no—
142C2×C3×C4—121no—
143C2×C3×C4—121no—
144#67—121no—
145#67—121no—
146C2×Dic3—21no—
147C2×Dic3—41no—
148C2×Dic3—41no—
149C2×Dic3—61no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C4×D3—41no—
154C4×D3—41no—
155Dic6—241no—
156Dic6—241no—
157Dic6—242no—
158C3×C8—22no—
159C3×C8—22no—
160C3×C8—121no—
161C3⋊C8—41no—
162C3⋊C8—62no—
163C3⋊C8—121no—
164C2×C32#46111yescharacteristic
165C2×C32#46811yescharacteristic
166C2×C32#47111yescharacteristic
167C3×D3—81no—
168C2×Q8—181no—
169C2×Q8—181no—
170C2×D4—91no—
171C22×C4—61no—
172SD16—362no—
173M16—122no—
174C2×C8—61no—
175C2×C8—91no—
176C2×C8—181no—
177C2×C8—181no—
178C2×C8GO+(4,𝔽2)11yescharacteristic
179C4⋊C4—61no—
180C4⋊C4—61no—
181C4⋊C4—91no—
182C4⋊C4—181no—
183C4⋊C4—181no—
184C22⋊C4—181no—
185C42—91no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3—121no—
189C22×C3—121no—
190C22×C3—121no—
191C2×D3—41no—
192C2×D3—41no—
193C2×D3—41no—
194C3×C4—21no—
195C3×C4—21no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—121no—
199C3×C4—241no—
200C3×C4—241no—
201Dic3—41no—
202Dic3—61no—
203Dic3—61no—
204Dic3—61no—
205Dic3—61no—
206Dic3—62no—
207Dic3—81no—
208Dic3—81no—
209Dic3—121no—
210C32#169111yescharacteristic, complemented, Sylow
211C23—61no—
212Q8—361no—
213Q8—361no—
214Q8—721no—
215D4—181no—
216D4—181no—
217C2×C4—61no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4—121no—
221C2×C4—121no—
222C2×C4—121no—
223C2×C4—121no—
224C2×C4C2×GO+(4,𝔽2)11yescharacteristic
225C8—121no—
226C8—181no—
227C8—361no—
228C8—361no—
229C8#377512yescomplemented
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—241no—
237D3—81no—
238C22—121no—
239C22—121no—
240C22—121no—
241C22#6423011yescharacteristic
242C4—91no—
243C4—91no—
244C4—121no—
245C4—181no—
246C4—241no—
247C4—241no—
248C4#6422611yescharacteristic
249C4C2×#377511yescharacteristic
250C3—21no—
251C3—21no—
252C2—241no—
253C2#1059328611yescharacteristic
254C2#1059330211yescharacteristic
255C2#1059343711yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC2×#625D4
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1691
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
3. #10590900C2semidirect
5. #10590171C2semidirect
6. #10590040C2semidirect
7. #10590039C2semidirect
74. C32×C8SD16semidirect
210. C32#1691semidirect
229. C8#3775semidirect

Maximal subgroups

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

subgroupindex
#105934372
#105933592
#105909002
#105907332
#105901712
#105900402
#105900392
#16919