Finite Group Databasebeta

← #11781319

Subgroups — #11781319

Order 1152.

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

normal subgroups only

This group has 272 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
1Q8×#622C211yesmaximal, characteristic, complemented
2#10593366C211yesmaximal, characteristic
3#10591631C211yesmaximal, characteristic, complemented
4#10591622C211yesmaximal, characteristic
5#10590041C211yesmaximal, characteristic, complemented
6#10590040C211yesmaximal, characteristic, complemented
7#10590037C211yesmaximal, characteristic
8Q8×C3⋊Dic3C2211yescharacteristic
9C2×C3×#215—21no—
10#63919C2211yescharacteristic
11#63914C2211yescharacteristic
12C4⋊#622—21no—
13C4⋊#622C2211yescharacteristic
14C4×#622—21no—
15C4×#622C2211yescharacteristic
16#63739—21no—
17#63739—21no—
18C3×#835—21no—
19#63575—21no—
20#63572C2211yescharacteristic
21#63572C2211yescharacteristic
22#63563—21no—
23#5163—61no—
24#4793—61no—
25C2×C32×Q8D411yescharacteristic
26C2×C3×D12—21no—
27C2×#627—21no—
28C2×#625—21no—
29C2×#625—21no—
30C2×#622—21no—
31C2×#622D411yescharacteristic
32C2×#622D411yescharacteristic
33C4⋊(C3⋊Dic3)—21no—
34C4⋊(C3⋊Dic3)D411yescharacteristic
35C4×C3⋊Dic3—21no—
36C4×C3⋊Dic3C2311yescharacteristic
37C3×#215—42no—
38C3×C4⋊Dic3—21no—
39C2×C3×C3⋊C8—21no—
40C2×C3×C3⋊C8—21no—
41#3724—21no—
42#1678—91nomaximal, Sylow
43C2×C3×SD16—61no—
44Q8×Dic3—61no—
45Q8×Dic3—61no—
46C2×#215—21no—
47#940—61no—
48#888—61no—
49C3×#103—61no—
50#835—21no—
51#832—61no—
52#821—61no—
53#818—61no—
54Dic3⋊C8—61no—
55Dic3⋊C8—61no—
56#807—61no—
57C22×C3×D3—41no—
58C32×Q8—21no—
59C32×Q8SD1612yes—
60C2×C32×C4—21no—
61C2×C32×C4C2×D411yescharacteristic
62C2×C3⋊Dic3—21no—
63C2×C3⋊Dic3C2×D411yescharacteristic
64C2×C3⋊Dic3#4111yescharacteristic
65C2×C3×Dic3—41no—
66C3×D12—41no—
67C3×D12—41no—
68#627—81no—
69#625—41no—
70#625—41no—
71#625—81no—
72#622—21no—
73#622—21no—
74#622—41no—
75C3×C3⋊C8—41no—
76C3×C3⋊C8—41no—
77#486—91no—
78#477—91no—
79#460—91no—
80C8×Q8—91no—
81#334—91no—
82#333—91no—
83#331—91no—
84C2×C3×Q8—21no—
85C2×C3×Q8—21no—
86C2×C3×D4—61no—
87C2×#67—121no—
88C2×#67—121no—
89C2×D12—21no—
90C2×Dic6—121no—
91C3×SD16—122no—
92C2×C3×C8—61no—
93C2×C3×C8—61no—
94C3×C4⋊C4—61no—
95#215—42no—
96C4⋊Dic3—21no—
97C4⋊Dic3—61no—
98C4⋊Dic3—61no—
99C4⋊Dic3—121no—
100C4⋊Dic3—121no—
101Dic3⋊C4—121no—
102C4×Dic3—61no—
103C4×Dic3—61no—
104C4×Dic3—121no—
105C4×Dic3—121no—
106C2×C3⋊C8—21no—
107C2×C3⋊C8—21no—
108C22×C32#12111yescharacteristic
109C2×C3×D3—81no—
110C2×C3×D3—81no—
111C2×C3×D3—81no—
112C32×C4—22no—
113C32×C4C2×SD1611yescharacteristic
114C32×C4#13511yescharacteristic
115C3⋊Dic3—21no—
116C3⋊Dic3—41no—
117C3⋊Dic3#13511yescharacteristic
118C3⋊Dic3#13711yescharacteristic
119C3×Dic3—81no—
120C2×SD16—61no—
121C4⋊Q8—91no—
122#127—91no—
123C4×Q8—91no—
124#107—181no—
125C4⋊C8—91no—
126C4⋊C8—91no—
127C4⋊C8—91no—
128C4⋊C8—181no—
129#103—61no—
130#102—181no—
131#102—181no—
132#102—181no—
133C4×C8—91no—
134C4×C8—181no—
135C23×C3—121no—
136C22×D3—41no—
137C3×Q8—22no—
138C3×Q8—22no—
139C3×Q8—41no—
140C3×Q8—41no—
141C3×D4—121no—
142C3×D4—121no—
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—41no—
146C2×C3×C4—41no—
147C2×C3×C4—121no—
148#67—241no—
149#67—241no—
150#67—242no—
151C2×Dic3—41no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—121no—
157C2×Dic3—121no—
158D12—41no—
159D12—41no—
160Dic6—242no—
161C3×C8—121no—
162C3×C8—121no—
163C3⋊C8—41no—
164C3⋊C8—41no—
165C2×C32#46411yescharacteristic
166C2×C32#46511yescharacteristic
167C2×C32#47211yescharacteristic
168C3×D3—161no—
169C2×Q8—181no—
170C2×Q8GO+(4,𝔽2)11yescharacteristic
171C2×D4—61no—
172C2×D4—181no—
173C2×D4—181no—
174SD16—122no—
175C2×C8—61no—
176C2×C8—61no—
177C2×C8—91no—
178C2×C8—91no—
179C2×C8—181no—
180C4⋊C4—61no—
181C4⋊C4—91no—
182C4⋊C4—181no—
183C4⋊C4—181no—
184C42—91no—
185C42—181no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3—241no—
189C22×C3—241no—
190C22×C3—241no—
191C2×D3—81no—
192C2×D3—81no—
193C2×D3—81no—
194C3×C4—21no—
195C3×C4—21no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—42no—
199C3×C4—42no—
200C3×C4—241no—
201Dic3—61no—
202Dic3—61no—
203Dic3—61no—
204Dic3—61no—
205Dic3—81no—
206Dic3—121no—
207Dic3—121no—
208Dic3—241no—
209Dic3—241no—
210C32#167811yescharacteristic, complemented, Sylow
211C23—121no—
212Q8—21no—
213Q8—721no—
214Q8#377512yes—
215D4—121no—
216D4—121no—
217D4—361no—
218D4—361no—
219D4—721no—
220C2×C4—21no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—121no—
224C2×C4—181no—
225C2×C4C2×GO+(4,𝔽2)11yescharacteristic
226C8—121no—
227C8—121no—
228C8—181no—
229C8—181no—
230C8—361no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—481no—
238D3—161no—
239C22—241no—
240C22—241no—
241C22—241no—
242C22#6424211yescharacteristic
243C4—22no—
244C4—91no—
245C4—91no—
246C4—181no—
247C4—241no—
248C4—361no—
249C4#6423711yescharacteristic
250C4C2×#377511yescharacteristic
251C3—21no—
252C3—21no—
253C2—481no—
254C2#1059347411yescharacteristic
255C2#1059347911yescharacteristic
256C2#1059352611yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×Q8D4
socleC22×C32#121
prime radical#63914C22
hypercenterC2×Q8GO+(4,𝔽2)
hypocenterC32#1678
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×#622C2semidirect
3. #10591631C2semidirect
5. #10590041C2semidirect
6. #10590040C2semidirect
210. C32#1678semidirect

Maximal subgroups

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

subgroupindex
Q8×#6222
#105933662
#105916312
#105916222
#105900412
#105900402
#105900372
#16789