Finite Group Databasebeta

← #11781550

Subgroups — #11781550

Order 1152.

276 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593359C211yesmaximal, characteristic
2#10593347C211yesmaximal, characteristic
3#10590901C211yesmaximal, characteristic, complemented
4C8×#625C211yesmaximal, characteristic
5#10590173C211yesmaximal, characteristic, complemented
6#10590040C211yesmaximal, characteristic, complemented
7#10590038C211yesmaximal, characteristic, complemented
8C2×C3×D3×C8—21no—
9#63919C2211yescharacteristic
10C4×#625C2211yescharacteristic
11#63873C2211yescharacteristic
12C4⋊#622C2211yescharacteristic
13C4⋊#622C2211yescharacteristic
14#63743—21no—
15#63742—21no—
16#63739—21no—
17#63739—21no—
18C8×C3⋊Dic3C2211yescharacteristic
19C3×#816—21no—
20#63572C2211yescharacteristic
21#63565—21no—
22(C2×D3)⋊(C3⋊C8)—21no—
23C8×#67—61no—
24#4792—61no—
25C2×C3×C4×D3—21no—
26C2×C3×Dic6—21no—
27C2×#627—21no—
28C2×#625D411yescharacteristic
29C2×#622—21no—
30C2×#622—21no—
31C2×C32×C8D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C3×C4⋊Dic3—21no—
35C2×C3×C3⋊C8—21no—
36C3×D3×C8—42no—
37#3724—21no—
38#3724—21no—
39#3724—21no—
40#3724D411yescharacteristic
41(C2×D3)⋊Dic3—21no—
42#1683—91nomaximal, Sylow
43C22×C3×C8—61no—
44#944—61no—
45C4×#67—61no—
46C2×D3×C8—21no—
47#888—61no—
48C3×#103—61no—
49#835—61no—
50#830—61no—
51(C2×D3)⋊C8—61no—
52#816—21no—
53Dic3⋊C8—61no—
54C8×Dic3—61no—
55C8×Dic3—61no—
56#810—61no—
57C22×C3×D3—21no—
58C2×C32×C4C2×D411yescharacteristic
59C2×C3⋊Dic3C2×D411yescharacteristic
60C2×C3⋊Dic3#4111yescharacteristic
61C2×C3×Dic3—21no—
62C2×C3×Dic3—41no—
63C2×C3×Dic3—41no—
64C3×C4×D3—41no—
65C3×C4×D3—41no—
66C3×Dic6—41no—
67C3×Dic6—41no—
68#627—81no—
69#625—21no—
70#625Q1612yes—
71#622—41no—
72#622—41no—
73C32×C8—21no—
74C3⋊(C3⋊C8)—21no—
75C3×C3⋊C8—41no—
76#487—91no—
77#476—91no—
78#474—91no—
79C8×D4—91no—
80#335—91no—
81#333—91no—
82#332—91no—
83C2×C3×Q8—61no—
84C22×C3×C4—61no—
85C2×#67—61no—
86C2×C4×D3—21no—
87C2×Dic6—21no—
88C2×Dic6—121no—
89C2×C3×C8—21no—
90C2×C3×C8—21no—
91C2×C3×C8—61no—
92C2×C3×C8—122no—
93C3×C4⋊C4—61no—
94#217—61no—
95(C2×D3)⋊C4—61no—
96C4⋊Dic3—21no—
97Dic3⋊C4—61no—
98Dic3⋊C4—121no—
99Dic3⋊C4—121no—
100Dic3⋊C4—121no—
101C4×Dic3—61no—
102C4×Dic3—61no—
103C2×C3⋊C8—21no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106D3×C8—42no—
107C22×C32#12111yescharacteristic
108C2×C3×D3—22no—
109C2×C3×D3—41no—
110C2×C3×D3—41no—
111C32×C4#13511yescharacteristic
112C32×C4AGL(1,ℤ/8)11yescharacteristic
113C3⋊Dic3—21no—
114C3⋊Dic3C2×Q1611yescharacteristic
115C3⋊Dic3#13511yescharacteristic
116C3×Dic3—41no—
117C3×Dic3—81no—
118C3×Dic3—81no—
119C22×C8—61no—
120C4⋊Q8—91no—
121C4⋊Q8—91no—
122C4×D4—91no—
123#107—181no—
124#106—181no—
125C4⋊C8—91no—
126C4⋊C8—91no—
127C4⋊C8—91no—
128#103—61no—
129#103—181no—
130#102—181no—
131#102—181no—
132C22⋊C8—181no—
133C4×C8—91no—
134C23×C3—61no—
135C22×D3—21no—
136C3×Q8—121no—
137C3×Q8—121no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—61no—
141C2×C3×C4—121no—
142C2×C3×C4—121no—
143C2×C3×C4—121no—
144C2×C3×C4—121no—
145#67—62no—
146#67—62no—
147C2×Dic3—21no—
148C2×Dic3—41no—
149C2×Dic3—41no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C4×D3—41no—
155C4×D3—41no—
156Dic6—41no—
157Dic6—41no—
158Dic6—242no—
159C3×C8—22no—
160C3×C8—41no—
161C3×C8—121no—
162C3⋊C8—41no—
163C3⋊C8—121no—
164C3⋊C8—121no—
165C2×C32#46311yescharacteristic
166C2×C32#46711yescharacteristic
167C2×C32#47111yescharacteristic
168C3×D3—42no—
169C2×Q8—61no—
170C2×Q8—181no—
171C2×D4—91no—
172C22×C4—61no—
173C2×C8—61no—
174C2×C8—91no—
175C2×C8—122no—
176C2×C8—181no—
177C2×C8—181no—
178C2×C8GO+(4,𝔽2)11yescharacteristic
179C4⋊C4—61no—
180C4⋊C4—91no—
181C4⋊C4—181no—
182C4⋊C4—181no—
183C4⋊C4—181no—
184C22⋊C4—181no—
185C42—91no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3—62no—
189C22×C3—121no—
190C22×C3—121no—
191C2×D3—22no—
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#168311yescharacteristic, complemented, Sylow
211C23—61no—
212Q8—121no—
213Q8—121no—
214Q8—721no—
215D4—92no—
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—21no—
226C8—121no—
227C8—181no—
228C8—361no—
229C8—361no—
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—122no—
237D3—42no—
238C22—62no—
239C22—121no—
240C22—121no—
241C22#6423011yescharacteristic
242C4—91no—
243C4—91no—
244C4—121no—
245C4—181no—
246C4—241no—
247C4—241no—
248C4#6422311yescharacteristic
249C4#6423611yescharacteristic
250C3—21no—
251C3—21no—
252C2—122no—
253C2#1059328811yescharacteristic
254C2#1059330011yescharacteristic
255C2#1059342211yescharacteristic
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#1683
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. #10590901C2semidirect
5. #10590173C2semidirect
6. #10590040C2semidirect
7. #10590038C2semidirect
210. C32#1683semidirect

Maximal subgroups

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

subgroupindex
#105933592
#105933472
#105909012
C8×#6252
#105901732
#105900402
#105900382
#16839