Finite Group Databasebeta

← #11781271

Subgroups — #11781271

Order 1152.

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

normal subgroups only

This group has 302 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#10593417C211yesmaximal, characteristic
2#10593359C211yesmaximal, characteristic, complemented
3#10590885C211yesmaximal, characteristic, complemented
4#10590718C211yesmaximal, characteristic, complemented
5#10590170C211yesmaximal, characteristic, complemented
6#10590040C211yesmaximal, characteristic, complemented
7#10590037C211yesmaximal, characteristic, complemented
8C2×#3774—21no—
9#63919C2211yescharacteristic
10#63914C2211yescharacteristic
11C4×#625C2211yescharacteristic
12C2×D3×C3⋊C8—21no—
13C4⋊#622C2211yescharacteristic
14C4⋊#622C2211yescharacteristic
15#63742—21no—
16#63739—21no—
17#63739—21no—
18C8×C3⋊Dic3C2211yescharacteristic
19C3×#821—21no—
20C3×(C2×D3)⋊C8—21no—
21#63572C2211yescharacteristic
22#63562—21no—
23#4760—61no—
24#67⋊C8—61no—
25C2×C3×D12—21no—
26C2×C3×C4×D3—21no—
27C2×#627—21no—
28C2×#625—21no—
29C2×#625—21no—
30C2×#625D411yescharacteristic
31C2×#622—21no—
32C2×#622—21no—
33#3774—42no—
34C2×C32×C8D411yescharacteristic
35C4×C3⋊Dic3C2311yescharacteristic
36C2×C3⋊(C3⋊C8)D411yescharacteristic
37C3×C4⋊Dic3—21no—
38C2×C3×C3⋊C8—21no—
39#3724—21no—
40#3724D411yescharacteristic
41(C2×D3)⋊Dic3—21no—
42D3×C3⋊C8—42no—
43#1677—91nomaximal, Sylow
44#940—61no—
45C4×#67—61no—
46C22×C3⋊C8—61no—
47C2×D3×C8—61no—
48#888—61no—
49C3×#102—61no—
50C3×C22⋊C8—61no—
51#832—61no—
52#821—21no—
53(C2×D3)⋊C8—21no—
54Dic3⋊C8—61no—
55C8×Dic3—61no—
56C8×Dic3—61no—
57#809—61no—
58C22×C3×D3—21no—
59C22×C3×D3—41no—
60C2×C32×C4C2×D411yescharacteristic
61C2×C3⋊Dic3C2×D411yescharacteristic
62C2×C3⋊Dic3#4111yescharacteristic
63C2×C3×Dic3—21no—
64C2×C3×Dic3—41no—
65C3×D12—41no—
66C3×D12—41no—
67C3×C4×D3—41no—
68C3×C4×D3—41no—
69#627—81no—
70#625—21no—
71#625—41no—
72#625—41no—
73#625—81no—
74#625SD1612yes—
75#622—41no—
76#622—41no—
77C32×C8—21no—
78C3⋊(C3⋊C8)—21no—
79C3×C3⋊C8—41no—
80#486—91no—
81#476—91no—
82#459—91no—
83C8×D4—91no—
84#334—91no—
85#333—91no—
86#331—91no—
87C2×C3×D4—61no—
88C22×C3×C4—61no—
89C2×#67—61no—
90C2×#67—121no—
91C2×#67—121no—
92C2×D12—21no—
93C2×C4×D3—21no—
94C2×Dic6—121no—
95C2×C3×C8—21no—
96C2×C3×C8—21no—
97C2×C3×C8—61no—
98C3×C4⋊C4—61no—
99#217—61no—
100(C2×D3)⋊C4—61no—
101C4⋊Dic3—21no—
102Dic3⋊C4—61no—
103Dic3⋊C4—121no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C2×C3⋊C8—21no—
107C2×C3⋊C8—61no—
108C2×C3⋊C8—61no—
109C2×C3⋊C8—122no—
110D3×C8—122no—
111C22×C32#12111yescharacteristic
112C2×C3×D3—22no—
113C2×C3×D3—41no—
114C2×C3×D3—41no—
115C2×C3×D3—81no—
116C2×C3×D3—81no—
117C2×C3×D3—81no—
118C32×C4#13511yescharacteristic
119C32×C4AGL(1,ℤ/8)11yescharacteristic
120C3⋊Dic3—21no—
121C3⋊Dic3C2×SD1611yescharacteristic
122C3⋊Dic3#13511yescharacteristic
123C3×Dic3—41no—
124C3×Dic3—81no—
125C2×D8—181no—
126C22×C8—181no—
127C4⋊Q8—91no—
128#127—91no—
129C4×D4—91no—
130#106—181no—
131C4⋊C8—91no—
132C4⋊C8—91no—
133C4⋊C8—91no—
134#102—61no—
135#102—181no—
136#102—181no—
137#102—181no—
138C22⋊C8—61no—
139C4×C8—91no—
140C23×C3—61no—
141C23×C3—121no—
142C22×D3—21no—
143C22×D3—41no—
144C3×D4—121no—
145C3×D4—121no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—61no—
149C2×C3×C4—121no—
150C2×C3×C4—121no—
151C2×C3×C4—121no—
152#67—62no—
153#67—62no—
154#67—241no—
155#67—241no—
156#67—242no—
157C2×Dic3—21no—
158C2×Dic3—41no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163D12—41no—
164D12—41no—
165C4×D3—41no—
166C4×D3—41no—
167Dic6—242no—
168C3×C8—41no—
169C3×C8—41no—
170C3×C8—121no—
171C3⋊C8—41no—
172C3⋊C8—62no—
173C3⋊C8—121no—
174C2×C32#46311yescharacteristic
175C2×C32#46511yescharacteristic
176C2×C32#47211yescharacteristic
177C3×D3—42no—
178C3×D3—161no—
179C2×Q8—181no—
180C2×D4—61no—
181C2×D4—91no—
182C2×D4—181no—
183C2×D4—181no—
184C22×C4—61no—
185D8—362no—
186C2×C8—61no—
187C2×C8—91no—
188C2×C8—181no—
189C2×C8—181no—
190C2×C8—362no—
191C2×C8GO+(4,𝔽2)11yescharacteristic
192C4⋊C4—61no—
193C4⋊C4—91no—
194C4⋊C4—181no—
195C22⋊C4—181no—
196C42—91no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—62no—
200C22×C3—121no—
201C22×C3—121no—
202C22×C3—241no—
203C22×C3—241no—
204C22×C3—241no—
205C2×D3—22no—
206C2×D3—41no—
207C2×D3—41no—
208C2×D3—81no—
209C2×D3—81no—
210C2×D3—81no—
211C3×C4—21no—
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—21no—
215C3×C4—121no—
216C3×C4—241no—
217Dic3—41no—
218Dic3—61no—
219Dic3—61no—
220Dic3—61no—
221Dic3—61no—
222Dic3—62no—
223Dic3—81no—
224Dic3—121no—
225C32#167711yescharacteristic, complemented, Sylow
226C23—61no—
227C23—121no—
228Q8—721no—
229D4—92no—
230D4—121no—
231D4—121no—
232D4—181no—
233D4—361no—
234D4—361no—
235D4—721no—
236C2×C4—61no—
237C2×C4—91no—
238C2×C4—91no—
239C2×C4—121no—
240C2×C4—121no—
241C2×C4—121no—
242C2×C4C2×GO+(4,𝔽2)11yescharacteristic
243C8—21no—
244C8—121no—
245C8—181no—
246C8—361no—
247C8—361no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—122no—
255C2×C3—481no—
256D3—42no—
257D3—161no—
258C22—62no—
259C22—121no—
260C22—121no—
261C22—241no—
262C22—241no—
263C22—241no—
264C22#6423011yescharacteristic
265C4—91no—
266C4—91no—
267C4—121no—
268C4—181no—
269C4—241no—
270C4#6422411yescharacteristic
271C4#6423711yescharacteristic
272C3—21no—
273C3—21no—
274C2—122no—
275C2—481no—
276C2#1059328411yescharacteristic
277C2#1059330311yescharacteristic
278C2#1059342811yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radical#10593417C2
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1677
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
2. #10593359C2semidirect
3. #10590885C2semidirect
4. #10590718C2semidirect
5. #10590170C2semidirect
6. #10590040C2semidirect
7. #10590037C2semidirect
225. C32#1677semidirect

Maximal subgroups

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

subgroupindex
#105934172
#105933592
#105908852
#105907182
#105901702
#105900402
#105900372
#16779