Finite Group Databasebeta

← #11799849

Subgroups — #11799849

Order 1152.

341 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 341 conjugacy classes of subgroups — too many to draw. Only its 84 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#10592805C211yesmaximal, characteristic, complemented
2C3×#5115C211yesmaximal, characteristic
3C3×#4549C211yesmaximal, characteristic, complemented
4#10589141C211yesmaximal, characteristic, complemented
5#10589139C211yesmaximal, characteristic, complemented
6#10589115C211yesmaximal, characteristic, complemented
7#10589115C211yesmaximal, characteristic, complemented
8#71070—31nomaximal
9#69097—31nomaximal
10C22×C32×C8C2211yescharacteristic
11#64135—21no—
12C3×#930—21no—
13C2×C3×D24C2211yescharacteristic
14#63645C2211yescharacteristic
15#63645C2211yescharacteristic
16#63644—21no—
17C3×#821—21no—
18C3×#818C2211yescharacteristic
19C2×C3×C3⋊C16C2211yescharacteristic
20C2×C3×C3⋊C16C2211yescharacteristic
21C3×#466—31no—
22#5115D311yescharacteristic
23#5106—31no—
24#5106—31no—
25#5106—61no—
26C3×C22⋊C16—31no—
27#4562—31no—
28#4562—31no—
29#4549D311yescharacteristic, complemented
30#4509—31no—
31#4509—31no—
32#4505—31no—
33#4504—31no—
34#4490—31no—
35#4489—31no—
36C22×C32×C4D411yescharacteristic
37C2×C3×#67—41no—
38C2×C3×D12—21no—
39C2×C32×C8—21no—
40C2×C32×C8—21no—
41C2×C32×C8D411yescharacteristic
42C2×C32×C8C2311yescharacteristic
43#3757—41no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4×C3⋊Dic3—41no—
47C3×(C2×D3)⋊C4—41no—
48C3×C4⋊Dic3—21no—
49C3×D24—21no—
50C3×D24—21no—
51C3×C3⋊C16—21no—
52C3×C3⋊C16—21no—
53#2234—91noSylow
54C2×C3×D8—31no—
55C22×C3×C8—21no—
56C22×C3×C8C2×D311yescharacteristic
57C22×C3×C8C2×D311yescharacteristic
58C3×#121—61no—
59#930—21no—
60#926—62no—
61#926—61no—
62#926—61no—
63C2×D24C2×D311yescharacteristic
64C2×C3×C16—31no—
65C2×C3×C16—31no—
66C3×#107—31no—
67C3×#102—61no—
68#821—21no—
69#818—31no—
70#818—31no—
71#818—31no—
72#818—31no—
73#818—61no—
74#818—61no—
75#818C2×D311yescharacteristic
76#817—62no—
77#817—61no—
78#817—61no—
79C2×C3⋊C16C2×D311yescharacteristic
80C2×C3⋊C16C2×D311yescharacteristic
81C23×C32D811yescharacteristic
82C22×C3×D3—41no—
83C2×C32×C4—21no—
84C2×C32×C4—21no—
85C2×C32×C4D811yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—41no—
89C3×#67—82no—
90C2×C3×Dic3—41no—
91C3×D12—41no—
92C3×D12—41no—
93C32×C8—21no—
94C32×C8#4111yescharacteristic
95C32×C8#4111yescharacteristic
96#466—31no—
97#427—91no—
98#367—91no—
99#366—91no—
100#357—91no—
101#357—91no—
102C22⋊C16—31no—
103C2×C3×D4—61no—
104C2×C3×D4—121no—
105C22×C3×C4—21no—
106C22×C3×C4D1211yescharacteristic
107C22×C3×C4#6711yescharacteristic
108C2×#67—41no—
109C2×D12—21no—
110C3×D8—61no—
111C3×D8—61no—
112C2×C3×C8—22no—
113C2×C3×C8—22no—
114C2×C3×C8—21no—
115C2×C3×C8—21no—
116C2×C3×C8—21no—
117C2×C3×C8—21no—
118C2×C3×C8—21no—
119C2×C3×C8—21no—
120C2×C3×C8D1211yescharacteristic
121C2×C3×C8#6711yescharacteristic
122C2×C3×C8C22×D311yescharacteristic
123C2×C3×C8C22×D311yescharacteristic
124C3×C4⋊C4—61no—
125C3×C22⋊C4—121no—
126#217—122no—
127#217—121no—
128#217—121no—
129(C2×D3)⋊C4—41no—
130C4⋊Dic3—21no—
131C4⋊Dic3—62no—
132C4⋊Dic3—62no—
133C4⋊Dic3—61no—
134C4⋊Dic3—61no—
135C4⋊Dic3—61no—
136C4⋊Dic3—61no—
137C4×Dic3—122no—
138C4×Dic3—121no—
139C4×Dic3—121no—
140D24—21no—
141D24—21no—
142C3×C16—61no—
143C3×C16—61no—
144C3⋊C16—21no—
145C3⋊C16—21no—
146C22×C32—21no—
147C22×C32—21no—
148C22×C32—21no—
149C22×C32C2×D811yescharacteristic
150C2×C3×D3—81no—
151C2×C3×D3—81no—
152C2×C3×D3—81no—
153C32×C4—21no—
154C32×C4#12311yescharacteristic
155C32×C4#13711yescharacteristic
156C3⋊Dic3—81no—
157C3⋊Dic3—81no—
158C3×Dic3—81no—
159C2×D8—31no—
160C22×C8D3211yescharacteristic
161#121—61no—
162#117—181no—
163C2×C16—31no—
164C2×C16—31no—
165#107—31no—
166#107—91no—
167#107—91no—
168#106—181no—
169#102—61no—
170C23×C3—21no—
171C23×C3—121no—
172C23×C3D2411yescharacteristic
173C23×C3#21311yescharacteristic
174C22×D3—41no—
175C3×D4—121no—
176C3×D4—121no—
177C3×D4—242no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—121no—
187C2×C3×C4D2411yescharacteristic
188C2×C3×C4#21311yescharacteristic
189C2×C3×C4C2×D1211yescharacteristic
190C2×C3×C4C2×#6711yescharacteristic
191#67—82no—
192C2×Dic3—41no—
193C2×Dic3—122no—
194C2×Dic3—122no—
195C2×Dic3—121no—
196C2×Dic3—121no—
197C2×Dic3—121no—
198C2×Dic3—121no—
199D12—41no—
200D12—41no—
201C3×C8—22no—
202C3×C8—21no—
203C3×C8—21no—
204C3×C8—21no—
205C3×C8—21no—
206C3×C8#23711yescharacteristic
207C3×C8#23711yescharacteristic
208C3×C8#23711yescharacteristic
209C3×C8#23711yescharacteristic
210C2×C32—41no—
211C2×C32#48011yescharacteristic
212C2×C32#50811yescharacteristic
213C2×C32#50911yescharacteristic
214C3×D3—161no—
215C2×D4—61no—
216C2×D4—121no—
217C22×C4#62611yescharacteristic
218D8—61no—
219D8—61no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8#62611yescharacteristic
223C2×C8C2×D3211yescharacteristic
224C4⋊C4—61no—
225C4⋊C4—181no—
226C4⋊C4—181no—
227C22⋊C4—121no—
228C22⋊C4—361no—
229C42—361no—
230C16—61no—
231C16—61no—
232C22×C3—22no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—41no—
241C22×C3—41no—
242C22×C3—241no—
243C22×C3—241no—
244C22×C3—241no—
245C22×C3C2×D2411yescharacteristic
246C22×C3C2×#21311yescharacteristic
247C2×D3—81no—
248C2×D3—81no—
249C2×D3—81no—
250C3×C4—22no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—241no—
256C3×C4#88611yescharacteristic
257C3×C4#90911yescharacteristic
258C3×C4#93511yescharacteristic
259C3×C4#95111yescharacteristic
260Dic3—81no—
261Dic3—242no—
262Dic3—242no—
263Dic3—241no—
264Dic3—241no—
265Dic3—241no—
266Dic3—241no—
267C32#223411yescharacteristic, complemented, Sylow
268C23—121no—
269C23#371411yescharacteristic
270D4—121no—
271D4—121no—
272D4—242no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—121no—
276C2×C4—361no—
277C2×C4—361no—
278C2×C4#371411yescharacteristic
279C2×C4C2×#62611yescharacteristic
280C8—21no—
281C8#380511yescharacteristic
282C8#380511yescharacteristic
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—42no—
287C2×C3—41no—
288C2×C3—41no—
289C2×C3—481no—
290C2×C3#473611yescharacteristic
291C2×C3#490411yescharacteristic
292C2×C3#490811yescharacteristic
293C2×C3#503311yescharacteristic
294C2×C3#514711yescharacteristic
295C2×C3#519411yescharacteristic
296D3—161no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—241no—
301C22—241no—
302C22—241no—
303C22C2×#371411yescharacteristic
304C4—21no—
305C4—241no—
306C4—721no—
307C4—721no—
308C4#6383111yescharacteristic
309C4#6396211yescharacteristic
310C3—21no—
311C3#6909711yescharacteristic, complemented
312C3#7107011yescharacteristic, complemented
313C2—41no—
314C2—481no—
315C2#1059063211yescharacteristic
316C2#1059063311yescharacteristic
317C2#1059109411yescharacteristic
subgroupG/H
centerC22C2×#3714
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC22×C32×C8C22
socleC22×C32C2×D8
prime radicalC3×#5115C2
hypercenterC22×C8D32
hypocenterC32#2234
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #10592805C2semidirect
3. C3×#4549C2semidirect
4. #10589141C2semidirect
5. #10589139C2semidirect
6. #10589115C2semidirect
7. #10589115C2semidirect
29. #4549D3semidirect
267. C32#2234semidirect
311. C3#69097semidirect
312. C3#71070semidirect

Maximal subgroups

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

subgroupindex
#105928052
C3×#51152
C3×#45492
#105891412
#105891392
#105891152
#710703
#690973