Finite Group Databasebeta

← #11781899

Subgroups — #11781899

Order 1152.

340 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 92 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#10592720C211yesmaximal, characteristic
2C3×#5031C211yesmaximal, characteristic
3C3×#5024C211yesmaximal, characteristic
4#10590303C211yesmaximal, characteristic
5#10589099C211yesmaximal, characteristic
6#10589096C211yesmaximal, characteristic
7#10589092C211yesmaximal, characteristic
8#71056—31nomaximal
9#70963—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#216—21no—
13C3×#869C2211yescharacteristic
14#63662—21no—
15#63634—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#810—21no—
18C3×C4⋊(C3⋊C8)—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#803—21no—
22C3×C4×C3⋊C8C2211yescharacteristic
23#63573—21no—
24#63573—21no—
25C3×#462—31no—
26C3×#446—31no—
27#5080—31no—
28#5031D311yescharacteristic
29#5024D311yescharacteristic
30#5021—31no—
31#5021—31no—
32#5021—61no—
33#4680—31no—
34#4547—31no—
35#4486—31no—
36#4481—31no—
37#4481—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×Q8D411yescharacteristic
41C2×#634—21no—
42C2×C3×Dic6—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C42—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C3×#216—42no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1692—91noSylow
58C2×C3×Q16—61no—
59C3×C4⋊Q8—31no—
60C3×C4×Q8—21no—
61C3×C4×Q8C2×D311yescharacteristic
62C3×C4×Q8C2×D311yescharacteristic
63C2×#216—21no—
64#869—31no—
65#869—31no—
66#869—61no—
67#869C2×D311yescharacteristic
68C3×C4⋊C8—31no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—61no—
71C3×#103—61no—
72C3×#97—61no—
73C3×C4×C8—31no—
74#835—62no—
75#835—61no—
76#835—61no—
77#817—61no—
78#817—61no—
79#810—21no—
80#808—61no—
81#808—61no—
82#807—62no—
83#807—61no—
84#807—61no—
85C4⋊(C3⋊C8)—21no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91#803—21no—
92C4×C3⋊C8C2×D311yescharacteristic
93C32×Q8—21no—
94C32×Q8—21no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3⋊Dic3—41no—
101#634—81no—
102C2×C3×Dic3—41no—
103C3×Dic6—41no—
104C3×Dic6—41no—
105C3⋊(C3⋊C8)—41no—
106C3×C3⋊C8—21no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8Q1612yescomplemented
110#498—91no—
111#477—91no—
112#462—31no—
113#446—31no—
114#335—91no—
115#333—91no—
116#332—91no—
117C2×C3×Q8—21no—
118C2×C3×Q8—61no—
119C2×C3×Q8D1211yescharacteristic
120C2×C3×Q8#6711yescharacteristic
121C2×Dic6—21no—
122C2×Dic6—61no—
123C2×Dic6—61no—
124C2×Dic6—121no—
125C3×Q16—122no—
126C2×C3×C8—31no—
127C2×C3×C8—31no—
128C2×C3×C8—61no—
129C2×C3×C8—61no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—41no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4D1211yescharacteristic
137C3×C4⋊C4#6711yescharacteristic
138C3×C42—21no—
139C3×C42—21no—
140C3×C42—21no—
141C3×C42—41no—
142C3×C42C22×D311yescharacteristic
143C3×C42C22×D311yescharacteristic
144#216—42no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—62no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—121no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—62no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8#6711yescharacteristic
159C2×C3⋊C8#6711yescharacteristic
160C22×C32#12111yescharacteristic
161C32×C4—21no—
162C32×C4—41no—
163C32×C4—41no—
164C32×C4C2×Q1611yescharacteristic
165C32×C4AGL(1,ℤ/8)11yescharacteristic
166C32×C4#13711yescharacteristic
167C32×C4#13711yescharacteristic
168C3⋊Dic3—81no—
169C3×Dic3—81no—
170C2×Q16—61no—
171C4⋊Q8—31no—
172C4⋊Q8—91no—
173C4×Q8D3211yescharacteristic
174#107—181no—
175#106—181no—
176#106—181no—
177C4⋊C8—31no—
178C4⋊C8—31no—
179C4⋊C8—61no—
180C4⋊C8—91no—
181#103—61no—
182#103—181no—
183#97—61no—
184C4×C8—31no—
185C3×Q8—22no—
186C3×Q8—21no—
187C3×Q8—21no—
188C3×Q8—21no—
189C3×Q8—21no—
190C3×Q8—41no—
191C3×Q8—121no—
192C3×Q8—121no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—41no—
201C2×C3×C4—41no—
202C2×C3×C4—121no—
203C2×C3×C4C2×D1211yescharacteristic
204C2×C3×C4#23511yescharacteristic
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4#23711yescharacteristic
207C2×C3×C4C2×#6711yescharacteristic
208C2×C3×C4C2×#6711yescharacteristic
209C2×Dic3—41no—
210C2×Dic3—122no—
211C2×Dic3—121no—
212C2×Dic3—121no—
213Dic6—41no—
214Dic6—41no—
215Dic6—242no—
216Dic6—241no—
217Dic6—241no—
218C3×C8—32no—
219C3×C8—61no—
220C3×C8—121no—
221C3×C8—121no—
222C3⋊C8—21no—
223C3⋊C8—41no—
224C3⋊C8—41no—
225C3⋊C8—122no—
226C3⋊C8—121no—
227C3⋊C8—121no—
228C3⋊C8#21612yescomplemented
229C2×C32#46211yescharacteristic
230C2×C32#46811yescharacteristic
231C2×C32#47111yescharacteristic
232C2×Q8—61no—
233C2×Q8—181no—
234C2×Q8#62611yescharacteristic
235Q16—122no—
236C2×C8—31no—
237C2×C8—31no—
238C2×C8—61no—
239C2×C8—61no—
240C2×C8—181no—
241C4⋊C4—21no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—181no—
245C4⋊C4—181no—
246C4⋊C4#62611yescharacteristic
247C42—21no—
248C42C2×D3211yescharacteristic
249C22×C3—21no—
250C22×C3#93011yescharacteristic
251C22×C3#93911yescharacteristic
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—41no—
259C3×C4—42no—
260C3×C4—41no—
261C3×C4—41no—
262C3×C4—41no—
263C3×C4—41no—
264C3×C4—81no—
265C3×C4—241no—
266C3×C4#90811yescharacteristic
267C3×C4#90911yescharacteristic
268C3×C4D3×Q1611yescharacteristic
269C3×C4#91811yescharacteristic
270C3×C4#93211yescharacteristic
271C3×C4C2×#21611yescharacteristic
272C3×C4#95111yescharacteristic
273C3×C4#95111yescharacteristic
274Dic3—81no—
275Dic3—242no—
276Dic3—241no—
277Dic3—241no—
278C32#169211yescharacteristic, complemented, Sylow
279Q8—21no—
280Q8—21no—
281Q8—121no—
282Q8—121no—
283Q8—721no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—121no—
287C2×C4—361no—
288C2×C4#380411yescharacteristic
289C2×C4C2×#62611yescharacteristic
290C2×C4D3×#6711yescharacteristic
291C8—32no—
292C8—61no—
293C8—121no—
294C8—121no—
295C8—361no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3#503111yescharacteristic
300C2×C3#504211yescharacteristic
301C2×C3#513411yescharacteristic
302C2×C3#514111yescharacteristic
303C2×C3#518211yescharacteristic
304C2×C3#520311yescharacteristic
305C22#6397811yescharacteristic
306C4—21no—
307C4—41no—
308C4—41no—
309C4—241no—
310C4—721no—
311C4#6383011yescharacteristic
312C4#6383111yescharacteristic
313C4D3×#21611yescharacteristic
314C4#6394311yescharacteristic
315C3—21no—
316C3#7096311yescharacteristic, complemented
317C3#7105611yescharacteristic, complemented
318C2#1059117611yescharacteristic
319C2#1059162511yescharacteristic
320C2#1059168011yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#121
hypercenterC4×Q8D32
hypocenterC32#1692
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
109. C3×C3⋊C8Q16semidirect
228. C3⋊C8#216semidirect
278. C32#1692semidirect
316. C3#70963semidirect
317. C3#71056semidirect

Maximal subgroups

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

subgroupindex
#105927202
C3×#50312
C3×#50242
#105903032
#105890992
#105890962
#105890922
#710563
#709633