Finite Group Databasebeta

← #11781583

Subgroups — #11781583

Order 1152.

336 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 96 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×Q8×C3⋊C8C211yesmaximal, characteristic
3C3×#5020C211yesmaximal, characteristic
4#10590287C211yesmaximal, characteristic
5#10589099C211yesmaximal, characteristic
6#10589096C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71119—31nomaximal
9#70947—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#869C2211yescharacteristic
13#63662—21no—
14#63634—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#835—21no—
17C3×#808—21no—
18C3×C4⋊(C3⋊C8)—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8—21no—
22C3×C4×C3⋊C8C2211yescharacteristic
23#63566—21no—
24#63566—21no—
25C3×#475—31no—
26C3×C8×Q8—31no—
27#5079—31no—
28Q8×C3⋊C8D311yescharacteristic
29#5021—31no—
30#5021—31no—
31#5021—61no—
32#5020D311yescharacteristic
33#4681—31no—
34#4547—31no—
35#4482—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×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#1684—91noSylow
57C3×C4⋊Q8—31no—
58C3×C4×Q8—21no—
59C3×C4×Q8C2×D311yescharacteristic
60C3×C4×Q8C2×D311yescharacteristic
61#869—31no—
62#869—31no—
63#869—61no—
64#869C2×D311yescharacteristic
65C3×#106—61no—
66C3×C4⋊C8—31no—
67C3×C4⋊C8—31no—
68C3×C4⋊C8—61no—
69C3×#103—61no—
70C3×C4×C8—31no—
71C3×C4×C8—61no—
72#835—21no—
73#835—62no—
74#835—61no—
75#835—61no—
76#835—61no—
77#835—61no—
78#816—61no—
79#816—61no—
80#808—21no—
81#807—62no—
82#807—61no—
83#807—61no—
84C4⋊(C3⋊C8)—21no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—21no—
91C4×C3⋊C8C2×D311yescharacteristic
92C32×Q8—21no—
93C32×Q8Q1612yes—
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3⋊Dic3—41no—
100#634—81no—
101C2×C3×Dic3—41no—
102C3×Dic6—41no—
103C3×Dic6—41no—
104C3⋊(C3⋊C8)—41no—
105C3×C3⋊C8—21no—
106C3×C3⋊C8—21no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109#487—91no—
110#477—91no—
111#475—31no—
112C8×Q8—31no—
113#335—91no—
114#333—91no—
115#332—91no—
116C2×C3×Q8—21no—
117C2×C3×Q8—61no—
118C2×C3×Q8D1211yescharacteristic
119C2×C3×Q8#6711yescharacteristic
120C2×Dic6—21no—
121C2×Dic6—61no—
122C2×Dic6—61no—
123C2×Dic6—121no—
124C2×C3×C8—31no—
125C2×C3×C8—31no—
126C2×C3×C8—61no—
127C2×C3×C8—61no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—41no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4D1211yescharacteristic
135C3×C4⋊C4#6711yescharacteristic
136C3×C42—21no—
137C3×C42—21no—
138C3×C42—21no—
139C3×C42—41no—
140C3×C42C22×D311yescharacteristic
141C3×C42C22×D311yescharacteristic
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3—62no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—61no—
148C4⋊Dic3—61no—
149C4⋊Dic3—121no—
150C2×C3⋊C8—21no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—62no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8#6711yescharacteristic
156C2×C3⋊C8#6711yescharacteristic
157C22×C32#12111yescharacteristic
158C32×C4—22no—
159C32×C4—21no—
160C32×C4—41no—
161C32×C4C2×Q1611yescharacteristic
162C32×C4#13511yescharacteristic
163C32×C4#13511yescharacteristic
164C32×C4#13711yescharacteristic
165C3⋊Dic3—81no—
166C3×Dic3—81no—
167C4⋊Q8—31no—
168C4⋊Q8—91no—
169C4×Q8D3211yescharacteristic
170#107—181no—
171#106—61no—
172C4⋊C8—31no—
173C4⋊C8—31no—
174C4⋊C8—61no—
175C4⋊C8—91no—
176#103—61no—
177#103—181no—
178#103—181no—
179#103—181no—
180C4×C8—31no—
181C4×C8—61no—
182C3×Q8—21no—
183C3×Q8—21no—
184C3×Q8—22no—
185C3×Q8—41no—
186C3×Q8—121no—
187C3×Q8—121no—
188C3×Q8Dic1212yes—
189C3×Q8#21612yes—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—41no—
198C2×C3×C4—41no—
199C2×C3×C4—121no—
200C2×C3×C4C2×D1211yescharacteristic
201C2×C3×C4#23511yescharacteristic
202C2×C3×C4D3×D411yescharacteristic
203C2×C3×C4#23711yescharacteristic
204C2×C3×C4C2×#6711yescharacteristic
205C2×C3×C4C2×#6711yescharacteristic
206C2×Dic3—41no—
207C2×Dic3—122no—
208C2×Dic3—121no—
209C2×Dic3—121no—
210Dic6—41no—
211Dic6—41no—
212Dic6—242no—
213Dic6—241no—
214Dic6—241no—
215C3×C8—61no—
216C3×C8—61no—
217C3×C8—121no—
218C3×C8—121no—
219C3⋊C8—21no—
220C3⋊C8—21no—
221C3⋊C8—41no—
222C3⋊C8—41no—
223C3⋊C8—122no—
224C3⋊C8—121no—
225C3⋊C8—121no—
226C2×C32#46411yescharacteristic
227C2×C32#46711yescharacteristic
228C2×C32#47111yescharacteristic
229C2×Q8—61no—
230C2×Q8—181no—
231C2×Q8#62611yescharacteristic
232C2×C8—31no—
233C2×C8—31no—
234C2×C8—61no—
235C2×C8—61no—
236C2×C8—181no—
237C4⋊C4—21no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—181no—
241C4⋊C4—181no—
242C4⋊C4#62611yescharacteristic
243C42—21no—
244C42C2×D3211yescharacteristic
245C22×C3—21no—
246C22×C3#93011yescharacteristic
247C22×C3#93911yescharacteristic
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—22no—
251C3×C4—22no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—41no—
257C3×C4—42no—
258C3×C4—41no—
259C3×C4—41no—
260C3×C4—81no—
261C3×C4—241no—
262C3×C4#90411yescharacteristic
263C3×C4C2×Dic1211yescharacteristic
264C3×C4#91511yescharacteristic
265C3×C4#91611yescharacteristic
266C3×C4#94211yescharacteristic
267C3×C4C2×#21611yescharacteristic
268C3×C4#95011yescharacteristic
269C3×C4#95011yescharacteristic
270Dic3—81no—
271Dic3—242no—
272Dic3—241no—
273Dic3—241no—
274C32#168411yescharacteristic, complemented, Sylow
275Q8—21no—
276Q8—121no—
277Q8—121no—
278Q8—721no—
279Q8#371912yes—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—121no—
283C2×C4—361no—
284C2×C4#380411yescharacteristic
285C2×C4C2×#62611yescharacteristic
286C2×C4D3×#6711yescharacteristic
287C8—61no—
288C8—61no—
289C8—121no—
290C8—121no—
291C8—361no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3#502811yescharacteristic
296C2×C3#505111yescharacteristic
297C2×C3#511611yescharacteristic
298C2×C3#514111yescharacteristic
299C2×C3#516611yescharacteristic
300C2×C3#520311yescharacteristic
301C22#6397811yescharacteristic
302C4—21no—
303C4—22no—
304C4—41no—
305C4—241no—
306C4—721no—
307C4#6382911yescharacteristic
308C4C2×#371911yescharacteristic
309C4#6394611yescharacteristic
310C4#6394711yescharacteristic
311C3—21no—
312C3#7094711yescharacteristic, complemented
313C3#7111911yescharacteristic, complemented
314C2#1059118711yescharacteristic
315C2#1059160411yescharacteristic
316C2#1059168011yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#121
hypercenterC4×Q8D32
hypocenterC32#1684
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
274. C32#1684semidirect
312. C3#70947semidirect
313. C3#71119semidirect

Maximal subgroups

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

subgroupindex
#105927202
C3×Q8×C3⋊C82
C3×#50202
#105902872
#105890992
#105890962
#105890932
#711193
#709473