Finite Group Databasebeta

← #11781396

Subgroups — #11781396

Order 1152.

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

normal subgroups only

This group has 348 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#10592719C211yesmaximal, characteristic
2C3×#5031C211yesmaximal, characteristic
3C3×Q8×C3⋊C8C211yesmaximal, characteristic
4#10590288C211yesmaximal, characteristic
5#10589097C211yesmaximal, characteristic
6#10589094C211yesmaximal, characteristic
7#10589092C211yesmaximal, characteristic
8#71054—31nomaximal
9#70946—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#216—21no—
13C3×#869C2211yescharacteristic
14#63662—21no—
15#63635—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×C4×C3⋊C8—21no—
22C3×C4×C3⋊C8C2211yescharacteristic
23#63567—21no—
24#63567—21no—
25C3×#462—31no—
26C3×C8×Q8—31no—
27#5093—31no—
28#5031D311yescharacteristic
29Q8×C3⋊C8D311yescharacteristic
30#5020—31no—
31#5020—31no—
32#5020—61no—
33#4681—31no—
34#4547—31no—
35#4486—31no—
36#4486—31no—
37#4482—31no—
38#4480—31no—
39#4457—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#1680—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×C4×C8—31no—
73C3×C4×C8—61no—
74#835—62no—
75#835—61no—
76#835—61no—
77#816—61no—
78#816—61no—
79#810—21no—
80#810—61no—
81#810—61no—
82#808—62no—
83#808—61no—
84#808—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
91C4×C3⋊C8—21no—
92C4×C3⋊C8C2×D311yescharacteristic
93C32×Q8—21no—
94C32×Q8SD1612yes—
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—41no—
102#634—41no—
103C2×C3×Dic3—41no—
104C3×Dic6—41no—
105C3×Dic6—41no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111#487—91no—
112#475—91no—
113#462—31no—
114C8×Q8—31no—
115#334—91no—
116#332—91no—
117#332—91no—
118C2×C3×Q8—21no—
119C2×C3×Q8—61no—
120C2×C3×Q8D1211yescharacteristic
121C2×C3×Q8#6711yescharacteristic
122C2×Dic6—21no—
123C2×Dic6—61no—
124C2×Dic6—61no—
125C2×Dic6—121no—
126C3×Q16—122no—
127C2×C3×C8—31no—
128C2×C3×C8—31no—
129C2×C3×C8—61no—
130C2×C3×C8—61no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—41no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4D1211yescharacteristic
138C3×C4⋊C4#6711yescharacteristic
139C3×C42—21no—
140C3×C42—21no—
141C3×C42—21no—
142C3×C42—41no—
143C3×C42C22×D311yescharacteristic
144C3×C42C22×D311yescharacteristic
145#216—42no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—62no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—121no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8#6711yescharacteristic
160C2×C3⋊C8#6711yescharacteristic
161C22×C32#12111yescharacteristic
162C32×C4—22no—
163C32×C4—21no—
164C32×C4—41no—
165C32×C4C2×SD1611yescharacteristic
166C32×C4#13511yescharacteristic
167C32×C4#13511yescharacteristic
168C32×C4#13711yescharacteristic
169C3⋊Dic3—81no—
170C3×Dic3—81no—
171C2×Q16—61no—
172C4⋊Q8—31no—
173C4⋊Q8—91no—
174C4×Q8D3211yescharacteristic
175#106—181no—
176C4⋊C8—31no—
177C4⋊C8—31no—
178C4⋊C8—61no—
179C4⋊C8—91no—
180#103—61no—
181#103—181no—
182#103—181no—
183#103—181no—
184C4×C8—31no—
185C4×C8—61no—
186C3×Q8—21no—
187C3×Q8—21no—
188C3×Q8—22no—
189C3×Q8—41no—
190C3×Q8—121no—
191C3×Q8—121no—
192C3×Q8#20412yes—
193C3×Q8#21412yes—
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—21no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—121no—
204C2×C3×C4C2×D1211yescharacteristic
205C2×C3×C4#23511yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4#23711yescharacteristic
208C2×C3×C4C2×#6711yescharacteristic
209C2×C3×C4C2×#6711yescharacteristic
210C2×Dic3—41no—
211C2×Dic3—122no—
212C2×Dic3—121no—
213C2×Dic3—121no—
214Dic6—41no—
215Dic6—41no—
216Dic6—121no—
217Dic6—121no—
218Dic6—121no—
219Dic6—121no—
220Dic6—241no—
221Dic6—241no—
222C3×C8—61no—
223C3×C8—61no—
224C3×C8—121no—
225C3×C8—121no—
226C3⋊C8—21no—
227C3⋊C8—21no—
228C3⋊C8—41no—
229C3⋊C8—41no—
230C3⋊C8—122no—
231C3⋊C8—121no—
232C3⋊C8—121no—
233C2×C32#46411yescharacteristic
234C2×C32#46511yescharacteristic
235C2×C32#47311yescharacteristic
236C2×Q8—61no—
237C2×Q8—181no—
238C2×Q8#62611yescharacteristic
239Q16—122no—
240C2×C8—31no—
241C2×C8—31no—
242C2×C8—61no—
243C2×C8—61no—
244C2×C8—181no—
245C4⋊C4—21no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4—181no—
249C4⋊C4—181no—
250C4⋊C4#62611yescharacteristic
251C42—21no—
252C42C2×D3211yescharacteristic
253C22×C3—21no—
254C22×C3#93011yescharacteristic
255C22×C3#93911yescharacteristic
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—41no—
265C3×C4—42no—
266C3×C4—41no—
267C3×C4—41no—
268C3×C4—81no—
269C3×C4—241no—
270C3×C4C2×#20411yescharacteristic
271C3×C4#90411yescharacteristic
272C3×C4#91811yescharacteristic
273C3×C4#91911yescharacteristic
274C3×C4C2×#21411yescharacteristic
275C3×C4#94211yescharacteristic
276C3×C4#95011yescharacteristic
277C3×C4#95011yescharacteristic
278Dic3—81no—
279Dic3—242no—
280Dic3—241no—
281Dic3—241no—
282C32#168011yescharacteristic, complemented, Sylow
283Q8—21no—
284Q8—121no—
285Q8—121no—
286Q8—361no—
287Q8—361no—
288Q8#371612yes—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—121no—
292C2×C4—361no—
293C2×C4#380411yescharacteristic
294C2×C4C2×#62611yescharacteristic
295C2×C4D3×#6711yescharacteristic
296C8—61no—
297C8—61no—
298C8—121no—
299C8—121no—
300C8—361no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3#502811yescharacteristic
305C2×C3#504111yescharacteristic
306C2×C3#511411yescharacteristic
307C2×C3#514311yescharacteristic
308C2×C3#518511yescharacteristic
309C2×C3#520411yescharacteristic
310C22#6397811yescharacteristic
311C4—21no—
312C4—22no—
313C4—41no—
314C4—241no—
315C4—721no—
316C4C2×#371611yescharacteristic
317C4#6382911yescharacteristic
318C4#6394811yescharacteristic
319C4#6394911yescharacteristic
320C3—21no—
321C3#7094611yescharacteristic, complemented
322C3#7105411yescharacteristic, complemented
323C2#1059117511yescharacteristic
324C2#1059160711yescharacteristic
325C2#1059168211yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#121
hypercenterC4×Q8D32
hypocenterC32#1680
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
282. C32#1680semidirect
321. C3#70946semidirect
322. C3#71054semidirect

Maximal subgroups

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

subgroupindex
#105927192
C3×#50312
C3×Q8×C3⋊C82
#105902882
#105890972
#105890942
#105890922
#710543
#709463