Finite Group Databasebeta

← #11782393

Subgroups — #11782393

Order 1152.

327 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 327 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592378C211yesmaximal, characteristic
2C3×#4681C211yesmaximal, characteristic
3#10590307C211yesmaximal, characteristic
4#10590284C211yesmaximal, characteristic
5C3×#4457C211yesmaximal, characteristic
6#10589095C211yesmaximal, characteristic
7#10589092C211yesmaximal, characteristic
8#71243—31nomaximal
9#68555—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C32×C4×C8C2211yescharacteristic
14#63642—21no—
15#63641—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#816—21no—
18C3×#816—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63575—21no—
22#63573—21no—
23#63567—21no—
24#63567—21no—
25C3×#487—31no—
26#5094—31no—
27#5091—31no—
28#4851—31no—
29#4850—31no—
30#4681D311yescharacteristic
31#4679—31no—
32#4679—31no—
33#4679—61no—
34C3×#334—31no—
35#4547—31no—
36#4546—31no—
37#4486—31no—
38#4481—31no—
39#4457D311yescharacteristic
40C2×#634D411yescharacteristic
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C32×C8D411yescharacteristic
44C2×C32×C8D411yescharacteristic
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)D411yescharacteristic
47#3750—21no—
48C4×C3⋊Dic3—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#1704—91noSylow
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59#869C2×D311yescharacteristic
60#869C2×D311yescharacteristic
61C4×Dic6—31no—
62C4×Dic6—31no—
63C4×Dic6—61no—
64C3×C4⋊C8—31no—
65C3×C4⋊C8—31no—
66C3×#103—61no—
67C3×#103—61no—
68C3×C4×C8—21no—
69C3×C4×C8C2×D311yescharacteristic
70C3×C4×C8C2×D311yescharacteristic
71#818—61no—
72#817—61no—
73#816—21no—
74#816—21no—
75#816—61no—
76#816—61no—
77#815—62no—
78#815—61no—
79#815—61no—
80Dic3⋊C8—62no—
81Dic3⋊C8—61no—
82Dic3⋊C8—61no—
83#810—61no—
84#810—61no—
85#808—61no—
86#807—61no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—21no—
97#634—21no—
98#634—21no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C3×Dic6—41no—
102C3×Dic6—41no—
103C3×Dic6—81no—
104C32×C8—21no—
105C32×C8—21no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109#487—31no—
110#477—91no—
111#475—91no—
112#446—91no—
113#334—31no—
114#333—91no—
115#332—91no—
116C2×C3×Q8—61no—
117C2×C3×Q8—61no—
118C2×Dic6—21no—
119C2×Dic6—21no—
120C2×Dic6—31no—
121C2×Dic6—31no—
122C2×Dic6—61no—
123C2×C3×C8—21no—
124C2×C3×C8—21no—
125C2×C3×C8—61no—
126C2×C3×C8—61no—
127C2×C3×C8D1211yescharacteristic
128C2×C3×C8D1211yescharacteristic
129C2×C3×C8#6711yescharacteristic
130C2×C3×C8#6711yescharacteristic
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C42—21no—
136C3×C42C22×D311yescharacteristic
137C3×C42C22×D311yescharacteristic
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—31no—
143C4⋊Dic3—31no—
144C4⋊Dic3—61no—
145Dic3⋊C4—62no—
146Dic3⋊C4—61no—
147Dic3⋊C4—61no—
148C4×Dic3—62no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—62no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—61no—
156C22×C32#12111yescharacteristic
157C32×C4—21no—
158C32×C4#13511yescharacteristic
159C32×C4#13711yescharacteristic
160C32×C4#13711yescharacteristic
161C32×C4#13711yescharacteristic
162C3⋊Dic3—41no—
163C3⋊Dic3—41no—
164C3×Dic3—81no—
165C3×Dic3—81no—
166C4⋊Q8—31no—
167C4⋊Q8—31no—
168C4×Q8—91no—
169#107—181no—
170#106—181no—
171C4⋊C8—31no—
172C4⋊C8—31no—
173C4⋊C8—91no—
174C4⋊C8—181no—
175#103—61no—
176#103—61no—
177#103—181no—
178#103—181no—
179#97—181no—
180C4×C8D3211yescharacteristic
181C3×Q8—121no—
182C3×Q8—121no—
183C3×Q8—241no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—121no—
188C2×C3×C4—121no—
189C2×C3×C4C2×D1211yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192C2×C3×C4#23711yescharacteristic
193C2×C3×C4#23911yescharacteristic
194C2×C3×C4C2×#6711yescharacteristic
195C2×Dic3—41no—
196C2×Dic3—41no—
197C2×Dic3—62no—
198C2×Dic3—62no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203Dic6—41no—
204Dic6—41no—
205Dic6—61no—
206Dic6—61no—
207Dic6—61no—
208Dic6—61no—
209Dic6—81no—
210Dic6—121no—
211Dic6—121no—
212C3×C8—22no—
213C3×C8—21no—
214C3×C8—21no—
215C3×C8—21no—
216C3×C8—21no—
217C3×C8—41no—
218C3×C8—121no—
219C3×C8—121no—
220C3⋊C8—41no—
221C3⋊C8—41no—
222C3⋊C8—122no—
223C3⋊C8—121no—
224C3⋊C8—121no—
225C2×C32#46411yescharacteristic
226C2×C32#47011yescharacteristic
227C2×C32#47111yescharacteristic
228C2×Q8—61no—
229C2×Q8—61no—
230C2×Q8—91no—
231C2×C8—61no—
232C2×C8—61no—
233C2×C8—181no—
234C2×C8#62611yescharacteristic
235C2×C8#62611yescharacteristic
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—91no—
241C4⋊C4—181no—
242C42—181no—
243C42C2×D3211yescharacteristic
244C22×C3—21no—
245C22×C3#89511yescharacteristic
246C22×C3#93811yescharacteristic
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—41no—
254C3×C4—241no—
255C3×C4—241no—
256C3×C4#90411yescharacteristic
257C3×C4#90911yescharacteristic
258C3×C4#91511yescharacteristic
259C3×C4#91511yescharacteristic
260C3×C4#91811yescharacteristic
261C3×C4#91811yescharacteristic
262C3×C4#95011yescharacteristic
263C3×C4#95111yescharacteristic
264Dic3—81no—
265Dic3—81no—
266Dic3—122no—
267Dic3—122no—
268Dic3—121no—
269Dic3—121no—
270Dic3—121no—
271Dic3—121no—
272C32#170411yescharacteristic, complemented, Sylow
273Q8—121no—
274Q8—121no—
275Q8—181no—
276Q8—181no—
277Q8—241no—
278C2×C4—121no—
279C2×C4—121no—
280C2×C4—181no—
281C2×C4—181no—
282C2×C4#379611yescharacteristic
283C2×C4#380211yescharacteristic
284C2×C4C2×#62611yescharacteristic
285C8—21no—
286C8—21no—
287C8—121no—
288C8—121no—
289C8—361no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3#484511yescharacteristic
294C2×C3#486711yescharacteristic
295C2×C3#489811yescharacteristic
296C2×C3#505411yescharacteristic
297C2×C3#517711yescharacteristic
298C2×C3#518911yescharacteristic
299C22#6391611yescharacteristic
300C4—21no—
301C4—241no—
302C4—241no—
303C4—361no—
304C4—361no—
305C4#6381111yescharacteristic
306C4#6381111yescharacteristic
307C4#6382911yescharacteristic
308C4#6383111yescharacteristic
309C3—21no—
310C3#6855511yescharacteristic, complemented
311C3#7124311yescharacteristic, complemented
312C2#1059037811yescharacteristic
313C2#1059085811yescharacteristic
314C2#1059092811yescharacteristic
subgroupG/H
centerC22#63916
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#121
hypercenterC4×C8D32
hypocenterC32#1704
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
272. C32#1704semidirect
310. C3#68555semidirect
311. C3#71243semidirect

Maximal subgroups

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

subgroupindex
#105923782
C3×#46812
#105903072
#105902842
C3×#44572
#105890952
#105890922
#712433
#685553