Finite Group Databasebeta

← #11781410

Subgroups — #11781410

Order 1152.

332 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C3×#4849C211yesmaximal, characteristic
2#10590301C211yesmaximal, characteristic
3#10590288C211yesmaximal, characteristic
4C3⋊C8×Dic6C211yesmaximal, characteristic
5#10589352C211yesmaximal, characteristic
6C3×#4480C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71054—31nomaximal
9#68549—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×Dic12—21no—
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#816—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63573—21no—
20Dic3⋊(C3⋊C8)—21no—
21#63567—21no—
22#63567—21no—
23#63566—21no—
24Dic3×C3⋊C8—21no—
25C3×#462—31no—
26#5093—31no—
27Q8×C3⋊C8—31no—
28#5020—31no—
29#4851—31no—
30#4849D311yescharacteristic
31#4681—31no—
32C8×Dic6—31no—
33C3×#334—31no—
34#4547—31no—
35#4486—31no—
36#4486—31no—
37#4486—61no—
38#4482—31no—
39#4480D311yescharacteristic
40C2×#634—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×Dic12—42no—
57#1680—91noSylow
58C2×C3×Q16—61no—
59C3×C4⋊Q8—31no—
60C3×C4×Q8—31no—
61C2×Dic12—21no—
62#869—31no—
63#869—31no—
64#869—61no—
65#869C2×D311yescharacteristic
66C4×Dic6C2×D311yescharacteristic
67C3×C4⋊C8—21no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4⋊C8C2×D311yescharacteristic
71C3×#103—61no—
72C3×C4×C8—31no—
73#835—61no—
74#817—61no—
75#816—21no—
76#816—61no—
77#816—61no—
78#816—61no—
79Dic3⋊C8—61no—
80C8×Dic3—61no—
81#810—61no—
82#810—61no—
83#808—61no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4×C3⋊C8—61no—
90C4×C3⋊C8C2×D311yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3⋊Dic3—41no—
95#634—41no—
96#634—41no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—41no—
100C3×Dic6—21no—
101C3×Dic6—41no—
102C3×Dic6—41no—
103C3×Dic6SD1612yes—
104C32×C8—41no—
105C3⋊(C3⋊C8)—41no—
106C3×C3⋊C8—21no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—41no—
109#487—91no—
110#475—91no—
111#462—31no—
112C8×Q8—91no—
113#334—31no—
114#332—91no—
115#332—91no—
116C2×C3×Q8—31no—
117C2×C3×Q8—61no—
118C2×Dic6—21no—
119C2×Dic6—61no—
120C2×Dic6—61no—
121C2×Dic6—121no—
122C2×Dic6#6711yescharacteristic
123C3×Q16—122no—
124C2×C3×C8—21no—
125C2×C3×C8—21no—
126C2×C3×C8—31no—
127C2×C3×C8—31no—
128C2×C3×C8—41no—
129C2×C3×C8—61no—
130C3×C4⋊C4—31no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C42—21no—
135C3×C42—61no—
136C3×C42C22×D311yescharacteristic
137C3×C42C22×D311yescharacteristic
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—62no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—121no—
146C4⋊Dic3#6711yescharacteristic
147Dic3⋊C4—21no—
148C4×Dic3—21no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—121no—
153C2×C3⋊C8D1211yescharacteristic
154C2×C3⋊C8D1211yescharacteristic
155Dic12—42no—
156C22×C32#12111yescharacteristic
157C32×C4—21no—
158C32×C4C2×SD1611yescharacteristic
159C32×C4#13511yescharacteristic
160C32×C4#13511yescharacteristic
161C32×C4#13711yescharacteristic
162C3⋊Dic3—81no—
163C3×Dic3—22no—
164C3×Dic3—41no—
165C3×Dic3—81no—
166C2×Q16—61no—
167C4⋊Q8—31no—
168C4⋊Q8—91no—
169C4×Q8—31no—
170#106—181no—
171C4⋊C8—31no—
172C4⋊C8—91no—
173C4⋊C8—181no—
174C4⋊C8D3211yescharacteristic
175#103—61no—
176#103—181no—
177#103—181no—
178#103—181no—
179C4×C8—31no—
180C4×C8—181no—
181C3×Q8—32no—
182C3×Q8—61no—
183C3×Q8—121no—
184C3×Q8—121no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—61no—
189C2×C3×C4—61no—
190C2×C3×C4—121no—
191C2×C3×C4C2×D1211yescharacteristic
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4#23711yescharacteristic
195C2×C3×C4#23911yescharacteristic
196C2×C3×C4C2×#6711yescharacteristic
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—41no—
200C2×Dic3—122no—
201C2×Dic3—121no—
202C2×Dic3—121no—
203Dic6—21no—
204Dic6—41no—
205Dic6—41no—
206Dic6—121no—
207Dic6—121no—
208Dic6—121no—
209Dic6—121no—
210Dic6—241no—
211Dic6—241no—
212Dic6#21412yes—
213C3×C8—41no—
214C3×C8—41no—
215C3×C8—61no—
216C3×C8—61no—
217C3×C8—81no—
218C3×C8—121no—
219C3⋊C8—21no—
220C3⋊C8—21no—
221C3⋊C8—41no—
222C3⋊C8—121no—
223C3⋊C8—121no—
224C3⋊C8—241no—
225C2×C32#46411yescharacteristic
226C2×C32#46511yescharacteristic
227C2×C32#47311yescharacteristic
228C2×Q8—31no—
229C2×Q8—61no—
230C2×Q8—181no—
231Q16—122no—
232C2×C8—21no—
233C2×C8—31no—
234C2×C8—31no—
235C2×C8—61no—
236C2×C8—181no—
237C4⋊C4—31no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—61no—
241C4⋊C4—181no—
242C4⋊C4—181no—
243C42—61no—
244C42C2×D3211yescharacteristic
245C22×C3—21no—
246C22×C3#89511yescharacteristic
247C22×C3#93911yescharacteristic
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—41no—
255C3×C4—62no—
256C3×C4—121no—
257C3×C4—241no—
258C3×C4#90411yescharacteristic
259C3×C4#90911yescharacteristic
260C3×C4D3×SD1611yescharacteristic
261C3×C4#91611yescharacteristic
262C3×C4#91811yescharacteristic
263C3×C4#91911yescharacteristic
264C3×C4C2×#21411yescharacteristic
265C3×C4#95011yescharacteristic
266Dic3—22no—
267Dic3—41no—
268Dic3—81no—
269Dic3—242no—
270Dic3—241no—
271Dic3—241no—
272C32#168011yescharacteristic, complemented, Sylow
273Q8—32no—
274Q8—61no—
275Q8—121no—
276Q8—121no—
277Q8—361no—
278Q8—361no—
279C2×C4—61no—
280C2×C4—61no—
281C2×C4—121no—
282C2×C4—361no—
283C2×C4#379611yescharacteristic
284C2×C4D3×D1211yescharacteristic
285C2×C4D3×#6711yescharacteristic
286C8—41no—
287C8—61no—
288C8—61no—
289C8—121no—
290C8—361no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3#484511yescharacteristic
295C2×C3#486411yescharacteristic
296C2×C3#489611yescharacteristic
297C2×C3#504111yescharacteristic
298C2×C3#518511yescharacteristic
299C2×C3#520411yescharacteristic
300C22#6388611yescharacteristic
301C4—21no—
302C4—62no—
303C4—121no—
304C4—241no—
305C4—721no—
306C4#6380111yescharacteristic
307C4#6380811yescharacteristic
308C4D3×#21411yescharacteristic
309C4#6394711yescharacteristic
310C3—21no—
311C3#6854911yescharacteristic, complemented
312C3#7105411yescharacteristic, complemented
313C2#1059057811yescharacteristic
314C2#1059080111yescharacteristic
315C2#1059098311yescharacteristic
subgroupG/H
centerC22#63886
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1680
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#1680semidirect
311. C3#68549semidirect
312. C3#71054semidirect

Maximal subgroups

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

subgroupindex
C3×#48492
#105903012
#105902882
C3⋊C8×Dic62
#105893522
C3×#44802
#105890932
#710543
#685493