Finite Group Databasebeta

← #11781578

Subgroups — #11781578

Order 1152.

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

normal subgroups only

This group has 337 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#10592380C211yesmaximal, characteristic
2C3×C8×Dic6C211yesmaximal, characteristic
3#10590301C211yesmaximal, characteristic
4#10590283C211yesmaximal, characteristic
5C3×#4458C211yesmaximal, characteristic
6#10589096C211yesmaximal, characteristic
7#10589094C211yesmaximal, characteristic
8#70947—31nomaximal
9#68591—31nomaximal
10#64078C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C32×C4×C8C2211yescharacteristic
14#63643—21no—
15#63643—21no—
16C3×Dic3⋊C8—21no—
17C3×C8×Dic3—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63575—21no—
22#63573—21no—
23#63566—21no—
24#63566—21no—
25C3×C8×Q8—31no—
26#5021—31no—
27#5020—31no—
28#4851—31no—
29#4850—31no—
30#4681—31no—
31#4681—31no—
32#4681—61no—
33C8×Dic6D311yescharacteristic
34C3×#335—31no—
35#4486—31no—
36#4482—31no—
37#4481—31no—
38#4481—31no—
39#4458D311yescharacteristic
40C2×#634—21no—
41C2×#634—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8D411yescharacteristic
44C2×C32×C8D411yescharacteristic
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#1684—91noSylow
57C3×C4×Q8—31no—
58#869—31no—
59#869—31no—
60#869—31no—
61#869—31no—
62#869—61no—
63#869—61no—
64C4×Dic6C2×D311yescharacteristic
65C3×C4⋊C8—31no—
66C3×C4⋊C8—31no—
67C3×C4⋊C8—31no—
68C3×C4⋊C8—61no—
69C3×C4×C8—21no—
70C3×C4×C8—61no—
71C3×C4×C8C2×D311yescharacteristic
72C3×C4×C8C2×D311yescharacteristic
73#835—61no—
74#835—61no—
75#818—61no—
76#817—61no—
77#816—62no—
78#816—62no—
79#816—61no—
80#816—61no—
81#816—61no—
82#816—61no—
83#816—61no—
84#816—61no—
85Dic3⋊C8—21no—
86C8×Dic3—21no—
87#808—61no—
88#807—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
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—41no—
96C2×C3⋊Dic3—41no—
97#634—41no—
98#634—41no—
99#634—81no—
100C2×C3×Dic3—21no—
101C2×C3×Dic3—21no—
102C3×Dic6—21no—
103C3×Dic6Q1612yes—
104C32×C8—21no—
105C32×C8—21no—
106C3×C3⋊C8—41no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109#487—91no—
110#477—91no—
111#475—91no—
112C8×Q8—31no—
113#335—31no—
114#333—91no—
115#332—91no—
116C2×C3×Q8—31no—
117C2×Dic6—62no—
118C2×Dic6—61no—
119C2×Dic6—61no—
120C2×Dic6—61no—
121C2×Dic6—61no—
122C2×Dic6—121no—
123C2×Dic6D1211yescharacteristic
124C2×C3×C8—21no—
125C2×C3×C8—21no—
126C2×C3×C8—61no—
127C2×C3×C8—61no—
128C2×C3×C8—61no—
129C2×C3×C8D1211yescharacteristic
130C2×C3×C8D1211yescharacteristic
131C2×C3×C8#6711yescharacteristic
132C2×C3×C8#6711yescharacteristic
133C3×C4⋊C4—31no—
134C3×C4⋊C4—61no—
135C3×C42—21no—
136C3×C42—61no—
137C3×C42C22×D311yescharacteristic
138C3×C42C22×D311yescharacteristic
139C4⋊Dic3—62no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—61no—
148C4⋊Dic3—121no—
149C4⋊Dic3—121no—
150C4⋊Dic3—121no—
151C4⋊Dic3D1211yescharacteristic
152Dic3⋊C4—21no—
153C4×Dic3—21no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—21no—
157C22×C32#12111yescharacteristic
158C32×C4—21no—
159C32×C4C2×Q1611yescharacteristic
160C32×C4#13511yescharacteristic
161C32×C4#13511yescharacteristic
162C32×C4#13711yescharacteristic
163C3⋊Dic3—81no—
164C3⋊Dic3—81no—
165C3×Dic3—22no—
166C3×Dic3—41no—
167C4⋊Q8—91no—
168C4⋊Q8—91no—
169C4×Q8—31no—
170#107—181no—
171#106—181no—
172C4⋊C8—31no—
173C4⋊C8—31no—
174C4⋊C8—31no—
175C4⋊C8—61no—
176#103—181no—
177#103—181no—
178#103—181no—
179#103—181no—
180C4×C8—61no—
181C4×C8D3211yescharacteristic
182C3×Q8—32no—
183C3×Q8—61no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—61no—
188C2×C3×C4—61no—
189C2×C3×C4C2×D1211yescharacteristic
190C2×C3×C4C2×D1211yescharacteristic
191C2×C3×C4#23511yescharacteristic
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4#23911yescharacteristic
194C2×C3×C4C2×#6711yescharacteristic
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—122no—
198C2×Dic3—122no—
199C2×Dic3—121no—
200C2×Dic3—121no—
201C2×Dic3—121no—
202C2×Dic3—121no—
203Dic6—21no—
204Dic6—122no—
205Dic6—122no—
206Dic6—121no—
207Dic6—121no—
208Dic6—121no—
209Dic6—121no—
210Dic6—242no—
211Dic6—241no—
212Dic6—241no—
213Dic6Dic1212yes—
214C3×C8—21no—
215C3×C8—21no—
216C3×C8—21no—
217C3×C8—21no—
218C3×C8—41no—
219C3×C8—41no—
220C3×C8—121no—
221C3×C8—121no—
222C3×C8—121no—
223C3⋊C8—41no—
224C3⋊C8—41no—
225C3⋊C8—41no—
226C2×C32#46411yescharacteristic
227C2×C32#46711yescharacteristic
228C2×C32#47111yescharacteristic
229C2×Q8—31no—
230C2×Q8—181no—
231C2×Q8—181no—
232C2×C8—61no—
233C2×C8—61no—
234C2×C8—61no—
235C2×C8#62611yescharacteristic
236C2×C8#62611yescharacteristic
237C4⋊C4—31no—
238C4⋊C4—61no—
239C4⋊C4—181no—
240C4⋊C4—181no—
241C4⋊C4—181no—
242C4⋊C4—181no—
243C42—61no—
244C42C2×D3211yescharacteristic
245C22×C3—21no—
246C22×C3#89511yescharacteristic
247C22×C3#93011yescharacteristic
248C3×C4—22no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—62no—
256C3×C4—121no—
257C3×C4#90411yescharacteristic
258C3×C4#90411yescharacteristic
259C3×C4C2×Dic1211yescharacteristic
260C3×C4#90911yescharacteristic
261C3×C4#91211yescharacteristic
262C3×C4D3×Q1611yescharacteristic
263C3×C4#94211yescharacteristic
264C3×C4#95011yescharacteristic
265Dic3—22no—
266Dic3—41no—
267Dic3—242no—
268Dic3—242no—
269Dic3—241no—
270Dic3—241no—
271Dic3—241no—
272Dic3—241no—
273C32#168411yescharacteristic, complemented, Sylow
274Q8—32no—
275Q8—61no—
276Q8—361no—
277Q8—361no—
278Q8—721no—
279C2×C4—61no—
280C2×C4—61no—
281C2×C4—361no—
282C2×C4—361no—
283C2×C4#379911yescharacteristic
284C2×C4D3×D1211yescharacteristic
285C2×C4C2×#62611yescharacteristic
286C8—21no—
287C8—21no—
288C8—121no—
289C8—121no—
290C8—121no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3#484511yescharacteristic
295C2×C3#488711yescharacteristic
296C2×C3#489811yescharacteristic
297C2×C3#502811yescharacteristic
298C2×C3#511611yescharacteristic
299C2×C3#514111yescharacteristic
300C22#6390911yescharacteristic
301C4—21no—
302C4—62no—
303C4—121no—
304C4—721no—
305C4—721no—
306C4D3×Dic1211yescharacteristic
307C4#6380711yescharacteristic
308C4#6382911yescharacteristic
309C4#6383311yescharacteristic
310C3—21no—
311C3#6859111yescharacteristic, complemented
312C3#7094711yescharacteristic, complemented
313C2#1059036811yescharacteristic
314C2#1059085211yescharacteristic
315C2#1059093111yescharacteristic
subgroupG/H
centerC22#63909
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#121
hypercenterC4×C8D32
hypocenterC32#1684
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
273. C32#1684semidirect
311. C3#68591semidirect
312. C3#70947semidirect

Maximal subgroups

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

subgroupindex
#105923802
C3×C8×Dic62
#105903012
#105902832
C3×#44582
#105890962
#105890942
#709473
#685913