Finite Group Databasebeta

← #11781393

Subgroups — #11781393

Order 1152.

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

normal subgroups only

This group has 349 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#10590385C211yesmaximal, characteristic
4#10590301C211yesmaximal, characteristic
5C3×#4457C211yesmaximal, characteristic
6#10589094C211yesmaximal, characteristic
7#10589094C211yesmaximal, characteristic
8#70946—31nomaximal
9#68549—31nomaximal
10#64078C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3719—21no—
14C32×C4×C8C2211yescharacteristic
15#63643—21no—
16#63643—21no—
17C3×Dic3⋊C8—21no—
18C3×C8×Dic3—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63573—21no—
23#63567—21no—
24#63566—21no—
25C3×C8×Q8—31no—
26#5031—31no—
27#5020—31no—
28#4851—31no—
29#4849—31no—
30#4681—31no—
31#4681—31no—
32#4681—61no—
33C8×Dic6D311yescharacteristic
34C3×#334—31no—
35#4486—31no—
36#4486—31no—
37#4482—31no—
38#4482—31no—
39#4457D311yescharacteristic
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#3719—42no—
57#1680—91noSylow
58C3×C4×Q8—31no—
59C2×#216—61no—
60C2×Dic12—61no—
61#869—31no—
62#869—31no—
63#869—31no—
64#869—31no—
65#869—61no—
66#869—61no—
67C4×Dic6C2×D311yescharacteristic
68C3×C4⋊C8—31no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—61no—
72C3×C4×C8—21no—
73C3×C4×C8—61no—
74C3×C4×C8C2×D311yescharacteristic
75C3×C4×C8C2×D311yescharacteristic
76#835—61no—
77#817—61no—
78#816—62no—
79#816—62no—
80#816—61no—
81#816—61no—
82#816—61no—
83#816—61no—
84#816—61no—
85#816—61no—
86Dic3⋊C8—21no—
87C8×Dic3—21no—
88#810—61no—
89#808—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—41no—
97C2×C3⋊Dic3—41no—
98#634—41no—
99#634—41no—
100#634—41no—
101#634—41no—
102C2×C3×Dic3—21no—
103C2×C3×Dic3—21no—
104C3×Dic6—21no—
105C3×Dic6SD1612yes—
106C32×C8—21no—
107C32×C8—21no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111#487—91no—
112#475—91no—
113#462—91no—
114C8×Q8—31no—
115#334—31no—
116#332—91no—
117#332—91no—
118C2×C3×Q8—31no—
119C2×Dic6—62no—
120C2×Dic6—61no—
121C2×Dic6—61no—
122C2×Dic6—61no—
123C2×Dic6—61no—
124C2×Dic6—121no—
125C2×Dic6D1211yescharacteristic
126C2×C3×C8—21no—
127C2×C3×C8—21no—
128C2×C3×C8—61no—
129C2×C3×C8—61no—
130C2×C3×C8—61no—
131C2×C3×C8D1211yescharacteristic
132C2×C3×C8D1211yescharacteristic
133C2×C3×C8#6711yescharacteristic
134C2×C3×C8#6711yescharacteristic
135C3×C4⋊C4—31no—
136C3×C4⋊C4—61no—
137C3×C42—21no—
138C3×C42—61no—
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141#216—122no—
142C4⋊Dic3—62no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—61no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—121no—
152C4⋊Dic3—121no—
153C4⋊Dic3—121no—
154C4⋊Dic3D1211yescharacteristic
155Dic3⋊C4—21no—
156C4×Dic3—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160Dic12—122no—
161C22×C32#12111yescharacteristic
162C32×C4—21no—
163C32×C4C2×SD1611yescharacteristic
164C32×C4#13511yescharacteristic
165C32×C4#13511yescharacteristic
166C32×C4#13711yescharacteristic
167C3⋊Dic3—81no—
168C3⋊Dic3—81no—
169C3×Dic3—22no—
170C3×Dic3—41no—
171C2×Q16—181no—
172C4⋊Q8—91no—
173C4⋊Q8—91no—
174C4×Q8—31no—
175#106—181no—
176C4⋊C8—31no—
177C4⋊C8—31no—
178C4⋊C8—31no—
179C4⋊C8—61no—
180#103—181no—
181#103—181no—
182#103—181no—
183#103—181no—
184C4×C8—61no—
185C4×C8D3211yescharacteristic
186C3×Q8—32no—
187C3×Q8—61no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—61no—
192C2×C3×C4—61no—
193C2×C3×C4C2×D1211yescharacteristic
194C2×C3×C4C2×D1211yescharacteristic
195C2×C3×C4#23511yescharacteristic
196C2×C3×C4D3×D411yescharacteristic
197C2×C3×C4#23911yescharacteristic
198C2×C3×C4C2×#6711yescharacteristic
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—122no—
202C2×Dic3—122no—
203C2×Dic3—121no—
204C2×Dic3—121no—
205C2×Dic3—121no—
206C2×Dic3—121no—
207Dic6—21no—
208Dic6—122no—
209Dic6—122no—
210Dic6—121no—
211Dic6—121no—
212Dic6—121no—
213Dic6—121no—
214Dic6—121no—
215Dic6—121no—
216Dic6—121no—
217Dic6—121no—
218Dic6—241no—
219Dic6—241no—
220Dic6#20412yes—
221C3×C8—21no—
222C3×C8—21no—
223C3×C8—21no—
224C3×C8—21no—
225C3×C8—41no—
226C3×C8—41no—
227C3×C8—121no—
228C3×C8—121no—
229C3×C8—121no—
230C3⋊C8—41no—
231C3⋊C8—41no—
232C3⋊C8—41no—
233C2×C32#46411yescharacteristic
234C2×C32#46511yescharacteristic
235C2×C32#47311yescharacteristic
236C2×Q8—31no—
237C2×Q8—181no—
238C2×Q8—181no—
239Q16—362no—
240C2×C8—61no—
241C2×C8—61no—
242C2×C8—61no—
243C2×C8#62611yescharacteristic
244C2×C8#62611yescharacteristic
245C4⋊C4—31no—
246C4⋊C4—61no—
247C4⋊C4—181no—
248C4⋊C4—181no—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C42—61no—
252C42C2×D3211yescharacteristic
253C22×C3—21no—
254C22×C3#89511yescharacteristic
255C22×C3#93011yescharacteristic
256C3×C4—22no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—62no—
264C3×C4—121no—
265C3×C4C2×#20411yescharacteristic
266C3×C4#90411yescharacteristic
267C3×C4#90411yescharacteristic
268C3×C4#90911yescharacteristic
269C3×C4D3×SD1611yescharacteristic
270C3×C4#91611yescharacteristic
271C3×C4#94211yescharacteristic
272C3×C4#95011yescharacteristic
273Dic3—22no—
274Dic3—41no—
275Dic3—242no—
276Dic3—242no—
277Dic3—241no—
278Dic3—241no—
279Dic3—241no—
280Dic3—241no—
281C32#168011yescharacteristic, complemented, Sylow
282Q8—32no—
283Q8—61no—
284Q8—361no—
285Q8—361no—
286Q8—361no—
287Q8—361no—
288C2×C4—61no—
289C2×C4—61no—
290C2×C4—361no—
291C2×C4—361no—
292C2×C4#379911yescharacteristic
293C2×C4D3×D1211yescharacteristic
294C2×C4C2×#62611yescharacteristic
295C8—21no—
296C8—21no—
297C8—121no—
298C8—121no—
299C8—121no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3#484511yescharacteristic
304C2×C3#486411yescharacteristic
305C2×C3#489611yescharacteristic
306C2×C3#502811yescharacteristic
307C2×C3#511411yescharacteristic
308C2×C3#514311yescharacteristic
309C22#6390911yescharacteristic
310C4—21no—
311C4—62no—
312C4—121no—
313C4—721no—
314C4—721no—
315C4D3×#20411yescharacteristic
316C4#6380611yescharacteristic
317C4#6382911yescharacteristic
318C4#6383311yescharacteristic
319C3—21no—
320C3#6854911yescharacteristic, complemented
321C3#7094611yescharacteristic, complemented
322C2#1059036811yescharacteristic
323C2#1059083011yescharacteristic
324C2#1059093211yescharacteristic
subgroupG/H
centerC22#63909
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
281. C32#1680semidirect
320. C3#68549semidirect
321. C3#70946semidirect

Maximal subgroups

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

subgroupindex
#105923802
C3×C8×Dic62
#105903852
#105903012
C3×#44572
#105890942
#709463
#685493