Finite Group Databasebeta

← #11781894

Subgroups — #11781894

Order 1152.

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

normal subgroups only

This group has 341 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#10592379C211yesmaximal, characteristic
2C3×#4679C211yesmaximal, characteristic
3#10590385C211yesmaximal, characteristic
4#10590283C211yesmaximal, characteristic
5C3×#4458C211yesmaximal, characteristic
6#10589096C211yesmaximal, characteristic
7#10589094C211yesmaximal, characteristic
8#70963—31nomaximal
9#68593—31nomaximal
10#64078C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3719—21no—
14C32×C4×C8C2211yescharacteristic
15#63644—21no—
16#63644—21no—
17C3×#815—21no—
18C3×Dic3⋊C8—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63575—21no—
23#63567—21no—
24#63566—21no—
25C3×#446—31no—
26#5031—31no—
27#5021—31no—
28#4850—31no—
29#4849—31no—
30#4680—31no—
31#4680—31no—
32#4680—61no—
33#4679D311yescharacteristic
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#3719—42no—
57#1692—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×#97—61no—
73C3×C4×C8—21no—
74C3×C4×C8C2×D311yescharacteristic
75C3×C4×C8C2×D311yescharacteristic
76#835—61no—
77#818—61no—
78#817—62no—
79#817—62no—
80#817—61no—
81#817—61no—
82#817—61no—
83#817—61no—
84#816—61no—
85#816—61no—
86#815—21no—
87Dic3⋊C8—21no—
88#810—61no—
89#807—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—81no—
101C2×C3×Dic3—21no—
102C2×C3×Dic3—21no—
103C3×Dic6—21no—
104C3×Dic6—21no—
105C32×C8—21no—
106C32×C8Q1612yescomplemented
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8—41no—
110#498—91no—
111#477—91no—
112#462—91no—
113#446—31no—
114#335—31no—
115#333—91no—
116#332—91no—
117C2×C3×Q8—31no—
118C2×Dic6—61no—
119C2×Dic6—61no—
120C2×Dic6—61no—
121C2×Dic6—61no—
122C2×Dic6—121no—
123C2×Dic6—121no—
124C2×Dic6D1211yescharacteristic
125C2×C3×C8—21no—
126C2×C3×C8—21no—
127C2×C3×C8—61no—
128C2×C3×C8—61no—
129C2×C3×C8—61no—
130C2×C3×C8D1211yescharacteristic
131C2×C3×C8D1211yescharacteristic
132C2×C3×C8#6711yescharacteristic
133C2×C3×C8#6711yescharacteristic
134C3×C4⋊C4—31no—
135C3×C4⋊C4—61no—
136C3×C42—21no—
137C3×C42—61no—
138C3×C42C22×D311yescharacteristic
139C3×C42C22×D311yescharacteristic
140#216—122no—
141C4⋊Dic3—62no—
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⋊Dic3D1211yescharacteristic
154Dic3⋊C4—21no—
155C4×Dic3—21no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—21no—
159Dic12—122no—
160C22×C32#12111yescharacteristic
161C32×C4—21no—
162C32×C4C2×Q1611yescharacteristic
163C32×C4AGL(1,ℤ/8)11yescharacteristic
164C32×C4#13711yescharacteristic
165C32×C4#13711yescharacteristic
166C3⋊Dic3—81no—
167C3⋊Dic3—81no—
168C3×Dic3—41no—
169C3×Dic3—41no—
170C2×Q16—181no—
171C4⋊Q8—91no—
172C4⋊Q8—91no—
173C4×Q8—31no—
174#107—181no—
175#106—181no—
176#106—181no—
177C4⋊C8—31no—
178C4⋊C8—31no—
179C4⋊C8—31no—
180C4⋊C8—61no—
181#103—181no—
182#103—181no—
183#97—61no—
184C4×C8D3211yescharacteristic
185C3×Q8—61no—
186C3×Q8—61no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—61no—
191C2×C3×C4—61no—
192C2×C3×C4C2×D1211yescharacteristic
193C2×C3×C4C2×D1211yescharacteristic
194C2×C3×C4#23511yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4#23911yescharacteristic
197C2×C3×C4C2×#6711yescharacteristic
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—122no—
201C2×Dic3—122no—
202C2×Dic3—121no—
203C2×Dic3—121no—
204C2×Dic3—121no—
205C2×Dic3—121no—
206Dic6—21no—
207Dic6—21no—
208Dic6—121no—
209Dic6—121no—
210Dic6—121no—
211Dic6—121no—
212Dic6—241no—
213Dic6—241no—
214Dic6—242no—
215Dic6—241no—
216Dic6—241no—
217C3×C8—22no—
218C3×C8—21no—
219C3×C8—21no—
220C3×C8—22no—
221C3×C8—121no—
222C3×C8—121no—
223C3×C8—121no—
224C3×C8Dic1212yescomplemented
225C3×C8#21612yescomplemented
226C3⋊C8—41no—
227C3⋊C8—41no—
228C3⋊C8—41no—
229C2×C32#46211yescharacteristic
230C2×C32#46811yescharacteristic
231C2×C32#47111yescharacteristic
232C2×Q8—31no—
233C2×Q8—181no—
234C2×Q8—181no—
235Q16—362no—
236C2×C8—61no—
237C2×C8—61no—
238C2×C8—61no—
239C2×C8#62611yescharacteristic
240C2×C8#62611yescharacteristic
241C4⋊C4—31no—
242C4⋊C4—61no—
243C4⋊C4—181no—
244C4⋊C4—181no—
245C4⋊C4—181no—
246C4⋊C4—181no—
247C42—61no—
248C42C2×D3211yescharacteristic
249C22×C3—21no—
250C22×C3#89511yescharacteristic
251C22×C3#93011yescharacteristic
252C3×C4—22no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—121no—
260C3×C4—121no—
261C3×C4C2×Dic1211yescharacteristic
262C3×C4#90811yescharacteristic
263C3×C4#90911yescharacteristic
264C3×C4#90911yescharacteristic
265C3×C4#91111yescharacteristic
266C3×C4#91811yescharacteristic
267C3×C4C2×#21611yescharacteristic
268C3×C4#95111yescharacteristic
269Dic3—41no—
270Dic3—41no—
271Dic3—242no—
272Dic3—242no—
273Dic3—241no—
274Dic3—241no—
275Dic3—241no—
276Dic3—241no—
277C32#169211yescharacteristic, complemented, Sylow
278Q8—61no—
279Q8—61no—
280Q8—361no—
281Q8—361no—
282Q8—721no—
283C2×C4—61no—
284C2×C4—61no—
285C2×C4—361no—
286C2×C4—361no—
287C2×C4#379911yescharacteristic
288C2×C4D3×D1211yescharacteristic
289C2×C4C2×#62611yescharacteristic
290C8—21no—
291C8—121no—
292C8—121no—
293C8—121no—
294C8#371912yescomplemented
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3#484911yescharacteristic
299C2×C3#488611yescharacteristic
300C2×C3#489811yescharacteristic
301C2×C3#503111yescharacteristic
302C2×C3#513411yescharacteristic
303C2×C3#514111yescharacteristic
304C22#6390911yescharacteristic
305C4—21no—
306C4—121no—
307C4—121no—
308C4—721no—
309C4—721no—
310C4#6379511yescharacteristic
311C4#6380111yescharacteristic
312C4#6383111yescharacteristic
313C4C2×#371911yescharacteristic
314C3—21no—
315C3#6859311yescharacteristic, complemented
316C3#7096311yescharacteristic, complemented
317C2#1059038511yescharacteristic
318C2#1059083811yescharacteristic
319C2#1059093111yescharacteristic
subgroupG/H
centerC22#63909
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#121
hypercenterC4×C8D32
hypocenterC32#1692
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
106. C32×C8Q16semidirect
224. C3×C8Dic12semidirect
225. C3×C8#216semidirect
277. C32#1692semidirect
294. C8#3719semidirect
315. C3#68593semidirect
316. C3#70963semidirect

Maximal subgroups

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

subgroupindex
#105923792
C3×#46792
#105903852
#105902832
C3×#44582
#105890962
#105890942
#709633
#685933