Finite Group Databasebeta

← #11781397

Subgroups — #11781397

Order 1152.

351 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic
2C3×#5031C211yesmaximal, characteristic
3C3×#5020C211yesmaximal, characteristic
4#10590290C211yesmaximal, characteristic
5#10589098C211yesmaximal, characteristic
6#10589093C211yesmaximal, characteristic
7#10589092C211yesmaximal, characteristic
8#71118—31nomaximal
9#71054—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C2×C3×#216—21no—
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C4⋊(C3⋊(C3⋊C8))—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C4×C3⋊(C3⋊C8)—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#835—21no—
19C3×#810—21no—
20C3×#808—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63565—21no—
24#63565—21no—
25C3×#475—31no—
26C3×#462—31no—
27#5093—31no—
28#5079—31no—
29#5031D311yescharacteristic
30Q8×C3⋊C8—31no—
31Q8×C3⋊C8—31no—
32Q8×C3⋊C8—61no—
33#5020D311yescharacteristic
34#4547—31no—
35#4547—31no—
36#4486—31no—
37#4482—31no—
38#4480—31no—
39#4480—31no—
40C2×C32×Q8D411yescharacteristic
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C42—21no—
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×#216—42no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57#1680—91noSylow
58C2×C3×Q16—61no—
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8—31no—
61C3×C4×Q8—21no—
62C3×C4×Q8C2×D311yescharacteristic
63C3×C4×Q8C2×D311yescharacteristic
64C2×#216—21no—
65#869C2×D311yescharacteristic
66#869C2×D311yescharacteristic
67C3×#106—61no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8—31no—
70C3×#103—61no—
71C3×#103—61no—
72#835—21no—
73#835—61no—
74#835—61no—
75#810—21no—
76#810—61no—
77#810—61no—
78#808—21no—
79C4⋊(C3⋊C8)—31no—
80C4⋊(C3⋊C8)—31no—
81C4⋊(C3⋊C8)—61no—
82C4⋊(C3⋊C8)—61no—
83C4⋊(C3⋊C8)—61no—
84C4⋊(C3⋊C8)—62no—
85C4⋊(C3⋊C8)C2×D311yescharacteristic
86C4⋊(C3⋊C8)C2×D311yescharacteristic
87C4×C3⋊C8—31no—
88C4×C3⋊C8—31no—
89C4×C3⋊C8—61no—
90C4×C3⋊C8—61no—
91C4×C3⋊C8—61no—
92C4×C3⋊C8—62no—
93C32×Q8—21no—
94C32×Q8SD1612yes—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C3×Dic6—41no—
103C3×Dic6—41no—
104C3×Dic6—41no—
105C3×Dic6—41no—
106C3⋊(C3⋊C8)—21no—
107C3⋊(C3⋊C8)—21no—
108C3⋊(C3⋊C8)—41no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111#487—91no—
112#475—31no—
113#462—31no—
114C8×Q8—91no—
115#334—91no—
116#332—91no—
117#332—91no—
118C2×C3×Q8—21no—
119C2×C3×Q8—61no—
120C2×C3×Q8—61no—
121C2×C3×Q8#6711yescharacteristic
122C2×C3×Q8#6711yescharacteristic
123C2×Dic6—21no—
124C2×Dic6—21no—
125C3×Q16—122no—
126C2×C3×C8—61no—
127C2×C3×C8—61no—
128C3×C4⋊C4—22no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4#6711yescharacteristic
137C3×C4⋊C4#6711yescharacteristic
138C3×C42—22no—
139C3×C42—21no—
140C3×C42—21no—
141C3×C42—21no—
142C3×C42C22×D311yescharacteristic
143C3×C42C22×D311yescharacteristic
144#216—42no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—21no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—62no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160C22×C32#12111yescharacteristic
161C32×C4—22no—
162C32×C4—21no—
163C32×C4—41no—
164C32×C4C2×SD1611yescharacteristic
165C32×C4#13511yescharacteristic
166C32×C4#13511yescharacteristic
167C32×C4#13711yescharacteristic
168C3×Dic3—81no—
169C3×Dic3—81no—
170C2×Q16—61no—
171C4⋊Q8—31no—
172C4⋊Q8—31no—
173C4×Q8D3211yescharacteristic
174#106—61no—
175C4⋊C8—31no—
176C4⋊C8—31no—
177C4⋊C8—91no—
178C4⋊C8—181no—
179#103—61no—
180#103—61no—
181#103—181no—
182#103—181no—
183C4×C8—91no—
184C4×C8—181no—
185C3×Q8—22no—
186C3×Q8—21no—
187C3×Q8—21no—
188C3×Q8—22no—
189C3×Q8—121no—
190C3×Q8—121no—
191C3×Q8—121no—
192C3×Q8—121no—
193C3×Q8#21412yes—
194C3×Q8#21512yes—
195C2×C3×C4—22no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—22no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—121no—
205C2×C3×C4—121no—
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4#23711yescharacteristic
209C2×C3×C4#23711yescharacteristic
210C2×C3×C4C2×#6711yescharacteristic
211C2×C3×C4C2×#6711yescharacteristic
212C2×Dic3—41no—
213C2×Dic3—41no—
214Dic6—41no—
215Dic6—41no—
216Dic6—41no—
217Dic6—41no—
218C3×C8—121no—
219C3×C8—121no—
220C3⋊C8—41no—
221C3⋊C8—41no—
222C3⋊C8—62no—
223C3⋊C8—61no—
224C3⋊C8—61no—
225C3⋊C8—61no—
226C3⋊C8—61no—
227C3⋊C8—121no—
228C3⋊C8—122no—
229C3⋊C8—121no—
230C3⋊C8—121no—
231C2×C32#46411yescharacteristic
232C2×C32#46511yescharacteristic
233C2×C32#47311yescharacteristic
234C2×Q8—61no—
235C2×Q8—61no—
236C2×Q8#62511yescharacteristic
237Q16—122no—
238C2×C8—61no—
239C2×C8—61no—
240C2×C8—91no—
241C2×C8—91no—
242C2×C8—181no—
243C4⋊C4—21no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4#62511yescharacteristic
249C42—21no—
250C42C2×D3211yescharacteristic
251C22×C3—21no—
252C22×C3#93911yescharacteristic
253C22×C3#93911yescharacteristic
254C3×C4—24no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—22no—
258C3×C4—22no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—41no—
264C3×C4—42no—
265C3×C4—41no—
266C3×C4—41no—
267C3×C4—241no—
268C3×C4—241no—
269C3×C4#91511yescharacteristic
270C3×C4#91611yescharacteristic
271C3×C4#91811yescharacteristic
272C3×C4#91911yescharacteristic
273C3×C4C2×#21411yescharacteristic
274C3×C4C2×#21511yescharacteristic
275C3×C4#95011yescharacteristic
276C3×C4#95011yescharacteristic
277Dic3—81no—
278Dic3—81no—
279C32#168011yescharacteristic, complemented, Sylow
280Q8—21no—
281Q8—121no—
282Q8—121no—
283Q8—121no—
284Q8—121no—
285Q8#371512yes—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—121no—
289C2×C4—121no—
290C2×C4#380511yescharacteristic
291C2×C4C2×#62511yescharacteristic
292C2×C4#381111yescharacteristic
293C8—121no—
294C8—121no—
295C8—181no—
296C8—181no—
297C8—361no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3#504111yescharacteristic
302C2×C3#504811yescharacteristic
303C2×C3#516611yescharacteristic
304C2×C3#518511yescharacteristic
305C2×C3#520411yescharacteristic
306C2×C3#520411yescharacteristic
307C22#6398011yescharacteristic
308C4—21no—
309C4—22no—
310C4—41no—
311C4—241no—
312C4—241no—
313C4#6382211yescharacteristic
314C4C2×#371511yescharacteristic
315C4#6395011yescharacteristic
316C4#6395111yescharacteristic
317C3—21no—
318C3#7105411yescharacteristic, complemented
319C3#7111811yescharacteristic, complemented
320C2#1059117911yescharacteristic
321C2#1059161211yescharacteristic
322C2#1059168311yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#121
hypercenterC4×Q8D32
hypocenterC32#1680
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
279. C32#1680semidirect
318. C3#71054semidirect
319. C3#71118semidirect

Maximal subgroups

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

subgroupindex
Q8×C3⋊(C3⋊C8)2
C3×#50312
C3×#50202
#105902902
#105890982
#105890932
#105890922
#711183
#710543