Finite Group Databasebeta

← #11780991

Subgroups — #11780991

Order 1152.

360 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 100 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#10592719C211yesmaximal, characteristic
2C3×Q8×C3⋊C8C211yesmaximal, characteristic
3C3×#5020C211yesmaximal, characteristic
4#10590386C211yesmaximal, characteristic
5#10589099C211yesmaximal, characteristic
6#10589094C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71117—31nomaximal
9#70942—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3719—21no—
14C2×#3719—21no—
15#63662—21no—
16#63635—21no—
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#835—21no—
19C3×#808—21no—
20C3×C4⋊(C3⋊C8)—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#475—31no—
26C3×C8×Q8—31no—
27#5092—31no—
28Q8×C3⋊C8D311yescharacteristic
29#5020—31no—
30#5020—31no—
31#5020—61no—
32#5020D311yescharacteristic
33#4699—31no—
34#4547—31no—
35#4486—31no—
36#4482—31no—
37#4482—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×Q8D411yescharacteristic
41C2×#634—21no—
42C2×C3×Dic6—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C42—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3719—42no—
57#3719—42no—
58#1670—91noSylow
59C3×C4⋊Q8—31no—
60C3×C4×Q8—21no—
61C3×C4×Q8C2×D311yescharacteristic
62C3×C4×Q8C2×D311yescharacteristic
63C2×#216—61no—
64C2×#216—61no—
65C2×Dic12—61no—
66C2×Dic12—61no—
67#869—31no—
68#869—31no—
69#869—61no—
70#869C2×D311yescharacteristic
71C3×#106—61no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—61no—
75C3×#103—61no—
76C3×C4×C8—31no—
77C3×C4×C8—61no—
78#835—21no—
79#835—62no—
80#835—61no—
81#835—61no—
82#808—21no—
83#808—62no—
84#808—61no—
85#808—61no—
86C4⋊(C3⋊C8)—21no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8—21no—
93C4×C3⋊C8C2×D311yescharacteristic
94C32×Q8—21no—
95C32×Q8Q1612yescomplemented
96C2×C32×C4—21no—
97C2×C32×C4—21no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3⋊Dic3—41no—
102#634—41no—
103#634—41no—
104C2×C3×Dic3—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8SD1612yes—
112#494—91no—
113#475—31no—
114#475—91no—
115C8×Q8—31no—
116#335—91no—
117#332—91no—
118#332—91no—
119C2×C3×Q8—21no—
120C2×C3×Q8—61no—
121C2×C3×Q8D1211yescharacteristic
122C2×C3×Q8#6711yescharacteristic
123C2×Dic6—21no—
124C2×Dic6—61no—
125C2×Dic6—61no—
126C2×Dic6—121no—
127C2×C3×C8—31no—
128C2×C3×C8—31no—
129C2×C3×C8—61no—
130C2×C3×C8—61no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—41no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4D1211yescharacteristic
138C3×C4⋊C4#6711yescharacteristic
139C3×C42—21no—
140C3×C42—21no—
141C3×C42—21no—
142C3×C42—41no—
143C3×C42C22×D311yescharacteristic
144C3×C42C22×D311yescharacteristic
145#216—122no—
146#216—122no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C4⋊Dic3—62no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—121no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—62no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8#6711yescharacteristic
161C2×C3⋊C8#6711yescharacteristic
162Dic12—122no—
163Dic12—122no—
164C22×C32#12111yescharacteristic
165C32×C4—22no—
166C32×C4—21no—
167C32×C4—41no—
168C32×C4C2×SD1611yescharacteristic
169C32×C4C2×Q1611yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C3⋊Dic3—81no—
173C3×Dic3—81no—
174C2×Q16—181no—
175C2×Q16—181no—
176C4⋊Q8—31no—
177C4⋊Q8—91no—
178C4×Q8D3211yescharacteristic
179#106—61no—
180#106—181no—
181C4⋊C8—31no—
182C4⋊C8—31no—
183C4⋊C8—61no—
184C4⋊C8—91no—
185#103—61no—
186#103—181no—
187C4×C8—31no—
188C4×C8—61no—
189C3×Q8—21no—
190C3×Q8—21no—
191C3×Q8—22no—
192C3×Q8—41no—
193C3×Q8—121no—
194C3×Q8—121no—
195C3×Q8Dic1212yescomplemented
196C3×Q8#21612yescomplemented
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4—121no—
207C2×C3×C4C2×D1211yescharacteristic
208C2×C3×C4#23511yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4#23711yescharacteristic
211C2×C3×C4C2×#6711yescharacteristic
212C2×C3×C4C2×#6711yescharacteristic
213C2×Dic3—41no—
214C2×Dic3—122no—
215C2×Dic3—121no—
216C2×Dic3—121no—
217Dic6—41no—
218Dic6—41no—
219Dic6—121no—
220Dic6—121no—
221Dic6—121no—
222Dic6—121no—
223Dic6—241no—
224Dic6—241no—
225C3×C8—32no—
226C3×C8—61no—
227C3×C8—121no—
228C3×C8—121no—
229C3⋊C8—21no—
230C3⋊C8—41no—
231C3⋊C8—41no—
232C3⋊C8—122no—
233C3⋊C8—121no—
234C3⋊C8—121no—
235C3⋊C8#21512yes—
236C2×C32#46011yescharacteristic
237C2×C32#46711yescharacteristic
238C2×C32#47311yescharacteristic
239C2×Q8—61no—
240C2×Q8—181no—
241C2×Q8#62611yescharacteristic
242Q16—362no—
243Q16—362no—
244C2×C8—31no—
245C2×C8—31no—
246C2×C8—61no—
247C2×C8—61no—
248C2×C8—181no—
249C4⋊C4—21no—
250C4⋊C4—61no—
251C4⋊C4—61no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C4⋊C4#62611yescharacteristic
255C42—21no—
256C42C2×D3211yescharacteristic
257C22×C3—21no—
258C22×C3#93011yescharacteristic
259C22×C3#93911yescharacteristic
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—41no—
269C3×C4—42no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—81no—
273C3×C4—241no—
274C3×C4#90411yescharacteristic
275C3×C4C2×Dic1211yescharacteristic
276C3×C4D3×SD1611yescharacteristic
277C3×C4#91411yescharacteristic
278C3×C4C2×#21511yescharacteristic
279C3×C4C2×#21611yescharacteristic
280C3×C4#94911yescharacteristic
281C3×C4#95011yescharacteristic
282Dic3—81no—
283Dic3—242no—
284Dic3—241no—
285Dic3—241no—
286C32#167011yescharacteristic, complemented, Sylow
287Q8—21no—
288Q8—121no—
289Q8—121no—
290Q8—361no—
291Q8—361no—
292Q8#371912yescomplemented
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—121no—
296C2×C4—361no—
297C2×C4#380411yescharacteristic
298C2×C4C2×#62611yescharacteristic
299C2×C4D3×#6711yescharacteristic
300C8—32no—
301C8—61no—
302C8—121no—
303C8—121no—
304C8—361no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3#502711yescharacteristic
309C2×C3#505111yescharacteristic
310C2×C3#511611yescharacteristic
311C2×C3#514311yescharacteristic
312C2×C3#516311yescharacteristic
313C2×C3#520411yescharacteristic
314C22#6397811yescharacteristic
315C4—21no—
316C4—22no—
317C4—41no—
318C4—241no—
319C4—721no—
320C4#6382911yescharacteristic
321C4C2×#371911yescharacteristic
322C4D3×#21511yescharacteristic
323C4#6393911yescharacteristic
324C3—21no—
325C3#7094211yescharacteristic, complemented
326C3#7111711yescharacteristic, complemented
327C2#1059118711yescharacteristic
328C2#1059161711yescharacteristic
329C2#1059168211yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#121
hypercenterC4×Q8D32
hypocenterC32#1670
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
95. C32×Q8Q16semidirect
195. C3×Q8Dic12semidirect
196. C3×Q8#216semidirect
286. C32#1670semidirect
292. Q8#3719semidirect
325. C3#70942semidirect
326. C3#71117semidirect

Maximal subgroups

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

subgroupindex
#105927192
C3×Q8×C3⋊C82
C3×#50202
#105903862
#105890992
#105890942
#105890932
#711173
#709423