Finite Group Databasebeta

← #11781357

Subgroups — #11781357

Order 1152.

364 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C3×#4846C211yesmaximal, characteristic
2#10590365C211yesmaximal, characteristic
3C3⋊C8×D12C211yesmaximal, characteristic
4#10590287C211yesmaximal, characteristic, complemented
5#10589348C211yesmaximal, characteristic, complemented
6C3×#4480C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71102—31nomaximal
9#68539—31nomaximal
10#64078C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3716—21no—
14C2×D3×C3⋊C8—21no—
15C32×C4⋊C8C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#821—21no—
18C3×#818—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63567—21no—
22#63566—21no—
23#63566—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#474—31no—
26#5079—31no—
27#5019—31no—
28D4×C3⋊C8—31no—
29#4846D311yescharacteristic
30#4841—31no—
31C8×D12—31no—
32#4681—31no—
33C3×#334—31no—
34#4547—31no—
35#4486—31no—
36#4482—31no—
37#4482—31no—
38#4482—61no—
39#4480D311yescharacteristic, complemented
40C2×#634—21no—
41C2×C3×D12D411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C2×C3⋊(C3⋊C8)—21no—
49C3×(C2×D3)⋊C4—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3716—42no—
57D3×C3⋊C8—42no—
58#1679—91noSylow
59C3×C4⋊Q8—31no—
60C3×C4×D4—31no—
61C2×#214—61no—
62C22×C3⋊C8—61no—
63C2×#204—61no—
64C2×D3×C8—61no—
65C4×D12C2×D311yescharacteristic
66#869—31no—
67#869—31no—
68#869—61no—
69#869C2×D311yescharacteristic
70C3×#107—61no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8C2×D311yescharacteristic
74C3×C4⋊C8C2×D311yescharacteristic
75C3×#102—61no—
76C3×C4×C8—31no—
77#835—61no—
78#835—61no—
79#830—61no—
80#821—21no—
81(C2×D3)⋊C8—61no—
82#818—21no—
83#816—61no—
84#816—61no—
85#816—61no—
86#810—61no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8C2×D311yescharacteristic
92C22×C3×D3—21no—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—41no—
97#634—41no—
98#634—41no—
99C2×C3×Dic3—21no—
100C2×C3×Dic3—41no—
101C3×D12—21no—
102C3×D12SD1612yes—
103C3×C4×D3—41no—
104C3×C4×D3—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C32×C8—41no—
108C3⋊(C3⋊C8)—41no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—41no—
112#487—91no—
113#474—31no—
114#461—91no—
115C8×D4—91no—
116#334—31no—
117#332—91no—
118#332—91no—
119C2×C3×Q8—61no—
120C2×C3×D4—31no—
121C22×C3×C4—61no—
122C2×D12#6711yescharacteristic
123C2×C4×D3—21no—
124C2×Dic6—21no—
125C2×Dic6—61no—
126C2×Dic6—61no—
127C2×Dic6—121no—
128C2×C3×C8—21no—
129C2×C3×C8—21no—
130C2×C3×C8—31no—
131C2×C3×C8—31no—
132C2×C3×C8—41no—
133C2×C3×C8—61no—
134C3×C4⋊C4—31no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C22⋊C4—61no—
138C3×C42—21no—
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141#214—122no—
142(C2×D3)⋊C4—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3—21no—
145C4⋊Dic3—62no—
146C4⋊Dic3—61no—
147C4⋊Dic3—61no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—121no—
151C4⋊Dic3#6711yescharacteristic
152C2×C3⋊C8—21no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—121no—
156C2×C3⋊C8—122no—
157C2×C3⋊C8D1211yescharacteristic
158C2×C3⋊C8D1211yescharacteristic
159#204—122no—
160D3×C8—122no—
161C22×C32#12111yescharacteristic
162C2×C3×D3—22no—
163C2×C3×D3—41no—
164C2×C3×D3—41no—
165C32×C4—21no—
166C32×C4C2×SD1611yescharacteristic
167C32×C4#13511yescharacteristic
168C32×C4#13511yescharacteristic
169C32×C4AGL(1,ℤ/8)11yescharacteristic
170C3⋊Dic3—81no—
171C3×Dic3—41no—
172C3×Dic3—81no—
173C2×SD16—181no—
174C22×C8—181no—
175C4⋊Q8—31no—
176C4⋊Q8—91no—
177C4×D4—31no—
178#107—61no—
179C4⋊C8—31no—
180C4⋊C8—91no—
181C4⋊C8D3211yescharacteristic
182#103—181no—
183#103—181no—
184#103—181no—
185#102—61no—
186C22⋊C8—181no—
187C4×C8—31no—
188C23×C3—61no—
189C22×D3—21no—
190C3×Q8—121no—
191C3×Q8—121no—
192C3×D4—32no—
193C3×D4—61no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—61no—
198C2×C3×C4—121no—
199C2×C3×C4—121no—
200C2×C3×C4—121no—
201C2×C3×C4C2×D1211yescharacteristic
202C2×C3×C4D3×D411yescharacteristic
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4#23711yescharacteristic
205C2×C3×C4#23911yescharacteristic
206C2×C3×C4C2×#6711yescharacteristic
207C2×Dic3—21no—
208C2×Dic3—41no—
209C2×Dic3—122no—
210C2×Dic3—121no—
211C2×Dic3—121no—
212D12—21no—
213D12#21512yes—
214C4×D3—41no—
215C4×D3—41no—
216Dic6—41no—
217Dic6—41no—
218Dic6—121no—
219Dic6—121no—
220Dic6—121no—
221Dic6—121no—
222Dic6—241no—
223Dic6—241no—
224C3×C8—41no—
225C3×C8—41no—
226C3×C8—61no—
227C3×C8—61no—
228C3×C8—81no—
229C3×C8—121no—
230C3⋊C8—21no—
231C3⋊C8—21no—
232C3⋊C8—41no—
233C3⋊C8—121no—
234C3⋊C8—121no—
235C3⋊C8—241no—
236C2×C32#46311yescharacteristic
237C2×C32#46511yescharacteristic
238C2×C32#47311yescharacteristic
239C3×D3—42no—
240C2×Q8—61no—
241C2×Q8—181no—
242C2×D4—31no—
243C22×C4—61no—
244SD16—362no—
245C2×C8—21no—
246C2×C8—31no—
247C2×C8—31no—
248C2×C8—61no—
249C2×C8—181no—
250C2×C8—362no—
251C4⋊C4—31no—
252C4⋊C4—61no—
253C4⋊C4—61no—
254C4⋊C4—181no—
255C4⋊C4—181no—
256C22⋊C4—61no—
257C42C2×D3211yescharacteristic
258C22×C3—21no—
259C22×C3—62no—
260C22×C3—121no—
261C22×C3—121no—
262C22×C3#89511yescharacteristic
263C22×C3#93911yescharacteristic
264C2×D3—22no—
265C2×D3—41no—
266C2×D3—41no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—41no—
274C3×C4—121no—
275C3×C4—241no—
276C3×C4#90411yescharacteristic
277C3×C4#90811yescharacteristic
278C3×C4#91111yescharacteristic
279C3×C4#91211yescharacteristic
280C3×C4D3×SD1611yescharacteristic
281C3×C4#91611yescharacteristic
282C3×C4C2×#21511yescharacteristic
283C3×C4#95011yescharacteristic
284Dic3—41no—
285Dic3—81no—
286Dic3—242no—
287Dic3—241no—
288Dic3—241no—
289C32#167911yescharacteristic, complemented, Sylow
290C23—61no—
291Q8—121no—
292Q8—121no—
293Q8—361no—
294Q8—361no—
295D4—32no—
296D4—61no—
297C2×C4—61no—
298C2×C4—121no—
299C2×C4—121no—
300C2×C4—121no—
301C2×C4—361no—
302C2×C4#379611yescharacteristic
303C2×C4D3×D1211yescharacteristic
304C2×C4D3×#6711yescharacteristic
305C8—41no—
306C8—61no—
307C8—61no—
308C8—121no—
309C8—361no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—122no—
314C2×C3#484411yescharacteristic
315C2×C3#486411yescharacteristic
316C2×C3#489611yescharacteristic
317C2×C3#504811yescharacteristic
318C2×C3#515311yescharacteristic
319C2×C3#520411yescharacteristic
320D3—42no—
321C22—62no—
322C22—121no—
323C22—121no—
324C22#6388611yescharacteristic
325C4—21no—
326C4—121no—
327C4—241no—
328C4—721no—
329C4#6379511yescharacteristic
330C4#6380711yescharacteristic
331C4#6393511yescharacteristic
332C4D3×#21511yescharacteristic
333C3—21no—
334C3#6853911yescharacteristic, complemented
335C3#7110211yescharacteristic, complemented
336C2—122no—
337C2#1059057711yescharacteristic
338C2#1059075511yescharacteristic
339C2#1059098311yescharacteristic
subgroupG/H
centerC22#63886
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1679
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
4. #10590287C2semidirect
5. #10589348C2semidirect
6. C3×#4480C2semidirect
7. #10589092C2semidirect
39. #4480D3semidirect
289. C32#1679semidirect
334. C3#68539semidirect
335. C3#71102semidirect

Maximal subgroups

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

subgroupindex
C3×#48462
#105903652
C3⋊C8×D122
#105902872
#105893482
C3×#44802
#105890922
#711023
#685393