Finite Group Databasebeta

← #11781315

Subgroups — #11781315

Order 1152.

368 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 84 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#10592549C211yesmaximal, characteristic, complemented
2#10590377C211yesmaximal, characteristic
3#10590273C211yesmaximal, characteristic
4#10590254C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic
6C3×#4480C211yesmaximal, characteristic, complemented
7#10589096C211yesmaximal, characteristic, complemented
8#68548—31nomaximal
9#68410—31nomaximal
10#64078C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C2×#3716—21no—
14C32×C4⋊C8C2211yescharacteristic
15#63645—21no—
16#63643—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63572—21no—
21#63563—21no—
22#63563—21no—
23#63563—21no—
24#63553—21no—
25#5075—31no—
26#5070—31no—
27#4850—31no—
28#4850—31no—
29#4850—61no—
30#4848—31no—
31#4830—31no—
32#4694—31no—
33C8×Dic6—31no—
34C3×#334—31no—
35C3×#331—31no—
36#4485D311yescharacteristic
37#4481—31no—
38#4481—31no—
39#4480D311yescharacteristic, complemented
40C2×#634—21no—
41C2×#634D411yescharacteristic
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C32×C8—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)D411yescharacteristic
50#3750—21no—
51C4×C3⋊Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3716—42no—
57#1678—91noSylow
58C3×#127—31no—
59C2×#214—61no—
60C2×#204—61no—
61#874C2×D311yescharacteristic
62#869—31no—
63#869—31no—
64#869—61no—
65C4×Dic6—31no—
66C4×Dic6—31no—
67C4×Dic6—61no—
68C3×C4⋊C8—21no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8C2×D311yescharacteristic
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C4×C8—31no—
74#832—61no—
75#832—61no—
76#832—61no—
77#821—61no—
78#821—61no—
79#821—61no—
80#818—61no—
81#818—61no—
82#818—62no—
83#816—61no—
84#816—61no—
85#816—62no—
86Dic3⋊C8—61no—
87Dic3⋊C8—61no—
88C8×Dic3—61no—
89C8×Dic3—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C22×C3×D3—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—41no—
100#634—21no—
101#634—81no—
102#634SD1612yes—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—81no—
108C32×C8—41no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#486—91no—
114#477—91no—
115#460—91no—
116C8×Q8—91no—
117#334—31no—
118#333—91no—
119#331—31no—
120C2×C3×D4—61no—
121C2×C3×D4—61no—
122C2×C3×D4—61no—
123C2×D12—21no—
124C2×D12—21no—
125C2×D12—21no—
126C2×Dic6—31no—
127C2×Dic6—31no—
128C2×Dic6—61no—
129C2×Dic6—61no—
130C2×Dic6—61no—
131C2×Dic6—121no—
132C2×C3×C8—22no—
133C2×C3×C8—21no—
134C2×C3×C8—21no—
135C2×C3×C8—31no—
136C2×C3×C8—31no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C3×C42—21no—
140C3×C42C22×D311yescharacteristic
141C3×C42C22×D311yescharacteristic
142#214—122no—
143C4⋊Dic3—31no—
144C4⋊Dic3—31no—
145C4⋊Dic3—61no—
146C4⋊Dic3—62no—
147C4⋊Dic3—61no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—121no—
152Dic3⋊C4—61no—
153Dic3⋊C4—61no—
154Dic3⋊C4—121no—
155C4×Dic3—61no—
156C4×Dic3—61no—
157C4×Dic3—121no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8D1211yescharacteristic
161C2×C3⋊C8D1211yescharacteristic
162#204—122no—
163C22×C32#12111yescharacteristic
164C2×C3×D3—81no—
165C2×C3×D3—81no—
166C2×C3×D3—81no—
167C32×C4—21no—
168C32×C4C2×SD1611yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4#13711yescharacteristic
172C3⋊Dic3—22no—
173C3⋊Dic3—41no—
174C3⋊Dic3—81no—
175C2×SD16—181no—
176C4⋊Q8—91no—
177#127—31no—
178C4×Q8—91no—
179#107—181no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8—181no—
183C4⋊C8D3211yescharacteristic
184#103—181no—
185#102—181no—
186#102—181no—
187#102—181no—
188C4×C8—31no—
189C4×C8—181no—
190C23×C3—121no—
191C22×D3—41no—
192C3×D4—121no—
193C3×D4—121no—
194C3×D4—121no—
195C3×D4—121no—
196C3×D4—241no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4C2×D1211yescharacteristic
201C2×C3×C4#23511yescharacteristic
202C2×C3×C4D3×D411yescharacteristic
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4#23911yescharacteristic
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—121no—
211C2×Dic3—121no—
212C2×Dic3—122no—
213C2×Dic3—121no—
214C2×Dic3—121no—
215D12—41no—
216D12—41no—
217D12—41no—
218D12—41no—
219D12—81no—
220Dic6—32no—
221Dic6—32no—
222Dic6—62no—
223Dic6—61no—
224Dic6—61no—
225Dic6—121no—
226Dic6—242no—
227Dic6—241no—
228Dic6—241no—
229C3×C8—42no—
230C3×C8—41no—
231C3×C8—41no—
232C3×C8—61no—
233C3×C8—61no—
234C3×C8—121no—
235C3×C8—121no—
236C3⋊C8—21no—
237C3⋊C8—21no—
238C3⋊C8—41no—
239C3⋊C8—41no—
240C2×C32#46411yescharacteristic
241C2×C32#46511yescharacteristic
242C2×C32#47211yescharacteristic
243C3×D3—161no—
244C2×Q8—91no—
245C2×Q8—181no—
246C2×D4—61no—
247C2×D4—61no—
248C2×D4—61no—
249SD16—362no—
250C2×C8—21no—
251C2×C8—31no—
252C2×C8—31no—
253C2×C8—61no—
254C2×C8—61no—
255C4⋊C4—91no—
256C4⋊C4—181no—
257C4⋊C4—181no—
258C4⋊C4—181no—
259C42—181no—
260C42C2×D3211yescharacteristic
261C22×C3—21no—
262C22×C3—241no—
263C22×C3—241no—
264C22×C3—241no—
265C22×C3#88411yescharacteristic
266C22×C3#89511yescharacteristic
267C2×D3—81no—
268C2×D3—81no—
269C2×D3—81no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—41no—
277C3×C4#90411yescharacteristic
278C3×C4#90911yescharacteristic
279C3×C4#91211yescharacteristic
280C3×C4#91211yescharacteristic
281C3×C4D3×SD1611yescharacteristic
282C3×C4D3×SD1611yescharacteristic
283C3×C4#91511yescharacteristic
284C3×C4#91611yescharacteristic
285Dic3—62no—
286Dic3—62no—
287Dic3—122no—
288Dic3—121no—
289Dic3—121no—
290Dic3—241no—
291Dic3—242no—
292Dic3—241no—
293Dic3—241no—
294C32#167811yescharacteristic, complemented, Sylow
295C23—121no—
296Q8—92no—
297Q8—181no—
298Q8—721no—
299D4—121no—
300D4—121no—
301D4—121no—
302D4—121no—
303D4—241no—
304C2×C4—181no—
305C2×C4—181no—
306C2×C4—361no—
307C2×C4#379911yescharacteristic
308C2×C4D3×D1211yescharacteristic
309C2×C4#381111yescharacteristic
310C8—41no—
311C8—61no—
312C8—61no—
313C8—121no—
314C8—121no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—481no—
319C2×C3#474911yescharacteristic
320C2×C3#476711yescharacteristic
321C2×C3#477811yescharacteristic
322C2×C3#484511yescharacteristic
323C2×C3#486411yescharacteristic
324C2×C3#489711yescharacteristic
325D3—161no—
326C22—241no—
327C22—241no—
328C22—241no—
329C22#6391011yescharacteristic
330C4—21no—
331C4—182no—
332C4—361no—
333C4—721no—
334C4#6380011yescharacteristic
335C4#6380711yescharacteristic
336C4#6393611yescharacteristic
337C4#6394011yescharacteristic
338C3—21no—
339C3#6841011yescharacteristic, complemented
340C3#6854811yescharacteristic, complemented
341C2—481no—
342C2#1059050711yescharacteristic
343C2#1059086111yescharacteristic
344C2#1059098711yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC4⋊C8D32
hypocenterC32#1678
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
1. #10592549C2semidirect
4. #10590254C2semidirect
6. C3×#4480C2semidirect
7. #10589096C2semidirect
39. #4480D3semidirect
294. C32#1678semidirect
339. C3#68410semidirect
340. C3#68548semidirect

Maximal subgroups

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

subgroupindex
#105925492
#105903772
#105902732
#105902542
C3×#44852
C3×#44802
#105890962
#685483
#684103