Finite Group Databasebeta

← #11781299

Subgroups — #11781299

Order 1152.

379 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 379 conjugacy classes of subgroups — too many to draw. Only its 92 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#10592393C211yesmaximal, characteristic
2C3×C8×Dic6C211yesmaximal, characteristic, complemented
3#10590367C211yesmaximal, characteristic
4#10590283C211yesmaximal, characteristic, complemented
5C3×#4457C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic
8#70940—31nomaximal
9#68548—31nomaximal
10#64083C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3717—21no—
14C32×C4×C8C2211yescharacteristic
15#63648—21no—
16#63648—21no—
17C3×Dic3⋊C8—21no—
18C3×C8×Dic3—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63575—21no—
23#63566—21no—
24#63564—21no—
25C3×C8×Q8—31no—
26#5027—31no—
27#5021—31no—
28#4850—31no—
29#4848—31no—
30#4694—31no—
31#4694—31no—
32#4694—61no—
33C8×Dic6D311yescharacteristic, complemented
34C3×#334—31no—
35#4485—31no—
36#4485—31no—
37#4481—31no—
38#4481—31no—
39#4457D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×#634—21no—
44C2×C3×Dic6D411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C2×C32×C8D411yescharacteristic
47C32×C42C2311yescharacteristic
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#3717—42no—
57#1678—91noSylow
58C3×C4×Q8—31no—
59C2×#215—61no—
60C2×#204—61no—
61#874—31no—
62#874—31no—
63#874—61no—
64#869—31no—
65#869—31no—
66#869—61no—
67C4×Dic6C2×D311yescharacteristic
68C3×C4⋊C8—31no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—61no—
72C3×C4×C8—21no—
73C3×C4×C8—61no—
74C3×C4×C8C2×D311yescharacteristic
75C3×C4×C8C2×D311yescharacteristic
76#835—61no—
77#821—62no—
78#821—62no—
79#821—61no—
80#821—61no—
81#821—61no—
82#821—61no—
83#821—61no—
84#818—61no—
85#816—61no—
86Dic3⋊C8—21no—
87C8×Dic3—21no—
88#809—61no—
89#807—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C22×C3⋊D3—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—41no—
98C4⋊(C3⋊D3)—41no—
99C4⋊(C3⋊D3)—41no—
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—81no—
103#634—81no—
104C2×C3×Dic3—21no—
105C2×C3×Dic3—21no—
106C3×Dic6—21no—
107C3×Dic6SD1612yes—
108C32×C8—21no—
109C32×C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#486—91no—
114#477—91no—
115#460—91no—
116C8×Q8—31no—
117#334—31no—
118#333—91no—
119#331—91no—
120C2×C3×Q8—31no—
121C2×D12—62no—
122C2×D12—61no—
123C2×D12—61no—
124C2×D12—61no—
125C2×D12—61no—
126C2×D12—61no—
127C2×D12—61no—
128C2×D12—121no—
129C2×D12—121no—
130C2×Dic6—61no—
131C2×Dic6—61no—
132C2×Dic6—121no—
133C2×Dic6D1211yescharacteristic
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—61no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C2×C3×C8D1211yescharacteristic
140C2×C3×C8D1211yescharacteristic
141C2×C3×C8#6711yescharacteristic
142C2×C3×C8#6711yescharacteristic
143C3×C4⋊C4—31no—
144C3×C4⋊C4—61no—
145C3×C42—21no—
146C3×C42—61no—
147C3×C42C22×D311yescharacteristic
148C3×C42C22×D311yescharacteristic
149#215—122no—
150C4⋊Dic3—62no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—121no—
156C4⋊Dic3D1211yescharacteristic
157Dic3⋊C4—21no—
158C4×Dic3—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
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—81no—
173C3×Dic3—22no—
174C3×Dic3—41no—
175C2×SD16—181no—
176C4⋊Q8—91no—
177#127—91no—
178C4×Q8—31no—
179#107—181no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8—31no—
183C4⋊C8—61no—
184#103—181no—
185#102—181no—
186#102—181no—
187#102—181no—
188C4×C8—61no—
189C4×C8D3211yescharacteristic
190C22×D3—122no—
191C22×D3—121no—
192C22×D3—121no—
193C3×Q8—32no—
194C3×Q8—61no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—61no—
199C2×C3×C4—61no—
200C2×C3×C4C2×D1211yescharacteristic
201C2×C3×C4C2×D1211yescharacteristic
202C2×C3×C4#23511yescharacteristic
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4#23911yescharacteristic
205C2×C3×C4C2×#6711yescharacteristic
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3—122no—
209C2×Dic3—121no—
210C2×Dic3—121no—
211D12—122no—
212D12—122no—
213D12—121no—
214D12—121no—
215D12—121no—
216D12—121no—
217D12—121no—
218D12—121no—
219D12—121no—
220D12—121no—
221D12—241no—
222D12—241no—
223D12—241no—
224D12—241no—
225D12—242no—
226Dic6—21no—
227Dic6—242no—
228Dic6—241no—
229Dic6—241no—
230Dic6#20412yes—
231C3×C8—21no—
232C3×C8—21no—
233C3×C8—21no—
234C3×C8—21no—
235C3×C8—41no—
236C3×C8—41no—
237C3×C8—121no—
238C3×C8—121no—
239C3×C8—121no—
240C3⋊C8—41no—
241C3⋊C8—41no—
242C3⋊C8—41no—
243C2×C32#46411yescharacteristic
244C2×C32#46511yescharacteristic
245C2×C32#47211yescharacteristic
246C3⋊D3—161no—
247C2×Q8—31no—
248C2×Q8—181no—
249C2×D4—181no—
250C2×D4—181no—
251C2×D4—181no—
252SD16—362no—
253C2×C8—61no—
254C2×C8—61no—
255C2×C8—61no—
256C2×C8#62611yescharacteristic
257C2×C8#62611yescharacteristic
258C4⋊C4—31no—
259C4⋊C4—61no—
260C4⋊C4—181no—
261C4⋊C4—181no—
262C42—61no—
263C42C2×D3211yescharacteristic
264C22×C3—21no—
265C22×C3#89511yescharacteristic
266C22×C3#93011yescharacteristic
267C2×D3—242no—
268C2×D3—242no—
269C2×D3—242no—
270C2×D3—241no—
271C2×D3—241no—
272C2×D3—241no—
273C2×D3—241no—
274C2×D3—241no—
275C2×D3—241no—
276C3×C4—22no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—62no—
284C3×C4—121no—
285C3×C4C2×#20411yescharacteristic
286C3×C4#90411yescharacteristic
287C3×C4#90411yescharacteristic
288C3×C4#90911yescharacteristic
289C3×C4D3×SD1611yescharacteristic
290C3×C4#91611yescharacteristic
291C3×C4#94211yescharacteristic
292C3×C4#95011yescharacteristic
293Dic3—22no—
294Dic3—41no—
295Dic3—242no—
296Dic3—241no—
297Dic3—241no—
298C32#167811yescharacteristic, complemented, Sylow
299C23—361no—
300Q8—32no—
301Q8—61no—
302Q8—721no—
303D4—361no—
304D4—361no—
305D4—361no—
306D4—361no—
307D4—721no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—361no—
311C2×C4#379911yescharacteristic
312C2×C4D3×D1211yescharacteristic
313C2×C4C2×#62611yescharacteristic
314C8—21no—
315C8—21no—
316C8—121no—
317C8—121no—
318C8—121no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3#484511yescharacteristic
323C2×C3#486411yescharacteristic
324C2×C3#489711yescharacteristic
325C2×C3#502811yescharacteristic
326C2×C3#511411yescharacteristic
327C2×C3#514211yescharacteristic
328D3—482no—
329D3—481no—
330D3—481no—
331C22—721no—
332C22—721no—
333C22—721no—
334C22#6390911yescharacteristic
335C4—21no—
336C4—62no—
337C4—121no—
338C4—721no—
339C4D3×#20411yescharacteristic
340C4#6380611yescharacteristic
341C4#6382911yescharacteristic
342C4#6383311yescharacteristic
343C3—21no—
344C3#6854811yescharacteristic, complemented
345C3#7094011yescharacteristic, complemented
346C2—1441no—
347C2#1059036811yescharacteristic
348C2#1059083011yescharacteristic
349C2#1059092711yescharacteristic
subgroupG/H
centerC22#63909
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#121
prime radical#64083C22
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
2. C3×C8×Dic6C2semidirect
4. #10590283C2semidirect
5. C3×#4457C2semidirect
6. #10589096C2semidirect
33. C8×Dic6D3semidirect
39. #4457D3semidirect
298. C32#1678semidirect
344. C3#68548semidirect
345. C3#70940semidirect

Maximal subgroups

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

subgroupindex
#105923932
C3×C8×Dic62
#105903672
#105902832
C3×#44572
#105890962
#105890912
#709403
#685483