Finite Group Databasebeta

← #11781306

Subgroups — #11781306

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#10592790C211yesmaximal, characteristic, complemented
2C3×#5088C211yesmaximal, characteristic
3#10590377C211yesmaximal, characteristic
4#10590254C211yesmaximal, characteristic, complemented
5C3×#4546C211yesmaximal, characteristic, complemented
6#10589097C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic
8#71208—31nomaximal
9#68510—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C2×#3716—21no—
14#63637—21no—
15#63634—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#809—21no—
18C3×#809—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22#63572—21no—
23#63563—21no—
24#63553—21no—
25C3×#486—31no—
26#5091—31no—
27#5091—31no—
28#5091—61no—
29#5088D311yescharacteristic
30#5075—31no—
31#4848—31no—
32#4830—31no—
33C8×Dic6—31no—
34C3×#333—31no—
35#4546D311yescharacteristic, complemented
36#4544—31no—
37#4485—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×Q8—21no—
41C2×#634D411yescharacteristic
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C42C2311yescharacteristic
48C4⋊(C3⋊Dic3)D411yescharacteristic
49#3750—21no—
50C4×C3⋊Dic3—21no—
51C2×C3⋊(C3⋊C8)—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×C4⋊Q8—21no—
59C3×C4⋊Q8C2×D311yescharacteristic
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×#127—31no—
62C2×#214—61no—
63C2×#204—61no—
64#874C2×D311yescharacteristic
65C4×Dic6—31no—
66C4×Dic6—31no—
67C4×Dic6—61no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8—31no—
70C3×#102—61no—
71C3×#102—61no—
72C3×C4×C8—31no—
73#832—61no—
74#821—61no—
75Dic3⋊C8—61no—
76Dic3⋊C8—61no—
77C8×Dic3—61no—
78C8×Dic3—61no—
79#810—61no—
80#810—61no—
81#810—62no—
82#809—21no—
83#809—21no—
84#807—61no—
85#807—61no—
86#807—62no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C22×C3×D3—41no—
94C32×Q8—81no—
95C2×C32×C4—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101#634—21no—
102#634SD1612yes—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—81no—
108C3⋊(C3⋊C8)—41no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#486—31no—
114#477—91no—
115#460—91no—
116C8×Q8—91no—
117#334—91no—
118#333—31no—
119#331—91no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—41no—
123C2×C3×D4—61no—
124C2×C3×D4—61no—
125C2×C3×D4—61no—
126C2×D12—21no—
127C2×D12—21no—
128C2×D12—21no—
129C2×Dic6—31no—
130C2×Dic6—31no—
131C2×Dic6—61no—
132C2×C3×C8—31no—
133C2×C3×C8—31no—
134C2×C3×C8—61no—
135C2×C3×C8—61no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—41no—
142C3×C42—21no—
143C3×C42C22×D311yescharacteristic
144C3×C42C22×D311yescharacteristic
145#214—122no—
146C4⋊Dic3—31no—
147C4⋊Dic3—31no—
148C4⋊Dic3—61no—
149Dic3⋊C4—61no—
150Dic3⋊C4—61no—
151Dic3⋊C4—121no—
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
162#204—122no—
163C22×C32#12111yescharacteristic
164C2×C3×D3—81no—
165C2×C3×D3—81no—
166C2×C3×D3—81no—
167C32×C4—21no—
168C32×C4—81no—
169C32×C4C2×SD1611yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4#13511yescharacteristic
172C32×C4#13711yescharacteristic
173C3⋊Dic3—22no—
174C3⋊Dic3—41no—
175C2×SD16—181no—
176C4⋊Q8D3211yescharacteristic
177#127—31no—
178C4×Q8—91no—
179#107—181no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8—91no—
183C4⋊C8—181no—
184#103—181no—
185#102—61no—
186#102—61no—
187#102—181no—
188C4×C8—31no—
189C4×C8—181no—
190C23×C3—121no—
191C22×D3—41no—
192C3×Q8—81no—
193C3×Q8—81no—
194C3×Q8—82no—
195C3×D4—121no—
196C3×D4—121no—
197C3×D4—121no—
198C3×D4—121no—
199C3×D4—241no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—42no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4#23511yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4#23711yescharacteristic
211C2×C3×C4C2×#6711yescharacteristic
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218D12—41no—
219D12—41no—
220D12—41no—
221D12—41no—
222D12—81no—
223Dic6—32no—
224Dic6—32no—
225Dic6—62no—
226Dic6—61no—
227Dic6—61no—
228Dic6—121no—
229C3×C8—61no—
230C3×C8—61no—
231C3×C8—121no—
232C3×C8—121no—
233C3⋊C8—21no—
234C3⋊C8—21no—
235C3⋊C8—41no—
236C3⋊C8—41no—
237C3⋊C8—122no—
238C3⋊C8—121no—
239C3⋊C8—121no—
240C2×C32#46411yescharacteristic
241C2×C32#46511yescharacteristic
242C2×C32#47211yescharacteristic
243C3×D3—161no—
244C2×Q8—21no—
245C2×Q8—91no—
246C2×D4—61no—
247C2×D4—61no—
248C2×D4—61no—
249SD16—362no—
250C2×C8—31no—
251C2×C8—31no—
252C2×C8—61no—
253C2×C8—61no—
254C2×C8—181no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—91no—
258C4⋊C4—181no—
259C42—181no—
260C42C2×D3211yescharacteristic
261C22×C3—21no—
262C22×C3—241no—
263C22×C3—241no—
264C22×C3—241no—
265C22×C3#88411yescharacteristic
266C22×C3#93811yescharacteristic
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—82no—
278C3×C4—81no—
279C3×C4—81no—
280C3×C4D3×SD1611yescharacteristic
281C3×C4D3×SD1611yescharacteristic
282C3×C4#91611yescharacteristic
283C3×C4#91611yescharacteristic
284C3×C4#91811yescharacteristic
285C3×C4#91911yescharacteristic
286C3×C4#95011yescharacteristic
287C3×C4#95111yescharacteristic
288Dic3—62no—
289Dic3—62no—
290Dic3—122no—
291Dic3—121no—
292Dic3—121no—
293Dic3—241no—
294C32#167811yescharacteristic, complemented, Sylow
295C23—121no—
296Q8—81no—
297Q8—92no—
298Q8—181no—
299D4—121no—
300D4—121no—
301D4—121no—
302D4—121no—
303D4—241no—
304C2×C4—41no—
305C2×C4—181no—
306C2×C4—181no—
307C2×C4#380411yescharacteristic
308C2×C4D3×#6711yescharacteristic
309C2×C4#381111yescharacteristic
310C8—61no—
311C8—61no—
312C8—121no—
313C8—121no—
314C8—361no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—481no—
319C2×C3#474911yescharacteristic
320C2×C3#479811yescharacteristic
321C2×C3#480711yescharacteristic
322C2×C3#505411yescharacteristic
323C2×C3#516011yescharacteristic
324C2×C3#517111yescharacteristic
325D3—161no—
326C22—241no—
327C22—241no—
328C22—241no—
329C22#6395811yescharacteristic
330C4—21no—
331C4—81no—
332C4—182no—
333C4—361no—
334C4#6394011yescharacteristic
335C4#6394311yescharacteristic
336C4#6394711yescharacteristic
337C4#6395011yescharacteristic
338C3—21no—
339C3#6851011yescharacteristic, complemented
340C3#7120811yescharacteristic, complemented
341C2—481no—
342C2#1059140611yescharacteristic
343C2#1059157711yescharacteristic
344C2#1059159111yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC4⋊Q8D32
hypocenterC32#1678
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
1. #10592790C2semidirect
4. #10590254C2semidirect
5. C3×#4546C2semidirect
6. #10589097C2semidirect
35. #4546D3semidirect
294. C32#1678semidirect
339. C3#68510semidirect
340. C3#71208semidirect

Maximal subgroups

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

subgroupindex
#105927902
C3×#50882
#105903772
#105902542
C3×#45462
#105890972
#105890902
#712083
#685103