Finite Group Databasebeta

← #11781312

Subgroups — #11781312

Order 1152.

371 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 371 conjugacy classes of subgroups — too many to draw. Only its 82 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#10592529C211yesmaximal, characteristic, complemented
2#10590377C211yesmaximal, characteristic
3#10590284C211yesmaximal, characteristic, complemented
4#10590277C211yesmaximal, characteristic
5C3×#4485C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589098C211yesmaximal, characteristic, complemented
8#68510—31nomaximal
9#68410—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#874C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3716—21no—
14C32×C4⋊C8C2211yescharacteristic
15#63641—21no—
16C8×C3⋊Dic3—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20#63575—21no—
21#63567—21no—
22#63563—21no—
23#63562—21no—
24#63562—21no—
25#5091—31no—
26#5088—31no—
27#5075—31no—
28#5070—31no—
29#4850—31no—
30#4848—31no—
31#4830—31no—
32#4830—31no—
33#4830—61no—
34C3×#333—31no—
35C3×#331—31no—
36#4485D311yescharacteristic
37#4481D311yescharacteristic, complemented
38#4480—31no—
39#4480—31no—
40C2×#634D411yescharacteristic
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×Dic6—21no—
45C2×C32×C8—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)D411yescharacteristic
48#3750—21no—
49C4×C3⋊Dic3—21no—
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C2×C3⋊(C3⋊C8)D411yescharacteristic
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#3716—42no—
57#1678—91noSylow
58C3×C4⋊Q8—31no—
59C3×#127—31no—
60C2×#214—61no—
61C2×#204—61no—
62#874C2×D311yescharacteristic
63#869C2×D311yescharacteristic
64C4×Dic6—31no—
65C4×Dic6—31no—
66C4×Dic6—61no—
67C3×C4⋊C8—21no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8C2×D311yescharacteristic
71C3×C4⋊C8C2×D311yescharacteristic
72#832—61no—
73#832—61no—
74#832—61no—
75#821—61no—
76#818—61no—
77#816—61no—
78Dic3⋊C8—61no—
79Dic3⋊C8—61no—
80Dic3⋊C8—62no—
81C8×Dic3—61no—
82C8×Dic3—61no—
83C8×Dic3—62no—
84#810—61no—
85#809—61no—
86#809—61no—
87#807—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C22×C3×D3—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99#634—21no—
100#634SD1612yes—
101C2×C3×Dic3—41no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—81no—
107C3×Dic6—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—91no—
118#333—31no—
119#331—31no—
120C2×C3×Q8—61no—
121C2×C3×D4—61no—
122C2×C3×D4—61no—
123C2×C3×D4—61no—
124C2×D12—21no—
125C2×D12—21no—
126C2×D12—21no—
127C2×Dic6—21no—
128C2×Dic6—31no—
129C2×Dic6—31no—
130C2×Dic6—61no—
131C2×C3×C8—22no—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—61no—
135C2×C3×C8—61no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C42—21no—
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141#214—122no—
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3—31no—
145C4⋊Dic3—31no—
146C4⋊Dic3—61no—
147Dic3⋊C4—62no—
148Dic3⋊C4—61no—
149Dic3⋊C4—61no—
150C4×Dic3—62no—
151C4×Dic3—61no—
152C4×Dic3—61no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—31no—
158C2×C3⋊C8—31no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—61no—
161#204—122no—
162C22×C32#12111yescharacteristic
163C2×C3×D3—81no—
164C2×C3×D3—81no—
165C2×C3×D3—81no—
166C32×C4—21no—
167C32×C4C2×SD1611yescharacteristic
168C32×C4#13511yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4#13711yescharacteristic
171C3⋊Dic3—22no—
172C3⋊Dic3—41no—
173C3×Dic3—81no—
174C2×SD16—181no—
175C4⋊Q8—31no—
176#127—31no—
177C4×Q8—91no—
178#107—181no—
179C4⋊C8—31no—
180C4⋊C8—31no—
181C4⋊C8—181no—
182C4⋊C8D3211yescharacteristic
183#103—181no—
184#102—181no—
185#102—181no—
186#102—181no—
187C4×C8—91no—
188C4×C8—181no—
189C23×C3—121no—
190C22×D3—41no—
191C3×Q8—241no—
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×C4—121no—
201C2×C3×C4#23511yescharacteristic
202C2×C3×C4#23511yescharacteristic
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×Dic3—41no—
208C2×Dic3—62no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211C2×Dic3—62no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214D12—41no—
215D12—41no—
216D12—41no—
217D12—41no—
218D12—81no—
219Dic6—32no—
220Dic6—32no—
221Dic6—62no—
222Dic6—62no—
223Dic6—61no—
224Dic6—61no—
225Dic6—81no—
226C3×C8—42no—
227C3×C8—41no—
228C3×C8—41no—
229C3×C8—121no—
230C3×C8—121no—
231C3⋊C8—41no—
232C3⋊C8—41no—
233C3⋊C8—62no—
234C3⋊C8—61no—
235C3⋊C8—61no—
236C3⋊C8—61no—
237C3⋊C8—61no—
238C3⋊C8—121no—
239C2×C32#46411yescharacteristic
240C2×C32#46511yescharacteristic
241C2×C32#47211yescharacteristic
242C3×D3—161no—
243C2×Q8—61no—
244C2×Q8—91no—
245C2×D4—61no—
246C2×D4—61no—
247C2×D4—61no—
248SD16—362no—
249C2×C8—21no—
250C2×C8—61no—
251C2×C8—61no—
252C2×C8—91no—
253C2×C8—91no—
254C4⋊C4—61no—
255C4⋊C4—61no—
256C4⋊C4—91no—
257C4⋊C4—181no—
258C42—181no—
259C42C2×D3211yescharacteristic
260C22×C3—21no—
261C22×C3—241no—
262C22×C3—241no—
263C22×C3—241no—
264C22×C3#88411yescharacteristic
265C22×C3#88411yescharacteristic
266C2×D3—81no—
267C2×D3—81no—
268C2×D3—81no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—241no—
277C3×C4#91211yescharacteristic
278C3×C4#91211yescharacteristic
279C3×C4D3×SD1611yescharacteristic
280C3×C4D3×SD1611yescharacteristic
281C3×C4#91511yescharacteristic
282C3×C4#91611yescharacteristic
283C3×C4#91811yescharacteristic
284C3×C4#91911yescharacteristic
285Dic3—64no—
286Dic3—62no—
287Dic3—62no—
288Dic3—81no—
289Dic3—122no—
290Dic3—121no—
291Dic3—121no—
292C32#167811yescharacteristic, complemented, Sylow
293C23—121no—
294Q8—92no—
295Q8—181no—
296Q8—241no—
297D4—121no—
298D4—121no—
299D4—121no—
300D4—121no—
301D4—241no—
302C2×C4—121no—
303C2×C4—181no—
304C2×C4—181no—
305C2×C4#379811yescharacteristic
306C2×C4#380211yescharacteristic
307C2×C4#381111yescharacteristic
308C8—41no—
309C8—121no—
310C8—121no—
311C8—181no—
312C8—181no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—481no—
317C2×C3#474911yescharacteristic
318C2×C3#474911yescharacteristic
319C2×C3#476711yescharacteristic
320C2×C3#477811yescharacteristic
321C2×C3#479811yescharacteristic
322C2×C3#480711yescharacteristic
323D3—161no—
324C22—241no—
325C22—241no—
326C22—241no—
327C22#6391211yescharacteristic
328C4—21no—
329C4—182no—
330C4—241no—
331C4—361no—
332C4#6379611yescharacteristic
333C4#6381011yescharacteristic
334C4#6393611yescharacteristic
335C4#6395111yescharacteristic
336C3—21no—
337C3#6841011yescharacteristic, complemented
338C3#6851011yescharacteristic, complemented
339C2—481no—
340C2#1059053811yescharacteristic
341C2#1059084111yescharacteristic
342C2#1059098811yescharacteristic
subgroupG/H
centerC22#63912
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. #10592529C2semidirect
3. #10590284C2semidirect
6. C3×#4481C2semidirect
7. #10589098C2semidirect
37. #4481D3semidirect
292. C32#1678semidirect
337. C3#68410semidirect
338. C3#68510semidirect

Maximal subgroups

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

subgroupindex
#105925292
#105903772
#105902842
#105902772
C3×#44852
C3×#44812
#105890982
#685103
#684103