Finite Group Databasebeta

← #11781592

Subgroups — #11781592

Order 1152.

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

normal subgroups only

This group has 320 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×#4830C211yesmaximal, characteristic
2#10590287C211yesmaximal, characteristic
3#10590285C211yesmaximal, characteristic
4#10590283C211yesmaximal, characteristic
5#10589347C211yesmaximal, characteristic
6C3×#4482C211yesmaximal, characteristic
7#10589099C211yesmaximal, characteristic
8#70947—31nomaximal
9#68471—31nomaximal
10#64078C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C3×Dic3⋊C8—21no—
16C3×C8×Dic3—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63575—21no—
20#63574—21no—
21#63566—21no—
22#63566—21no—
23#63566—21no—
24#63565—21no—
25C3×C8×Q8—31no—
26#5094—31no—
27#5079—31no—
28#5021—31no—
29#5020—31no—
30#4850—31no—
31#4830D311yescharacteristic
32#4681—31no—
33C3×#332—31no—
34#4482D311yescharacteristic
35#4481—31no—
36#4481—31no—
37#4481—61no—
38#4479—31no—
39#4458—31no—
40C2×#634—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#1684—91noSylow
57C3×C4⋊Q8—31no—
58C3×C4×Q8—31no—
59#869—31no—
60#869—31no—
61#869—61no—
62#869C2×D311yescharacteristic
63C4×Dic6C2×D311yescharacteristic
64C3×C4⋊C8—21no—
65C3×C4⋊C8—31no—
66C3×C4⋊C8—61no—
67C3×C4⋊C8C2×D311yescharacteristic
68C3×C4⋊C8C2×D311yescharacteristic
69C3×C4×C8—31no—
70C3×C4×C8—61no—
71#835—61no—
72#835—61no—
73#835—61no—
74#835—61no—
75#818—61no—
76#816—61no—
77#816—61no—
78#816—61no—
79Dic3⋊C8—21no—
80C8×Dic3—21no—
81#810—61no—
82#808—61no—
83#808—61no—
84#807—61no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4×C3⋊C8C2×D311yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4#4111yescharacteristic
93C2×C3⋊Dic3—41no—
94#634—81no—
95C2×C3×Dic3—21no—
96C2×C3×Dic3—21no—
97C2×C3×Dic3—41no—
98C3×Dic6—21no—
99C3×Dic6—41no—
100C3×Dic6—41no—
101C3×Dic6Q1612yes—
102C32×C8—41no—
103C3⋊(C3⋊C8)—41no—
104C3×C3⋊C8—21no—
105C3×C3⋊C8—21no—
106C3×C3⋊C8—41no—
107#487—91no—
108#477—91no—
109#475—91no—
110C8×Q8—31no—
111#335—91no—
112#333—91no—
113#332—31no—
114C2×C3×Q8—31no—
115C2×C3×Q8—61no—
116C2×Dic6—21no—
117C2×Dic6—62no—
118C2×Dic6—61no—
119C2×Dic6—61no—
120C2×Dic6D1211yescharacteristic
121C2×C3×C8—21no—
122C2×C3×C8—21no—
123C2×C3×C8—31no—
124C2×C3×C8—31no—
125C2×C3×C8—41no—
126C2×C3×C8—61no—
127C3×C4⋊C4—31no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C42—21no—
132C3×C42—61no—
133C3×C42C22×D311yescharacteristic
134C3×C42C22×D311yescharacteristic
135C4⋊Dic3—21no—
136C4⋊Dic3—21no—
137C4⋊Dic3—61no—
138C4⋊Dic3—61no—
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141C4⋊Dic3—121no—
142C4⋊Dic3—121no—
143C4⋊Dic3D1211yescharacteristic
144Dic3⋊C4—21no—
145C4×Dic3—21no—
146C2×C3⋊C8—21no—
147C2×C3⋊C8—61no—
148C2×C3⋊C8—61no—
149C2×C3⋊C8—121no—
150C2×C3⋊C8#6711yescharacteristic
151C2×C3⋊C8#6711yescharacteristic
152C22×C32#12111yescharacteristic
153C32×C4—21no—
154C32×C4C2×Q1611yescharacteristic
155C32×C4#13511yescharacteristic
156C32×C4#13511yescharacteristic
157C32×C4#13711yescharacteristic
158C3⋊Dic3—81no—
159C3×Dic3—22no—
160C3×Dic3—41no—
161C3×Dic3—81no—
162C4⋊Q8—31no—
163C4⋊Q8—91no—
164C4×Q8—31no—
165#107—181no—
166#106—181no—
167C4⋊C8—31no—
168C4⋊C8—61no—
169C4⋊C8—91no—
170C4⋊C8D3211yescharacteristic
171#103—181no—
172#103—181no—
173#103—181no—
174#103—181no—
175C4×C8—31no—
176C4×C8—61no—
177C3×Q8—32no—
178C3×Q8—61no—
179C3×Q8—121no—
180C3×Q8—121no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—61no—
185C2×C3×C4—61no—
186C2×C3×C4—121no—
187C2×C3×C4C2×D1211yescharacteristic
188C2×C3×C4#23511yescharacteristic
189C2×C3×C4#23511yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192C2×C3×C4C2×#6711yescharacteristic
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—41no—
196C2×Dic3—122no—
197C2×Dic3—121no—
198C2×Dic3—121no—
199Dic6—21no—
200Dic6—41no—
201Dic6—41no—
202Dic6—241no—
203Dic6—241no—
204Dic6—242no—
205Dic6Dic1212yes—
206C3×C8—41no—
207C3×C8—41no—
208C3×C8—61no—
209C3×C8—61no—
210C3×C8—81no—
211C3×C8—121no—
212C3⋊C8—21no—
213C3⋊C8—21no—
214C3⋊C8—41no—
215C3⋊C8—121no—
216C3⋊C8—121no—
217C3⋊C8—241no—
218C2×C32#46411yescharacteristic
219C2×C32#46711yescharacteristic
220C2×C32#47111yescharacteristic
221C2×Q8—31no—
222C2×Q8—61no—
223C2×Q8—181no—
224C2×C8—21no—
225C2×C8—31no—
226C2×C8—31no—
227C2×C8—61no—
228C2×C8—181no—
229C4⋊C4—31no—
230C4⋊C4—61no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4—181no—
234C4⋊C4—181no—
235C42—61no—
236C42C2×D3211yescharacteristic
237C22×C3—21no—
238C22×C3#88411yescharacteristic
239C22×C3#93011yescharacteristic
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—21no—
246C3×C4—41no—
247C3×C4—62no—
248C3×C4—121no—
249C3×C4—241no—
250C3×C4#90411yescharacteristic
251C3×C4C2×Dic1211yescharacteristic
252C3×C4#91211yescharacteristic
253C3×C4#91511yescharacteristic
254C3×C4#91611yescharacteristic
255C3×C4D3×Q1611yescharacteristic
256C3×C4#94211yescharacteristic
257C3×C4#95011yescharacteristic
258Dic3—22no—
259Dic3—41no—
260Dic3—81no—
261Dic3—242no—
262Dic3—241no—
263Dic3—241no—
264C32#168411yescharacteristic, complemented, Sylow
265Q8—32no—
266Q8—61no—
267Q8—121no—
268Q8—121no—
269Q8—721no—
270C2×C4—61no—
271C2×C4—61no—
272C2×C4—121no—
273C2×C4—361no—
274C2×C4#379811yescharacteristic
275C2×C4D3×D1211yescharacteristic
276C2×C4D3×#6711yescharacteristic
277C8—41no—
278C8—61no—
279C8—61no—
280C8—121no—
281C8—361no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3#475411yescharacteristic
286C2×C3#476711yescharacteristic
287C2×C3#481311yescharacteristic
288C2×C3#502811yescharacteristic
289C2×C3#511611yescharacteristic
290C2×C3#514111yescharacteristic
291C22#6390611yescharacteristic
292C4—21no—
293C4—62no—
294C4—121no—
295C4—241no—
296C4—721no—
297C4D3×Dic1211yescharacteristic
298C4#6380611yescharacteristic
299C4#6393311yescharacteristic
300C4#6394611yescharacteristic
301C3—21no—
302C3#6847111yescharacteristic, complemented
303C3#7094711yescharacteristic, complemented
304C2#1059053211yescharacteristic
305C2#1059084811yescharacteristic
306C2#1059099811yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1684
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
264. C32#1684semidirect
302. C3#68471semidirect
303. C3#70947semidirect

Maximal subgroups

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

subgroupindex
C3×#48302
#105902872
#105902852
#105902832
#105893472
C3×#44822
#105890992
#709473
#684713