Finite Group Databasebeta

← #11781591

Subgroups — #11781591

Order 1152.

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

normal subgroups only

This group has 339 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
2#10590307C211yesmaximal, characteristic
3#10590290C211yesmaximal, characteristic
4#10590284C211yesmaximal, characteristic
5C3×#4482C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic
7#10589100C211yesmaximal, characteristic
8#68511—31nomaximal
9#68471—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14#63641—21no—
15C8×C3⋊Dic3—21no—
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19#63575—21no—
20#63573—21no—
21#63567—21no—
22#63567—21no—
23#63565—21no—
24#63565—21no—
25#5094—31no—
26#5093—31no—
27#5091—31no—
28#5079—31no—
29#4851—31no—
30#4850—31no—
31#4830—31no—
32#4830—31no—
33#4830—61no—
34C3×#333—31no—
35C3×#332—31no—
36#4482D311yescharacteristic
37#4481D311yescharacteristic
38#4479—31no—
39#4479—31no—
40C2×#634D411yescharacteristic
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)D411yescharacteristic
46#3750—21no—
47C4×C3⋊Dic3—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#1684—91noSylow
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59#869C2×D311yescharacteristic
60#869C2×D311yescharacteristic
61C4×Dic6—31no—
62C4×Dic6—31no—
63C4×Dic6—61no—
64C3×C4⋊C8—21no—
65C3×C4⋊C8—31no—
66C3×C4⋊C8—31no—
67C3×C4⋊C8C2×D311yescharacteristic
68C3×C4⋊C8C2×D311yescharacteristic
69#835—61no—
70#835—61no—
71#818—61no—
72#817—61no—
73#816—61no—
74#816—61no—
75Dic3⋊C8—61no—
76Dic3⋊C8—61no—
77Dic3⋊C8—62no—
78C8×Dic3—61no—
79C8×Dic3—61no—
80C8×Dic3—62no—
81#810—61no—
82#810—61no—
83#810—61no—
84#810—61no—
85#808—61no—
86#807—61no—
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4×C3⋊C8—31no—
90C4×C3⋊C8—31no—
91C4×C3⋊C8—61no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—21no—
97#634—21no—
98#634Q1612yes—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C3×Dic6—41no—
102C3×Dic6—41no—
103C3×Dic6—81no—
104C32×C8—41no—
105C3⋊(C3⋊C8)—21no—
106C3⋊(C3⋊C8)—21no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109#487—91no—
110#477—91no—
111#475—91no—
112C8×Q8—91no—
113#335—91no—
114#333—31no—
115#332—31no—
116C2×C3×Q8—61no—
117C2×C3×Q8—61no—
118C2×Dic6—21no—
119C2×Dic6—21no—
120C2×Dic6—31no—
121C2×Dic6—31no—
122C2×Dic6—61no—
123C2×C3×C8—22no—
124C2×C3×C8—21no—
125C2×C3×C8—21no—
126C2×C3×C8—61no—
127C2×C3×C8—61no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C42—21no—
133C3×C42C22×D311yescharacteristic
134C3×C42C22×D311yescharacteristic
135C4⋊Dic3—21no—
136C4⋊Dic3—21no—
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—31no—
140C4⋊Dic3—31no—
141C4⋊Dic3—61no—
142Dic3⋊C4—62no—
143Dic3⋊C4—61no—
144Dic3⋊C4—61no—
145C4×Dic3—62no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—61no—
156C22×C32#12111yescharacteristic
157C32×C4—21no—
158C32×C4C2×Q1611yescharacteristic
159C32×C4#13511yescharacteristic
160C32×C4#13511yescharacteristic
161C32×C4#13711yescharacteristic
162C3⋊Dic3—22no—
163C3⋊Dic3—41no—
164C3×Dic3—81no—
165C3×Dic3—81no—
166C4⋊Q8—31no—
167C4⋊Q8—31no—
168C4×Q8—91no—
169#107—181no—
170#106—181no—
171C4⋊C8—31no—
172C4⋊C8—31no—
173C4⋊C8—181no—
174C4⋊C8D3211yescharacteristic
175#103—181no—
176#103—181no—
177#103—181no—
178#103—181no—
179C4×C8—91no—
180C4×C8—181no—
181C3×Q8—121no—
182C3×Q8—121no—
183C3×Q8—241no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—121no—
188C2×C3×C4—121no—
189C2×C3×C4#23511yescharacteristic
190C2×C3×C4#23511yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×Dic3—41no—
196C2×Dic3—41no—
197C2×Dic3—62no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—62no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203Dic6—32no—
204Dic6—32no—
205Dic6—41no—
206Dic6—41no—
207Dic6—62no—
208Dic6—62no—
209Dic6—61no—
210Dic6—61no—
211Dic6—81no—
212C3×C8—42no—
213C3×C8—41no—
214C3×C8—41no—
215C3×C8—121no—
216C3×C8—121no—
217C3⋊C8—41no—
218C3⋊C8—41no—
219C3⋊C8—62no—
220C3⋊C8—61no—
221C3⋊C8—61no—
222C3⋊C8—61no—
223C3⋊C8—61no—
224C3⋊C8—121no—
225C2×C32#46411yescharacteristic
226C2×C32#46711yescharacteristic
227C2×C32#47111yescharacteristic
228C2×Q8—61no—
229C2×Q8—61no—
230C2×Q8—91no—
231C2×C8—21no—
232C2×C8—61no—
233C2×C8—61no—
234C2×C8—91no—
235C2×C8—91no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—91no—
241C4⋊C4—181no—
242C42—181no—
243C42C2×D3211yescharacteristic
244C22×C3—21no—
245C22×C3#88411yescharacteristic
246C22×C3#88411yescharacteristic
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—41no—
254C3×C4—241no—
255C3×C4—241no—
256C3×C4#91211yescharacteristic
257C3×C4#91511yescharacteristic
258C3×C4#91611yescharacteristic
259C3×C4#91611yescharacteristic
260C3×C4#91611yescharacteristic
261C3×C4D3×Q1611yescharacteristic
262C3×C4D3×Q1611yescharacteristic
263C3×C4#91811yescharacteristic
264Dic3—64no—
265Dic3—62no—
266Dic3—62no—
267Dic3—81no—
268Dic3—81no—
269Dic3—122no—
270Dic3—121no—
271Dic3—121no—
272C32#168411yescharacteristic, complemented, Sylow
273Q8—92no—
274Q8—121no—
275Q8—121no—
276Q8—181no—
277Q8—241no—
278C2×C4—121no—
279C2×C4—121no—
280C2×C4—181no—
281C2×C4—181no—
282C2×C4#379811yescharacteristic
283C2×C4#380211yescharacteristic
284C2×C4#381111yescharacteristic
285C8—41no—
286C8—121no—
287C8—121no—
288C8—181no—
289C8—181no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3#474811yescharacteristic
294C2×C3#475411yescharacteristic
295C2×C3#476711yescharacteristic
296C2×C3#479811yescharacteristic
297C2×C3#481311yescharacteristic
298C2×C3#481311yescharacteristic
299C22#6391211yescharacteristic
300C4—21no—
301C4—182no—
302C4—241no—
303C4—241no—
304C4—361no—
305C4#6380211yescharacteristic
306C4#6380911yescharacteristic
307C4#6393611yescharacteristic
308C4#6395111yescharacteristic
309C3—21no—
310C3#6847111yescharacteristic, complemented
311C3#6851111yescharacteristic, complemented
312C2#1059053811yescharacteristic
313C2#1059085511yescharacteristic
314C2#1059099111yescharacteristic
subgroupG/H
centerC22#63912
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
272. C32#1684semidirect
310. C3#68471semidirect
311. C3#68511semidirect

Maximal subgroups

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

subgroupindex
#105925292
#105903072
#105902902
#105902842
C3×#44822
C3×#44812
#105891002
#685113
#684713