Finite Group Databasebeta

← #11781588

Subgroups — #11781588

Order 1152.

336 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 336 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#10592550C211yesmaximal, characteristic
2#10590288C211yesmaximal, characteristic
3#10590284C211yesmaximal, characteristic
4#10590254C211yesmaximal, characteristic
5C3×#4481C211yesmaximal, characteristic
6C3×#4479C211yesmaximal, characteristic
7#10589094C211yesmaximal, characteristic
8#68591—31nomaximal
9#68511—31nomaximal
10#64078C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14#63644—21no—
15#63643—21no—
16C3×C4⋊(C3⋊C8)C2211yescharacteristic
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63575—21no—
20#63572—21no—
21#63567—21no—
22#63567—21no—
23#63567—21no—
24#63553—21no—
25#5093—31no—
26#5091—31no—
27#4851—31no—
28#4851—31no—
29#4851—61no—
30#4850—31no—
31#4830—31no—
32#4681—31no—
33C8×Dic6—31no—
34C3×#335—31no—
35C3×#333—31no—
36#4486—31no—
37#4482—31no—
38#4481D311yescharacteristic
39#4479D311yescharacteristic
40C2×#634—21no—
41C2×#634D411yescharacteristic
42C2×C3×Dic6—21no—
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)D411yescharacteristic
48#3750—21no—
49C4×C3⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#1684—91noSylow
57C3×C4⋊Q8—31no—
58#869—31no—
59#869—31no—
60#869—61no—
61#869C2×D311yescharacteristic
62C4×Dic6—31no—
63C4×Dic6—31no—
64C4×Dic6—61no—
65C3×C4⋊C8—21no—
66C3×C4⋊C8—31no—
67C3×C4⋊C8—31no—
68C3×C4⋊C8C2×D311yescharacteristic
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4×C8—31no—
71#818—61no—
72#817—61no—
73#817—61no—
74#817—62no—
75#816—61no—
76#816—61no—
77#816—61no—
78#816—61no—
79#816—61no—
80#816—62no—
81Dic3⋊C8—61no—
82Dic3⋊C8—61no—
83C8×Dic3—61no—
84C8×Dic3—61no—
85#810—61no—
86#810—61no—
87#810—61no—
88#807—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8C2×D311yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—41no—
98#634—21no—
99#634—41no—
100#634—41no—
101#634Q1612yes—
102C2×C3×Dic3—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—31no—
114#333—31no—
115#332—91no—
116C2×C3×Q8—61no—
117C2×Dic6—21no—
118C2×Dic6—31no—
119C2×Dic6—31no—
120C2×Dic6—61no—
121C2×Dic6—61no—
122C2×Dic6—61no—
123C2×Dic6—121no—
124C2×C3×C8—22no—
125C2×C3×C8—21no—
126C2×C3×C8—21no—
127C2×C3×C8—31no—
128C2×C3×C8—31no—
129C2×C3×C8—61no—
130C2×C3×C8—61no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C42—21no—
134C3×C42C22×D311yescharacteristic
135C3×C42C22×D311yescharacteristic
136C4⋊Dic3—21no—
137C4⋊Dic3—21no—
138C4⋊Dic3—31no—
139C4⋊Dic3—31no—
140C4⋊Dic3—61no—
141C4⋊Dic3—62no—
142C4⋊Dic3—61no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—121no—
147Dic3⋊C4—61no—
148Dic3⋊C4—61no—
149Dic3⋊C4—121no—
150C4×Dic3—61no—
151C4×Dic3—61no—
152C4×Dic3—121no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8D1211yescharacteristic
156C2×C3⋊C8D1211yescharacteristic
157C22×C32#12111yescharacteristic
158C32×C4—21no—
159C32×C4C2×Q1611yescharacteristic
160C32×C4#13511yescharacteristic
161C32×C4#13511yescharacteristic
162C32×C4#13711yescharacteristic
163C3⋊Dic3—22no—
164C3⋊Dic3—41no—
165C3⋊Dic3—81no—
166C3×Dic3—81no—
167C4⋊Q8—31no—
168C4⋊Q8—91no—
169C4×Q8—91no—
170#107—181no—
171#106—181no—
172C4⋊C8—31no—
173C4⋊C8—31no—
174C4⋊C8—181no—
175C4⋊C8D3211yescharacteristic
176#103—181no—
177#103—181no—
178#103—181no—
179#103—181no—
180C4×C8—31no—
181C4×C8—181no—
182C3×Q8—241no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—121no—
187C2×C3×C4C2×D1211yescharacteristic
188C2×C3×C4#23511yescharacteristic
189C2×C3×C4D3×D411yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192C2×C3×C4#23911yescharacteristic
193C2×Dic3—41no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—121no—
199C2×Dic3—121no—
200C2×Dic3—122no—
201C2×Dic3—121no—
202C2×Dic3—121no—
203Dic6—32no—
204Dic6—32no—
205Dic6—62no—
206Dic6—61no—
207Dic6—61no—
208Dic6—81no—
209Dic6—121no—
210Dic6—121no—
211Dic6—121no—
212Dic6—121no—
213Dic6—121no—
214Dic6—241no—
215Dic6—241no—
216C3×C8—42no—
217C3×C8—41no—
218C3×C8—41no—
219C3×C8—61no—
220C3×C8—61no—
221C3×C8—121no—
222C3×C8—121no—
223C3⋊C8—21no—
224C3⋊C8—21no—
225C3⋊C8—41no—
226C3⋊C8—41no—
227C2×C32#46411yescharacteristic
228C2×C32#46711yescharacteristic
229C2×C32#47111yescharacteristic
230C2×Q8—61no—
231C2×Q8—91no—
232C2×Q8—181no—
233C2×C8—21no—
234C2×C8—31no—
235C2×C8—31no—
236C2×C8—61no—
237C2×C8—61no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—91no—
241C4⋊C4—181no—
242C4⋊C4—181no—
243C4⋊C4—181no—
244C42—181no—
245C42C2×D3211yescharacteristic
246C22×C3—21no—
247C22×C3#88411yescharacteristic
248C22×C3#89511yescharacteristic
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—41no—
256C3×C4—241no—
257C3×C4#90411yescharacteristic
258C3×C4#90911yescharacteristic
259C3×C4#91211yescharacteristic
260C3×C4#91611yescharacteristic
261C3×C4#91611yescharacteristic
262C3×C4D3×Q1611yescharacteristic
263C3×C4D3×Q1611yescharacteristic
264C3×C4#91811yescharacteristic
265Dic3—62no—
266Dic3—62no—
267Dic3—81no—
268Dic3—122no—
269Dic3—121no—
270Dic3—121no—
271Dic3—241no—
272Dic3—242no—
273Dic3—241no—
274Dic3—241no—
275C32#168411yescharacteristic, complemented, Sylow
276Q8—92no—
277Q8—181no—
278Q8—241no—
279Q8—361no—
280Q8—361no—
281C2×C4—121no—
282C2×C4—181no—
283C2×C4—181no—
284C2×C4—361no—
285C2×C4#379911yescharacteristic
286C2×C4D3×D1211yescharacteristic
287C2×C4#381111yescharacteristic
288C8—41no—
289C8—61no—
290C8—61no—
291C8—121no—
292C8—121no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3#474811yescharacteristic
297C2×C3#479811yescharacteristic
298C2×C3#481311yescharacteristic
299C2×C3#484511yescharacteristic
300C2×C3#488711yescharacteristic
301C2×C3#489811yescharacteristic
302C22#6391011yescharacteristic
303C4—21no—
304C4—182no—
305C4—241no—
306C4—361no—
307C4—721no—
308C4#6380111yescharacteristic
309C4#6380611yescharacteristic
310C4#6393611yescharacteristic
311C4#6394411yescharacteristic
312C3—21no—
313C3#6851111yescharacteristic, complemented
314C3#6859111yescharacteristic, complemented
315C2#1059052511yescharacteristic
316C2#1059081311yescharacteristic
317C2#1059098911yescharacteristic
subgroupG/H
centerC22#63910
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
275. C32#1684semidirect
313. C3#68511semidirect
314. C3#68591semidirect

Maximal subgroups

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

subgroupindex
#105925502
#105902882
#105902842
#105902542
C3×#44812
C3×#44792
#105890942
#685913
#685113