Finite Group Databasebeta

← #11781220

Subgroups — #11781220

Order 1152.

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

normal subgroups only

This group has 336 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
1#10592549C211yesmaximal, characteristic
2#10590311C211yesmaximal, characteristic
3#10590284C211yesmaximal, characteristic
4#10590254C211yesmaximal, characteristic
5C3×#4481C211yesmaximal, characteristic
6C3×#4479C211yesmaximal, characteristic
7#10589096C211yesmaximal, characteristic
8#68589—31nomaximal
9#68509—31nomaximal
10#64078C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14#63645—21no—
15#63643—21no—
16C3×C4⋊(C3⋊C8)C2211yescharacteristic
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63575—21no—
20#63575—21no—
21#63575—21no—
22#63572—21no—
23#63567—21no—
24#63553—21no—
25#5091—31no—
26#5078—31no—
27#4850—31no—
28#4850—31no—
29#4850—31no—
30#4850—61no—
31#4830—31no—
32#4682—31no—
33C8×Dic6—31no—
34C3×#335—31no—
35C3×#333—31no—
36#4481—31no—
37#4481—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#1676—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#818—61no—
73#818—61no—
74#818—61no—
75#818—61no—
76#818—62no—
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#807—61no—
87#807—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—81no—
100#634Q1612yes—
101C2×C3×Dic3—41no—
102C3×Dic6—81no—
103C32×C8—41no—
104C3×C3⋊C8—21no—
105C3×C3⋊C8—41no—
106C3×C3⋊C8—41no—
107C3×C3⋊C8Q1612yes—
108#500—91no—
109#477—91no—
110#477—91no—
111C8×Q8—91no—
112#335—31no—
113#333—31no—
114#333—91no—
115C2×C3×Q8—61no—
116C2×Dic6—21no—
117C2×Dic6—31no—
118C2×Dic6—31no—
119C2×Dic6—61no—
120C2×Dic6—61no—
121C2×Dic6—61no—
122C2×Dic6—121no—
123C2×C3×C8—22no—
124C2×C3×C8—21no—
125C2×C3×C8—21no—
126C2×C3×C8—31no—
127C2×C3×C8—31no—
128C2×C3×C8—61no—
129C2×C3×C8—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—31no—
138C4⋊Dic3—31no—
139C4⋊Dic3—61no—
140C4⋊Dic3—62no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—121no—
146Dic3⋊C4—61no—
147Dic3⋊C4—61no—
148Dic3⋊C4—121no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C4×Dic3—121no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8D1211yescharacteristic
155C2×C3⋊C8D1211yescharacteristic
156C22×C32#12111yescharacteristic
157C32×C4—21no—
158C32×C4C2×Q1611yescharacteristic
159C32×C4C2×Q1611yescharacteristic
160C32×C4#13511yescharacteristic
161C32×C4#13711yescharacteristic
162C3⋊Dic3—22no—
163C3⋊Dic3—41no—
164C3⋊Dic3—81no—
165C3×Dic3—81no—
166C4⋊Q8—31no—
167C4⋊Q8—91no—
168C4×Q8—91no—
169#107—181no—
170#107—181no—
171#107—181no—
172#107—181no—
173C4⋊C8—31no—
174C4⋊C8—31no—
175C4⋊C8—181no—
176C4⋊C8D3211yescharacteristic
177#103—181no—
178#103—181no—
179C4×C8—31no—
180C4×C8—181no—
181C3×Q8—241no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—121no—
186C2×C3×C4C2×D1211yescharacteristic
187C2×C3×C4#23511yescharacteristic
188C2×C3×C4D3×D411yescharacteristic
189C2×C3×C4D3×D411yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4#23911yescharacteristic
192C2×Dic3—41no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—121no—
198C2×Dic3—121no—
199C2×Dic3—122no—
200C2×Dic3—121no—
201C2×Dic3—121no—
202Dic6—32no—
203Dic6—32no—
204Dic6—62no—
205Dic6—61no—
206Dic6—61no—
207Dic6—81no—
208Dic6—121no—
209Dic6—242no—
210Dic6—241no—
211Dic6—241no—
212C3×C8—32no—
213C3×C8—42no—
214C3×C8—41no—
215C3×C8—41no—
216C3×C8—61no—
217C3×C8—121no—
218C3×C8—121no—
219C3⋊C8—21no—
220C3⋊C8—41no—
221C3⋊C8—41no—
222C3⋊C8Dic1212yes—
223C2×C32#46211yescharacteristic
224C2×C32#46711yescharacteristic
225C2×C32#47211yescharacteristic
226C2×Q8—61no—
227C2×Q8—91no—
228C2×Q8—181no—
229C2×C8—21no—
230C2×C8—31no—
231C2×C8—31no—
232C2×C8—61no—
233C2×C8—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—91no—
237C4⋊C4—181no—
238C4⋊C4—181no—
239C4⋊C4—181no—
240C42—181no—
241C42C2×D3211yescharacteristic
242C22×C3—21no—
243C22×C3#88411yescharacteristic
244C22×C3#89511yescharacteristic
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—41no—
252C3×C4—241no—
253C3×C4C2×Dic1211yescharacteristic
254C3×C4#90911yescharacteristic
255C3×C4#91211yescharacteristic
256C3×C4#91511yescharacteristic
257C3×C4#91611yescharacteristic
258C3×C4D3×Q1611yescharacteristic
259C3×C4D3×Q1611yescharacteristic
260C3×C4D3×Q1611yescharacteristic
261Dic3—62no—
262Dic3—62no—
263Dic3—81no—
264Dic3—122no—
265Dic3—121no—
266Dic3—121no—
267Dic3—241no—
268Dic3—242no—
269Dic3—241no—
270Dic3—241no—
271C32#167611yescharacteristic, complemented, Sylow
272Q8—92no—
273Q8—181no—
274Q8—241no—
275Q8—721no—
276C2×C4—121no—
277C2×C4—181no—
278C2×C4—181no—
279C2×C4—361no—
280C2×C4#379911yescharacteristic
281C2×C4D3×D1211yescharacteristic
282C2×C4#381111yescharacteristic
283C8—32no—
284C8—41no—
285C8—61no—
286C8—121no—
287C8—121no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3#474911yescharacteristic
292C2×C3#479511yescharacteristic
293C2×C3#481311yescharacteristic
294C2×C3#484911yescharacteristic
295C2×C3#488711yescharacteristic
296C2×C3#489711yescharacteristic
297C22#6391011yescharacteristic
298C4—21no—
299C4—182no—
300C4—241no—
301C4—361no—
302C4—721no—
303C4D3×Dic1211yescharacteristic
304C4#6380011yescharacteristic
305C4#6393611yescharacteristic
306C4#6394411yescharacteristic
307C3—21no—
308C3#6850911yescharacteristic, complemented
309C3#6858911yescharacteristic, complemented
310C2#1059052511yescharacteristic
311C2#1059080811yescharacteristic
312C2#1059098711yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1676
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
271. C32#1676semidirect
308. C3#68509semidirect
309. C3#68589semidirect

Maximal subgroups

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

subgroupindex
#105925492
#105903112
#105902842
#105902542
C3×#44812
C3×#44792
#105890962
#685893
#685093