Finite Group Databasebeta

← #11782950

Subgroups — #11782950

Order 1152.

429 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 429 conjugacy classes of subgroups — too many to draw. Only its 100 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×#4694C211yesmaximal, characteristic
2C3×#4682C211yesmaximal, characteristic, complemented
3#10590387C211yesmaximal, characteristic, complemented
4#10590375C211yesmaximal, characteristic
5#10590312C211yesmaximal, characteristic, complemented
6#10590277C211yesmaximal, characteristic
7#10589320C211yesmaximal, characteristic, complemented
8#71366—31nomaximal
9#71195—31nomaximal
10C3×#874C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3718—22no—
15C2×#3715—22no—
16C32×C4×C8C2211yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#821—22no—
20C3×#818—22no—
21#63576—22no—
22#63562—22no—
23C3×#500—31no—
24C3×#486—31no—
25#5092—31no—
26#5092—31no—
27#5088—31no—
28#5085—31no—
29#5078—31no—
30#5078—31no—
31#5076—31no—
32#5070—31no—
33#4694D311yescharacteristic
34#4682D311yescharacteristic, complemented
35#4454—31no—
36#4454—31no—
37#4454—61no—
38C2×C3×D12—21no—
39C2×C3×D12—21no—
40C2×C3×D12—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8D412yes—
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)D412yes—
47C2×C3⋊(C3⋊C8)D412yes—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54#3718—44no—
55#3715—44no—
56#1722—91noSylow
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8—31no—
60C3×#127—31no—
61C2×#216—62no—
62C2×#216—62no—
63C2×#215—62no—
64C2×#214—62no—
65#874C2×D311yescharacteristic
66#869C2×D311yescharacteristic
67#869C2×D311yescharacteristic
68#869C2×D311yescharacteristic
69C3×#107—62no—
70C3×#102—62no—
71C3×C4×C8—21no—
72C3×C4×C8C2×D311yescharacteristic
73C3×C4×C8C2×D311yescharacteristic
74#832—62no—
75#821—22no—
76#818—22no—
77#809—62no—
78#807—62no—
79#807—62no—
80C4×C3⋊C8—31no—
81C4×C3⋊C8—31no—
82C4×C3⋊C8—31no—
83C4×C3⋊C8—31no—
84C4×C3⋊C8—61no—
85C4×C3⋊C8—61no—
86C22×C3×D3—41no—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C3×Dic3—41no—
91C2×C3×Dic3—41no—
92C2×C3×Dic3—41no—
93C3×D12—42no—
94C3×D12—42no—
95C3×D12—42no—
96C3×Dic6—42no—
97C3×Dic6—42no—
98C3×Dic6—42no—
99C32×C8—22no—
100C3⋊(C3⋊C8)—22no—
101C3⋊(C3⋊C8)D814yes—
102#500—31no—
103#500—91no—
104#494—91no—
105#492—91no—
106#486—31no—
107#486—91no—
108#322—91no—
109C2×C3×Q8—61no—
110C2×C3×Q8—61no—
111C2×C3×Q8—61no—
112C2×C3×D4—61no—
113C2×C3×D4—61no—
114C2×C3×D4—61no—
115C2×D12—21no—
116C2×D12—21no—
117C2×D12—21no—
118C2×Dic6—21no—
119C2×Dic6—21no—
120C2×Dic6—21no—
121C2×C3×C8—22no—
122C2×C3×C8#6712yes—
123C2×C3×C8#6712yes—
124C3×C4⋊C4—61no—
125C3×C4⋊C4—61no—
126C3×C4⋊C4—61no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C42—21no—
131C3×C42C22×D311yescharacteristic
132C3×C42C22×D311yescharacteristic
133#216—124no—
134#216—124no—
135#215—124no—
136#214—124no—
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C2×C3⋊C8—32no—
144C2×C3⋊C8—32no—
145C2×C3⋊C8—32no—
146C2×C3⋊C8—32no—
147C2×C3⋊C8—62no—
148C2×C3⋊C8—62no—
149C22×C32#12711yescharacteristic
150C2×C3×D3—81no—
151C2×C3×D3—81no—
152C2×C3×D3—81no—
153C32×C4C2×D812yes—
154C32×C4#13712yes—
155C32×C4#13712yes—
156C3×Dic3—81no—
157C3×Dic3—81no—
158C3×Dic3—81no—
159C2×Q16—182no—
160C2×SD16—182no—
161C4⋊Q8—31no—
162C4⋊Q8—31no—
163C4⋊Q8—31no—
164#127—31no—
165#107—62no—
166#107—182no—
167#102—62no—
168#102—182no—
169C4×C8—91no—
170C4×C8—91no—
171C4×C8D3211yescharacteristic
172C23×C3—121no—
173C22×D3—41no—
174C3×Q8—122no—
175C3×Q8—122no—
176C3×Q8—122no—
177C3×D4—122no—
178C3×D4—122no—
179C3×D4—122no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—121no—
184C2×C3×C4—121no—
185C2×C3×C4—121no—
186C2×C3×C4D3×D411yescharacteristic
187C2×C3×C4D3×D411yescharacteristic
188C2×C3×C4D3×D411yescharacteristic
189C2×C3×C4D3×D411yescharacteristic
190C2×C3×C4C2×#6711yescharacteristic
191C2×C3×C4C2×#6711yescharacteristic
192C2×Dic3—41no—
193C2×Dic3—41no—
194C2×Dic3—41no—
195D12—42no—
196D12—42no—
197D12—42no—
198Dic6—42no—
199Dic6—42no—
200Dic6—42no—
201C3×C8—22no—
202C3×C8—22no—
203C3×C8—42no—
204C3⋊C8—34no—
205C3⋊C8—34no—
206C3⋊C8—64no—
207C3⋊C8—62no—
208C3⋊C8—62no—
209C3⋊C8—122no—
210C2×C32#49311yescharacteristic
211C2×C32#49711yescharacteristic
212C2×C32#49711yescharacteristic
213C3×D3—161no—
214C2×Q8—61no—
215C2×Q8—61no—
216C2×Q8—61no—
217C2×D4—61no—
218C2×D4—61no—
219C2×D4—61no—
220Q16—364no—
221SD16—364no—
222C2×C8—92no—
223C2×C8—92no—
224C2×C8#62512yes—
225C4⋊C4—61no—
226C4⋊C4—61no—
227C4⋊C4—61no—
228C4⋊C4—61no—
229C4⋊C4—61no—
230C4⋊C4—61no—
231C42C2×D3211yescharacteristic
232C22×C3—21no—
233C22×C3—241no—
234C22×C3—241no—
235C22×C3—241no—
236C22×C3#94011yescharacteristic
237C22×C3#94011yescharacteristic
238C2×D3—81no—
239C2×D3—81no—
240C2×D3—81no—
241C3×C4—22no—
242C3×C4—22no—
243C3×C4—22no—
244C3×C4—241no—
245C3×C4—241no—
246C3×C4—241no—
247C3×C4D3×D812yes—
248C3×C4D3×D812yes—
249C3×C4#91512yes—
250C3×C4#91812yes—
251C3×C4#94212yes—
252C3×C4#95112yes—
253Dic3—81no—
254Dic3—81no—
255Dic3—81no—
256C32#172211yescharacteristic, complemented, Sylow
257C23—121no—
258Q8—122no—
259Q8—122no—
260Q8—122no—
261D4—122no—
262D4—122no—
263D4—122no—
264C2×C4—121no—
265C2×C4—121no—
266C2×C4—121no—
267C2×C4#380211yescharacteristic
268C2×C4#380211yescharacteristic
269C2×C4C2×#62511yescharacteristic
270C8—22no—
271C8—94no—
272C8—182no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—481no—
277C2×C3#506011yescharacteristic
278C2×C3#508611yescharacteristic
279C2×C3#515111yescharacteristic
280C2×C3#515111yescharacteristic
281C2×C3#516711yescharacteristic
282C2×C3#519011yescharacteristic
283D3—161no—
284C22—241no—
285C22—241no—
286C22—241no—
287C22#6391411yescharacteristic
288C4—241no—
289C4—241no—
290C4—241no—
291C4#6379712yes—
292C4#6381112yes—
293C4#6382712yes—
294C3—21no—
295C3#7119511yescharacteristic, complemented
296C3#7136611yescharacteristic, complemented
297C2—481no—
298C2#1059037611yescharacteristic
299C2#1059087011yescharacteristic
300C2#1059088611yescharacteristic
subgroupG/H
centerC22#63914
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#127
prime radicalC3×#874C22
hypercenterC4×C8D32
hypocenterC32#1722
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
2. C3×#4682C2semidirect
3. #10590387C2semidirect
5. #10590312C2semidirect
7. #10589320C2semidirect
34. #4682D3semidirect
256. C32#1722semidirect
295. C3#71195semidirect
296. C3#71366semidirect

Maximal subgroups

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

subgroupindex
C3×#46942
C3×#46822
#105903872
#105903752
#105903122
#105902772
#105893202
#713663
#711953