Finite Group Databasebeta

← #11782894

Subgroups — #11782894

Order 1152.

431 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 431 conjugacy classes of subgroups — too many to draw. Only its 94 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#10592769C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic
3C3×#5070C211yesmaximal, characteristic
4#10590386C211yesmaximal, characteristic, complemented
5#10590309C211yesmaximal, characteristic, complemented
6#10590287C211yesmaximal, characteristic, complemented
7#10589078C211yesmaximal, characteristic, complemented
8#71193—31nomaximal
9#71192—31nomaximal
10C32×#127C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3719—22no—
15#63659—22no—
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#832—22no—
18C3×#832—22no—
19C3×C4×C3⋊C8C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63574—22no—
22#63566—22no—
23C3×#486—31no—
24C3×#486—31no—
25#5092—31no—
26#5080—31no—
27#5080—31no—
28#5079—31no—
29#5070—31no—
30#5070—31no—
31#5070—61no—
32#5070D311yescharacteristic
33#5070D311yescharacteristic
34#4699—31no—
35#4681—31no—
36#4455—31no—
37#4454—31no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×#634—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C2×C3⋊(C3⋊C8)D412yes—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8D412yes—
53C2×C3×C3⋊C8D412yes—
54#3719—44no—
55#1720—91noSylow
56C3×C4⋊Q8—31no—
57C3×C4⋊Q8—31no—
58C3×#127—21no—
59C3×#127C2×D311yescharacteristic
60C3×#127C2×D311yescharacteristic
61C2×#216—62no—
62C2×Dic12—62no—
63#869—31no—
64#869—31no—
65#869—61no—
66#869C2×D311yescharacteristic
67#869C2×D311yescharacteristic
68C3×#102—62no—
69C3×#102—62no—
70C3×C4×C8—31no—
71C3×C4×C8—31no—
72#835—62no—
73#832—22no—
74#832—22no—
75#832—62no—
76#832—62no—
77#832—64no—
78#816—62no—
79#808—62no—
80#808—62no—
81C4×C3⋊C8—31no—
82C4×C3⋊C8—31no—
83C4×C3⋊C8—61no—
84C4×C3⋊C8C2×D311yescharacteristic
85C4×C3⋊C8C2×D311yescharacteristic
86C23×C32—41no—
87C32×D4—42no—
88C32×D4—42no—
89C32×D4—42no—
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C3⋊Dic3—41no—
94#634—42no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C3×Dic6—42no—
98C3×Dic6—42no—
99C3⋊(C3⋊C8)—22no—
100C3×C3⋊C8—22no—
101C3×C3⋊C8—22no—
102#498—91no—
103#494—91no—
104#487—91no—
105#486—31no—
106#486—31no—
107#486—91no—
108#322—91no—
109C2×C3×Q8—61no—
110C2×C3×Q8—61no—
111C2×C3×D4—22no—
112C2×C3×D4—21no—
113C2×C3×D4—21no—
114C2×C3×D4—21no—
115C2×C3×D4—21no—
116C2×C3×D4—21no—
117C2×C3×D4—21no—
118C2×C3×D4—41no—
119C2×C3×D4—41no—
120C2×Dic6—21no—
121C2×Dic6—21no—
122C2×Dic6—61no—
123C2×Dic6—61no—
124C2×Dic6—121no—
125C2×C3×C8—32no—
126C2×C3×C8—32no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C42—21no—
132C3×C42C22×D311yescharacteristic
133C3×C42C22×D311yescharacteristic
134#216—124no—
135C4⋊Dic3—21no—
136C4⋊Dic3—21no—
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—62no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—61no—
144C4⋊Dic3—121no—
145C2×C3⋊C8—32no—
146C2×C3⋊C8—32no—
147C2×C3⋊C8—62no—
148C2×C3⋊C8#6712yes—
149C2×C3⋊C8#6712yes—
150Dic12—124no—
151C22×C32—81no—
152C22×C32—81no—
153C22×C32—81no—
154C22×C32#12711yescharacteristic
155C32×C4#13512yes—
156C32×C4AGL(1,ℤ/8)12yes—
157C32×C4#13712yes—
158C3⋊Dic3—81no—
159C3×Dic3—81no—
160C3×Dic3—81no—
161C2×Q16—182no—
162C4⋊Q8—31no—
163C4⋊Q8—31no—
164C4⋊Q8—91no—
165#127D3211yescharacteristic
166#106—182no—
167#103—182no—
168#102—62no—
169#102—62no—
170#102—182no—
171C4×C8—31no—
172C4×C8—31no—
173C4×C8—91no—
174C23×C3—42no—
175C23×C3—41no—
176C23×C3—41no—
177C3×Q8—122no—
178C3×Q8—122no—
179C3×D4—44no—
180C3×D4—42no—
181C3×D4—42no—
182C3×D4—42no—
183C3×D4—42no—
184C3×D4—42no—
185C3×D4—42no—
186C3×D4—82no—
187C3×D4—82no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—121no—
192C2×C3×C4—121no—
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4D3×D411yescharacteristic
197C2×C3×C4C2×#6711yescharacteristic
198C2×C3×C4C2×#6711yescharacteristic
199C2×Dic3—41no—
200C2×Dic3—41no—
201C2×Dic3—122no—
202C2×Dic3—121no—
203C2×Dic3—121no—
204Dic6—42no—
205Dic6—42no—
206Dic6—122no—
207Dic6—122no—
208Dic6—242no—
209C3×C8—62no—
210C3×C8—62no—
211C3⋊C8—22no—
212C3⋊C8—22no—
213C3⋊C8—62no—
214C3⋊C8—62no—
215C3⋊C8—122no—
216C2×C32—161no—
217C2×C32#49511yescharacteristic
218C2×C32#49611yescharacteristic
219C2×C32#49711yescharacteristic
220C2×Q8—61no—
221C2×Q8—61no—
222C2×Q8—181no—
223C2×D4—21no—
224C2×D4—21no—
225C2×D4—21no—
226Q16—364no—
227C2×C8—32no—
228C2×C8—32no—
229C2×C8—92no—
230C4⋊C4—61no—
231C4⋊C4—61no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—181no—
235C4⋊C4—181no—
236C42C2×D3211yescharacteristic
237C22×C3—21no—
238C22×C3—82no—
239C22×C3—82no—
240C22×C3—82no—
241C22×C3—81no—
242C22×C3—81no—
243C22×C3—81no—
244C22×C3—81no—
245C22×C3—81no—
246C22×C3—81no—
247C22×C3#94011yescharacteristic
248C22×C3#94011yescharacteristic
249C3×C4—22no—
250C3×C4—22no—
251C3×C4—22no—
252C3×C4—241no—
253C3×C4—241no—
254C3×C4#91112yes—
255C3×C4#91212yes—
256C3×C4#91512yes—
257C3×C4#91512yes—
258C3×C4#94912yes—
259C3×C4#95012yes—
260Dic3—81no—
261Dic3—81no—
262Dic3—242no—
263Dic3—241no—
264Dic3—241no—
265C32#172011yescharacteristic, complemented, Sylow
266C23—41no—
267Q8—122no—
268Q8—122no—
269Q8—362no—
270D4—42no—
271D4—42no—
272D4—42no—
273C2×C4—121no—
274C2×C4—121no—
275C2×C4—361no—
276C2×C4D3×#6711yescharacteristic
277C2×C4D3×#6711yescharacteristic
278C2×C4#381111yescharacteristic
279C8—62no—
280C8—62no—
281C8—182no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—162no—
286C2×C3—161no—
287C2×C3—161no—
288C2×C3#505811yescharacteristic
289C2×C3#505911yescharacteristic
290C2×C3#515411yescharacteristic
291C2×C3#515511yescharacteristic
292C2×C3#516711yescharacteristic
293C2×C3#516711yescharacteristic
294C22—81no—
295C22—81no—
296C22—81no—
297C22#6397911yescharacteristic
298C4—241no—
299C4—241no—
300C4—721no—
301C4#6392512yes—
302C4#6393112yes—
303C4#6393312yes—
304C3—21no—
305C3#7119211yescharacteristic, complemented
306C3#7119311yescharacteristic, complemented
307C2—161no—
308C2#1059147011yescharacteristic
309C2#1059148311yescharacteristic
310C2#1059149311yescharacteristic
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
Fitting, prime radicalC32×#127C22
socleC22×C32#127
hypercenter#127D32
hypocenterC32#1720
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #10590386C2semidirect
5. #10590309C2semidirect
6. #10590287C2semidirect
7. #10589078C2semidirect
265. C32#1720semidirect
305. C3#71192semidirect
306. C3#71193semidirect

Maximal subgroups

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

subgroupindex
#105927692
C3×#50702
#105903862
#105903092
#105902872
#105890782
#711933
#711923