Finite Group Databasebeta

← #11781813

Subgroups — #11781813

Order 1152.

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

normal subgroups only

This group has 331 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
1C3×#4851C211yesmaximal, characteristic
2#10590387C211yesmaximal, characteristic
3#10590285C211yesmaximal, characteristic
4#10590259C211yesmaximal, characteristic
5#10589346C211yesmaximal, characteristic
6C3×#4486C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71121—31nomaximal
9#68473—31nomaximal
10C3×#869C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3718—21no—
14C2×#3718—21no—
15C32×C4⋊C8C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#817—21no—
19C3×#816—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63574—21no—
22Dic3⋊(C3⋊C8)—21no—
23#63565—21no—
24#63554—21no—
25C3×#475—31no—
26#5094—31no—
27#5092—31no—
28#5092—31no—
29#5024—31no—
30#5020—31no—
31#4851D311yescharacteristic
32#4831—31no—
33C3×#332—31no—
34#4547—31no—
35#4486D311yescharacteristic
36#4482—31no—
37#4480—31no—
38#4480—31no—
39#4480—61no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C3×Dic3⋊C4—21no—
54C3×C4×Dic3—21no—
55C2×C3×C3⋊C8—21no—
56#3718—42no—
57#3718—42no—
58#1690—91noSylow
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8—31no—
61C3×C4×Q8—31no—
62C2×#216—61no—
63C2×#216—61no—
64C2×#216—61no—
65C2×#216—61no—
66#869C2×D311yescharacteristic
67#869C2×D311yescharacteristic
68C4×Dic6C2×D311yescharacteristic
69C3×#106—61no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C4⋊C8C2×D311yescharacteristic
74C3×#103—61no—
75#835—61no—
76#817—21no—
77#816—21no—
78#815—61no—
79Dic3⋊C8—61no—
80#810—61no—
81#808—61no—
82#808—61no—
83C4⋊(C3⋊C8)—31no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—61no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88#803—61no—
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—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—41no—
99C3×Dic6—21no—
100C3×Dic6—21no—
101C3×Dic6—41no—
102C3×Dic6—41no—
103C3×Dic6—41no—
104C3×Dic6—41no—
105C32×C8—41no—
106C3⋊(C3⋊C8)—21no—
107C3⋊(C3⋊C8)—41no—
108C3⋊(C3⋊C8)SD1612yes—
109C3×C3⋊C8—41no—
110#494—91no—
111#475—31no—
112#475—91no—
113#446—91no—
114#334—91no—
115#332—31no—
116#332—91no—
117C2×C3×Q8—31no—
118C2×C3×Q8—61no—
119C2×C3×Q8—61no—
120C2×Dic6—21no—
121C2×Dic6—21no—
122C2×Dic6#6711yescharacteristic
123C2×C3×C8—21no—
124C2×C3×C8—21no—
125C2×C3×C8—41no—
126C2×C3×C8—61no—
127C3×C4⋊C4—31no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C42—21no—
134C3×C42—61no—
135C3×C42C22×D311yescharacteristic
136C3×C42C22×D311yescharacteristic
137#216—122no—
138#216—122no—
139#216—122no—
140#216—122no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3—21no—
145C4⋊Dic3#6711yescharacteristic
146Dic3⋊C4—21no—
147C4×Dic3—21no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8—31no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—121no—
158C22×C32#12111yescharacteristic
159C32×C4—21no—
160C32×C4C2×SD1611yescharacteristic
161C32×C4AGL(1,ℤ/8)11yescharacteristic
162C32×C4#13711yescharacteristic
163C32×C4#13711yescharacteristic
164C3×Dic3—41no—
165C3×Dic3—41no—
166C3×Dic3—81no—
167C3×Dic3—81no—
168C2×Q16—181no—
169C2×Q16—181no—
170C4⋊Q8—31no—
171C4⋊Q8—31no—
172C4×Q8—31no—
173#106—61no—
174#106—181no—
175C4⋊C8—31no—
176C4⋊C8—91no—
177C4⋊C8—181no—
178C4⋊C8D3211yescharacteristic
179#103—61no—
180#103—181no—
181#97—181no—
182C4×C8—91no—
183C3×Q8—61no—
184C3×Q8—61no—
185C3×Q8—121no—
186C3×Q8—121no—
187C3×Q8—121no—
188C3×Q8—121no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—61no—
193C2×C3×C4—61no—
194C2×C3×C4—121no—
195C2×C3×C4—121no—
196C2×C3×C4#23511yescharacteristic
197C2×C3×C4D3×D411yescharacteristic
198C2×C3×C4D3×D411yescharacteristic
199C2×C3×C4D3×D411yescharacteristic
200C2×C3×C4#23711yescharacteristic
201C2×C3×C4C2×#6711yescharacteristic
202C2×Dic3—21no—
203C2×Dic3—21no—
204C2×Dic3—41no—
205C2×Dic3—41no—
206Dic6—21no—
207Dic6—21no—
208Dic6—41no—
209Dic6—41no—
210Dic6—41no—
211Dic6—41no—
212C3×C8—41no—
213C3×C8—41no—
214C3×C8—81no—
215C3×C8—121no—
216C3⋊C8—32no—
217C3⋊C8—32no—
218C3⋊C8—41no—
219C3⋊C8—62no—
220C3⋊C8—61no—
221C3⋊C8—61no—
222C3⋊C8—121no—
223C3⋊C8—121no—
224C3⋊C8—121no—
225C3⋊C8—241no—
226C2×C32#46011yescharacteristic
227C2×C32#47011yescharacteristic
228C2×C32#47311yescharacteristic
229C2×Q8—31no—
230C2×Q8—61no—
231C2×Q8—61no—
232Q16—362no—
233Q16—362no—
234C2×C8—21no—
235C2×C8—61no—
236C2×C8—91no—
237C2×C8—91no—
238C2×C8—181no—
239C4⋊C4—31no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C42—61no—
246C42C2×D3211yescharacteristic
247C22×C3—21no—
248C22×C3#88411yescharacteristic
249C22×C3#93911yescharacteristic
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—41no—
257C3×C4—121no—
258C3×C4—121no—
259C3×C4—241no—
260C3×C4—241no—
261C3×C4#91111yescharacteristic
262C3×C4D3×SD1611yescharacteristic
263C3×C4D3×SD1611yescharacteristic
264C3×C4#91411yescharacteristic
265C3×C4#91511yescharacteristic
266C3×C4#91811yescharacteristic
267C3×C4#94211yescharacteristic
268C3×C4#95111yescharacteristic
269Dic3—41no—
270Dic3—41no—
271Dic3—81no—
272Dic3—81no—
273C32#169011yescharacteristic, complemented, Sylow
274Q8—61no—
275Q8—61no—
276Q8—121no—
277Q8—121no—
278Q8—121no—
279Q8—121no—
280C2×C4—61no—
281C2×C4—61no—
282C2×C4—121no—
283C2×C4—121no—
284C2×C4#379511yescharacteristic
285C2×C4#380211yescharacteristic
286C2×C4D3×#6711yescharacteristic
287C8—41no—
288C8—92no—
289C8—121no—
290C8—181no—
291C8—361no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3#475511yescharacteristic
296C2×C3#476211yescharacteristic
297C2×C3#481611yescharacteristic
298C2×C3#505211yescharacteristic
299C2×C3#516311yescharacteristic
300C2×C3#520411yescharacteristic
301C22#6388511yescharacteristic
302C4—21no—
303C4—121no—
304C4—121no—
305C4—241no—
306C4—241no—
307C4#6379611yescharacteristic
308C4#6379811yescharacteristic
309C4#6392911yescharacteristic
310C4#6394811yescharacteristic
311C3—21no—
312C3#6847311yescharacteristic, complemented
313C3#7112111yescharacteristic, complemented
314C2#1059052011yescharacteristic
315C2#1059087611yescharacteristic
316C2#1059098111yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1690
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
273. C32#1690semidirect
312. C3#68473semidirect
313. C3#71121semidirect

Maximal subgroups

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

subgroupindex
C3×#48512
#105903872
#105902852
#105902592
#105893462
C3×#44862
#105890932
#711213
#684733