Finite Group Databasebeta

← #11781898

Subgroups — #11781898

Order 1152.

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

normal subgroups only

This group has 339 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#10592723C211yesmaximal, characteristic
2C3×#5031C211yesmaximal, characteristic
3C3×#5021C211yesmaximal, characteristic
4#10590309C211yesmaximal, characteristic
5#10589100C211yesmaximal, characteristic
6#10589095C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71152—31nomaximal
9#71056—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C2×C3×#216—21no—
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C4⋊(C3⋊(C3⋊C8))—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16#63630—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#835—21no—
19C3×#810—21no—
20C3×#807—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63574—21no—
24#63574—21no—
25C3×#477—31no—
26C3×#462—31no—
27#5080—31no—
28#5080—31no—
29#5031D311yescharacteristic
30#5024—31no—
31#5024—31no—
32#5024—61no—
33#5021D311yescharacteristic
34#4547—31no—
35#4546—31no—
36#4482—31no—
37#4481—31no—
38#4479—31no—
39#4479—31no—
40C2×C32×Q8D411yescharacteristic
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C42—21no—
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×#216—42no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57#1692—91noSylow
58C2×C3×Q16—61no—
59C3×C4⋊Q8—31no—
60C3×C4⋊Q8—31no—
61C3×C4×Q8—21no—
62C3×C4×Q8C2×D311yescharacteristic
63C3×C4×Q8C2×D311yescharacteristic
64C2×#216—21no—
65#869C2×D311yescharacteristic
66#869C2×D311yescharacteristic
67C3×#107—61no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8—31no—
70C3×#103—61no—
71C3×#103—61no—
72#835—21no—
73#810—21no—
74#808—61no—
75#808—61no—
76#808—61no—
77#808—61no—
78#807—21no—
79C4⋊(C3⋊C8)—31no—
80C4⋊(C3⋊C8)—31no—
81C4⋊(C3⋊C8)—61no—
82C4⋊(C3⋊C8)—61no—
83C4⋊(C3⋊C8)—61no—
84C4⋊(C3⋊C8)—62no—
85C4⋊(C3⋊C8)C2×D311yescharacteristic
86C4⋊(C3⋊C8)C2×D311yescharacteristic
87#803—61no—
88#803—61no—
89#803—62no—
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C32×Q8—21no—
94C32×Q8—21no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C3×Dic6—41no—
103C3×Dic6—41no—
104C3×Dic6—81no—
105C3⋊(C3⋊C8)—21no—
106C3⋊(C3⋊C8)—41no—
107C3⋊(C3⋊C8)Q1612yescomplemented
108C3×C3⋊C8—41no—
109C3×C3⋊C8—41no—
110#498—91no—
111#477—31no—
112#462—31no—
113#446—91no—
114#335—91no—
115#333—91no—
116#332—91no—
117C2×C3×Q8—21no—
118C2×C3×Q8—61no—
119C2×C3×Q8—61no—
120C2×C3×Q8#6711yescharacteristic
121C2×C3×Q8#6711yescharacteristic
122C2×Dic6—21no—
123C2×Dic6—21no—
124C3×Q16—122no—
125C2×C3×C8—61no—
126C2×C3×C8—61no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4#6711yescharacteristic
136C3×C4⋊C4#6711yescharacteristic
137C3×C42—22no—
138C3×C42—21no—
139C3×C42—21no—
140C3×C42—21no—
141C3×C42C22×D311yescharacteristic
142C3×C42C22×D311yescharacteristic
143#216—42no—
144C4⋊Dic3—21no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C22×C32#12111yescharacteristic
160C32×C4—21no—
161C32×C4—41no—
162C32×C4—41no—
163C32×C4C2×Q1611yescharacteristic
164C32×C4AGL(1,ℤ/8)11yescharacteristic
165C32×C4#13711yescharacteristic
166C32×C4#13711yescharacteristic
167C3×Dic3—81no—
168C3×Dic3—81no—
169C2×Q16—61no—
170C4⋊Q8—31no—
171C4⋊Q8—31no—
172C4×Q8D3211yescharacteristic
173#107—61no—
174#106—181no—
175#106—181no—
176C4⋊C8—31no—
177C4⋊C8—31no—
178C4⋊C8—91no—
179C4⋊C8—181no—
180#103—61no—
181#103—61no—
182#97—181no—
183C4×C8—91no—
184C3×Q8—21no—
185C3×Q8—21no—
186C3×Q8—21no—
187C3×Q8—21no—
188C3×Q8—41no—
189C3×Q8—41no—
190C3×Q8—121no—
191C3×Q8—121no—
192C3×Q8—241no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—121no—
203C2×C3×C4—121no—
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4#23711yescharacteristic
207C2×C3×C4#23711yescharacteristic
208C2×C3×C4C2×#6711yescharacteristic
209C2×C3×C4C2×#6711yescharacteristic
210C2×Dic3—41no—
211C2×Dic3—41no—
212Dic6—41no—
213Dic6—41no—
214Dic6—81no—
215C3×C8—121no—
216C3×C8—121no—
217C3⋊C8—32no—
218C3⋊C8—32no—
219C3⋊C8—41no—
220C3⋊C8—41no—
221C3⋊C8—62no—
222C3⋊C8—61no—
223C3⋊C8—61no—
224C3⋊C8—121no—
225C3⋊C8—122no—
226C3⋊C8—121no—
227C3⋊C8—121no—
228C2×C32#46211yescharacteristic
229C2×C32#46811yescharacteristic
230C2×C32#47111yescharacteristic
231C2×Q8—61no—
232C2×Q8—61no—
233C2×Q8#62511yescharacteristic
234Q16—122no—
235C2×C8—61no—
236C2×C8—61no—
237C2×C8—91no—
238C2×C8—91no—
239C2×C8—181no—
240C4⋊C4—21no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4#62511yescharacteristic
246C42—21no—
247C42C2×D3211yescharacteristic
248C22×C3—21no—
249C22×C3#93911yescharacteristic
250C22×C3#93911yescharacteristic
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—41no—
258C3×C4—42no—
259C3×C4—42no—
260C3×C4—41no—
261C3×C4—41no—
262C3×C4—41no—
263C3×C4—41no—
264C3×C4—241no—
265C3×C4—241no—
266C3×C4D3×Q1611yescharacteristic
267C3×C4D3×Q1611yescharacteristic
268C3×C4#91811yescharacteristic
269C3×C4#91811yescharacteristic
270C3×C4#93211yescharacteristic
271C3×C4#94211yescharacteristic
272C3×C4#94911yescharacteristic
273C3×C4#95111yescharacteristic
274Dic3—81no—
275Dic3—81no—
276C32#169211yescharacteristic, complemented, Sylow
277Q8—21no—
278Q8—21no—
279Q8—121no—
280Q8—121no—
281Q8—241no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—121no—
285C2×C4—121no—
286C2×C4#380511yescharacteristic
287C2×C4C2×#62511yescharacteristic
288C2×C4#381111yescharacteristic
289C8—92no—
290C8—121no—
291C8—121no—
292C8—181no—
293C8—361no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3#504211yescharacteristic
298C2×C3#504911yescharacteristic
299C2×C3#518211yescharacteristic
300C2×C3#518211yescharacteristic
301C2×C3#520011yescharacteristic
302C2×C3#520311yescharacteristic
303C22#6398011yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—241no—
308C4—241no—
309C4#6382311yescharacteristic
310C4#6382711yescharacteristic
311C4#6394411yescharacteristic
312C4#6394511yescharacteristic
313C3—21no—
314C3#7105611yescharacteristic, complemented
315C3#7115211yescharacteristic, complemented
316C2#1059118011yescharacteristic
317C2#1059163311yescharacteristic
318C2#1059168111yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#121
hypercenterC4×Q8D32
hypocenterC32#1692
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
107. C3⋊(C3⋊C8)Q16semidirect
276. C32#1692semidirect
314. C3#71056semidirect
315. C3#71152semidirect

Maximal subgroups

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

subgroupindex
#105927232
C3×#50312
C3×#50212
#105903092
#105891002
#105890952
#105890932
#711523
#710563