Finite Group Databasebeta

← #11781895

Subgroups — #11781895

Order 1152.

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

normal subgroups only

This group has 339 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#10592378C211yesmaximal, characteristic
2C3×#4680C211yesmaximal, characteristic
3#10590388C211yesmaximal, characteristic
4#10590284C211yesmaximal, characteristic
5C3×#4458C211yesmaximal, characteristic
6#10589095C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71349—31nomaximal
9#68593—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3719—21no—
14C32×C4×C8C2211yescharacteristic
15#63642—21no—
16#63641—21no—
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#817—21no—
19C3×#817—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63575—21no—
23#63567—21no—
24#63566—21no—
25C3×#498—31no—
26#5091—31no—
27#5090—31no—
28#4850—31no—
29#4849—31no—
30#4680D311yescharacteristic
31#4679—31no—
32#4679—31no—
33#4679—61no—
34C3×#335—31no—
35#4547—31no—
36#4546—31no—
37#4482—31no—
38#4481—31no—
39#4458D311yescharacteristic
40C2×#634D411yescharacteristic
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C32×C8D411yescharacteristic
44C2×C32×C8D411yescharacteristic
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)D411yescharacteristic
47#3750—21no—
48C4×C3⋊Dic3—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#3719—42no—
57#1692—91noSylow
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8—31no—
60C2×#216—61no—
61C2×Dic12—61no—
62#869C2×D311yescharacteristic
63#869C2×D311yescharacteristic
64C4×Dic6—31no—
65C4×Dic6—31no—
66C4×Dic6—61no—
67C3×#106—61no—
68C3×#106—61no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×C4×C8—21no—
72C3×C4×C8C2×D311yescharacteristic
73C3×C4×C8C2×D311yescharacteristic
74#835—61no—
75#818—61no—
76#817—21no—
77#817—21no—
78#816—61no—
79#816—61no—
80#815—62no—
81#815—61no—
82#815—61no—
83Dic3⋊C8—62no—
84Dic3⋊C8—61no—
85Dic3⋊C8—61no—
86#810—61no—
87#807—61no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98#634—21no—
99#634—21no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C3×Dic6—41no—
103C3×Dic6—41no—
104C3×Dic6—81no—
105C32×C8—21no—
106C32×C8Q1612yescomplemented
107C3⋊(C3⋊C8)—41no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8—41no—
110#498—31no—
111#477—91no—
112#462—91no—
113#446—91no—
114#335—31no—
115#333—91no—
116#332—91no—
117C2×C3×Q8—61no—
118C2×C3×Q8—61no—
119C2×Dic6—21no—
120C2×Dic6—21no—
121C2×Dic6—31no—
122C2×Dic6—31no—
123C2×Dic6—61no—
124C2×C3×C8—21no—
125C2×C3×C8—21no—
126C2×C3×C8—61no—
127C2×C3×C8—61no—
128C2×C3×C8D1211yescharacteristic
129C2×C3×C8D1211yescharacteristic
130C2×C3×C8#6711yescharacteristic
131C2×C3×C8#6711yescharacteristic
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C42—21no—
137C3×C42C22×D311yescharacteristic
138C3×C42C22×D311yescharacteristic
139#216—122no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3—31no—
145C4⋊Dic3—31no—
146C4⋊Dic3—61no—
147Dic3⋊C4—62no—
148Dic3⋊C4—61no—
149Dic3⋊C4—61no—
150C4×Dic3—62no—
151C4×Dic3—61no—
152C4×Dic3—61no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—62no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158Dic12—122no—
159C22×C32#12111yescharacteristic
160C32×C4—21no—
161C32×C4C2×Q1611yescharacteristic
162C32×C4AGL(1,ℤ/8)11yescharacteristic
163C32×C4#13711yescharacteristic
164C32×C4#13711yescharacteristic
165C3⋊Dic3—41no—
166C3⋊Dic3—41no—
167C3×Dic3—81no—
168C3×Dic3—81no—
169C2×Q16—181no—
170C4⋊Q8—31no—
171C4⋊Q8—31no—
172C4×Q8—91no—
173#107—181no—
174#106—61no—
175#106—61no—
176C4⋊C8—31no—
177C4⋊C8—31no—
178C4⋊C8—91no—
179C4⋊C8—181no—
180#103—181no—
181#103—181no—
182#97—181no—
183C4×C8D3211yescharacteristic
184C3×Q8—121no—
185C3×Q8—121no—
186C3×Q8—241no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—121no—
191C2×C3×C4—121no—
192C2×C3×C4C2×D1211yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4#23711yescharacteristic
196C2×C3×C4#23911yescharacteristic
197C2×C3×C4C2×#6711yescharacteristic
198C2×Dic3—41no—
199C2×Dic3—41no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206Dic6—41no—
207Dic6—41no—
208Dic6—61no—
209Dic6—61no—
210Dic6—61no—
211Dic6—61no—
212Dic6—81no—
213Dic6—121no—
214Dic6—121no—
215C3×C8—21no—
216C3×C8—21no—
217C3×C8—22no—
218C3×C8—41no—
219C3×C8—121no—
220C3×C8—121no—
221C3×C8Dic1212yescomplemented
222C3×C8#21612yescomplemented
223C3⋊C8—41no—
224C3⋊C8—41no—
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—91no—
234Q16—362no—
235C2×C8—61no—
236C2×C8—61no—
237C2×C8—181no—
238C2×C8#62611yescharacteristic
239C2×C8#62611yescharacteristic
240C4⋊C4—61no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—91no—
245C4⋊C4—181no—
246C42—181no—
247C42C2×D3211yescharacteristic
248C22×C3—21no—
249C22×C3#89511yescharacteristic
250C22×C3#93811yescharacteristic
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—41no—
258C3×C4—241no—
259C3×C4—241no—
260C3×C4C2×Dic1211yescharacteristic
261C3×C4#90911yescharacteristic
262C3×C4#91111yescharacteristic
263C3×C4#91411yescharacteristic
264C3×C4#91511yescharacteristic
265C3×C4#91811yescharacteristic
266C3×C4#94211yescharacteristic
267C3×C4C2×#21611yescharacteristic
268Dic3—81no—
269Dic3—81no—
270Dic3—122no—
271Dic3—122no—
272Dic3—121no—
273Dic3—121no—
274Dic3—121no—
275Dic3—121no—
276C32#169211yescharacteristic, complemented, Sylow
277Q8—121no—
278Q8—121no—
279Q8—181no—
280Q8—181no—
281Q8—241no—
282C2×C4—121no—
283C2×C4—121no—
284C2×C4—181no—
285C2×C4—181no—
286C2×C4#379611yescharacteristic
287C2×C4#380211yescharacteristic
288C2×C4C2×#62611yescharacteristic
289C8—21no—
290C8—121no—
291C8—121no—
292C8—361no—
293C8#371912yescomplemented
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3#484911yescharacteristic
298C2×C3#488611yescharacteristic
299C2×C3#489811yescharacteristic
300C2×C3#509011yescharacteristic
301C2×C3#517411yescharacteristic
302C2×C3#517711yescharacteristic
303C22#6391611yescharacteristic
304C4—21no—
305C4—241no—
306C4—241no—
307C4—361no—
308C4—361no—
309C4#6379811yescharacteristic
310C4#6381111yescharacteristic
311C4#6383311yescharacteristic
312C4C2×#371911yescharacteristic
313C3—21no—
314C3#6859311yescharacteristic, complemented
315C3#7134911yescharacteristic, complemented
316C2#1059038811yescharacteristic
317C2#1059084511yescharacteristic
318C2#1059092811yescharacteristic
subgroupG/H
centerC22#63916
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#121
hypercenterC4×C8D32
hypocenterC32#1692
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
106. C32×C8Q16semidirect
221. C3×C8Dic12semidirect
222. C3×C8#216semidirect
276. C32#1692semidirect
293. C8#3719semidirect
314. C3#68593semidirect
315. C3#71349semidirect

Maximal subgroups

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

subgroupindex
#105923782
C3×#46802
#105903882
#105902842
C3×#44582
#105890952
#105890932
#713493
#685933