Finite Group Databasebeta

← #11781088

Subgroups — #11781088

Order 1152.

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

normal subgroups only

This group has 351 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
1#10592529C211yesmaximal, characteristic
2#10590388C211yesmaximal, characteristic
3#10590309C211yesmaximal, characteristic
4#10590284C211yesmaximal, characteristic
5C3×#4486C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic
7#10589098C211yesmaximal, characteristic
8#68508—31nomaximal
9#68466—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3719—21no—
14C32×C4⋊C8C2211yescharacteristic
15#63641—21no—
16C8×C3⋊Dic3—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20#63575—21no—
21#63574—21no—
22#63574—21no—
23#63567—21no—
24#63566—21no—
25#5091—31no—
26#5090—31no—
27#5080—31no—
28#5080—31no—
29#4850—31no—
30#4849—31no—
31#4830—31no—
32#4830—31no—
33#4830—61no—
34C3×#333—31no—
35C3×#332—31no—
36#4486D311yescharacteristic
37#4481D311yescharacteristic
38#4480—31no—
39#4480—31no—
40C2×#634D411yescharacteristic
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)D411yescharacteristic
46#3750—21no—
47C4×C3⋊Dic3—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
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#1672—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×C4⋊C8—21no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8C2×D311yescharacteristic
71C3×C4⋊C8C2×D311yescharacteristic
72#835—61no—
73#818—61no—
74#816—61no—
75#816—61no—
76Dic3⋊C8—61no—
77Dic3⋊C8—61no—
78Dic3⋊C8—62no—
79C8×Dic3—61no—
80C8×Dic3—61no—
81C8×Dic3—62no—
82#810—61no—
83#808—61no—
84#808—61no—
85#808—61no—
86#808—61no—
87#807—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98#634—21no—
99#634SD1612yes—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C3×Dic6—41no—
103C3×Dic6—41no—
104C3×Dic6—81no—
105C32×C8—41no—
106C3⋊(C3⋊C8)—21no—
107C3⋊(C3⋊C8)Q1612yescomplemented
108C3×C3⋊C8—41no—
109C3×C3⋊C8—41no—
110#498—91no—
111#477—91no—
112#462—91no—
113C8×Q8—91no—
114#334—91no—
115#333—31no—
116#332—31no—
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—22no—
125C2×C3×C8—21no—
126C2×C3×C8—21no—
127C2×C3×C8—61no—
128C2×C3×C8—61no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C42—21no—
134C3×C42C22×D311yescharacteristic
135C3×C42C22×D311yescharacteristic
136#216—122no—
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—31no—
142C4⋊Dic3—31no—
143C4⋊Dic3—61no—
144Dic3⋊C4—62no—
145Dic3⋊C4—61no—
146Dic3⋊C4—61no—
147C4×Dic3—62no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C2×C3⋊C8—21no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158Dic12—122no—
159C22×C32#12111yescharacteristic
160C32×C4—21no—
161C32×C4C2×SD1611yescharacteristic
162C32×C4C2×Q1611yescharacteristic
163C32×C4#13511yescharacteristic
164C32×C4#13711yescharacteristic
165C3⋊Dic3—22no—
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—181no—
175#106—181no—
176C4⋊C8—31no—
177C4⋊C8—31no—
178C4⋊C8—181no—
179C4⋊C8D3211yescharacteristic
180#103—181no—
181#103—181no—
182C4×C8—91no—
183C4×C8—181no—
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×C4#23511yescharacteristic
193C2×C3×C4#23511yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4D3×D411yescharacteristic
197C2×C3×C4D3×D411yescharacteristic
198C2×Dic3—41no—
199C2×Dic3—41no—
200C2×Dic3—62no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—62no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206Dic6—32no—
207Dic6—32no—
208Dic6—41no—
209Dic6—41no—
210Dic6—62no—
211Dic6—62no—
212Dic6—61no—
213Dic6—61no—
214Dic6—81no—
215C3×C8—42no—
216C3×C8—41no—
217C3×C8—41no—
218C3×C8—121no—
219C3×C8—121no—
220C3⋊C8—32no—
221C3⋊C8—32no—
222C3⋊C8—41no—
223C3⋊C8—41no—
224C3⋊C8—62no—
225C3⋊C8—61no—
226C3⋊C8—61no—
227C3⋊C8—121no—
228C2×C32#46211yescharacteristic
229C2×C32#46511yescharacteristic
230C2×C32#47111yescharacteristic
231C2×Q8—61no—
232C2×Q8—61no—
233C2×Q8—91no—
234Q16—362no—
235C2×C8—21no—
236C2×C8—61no—
237C2×C8—61no—
238C2×C8—91no—
239C2×C8—91no—
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#88411yescharacteristic
250C22×C3#88411yescharacteristic
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×C4#91211yescharacteristic
261C3×C4D3×SD1611yescharacteristic
262C3×C4D3×SD1611yescharacteristic
263C3×C4#91511yescharacteristic
264C3×C4#91511yescharacteristic
265C3×C4D3×Q1611yescharacteristic
266C3×C4D3×Q1611yescharacteristic
267C3×C4#91911yescharacteristic
268Dic3—64no—
269Dic3—62no—
270Dic3—62no—
271Dic3—81no—
272Dic3—81no—
273Dic3—122no—
274Dic3—121no—
275Dic3—121no—
276C32#167211yescharacteristic, complemented, Sylow
277Q8—92no—
278Q8—121no—
279Q8—121no—
280Q8—181no—
281Q8—241no—
282C2×C4—121no—
283C2×C4—121no—
284C2×C4—181no—
285C2×C4—181no—
286C2×C4#379811yescharacteristic
287C2×C4#380211yescharacteristic
288C2×C4#381111yescharacteristic
289C8—41no—
290C8—92no—
291C8—121no—
292C8—121no—
293C8—181no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3#474811yescharacteristic
298C2×C3#475411yescharacteristic
299C2×C3#477811yescharacteristic
300C2×C3#479511yescharacteristic
301C2×C3#479511yescharacteristic
302C2×C3#480711yescharacteristic
303C22#6391211yescharacteristic
304C4—21no—
305C4—182no—
306C4—241no—
307C4—241no—
308C4—361no—
309C4#6379611yescharacteristic
310C4#6381011yescharacteristic
311C4#6393111yescharacteristic
312C4#6394411yescharacteristic
313C3—21no—
314C3#6846611yescharacteristic, complemented
315C3#6850811yescharacteristic, complemented
316C2#1059056611yescharacteristic
317C2#1059084111yescharacteristic
318C2#1059099111yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1672
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
107. C3⋊(C3⋊C8)Q16semidirect
276. C32#1672semidirect
314. C3#68466semidirect
315. C3#68508semidirect

Maximal subgroups

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

subgroupindex
#105925292
#105903882
#105903092
#105902842
C3×#44862
C3×#44812
#105890982
#685083
#684663