Finite Group Databasebeta

← #11781974

Subgroups — #11781974

Order 1152.

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

normal subgroups only

This group has 336 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
1C3×#4849C211yesmaximal, characteristic
2#10590385C211yesmaximal, characteristic
3#10590311C211yesmaximal, characteristic
4#10590258C211yesmaximal, characteristic
5#10589348C211yesmaximal, characteristic
6C3×#4480C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71057—31nomaximal
9#68552—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×Dic12—21no—
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14C2×#3719—21no—
15C32×C4⋊C8C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#816—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63575—21no—
21#63575—21no—
22Dic3⋊(C3⋊C8)—21no—
23#63567—21no—
24#63554—21no—
25C3×#462—31no—
26#5078—31no—
27#5031—31no—
28#5024—31no—
29#4849—31no—
30#4849D311yescharacteristic
31#4682—31no—
32#4679—31no—
33C3×#334—31no—
34#4547—31no—
35#4482—31no—
36#4482—31no—
37#4482—31no—
38#4482—61no—
39#4480D311yescharacteristic
40C2×#634—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×Dic12—42no—
57#3719—42no—
58#1694—91noSylow
59C2×C3×Q16—61no—
60C3×C4⋊Q8—31no—
61C3×C4×Q8—31no—
62C2×#216—61no—
63C2×Dic12—21no—
64C2×Dic12—61no—
65#869—31no—
66#869—31no—
67#869—61no—
68#869C2×D311yescharacteristic
69C4×Dic6C2×D311yescharacteristic
70C3×C4⋊C8—21no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C4⋊C8C2×D311yescharacteristic
74C3×#103—61no—
75C3×C4×C8—31no—
76#818—61no—
77#818—61no—
78#816—21no—
79#816—61no—
80#815—61no—
81Dic3⋊C8—61no—
82#810—61no—
83#807—61no—
84#807—61no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90#803—61no—
91C4×C3⋊C8C2×D311yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C3⋊Dic3—41no—
96#634—41no—
97#634—41no—
98C2×C3×Dic3—21no—
99C2×C3×Dic3—21no—
100C2×C3×Dic3—41no—
101C3×Dic6—21no—
102C3×Dic6—21no—
103C3×Dic6—41no—
104C3×Dic6—41no—
105C32×C8—41no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8Q1612yescomplemented
110#500—91no—
111#462—31no—
112#462—91no—
113#446—91no—
114#334—31no—
115#332—91no—
116#332—91no—
117C2×C3×Q8—31no—
118C2×C3×Q8—61no—
119C2×Dic6—21no—
120C2×Dic6—61no—
121C2×Dic6—61no—
122C2×Dic6—121no—
123C2×Dic6#6711yescharacteristic
124C3×Q16—122no—
125C2×C3×C8—21no—
126C2×C3×C8—21no—
127C2×C3×C8—31no—
128C2×C3×C8—31no—
129C2×C3×C8—41no—
130C2×C3×C8—61no—
131C3×C4⋊C4—31no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C42—21no—
136C3×C42—61no—
137C3×C42C22×D311yescharacteristic
138C3×C42C22×D311yescharacteristic
139#216—122no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—62no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—121no—
148C4⋊Dic3#6711yescharacteristic
149Dic3⋊C4—21no—
150C4×Dic3—21no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—121no—
155C2×C3⋊C8D1211yescharacteristic
156C2×C3⋊C8D1211yescharacteristic
157Dic12—42no—
158Dic12—122no—
159C22×C32#12111yescharacteristic
160C32×C4—21no—
161C32×C4C2×Q1611yescharacteristic
162C32×C4AGL(1,ℤ/8)11yescharacteristic
163C32×C4AGL(1,ℤ/8)11yescharacteristic
164C32×C4#13711yescharacteristic
165C3⋊Dic3—81no—
166C3×Dic3—41no—
167C3×Dic3—41no—
168C3×Dic3—81no—
169C2×Q16—61no—
170C2×Q16—181no—
171C4⋊Q8—31no—
172C4⋊Q8—91no—
173C4×Q8—31no—
174#107—181no—
175#107—181no—
176C4⋊C8—31no—
177C4⋊C8—91no—
178C4⋊C8—181no—
179C4⋊C8D3211yescharacteristic
180#103—61no—
181#103—181no—
182#97—181no—
183C4×C8—31no—
184C3×Q8—61no—
185C3×Q8—61no—
186C3×Q8—121no—
187C3×Q8—121no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—61no—
192C2×C3×C4—61no—
193C2×C3×C4—121no—
194C2×C3×C4C2×D1211yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4D3×D411yescharacteristic
197C2×C3×C4#23711yescharacteristic
198C2×C3×C4#23911yescharacteristic
199C2×C3×C4C2×#6711yescharacteristic
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—41no—
203C2×Dic3—122no—
204C2×Dic3—121no—
205C2×Dic3—121no—
206Dic6—21no—
207Dic6—21no—
208Dic6—41no—
209Dic6—41no—
210Dic6—121no—
211Dic6—121no—
212Dic6—121no—
213Dic6—121no—
214Dic6—241no—
215Dic6—241no—
216C3×C8—32no—
217C3×C8—41no—
218C3×C8—41no—
219C3×C8—61no—
220C3×C8—81no—
221C3×C8—121no—
222C3⋊C8—21no—
223C3⋊C8—41no—
224C3⋊C8—121no—
225C3⋊C8—121no—
226C3⋊C8—241no—
227C3⋊C8Dic1212yescomplemented
228C2×C32#46211yescharacteristic
229C2×C32#46911yescharacteristic
230C2×C32#47311yescharacteristic
231C2×Q8—31no—
232C2×Q8—61no—
233C2×Q8—181no—
234Q16—122no—
235Q16—362no—
236C2×C8—21no—
237C2×C8—31no—
238C2×C8—31no—
239C2×C8—61no—
240C2×C8—181no—
241C4⋊C4—31no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—181no—
246C4⋊C4—181no—
247C42—61no—
248C42C2×D3211yescharacteristic
249C22×C3—21no—
250C22×C3#89511yescharacteristic
251C22×C3#93911yescharacteristic
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—41no—
259C3×C4—121no—
260C3×C4—121no—
261C3×C4—241no—
262C3×C4C2×Dic1211yescharacteristic
263C3×C4#90911yescharacteristic
264C3×C4#91411yescharacteristic
265C3×C4#91411yescharacteristic
266C3×C4D3×Q1611yescharacteristic
267C3×C4#91811yescharacteristic
268C3×C4#93211yescharacteristic
269C3×C4#94911yescharacteristic
270Dic3—41no—
271Dic3—41no—
272Dic3—81no—
273Dic3—242no—
274Dic3—241no—
275Dic3—241no—
276C32#169411yescharacteristic, complemented, Sylow
277Q8—61no—
278Q8—61no—
279Q8—121no—
280Q8—121no—
281Q8—361no—
282Q8—361no—
283C2×C4—61no—
284C2×C4—61no—
285C2×C4—121no—
286C2×C4—361no—
287C2×C4#379611yescharacteristic
288C2×C4D3×D1211yescharacteristic
289C2×C4D3×#6711yescharacteristic
290C8—32no—
291C8—41no—
292C8—61no—
293C8—121no—
294C8—361no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3#484911yescharacteristic
299C2×C3#486511yescharacteristic
300C2×C3#489611yescharacteristic
301C2×C3#503911yescharacteristic
302C2×C3#518211yescharacteristic
303C2×C3#520411yescharacteristic
304C22#6388611yescharacteristic
305C4—21no—
306C4—121no—
307C4—121no—
308C4—241no—
309C4—721no—
310C4D3×Dic1211yescharacteristic
311C4#6380111yescharacteristic
312C4#6393411yescharacteristic
313C4#6393911yescharacteristic
314C3—21no—
315C3#6855211yescharacteristic, complemented
316C3#7105711yescharacteristic, complemented
317C2#1059058611yescharacteristic
318C2#1059080011yescharacteristic
319C2#1059098311yescharacteristic
subgroupG/H
centerC22#63886
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1694
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
109. C3×C3⋊C8Q16semidirect
227. C3⋊C8Dic12semidirect
276. C32#1694semidirect
315. C3#68552semidirect
316. C3#71057semidirect

Maximal subgroups

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

subgroupindex
C3×#48492
#105903852
#105903112
#105902582
#105893482
C3×#44802
#105890932
#710573
#685523