Finite Group Databasebeta

← #11781544

Subgroups — #11781544

Order 1152.

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

normal subgroups only

This group has 352 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×#4834C211yesmaximal, characteristic
2#10590288C211yesmaximal, characteristic, complemented
3#10590272C211yesmaximal, characteristic
4#10590266C211yesmaximal, characteristic
5#10589348C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589099C211yesmaximal, characteristic, complemented
8#70855—31nomaximal
9#68499—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×D3×C8—21no—
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×(C2×D3)⋊C8—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63575—21no—
20#63574—21no—
21#63567—21no—
22#63567—21no—
23#63563—21no—
24#63562—21no—
25C3×C8×D4—31no—
26#5093—31no—
27#5084—31no—
28#5008—31no—
29#5007—31no—
30#4846—31no—
31#4834D311yescharacteristic
32#4681—31no—
33C3×#333—31no—
34#4482—31no—
35#4482—31no—
36#4482—61no—
37#4481D311yescharacteristic, complemented
38#4479—31no—
39#4458—31no—
40C2×#634—21no—
41C2×C3×D12D411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C2×C3⋊(C3⋊C8)—21no—
49C3×(C2×D3)⋊C4—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×D3×C8—42no—
57#1683—91noSylow
58C22×C3×C8—61no—
59C3×C4⋊Q8—31no—
60C3×C4×D4—31no—
61C2×D3×C8—21no—
62C4×D12C2×D311yescharacteristic
63#869—31no—
64#869—31no—
65#869—61no—
66#869C2×D311yescharacteristic
67C3×C4⋊C8—21no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4⋊C8C2×D311yescharacteristic
71C3×C22⋊C8—61no—
72C3×C4×C8—31no—
73#832—61no—
74#832—61no—
75#821—61no—
76(C2×D3)⋊C8—21no—
77#818—61no—
78#816—61no—
79#816—61no—
80#810—61no—
81#810—61no—
82#809—61no—
83#808—61no—
84#808—61no—
85#807—61no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8C2×D311yescharacteristic
91C22×C3×D3—21no—
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—41no—
100C3×D12—21no—
101C3×D12Q1612yes—
102C3×C4×D3—41no—
103C3×C4×D3—41no—
104C3×Dic6—81no—
105C32×C8—41no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110#487—91no—
111#476—91no—
112#474—91no—
113C8×D4—31no—
114#335—91no—
115#333—31no—
116#332—91no—
117C2×C3×Q8—61no—
118C2×C3×D4—31no—
119C22×C3×C4—61no—
120C2×D12D1211yescharacteristic
121C2×C4×D3—21no—
122C2×Dic6—21no—
123C2×Dic6—61no—
124C2×Dic6—61no—
125C2×Dic6—121no—
126C2×C3×C8—21no—
127C2×C3×C8—21no—
128C2×C3×C8—31no—
129C2×C3×C8—31no—
130C2×C3×C8—41no—
131C2×C3×C8—61no—
132C2×C3×C8—122no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C22⋊C4—61no—
137C3×C42—21no—
138C3×C42C22×D311yescharacteristic
139C3×C42C22×D311yescharacteristic
140(C2×D3)⋊C4—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—62no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—61no—
148C4⋊Dic3—121no—
149C4⋊Dic3D1211yescharacteristic
150C2×C3⋊C8—21no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—121no—
154C2×C3⋊C8#6711yescharacteristic
155C2×C3⋊C8#6711yescharacteristic
156D3×C8—42no—
157C22×C32#12111yescharacteristic
158C2×C3×D3—22no—
159C2×C3×D3—41no—
160C2×C3×D3—41no—
161C32×C4—21no—
162C32×C4C2×Q1611yescharacteristic
163C32×C4#13511yescharacteristic
164C32×C4#13511yescharacteristic
165C32×C4AGL(1,ℤ/8)11yescharacteristic
166C3⋊Dic3—81no—
167C3×Dic3—41no—
168C3×Dic3—81no—
169C22×C8—61no—
170C4⋊Q8—31no—
171C4⋊Q8—91no—
172C4×D4—31no—
173#107—181no—
174#106—181no—
175C4⋊C8—31no—
176C4⋊C8—91no—
177C4⋊C8D3211yescharacteristic
178#103—181no—
179#103—181no—
180#102—181no—
181#102—181no—
182C22⋊C8—61no—
183C4×C8—31no—
184C23×C3—61no—
185C22×D3—21no—
186C3×Q8—241no—
187C3×D4—32no—
188C3×D4—61no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—61no—
193C2×C3×C4—121no—
194C2×C3×C4—121no—
195C2×C3×C4—121no—
196C2×C3×C4C2×D1211yescharacteristic
197C2×C3×C4#23511yescharacteristic
198C2×C3×C4#23511yescharacteristic
199C2×C3×C4D3×D411yescharacteristic
200C2×C3×C4D3×D411yescharacteristic
201C2×C3×C4C2×#6711yescharacteristic
202C2×Dic3—21no—
203C2×Dic3—41no—
204C2×Dic3—122no—
205C2×Dic3—121no—
206C2×Dic3—121no—
207D12—21no—
208D12Dic1212yes—
209C4×D3—41no—
210C4×D3—41no—
211Dic6—81no—
212Dic6—121no—
213Dic6—121no—
214Dic6—121no—
215Dic6—121no—
216Dic6—241no—
217Dic6—241no—
218C3×C8—41no—
219C3×C8—41no—
220C3×C8—61no—
221C3×C8—61no—
222C3×C8—81no—
223C3×C8—121no—
224C3⋊C8—21no—
225C3⋊C8—21no—
226C3⋊C8—41no—
227C3⋊C8—121no—
228C3⋊C8—121no—
229C3⋊C8—241no—
230C2×C32#46311yescharacteristic
231C2×C32#46711yescharacteristic
232C2×C32#47111yescharacteristic
233C3×D3—42no—
234C2×Q8—61no—
235C2×Q8—181no—
236C2×D4—31no—
237C22×C4—61no—
238C2×C8—21no—
239C2×C8—31no—
240C2×C8—31no—
241C2×C8—61no—
242C2×C8—122no—
243C2×C8—181no—
244C4⋊C4—31no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—181no—
248C4⋊C4—181no—
249C22⋊C4—61no—
250C42C2×D3211yescharacteristic
251C22×C3—21no—
252C22×C3—62no—
253C22×C3—121no—
254C22×C3—121no—
255C22×C3#88411yescharacteristic
256C22×C3#93011yescharacteristic
257C2×D3—22no—
258C2×D3—41no—
259C2×D3—41no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—41no—
267C3×C4—121no—
268C3×C4—241no—
269C3×C4#90411yescharacteristic
270C3×C4C2×Dic1211yescharacteristic
271C3×C4#91411yescharacteristic
272C3×C4#91611yescharacteristic
273C3×C4D3×Q1611yescharacteristic
274C3×C4#91911yescharacteristic
275C3×C4#93211yescharacteristic
276C3×C4#95011yescharacteristic
277Dic3—41no—
278Dic3—81no—
279Dic3—242no—
280Dic3—241no—
281Dic3—241no—
282C32#168311yescharacteristic, complemented, Sylow
283C23—61no—
284Q8—241no—
285Q8—361no—
286Q8—361no—
287D4—32no—
288D4—61no—
289C2×C4—61no—
290C2×C4—121no—
291C2×C4—121no—
292C2×C4—121no—
293C2×C4—361no—
294C2×C4#379811yescharacteristic
295C2×C4D3×D1211yescharacteristic
296C2×C4D3×#6711yescharacteristic
297C8—41no—
298C8—61no—
299C8—61no—
300C8—121no—
301C8—361no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—122no—
306C2×C3#474811yescharacteristic
307C2×C3#481311yescharacteristic
308C2×C3#481911yescharacteristic
309C2×C3#501611yescharacteristic
310C2×C3#511611yescharacteristic
311C2×C3#514111yescharacteristic
312D3—42no—
313C22—62no—
314C22—121no—
315C22—121no—
316C22#6390611yescharacteristic
317C4—21no—
318C4—121no—
319C4—241no—
320C4—721no—
321C4D3×Dic1211yescharacteristic
322C4#6380611yescharacteristic
323C4#6393411yescharacteristic
324C4#6394911yescharacteristic
325C3—21no—
326C3#6849911yescharacteristic, complemented
327C3#7085511yescharacteristic, complemented
328C2—122no—
329C2#1059053411yescharacteristic
330C2#1059084811yescharacteristic
331C2#1059099611yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1683
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
2. #10590288C2semidirect
5. #10589348C2semidirect
6. C3×#4481C2semidirect
7. #10589099C2semidirect
37. #4481D3semidirect
282. C32#1683semidirect
326. C3#68499semidirect
327. C3#70855semidirect

Maximal subgroups

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

subgroupindex
C3×#48342
#105902882
#105902722
#105902662
#105893482
C3×#44812
#105890992
#708553
#684993