Finite Group Databasebeta

← #11780193

Subgroups — #11780193

Order 1152.

702 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 143 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
1D4×#634C211yesmaximal, characteristic
2#10592706C211yesmaximal, characteristic
3#10592548C211yesmaximal, characteristic, complemented
4#10592381C211yesmaximal, characteristic, complemented
5C32×D4⋊C8C211yesmaximal, characteristic
6#10589348C211yesmaximal, characteristic, complemented
7#10589322C211yesmaximal, characteristic, complemented
8#68192—34nomaximal
9C22×#634—21no—
10C32×C4×D4C2211yescharacteristic
11D4×C3⋊Dic3—21no—
12#64133—21no—
13C2×#3746—21no—
14#64097—21no—
15#64087—22no—
16#64078C2211yescharacteristic
17#64078C2211yescharacteristic
18C4×#634C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×C4×C8C2211yescharacteristic
21#63659—21no—
22#63645—22no—
23#63643—21no—
24#63634—21no—
25C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
26D4×Dic6—34no—
27#5007—34no—
28#4849—34no—
29#4682—34no—
30C3×D4⋊C8D314yes—
31#4482—34no—
32#4456—34no—
33C2×C32×D4D411yescharacteristic
34C22×C32×C4—21no—
35C22×C3⋊Dic3—22no—
36C2×#634—22no—
37C2×#634—21no—
38C2×#634—21no—
39C2×#634—42no—
40C2×#634—42no—
41C2×#634D411yescharacteristic
42C2×C32×C8—21no—
43C2×C32×C8—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C22⋊C4—21no—
46C32×C42C2311yescharacteristic
47#3757—22no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)D411yescharacteristic
52C4⋊(C3⋊Dic3)D412yes—
53#3750—22no—
54#3750—21no—
55C4×C3⋊Dic3—21no—
56C2×C3⋊(C3⋊C8)—21no—
57#3746—42no—
58#1649—91noSylow
59C22×Dic6—64no—
60C3×C4×D4C2×D314yes—
61D4×Dic3—64no—
62#924—64no—
63C2×Dic12—64no—
64#888—64no—
65#878—68no—
66#869—34no—
67#869—34no—
68C4×Dic6—34no—
69C3×C4⋊C8C2×D314yes—
70C3×C4×C8C2×D314yes—
71#832—64no—
72#818—68no—
73#816—64no—
74#807—64no—
75C4⋊(C3⋊C8)—34no—
76C23×C32—21no—
77C32×D4—21no—
78C32×D4Q1612yescomplemented
79C2×C32×C4—21no—
80C2×C32×C4—41no—
81C2×C32×C4—41no—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—44no—
89C2×C3⋊Dic3—41no—
90#634—21no—
91#634—44no—
92#634—41no—
93#634—41no—
94#634—41no—
95#634—41no—
96#634D812yes—
97C32×C8—22no—
98C32×C8—41no—
99C3⋊(C3⋊C8)—41no—
100D4×Q8—91no—
101#500—91no—
102#474—91no—
103#462—91no—
104#332—91no—
105Q8⋊C8—91no—
106D4⋊C8C3⋊D311yescharacteristic
107C2×C3×D4D1214yes—
108C22×C3×C4—24no—
109C22×Dic3—68no—
110C2×Dic6—34no—
111C2×Dic6—68no—
112C2×Dic6—64no—
113C2×Dic6—64no—
114C2×Dic6—128no—
115C2×Dic6—128no—
116C2×C3×C8—24no—
117C2×C3×C8—24no—
118C3×C4⋊C4D1214yes—
119C3×C22⋊C4—24no—
120C3×C42C22×D314yes—
121#217—68no—
122C4⋊Dic3—34no—
123C4⋊Dic3—38no—
124C4⋊Dic3—64no—
125C4⋊Dic3—64no—
126C4⋊Dic3—64no—
127Dic3⋊C4—68no—
128Dic3⋊C4—64no—
129C4×Dic3—64no—
130C2×C3⋊C8—64no—
131Dic12—128no—
132C22×C32—22no—
133C22×C32—41no—
134C22×C32—41no—
135C22×C32#12011yescharacteristic
136C32×C4—21no—
137C32×C4—41no—
138C32×C4C2×D811yescharacteristic
139C32×C4C2×Q1611yescharacteristic
140C32×C4AGL(1,ℤ/8)11yescharacteristic
141C32×C4#13711yescharacteristic
142C3⋊Dic3—22no—
143C3⋊Dic3—42no—
144C3⋊Dic3—41no—
145C3⋊Dic3—81no—
146C22×Q8—181no—
147C2×Q16—181no—
148C4⋊Q8—91no—
149C4⋊Q8—91no—
150C4⋊Q8—181no—
151C22⋊Q8—182no—
152C22⋊Q8—181no—
153C4×Q8—91no—
154C4×D4—181no—
155C4×D4C2×C3⋊D311yescharacteristic
156#107—182no—
157#107—181no—
158C4⋊C8—91no—
159C4⋊C8C2×C3⋊D311yescharacteristic
160#103—181no—
161#102—181no—
162C4×C8C2×C3⋊D311yescharacteristic
163C23×C3—24no—
164C3×D4—24no—
165C3×D4Dic1218yescomplemented
166C2×C3×C4—24no—
167C2×C3×C4—44no—
168C2×C3×C4—44no—
169C2×C3×C4C2×D1214yes—
170C2×C3×C4D3×D414yes—
171C2×C3×C4D3×D414yes—
172C2×Dic3—64no—
173C2×Dic3—64no—
174C2×Dic3—68no—
175C2×Dic3—1216no—
176C2×Dic3—124no—
177Dic6—38no—
178Dic6—64no—
179Dic6—1216no—
180Dic6—124no—
181Dic6—124no—
182Dic6—124no—
183Dic6—124no—
184C3×C8—28no—
185C3×C8—44no—
186C3⋊C8—124no—
187C2×C32—42no—
188C2×C32#44711yescharacteristic
189C2×C32#45111yescharacteristic
190C2×C32#45611yescharacteristic
191C2×Q8—91no—
192C2×Q8—182no—
193C2×Q8—181no—
194C2×Q8—181no—
195C2×Q8—362no—
196C2×Q8—362no—
197C2×D4C4⋊(C3⋊D3)11yescharacteristic
198C22×C4—21no—
199C22×C4—182no—
200Q16—362no—
201C2×C8—21no—
202C2×C8—21no—
203C2×C8—181no—
204C4⋊C4—91no—
205C4⋊C4—92no—
206C4⋊C4—182no—
207C4⋊C4—181no—
208C4⋊C4—181no—
209C4⋊C4—181no—
210C4⋊C4—181no—
211C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
212C22⋊C4—21no—
213C22⋊C4—182no—
214C42—181no—
215C42C22×C3⋊D311yescharacteristic
216C22×C3—28no—
217C22×C3—44no—
218C22×C3—44no—
219C22×C3#88214yes—
220C3×C4—24no—
221C3×C4—44no—
222C3×C4C2×Dic1214yes—
223C3×C4#90914yes—
224C3×C4D3×D814yes—
225C3×C4#91414yes—
226Dic3—68no—
227Dic3—128no—
228Dic3—124no—
229Dic3—244no—
230C32#164911yescharacteristic, complemented, Sylow
231C23—21no—
232Q8—92no—
233Q8—181no—
234Q8—364no—
235Q8—361no—
236Q8—361no—
237Q8—361no—
238Q8—361no—
239D4—21no—
240D4#374612yescomplemented
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—181no—
245C2×C4—181no—
246C2×C4—182no—
247C2×C4—364no—
248C2×C4—361no—
249C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
250C2×C4D4×C3⋊D311yescharacteristic
251C2×C4D4×C3⋊D311yescharacteristic
252C8—22no—
253C8—41no—
254C8—361no—
255C2×C3—48no—
256C2×C3#473914yes—
257C2×C3#477314yes—
258C2×C3#482614yes—
259C22—22no—
260C22—41no—
261C22—41no—
262C22#6409111yescharacteristic
263C4—21no—
264C4—41no—
265C4—182no—
266C4—361no—
267C4—362no—
268C4—721no—
269C4C2×#374611yescharacteristic
270C4#6411811yescharacteristic
271C4D8×C3⋊D311yescharacteristic
272C4#6412311yescharacteristic
273C3#6819214yescomplemented
274C2—42no—
275C2#1059243811yescharacteristic
276C2#1059247211yescharacteristic
277C2#1059252511yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×D4⋊C8C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterD4⋊C8C3⋊D3
hypocenterC32#1649
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
3. #10592548C2semidirect
4. #10592381C2semidirect
6. #10589348C2semidirect
7. #10589322C2semidirect
78. C32×D4Q16semidirect
165. C3×D4Dic12semidirect
230. C32#1649semidirect
240. D4#3746semidirect
273. C3#68192semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
#105927062
#105925482
#105923812
C32×D4⋊C82
#105893482
#105893222
#681923