Finite Group Databasebeta

← #11780187

Subgroups — #11780187

Order 1152.

702 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 133 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#10596198C211yesmaximal, characteristic
2#10592777C211yesmaximal, characteristic, complemented
3#10592548C211yesmaximal, characteristic, complemented
4#10592545C211yesmaximal, characteristic
5C32×#332C211yesmaximal, characteristic, complemented
6#10589350C211yesmaximal, characteristic, complemented
7#10589349C211yesmaximal, characteristic
8#68461—34nomaximal
9C2×Q8×C3⋊D3—21no—
10C32×C4⋊Q8C2211yescharacteristic
11#64155—21no—
12C2×#3746—21no—
13#64105—22no—
14#64102—21no—
15#64097—21no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic
18C4×#634C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21#63648—21no—
22#63645—21no—
23#63643—21no—
24#63634—22no—
25C4×C3⋊(C3⋊C8)C2211yescharacteristic
26#5727—34no—
27#5078—34no—
28#4849—34no—
29#4846—34no—
30C3×#332D314yescomplemented
31#4484—34no—
32#4483—34no—
33C2×C32×Q8—21no—
34Q8×C3⋊D3—42no—
35Q8×C3⋊D3—42no—
36C2×C4⋊(C3⋊D3)D411yescharacteristic
37C2×C4×C3⋊D3—22no—
38C2×C4×C3⋊D3—21no—
39C2×#634—22no—
40C2×#634—21no—
41C2×#634D411yescharacteristic
42C2×C32×C8—21no—
43C2×C32×C8—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4D412yes—
46C32×C42C2311yescharacteristic
47#3752—22no—
48#3752—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)D411yescharacteristic
52C4⋊(C3⋊Dic3)D411yescharacteristic
53#3750—22no—
54#3750—21no—
55C4×C3⋊Dic3—21no—
56C2×C3⋊(C3⋊C8)—21no—
57#3746—42no—
58#1649—91noSylow
59C2×D3×Q8—64no—
60C3×C4⋊Q8C2×D314yes—
61#946—64no—
62C2×Dic12—64no—
63#896—68no—
64#893—64no—
65#888—64no—
66C4×D12—34no—
67#869—34no—
68C4×Dic6—34no—
69C3×C4⋊C8C2×D314yes—
70C3×C4⋊C8C2×D314yes—
71#821—64no—
72#818—64no—
73#816—64no—
74#807—68no—
75C4×C3⋊C8—34no—
76C22×C3⋊D3—21no—
77C32×Q8—41no—
78C32×Q8—41no—
79C2×C32×C4—22no—
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—41no—
87C4⋊(C3⋊D3)—21no—
88C4⋊(C3⋊D3)Q1612yescomplemented
89C4×C3⋊D3—44no—
90C4×C3⋊D3—41no—
91C4×C3⋊D3—41no—
92#634—21no—
93#634—44no—
94#634—41no—
95#634—41no—
96#634D812yes—
97C32×C8—41no—
98C32×C8—41no—
99C3⋊(C3⋊C8)—22no—
100D4×Q8—91no—
101#500—91no—
102#474—91no—
103#462—91no—
104#332C3⋊D311yescharacteristic, complemented
105Q8⋊C8—91no—
106D4⋊C8—91no—
107C2×C3×Q8—24no—
108D3×Q8—128no—
109D3×Q8—128no—
110C2×D12—34no—
111C2×C4×D3—68no—
112C2×C4×D3—64no—
113C2×Dic6—34no—
114C2×Dic6—68no—
115C2×Dic6—64no—
116C2×C3×C8—24no—
117C2×C3×C8—24no—
118C3×C4⋊C4—24no—
119C3×C4⋊C4D1218yes—
120C3×C42C22×D314yes—
121(C2×D3)⋊C4—68no—
122(C2×D3)⋊C4—64no—
123C4⋊Dic3—34no—
124C4⋊Dic3—34no—
125C4⋊Dic3—64no—
126C4⋊Dic3—64no—
127Dic3⋊C4—68no—
128Dic3⋊C4—64no—
129C4×Dic3—64no—
130C2×C3⋊C8—64no—
131Dic12—128no—
132C22×C32#12011yescharacteristic
133C2×C3⋊D3—22no—
134C2×C3⋊D3—41no—
135C2×C3⋊D3—41no—
136C32×C4—21no—
137C32×C4—42no—
138C32×C4C2×D811yescharacteristic
139C32×C4C2×Q1611yescharacteristic
140C32×C4AGL(1,ℤ/8)11yescharacteristic
141C32×C4#13711yescharacteristic
142C3⋊Dic3—22no—
143C3⋊Dic3—41no—
144C3⋊Dic3—41no—
145C3⋊Dic3—81no—
146C22×Q8—181no—
147C2×Q16—181no—
148C4⋊Q8—91no—
149C4⋊Q8—181no—
150C4⋊Q8C2×C3⋊D311yescharacteristic
151C22⋊Q8—181no—
152C22⋊Q8—182no—
153C4×Q8—91no—
154C4×D4—91no—
155C4×D4—181no—
156#107—181no—
157#107—182no—
158C4⋊C8C2×C3⋊D311yescharacteristic
159C4⋊C8C2×C3⋊D311yescharacteristic
160#103—181no—
161#102—181no—
162C4×C8—91no—
163C22×D3—64no—
164C3×Q8—44no—
165C3×Q8—44no—
166C2×C3×C4—28no—
167C2×C3×C4C2×D1214yes—
168C2×C3×C4D3×D414yes—
169C2×C3×C4D3×D414yes—
170C2×Dic3—64no—
171C2×Dic3—64no—
172C2×Dic3—64no—
173C2×Dic3—124no—
174D12—38no—
175D12—64no—
176C4×D3—1216no—
177C4×D3—124no—
178C4×D3—124no—
179Dic6—38no—
180Dic6—64no—
181Dic6—1216no—
182Dic6—124no—
183Dic6—124no—
184C3×C8—44no—
185C3×C8—44no—
186C3⋊C8—68no—
187C2×C32#44711yescharacteristic
188C2×C32#45111yescharacteristic
189C2×C32#45611yescharacteristic
190C3⋊D3—42no—
191C2×Q8—21no—
192C2×Q8—91no—
193C2×Q8—182no—
194C2×Q8—181no—
195C2×Q8—362no—
196C2×Q8—362no—
197C2×D4—91no—
198C22×C4—182no—
199C22×C4—181no—
200Q16—362no—
201C2×C8—21no—
202C2×C8—21no—
203C2×C8—181no—
204C4⋊C4—21no—
205C4⋊C4—91no—
206C4⋊C4—91no—
207C4⋊C4—182no—
208C4⋊C4—181no—
209C4⋊C4—181no—
210C4⋊C4—181no—
211C4⋊C4C4⋊(C3⋊D3)12yes—
212C22⋊C4—182no—
213C22⋊C4—181no—
214C42—181no—
215C42C22×C3⋊D311yescharacteristic
216C22×C3#88214yes—
217C2×D3—68no—
218C2×D3—124no—
219C2×D3—124no—
220C3×C4—24no—
221C3×C4—48no—
222C3×C4D3×D814yes—
223C3×C4#91414yes—
224C3×C4#91514yes—
225C3×C4D3×Q1614yes—
226Dic3—68no—
227Dic3—124no—
228Dic3—124no—
229Dic3—244no—
230C32#164911yescharacteristic, complemented, Sylow
231C23—181no—
232Q8—41no—
233Q8—41no—
234Q8—92no—
235Q8—181no—
236Q8—364no—
237Q8—361no—
238Q8—361no—
239D4—92no—
240D4—181no—
241C2×C4—22no—
242C2×C4—181no—
243C2×C4—181no—
244C2×C4—181no—
245C2×C4—364no—
246C2×C4—361no—
247C2×C4—361no—
248C2×C4—361no—
249C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
250C2×C4D4×C3⋊D311yescharacteristic
251C2×C4D4×C3⋊D311yescharacteristic
252C8—41no—
253C8—41no—
254C8—182no—
255C2×C3#475214yes—
256C2×C3#477314yes—
257C2×C3#480914yes—
258D3—128no—
259C22—182no—
260C22—361no—
261C22—361no—
262C22#6409111yescharacteristic
263C4—21no—
264C4—42no—
265C4—182no—
266C4—361no—
267C4—361no—
268C4—721no—
269C4D8×C3⋊D311yescharacteristic
270C4#6412311yescharacteristic
271C4#6412411yescharacteristic
272C4Q16×C3⋊D311yescharacteristic
273C3#6846114yescomplemented
274C2—362no—
275C2#1059245111yescharacteristic
276C2#1059247211yescharacteristic
277C2#1059250811yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#332C2
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#332C3⋊D3
hypocenterC32#1649
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #10592777C2semidirect
3. #10592548C2semidirect
5. C32×#332C2semidirect
6. #10589350C2semidirect
30. C3×#332D3semidirect
88. C4⋊(C3⋊D3)Q16semidirect
104. #332C3⋊D3semidirect
230. C32#1649semidirect
273. C3#68461semidirect

Maximal subgroups

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

subgroupindex
#105961982
#105927772
#105925482
#105925452
C32×#3322
#105893502
#105893492
#684613