Finite Group Databasebeta

← #11795374

Subgroups — #11795374

Order 1152.

822 conjugacy classes of subgroups; only the 215 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 215 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
1C2×C32×#107C211yesmaximal, characteristic, complemented
2C2×#63648C211yesmaximal, characteristic
3#10592687C211yesmaximal, characteristic
4#10592676C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic
6C2×#63635C211yesmaximal, characteristic, complemented
7#10589416C211yesmaximal, characteristic, complemented
8#70640—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×C32×C8C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3752—22no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C32×#107—22no—
18#63658—22no—
19#63648—22no—
20#63636—22no—
21#63635—22no—
22C2×C3×#107D314yescomplemented
23C2×#821—34no—
24#4988—34no—
25#4977—34no—
26C2×#809—34no—
27C2×#808—34no—
28#4550—34no—
29C23×C3⋊D3—21no—
30C22×C32×C4—21no—
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3D412yes—
35C2×C4⋊(C3⋊D3)—21no—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)Q812yes—
41C2×C32×C8—21no—
42C2×C32×C8—21no—
43C2×C32×C8D412yes—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48#3752—44no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)D412yes—
56#2092—91noSylow
57C22×D12—34no—
58C22×C3×C8C2×D314yes—
59C2×C3×C4⋊C4C2×D314yes—
60C2×C3×C4⋊C4C2×D314yes—
61C2×(C2×D3)⋊C4—68no—
62C2×C4⋊Dic3—34no—
63C2×C4×Dic3—34no—
64C22×C3⋊C8—34no—
65C3×#107—28no—
66C3⋊#95—68no—
67#821—68no—
68#809—68no—
69#808—68no—
70C23×C32C2×D411yescharacteristic
71C22×C3⋊D3—22no—
72C22×C3⋊D3—41no—
73C22×C3⋊D3—41no—
74C22×C3⋊D3—42no—
75C22×C3⋊D3—42no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4—42no—
79C2×C32×C4—42no—
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×Q811yescharacteristic
83C2×C32×C4#4111yescharacteristic
84C2×C32×C4#4111yescharacteristic
85C2×C32×C4#4111yescharacteristic
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3—42no—
91C4⋊(C3⋊D3)—22no—
92C4⋊(C3⋊D3)—22no—
93C4⋊(C3⋊D3)—41no—
94C4⋊(C3⋊D3)—41no—
95C32×C8—22no—
96C3⋊(C3⋊C8)—22no—
97C2×#107C3⋊D311yescharacteristic, complemented
98C2×#106—91no—
99C2×#102—91no—
100C2×#102—91no—
101#390—91no—
102#382—91no—
103#336—91no—
104C23×D3—64no—
105C22×C3×C4—24no—
106C22×C3×C4—24no—
107C22×C3×C4C22×D314yes—
108C22×Dic3—38no—
109C22×Dic3—64no—
110C2×D12—38no—
111C2×D12—64no—
112C2×D12—64no—
113C2×D12—64no—
114C2×D12—64no—
115C2×D12—64no—
116C2×C3×C8—24no—
117C2×C3×C8—24no—
118C2×C3×C8#6718yes—
119C3×C4⋊C4—24no—
120C3×C4⋊C4—24no—
121C3×C4⋊C4—24no—
122C3×C4⋊C4—24no—
123(C2×D3)⋊C4—1216no—
124C4⋊Dic3—64no—
125C4⋊Dic3—64no—
126C4×Dic3—64no—
127C4×Dic3—64no—
128C2×C3⋊C8—38no—
129C2×C3⋊C8—64no—
130C2×C3⋊C8—64no—
131C22×C32C22⋊Q811yescharacteristic
132C22×C32#12311yescharacteristic
133C22×C32#12711yescharacteristic
134C22×C32#13512yes—
135C22×C32AGL(1,ℤ/8)12yes—
136C2×C3⋊D3—42no—
137C2×C3⋊D3—44no—
138C2×C3⋊D3—82no—
139C2×C3⋊D3—81no—
140C2×C3⋊D3—81no—
141C32×C4—81no—
142C32×C4—81no—
143C32×C4C22⋊Q811yescharacteristic
144C32×C4C22⋊Q811yescharacteristic
145C32×C4#12311yescharacteristic
146C32×C4#12311yescharacteristic
147C3⋊Dic3—42no—
148C3⋊Dic3—81no—
149C22×D4—91no—
150C22×C8—91no—
151C22×C8C2×C3⋊D311yescharacteristic
152C2×C4⋊C4—91no—
153C2×C4⋊C4C2×C3⋊D311yescharacteristic
154C2×C4⋊C4C2×C3⋊D311yescharacteristic
155C2×C22⋊C4—182no—
156C2×C42—91no—
157#107—22no—
158#106—182no—
159#102—182no—
160#102—182no—
161#95—182no—
162C23×C3D3×D414yes—
163C22×D3—68no—
164C22×D3—124no—
165C22×D3—128no—
166C22×D3—128no—
167C22×D3—124no—
168C2×C3×C4—48no—
169C2×C3×C4—48no—
170C2×C3×C4—44no—
171C2×C3×C4—44no—
172C2×C3×C4#23514yes—
173C2×C3×C4#23514yes—
174C2×C3×C4D3×D414yes—
175C2×C3×C4D3×Q814yes—
176C2×C3×C4#23914yes—
177C2×C3×C4C2×#6714yes—
178C2×Dic3—68no—
179C2×Dic3—68no—
180C2×Dic3—68no—
181C2×Dic3—128no—
182C2×Dic3—124no—
183D12—68no—
184D12—68no—
185D12—124no—
186D12—124no—
187C3×C8—28no—
188C3⋊C8—68no—
189C2×C32#39911yescharacteristic
190C2×C32#47812yes—
191C2×C32#48212yes—
192C2×C32#49511yescharacteristic
193C2×C32#49611yescharacteristic
194C3⋊D3—82no—
195C24—181no—
196C2×D4—92no—
197C2×D4—181no—
198C2×D4—181no—
199C2×D4—181no—
200C2×D4—181no—
201C2×D4—181no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—92no—
205C22×C4—181no—
206C22×C4C22×C3⋊D311yescharacteristic
207C2×C8—21no—
208C2×C8—21no—
209C2×C8—92no—
210C2×C8—181no—
211C2×C8—181no—
212C2×C8#63812yes—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C22⋊C4—364no—
220C42—181no—
221C42—181no—
222C22×C3#89414yes—
223C22×C3#89614yes—
224C22×C3#91118yes—
225C22×C3#91918yes—
226C22×C3#94014yes—
227C2×D3—1216no—
228C2×D3—128no—
229C2×D3—248no—
230C2×D3—244no—
231C2×D3—244no—
232C3×C4—84no—
233C3×C4—84no—
234C3×C4#89414yes—
235C3×C4#89614yes—
236C3×C4#92914yes—
237C3×C4#94614yes—
238Dic3—128no—
239Dic3—244no—
240C32#209211yescharacteristic, complemented, Sylow
241C23—182no—
242C23—361no—
243C23—362no—
244C23—362no—
245C23—361no—
246C23D4×C3⋊D311yescharacteristic
247D4—182no—
248D4—182no—
249D4—361no—
250D4—361no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—182no—
256C2×C4—182no—
257C2×C4—182no—
258C2×C4—362no—
259C2×C4—361no—
260C2×C4#382811yescharacteristic
261C2×C4#382811yescharacteristic
262C2×C4D4×C3⋊D311yescharacteristic
263C2×C4Q8×C3⋊D311yescharacteristic
264C2×C4#383211yescharacteristic
265C2×C4C2×#63811yescharacteristic
266C8—22no—
267C8—182no—
268C2×C3#488518yes—
269C2×C3#489118yes—
270C2×C3#499314yes—
271C2×C3#515414yes—
272C2×C3#519114yes—
273D3—248no—
274C22—364no—
275C22—362no—
276C22—722no—
277C22—721no—
278C22—721no—
279C22#6410311yescharacteristic
280C22#6410511yescharacteristic
281C22#6412012yes—
282C22#6412812yes—
283C22#6414911yescharacteristic
284C4—81no—
285C4—81no—
286C4—362no—
287C4—721no—
288C4#6410311yescharacteristic
289C4#6410511yescharacteristic
290C4#6413811yescharacteristic
291C4#6415511yescharacteristic
292C3#7064014yescomplemented
293C2—722no—
294C2#1059258412yes—
295C2#1059259012yes—
296C2#1059269211yescharacteristic
297C2#1059285311yescharacteristic
298C2#1059289011yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#107C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×#107C3⋊D3
hypocenterC32#2092
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×C32×#107C2semidirect
4. #10592676C2semidirect
6. C2×#63635C2semidirect
7. #10589416C2semidirect
22. C2×C3×#107D3semidirect
97. C2×#107C3⋊D3semidirect
240. C32#2092semidirect
292. C3#70640semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1072
C2×#636482
#105926872
#105926762
C2×#636362
C2×#636352
#105894162
#706403