Finite Group Databasebeta

← #11795420

Subgroups — #11795420

Order 1152.

870 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 870 conjugacy classes of subgroups — too many to draw. Only its 219 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#10592674C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic
6C2×#63634C211yesmaximal, characteristic, complemented
7#10589416C211yesmaximal, characteristic, complemented
8#70641—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×#3750—22no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C32×#107—22no—
19#63648—22no—
20#63636—22no—
21#63634—22no—
22C2×C3×#107D314yescomplemented
23C2×#821—34no—
24#4988—34no—
25#4975—34no—
26C2×#809—34no—
27C2×#807—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—
51#3750—44no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)D412yes—
57#2093—91noSylow
58C22×D12—34no—
59C22×C3×C8C2×D314yes—
60C2×C3×C4⋊C4C2×D314yes—
61C2×C3×C4⋊C4C2×D314yes—
62C2×(C2×D3)⋊C4—68no—
63C2×C4⋊Dic3—34no—
64C2×Dic3⋊C4—68no—
65C2×C4×Dic3—34no—
66C22×C3⋊C8—34no—
67C3×#107—28no—
68#821—68no—
69#809—68no—
70#807—68no—
71C23×C32C2×D411yescharacteristic
72C22×C3⋊D3—22no—
73C22×C3⋊D3—41no—
74C22×C3⋊D3—41no—
75C22×C3⋊D3—42no—
76C22×C3⋊D3—42no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4—42no—
80C2×C32×C4—42no—
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×Q811yescharacteristic
84C2×C32×C4#4111yescharacteristic
85C2×C32×C4#4111yescharacteristic
86C2×C32×C4#4111yescharacteristic
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3—42no—
91C2×C3⋊Dic3D814yes—
92C4⋊(C3⋊D3)—22no—
93C4⋊(C3⋊D3)—22no—
94C4⋊(C3⋊D3)—41no—
95C4⋊(C3⋊D3)—41no—
96C32×C8—22no—
97C3⋊(C3⋊C8)—22no—
98C2×#107—91no—
99C2×#107C3⋊D311yescharacteristic, complemented
100C2×#102—91no—
101C2×#102—91no—
102#390—91no—
103#384—91no—
104#336—91no—
105C23×D3—64no—
106C22×C3×C4—24no—
107C22×C3×C4—24no—
108C22×C3×C4C22×D314yes—
109C22×Dic3—38no—
110C22×Dic3—64no—
111C2×D12—38no—
112C2×D12—64no—
113C2×D12—64no—
114C2×D12—64no—
115C2×D12—64no—
116C2×D12—64no—
117C2×C3×C8—24no—
118C2×C3×C8—24no—
119C2×C3×C8#6718yes—
120C3×C4⋊C4—24no—
121C3×C4⋊C4—24no—
122C3×C4⋊C4—24no—
123C3×C4⋊C4—24no—
124(C2×D3)⋊C4—1216no—
125C4⋊Dic3—64no—
126C4⋊Dic3—64no—
127Dic3⋊C4—1216no—
128C4×Dic3—64no—
129C4×Dic3—64no—
130C2×C3⋊C8—38no—
131C2×C3⋊C8—64no—
132C2×C3⋊C8—64no—
133C22×C32C22⋊Q811yescharacteristic
134C22×C32#12311yescharacteristic
135C22×C32#12711yescharacteristic
136C22×C32C2×D812yes—
137C22×C32#13712yes—
138C2×C3⋊D3—42no—
139C2×C3⋊D3—44no—
140C2×C3⋊D3—82no—
141C2×C3⋊D3—81no—
142C2×C3⋊D3—81no—
143C32×C4—81no—
144C32×C4—81no—
145C32×C4C22⋊Q811yescharacteristic
146C32×C4C22⋊Q811yescharacteristic
147C32×C4#12311yescharacteristic
148C32×C4#12311yescharacteristic
149C3⋊Dic3—24no—
150C3⋊Dic3—81no—
151C22×D4—91no—
152C22×C8—91no—
153C22×C8C2×C3⋊D311yescharacteristic
154C2×C4⋊C4—91no—
155C2×C4⋊C4—182no—
156C2×C4⋊C4C2×C3⋊D311yescharacteristic
157C2×C4⋊C4C2×C3⋊D311yescharacteristic
158C2×C22⋊C4—182no—
159C2×C42—91no—
160#107—22no—
161#107—182no—
162#102—182no—
163#102—182no—
164C23×C3D3×D414yes—
165C22×D3—68no—
166C22×D3—124no—
167C22×D3—128no—
168C22×D3—128no—
169C22×D3—124no—
170C2×C3×C4—48no—
171C2×C3×C4—48no—
172C2×C3×C4—44no—
173C2×C3×C4—44no—
174C2×C3×C4#23514yes—
175C2×C3×C4#23514yes—
176C2×C3×C4D3×D414yes—
177C2×C3×C4D3×Q814yes—
178C2×C3×C4#23914yes—
179C2×C3×C4C2×#6714yes—
180C2×Dic3—316no—
181C2×Dic3—68no—
182C2×Dic3—68no—
183C2×Dic3—128no—
184C2×Dic3—124no—
185D12—68no—
186D12—68no—
187D12—124no—
188D12—124no—
189C3×C8—28no—
190C3⋊C8—68no—
191C2×C32#39911yescharacteristic
192C2×C32#47412yes—
193C2×C32#48012yes—
194C2×C32#49311yescharacteristic
195C2×C32#49711yescharacteristic
196C3⋊D3—82no—
197C24—181no—
198C2×D4—92no—
199C2×D4—181no—
200C2×D4—181no—
201C2×D4—181no—
202C2×D4—181no—
203C2×D4—181no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—92no—
207C22×C4—181no—
208C22×C4C22×C3⋊D311yescharacteristic
209C2×C8—21no—
210C2×C8—21no—
211C2×C8—92no—
212C2×C8—181no—
213C2×C8—181no—
214C2×C8#63812yes—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C4⋊C4—364no—
222C22⋊C4—364no—
223C42—181no—
224C42—181no—
225C22×C3#89414yes—
226C22×C3#89614yes—
227C22×C3D3×D818yes—
228C22×C3#91818yes—
229C22×C3#94014yes—
230C2×D3—1216no—
231C2×D3—128no—
232C2×D3—248no—
233C2×D3—244no—
234C2×D3—244no—
235C3×C4—84no—
236C3×C4—84no—
237C3×C4#89414yes—
238C3×C4#89614yes—
239C3×C4#92914yes—
240C3×C4#94614yes—
241Dic3—616no—
242Dic3—244no—
243C32#209311yescharacteristic, complemented, Sylow
244C23—182no—
245C23—361no—
246C23—362no—
247C23—362no—
248C23—361no—
249C23D4×C3⋊D311yescharacteristic
250D4—182no—
251D4—182no—
252D4—361no—
253D4—361no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—94no—
259C2×C4—182no—
260C2×C4—182no—
261C2×C4—362no—
262C2×C4—361no—
263C2×C4#382811yescharacteristic
264C2×C4#382811yescharacteristic
265C2×C4D4×C3⋊D311yescharacteristic
266C2×C4Q8×C3⋊D311yescharacteristic
267C2×C4#383211yescharacteristic
268C2×C4C2×#63811yescharacteristic
269C8—22no—
270C8—182no—
271C2×C3#488218yes—
272C2×C3#489018yes—
273C2×C3#499314yes—
274C2×C3#515114yes—
275C2×C3#519014yes—
276D3—248no—
277C22—364no—
278C22—362no—
279C22—722no—
280C22—721no—
281C22—721no—
282C22#6410311yescharacteristic
283C22#6410511yescharacteristic
284C22D8×C3⋊D312yes—
285C22#6412712yes—
286C22#6414911yescharacteristic
287C4—81no—
288C4—81no—
289C4—184no—
290C4—721no—
291C4#6410311yescharacteristic
292C4#6410511yescharacteristic
293C4#6413811yescharacteristic
294C4#6415511yescharacteristic
295C3#7064114yescomplemented
296C2—722no—
297C2#1059258112yes—
298C2#1059258912yes—
299C2#1059269211yescharacteristic
300C2#1059285011yescharacteristic
301C2#1059288911yescharacteristic
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#2093
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. #10592674C2semidirect
6. C2×#63634C2semidirect
7. #10589416C2semidirect
22. C2×C3×#107D3semidirect
99. C2×#107C3⋊D3semidirect
243. C32#2093semidirect
295. C3#70641semidirect

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
#105926742
C2×#636362
C2×#636342
#105894162
#706413