Finite Group Databasebeta

← #13078277

Subgroups — #13078277

Order 1408.

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

normal subgroups only

This group has 484 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#10623364C211yesmaximal, characteristic, complemented
2C2×#67003C211yesmaximal, characteristic, complemented
3C2×#66960C211yesmaximal, characteristic, complemented
4#10623041C211yesmaximal, characteristic, complemented
5C11×#417C211yesmaximal, characteristic, complemented
6#10622746C211yesmaximal, characteristic, complemented
7C2×#66872C211yesmaximal, characteristic, complemented
8#10622429C212yesmaximal, complemented
9#10622420C212yesmaximal, complemented
10#10622395C212yesmaximal, complemented
11#10622391C212yesmaximal, complemented
12C2×C11×#41C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C2×#4339C2211yescharacteristic
15C2×C11×M16C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17#67003—24no—
18#66999C2212yes—
19C2×#4326C2211yescharacteristic
20C2×#4325C2211yescharacteristic
21#66992—22no—
22#66991C2212yes—
23C2×#4324C2211yescharacteristic
24C2×#4323C2211yescharacteristic
25#66983—22no—
26#66983—21no—
27C2×C4⋊Dic11C2211yescharacteristic
28#66977—21no—
29C22×C11⋊C8C2211yescharacteristic
30#66960—24no—
31C2×#4313C2212yes—
32C2×C8×D11C2212yes—
33#66950—21no—
34#66950C2212yes—
35#66948—21no—
36#66948C2212yes—
37C11×#103C2212yes—
38C11×#102C2212yes—
39#66885C2212yes—
40#66880C2212yes—
41#66872C2212yes—
42#66872C2212yes—
43C11×#41—22no—
44C11×#41—22no—
45C2×Q8×C11C2311yescharacteristic
46C2×D4×C11—21no—
47C2×D4×C11C2311yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11C2311yescharacteristic
51C2×C22⋊D11—21no—
52C2×C22⋊D11—22no—
53C2×C22⋊D11D412yes—
54C22×Dic11—21no—
55#4339—22no—
56#4339—22no—
57#4339—22no—
58#4339—22no—
59C2×D44—22no—
60C2×D44D411yescharacteristic
61C2×D44C2311yescharacteristic
62C2×C4×D11—21no—
63C2×C4×D11C2312yes—
64C2×Dic22D411yescharacteristic
65C2×Dic22C2311yescharacteristic
66C11×M16—22no—
67C2×C8×C11C2312yes—
68C11×C4⋊C4—21no—
69C11×C4⋊C4C2312yes—
70C22⋊Dic11—22no—
71#4326—22no—
72#4325—22no—
73#4324—22no—
74#4323—22no—
75(C2×D11)⋊C4—22no—
76(C2×D11)⋊C4—22no—
77(C2×D11)⋊C4—22no—
78C4⋊Dic11—22no—
79C4⋊Dic11—21no—
80C4⋊Dic11C2312yes—
81Dic11⋊C4—22no—
82C2×C11⋊C8D414yescomplemented
83C2×C11⋊C8C2311yescharacteristic
84C2×C11⋊C8C2311yescharacteristic
85#4313—24no—
86C8×D11—24no—
87#3060—111nomaximal, Sylow
88C23×C11—21no—
89C23×C11C2×D411yescharacteristic
90C22×D11—21no—
91C22×D11C2×D412yes—
92Q8×C11—21no—
93Q8×C11—21no—
94D4×C11—21no—
95D4×C11—21no—
96D4×C11—42no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—42no—
100C2×C4×C11—81no—
101C2×C4×C11C2×D411yescharacteristic
102C2×C4×C11C2×D412yes—
103C2×C4×C11#4112yes—
104C2×C4×C11C2411yescharacteristic
105C22⋊D11—24no—
106C22⋊D11—42no—
107C22⋊D11—82no—
108C2×Dic11—22no—
109C2×Dic11—21no—
110C2×Dic11—81no—
111C2×Dic11C2×D412yes—
112D44—22no—
113D44—21no—
114D44—21no—
115D44—82no—
116C4×D11—22no—
117C4×D11—22no—
118C4×D11—42no—
119Dic22—22no—
120Dic22—21no—
121Dic22—21no—
122C8×C11—22no—
123C11⋊C8C2×D412yes—
124C11⋊C8C2×D412yes—
125C2×#135—111no—
126C2×#131—111no—
127#537—111no—
128#537—111no—
129#470—112no—
130#469—112no—
131#465—112no—
132#465—112no—
133C2×#106—111no—
134#417—111no—
135#417D1111yescharacteristic, complemented
136C22×C11—21no—
137C22×C11—21no—
138C22×C11—41no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11#12112yes—
142C22×C11C22×D411yescharacteristic
143C2×D11—22no—
144C2×D11—22no—
145C2×D11—22no—
146C2×D11—41no—
147C2×D11—41no—
148C2×D11—41no—
149C4×C11—41no—
150C4×C11—42no—
151C4×C11#12112yes—
152C4×C11C22×D411yescharacteristic
153C4×C11C2×#4111yescharacteristic
154Dic11—22no—
155Dic11—41no—
156Dic11—42no—
157C2×#41—111no—
158C2×#41—111no—
159C2×#41C2×D1111yescharacteristic
160#135—224no—
161C2×Q16—111no—
162C2×SD16—111no—
163C2×SD16—111no—
164C2×D8—111no—
165#131—224no—
166C2×M16—112no—
167C2×M16C2×D1111yescharacteristic
168C22×C8—111no—
169C22×C8—112no—
170C22⋊Q8—112no—
171C22⋊Q8—112no—
172C22⋊Q8—221no—
173C22⋊Q8—221no—
174#121—112no—
175#121—112no—
176#121—221no—
177#121—222no—
178#121—221no—
179#121—222no—
180C2×C4⋊C4—111no—
181C2×C4⋊C4C2×D1111yescharacteristic
182#106—112no—
183#106—112no—
184#103—112no—
185#103C2×D1112yes—
186#102—112no—
187#102C2×D1112yes—
188C2×C11—22no—
189C2×C11—81no—
190C2×C11C2×#12111yescharacteristic
191C2×C11#57711yescharacteristic
192C2×C11#57711yescharacteristic
193D11—42no—
194D11—81no—
195#41—22no—
196#41—22no—
197#41—222no—
198#41—222no—
199#41—222no—
200#41—222no—
201C2×Q8—111no—
202C2×Q8—111no—
203C2×Q8C22×D1111yescharacteristic
204C2×D4—21no—
205C2×D4—112no—
206C2×D4—111no—
207C2×D4—111no—
208C2×D4—222no—
209C2×D4—221no—
210C2×D4—222no—
211C2×D4C22×D1111yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—112no—
215C22×C4—221no—
216C22×C4—221no—
217C22×C4C22×D1111yescharacteristic
218Q16—222no—
219SD16—222no—
220SD16—222no—
221D8—222no—
222M16—22no—
223M16—224no—
224C2×C8—114no—
225C2×C8—111no—
226C2×C8—111no—
227C2×C8—224no—
228C2×C8C22×D1112yes—
229C4⋊C4—21no—
230C4⋊C4—112no—
231C4⋊C4—222no—
232C4⋊C4—222no—
233C4⋊C4—221no—
234C4⋊C4C22×D1112yes—
235C22⋊C4—222no—
236C22⋊C4—222no—
237C22⋊C4—222no—
238C22⋊C4—222no—
239C11#306011yescharacteristic, complemented, Sylow
240C23—21no—
241C23—112no—
242C23—221no—
243C23D4×D1111yescharacteristic
244Q8—21no—
245Q8—21no—
246Q8—222no—
247Q8—221no—
248Q8—221no—
249D4—21no—
250D4—21no—
251D4—42no—
252D4—224no—
253D4—222no—
254D4—221no—
255D4—221no—
256D4—442no—
257D4—882no—
258D4—882no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—81no—
263C2×C4—112no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—222no—
267C2×C4—221no—
268C2×C4—442no—
269C2×C4—881no—
270C2×C4#433912yes—
271C2×C4D4×D1111yescharacteristic
272C2×C4D4×D1112yes—
273C2×C4C23×D1111yescharacteristic
274C8—22no—
275C8—112no—
276C8—112no—
277C22—21no—
278C22—21no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—222no—
283C22—222no—
284C22—222no—
285C22—441no—
286C22—441no—
287C22—441no—
288C22#6693712yes—
289C22C2×D4×D1111yescharacteristic
290C4—41no—
291C4—42no—
292C4—222no—
293C4—441no—
294C4—442no—
295C4#6693712yes—
296C4C2×#433911yescharacteristic
297C4C2×D4×D1111yescharacteristic
298C2—22no—
299C2—81no—
300C2—442no—
301C2—881no—
302C2C2×#6693711yescharacteristic
303C2#1062330611yescharacteristic
304C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#417C2
socleC22×C11C22×D4
hypercenter#417D11
hypocenterC11#3060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #10623364C2semidirect
2. C2×#67003C2semidirect
3. C2×#66960C2semidirect
4. #10623041C2semidirect
5. C11×#417C2semidirect
6. #10622746C2semidirect
7. C2×#66872C2semidirect
8. #10622429C2semidirect
9. #10622420C2semidirect
10. #10622395C2semidirect
11. #10622391C2semidirect
82. C2×C11⋊C8D4semidirect
135. #417D11semidirect
239. C11#3060semidirect

Maximal subgroups

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

subgroupindex
#106233642
C2×#670032
C2×#669602
#106230412
C11×#4172
#106227462
C2×#668722
#106224292
#106224202
#106223952
#106223912
#306011