Finite Group Databasebeta

← #13080418

Subgroups — #13080418

Order 1408.

444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C11×#578C211yesmaximal, characteristic, complemented
2#10623369C212yesmaximal, complemented
3#10623302C211yesmaximal, characteristic, complemented
4#10622859C212yesmaximal, complemented
5#10622818C212yesmaximal, complemented
6#10622817C212yesmaximal, complemented
7#10622809C211yesmaximal, characteristic, complemented
8#10622805C211yesmaximal, characteristic, complemented
9#10622794C211yesmaximal, characteristic, complemented
10#10622757C211yesmaximal, characteristic, complemented
11#10622756C211yesmaximal, characteristic, complemented
12C11×2−1+4C2212yes—
13#67043C2212yes—
14C11×#137—22no—
15C11×#137C2212yes—
16C11×#135—21no—
17C11×#135C2211yescharacteristic
18C2×C11×Q16—21no—
19C2×C11×Q16C2211yescharacteristic
20C11×#131C2211yescharacteristic
21#67004—22no—
22#67004C2212yes—
23#67004C2212yes—
24#67003—22no—
25#67003C2211yescharacteristic
26#67001C2212yes—
27#66997C2212yes—
28C2×#4326—22no—
29C2×#4326C2212yes—
30#66995—22no—
31#66995C2212yes—
32Q16×D11—21no—
33#66968—22no—
34#66965—21no—
35C2×Dic44C2211yescharacteristic
36#66954C2211yescharacteristic
37#66901C2211yescharacteristic
38#66901C2212yes—
39#66900C2212yes—
40#66889C2211yescharacteristic
41#66888C2212yes—
42#66886C2211yescharacteristic
43#66883C2211yescharacteristic
44C8×Dic11C2211yescharacteristic
45C11×#41—22no—
46C11×#41—22no—
47C11×#41—42no—
48C11×#41C2312yes—
49C11×#41C2311yescharacteristic
50C2×Q8×C11—22no—
51C2×Q8×C11—22no—
52C2×Q8×C11C2312yes—
53Q8×D11—22no—
54#4341—22no—
55#4341—42no—
56#4339—22no—
57#4339C2311yescharacteristic
58C2×Dic22—22no—
59C2×Dic22C2312yes—
60C11×Q16—21no—
61C11×Q16—21no—
62C11×Q16—22no—
63C11×Q16D411yescharacteristic
64C11×SD16—22no—
65C11×SD16D412yes—
66C11×D8D411yescharacteristic
67C11×M16—21no—
68C11×M16C2311yescharacteristic
69C2×C8×C11—21no—
70C2×C8×C11C2311yescharacteristic
71#4326—22no—
72#4326—22no—
73#4326—22no—
74#4326—22no—
75#4326—22no—
76#4326D411yescharacteristic
77#4325—22no—
78#4325D411yescharacteristic
79#4324—22no—
80#4324—22no—
81#4324D411yescharacteristic
82#4323D411yescharacteristic
83Dic11⋊C4—42no—
84C4×Dic11C2311yescharacteristic
85#4318—22no—
86#4318C2312yes—
87#4318C2311yescharacteristic
88C2×C11⋊C8—22no—
89C2×C11⋊C8C2311yescharacteristic
90Dic44—21no—
91Dic44—21no—
92#4313—21no—
93C8×D11—21no—
94#3293—111nomaximal, Sylow
95Q8×C11—22no—
96Q8×C11—22no—
97Q8×C11—42no—
98Q8×C11C2×D411yescharacteristic
99Q8×C11C2×D412yes—
100D4×C11—22no—
101D4×C11—21no—
102D4×C11—42no—
103D4×C11C2×D411yescharacteristic
104D4×C11C2×D412yes—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11C2411yescharacteristic
111C22⋊D11—21no—
112C22⋊D11—42no—
113C2×Dic11—21no—
114C2×Dic11—22no—
115C2×Dic11—42no—
116D44C2×D411yescharacteristic
117C4×D11—21no—
118C4×D11—42no—
119Dic22—22no—
120Dic22—22no—
121Dic22—42no—
122Dic22C2×D411yescharacteristic
123C8×C11—21no—
124C8×C11C2×D411yescharacteristic
125C8×C11C2×D411yescharacteristic
126C11⋊C8—21no—
127C11⋊C8—22no—
128C11⋊C8C2×D411yescharacteristic
129C11⋊C8C2×D411yescharacteristic
130#578—112no—
131#578—111no—
132#578D1111yescharacteristic, complemented
133#494—111no—
134#473—112no—
135#473—111no—
136#473—111no—
137#456—112no—
138#456—112no—
139#443—111no—
140#443—111no—
141C22×C11—21no—
142C22×C11—22no—
143C22×C11H(5,𝔽2)11yescharacteristic
144C2×D11—21no—
145C4×C11—21no—
146C4×C11—22no—
147C4×C11—42no—
148C4×C11C22×D411yescharacteristic
149C4×C11C22×D411yescharacteristic
150Dic11—22no—
151Dic11—21no—
152Dic11—42no—
1532−1+4—112no—
1542−1+4C2×D1112yes—
155#137—22no—
156#137—112no—
157#137—112no—
158#137—112no—
159#137—222no—
160#137—222no—
161#137—222no—
162#137C2×D1112yes—
163#135—21no—
164#135—111no—
165#135—222no—
166#135—221no—
167#135C2×D1111yescharacteristic
168C2×Q16—21no—
169C2×Q16—112no—
170C2×Q16—111no—
171C2×Q16—222no—
172C2×Q16—221no—
173C2×Q16C2×D1111yescharacteristic
174#131—112no—
175#131—111no—
176#131C2×D1111yescharacteristic
177C4⋊Q8—112no—
178#108—111no—
179#108—111no—
180#104—111no—
181#104—112no—
182#104—111no—
183#101—112no—
184#101—112no—
185C4×C8—111no—
186C2×C11—21no—
187C2×C11—41no—
188C2×C11—42no—
189C2×C11D4211yescharacteristic
190D11—41no—
191#41—22no—
192#41—22no—
193#41—42no—
194#41—111no—
195#41—222no—
196#41—222no—
197#41—442no—
198#41C22×D1111yescharacteristic
199#41C22×D1112yes—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—112no—
203C2×Q8—222no—
204C2×Q8—222no—
205C2×Q8C22×D1112yes—
206Q16—22no—
207Q16—21no—
208Q16—21no—
209Q16—111no—
210Q16—222no—
211Q16—222no—
212Q16—222no—
213Q16—222no—
214Q16—222no—
215Q16—221no—
216Q16—221no—
217Q16C22⋊D1111yescharacteristic
218SD16—22no—
219SD16—111no—
220SD16—111no—
221SD16—222no—
222SD16—222no—
223SD16—222no—
224SD16C22⋊D1112yes—
225D8—111no—
226D8C22⋊D1111yescharacteristic
227M16—21no—
228M16—112no—
229M16—111no—
230M16—222no—
231M16—221no—
232M16C22×D1111yescharacteristic
233C2×C8—21no—
234C2×C8—111no—
235C2×C8—222no—
236C2×C8—221no—
237C2×C8C22×D1111yescharacteristic
238C4⋊C4—442no—
239C42—111no—
240C11#329311yescharacteristic, complemented, Sylow
241Q8—22no—
242Q8—22no—
243Q8—42no—
244Q8—111no—
245Q8—222no—
246Q8—222no—
247Q8—442no—
248Q8D4×D1111yescharacteristic
249Q8C2×C22⋊D1112yes—
250D4—21no—
251D4—22no—
252D4—42no—
253D4—111no—
254D4—221no—
255D4—442no—
256D4D4×D1111yescharacteristic
257D4C2×C22⋊D1112yes—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—221no—
264C2×C4—221no—
265C2×C4—222no—
266C2×C4—442no—
267C2×C4—442no—
268C2×C4C23×D1111yescharacteristic
269C8—21no—
270C8—111no—
271C8—111no—
272C8—222no—
273C8—221no—
274C8C2×C22⋊D1111yescharacteristic
275C8C2×C22⋊D1111yescharacteristic
276C22—21no—
277C22—22no—
278C22—221no—
279C22#6703711yescharacteristic
280C4—21no—
281C4—22no—
282C4—42no—
283C4—222no—
284C4—221no—
285C4—442no—
286C4C2×D4×D1111yescharacteristic
287C4C22×C22⋊D1111yescharacteristic
288C2—21no—
289C2—41no—
290C2—42no—
291C2—441no—
292C2D4×C22⋊D1111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#578C2
socleC2×C11D42
hypercenter#578D11
hypocenterC11#3293
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #578

Complements

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

NH ≅ G/Ntype
1. C11×#578C2semidirect
2. #10623369C2semidirect
3. #10623302C2semidirect
4. #10622859C2semidirect
5. #10622818C2semidirect
6. #10622817C2semidirect
7. #10622809C2semidirect
8. #10622805C2semidirect
9. #10622794C2semidirect
10. #10622757C2semidirect
11. #10622756C2semidirect
132. #578D11semidirect
240. C11#3293semidirect

Maximal subgroups

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

subgroupindex
C11×#5782
#106233692
#106233022
#106228592
#106228182
#106228172
#106228092
#106228052
#106227942
#106227572
#106227562
#329311