Finite Group Databasebeta

← #14909643

Subgroups — #14909643

Order 2816.

552 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 127 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#13078266C212yesmaximal
2#13070827C212yesmaximal, complemented
3#13070822C212yesmaximal, complemented
4#13070724C211yesmaximal, characteristic, complemented
5#13070705C212yesmaximal, complemented
6#13070551C212yesmaximal, complemented
7#13070548C212yesmaximal, complemented
8#13070231C211yesmaximal, characteristic
9C11×#2219C211yesmaximal, characteristic, complemented
10C2×Q16×D11C2212yes—
11C2×#66954C2211yescharacteristic
12#10623159—22no—
13C2×C11×Q32C2211yescharacteristic
14C2×C11×M32C2211yescharacteristic
15C11×#467C2212yes—
16#10622801C2212yes—
17C2×#66893C2212yes—
18#10622729C2212yes—
19C22×C11⋊C16C2211yescharacteristic
20#10622665—22no—
21C2×Dic88C2211yescharacteristic
22#10622500C2212yes—
23#10622493C2212yes—
24#10622429—22no—
25#10622415—22no—
26C11×#367C2211yescharacteristic
27C11×#358C2212yes—
28#10622202C2212yes—
29(C2×D11)⋊C16C2212yes—
30(C2×D11)⋊C16C2212yes—
31#10622143C2211yescharacteristic
32#10622141C2212yes—
33#10622130C2212yes—
34#10622127C2212yes—
35C2×Q8×D11—22no—
36C2×#4339D411yescharacteristic
37C2×C11×Q16C2312yes—
38C22×C8×C11C2311yescharacteristic
39C11×C22⋊Q8—22no—
40#66999—22no—
41C2×#4326—22no—
42#66977—22no—
43C2×#4318D411yescharacteristic
44Q16×D11—42no—
45Q16×D11—42no—
46C2×Dic44C2312yes—
47#66954—41no—
48#66954—41no—
49C2×#4313D412yes—
50C2×C8×D11C2312yes—
51#66950—22no—
52#66947—42no—
53#66945—22no—
54#66941—42no—
55#66938—42no—
56#66936—42no—
57C11×Q32—41no—
58C11×M32—41no—
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107C2312yes—
62C11×#103—22no—
63#66899—22no—
64#66893—42no—
65#66882C2312yes—
66#66880—22no—
67C2×C11⋊C16—41no—
68C2×C11⋊C16C2312yes—
69#66874—22no—
70#66872—22no—
71Dic88—41no—
72#33768—111nomaximal, Sylow
73C2×Q8×C11—22no—
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11D812yes—
76Q8×D11—44no—
77Q8×D11—44no—
78#4339—41no—
79#4339—41no—
80C2×D44D811yescharacteristic
81C2×C4×D11—42no—
82C2×C4×D11C2×D412yes—
83C2×Dic22—22no—
84C2×Dic22—42no—
85C2×Dic22D811yescharacteristic
86C11×Q16—22no—
87C11×Q16—22no—
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2411yescharacteristic
92C11×C4⋊C4—22no—
93C11×C4⋊C4—42no—
94C11×C22⋊C4—42no—
95C22⋊Dic11—42no—
96#4326—44no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100C4⋊Dic11—22no—
101C4⋊Dic11—42no—
102Dic11⋊C4—42no—
103Dic11⋊C4—42no—
104C4×Dic11—42no—
105#4318—41no—
106C2×C11⋊C8C2×D412yes—
107Dic44—22no—
108Dic44—22no—
109#4313—42no—
110C8×D11—22no—
111C8×D11—22no—
112C11×C16—21no—
113C11×C16—21no—
114C11⋊C16—22no—
115#3059—112no—
116#2237—112no—
117#2237—112no—
118#2219—111no—
119#2219D1111yescharacteristic, complemented
120#2216—112no—
121#2188—112no—
122#2188—112no—
123#2113—111no—
124C23×C11C2×D811yescharacteristic
125C22×D11C2×D812yes—
126Q8×C11—42no—
127Q8×C11—42no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11C2×D811yescharacteristic
133C2×C4×C11C22×D411yescharacteristic
134C22⋊D11—42no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11C2×D812yes—
138D44—41no—
139C4×D11—22no—
140C4×D11—22no—
141C4×D11—84no—
142Dic22—41no—
143Dic22—42no—
144Dic22—42no—
145Dic22—84no—
146C8×C11—21no—
147C8×C11H(5,𝔽2)11yescharacteristic
148C8×C11H(5,𝔽2)11yescharacteristic
149C11⋊C8—22no—
150C22×Q16—112no—
151C2×#131—111no—
152#536—222no—
153C2×Q32—112no—
154C2×Q32—111no—
155C2×Q32C2×D1111yescharacteristic
156C2×M32C2×D1111yescharacteristic
157C22×C16—111no—
158#470—222no—
159#470—222no—
160#467—112no—
161#467—112no—
162#467—112no—
163#467C2×D1112yes—
164#427—112no—
165#419—222no—
166#367—111no—
167#367C2×D1111yescharacteristic
168#366—112no—
169#358—112no—
170#358—112no—
171#358—112no—
172#358C2×D1112yes—
173C22⋊C16—112no—
174C22⋊C16—112no—
175C22×C11—22no—
176C22×C11—21no—
177C22×C11C22×D811yescharacteristic
178C2×D11—24no—
179C2×D11—22no—
180C4×C11—21no—
181C4×C11—82no—
182C4×C11—82no—
183C4×C11#53411yescharacteristic
184C4×C11#57511yescharacteristic
185Dic11—22no—
186Dic11—82no—
187Dic11—82no—
188C2×#41—111no—
189C22×Q8—222no—
190C2×Q16—112no—
191C2×Q16—222no—
192C2×Q16—442no—
193C2×Q16—442no—
194C2×Q16C22×D1112yes—
195#131—441no—
196#131—441no—
197C2×M16—111no—
198C2×M16—112no—
199C22×C8—112no—
200C22×C8C22×D1111yescharacteristic
201C4⋊Q8—442no—
202#124—442no—
203#123—442no—
204#123—442no—
205C22⋊Q8—22no—
206C22⋊Q8—222no—
207C22⋊Q8—222no—
208C22⋊Q8—222no—
209#117—222no—
210Q32—41no—
211Q32—441no—
212Q32—442no—
213M32—41no—
214C2×C16—112no—
215C2×C16—441no—
216C2×C16C22×D1111yescharacteristic
217C2×C16C22×D1111yescharacteristic
218#107—112no—
219#107C22×D1112yes—
220#106—222no—
221#103—22no—
222#103—222no—
223#103—222no—
224#103—222no—
225C2×C11—41no—
226C2×C11#318611yescharacteristic
227C2×C11#341712yes—
228D11—42no—
229#41—441no—
230#41—441no—
231C2×Q8—22no—
232C2×Q8—111no—
233C2×Q8—222no—
234C2×Q8—442no—
235C2×Q8—444no—
236C2×Q8—444no—
237C2×D4—112no—
238C2×D4—111no—
239C22×C4—112no—
240C22×C4—442no—
241C22×C4D4×D1111yescharacteristic
242Q16—22no—
243Q16—22no—
244Q16—222no—
245Q16—222no—
246Q16—444no—
247M16—442no—
248M16—441no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—112no—
252C2×C8—222no—
253C2×C8—222no—
254C2×C8D4×D1111yescharacteristic
255C2×C8C23×D1111yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—42no—
258C4⋊C4—222no—
259C4⋊C4—442no—
260C4⋊C4—442no—
261C4⋊C4—442no—
262C22⋊C4—42no—
263C22⋊C4—442no—
264C22⋊C4—442no—
265C22⋊C4—442no—
266C22⋊C4—442no—
267C42—442no—
268C16—21no—
269C16—21no—
270C16—222no—
271C11#3376811yescharacteristic, complemented, Sylow
272C23—112no—
273C23D8×D1111yescharacteristic
274Q8—42no—
275Q8—42no—
276Q8—441no—
277Q8—442no—
278Q8—442no—
279Q8—884no—
280D4—441no—
281D4—442no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—112no—
287C2×C4—222no—
288C2×C4—222no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4—884no—
292C2×C4D8×D1111yescharacteristic
293C2×C4C2×D4×D1111yescharacteristic
294C8—21no—
295C8—222no—
296C8#6703711yescharacteristic
297C8#6704211yescharacteristic
298C22—21no—
299C22—22no—
300C22—222no—
301C22—224no—
302C22C2×D8×D1111yescharacteristic
303C4—21no—
304C4—82no—
305C4—82no—
306C4—222no—
307C4—882no—
308C4—882no—
309C4#1062313611yescharacteristic
310C4#1062329911yescharacteristic
311C2—41no—
312C2—442no—
313C2#1307936311yescharacteristic
314C2#1308176812yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2219C2
socleC22×C11C22×D8
prime radicalC2×#4339D4
hypercenter#2219D11
hypocenterC11#33768
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
2. #13070827C2semidirect
3. #13070822C2semidirect
4. #13070724C2semidirect
5. #13070705C2semidirect
6. #13070551C2semidirect
7. #13070548C2semidirect
9. C11×#2219C2semidirect
119. #2219D11semidirect
271. C11#33768semidirect

Maximal subgroups

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

subgroupindex
#130782662
#130708272
#130708222
#130707242
#130707052
#130705512
#130705482
#130702312
C11×#22192
#3376811