Finite Group Databasebeta

← #14909641

Subgroups — #14909641

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#13070826C212yesmaximal, complemented
3#13070823C212yesmaximal, complemented
4#13070722C212yesmaximal, complemented
5#13070707C211yesmaximal, characteristic, complemented
6#13070551C212yesmaximal, complemented
7#13070548C212yesmaximal, complemented
8#13070229C211yesmaximal, characteristic
9C11×#2216C211yesmaximal, characteristic, complemented
10C2×Q16×D11C2212yes—
11C2×#66954C2211yescharacteristic
12#10623159—22no—
13C2×C11×Q32C2211yescharacteristic
14C22×C11×C16C2211yescharacteristic
15C11×#467C2212yes—
16#10622801C2212yes—
17C2×#66893C2212yes—
18#10622729C2212yes—
19C2×#66876C2211yescharacteristic
20#10622665—22no—
21C2×Dic88C2211yescharacteristic
22#10622500C2212yes—
23#10622493C2212yes—
24#10622429—22no—
25#10622415—22no—
26C11×#366C2211yescharacteristic
27C11×#358C2212yes—
28#10622202C2212yes—
29(C2×D11)⋊C16C2212yes—
30(C2×D11)⋊C16C2212yes—
31#10622142C2211yescharacteristic
32#10622141C2212yes—
33#10622130C2212yes—
34#10622128C2212yes—
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—
58C2×C11×C16—41no—
59C2×C11×C16C2311yescharacteristic
60C2×C11×C16C2311yescharacteristic
61C11×#107C2312yes—
62C11×#103—22no—
63#66899—22no—
64#66893—42no—
65#66882C2312yes—
66#66880—22no—
67#66876—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—112no—
119#2216—111no—
120#2216D1111yescharacteristic, complemented
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×M32—111no—
157C22×C16C2×D1111yescharacteristic
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—112no—
167#366—111no—
168#366C2×D1111yescharacteristic
169#358—112no—
170#358—112no—
171#358—112no—
172#358C2×D1112yes—
173C22⋊C16—112no—
174C22⋊C16—112no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11C22×D811yescharacteristic
179C2×D11—22no—
180C2×D11—22no—
181C2×D11—22no—
182C4×C11—21no—
183C4×C11—82no—
184C4×C11—82no—
185C4×C11#53411yescharacteristic
186C4×C11#57511yescharacteristic
187Dic11—22no—
188Dic11—82no—
189Dic11—82no—
190C2×#41—111no—
191C22×Q8—222no—
192C2×Q16—112no—
193C2×Q16—222no—
194C2×Q16—442no—
195C2×Q16—442no—
196C2×Q16C22×D1112yes—
197#131—441no—
198#131—441no—
199C2×M16—111no—
200C2×M16—112no—
201C22×C8—112no—
202C22×C8C22×D1111yescharacteristic
203C4⋊Q8—442no—
204#124—442no—
205#123—442no—
206#123—442no—
207C22⋊Q8—22no—
208C22⋊Q8—222no—
209C22⋊Q8—222no—
210C22⋊Q8—222no—
211#117—222no—
212Q32—41no—
213Q32—441no—
214Q32—442no—
215M32—441no—
216C2×C16—41no—
217C2×C16—112no—
218C2×C16C22×D1111yescharacteristic
219C2×C16C22×D1111yescharacteristic
220#107—112no—
221#107C22×D1112yes—
222#106—222no—
223#103—22no—
224#103—222no—
225#103—222no—
226#103—222no—
227C2×C11—41no—
228C2×C11#318611yescharacteristic
229C2×C11#341711yescharacteristic
230C2×C11#341711yescharacteristic
231D11—42no—
232#41—441no—
233#41—441no—
234C2×Q8—22no—
235C2×Q8—111no—
236C2×Q8—222no—
237C2×Q8—442no—
238C2×Q8—444no—
239C2×Q8—444no—
240C2×D4—112no—
241C2×D4—111no—
242C22×C4—112no—
243C22×C4—442no—
244C22×C4D4×D1111yescharacteristic
245Q16—22no—
246Q16—22no—
247Q16—222no—
248Q16—222no—
249Q16—444no—
250M16—442no—
251M16—441no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—112no—
255C2×C8—222no—
256C2×C8—222no—
257C2×C8D4×D1111yescharacteristic
258C2×C8C23×D1111yescharacteristic
259C4⋊C4—22no—
260C4⋊C4—42no—
261C4⋊C4—222no—
262C4⋊C4—442no—
263C4⋊C4—442no—
264C4⋊C4—442no—
265C22⋊C4—42no—
266C22⋊C4—442no—
267C22⋊C4—442no—
268C22⋊C4—442no—
269C22⋊C4—442no—
270C42—442no—
271C16—21no—
272C16—21no—
273C16—222no—
274C11#3376811yescharacteristic, complemented, Sylow
275C23—112no—
276C23D8×D1111yescharacteristic
277Q8—42no—
278Q8—42no—
279Q8—441no—
280Q8—442no—
281Q8—442no—
282Q8—884no—
283D4—441no—
284D4—442no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—112no—
290C2×C4—222no—
291C2×C4—222no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4—884no—
295C2×C4D8×D1111yescharacteristic
296C2×C4C2×D4×D1111yescharacteristic
297C8—21no—
298C8—222no—
299C8#6703711yescharacteristic
300C8#6704211yescharacteristic
301C22—21no—
302C22—21no—
303C22—21no—
304C22—222no—
305C22—222no—
306C22—222no—
307C22C2×D8×D1111yescharacteristic
308C4—21no—
309C4—82no—
310C4—82no—
311C4—222no—
312C4—882no—
313C4—882no—
314C4#1062313611yescharacteristic
315C4#1062329911yescharacteristic
316C2—41no—
317C2—442no—
318C2#1307936311yescharacteristic
319C2#1308176511yescharacteristic
320C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2216C2
socleC22×C11C22×D8
prime radicalC2×#4339D4
hypercenter#2216D11
hypocenterC11#33768
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2216

Complements

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

NH ≅ G/Ntype
2. #13070826C2semidirect
3. #13070823C2semidirect
4. #13070722C2semidirect
5. #13070707C2semidirect
6. #13070551C2semidirect
7. #13070548C2semidirect
9. C11×#2216C2semidirect
120. #2216D11semidirect
274. C11#33768semidirect

Maximal subgroups

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

subgroupindex
#130782662
#130708262
#130708232
#130707222
#130707072
#130705512
#130705482
#130702292
C11×#22162
#3376811