Finite Group Databasebeta

← #14910697

Subgroups — #14910697

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081046C211yesmaximal, characteristic, complemented
2#13080337C211yesmaximal, characteristic
3#13070845C211yesmaximal, characteristic, complemented
4#13070826C212yesmaximal, complemented
5#13070708C212yesmaximal, complemented
6#13070667C211yesmaximal, characteristic, complemented
7#13070557C212yesmaximal, complemented
8C4×#66891C211yesmaximal, characteristic, complemented
9#13070435C211yesmaximal, characteristic, complemented
10#13070320C212yesmaximal, complemented
11C11×#2224C211yesmaximal, characteristic, complemented
12C2×#66965C2212yes—
13#10623263—21no—
14#10623086—21no—
15C11×#500C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17C2×#66891C2211yescharacteristic
18#10622707—21no—
19#10622632—21no—
20C2×Dic88C2212yes—
21C2×C16×D11C2212yes—
22#10622501—22no—
23#10622500C2212yes—
24#10622500C2212yes—
25#10622493C2212yes—
26#10622396—22no—
27#10622312C2211yescharacteristic
28C4×Dic44C2211yescharacteristic
29C8×D44C2211yescharacteristic
30C11×#366C2212yes—
31C11×C4⋊C16C2211yescharacteristic
32C11×#357C2212yes—
33#10622200C2211yescharacteristic
34(C2×D11)⋊C16C2212yes—
35#10622141C2212yes—
36#10622130C2211yescharacteristic
37#10622130C2212yes—
38#10622130C2212yes—
39#10622128C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4341—22no—
42C2×C11×D8C2311yescharacteristic
43C11×C4⋊Q8—21no—
44C4×D4×C11—21no—
45#67000—41no—
46Q8×Dic11—41no—
47C2×#4324—22no—
48#66983—41no—
49C2×C4⋊Dic11—41no—
50#66965—24no—
51#66965—42no—
52C2×Dic44—21no—
53C2×Dic44C2311yescharacteristic
54C2×Dic44C2312yes—
55C2×C8×D11C2312yes—
56#66951—42no—
57#66950—22no—
58#66950—22no—
59#66945—22no—
60#66939—42no—
61C4×D44D411yescharacteristic
62#66922—21no—
63C4×Dic22—21no—
64C2×C11×C16C2312yes—
65C11×#107—21no—
66C11×#107C2312yes—
67C11×#107C2311yescharacteristic
68C11×#102—21no—
69C4×C8×C11C2311yescharacteristic
70#66891—22no—
71(C2×D11)⋊C8D412yes—
72#66882C2311yescharacteristic
73#66880—21no—
74C2×C11⋊C16C2311yescharacteristic
75C2×C11⋊C16C2311yescharacteristic
76#66874—22no—
77#66874—22no—
78#66872—22no—
79C4⋊(C11⋊C8)D411yescharacteristic
80Dic88—42no—
81C16×D11—42no—
82#33869—111nomaximal, Sylow
83C2×Q8×C11—41no—
84C2×D4×C11—21no—
85C22×C4×C11—41no—
86C2×C22⋊D11—42no—
87C22×Dic11—42no—
88#4341—44no—
89#4341—82no—
90C2×D44D811yescharacteristic
91C2×C4×D11C2×D412yes—
92C2×Dic22—21no—
93C2×Dic22—22no—
94C11×D8—21no—
95C11×D8#4112yes—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2411yescharacteristic
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103#4324—44no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4D812yes—
108C4⋊Dic11—21no—
109C4⋊Dic11—42no—
110C4⋊Dic11—42no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11D811yescharacteristic
114Dic11⋊C4—41no—
115C4×Dic11—42no—
116C4×Dic11—41no—
117C2×C11⋊C8C2×D412yes—
118Dic44—21no—
119Dic44—22no—
120Dic44—21no—
121Dic44—22no—
122Dic44—81no—
123C8×D11—22no—
124C8×D11—22no—
125C11×C16—22no—
126C11⋊C16—21no—
127C11⋊C16—21no—
128#3342—111no—
129#3283—111no—
130#2241—111no—
131#2237—112no—
132#2224D1111yescharacteristic, complemented
133#2216—112no—
134#2209—111no—
135#2189—112no—
136C4×SD32—111no—
137D4×C16—111no—
138#2138—112no—
139C23×C11—41no—
140C22×D11C2×D812yes—
141Q8×C11—82no—
142D4×C11—22no—
143D4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—82no—
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C22×D411yescharacteristic
150C22⋊D11—84no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—84no—
155C2×Dic11C2×D812yes—
156D44—22no—
157C4×D11—22no—
158C4×D11—22no—
159Dic22—42no—
160Dic22—41no—
161Dic22—42no—
162Dic22—41no—
163C8×C11—21no—
164C8×C11C2×#4111yescharacteristic
165C8×C11H(5,𝔽2)11yescharacteristic
166C11⋊C8—22no—
167C2×#135—112no—
168#556—221no—
169#547—221no—
170C2×Q32—112no—
171C2×SD32—111no—
172C22×C16—112no—
173#500C2×D1111yescharacteristic
174#494—111no—
175#485—222no—
176#475—221no—
177#467—112no—
178#467—112no—
179#461—221no—
180#452—222no—
181C4×Q16—111no—
182C4×D8C2×D1111yescharacteristic
183C8×D4—111no—
184#427—112no—
185#367—111no—
186#366C2×D1112yes—
187C4⋊C16C2×D1111yescharacteristic
188#358—112no—
189#358—112no—
190#358—111no—
191#358—112no—
192#357—111no—
193#357C2×D1112yes—
194C22⋊C16—112no—
195C4×C16—111no—
196C22×C11—42no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11C22×D811yescharacteristic
200C2×D11—22no—
201C2×D11—22no—
202C2×D11—22no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11—82no—
206C4×C11#50812yes—
207C4×C11#54611yescharacteristic
208C4×C11#57711yescharacteristic
209Dic11—22no—
210Dic11—81no—
211Dic11—81no—
212Dic11—82no—
213C2×#41—222no—
214#135—224no—
215#135—442no—
216C2×Q16—112no—
217C2×Q16—111no—
218C2×Q16—221no—
219C2×SD16—222no—
220C2×D8C22×D1111yescharacteristic
221C22×C8—112no—
222C4⋊Q8—21no—
223C4⋊Q8—221no—
224#126—442no—
225#124—441no—
226#123—442no—
227C22⋊Q8—222no—
228C22⋊Q8—222no—
229#121—441no—
230C4×Q8—221no—
231C4×Q8—441no—
232C4×D4—21no—
233C4×D4—111no—
234#117—222no—
235C2×C4⋊C4—441no—
236Q32—442no—
237SD32—222no—
238C2×C16—111no—
239C2×C16—111no—
240C2×C16—442no—
241C2×C16C22×D1112yes—
242#107—21no—
243#107—111no—
244#107C22×D1112yes—
245#107C22×D1111yescharacteristic
246#106—222no—
247C4⋊C8—111no—
248#103—222no—
249#103—222no—
250#103—221no—
251#102—21no—
252C22⋊C8—112no—
253C4×C8C22×D1111yescharacteristic
254C2×C11—82no—
255C2×C11#329411yescharacteristic
256C2×C11C2×#50811yescharacteristic
257C2×C11#341711yescharacteristic
258D11—42no—
259#41—444no—
260#41—882no—
261C2×Q8—41no—
262C2×Q8—221no—
263C2×Q8—222no—
264C2×D4—21no—
265C2×D4—111no—
266C2×D4—442no—
267C22×C4—41no—
268C22×C4—112no—
269C22×C4—442no—
270Q16—221no—
271Q16—222no—
272Q16—221no—
273Q16—222no—
274Q16—881no—
275SD16—444no—
276D8—21no—
277D8#434312yes—
278C2×C8—112no—
279C2×C8—222no—
280C2×C8—222no—
281C2×C8D4×D1111yescharacteristic
282C2×C8C23×D1111yescharacteristic
283C4⋊C4—21no—
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—111no—
287C4⋊C4—221no—
288C4⋊C4—442no—
289C4⋊C4—442no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C22⋊C4—41no—
294C22⋊C4—112no—
295C22⋊C4—442no—
296C22⋊C4—442no—
297C22⋊C4—442no—
298C42—442no—
299C42—441no—
300C42D4×D1111yescharacteristic
301C16—22no—
302C16—221no—
303C16—221no—
304C11#3386911yescharacteristic, complemented, Sylow
305C23—41no—
306C23—112no—
307Q8—82no—
308Q8—442no—
309Q8—441no—
310Q8—442no—
311Q8—441no—
312D4—22no—
313D4—41no—
314D4—222no—
315D4—884no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—82no—
319C2×C4—112no—
320C2×C4—222no—
321C2×C4—222no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—442no—
325C2×C4—884no—
326C2×C4D8×D1111yescharacteristic
327C2×C4D8×D1111yescharacteristic
328C2×C4C2×D4×D1111yescharacteristic
329C8—21no—
330C8—222no—
331C8C2×#434311yescharacteristic
332C8#6704211yescharacteristic
333C22—42no—
334C22—81no—
335C22—81no—
336C22—222no—
337C22—222no—
338C22—222no—
339C22C2×D8×D1111yescharacteristic
340C4—21no—
341C4—81no—
342C4—82no—
343C4—222no—
344C4—882no—
345C4—881no—
346C4—881no—
347C4#1062252512yes—
348C4#1062316111yescharacteristic
349C4#1062330911yescharacteristic
350C2—82no—
351C2—442no—
352C2#1308042611yescharacteristic
353C2C2×#1062252511yescharacteristic
354C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2224C2
socleC22×C11C22×D8
prime radical#13080337C2
hypercenter#2224D11
hypocenterC11#33869
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
1. #13081046C2semidirect
3. #13070845C2semidirect
4. #13070826C2semidirect
5. #13070708C2semidirect
6. #13070667C2semidirect
7. #13070557C2semidirect
8. C4×#66891C2semidirect
9. #13070435C2semidirect
10. #13070320C2semidirect
11. C11×#2224C2semidirect
132. #2224D11semidirect
304. C11#33869semidirect

Maximal subgroups

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

subgroupindex
#130810462
#130803372
#130708452
#130708262
#130707082
#130706672
#130705572
C4×#668912
#130704352
#130703202
C11×#22242
#3386911