Finite Group Databasebeta

← #14910702

Subgroups — #14910702

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#13081048C211yesmaximal, characteristic, complemented
2#13080337C211yesmaximal, characteristic
3#13070844C211yesmaximal, characteristic, complemented
4#13070827C212yesmaximal, complemented
5#13070753C211yesmaximal, characteristic, complemented
6#13070706C212yesmaximal, complemented
7#13070666C211yesmaximal, characteristic, complemented
8#13070553C212yesmaximal, complemented
9C16×D44C211yesmaximal, characteristic, complemented
10#13070320C212yesmaximal, complemented
11C4×C11×SD32C211yesmaximal, characteristic, complemented
12C2×#66965C2212yes—
13#10623115—21no—
14#10623086—21no—
15C2×C11×SD32C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17C4×C11×D8C2211yescharacteristic
18#10622801C2212yes—
19C2×#66893C2212yes—
20#10622633—21no—
21#10622632—21no—
22C2×C16×D11C2212yes—
23#10622500C2212yes—
24#10622493C2212yes—
25#10622427—22no—
26#10622396—22no—
27#10622312C2211yescharacteristic
28C8×D44C2211yescharacteristic
29#10622295C2211yescharacteristic
30C11×#367C2211yescharacteristic
31C11×#358C2211yescharacteristic
32C11×#357C2211yescharacteristic
33C4×C11×C16C2211yescharacteristic
34#10622200C2212yes—
35(C2×D11)⋊C16C2212yes—
36#10622141C2212yes—
37#10622141C2212yes—
38#10622130C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4341—22no—
42C2×C11×Q16C2311yescharacteristic
43C2×C11×D8C2311yescharacteristic
44C4×Q8×C11—21no—
45C4×D4×C11—21no—
46#66999—22no—
47C2×#4324—22no—
48#66983—41no—
49C2×C4⋊Dic11—41no—
50#66965—24no—
51#66965—42no—
52C2×Dic44—21no—
53C2×Dic44C2312yes—
54C2×C8×D11C2312yes—
55#66951—42no—
56#66950—22no—
57#66945—22no—
58#66939—42no—
59#66928—41no—
60C4×D44D411yescharacteristic
61#66922—21no—
62#66922—21no—
63C4×Dic22—41no—
64C11×SD32—22no—
65C2×C11×C16C2311yescharacteristic
66C2×C11×C16C2311yescharacteristic
67C11×#107C2311yescharacteristic
68C11×#107C2311yescharacteristic
69C11×#103—21no—
70C11×#102—21no—
71C4×C8×C11C2311yescharacteristic
72#66899—22no—
73#66893—42no—
74(C2×D11)⋊C8D412yes—
75#66882—21no—
76#66882C2312yes—
77C2×C11⋊C16C2312yes—
78#66874—22no—
79#66872—22no—
80C4⋊(C11⋊C8)D411yescharacteristic
81C16×D11—42no—
82#33869—111nomaximal, Sylow
83C2×Q8×C11—21no—
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—22no—
93C2×Dic22—41no—
94C11×Q16—21no—
95C11×Q16—21no—
96C11×D8—21no—
97C11×D8#4112yes—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2411yescharacteristic
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—41no—
105C42×C11C2×D411yescharacteristic
106#4324—44no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4D812yes—
111C4⋊Dic11—22no—
112C4⋊Dic11—42no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11D811yescharacteristic
117Dic11⋊C4—42no—
118C4×Dic11—42no—
119C2×C11⋊C8C2×D412yes—
120Dic44—22no—
121Dic44—22no—
122Dic44—81no—
123C8×D11—22no—
124C8×D11—22no—
125C11×C16—21no—
126C11×C16—21no—
127C11⋊C16—22no—
128#3342—111no—
129#3283—111no—
130#2241—111no—
131#2237—112no—
132#2224—111no—
133#2216—112no—
134#2209—111no—
135#2189—112no—
136C4×SD32D1111yescharacteristic, complemented
137D4×C16—111no—
138#2138—112no—
139C23×C11—41no—
140C22×D11C2×D812yes—
141Q8×C11—41no—
142Q8×C11—41no—
143D4×C11—22no—
144D4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—82no—
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C22⋊D11—84no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—84no—
156C2×Dic11C2×D812yes—
157D44—22no—
158C4×D11—22no—
159C4×D11—22no—
160Dic22—42no—
161Dic22—42no—
162Dic22—82no—
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×SD32C2×D1111yescharacteristic
172C22×C16—112no—
173#500—111no—
174#494—111no—
175#485—222no—
176#475—221no—
177#467—112no—
178#467—112no—
179#461—221no—
180#452—222no—
181C4×Q16C2×D1111yescharacteristic
182C4×D8C2×D1111yescharacteristic
183C8×D4—111no—
184#427—112no—
185#367C2×D1111yescharacteristic
186#366—112no—
187C4⋊C16—111no—
188#358—112no—
189#358—112no—
190#358—112no—
191#358C2×D1111yescharacteristic
192#357—112no—
193#357C2×D1111yescharacteristic
194C22⋊C16—112no—
195C4×C16C2×D1111yescharacteristic
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—81no—
206C4×C11—81no—
207C4×C11#50812yes—
208C4×C11#54611yescharacteristic
209C4×C11#57711yescharacteristic
210Dic11—22no—
211Dic11—82no—
212Dic11—82no—
213C2×#41—222no—
214#135—224no—
215#135—442no—
216C2×Q16—112no—
217C2×Q16—221no—
218C2×Q16C22×D1111yescharacteristic
219C2×SD16—222no—
220C2×D8C22×D1111yescharacteristic
221C22×C8—112no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224#126—442no—
225#124—441no—
226#123—442no—
227C22⋊Q8—222no—
228C22⋊Q8—222no—
229#121—441no—
230C4×Q8—21no—
231C4×Q8—441no—
232C4×D4—21no—
233C4×D4—111no—
234#117—222no—
235C2×C4⋊C4—441no—
236Q32—442no—
237SD32—22no—
238C2×C16—112no—
239C2×C16—442no—
240C2×C16C22×D1111yescharacteristic
241C2×C16C22×D1111yescharacteristic
242#107—112no—
243#107—221no—
244#107C22×D1111yescharacteristic
245#107C22×D1111yescharacteristic
246#106—222no—
247C4⋊C8—111no—
248#103—21no—
249#103—222no—
250#103—222no—
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—21no—
262C2×Q8—222no—
263C2×Q8—441no—
264C2×D4—21no—
265C2×D4—111no—
266C2×D4—442no—
267C22×C4—41no—
268C22×C4—112no—
269C22×C4—442no—
270Q16—21no—
271Q16—21no—
272Q16—222no—
273Q16—222no—
274Q16—881no—
275SD16—444no—
276D8—21no—
277D8#433912yes—
278C2×C8—112no—
279C2×C8—222no—
280C2×C8—222no—
281C2×C8D4×D1111yescharacteristic
282C2×C8C23×D1111yescharacteristic
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—111no—
287C4⋊C4—222no—
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—41no—
299C42—442no—
300C42D4×D1111yescharacteristic
301C16—21no—
302C16—21no—
303C16—222no—
304C11#3386911yescharacteristic, complemented, Sylow
305C23—41no—
306C23—112no—
307Q8—41no—
308Q8—41no—
309Q8—442no—
310Q8—442no—
311Q8—882no—
312D4—22no—
313D4—41no—
314D4—222no—
315D4—884no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—82no—
320C2×C4—112no—
321C2×C4—222no—
322C2×C4—222no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4—884no—
326C2×C4D8×D1111yescharacteristic
327C2×C4D8×D1111yescharacteristic
328C2×C4C2×D4×D1111yescharacteristic
329C8—21no—
330C8—222no—
331C8C2×#433911yescharacteristic
332C8#6704211yescharacteristic
333C22—42no—
334C22—81no—
335C22—81no—
336C22—222no—
337C22—222no—
338C22—222no—
339C22C2×D8×D1111yescharacteristic
340C4—21no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—222no—
345C4—882no—
346C4—882no—
347C4#1062252912yes—
348C4#1062308111yescharacteristic
349C4#1062330111yescharacteristic
350C2—82no—
351C2—442no—
352C2#1308043111yescharacteristic
353C2C2×#1062252911yescharacteristic
354C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×SD32C2
socleC22×C11C22×D8
prime radical#13080337C2
hypercenterC4×SD32D11
hypocenterC11#33869
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #13081048C2semidirect
3. #13070844C2semidirect
4. #13070827C2semidirect
5. #13070753C2semidirect
6. #13070706C2semidirect
7. #13070666C2semidirect
8. #13070553C2semidirect
9. C16×D44C2semidirect
10. #13070320C2semidirect
11. C4×C11×SD32C2semidirect
136. C4×SD32D11semidirect
304. C11#33869semidirect

Maximal subgroups

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

subgroupindex
#130810482
#130803372
#130708442
#130708272
#130707532
#130707062
#130706662
#130705532
C16×D442
#130703202
C4×C11×SD322
#3386911