Finite Group Databasebeta

← #14910708

Subgroups — #14910708

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081038C211yesmaximal, characteristic, complemented
2#13080337C211yesmaximal, characteristic, complemented
3#13070845C211yesmaximal, characteristic, complemented
4#13070827C212yesmaximal, complemented
5#13070713C212yesmaximal, complemented
6#13070662C211yesmaximal, characteristic, complemented
7#13070540C212yesmaximal, complemented
8C4×#66890C211yesmaximal, characteristic, complemented
9#13070435C211yesmaximal, characteristic, complemented
10#13070320C212yesmaximal, complemented
11C11×#2226C211yesmaximal, characteristic, complemented
12C2×#66965C2212yes—
13#10623265—21no—
14#10623086—21no—
15C11×#500C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17C2×#66890C2211yescharacteristic
18#10622697—21no—
19#10622632—21no—
20C2×#66864C2212yes—
21C2×C16×D11C2212yes—
22#10622500C2212yes—
23#10622498—22no—
24#10622496C2212yes—
25#10622493C2212yes—
26#10622396—22no—
27#10622312C2211yescharacteristic
28C4×D88C2211yescharacteristic
29C8×D44C2211yescharacteristic
30C11×#367C2212yes—
31C11×C4⋊C16C2211yescharacteristic
32C11×#357C2212yes—
33#10622200C2211yescharacteristic
34(C2×D11)⋊C16C2212yes—
35#10622141C2212yes—
36#10622130C2212yes—
37#10622130C2212yes—
38#10622129C2211yescharacteristic
39#10622127C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4341—22no—
42C2×C11×D8C2311yescharacteristic
43C11×C4⋊Q8—21no—
44C4×D4×C11—21no—
45#67000—42no—
46C2×#4324—22no—
47#66983—41no—
48C2×C4⋊Dic11—41no—
49#66965—24no—
50#66965—42no—
51C2×Dic44—21no—
52C2×Dic44C2312yes—
53C2×D88C2311yescharacteristic
54C2×C8×D11C2312yes—
55#66950—22no—
56#66948—22no—
57#66948—41no—
58#66945—22no—
59#66945—41no—
60#66939—42no—
61C4×D44—21no—
62C4×D44D411yescharacteristic
63#66922—21no—
64C2×C11×C16C2312yes—
65C11×#107—21no—
66C11×#107C2312yes—
67C11×#107C2311yescharacteristic
68C11×#102—21no—
69C4×C8×C11C2311yescharacteristic
70#66890—22no—
71#66885—21no—
72(C2×D11)⋊C8D412yes—
73#66882C2311yescharacteristic
74C2×C11⋊C16C2311yescharacteristic
75C2×C11⋊C16C2311yescharacteristic
76#66874—22no—
77#66873—22no—
78#66872—22no—
79C4⋊(C11⋊C8)D411yescharacteristic
80#66864—42no—
81C16×D11—42no—
82#33870—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×D44—21no—
91C2×D44—42no—
92C2×D44D811yescharacteristic
93C2×C4×D11—41no—
94C2×C4×D11C2×D412yes—
95C2×Dic22—22no—
96C11×D8—21no—
97C11×D8#4112yes—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2411yescharacteristic
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11C2×D411yescharacteristic
105#4324—44no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4D812yes—
111C4⋊Dic11—21no—
112C4⋊Dic11—42no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C4⋊Dic11D811yescharacteristic
116C4×Dic11—42no—
117C2×C11⋊C8C2×D412yes—
118Dic44—22no—
119Dic44—22no—
120Dic44—81no—
121D88—21no—
122D88—21no—
123C8×D11—22no—
124C8×D11—22no—
125C11×C16—22no—
126C11⋊C16—21no—
127C11⋊C16—21no—
128#3341—111no—
129#3283—111no—
130#2241—111no—
131#2237—112no—
132#2226D1111yescharacteristic, complemented
133#2217—112no—
134#2208—111no—
135#2186—112no—
136C4×D16—111no—
137D4×C16—111no—
138#2138—112no—
139C23×C11—41no—
140C22×D11—41no—
141C22×D11C2×D812yes—
142Q8×C11—161no—
143D4×C11—22no—
144D4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—82no—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C22×D411yescharacteristic
151C22⋊D11—84no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—84no—
155C2×Dic11C2×D812yes—
156D44—22no—
157D44—41no—
158D44—41no—
159D44—162no—
160C4×D11—22no—
161C4×D11—22no—
162C4×D11—82no—
163Dic22—42no—
164Dic22—42no—
165C8×C11—21no—
166C8×C11C2×#4111yescharacteristic
167C8×C11H(5,𝔽2)11yescharacteristic
168C11⋊C8—22no—
169C2×#135—112no—
170#555—221no—
171#547—221no—
172C2×SD32—112no—
173C2×D16—111no—
174C22×C16—112no—
175#500C2×D1111yescharacteristic
176#494—111no—
177#482—222no—
178#476—221no—
179#467—112no—
180#466—112no—
181#461—221no—
182#452—222no—
183C4×D8—111no—
184C4×D8C2×D1111yescharacteristic
185C8×D4—111no—
186#427—112no—
187#367C2×D1112yes—
188#366—111no—
189C4⋊C16C2×D1111yescharacteristic
190#358—112no—
191#358—112no—
192#358—112no—
193#357—111no—
194#357—111no—
195#357C2×D1112yes—
196C22⋊C16—112no—
197C4×C16—111no—
198C22×C11—42no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11C22×D811yescharacteristic
202C2×D11—22no—
203C2×D11—22no—
204C2×D11—22no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—81no—
210C4×C11—82no—
211C4×C11#50812yes—
212C4×C11#54611yescharacteristic
213C4×C11#57711yescharacteristic
214Dic11—22no—
215Dic11—81no—
216Dic11—82no—
217C2×#41—222no—
218#135—224no—
219#135—442no—
220C2×Q16—112no—
221C2×Q16—221no—
222C2×SD16—222no—
223C2×D8—111no—
224C2×D8C22×D1111yescharacteristic
225C22×C8—112no—
226C4⋊Q8—21no—
227C4⋊Q8—221no—
228#124—442no—
229#123—442no—
230C22⋊Q8—222no—
231#121—222no—
232#121—441no—
233#121—441no—
234C4×D4—21no—
235C4×D4—111no—
236C4×D4—221no—
237#117—222no—
238#117—441no—
239C2×C4⋊C4—441no—
240SD32—442no—
241D16—222no—
242C2×C16—111no—
243C2×C16—111no—
244C2×C16—442no—
245C2×C16C22×D1112yes—
246#107—21no—
247#107—111no—
248#107C22×D1111yescharacteristic
249#107C22×D1112yes—
250#106—222no—
251C4⋊C8—111no—
252#103—222no—
253#102—21no—
254#102—222no—
255#102—221no—
256C22⋊C8—112no—
257C4×C8C22×D1111yescharacteristic
258C2×C11—82no—
259C2×C11#329411yescharacteristic
260C2×C11C2×#50811yescharacteristic
261C2×C11#341611yescharacteristic
262D11—42no—
263D11—161no—
264#41—444no—
265#41—882no—
266C2×Q8—41no—
267C2×Q8—222no—
268C2×D4—21no—
269C2×D4—111no—
270C2×D4—221no—
271C2×D4—442no—
272C2×D4—442no—
273C22×C4—41no—
274C22×C4—112no—
275C22×C4—442no—
276C22×C4—441no—
277Q16—222no—
278Q16—222no—
279Q16—881no—
280SD16—444no—
281D8—21no—
282D8—221no—
283D8—221no—
284D8#434312yes—
285C2×C8—112no—
286C2×C8—222no—
287C2×C8—222no—
288C2×C8D4×D1111yescharacteristic
289C2×C8C23×D1111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—111no—
294C4⋊C4—221no—
295C4⋊C4—442no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C22⋊C4—41no—
299C22⋊C4—112no—
300C22⋊C4—442no—
301C22⋊C4—442no—
302C22⋊C4—442no—
303C22⋊C4—441no—
304C42—442no—
305C42D4×D1111yescharacteristic
306C16—22no—
307C16—221no—
308C16—221no—
309C11#3387011yescharacteristic, complemented, Sylow
310C23—41no—
311C23—112no—
312C23—441no—
313Q8—161no—
314Q8—442no—
315Q8—442no—
316D4—22no—
317D4—41no—
318D4—222no—
319D4—441no—
320D4—441no—
321D4—884no—
322D4—1762no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—82no—
326C2×C4—112no—
327C2×C4—222no—
328C2×C4—222no—
329C2×C4—441no—
330C2×C4—442no—
331C2×C4—884no—
332C2×C4—882no—
333C2×C4D8×D1111yescharacteristic
334C2×C4D8×D1111yescharacteristic
335C2×C4C2×D4×D1111yescharacteristic
336C8—21no—
337C8—222no—
338C8C2×#434311yescharacteristic
339C8#6704211yescharacteristic
340C22—42no—
341C22—81no—
342C22—81no—
343C22—222no—
344C22—222no—
345C22—222no—
346C22—881no—
347C22—881no—
348C22—881no—
349C22C2×D8×D1111yescharacteristic
350C4—21no—
351C4—81no—
352C4—82no—
353C4—222no—
354C4—882no—
355C4—881no—
356C4#1062252912yes—
357C4#1062316111yescharacteristic
358C4#1062330911yescharacteristic
359C2—82no—
360C2—442no—
361C2—1761no—
362C2#1308042611yescharacteristic
363C2C2×#1062252911yescharacteristic
364C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2226C2
socleC22×C11C22×D8
hypercenter#2226D11
hypocenterC11#33870
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
1. #13081038C2semidirect
2. #13080337C2semidirect
3. #13070845C2semidirect
4. #13070827C2semidirect
5. #13070713C2semidirect
6. #13070662C2semidirect
7. #13070540C2semidirect
8. C4×#66890C2semidirect
9. #13070435C2semidirect
10. #13070320C2semidirect
11. C11×#2226C2semidirect
132. #2226D11semidirect
309. C11#33870semidirect

Maximal subgroups

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

subgroupindex
#130810382
#130803372
#130708452
#130708272
#130707132
#130706622
#130705402
C4×#668902
#130704352
#130703202
C11×#22262
#3387011