Finite Group Databasebeta

← #14911120

Subgroups — #14911120

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081008C211yesmaximal, characteristic, complemented
2#13080374C211yesmaximal, characteristic
3#13070795C212yesmaximal, complemented
4#13070765C211yesmaximal, characteristic, complemented
5#13070728C212yesmaximal, complemented
6#13070653C211yesmaximal, characteristic, complemented
7#13070557C212yesmaximal, complemented
8C4×Dic88C211yesmaximal, characteristic, complemented
9#13070449C211yesmaximal, characteristic, complemented
10#13070325C212yesmaximal, complemented
11C11×#2240C211yesmaximal, characteristic, complemented
12C2×#66965C2212yes—
13#10623261—21no—
14#10623249—21no—
15C11×#500C2211yescharacteristic
16C11×#493C2211yescharacteristic
17#10622771—22no—
18#10622770C2212yes—
19C2×#66891C2212yes—
20#10622704—21no—
21#10622688—21no—
22C2×Dic88C2211yescharacteristic
23C2×#66862C2212yes—
24#10622500C2212yes—
25#10622497—22no—
26D11×#107C2212yes—
27C4×Dic44C2211yescharacteristic
28C4×Dic44C2211yescharacteristic
29C8×D44C2211yescharacteristic
30C11×#357C2212yes—
31C11×#357C2212yes—
32C4×C11×C16C2211yescharacteristic
33#10622200C2212yes—
34(C2×D11)⋊C16C2212yes—
35#10622142C2211yescharacteristic
36#10622141C2211yescharacteristic
37#10622141C2211yescharacteristic
38#10622130C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4341—22no—
42C2×C11×D8—21no—
43C2×C11×D8C2312yes—
44C11×C4⋊Q8—21no—
45C11×#127—21no—
46#66999—42no—
47#66993—41no—
48#66992—42no—
49#66991—22no—
50D4×Dic11—41no—
51C2×#4324—22no—
52#66965—24no—
53#66965—42no—
54C2×Dic44C2311yescharacteristic
55C2×Dic44C2311yescharacteristic
56C2×C8×D11C2312yes—
57#66950—22no—
58#66946—41no—
59C4⋊C4×D11—22no—
60#66943—41no—
61C4×D44D411yescharacteristic
62C4×Dic22—21no—
63C4×Dic22—21no—
64C2×C11×C16C2311yescharacteristic
65C2×C11×C16C2311yescharacteristic
66C11×#107—21no—
67C11×#107C2312yes—
68C4×C8×C11C2311yescharacteristic
69#66896—22no—
70#66891—42no—
71(C2×D11)⋊C8D412yes—
72#66882C2311yescharacteristic
73#66882C2311yescharacteristic
74#66880—21no—
75#66880—21no—
76C2×C11⋊C16C2312yes—
77#66874—22no—
78#66871—22no—
79C4⋊(C11⋊C8)D411yescharacteristic
80Dic88—22no—
81#66862—42no—
82#33900—111nomaximal, Sylow
83C2×Q8×C11—41no—
84C2×D4×C11—22no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×C22⋊D11—42no—
88C2×C22⋊D11—42no—
89C22×Dic11—42no—
90#4341—44no—
91#4341—82no—
92C2×D44D811yescharacteristic
93C2×C4×D11—42no—
94C2×C4×D11C2×D412yes—
95C2×Dic22—21no—
96C2×Dic22—21no—
97C11×D8—22no—
98C11×D8—22no—
99C11×D8—81no—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2411yescharacteristic
102C11×C4⋊C4—22no—
103C11×C4⋊C4—41no—
104C42×C11C2×D411yescharacteristic
105C22⋊Dic11—42no—
106#4324—44no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4D812yes—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—42no—
112C4⋊Dic11D811yescharacteristic
113Dic11⋊C4—42no—
114Dic11⋊C4—41no—
115Dic11⋊C4—41no—
116C4×Dic11—41no—
117C4×Dic11—41no—
118C2×C11⋊C8C2×D412yes—
119Dic44—21no—
120Dic44—21no—
121Dic44—21no—
122Dic44#4112yes—
123C8×D11—22no—
124C8×D11—22no—
125C11×C16—21no—
126C11×C16—21no—
127C11⋊C16—22no—
128#3338—111no—
129#3287—111no—
130#2240D1111yescharacteristic, complemented
131#2232—112no—
132#2227—111no—
133#2220—112no—
134#2207—111no—
135#2189—112no—
136C4×Q32—111no—
137#2169—111no—
138#2139—112no—
139C23×C11—42no—
140C22×D11C2×D812yes—
141Q8×C11—161no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—82no—
145D4×C11—161no—
146C2×C4×C11—42no—
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C22×D411yescharacteristic
150C22⋊D11—84no—
151C22⋊D11—162no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—84no—
157C2×Dic11C2×D812yes—
158D44—22no—
159C4×D11—22no—
160C4×D11—22no—
161C4×D11—162no—
162Dic22—22no—
163Dic22—41no—
164Dic22—41no—
165Dic22—41no—
166C8×C11—21no—
167C8×C11C2×#4111yescharacteristic
168C8×C11H(5,𝔽2)11yescharacteristic
169C11⋊C8—22no—
170C2×#135—112no—
171#554—221no—
172#550—221no—
173C2×Q32—111no—
174C2×SD32—112no—
175C2×M32—112no—
176#500C2×D1111yescharacteristic
177#493C2×D1111yescharacteristic
178#484—222no—
179#477—221no—
180#467—112no—
181#466—112no—
182#460—221no—
183#449—222no—
184C4×Q16—111no—
185C4×Q16—111no—
186C8×D4—111no—
187C2×#107—112no—
188#366—111no—
189#366—112no—
190C4⋊C16—111no—
191#358—111no—
192#358—111no—
193#358—112no—
194#357—112no—
195#357C2×D1112yes—
196#357C2×D1112yes—
197C22⋊C16—112no—
198C4×C16C2×D1111yescharacteristic
199C22×C11—82no—
200C22×C11—82no—
201C22×C11—82no—
202C22×C11C22×D811yescharacteristic
203C2×D11—22no—
204C2×D11—22no—
205C2×D11—22no—
206C4×C11—21no—
207C4×C11—82no—
208C4×C11#51012yes—
209C4×C11#54611yescharacteristic
210C4×C11#57711yescharacteristic
211Dic11—22no—
212Dic11—42no—
213Dic11—81no—
214Dic11—81no—
215Dic11—81no—
216C2×#41—222no—
217#135—224no—
218#135—442no—
219C2×Q16—111no—
220C2×Q16—111no—
221C2×SD16—222no—
222C2×D8—21no—
223C2×D8C22×D1112yes—
224C22×C8—112no—
225C4⋊Q8—21no—
226#127—21no—
227#127—441no—
228#125—441no—
229C22⋊Q8—222no—
230C22⋊Q8—442no—
231#121—222no—
232#121—442no—
233C4×Q8—221no—
234C4×Q8—221no—
235C4×D4—111no—
236C4×D4—441no—
237C4×D4—441no—
238C2×C4⋊C4—222no—
239Q32—222no—
240SD32—442no—
241M32—442no—
242C2×C16—112no—
243C2×C16C22×D1111yescharacteristic
244C2×C16C22×D1111yescharacteristic
245#107—21no—
246#107—111no—
247#107—111no—
248#107—222no—
249#107C22×D1112yes—
250C4⋊C8—111no—
251#103—222no—
252#103—221no—
253#103—221no—
254#102—222no—
255C22⋊C8—112no—
256C4×C8C22×D1111yescharacteristic
257C2×C11—162no—
258C2×C11#329411yescharacteristic
259C2×C11C2×#51011yescharacteristic
260C2×C11#341511yescharacteristic
261D11—42no—
262#41—444no—
263#41—882no—
264C2×Q8—41no—
265C2×Q8—221no—
266C2×Q8—221no—
267C2×D4—22no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—111no—
271C2×D4—442no—
272C2×D4—442no—
273C22×C4—112no—
274C22×C4—442no—
275C22×C4—442no—
276Q16—112no—
277Q16—221no—
278Q16—221no—
279Q16—221no—
280SD16—444no—
281D8—22no—
282D8—22no—
283D8—81no—
284C2×C8—112no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8D4×D1111yescharacteristic
288C2×C8C23×D1111yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—111no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—442no—
295C4⋊C4—442no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C22⋊C4—112no—
299C22⋊C4—442no—
300C22⋊C4—442no—
301C42—441no—
302C42—441no—
303C42D4×D1111yescharacteristic
304C16—21no—
305C16—21no—
306C16—222no—
307C11#3390011yescharacteristic, complemented, Sylow
308C23—42no—
309C23—112no—
310Q8—161no—
311Q8—222no—
312Q8—441no—
313Q8—441no—
314Q8—441no—
315D4—42no—
316D4—42no—
317D4—82no—
318D4—161no—
319D4—222no—
320D4—884no—
321D4—1762no—
322C2×C4—42no—
323C2×C4—112no—
324C2×C4—222no—
325C2×C4—222no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—884no—
331C2×C4—1762no—
332C2×C4D8×D1111yescharacteristic
333C2×C4D8×D1111yescharacteristic
334C2×C4C2×D4×D1111yescharacteristic
335C8—21no—
336C8—222no—
337C8#41×D1111yescharacteristic
338C8#6704211yescharacteristic
339C22—82no—
340C22—82no—
341C22—82no—
342C22—222no—
343C22—222no—
344C22—222no—
345C22C2×D8×D1111yescharacteristic
346C4—21no—
347C4—82no—
348C4—222no—
349C4—442no—
350C4—881no—
351C4—881no—
352C4—881no—
353C4#1062252812yes—
354C4#1062320711yescharacteristic
355C4#1062329311yescharacteristic
356C2—162no—
357C2—442no—
358C2#1308042811yescharacteristic
359C2C2×#1062252811yescharacteristic
360C2#1308175311yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2240C2
socleC22×C11C22×D8
prime radical#13080374C2
hypercenter#2240D11
hypocenterC11#33900
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
1. #13081008C2semidirect
3. #13070795C2semidirect
4. #13070765C2semidirect
5. #13070728C2semidirect
6. #13070653C2semidirect
7. #13070557C2semidirect
8. C4×Dic88C2semidirect
9. #13070449C2semidirect
10. #13070325C2semidirect
11. C11×#2240C2semidirect
130. #2240D11semidirect
307. C11#33900semidirect

Maximal subgroups

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

subgroupindex
#130810082
#130803742
#130707952
#130707652
#130707282
#130706532
#130705572
C4×Dic882
#130704492
#130703252
C11×#22402
#3390011