Finite Group Databasebeta

← #14911111

Subgroups — #14911111

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080964C211yesmaximal, characteristic, complemented
2#13080376C211yesmaximal, characteristic, complemented
3#13070840C211yesmaximal, characteristic, complemented
4#13070802C212yesmaximal, complemented
5#13070759C211yesmaximal, characteristic, complemented
6#13070719C212yesmaximal, complemented
7#13070652C211yesmaximal, characteristic, complemented
8#13070541C212yesmaximal, complemented
9C4×#66864C211yesmaximal, characteristic, complemented
10#13070329C212yesmaximal, complemented
11C11×#2169C211yesmaximal, characteristic, complemented
12C2×#66957C2212yes—
13#10623086—21no—
14#10623084—21no—
15C2×C11×M32C2212yes—
16C8×D4×C11C2211yescharacteristic
17#10622728C2212yes—
18#10622728C2212yes—
19C2×#66882C2212yes—
20C2×#66864C2211yescharacteristic
21C2×D176C2212yes—
22#10622461—21no—
23#10622459—21no—
24#10622349—22no—
25#10622347—22no—
26C4×Dic44C2211yescharacteristic
27#10622308C2211yescharacteristic
28C4×D88C2211yescharacteristic
29#10622295C2211yescharacteristic
30C11×C4⋊C16C2211yescharacteristic
31C11×C22⋊C16C2212yes—
32C4×C11×C16C2211yescharacteristic
33#10622147C2212yes—
34#10622147C2211yescharacteristic
35#10622147C2212yes—
36#10622147C2212yes—
37#10622143C2212yes—
38#10622143C2211yescharacteristic
39#10622141C2211yescharacteristic
40#10622141C2212yes—
41C2×#4341—41no—
42C2×#4339—22no—
43C22×C8×C11C2312yes—
44C4×D4×C11D411yescharacteristic
45#66993—41no—
46#66983—22no—
47#66983—22no—
48C2×C4⋊Dic11—22no—
49C2×Dic44C2311yescharacteristic
50#66957—24no—
51#66957—42no—
52C2×D88—21no—
53C2×D88C2311yescharacteristic
54C2×D88C2312yes—
55C2×#4314—22no—
56#66950—41no—
57#66946—41no—
58#66939—42no—
59#66937—42no—
60#66927—21no—
61C4×D44—21no—
62#66922—21no—
63C4×Dic22—21no—
64C11×M32—42no—
65C2×C11×C16C2311yescharacteristic
66C2×C11×C16C2312yes—
67C2×C11×C16C2311yescharacteristic
68C11×C4⋊C8D411yescharacteristic
69C11×C22⋊C8D412yes—
70C4×C8×C11C2311yescharacteristic
71#66885—22no—
72#66885—22no—
73#66885—21no—
74#66882—21no—
75#66882—22no—
76#66882C2311yescharacteristic
77#66882C2312yes—
78#66882C2311yescharacteristic
79#66880—21no—
80#66864—22no—
81D176—42no—
82#33899—111nomaximal, Sylow
83C2×D4×C11D811yescharacteristic
84C22×C4×C11C2×D412yes—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—42no—
87C2×C22⋊D11—42no—
88C22×Dic11—42no—
89#4341—84no—
90#4339—44no—
91#4339—82no—
92C2×D44—21no—
93C2×D44—22no—
94C2×D44—41no—
95C2×D44—41no—
96C2×C4×D11—41no—
97C2×C4×D11—42no—
98C2×Dic22—21no—
99C2×Dic22—41no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D412yes—
104C2×C8×C11C2411yescharacteristic
105C11×C4⋊C4D811yescharacteristic
106C11×C22⋊C4D812yes—
107C42×C11C2×D411yescharacteristic
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—42no—
111C4⋊Dic11—21no—
112C4⋊Dic11—22no—
113C4⋊Dic11—21no—
114C4⋊Dic11—41no—
115C4⋊Dic11—42no—
116Dic11⋊C4—41no—
117C4×Dic11—41no—
118Dic44—21no—
119Dic44#4112yescomplemented
120D88—21no—
121D88—22no—
122D88—21no—
123D88—22no—
124D88—81no—
125#4314—44no—
126C11×C16—21no—
127C11×C16—22no—
128C11×C16—21no—
129#3334—111no—
130#3287—111no—
131#2240—111no—
132#2233—112no—
133#2225—111no—
134#2218—112no—
135#2206—111no—
136#2186—112no—
137C4×SD32—111no—
138#2169D1111yescharacteristic, complemented
139#2139—112no—
140C23×C11C2×D812yes—
141C22×D11—41no—
142C22×D11—42no—
143D4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C2×D812yes—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C22×D411yescharacteristic
150C22⋊D11—84no—
151C22⋊D11—84no—
152C22⋊D11—162no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—84no—
158D44—42no—
159D44—41no—
160D44—42no—
161D44—41no—
162D44—82no—
163D44—161no—
164C4×D11—84no—
165C4×D11—82no—
166Dic22—22no—
167Dic22—41no—
168Dic22—82no—
169C8×C11—22no—
170C8×C11—21no—
171C8×C11C2×#4111yescharacteristic
172C8×C11H(5,𝔽2)11yescharacteristic
173C2×#135—112no—
174#550—221no—
175#547—221no—
176C2×SD32—111no—
177C2×D16—112no—
178C2×M32C2×D1112yes—
179#500—111no—
180#493—111no—
181#480—222no—
182#474—221no—
183#466—112no—
184#466—112no—
185#460—221no—
186#449—222no—
187C4×Q16—111no—
188C4×D8—111no—
189C8×D4C2×D1111yescharacteristic
190C2×#107—112no—
191#367—111no—
192#367—112no—
193C4⋊C16C2×D1111yescharacteristic
194#358—111no—
195#358—112no—
196#357—112no—
197#357—112no—
198#357—111no—
199#357—112no—
200C22⋊C16C2×D1112yes—
201C4×C16C2×D1111yescharacteristic
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11C22×D811yescharacteristic
206C2×D11—81no—
207C2×D11—82no—
208C2×D11—81no—
209C2×D11—82no—
210C2×D11—82no—
211C2×D11—81no—
212C4×C11—21no—
213C4×C11—22no—
214C4×C11#50912yes—
215C4×C11#54611yescharacteristic
216C4×C11#57711yescharacteristic
217Dic11—42no—
218Dic11—82no—
219Dic11—81no—
220Dic11—81no—
221C2×#41—222no—
222C2×#41—441no—
223#135—224no—
224#135—442no—
225C2×Q16—111no—
226C2×SD16—222no—
227C2×D8—112no—
228C2×D8—111no—
229C2×D8—221no—
230C22×C8C22×D1112yes—
231C4⋊Q8—221no—
232#127—221no—
233#127—441no—
234#123—442no—
235C22⋊Q8—441no—
236#121—222no—
237#121—222no—
238#121—442no—
239C4×Q8—221no—
240C4×D4—221no—
241C4×D4—441no—
242C4×D4D4411yescharacteristic
243C2×C4⋊C4—222no—
244SD32—222no—
245D16—442no—
246M32—42no—
247C2×C16C22×D1111yescharacteristic
248C2×C16C22×D1111yescharacteristic
249C2×C16C22×D1112yes—
250#107—111no—
251#107—112no—
252#107—111no—
253#107—222no—
254#107—221no—
255C4⋊C8D4411yescharacteristic
256#103—221no—
257#102—221no—
258#102—222no—
259#102—222no—
260C22⋊C8D4412yes—
261C4×C8C22×D1111yescharacteristic
262C2×C11—42no—
263C2×C11#329411yescharacteristic
264C2×C11C2×#50911yescharacteristic
265C2×C11#341611yescharacteristic
266D11—161no—
267D11—162no—
268#41—444no—
269#41—882no—
270#41—884no—
271C2×Q8—221no—
272C2×Q8—441no—
273C2×D4—221no—
274C2×D4—222no—
275C2×D4—442no—
276C2×D4—442no—
277C2×D4—442no—
278C2×D4—441no—
279C2×D4—441no—
280C2×D4D8811yescharacteristic
281C22×C4—442no—
282C22×C4—441no—
283C22×C4—442no—
284C22×C4C2×D4412yes—
285Q16—112no—
286Q16—221no—
287SD16—444no—
288D8—221no—
289D8—222no—
290D8—221no—
291D8—222no—
292D8—881no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8C2×D4411yescharacteristic
296C2×C8C2×D4412yes—
297C2×C8C23×D1111yescharacteristic
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—222no—
301C4⋊C4—442no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4D8811yescharacteristic
305C22⋊C4—441no—
306C22⋊C4—442no—
307C22⋊C4—442no—
308C22⋊C4D8812yes—
309C42—441no—
310C42C2×D4411yescharacteristic
311C16—21no—
312C16—22no—
313C16—21no—
314C11#3389911yescharacteristic, complemented, Sylow
315C23—441no—
316C23—442no—
317C23C2×D8812yes—
318Q8—222no—
319Q8—441no—
320Q8—882no—
321D4—22no—
322D4—442no—
323D4—441no—
324D4—442no—
325D4—441no—
326D4—884no—
327D4—884no—
328D4—882no—
329D4—1761no—
330D4—1762no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—442no—
337C2×C4—884no—
338C2×C4—884no—
339C2×C4—882no—
340C2×C4C2×D8811yescharacteristic
341C2×C4C2×D8812yes—
342C2×C4C2×D8811yescharacteristic
343C2×C4C22×D4411yescharacteristic
344C8—21no—
345C8—22no—
346C8#6703711yescharacteristic
347C8#41×D1111yescharacteristic
348C22—22no—
349C22—22no—
350C22—22no—
351C22—882no—
352C22—881no—
353C22—881no—
354C22—882no—
355C22—882no—
356C22—881no—
357C22C22×D8811yescharacteristic
358C4—22no—
359C4—21no—
360C4—442no—
361C4—881no—
362C4—882no—
363C4—881no—
364C4#1062252112yes—
365C4#1062308511yescharacteristic
366C4#1062328211yescharacteristic
367C2—42no—
368C2—1762no—
369C2—1761no—
370C2#1308043011yescharacteristic
371C2C2×#1062252111yescharacteristic
372C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2169C2
socleC22×C11C22×D8
hypercenter#2169D11
hypocenterC11#33899
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2169

Complements

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

NH ≅ G/Ntype
1. #13080964C2semidirect
2. #13080376C2semidirect
3. #13070840C2semidirect
4. #13070802C2semidirect
5. #13070759C2semidirect
6. #13070719C2semidirect
7. #13070652C2semidirect
8. #13070541C2semidirect
9. C4×#66864C2semidirect
10. #13070329C2semidirect
11. C11×#2169C2semidirect
119. Dic44#41semidirect
138. #2169D11semidirect
314. C11#33899semidirect

Maximal subgroups

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

subgroupindex
#130809642
#130803762
#130708402
#130708022
#130707592
#130707192
#130706522
#130705412
C4×#668642
#130703292
C11×#21692
#3389911