Finite Group Databasebeta

← #14653158

Subgroups — #14653158

Order 2816.

408 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078941C211yesmaximal, characteristic
2#13068778C211yesmaximal, characteristic, complemented
3#13067180C211yesmaximal, characteristic, complemented
4#13067177C211yesmaximal, characteristic
5#13067175C211yesmaximal, characteristic
6#13066909C211yesmaximal, characteristic, complemented
7C11×#1518C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622706C411yescharacteristic, complemented
13#10622706C411yescharacteristic, complemented
14#10622701C411yescharacteristic, complemented
15#10622701C411yescharacteristic, complemented
16#10622681—21no—
17#10622681—21no—
18#10622615—21no—
19#10622615—21no—
20C2×#66872—21no—
21C2×#66871—21no—
22#10622549C2211yescharacteristic
23#10622538C2211yescharacteristic
24C2×C4×C11⋊C8C2211yescharacteristic
25C11×#328—22no—
26#10622176—22no—
27#10622108—22no—
28#10622093—21no—
29#10622092—21no—
30#10622089—22no—
31C2×#4339—21no—
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×C4⋊Q8C2×C411yescharacteristic
34C11×#125—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C11×#117—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42#66983—21no—
43#66983—21no—
44C2×C4⋊Dic11—21no—
45C22×C11⋊C8D411yescharacteristic
46C22×C11⋊C8D411yescharacteristic
47#66928—21no—
48#66927C2×C411yescharacteristic
49C4×D44—21no—
50C4×D44—21no—
51#66922C2×C411yescharacteristic
52C11×C4⋊C8—21no—
53C11×C22⋊C8D412yes—
54C4×C8×C11—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C22⋊(C11⋊C8)D412yes—
60#66874—21no—
61#66874—21no—
62#66874—21no—
63#66874—21no—
64#66873—21no—
65#66873—21no—
66#66873—21no—
67#66873—21no—
68#66872—42no—
69#66871—42no—
70C4⋊(C11⋊C8)—21no—
71C4×C11⋊C8—21no—
72C4×C11⋊C8C2×C411yescharacteristic
73C4×C11⋊C8C2×C411yescharacteristic
74C4×C11⋊C8D411yescharacteristic
75C4×C11⋊C8D411yescharacteristic
76#9758—111nomaximal, Sylow
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C2×C22⋊D11—41no—
84C22×Dic11—41no—
85#4339—41no—
86#4339—41no—
87#4339—41no—
88#4339—41no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×C4×D11—41no—
93C2×Dic22—21no—
94C2×C8×C11—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—41no—
105C42×C11C22×C411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11#4111yescharacteristic
108C42×C11#4111yescharacteristic
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8—21no—
118C2×C11⋊C8—21no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8C22⋊C411yescharacteristic
121C2×C11⋊C8C22⋊C411yescharacteristic
122C2×C11⋊C8C22⋊C411yescharacteristic
123C2×C11⋊C8C22⋊C411yescharacteristic
124#3131—111no—
125#1846—111no—
126#1518—111no—
127#1518D1111yescharacteristic, complemented
128#1517—111no—
129#1517—111no—
130#1452—111no—
131C23×C11#12711yescharacteristic
132C22×D11—41no—
133Q8×C11—81no—
134Q8×C11—81no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11C2×C22⋊C411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12411yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C22⋊D11—81no—
153C22⋊D11—81no—
154C2×Dic11—41no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158D44—41no—
159D44—41no—
160D44—81no—
161D44—81no—
162C4×D11—81no—
163C4×D11—81no—
164Dic22—41no—
165Dic22—41no—
166C8×C11—42no—
167C11⋊C8—21no—
168C11⋊C8—21no—
169C11⋊C8—21no—
170C11⋊C8—21no—
171C11⋊C8—42no—
172#533C2×D1111yescharacteristic
173#532—111no—
174#488—221no—
175#488—221no—
176#487—111no—
177#487—111no—
178#486—111no—
179#486—111no—
180#431—111no—
181#431C2×D1111yescharacteristic
182C2×#107—221no—
183C2×#106—221no—
184#416—221no—
185#416—221no—
186C2×C4×C8—111no—
187#382—111no—
188#382C2×D1111yescharacteristic
189#328—22no—
190#328—222no—
191#327—222no—
192#327—222no—
193#322—221no—
194#322—221no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11#39011yescharacteristic
198C22×C11#49611yescharacteristic
199C22×C11#49711yescharacteristic
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—161no—
210C4×C11#41711yescharacteristic
211C4×C11#41711yescharacteristic
212C4×C11#48911yescharacteristic
213C4×C11#48911yescharacteristic
214Dic11—81no—
215Dic11—161no—
216C2×#41—221no—
217C22×C8—111no—
218C22×C8—111no—
219C4⋊Q8—111no—
220C4⋊Q8C4×D1111yescharacteristic
221C4⋊Q8C4×D1111yescharacteristic
222#127—111no—
223#125—21no—
224#124—221no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227#121—221no—
228#121—221no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×D4—221no—
232C4×D4—221no—
233#117—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—221no—
236C2×C42C22×D1111yescharacteristic
237#107—442no—
238#106—442no—
239C4⋊C8—21no—
240C4⋊C8—221no—
241#103—221no—
242#103—221no—
243#103—221no—
244#103—221no—
245#102—221no—
246#102—221no—
247#102—221no—
248#102—221no—
249C22⋊C8—112no—
250C22⋊C8C22⋊D1112yes—
251C4×C8—21no—
252C4×C8—111no—
253C4×C8—111no—
254C4×C8—111no—
255C4×C8—111no—
256C4×C8—221no—
257#95—21no—
258#95—21no—
259#95—221no—
260#95—221no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11#195911yescharacteristic
264C2×C11#197611yescharacteristic
265C2×C11#197611yescharacteristic
266D11—161no—
267#41—441no—
268#41—441no—
269#41—441no—
270#41—441no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—221no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—441no—
278C22×C4—41no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4D4×D1111yescharacteristic
282C22×C4D4×D1111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284C2×C8—22no—
285C2×C8—111no—
286C2×C8—111no—
287C2×C8—111no—
288C2×C8—111no—
289C2×C8—221no—
290C2×C8—221no—
291C2×C8—221no—
292C2×C8—221no—
293C2×C8—222no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C22⋊C4—41no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C42—41no—
310C42C2×C4×D1111yescharacteristic
311C42#433911yescharacteristic
312C42D4×D1111yescharacteristic
313C42#434111yescharacteristic
314C11#975811yescharacteristic, complemented, Sylow
315C23—441no—
316C23#6699311yescharacteristic
317Q8—81no—
318Q8—81no—
319Q8—441no—
320Q8—441no—
321D4—441no—
322D4—441no—
323D4—881no—
324D4—881no—
325D4—881no—
326D4—881no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—441no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4—881no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4C22⋊C4×D1111yescharacteristic
341C2×C4(C22⋊D11)⋊C411yescharacteristic
342C2×C4#6693711yescharacteristic
343C2×C4#6693811yescharacteristic
344C2×C4#6696711yescharacteristic
345C2×C4#6696711yescharacteristic
346C2×C4#6697111yescharacteristic
347C2×C4#6697111yescharacteristic
348C2×C4C4×C22⋊D1111yescharacteristic
349C2×C4#6699211yescharacteristic
350C8—42no—
351C8—221no—
352C8—221no—
353C8—221no—
354C8—221no—
355C8—442no—
356C22—21no—
357C22—21no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22#1062257011yescharacteristic
362C22#1062278911yescharacteristic
363C22#1062280311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—81no—
369C4—81no—
370C4—161no—
371C4—881no—
372C4—1761no—
373C4#1062240811yescharacteristic
374C4#1062240811yescharacteristic
375C4#1062241611yescharacteristic
376C4#1062241611yescharacteristic
377C2—21no—
378C2—21no—
379C2—1761no—
380C2#1306942911yescharacteristic
381C2#1306951111yescharacteristic
382C2#1306951311yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1518C2
socleC22×C11#390
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1518D11
hypocenterC11#9758
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
2. #13068778C2semidirect
3. #13067180C2semidirect
6. #13066909C2semidirect
7. C11×#1518C2semidirect
12. #10622706C4semidirect
13. #10622706C4semidirect
14. #10622701C4semidirect
15. #10622701C4semidirect
127. #1518D11semidirect
314. C11#9758semidirect

Maximal subgroups

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

subgroupindex
#130789412
#130687782
#130671802
#130671772
#130671752
#130669092
C11×#15182
#975811