Finite Group Databasebeta

← #14909801

Subgroups — #14909801

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079266C211yesmaximal, characteristic, complemented
2#13070883C211yesmaximal, characteristic, complemented
3#13070865C211yesmaximal, characteristic, complemented
4#13070857C211yesmaximal, characteristic, complemented
5#13070847C211yesmaximal, characteristic, complemented
6#13070668C212yesmaximal, complemented
7#13070648C212yesmaximal, complemented
8#13070539C212yesmaximal, complemented
9#13070528C212yesmaximal, complemented
10#13070423C211yesmaximal, characteristic, complemented
11C11×#3155C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)—21no—
13C2×C11×#135C2211yescharacteristic
14C22×C11×D8C2211yescharacteristic
15C11×#535—21no—
16#10623066—21no—
17C11×#496—21no—
18C11×#496—21no—
19C11×#495C2211yescharacteristic
20C11×#495C2211yescharacteristic
21C11×#493C2211yescharacteristic
22C11×#493C2211yescharacteristic
23C11×#405C2211yescharacteristic
24C2×#66892C2212yescomplemented
25C2×#66890C2212yes—
26C2×#66890C2212yes—
27C2×#66890C2212yescomplemented
28#10622748—21no—
29#10622728C2212yes—
30#10622326—21no—
31#10622324—21no—
32#10622308C2211yescharacteristic, complemented
33C4×D88C2212yescomplemented
34#10622296C2211yescharacteristic, complemented
35#10622202C2212yescomplemented
36#10622200C2212yes—
37#10622200C2212yes—
38#10622200C2212yescomplemented
39C22⋊(C11⋊C16)C2212yes—
40C4⋊(C11⋊C16)C2212yescomplemented
41#10622099C2211yescharacteristic, complemented
42C4×C11⋊C16C2211yescharacteristic, complemented
43C2×C11×#41—21no—
44C22×D4×C11—21no—
45C11×AGL(1,ℤ/8)—44no—
46C11×#135—42no—
47C2×C11×Q16C2311yescharacteristic
48C2×C11×SD16—21no—
49C2×C11×SD16—21no—
50C2×C11×SD16—21no—
51C2×C11×D8—21no—
52C2×C11×D8—21no—
53C2×C11×D8—21no—
54C2×C11×D8—42no—
55C2×C11×D8C2311yescharacteristic
56C2×C11×D8C2311yescharacteristic
57C2×C11×D8C2311yescharacteristic
58C2×C11×M16D411yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×#127—21no—
61C11×#127—21no—
62C11×#124—21no—
63C11×#124—21no—
64C11×#121—42no—
65C11×#120—42no—
66C11×#117D411yescharacteristic
67#66983—22no—
68C2×D88—21no—
69C2×D88C2312yes—
70#66947—42no—
71#66937—42no—
72#66927—21no—
73C4×D44—22no—
74#66923—21no—
75C11×#97D411yescharacteristic
76C11×#97D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#66892—42no—
80#66890—42no—
81#66890—42no—
82#66890—42no—
83#66885—22no—
84#66885—22no—
85#66882C2312yes—
86#66881—21no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33786—111nomaximal, Sylow
90C24×C11—41no—
91C11×#41—42no—
92C11×#41—42no—
93C2×Q8×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—42no—
102C2×D4×C11—42no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C2×C22⋊D11—42no—
106C2×D44—22no—
107C2×D44—42no—
108C2×C4×D11—42no—
109C11×Q16—22no—
110C11×SD16—42no—
111C11×SD16—42no—
112C11×SD16—42no—
113C11×D8—22no—
114C11×D8—22no—
115C11×D8—22no—
116C11×D8—42no—
117C11×D8—42no—
118C11×D8—42no—
119C11×M16—22no—
120C2×C8×C11—22no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2411yescharacteristic
125C11×C4⋊C4D812yes—
126C11×C22⋊C4—42no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4D812yes—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131(C2×D11)⋊C4—42no—
132(C2×D11)⋊C4—42no—
133C4⋊Dic11—22no—
134Dic11⋊C4—42no—
135D88—22no—
136D88—22no—
137D88—42no—
138C11⋊C16—22no—
139C11⋊C16—22no—
140#3176—111no—
141#3155D1111yescharacteristic, complemented
142#2250—111no—
143#2246—111no—
144#2244—111no—
145#2242—111no—
146#2210—112no—
147#2206—112no—
148#2186—112no—
149#2184—112no—
150#2164—111no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—82no—
155C23×C11—162no—
156C23×C11C2×D811yescharacteristic
157C22×D11—42no—
158Q8×C11—41no—
159Q8×C11—41no—
160D4×C11—41no—
161D4×C11—41no—
162D4×C11—41no—
163D4×C11—41no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—82no—
167D4×C11—82no—
168D4×C11—162no—
169D4×C11—162no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—41no—
173C2×C4×C11—82no—
174C2×C4×C11C2×D812yes—
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C2×D812yes—
177C2×C4×C11C22×D411yescharacteristic
178C22⋊D11—162no—
179C2×Dic11—42no—
180D44—42no—
181D44—42no—
182D44—162no—
183C4×D11—162no—
184C8×C11—21no—
185C8×C11—21no—
186C8×C11AGL(1,ℤ/8)12yes—
187C8×C11H(5,𝔽2)12yes—
188C2×AGL(1,ℤ/8)—21no—
189C2×#135C2×D1111yescharacteristic
190C22×D8C2×D1111yescharacteristic
191#540—221no—
192#535—21no—
193C2×SD32—112no—
194C2×D16—112no—
195C2×D16—112no—
196C2×D16—112no—
197#499—111no—
198#496—21no—
199#496—21no—
200#495C2×D1111yescharacteristic
201#495C2×D1111yescharacteristic
202#493—111no—
203#493C2×D1111yescharacteristic
204#493C2×D1111yescharacteristic
205#490—221no—
206#469—221no—
207#466—112no—
208#442—221no—
209C4×D8—112no—
210#405C2×D1111yescharacteristic
211C4⋊C16—112no—
212#358—112no—
213#357—112no—
214#357—112no—
215#357—112no—
216C22⋊C16—112no—
217#346—111no—
218C4×C16—111no—
219C22×C11—22no—
220C22×C11—21no—
221C22×C11—82no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—164no—
228C22×C11C22×D811yescharacteristic
229C2×D11—82no—
230C2×D11—82no—
231C2×D11—82no—
232C4×C11—22no—
233C4×C11—22no—
234C4×C11—21no—
235C4×C11—81no—
236C4×C11#53511yescharacteristic
237C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
238Dic11—82no—
239C2×#41—21no—
240C22×D4—21no—
241AGL(1,ℤ/8)—44no—
242#135—42no—
243C2×Q16C22×D1111yescharacteristic
244C2×SD16—21no—
245C2×SD16—21no—
246C2×SD16—21no—
247C2×D8—21no—
248C2×D8—21no—
249C2×D8—21no—
250C2×D8—42no—
251C2×D8—112no—
252C2×D8—221no—
253C2×D8C22×D1111yescharacteristic
254C2×D8C22×D1111yescharacteristic
255C2×D8C22×D1111yescharacteristic
256C2×M16C22⋊D1111yescharacteristic
257C22×C8C22×D1111yescharacteristic
258#127—21no—
259#127—21no—
260#127—221no—
261#125—221no—
262#124—21no—
263#124—21no—
264#123—442no—
265#121—42no—
266#121—222no—
267#121—442no—
268#120—42no—
269C4×D4—222no—
270#117C22⋊D1111yescharacteristic
271SD32—442no—
272D16—442no—
273D16—442no—
274D16—442no—
275C2×C16—112no—
276C2×C16—112no—
277#107—112no—
278#106—221no—
279#102—222no—
280#102—222no—
281#97C22⋊D1111yescharacteristic
282#97C22⋊D1111yescharacteristic
283C4×C8C22×D1111yescharacteristic
284C4×C8C22×D1111yescharacteristic
285C2×C11—41no—
286C2×C11—161no—
287C2×C11—161no—
288C2×C11—161no—
289C2×C11#320511yescharacteristic
290C2×C11#341512yes—
291D11—162no—
292C24—41no—
293#41—42no—
294#41—42no—
295C2×Q8—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—42no—
304C2×D4—42no—
305C2×D4—222no—
306C2×D4—442no—
307C2×D4—442no—
308C22×C4—41no—
309C22×C4—442no—
310C22×C4C2×C22⋊D1111yescharacteristic
311Q16—22no—
312SD16—42no—
313SD16—42no—
314SD16—42no—
315D8—22no—
316D8—22no—
317D8—22no—
318D8—42no—
319D8—42no—
320D8—42no—
321D8—222no—
322D8—222no—
323D8—442no—
324M16—22no—
325C2×C8—22no—
326C2×C8C2×C22⋊D1111yescharacteristic
327C2×C8C2×C22⋊D1111yescharacteristic
328C2×C8C2×C22⋊D1111yescharacteristic
329C2×C8C23×D1111yescharacteristic
330C4⋊C4—222no—
331C4⋊C4—442no—
332C4⋊C4#432312yes—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—442no—
336C22⋊C4—442no—
337C22⋊C4#432312yes—
338C42C2×C22⋊D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C16—222no—
341C16—222no—
342C11#3378611yescharacteristic, complemented, Sylow
343C23—41no—
344C23—41no—
345C23—41no—
346C23—82no—
347C23—162no—
348C23—442no—
349C23C2×#432311yescharacteristic
350Q8—41no—
351Q8—41no—
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—41no—
358D4—82no—
359D4—82no—
360D4—162no—
361D4—162no—
362D4—442no—
363D4—442no—
364D4—1762no—
365D4—1762no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—82no—
370C2×C4—442no—
371C2×C4—1762no—
372C2×C4C2×#432312yes—
373C2×C4C2×#432312yes—
374C2×C4C2×#432311yescharacteristic
375C2×C4C22×C22⋊D1111yescharacteristic
376C8—21no—
377C8—21no—
378C8#6698512yes—
379C8#6703712yes—
380C22—22no—
381C22—21no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—164no—
389C22—882no—
390C22—882no—
391C22—882no—
392C22C22×#432311yescharacteristic
393C4—22no—
394C4—22no—
395C4—21no—
396C4—81no—
397C4—882no—
398C4C2×#6698511yescharacteristic
399C4#1062333611yescharacteristic
400C2—41no—
401C2—161no—
402C2—161no—
403C2—161no—
404C2—1762no—
405C2#1307953411yescharacteristic
406C2#1308175512yes—
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3155C2
socleC22×C11C22×D8
hypercenter#3155D11
hypocenterC11#33786
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3155

Complements

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

NH ≅ G/Ntype
1. #13079266C2semidirect
2. #13070883C2semidirect
3. #13070865C2semidirect
4. #13070857C2semidirect
5. #13070847C2semidirect
6. #13070668C2semidirect
7. #13070648C2semidirect
8. #13070539C2semidirect
9. #13070528C2semidirect
10. #13070423C2semidirect
11. C11×#3155C2semidirect
24. C2×#66892C22semidirect
27. C2×#66890C22semidirect
32. #10622308C22semidirect
33. C4×D88C22semidirect
34. #10622296C22semidirect
35. #10622202C22semidirect
38. #10622200C22semidirect
40. C4⋊(C11⋊C16)C22semidirect
41. #10622099C22semidirect
42. C4×C11⋊C16C22semidirect
141. #3155D11semidirect
342. C11#33786semidirect

Maximal subgroups

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

subgroupindex
#130792662
#130708832
#130708652
#130708572
#130708472
#130706682
#130706482
#130705392
#130705282
#130704232
C11×#31552
#3378611