Finite Group Databasebeta

← #14909105

Subgroups — #14909105

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079155C211yesmaximal, characteristic, complemented
2#13070857C212yesmaximal, complemented
3#13070852C212yesmaximal, complemented
4#13070847C212yesmaximal, complemented
5#13070839C212yesmaximal, complemented
6#13070332C211yesmaximal, characteristic, complemented
7#13070328C211yesmaximal, characteristic, complemented
8#13070323C211yesmaximal, characteristic, complemented
9C2×#10622200C211yesmaximal, characteristic, complemented
10#13070213C211yesmaximal, characteristic, complemented
11C11×#3155C211yesmaximal, characteristic
12C2×C11×AGL(1,ℤ/8)—21no—
13C2×C11×#135C2211yescharacteristic
14C22×C11×D8C2211yescharacteristic
15C11×#535—21no—
16#10623050—21no—
17C11×#496—22no—
18C11×#495C2212yes—
19C11×#493C2212yes—
20C11×#405C2211yescharacteristic
21#10622734—21no—
22#10622719C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622315—22no—
27#10622296C2212yescomplemented
28#10622295C2212yescomplemented
29#10622202C2211yescharacteristic, complemented
30#10622202C2212yescomplemented
31#10622202C2211yescharacteristic, complemented
32#10622200C2212yes—
33#10622200C2212yes—
34#10622200C2212yes—
35#10622200C2212yes—
36#10622200C2211yescharacteristic, complemented
37#10622200C2212yescomplemented
38#10622200C2211yescharacteristic, complemented
39#10622099C2212yescomplemented
40C4×C11⋊C16C2212yescomplemented
41C2×C11×#41—21no—
42C22×D4×C11—21no—
43C11×AGL(1,ℤ/8)—44no—
44C11×#135—22no—
45C11×#135—22no—
46C2×C11×Q16C2311yescharacteristic
47C2×C11×SD16—22no—
48C2×C11×SD16—21no—
49C2×C11×D8—22no—
50C2×C11×D8—21no—
51C2×C11×D8—22no—
52C2×C11×D8—22no—
53C2×C11×D8C2311yescharacteristic
54C2×C11×D8C2312yes—
55C2×C11×M16D411yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×#127—22no—
58C11×#124—22no—
59C11×#121—41no—
60C11×#121—41no—
61C11×#120—42no—
62C11×#117D411yescharacteristic
63#66979—21no—
64C2×C4⋊Dic11—21no—
65#66943—41no—
66#66941—41no—
67#66931—42no—
68#66923—22no—
69#66922—22no—
70C11×#97D412yes—
71C4×C8×C11C2312yes—
72#66882—22no—
73#66882—21no—
74#66882C2311yescharacteristic
75#66882C2312yes—
76#66882C2311yescharacteristic
77#66881—22no—
78#66881—21no—
79#66876—22no—
80C2×C11⋊C16—22no—
81C2×C11⋊C16C2311yescharacteristic
82C2×C11⋊C16C2312yes—
83C2×C11⋊C16C2311yescharacteristic
84#33702—111nomaximal, Sylow
85C24×C11—41no—
86C11×#41—42no—
87C11×#41—42no—
88C2×Q8×C11—21no—
89C2×D4×C11—22no—
90C2×D4×C11—21no—
91C2×D4×C11—41no—
92C2×D4×C11—42no—
93C2×D4×C11—41no—
94C2×D4×C11—42no—
95C2×D4×C11—42no—
96C2×D4×C11—42no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×Dic11—41no—
100C2×Dic22—42no—
101C11×Q16—21no—
102C11×Q16—21no—
103C11×SD16—42no—
104C11×SD16—44no—
105C11×D8—22no—
106C11×D8—22no—
107C11×D8—21no—
108C11×D8—21no—
109C11×D8—42no—
110C11×D8—44no—
111C11×M16SD1614yes—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D412yes—
114C2×C8×C11#4112yes—
115C2×C8×C11#4112yes—
116C2×C8×C11C2411yescharacteristic
117C11×C4⋊C4D811yescharacteristic
118C11×C4⋊C4D811yescharacteristic
119C11×C22⋊C4—42no—
120C11×C22⋊C4—42no—
121C11×C22⋊C4D812yes—
122C42×C11C2×D412yes—
123C22⋊Dic11—41no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—42no—
128C4⋊Dic11—41no—
129Dic11⋊C4—42no—
130Dic11⋊C4—42no—
131C4×Dic11—41no—
132C11⋊C16—21no—
133C11⋊C16—21no—
134C11⋊C16—22no—
135#3164—111no—
136#3155D1111yescharacteristic
137#2244—112no—
138#2243—112no—
139#2242—112no—
140#2240—112no—
141#2140—111no—
142#2139—111no—
143#2138—111no—
144C2×#357—111no—
145#2108—111no—
146C23×C11—42no—
147C23×C11—41no—
148C23×C11—82no—
149C23×C11—161no—
150C23×C11—161no—
151C23×C11C2×D811yescharacteristic
152Q8×C11—41no—
153Q8×C11—41no—
154D4×C11—42no—
155D4×C11—41no—
156D4×C11—41no—
157D4×C11—42no—
158D4×C11—82no—
159D4×C11—82no—
160D4×C11—162no—
161D4×C11—162no—
162C2×C4×C11—41no—
163C2×C4×C11—82no—
164C2×C4×C11#12412yes—
165C2×C4×C11C2×D812yes—
166C2×C4×C11C2×D812yes—
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C2×SD1612yes—
169C2×C4×C11C22×D411yescharacteristic
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—42no—
173C2×Dic11—161no—
174Dic22—162no—
175C8×C11#12412yes—
176C8×C11C2×SD1614yes—
177C8×C11C2×#4111yescharacteristic
178C8×C11C2×#4111yescharacteristic
179C2×AGL(1,ℤ/8)—21no—
180C2×#135C2×D1111yescharacteristic
181C22×D8C2×D1111yescharacteristic
182#544—221no—
183#535—21no—
184C2×M32—111no—
185C22×C16—111no—
186#501—222no—
187#500—112no—
188#499—112no—
189#496—22no—
190#495C2×D1112yes—
191#493C2×D1112yes—
192#428—221no—
193#427—111no—
194C2×#107—111no—
195#405C2×D1111yescharacteristic
196#358—111no—
197#358—111no—
198#358—112no—
199#357—112no—
200#357—112no—
201#357—111no—
202#357—111no—
203#357—112no—
204#357—112no—
205#357—112no—
206#346—112no—
207C4×C16—112no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—81no—
211C22×C11—82no—
212C22×C11—81no—
213C22×C11—82no—
214C22×C11—81no—
215C22×C11—82no—
216C22×C11—164no—
217C22×C11#48612yes—
218C22×C11C22×D811yescharacteristic
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—81no—
222C4×C11#48612yes—
223C4×C11C2×#12411yescharacteristic
224C4×C11C22×SD1611yescharacteristic
225Dic11—81no—
226Dic11—82no—
227Dic11—81no—
228C2×#41—21no—
229C22×D4—21no—
230AGL(1,ℤ/8)—44no—
231#135—22no—
232#135—22no—
233C2×Q16C22×D1111yescharacteristic
234C2×SD16—21no—
235C2×SD16—22no—
236C2×D8—22no—
237C2×D8—22no—
238C2×D8—21no—
239C2×D8—22no—
240C2×D8C22×D1112yes—
241C2×D8C22×D1111yescharacteristic
242C2×M16C22⋊D1111yescharacteristic
243C22×C8C22×D1111yescharacteristic
244C4⋊Q8—222no—
245C4⋊Q8—441no—
246#127—22no—
247#125—222no—
248#125—441no—
249#124—22no—
250C22⋊Q8—442no—
251#121—41no—
252#121—41no—
253#120—42no—
254#117—221no—
255#117C22⋊D1111yescharacteristic
256C2×C4⋊C4—221no—
257M32—222no—
258C2×C16—111no—
259C2×C16—112no—
260C2×C16—111no—
261C2×C16—222no—
262#107—112no—
263#107—111no—
264#107—111no—
265#107—221no—
266#107—222no—
267#106—221no—
268#106—222no—
269#97C22⋊D1112yes—
270C4×C8C22×D1112yes—
271C2×C11—22no—
272C2×C11—161no—
273C2×C11—162no—
274C2×C11C2×#48611yescharacteristic
275C2×C11#341511yescharacteristic
276C2×C11#341611yescharacteristic
277C24—41no—
278#41—42no—
279#41—42no—
280C2×Q8—21no—
281C2×Q8—442no—
282C2×D4—22no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—42no—
290C22×C4—41no—
291C22×C4—441no—
292C22×C4C2×C22⋊D1111yescharacteristic
293Q16—21no—
294Q16—21no—
295SD16—44no—
296SD16—42no—
297D8—22no—
298D8—22no—
299D8—21no—
300D8—21no—
301D8—44no—
302D8—42no—
303M16#432414yes—
304C2×C8#434112yes—
305C2×C8#434112yes—
306C2×C8C2×C22⋊D1112yes—
307C2×C8C2×C22⋊D1111yescharacteristic
308C2×C8C23×D1111yescharacteristic
309C4⋊C4—221no—
310C4⋊C4—222no—
311C4⋊C4—221no—
312C4⋊C4—441no—
313C4⋊C4—442no—
314C4⋊C4—442no—
315C4⋊C4—442no—
316C4⋊C4#432311yescharacteristic
317C4⋊C4#432311yescharacteristic
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—441no—
321C22⋊C4#432312yes—
322C42—441no—
323C42C2×C22⋊D1112yes—
324C16—221no—
325C16—221no—
326C16—222no—
327C11#3370211yescharacteristic, complemented, Sylow
328C23—42no—
329C23—41no—
330C23—82no—
331C23—161no—
332C23—161no—
333C23C2×#432311yescharacteristic
334Q8—41no—
335Q8—41no—
336Q8—1762no—
337D4—41no—
338D4—42no—
339D4—42no—
340D4—41no—
341D4—82no—
342D4—82no—
343D4—162no—
344D4—162no—
345C2×C4—41no—
346C2×C4—82no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—442no—
350C2×C4—1761no—
351C2×C4C2×#432312yes—
352C2×C4C2×#432312yes—
353C2×C4C2×#432311yescharacteristic
354C2×C4C2×#432412yes—
355C2×C4#6698912yes—
356C2×C4C22×C22⋊D1111yescharacteristic
357C8C2×#432414yes—
358C8#6698912yes—
359C8C2×#434111yescharacteristic
360C8C2×#434111yescharacteristic
361C22—21no—
362C22—21no—
363C22—81no—
364C22—82no—
365C22—81no—
366C22—82no—
367C22—81no—
368C22—82no—
369C22—164no—
370C22#1062268312yes—
371C22C22×#432311yescharacteristic
372C4—22no—
373C4—22no—
374C4—81no—
375C4—882no—
376C4—881no—
377C4—881no—
378C4#1062268312yes—
379C4C22×#432411yescharacteristic
380C4C2×#6698911yescharacteristic
381C2—22no—
382C2—162no—
383C2—161no—
384C2C2×#1062268311yescharacteristic
385C2#1308175511yescharacteristic
386C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3155C2
socleC22×C11C22×D8
hypercenter#3155D11
hypocenterC11#33702
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. #13079155C2semidirect
2. #13070857C2semidirect
3. #13070852C2semidirect
4. #13070847C2semidirect
5. #13070839C2semidirect
6. #13070332C2semidirect
7. #13070328C2semidirect
8. #13070323C2semidirect
9. C2×#10622200C2semidirect
10. #13070213C2semidirect
27. #10622296C22semidirect
28. #10622295C22semidirect
29. #10622202C22semidirect
30. #10622202C22semidirect
31. #10622202C22semidirect
36. #10622200C22semidirect
37. #10622200C22semidirect
38. #10622200C22semidirect
39. #10622099C22semidirect
40. C4×C11⋊C16C22semidirect
327. C11#33702semidirect

Maximal subgroups

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

subgroupindex
#130791552
#130708572
#130708522
#130708472
#130708392
#130703322
#130703282
#130703232
C2×#106222002
#130702132
C11×#31552
#3370211