Finite Group Databasebeta

← #14908672

Subgroups — #14908672

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078226C211yesmaximal, characteristic
2C2×#10622506C211yesmaximal, characteristic, complemented
3#13070837C214yesmaximal, complemented
4#13070832C214yesmaximal, complemented
5#13070388C211yesmaximal, characteristic, complemented
6#13070366C211yesmaximal, characteristic, complemented
7#13070363C211yesmaximal, characteristic, complemented
8C2×#10622152C211yesmaximal, characteristic, complemented
9C11×#2155C211yesmaximal, characteristic, complemented
10C2×M16×D11—21no—
11C2×#66957C2211yescharacteristic
12C22×#4313C2211yescharacteristic
13#10623055—21no—
14C2×C11×M32C2211yescharacteristic
15C2×C11×#108C2211yescharacteristic
16C11×#427C2211yescharacteristic
17C2×#66886—21no—
18C2×#66883C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20#10622615—21no—
21#10622506—22no—
22#10622506C2214yes—
23#10622499—22no—
24#10622481C2212yes—
25#10622478C2212yes—
26C11×#365C2214yescomplemented
27#10622155C2212yescomplemented
28#10622154C2212yescomplemented
29#10622152C2214yes—
30#10622134C2212yescomplemented
31#10622133C2212yescomplemented
32#10622125C2214yescomplemented
33C2×#4339—21no—
34C22×C4×D11D411yescharacteristic
35C2×C11×M16—21no—
36C22×C8×C11C2311yescharacteristic
37C11×#117—21no—
38C2×#4318—21no—
39C22×C11⋊C8D411yescharacteristic
40M16×D11—24no—
41M16×D11—42no—
42C2×Dic44C2311yescharacteristic
43#66957—21no—
44#66957—21no—
45#66957—21no—
46#66957—21no—
47C2×D88C2311yescharacteristic
48C2×#4314—21no—
49C2×#4313—21no—
50C2×#4313—21no—
51C2×#4313—21no—
52C2×#4313—21no—
53C2×#4313—41no—
54C2×#4313D412yes—
55C2×#4313C2312yes—
56C2×C8×D11—41no—
57#66950—22no—
58#66948—22no—
59#66939—41no—
60#66935—41no—
61C4×D44—42no—
62C11×M32—21no—
63C11×M32C2312yes—
64C2×C11×C16—21no—
65C11×#108—21no—
66C11×#108C2312yes—
67C11×#107—21no—
68C11×#106C2312yes—
69#66886—24no—
70#66883—21no—
71#66883C2312yes—
72#66876—21no—
73#66876C2312yes—
74C2×C11⋊C16—21no—
75#66874—22no—
76#66873—22no—
77#33656—111nomaximal, Sylow
78C23×D11SD1611yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C2×C22⋊D11—41no—
81C22×Dic11SD1611yescharacteristic
82#4339—41no—
83#4339—41no—
84#4339—41no—
85#4339—41no—
86C2×D44—21no—
87C2×D44—42no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—41no—
93C2×C4×D11SD1612yes—
94C2×C4×D11C2×D412yes—
95C2×Dic22—21no—
96C11×M16—22no—
97C11×M16—41no—
98C2×C8×C11—41no—
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11#4111yescharacteristic
101C2×C8×C11#4111yescharacteristic
102C2×C8×C11#4111yescharacteristic
103C2×C8×C11#4111yescharacteristic
104C2×C8×C11C2411yescharacteristic
105C11×C4⋊C4—22no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110C4⋊Dic11—42no—
111#4318—22no—
112#4318—41no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—21no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8C2×D412yes—
117Dic44—21no—
118Dic44—21no—
119D88—21no—
120D88—21no—
121#4314—41no—
122#4314—41no—
123#4313—22no—
124#4313—22no—
125#4313—22no—
126#4313—22no—
127#4313—44no—
128C8×D11—44no—
129C11×C16—22no—
130C11⋊C16—22no—
131#3054—111no—
132C2×#430—111no—
133#2239—114no—
134#2238—114no—
135#2155—111no—
136#2155D1111yescharacteristic, complemented
137#2148—111no—
138#2148—111no—
139C2×#349—111no—
140C23×C11C2×SD1611yescharacteristic
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—41no—
144C22×D11—81no—
145C22×D11C2×SD1612yes—
146C2×C4×C11—42no—
147C2×C4×C11#12311yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×C4×C11C2×SD1611yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C22⋊D11—81no—
154C22⋊D11—81no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—41no—
158C2×Dic11C2×SD1612yes—
159D44—41no—
160D44—41no—
161D44—84no—
162C4×D11—22no—
163C4×D11—22no—
164C4×D11—22no—
165C4×D11—22no—
166C4×D11—81no—
167C4×D11—81no—
168Dic22—41no—
169Dic22—41no—
170C8×C11—42no—
171C8×C11#12311yescharacteristic
172C8×C11#12311yescharacteristic
173C8×C11C2×#4111yescharacteristic
174C8×C11C2×#4111yescharacteristic
175C11⋊C8—22no—
176C11⋊C8—42no—
177C2×#135—111no—
178C22×M16—111no—
179C22×M16—221no—
180#525—221no—
181C2×M32—111no—
182C2×M32C2×D1111yescharacteristic
183#470—112no—
184#469—112no—
185#468—222no—
186#430—114no—
187#430—222no—
188C2×#108—111no—
189C2×#108—221no—
190C2×#108C2×D1111yescharacteristic
191#427C2×D1111yescharacteristic
192#416—221no—
193#365—114no—
194#365C2×D1114yescomplemented
195#362—112no—
196#362—112no—
197#361—112no—
198#361—112no—
199#349—114no—
200C22×C11—41no—
201C22×C11#48111yescharacteristic
202C22×C11#48111yescharacteristic
203C22×C11C22×SD1611yescharacteristic
204C2×D11—22no—
205C2×D11—42no—
206C2×D11—42no—
207C2×D11—81no—
208C2×D11—82no—
209C2×D11—81no—
210C4×C11—82no—
211C4×C11#48111yescharacteristic
212C4×C11#48111yescharacteristic
213C4×C11C2×#12311yescharacteristic
214C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
215Dic11—22no—
216Dic11—81no—
217C2×#41—221no—
218C23×C4—111no—
219#135—221no—
220#135—221no—
221#135—221no—
222#135—221no—
223C2×Q16—111no—
224C2×SD16—221no—
225C2×D8—111no—
226C2×M16—21no—
227C2×M16—112no—
228C2×M16—112no—
229C2×M16—221no—
230C2×M16—221no—
231C2×M16—221no—
232C2×M16—221no—
233C2×M16—224no—
234C2×M16—221no—
235C2×M16—441no—
236C2×M16—442no—
237C22×C8—111no—
238C22×C8—441no—
239C22×C8C22×D1111yescharacteristic
240#123—441no—
241C22⋊Q8—222no—
242#121—222no—
243#120—441no—
244C4×D4—442no—
245#117—21no—
246M32—21no—
247M32—112no—
248M32—221no—
249M32C22×D1112yes—
250C2×C16—21no—
251C2×C16—221no—
252#108—21no—
253#108—112no—
254#108—224no—
255#108—221no—
256#108C22×D1112yes—
257#107—21no—
258#106C22×D1112yes—
259#103—222no—
260#102—222no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—21no—
264C2×C11C2×#48111yescharacteristic
265D11—42no—
266D11—161no—
267C24—111no—
268#41—441no—
269#41—441no—
270#41—441no—
271#41—441no—
272C2×Q8—221no—
273C2×D4—221no—
274C2×D4—442no—
275C2×D4—441no—
276C22×C4—111no—
277C22×C4—112no—
278C22×C4—112no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—441no—
284C22×C4D4×D1111yescharacteristic
285Q16—221no—
286Q16—221no—
287SD16—441no—
288SD16—441no—
289D8—221no—
290D8—221no—
291M16—22no—
292M16—41no—
293M16—222no—
294M16—222no—
295M16—222no—
296M16—222no—
297M16—222no—
298M16—444no—
299M16—441no—
300C2×C8—41no—
301C2×C8—112no—
302C2×C8—221no—
303C2×C8—221no—
304C2×C8—444no—
305C2×C8—441no—
306C2×C8#433911yescharacteristic
307C2×C8#433911yescharacteristic
308C2×C8D4×D1111yescharacteristic
309C2×C8#434311yescharacteristic
310C2×C8#434311yescharacteristic
311C2×C8C23×D1111yescharacteristic
312C4⋊C4—22no—
313C4⋊C4—442no—
314C22⋊C4—41no—
315C22⋊C4—442no—
316C22⋊C4—442no—
317C42—41no—
318C16—22no—
319C16—222no—
320C11#3365611yescharacteristic, complemented, Sylow
321C23—112no—
322C23—221no—
323C23—221no—
324C23—441no—
325C23—881no—
326C23SD16×D1111yescharacteristic
327Q8—441no—
328Q8—441no—
329D4—441no—
330D4—441no—
331D4—884no—
332D4—881no—
333D4—881no—
334C2×C4—42no—
335C2×C4—112no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—222no—
339C2×C4—222no—
340C2×C4—222no—
341C2×C4—222no—
342C2×C4—441no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4#6694711yescharacteristic
346C2×C4#6694711yescharacteristic
347C2×C4SD16×D1111yescharacteristic
348C2×C4#6696711yescharacteristic
349C2×C4#6696711yescharacteristic
350C2×C4C2×D4×D1111yescharacteristic
351C8—42no—
352C8—222no—
353C8—442no—
354C8#6694711yescharacteristic
355C8#6694711yescharacteristic
356C8C2×#433911yescharacteristic
357C8C2×#434311yescharacteristic
358C22—41no—
359C22—222no—
360C22—442no—
361C22—442no—
362C22—881no—
363C22—882no—
364C22—881no—
365C22#1062247611yescharacteristic
366C22#1062247611yescharacteristic
367C22C2×SD16×D1111yescharacteristic
368C4—82no—
369C4—222no—
370C4—881no—
371C4#1062247611yescharacteristic
372C4#1062247611yescharacteristic
373C4C2×#6694711yescharacteristic
374C4C2×#6696711yescharacteristic
375C2—21no—
376C2—21no—
377C2—21no—
378C2—442no—
379C2—1761no—
380C2C2×#1062247611yescharacteristic
subgroupG/H
centerC4#10622476
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2155C2
socleC2×C11C2×#481
prime radical#13078226C2
hypercenter#2155D11
hypocenterC11#33656
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2155

Complements

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

NH ≅ G/Ntype
2. C2×#10622506C2semidirect
3. #13070837C2semidirect
4. #13070832C2semidirect
5. #13070388C2semidirect
6. #13070366C2semidirect
7. #13070363C2semidirect
8. C2×#10622152C2semidirect
9. C11×#2155C2semidirect
26. C11×#365C22semidirect
27. #10622155C22semidirect
28. #10622154C22semidirect
30. #10622134C22semidirect
31. #10622133C22semidirect
32. #10622125C22semidirect
136. #2155D11semidirect
194. #365C2×D11semidirect
320. C11#33656semidirect

Maximal subgroups

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

subgroupindex
#130782262
C2×#106225062
#130708372
#130708322
#130703882
#130703662
#130703632
C2×#106221522
C11×#21552
#3365611