Finite Group Databasebeta

← #14807190

Subgroups — #14807190

Order 2816.

1188 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078998C211yesmaximal, characteristic, complemented
2#13078103C211yesmaximal, characteristic, complemented
3#13076972C211yesmaximal, characteristic, complemented
4#13069643C214yesmaximal, complemented
5#13069594C211yesmaximal, characteristic, complemented
6#13069457C211yesmaximal, characteristic, complemented
7#13069004C214yesmaximal, complemented
8C4×#66901C211yesmaximal, characteristic, complemented
9C11×#3508C211yesmaximal, characteristic
10C11×#559—22no—
11C11×#550—22no—
12C11×#546—24no—
13C11×#540—22no—
14C11×#535C2212yes—
15C11×#533C2211yescharacteristic
16C11×#532—22no—
17C2×C11×#127C2211yescharacteristic
18C11×#518C2212yes—
19C4×C11×#41C2211yescharacteristic
20C2×#67004C2212yes—
21C2×#66989C2214yes—
22C2×#66922C2211yescharacteristic
23C2×#66901C2212yes—
24#10622834—24no—
25C2×#66897C2214yes—
26#10622706—22no—
27#10622682—22no—
28#10622644—22no—
29#10622632—22no—
30#10622617C2214yes—
31#10622617C2212yes—
32C42×Dic11C2211yescharacteristic
33#10622537C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622170C2214yes—
36#10622170C2212yes—
37C2×C11×#41—24no—
38C2×C11×#41C2311yescharacteristic
39C22×D4×C11D414yes—
40C22×D4×C11C2312yes—
41C22×Dic22C2312yes—
42C11×C4⋊Q8D412yes—
43C11×#127—22no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127—22no—
47C11×#125D412yes—
48C11×#124—24no—
49C11×#124—22no—
50C11×#123—28no—
51C11×C22⋊Q8—22no—
52C11×#121—24no—
53C11×#121—28no—
54C11×#121—24no—
55C11×#120—24no—
56C4×Q8×C11—22no—
57C4×Q8×C11D412yes—
58C4×D4×C11—24no—
59C4×D4×C11—22no—
60C4×D4×C11—24no—
61C4×D4×C11—24no—
62C4×D4×C11D412yes—
63C11×#117—21no—
64C11×#117C2311yescharacteristic
65C11×#117C2312yes—
66C2×C11×C22⋊C4—24no—
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—28no—
70#67004—44no—
71C2×#4326—22no—
72#66989—28no—
73#66989—44no—
74C2×#4324—22no—
75C2×C4⋊Dic11—22no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11C2312yes—
78C2×#4318C2312yes—
79C2×#4318C2312yes—
80#66922—22no—
81#66922—21no—
82#66922—21no—
83#66901—24no—
84#66897—44no—
85#66874—24no—
86#66874—28no—
87C4⋊(C11⋊C8)—22no—
88#66867—21no—
89C4×C11⋊C8—21no—
90#25590—111nomaximal, Sylow
91C24×C11C2×D414yes—
92C11×#41—22no—
93C11×#41—22no—
94C11×#41—88no—
95C2×Q8×C11—22no—
96C2×Q8×C11C2×D411yescharacteristic
97C2×D4×C11—21no—
98C2×D4×C11—28no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—24no—
104C2×D4×C11—24no—
105C2×D4×C11—48no—
106C2×D4×C11C2×D411yescharacteristic
107C22×C4×C11—28no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—22no—
113C22×Dic11—22no—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22—24no—
117C2×Dic22—24no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4C2×D412yes—
122C11×C4⋊C4C2×D414yes—
123C11×C22⋊C4—28no—
124C11×C22⋊C4—28no—
125C11×C22⋊C4—21no—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—22no—
128C42×C11—22no—
129C42×C11—21no—
130C42×C11—22no—
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D412yes—
134C22⋊Dic11—416no—
135#4326—44no—
136#4324—44no—
137C4⋊Dic11—42no—
138C4⋊Dic11—42no—
139C4×Dic11—22no—
140C4×Dic11—44no—
141C4×Dic11#4114yescomplemented
142#4318—22no—
143#4318—22no—
144#4318—24no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147#3508D1111yescharacteristic
148#3139—111no—
149#3039—111no—
150#2858—111no—
151#2004—114no—
152#1994—111no—
153#1965—111no—
154#1885—114no—
155C4×#104—111no—
156C23×C11—24no—
157C23×C11—21no—
158C23×C11—28no—
159C23×C11—48no—
160C23×C11C22×D411yescharacteristic
161Q8×C11—21no—
162Q8×C11—21no—
163Q8×C11—44no—
164D4×C11—21no—
165D4×C11—21no—
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—44no—
170D4×C11—48no—
171D4×C11—84no—
172D4×C11—88no—
173C2×C4×C11—24no—
174C2×C4×C11—21no—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—42no—
178C2×C4×C11—44no—
179C2×C4×C11—88no—
180C2×C4×C11#12012yes—
181C2×C4×C11#12012yes—
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C2×#4112yes—
185C2×C4×C11H(5,𝔽2)12yes—
186C2×Dic11—24no—
187C2×Dic11—44no—
188C2×Dic11—42no—
189C2×Dic11—44no—
190Dic22—42no—
191Dic22—42no—
192Dic22—44no—
193C11⋊C8—42no—
194C11⋊C8—42no—
195C2×#137—112no—
196#559—22no—
197#550—22no—
198#546—24no—
199#540—22no—
200#535C2×D1112yes—
201#533C2×D1111yescharacteristic
202#532—22no—
203C2×C4⋊Q8—111no—
204C2×#127C2×D1111yescharacteristic
205C2×#124—114no—
206#518C2×D1112yes—
207C4×#41C2×D1111yescharacteristic
208#491—222no—
209#487—222no—
210#462—222no—
211#461—222no—
212#423—111no—
213C2×#104—112no—
214#419—114no—
215#419—112no—
216C2×#100—114no—
217C4×M16—111no—
218#390—224no—
219C43—111no—
220#339—112no—
221#339—114no—
222C22×C11—22no—
223C22×C11—41no—
224C22×C11—44no—
225C22×C11—42no—
226C22×C11—48no—
227C22×C11—88no—
228C22×C11C2×#12011yescharacteristic
229C22×C11#54612yes—
230C4×C11—22no—
231C4×C11—41no—
232C4×C11—42no—
233C4×C11—44no—
234C4×C11#45514yes—
235C4×C11#53211yescharacteristic
236C4×C11#53511yescharacteristic
237C4×C11#55012yes—
238Dic11—44no—
239Dic11—82no—
240C2×#41—24no—
241C2×#41C22×D1111yescharacteristic
242C22×Q8—112no—
243C22×D4C22⋊D1114yes—
244C22×D4C22×D1112yes—
245#137—444no—
246C2×Q16—222no—
247C2×SD16—222no—
248C2×M16—112no—
249C2×M16—112no—
250C4⋊Q8—222no—
251C4⋊Q8—221no—
252C4⋊Q8—221no—
253C4⋊Q8C22⋊D1112yes—
254#127—22no—
255#127—21no—
256#127—21no—
257#127—22no—
258#125C22⋊D1112yes—
259#124—24no—
260#124—22no—
261#124—228no—
262#124—444no—
263#123—28no—
264C22⋊Q8—22no—
265#121—24no—
266#121—28no—
267#121—24no—
268#120—24no—
269C4×Q8—22no—
270C4×Q8C22⋊D1112yes—
271C4×D4—24no—
272C4×D4—22no—
273C4×D4—24no—
274C4×D4—24no—
275C4×D4C22⋊D1112yes—
276#117—21no—
277#117C22×D1111yescharacteristic
278#117C22×D1112yes—
279C2×C4⋊C4—222no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—228no—
282C2×C42—21no—
283C2×C42—112no—
284C2×C42—222no—
285C2×C42C22×D1111yescharacteristic
286C4⋊C8—222no—
287#104—224no—
288#103—224no—
289#103—228no—
290#100—444no—
291#97—221no—
292C4×C8—221no—
293C2×C11—22no—
294C2×C11—81no—
295C2×C11—84no—
296C2×C11#243111yescharacteristic
297C2×C11C2×#45512yes—
298C24C2×C22⋊D1114yes—
299#41—22no—
300#41—22no—
301#41—88no—
302C2×Q8—22no—
303C2×Q8—224no—
304C2×Q8—224no—
305C2×Q8—222no—
306C2×Q8—222no—
307C2×Q8C2×C22⋊D1111yescharacteristic
308C2×D4—21no—
309C2×D4—28no—
310C2×D4—24no—
311C2×D4—24no—
312C2×D4—24no—
313C2×D4—24no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—48no—
317C2×D4C2×C22⋊D1111yescharacteristic
318C22×C4—28no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—222no—
322C22×C4—222no—
323C22×C4C2×C22⋊D1112yes—
324C22×C4C23×D1111yescharacteristic
325Q16—444no—
326SD16—444no—
327M16—222no—
328M16—222no—
329M16—224no—
330C2×C8—222no—
331C2×C8—222no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—24no—
335C4⋊C4—442no—
336C4⋊C4—442no—
337C4⋊C4C2×C22⋊D1112yes—
338C4⋊C4C2×C22⋊D1114yes—
339C22⋊C4—28no—
340C22⋊C4—28no—
341C22⋊C4—21no—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—4416no—
345C42—22no—
346C42—21no—
347C42—22no—
348C42—114no—
349C42—222no—
350C42—444no—
351C42C2×C22⋊D1111yescharacteristic
352C42C2×C22⋊D1111yescharacteristic
353C42C2×C22⋊D1112yes—
354C11#2559011yescharacteristic, complemented, Sylow
355C23—24no—
356C23—21no—
357C23—28no—
358C23—48no—
359C23C22×C22⋊D1111yescharacteristic
360Q8—21no—
361Q8—21no—
362Q8—44no—
363Q8—442no—
364Q8—442no—
365Q8—444no—
366D4—21no—
367D4—21no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—44no—
372D4—48no—
373D4—84no—
374D4—88no—
375C2×C4—24no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—42no—
380C2×C4—44no—
381C2×C4—88no—
382C2×C4—224no—
383C2×C4—444no—
384C2×C4—444no—
385C2×C4—442no—
386C2×C4#6700612yes—
387C2×C4#6700612yes—
388C2×C4#41×D1112yes—
389C2×C4#6704212yes—
390C2×C4C22×C22⋊D1111yescharacteristic
391C2×C4C22×C22⋊D1111yescharacteristic
392C8—442no—
393C8—442no—
394C22—22no—
395C22—41no—
396C22—44no—
397C22—42no—
398C22—48no—
399C22—88no—
400C22#1062336012yes—
401C22C2×#6700611yescharacteristic
402C4—22no—
403C4—41no—
404C4—42no—
405C4—44no—
406C4—444no—
407C4—882no—
408C4#1062285514yes—
409C4#1062336111yescharacteristic
410C4#1062336311yescharacteristic
411C4#1062336512yes—
412C2—22no—
413C2—84no—
414C2—81no—
415C2#1307223111yescharacteristic
416C2C2×#1062285512yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3508C2
socleC22×C11C2×#120
hypercenter#3508D11
hypocenterC11#25590
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13078998C2semidirect
2. #13078103C2semidirect
3. #13076972C2semidirect
4. #13069643C2semidirect
5. #13069594C2semidirect
6. #13069457C2semidirect
7. #13069004C2semidirect
8. C4×#66901C2semidirect
141. C4×Dic11#41semidirect
354. C11#25590semidirect

Maximal subgroups

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

subgroupindex
#130789982
#130781032
#130769722
#130696432
#130695942
#130694572
#130690042
C4×#669012
C11×#35082
#2559011