Finite Group Databasebeta

← #14807199

Subgroups — #14807199

Order 2816.

1120 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078992C211yesmaximal, characteristic, complemented
2#13078096C211yesmaximal, characteristic
3#13076974C211yesmaximal, characteristic, complemented
4#13069636C214yesmaximal, complemented
5#13069594C211yesmaximal, characteristic, complemented
6#13069461C211yesmaximal, characteristic, complemented
7#13069019C214yesmaximal, complemented
8C4×#66901C211yesmaximal, characteristic, complemented
9C11×#3509C211yesmaximal, characteristic, complemented
10C11×#557—22no—
11C11×#556—22no—
12C11×#552—24no—
13C11×#541—22no—
14C11×#536C2212yes—
15C11×#533—22no—
16C11×#533C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C11×#519C2212yes—
19C4×C11×#41C2211yescharacteristic
20C2×#67002C2212yes—
21C2×#67000C2214yes—
22C2×#66927C2211yescharacteristic
23C2×#66901C2212yes—
24C2×#66900C2214yes—
25#10622701—22no—
26#10622680—22no—
27#10622640—22no—
28#10622628—22no—
29#10622614C2214yes—
30#10622614C2212yes—
31#10622601—24no—
32C42×Dic11C2211yescharacteristic
33#10622537C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622170C2214yes—
36#10622170C2212yes—
37C2×C11×#41C2311yescharacteristic
38C22×Q8×C11C2312yes—
39C22×D44—22no—
40C22×D44C2312yes—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8D412yes—
46C11×#126—28no—
47C11×#125—24no—
48C11×#125—28no—
49C11×#125D412yes—
50C11×#124—22no—
51C11×#123—24no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—24no—
55C4×Q8×C11—24no—
56C4×Q8×C11—24no—
57C4×Q8×C11—24no—
58C4×Q8×C11—22no—
59C4×Q8×C11D412yes—
60C4×D4×C11—22no—
61C4×D4×C11D412yes—
62C11×#117—24no—
63C11×#117—24no—
64C11×#117—21no—
65C11×#117C2311yescharacteristic
66C11×#117C2312yes—
67C2×C11×C4⋊C4D414yes—
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70#67002—44no—
71#67000—28no—
72#67000—44no—
73C2×#4325—22no—
74C2×#4323—22no—
75C2×(C2×D11)⋊C4—28no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11C2312yes—
78C2×#4318C2312yes—
79C2×#4318C2312yes—
80#66927—22no—
81#66927—21no—
82#66927—21no—
83#66901—24no—
84#66900—44no—
85#66873—24no—
86#66873—28no—
87C4⋊(C11⋊C8)—22no—
88#66867—21no—
89C4×C11⋊C8—21no—
90#25591—111nomaximal, Sylow
91C23×D11—22no—
92C11×#41—22no—
93C11×#41—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—24no—
98C2×Q8×C11—24no—
99C2×Q8×C11C2×D411yescharacteristic
100C2×D4×C11—21no—
101C2×D4×C11C2×D411yescharacteristic
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11C2×D414yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—24no—
111C2×D44—24no—
112C2×D44—48no—
113C2×D44—42no—
114C2×D44—42no—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—28no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4C2×D412yes—
123C11×C4⋊C4C2×D414yes—
124C11×C22⋊C4—28no—
125C11×C22⋊C4—21no—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—22no—
128C42×C11—28no—
129C42×C11—22no—
130C42×C11—21no—
131C42×C11—22no—
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D412yes—
135#4325—44no—
136#4323—44no—
137(C2×D11)⋊C4—416no—
138C4×Dic11—22no—
139C4×Dic11—44no—
140C4×Dic11#4114yes—
141#4318—22no—
142#4318—22no—
143#4318—24no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146#3509D1111yescharacteristic, complemented
147#3138—111no—
148#3038—111no—
149#2858—111no—
150#2003—114no—
151#1994—111no—
152#1966—111no—
153#1888—114no—
154C4×#104—111no—
155C23×C11—21no—
156C23×C11C22×D411yescharacteristic
157C22×D11—48no—
158C22×D11—42no—
159C22×D11—44no—
160Q8×C11—21no—
161Q8×C11—21no—
162Q8×C11—42no—
163Q8×C11—42no—
164Q8×C11—44no—
165Q8×C11—44no—
166D4×C11—21no—
167D4×C11—21no—
168D4×C11—42no—
169C2×C4×C11—24no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—21no—
174C2×C4×C11—28no—
175C2×C4×C11—42no—
176C2×C4×C11—44no—
177C2×C4×C11#12012yes—
178C2×C4×C11#12012yes—
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C2×#4112yes—
182C2×C4×C11H(5,𝔽2)12yes—
183C2×Dic11—24no—
184C2×Dic11—44no—
185D44—42no—
186D44—42no—
187D44—44no—
188D44—84no—
189D44—84no—
190C11⋊C8—42no—
191C11⋊C8—42no—
192C2×AGL(1,ℤ/8)—112no—
193#557—22no—
194#556—22no—
195#552—24no—
196#541—22no—
197#536C2×D1112yes—
198#533—22no—
199#533C2×D1111yescharacteristic
200C2×C4⋊Q8C2×D1111yescharacteristic
201C2×#127—111no—
202C2×#124—114no—
203#519C2×D1112yes—
204C4×#41C2×D1111yescharacteristic
205#490—222no—
206#486—222no—
207#460—222no—
208#459—222no—
209#423—111no—
210C2×#104—112no—
211#418—114no—
212#418—112no—
213C2×#101—114no—
214C4×M16—111no—
215#390—224no—
216C43—111no—
217#339—112no—
218#339—114no—
219C22×C11—22no—
220C22×C11—41no—
221C22×C11—42no—
222C22×C11C2×#12011yescharacteristic
223C22×C11#54612yes—
224C2×D11—88no—
225C2×D11—82no—
226C2×D11—84no—
227C4×C11—22no—
228C4×C11—44no—
229C4×C11—41no—
230C4×C11—42no—
231C4×C11—44no—
232C4×C11#45414yes—
233C4×C11#53211yescharacteristic
234C4×C11#53511yescharacteristic
235C4×C11#55012yes—
236Dic11—44no—
237C2×#41C22×D1111yescharacteristic
238C22×Q8C22×D1112yes—
239C22×D4—112no—
240C22×D4—222no—
241AGL(1,ℤ/8)—444no—
242C2×SD16—222no—
243C2×D8—222no—
244C2×M16—112no—
245C2×M16—112no—
246C4⋊Q8—22no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—22no—
250C4⋊Q8C22⋊D1112yes—
251#127—222no—
252#127—221no—
253#127—221no—
254#126—28no—
255#125—24no—
256#125—28no—
257#125C22⋊D1112yes—
258#124—22no—
259#124—228no—
260#124—444no—
261#123—24no—
262C22⋊Q8—24no—
263C22⋊Q8—22no—
264C22⋊Q8—24no—
265C4×Q8—24no—
266C4×Q8—24no—
267C4×Q8—24no—
268C4×Q8—22no—
269C4×Q8C22⋊D1112yes—
270C4×D4—22no—
271C4×D4C22⋊D1112yes—
272#117—24no—
273#117—24no—
274#117—21no—
275#117C22×D1111yescharacteristic
276#117C22×D1112yes—
277C2×C4⋊C4C22⋊D1114yes—
278C2×C22⋊C4—228no—
279C2×C42—21no—
280C2×C42—112no—
281C2×C42—222no—
282C2×C42C22×D1111yescharacteristic
283C4⋊C8—222no—
284#104—224no—
285#102—224no—
286#102—228no—
287#101—444no—
288#97—221no—
289C4×C8—221no—
290C2×C11—22no—
291C2×C11—81no—
292C2×C11#243111yescharacteristic
293C2×C11C2×#45412yes—
294D11—162no—
295C24—222no—
296#41—22no—
297#41—22no—
298C2×Q8—22no—
299C2×Q8—24no—
300C2×Q8—24no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8C2×C22⋊D1111yescharacteristic
304C2×D4—21no—
305C2×D4—224no—
306C2×D4—224no—
307C2×D4—222no—
308C2×D4—222no—
309C2×D4—448no—
310C2×D4—442no—
311C2×D4—442no—
312C2×D4C2×C22⋊D1111yescharacteristic
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—222no—
316C22×C4C2×C22⋊D1114yes—
317C22×C4C2×C22⋊D1112yes—
318C22×C4C23×D1111yescharacteristic
319SD16—444no—
320D8—444no—
321M16—222no—
322M16—222no—
323M16—224no—
324C2×C8—222no—
325C2×C8—222no—
326C4⋊C4—28no—
327C4⋊C4—28no—
328C4⋊C4—24no—
329C4⋊C4—24no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—24no—
333C4⋊C4C2×C22⋊D1112yes—
334C4⋊C4C2×C22⋊D1114yes—
335C22⋊C4—28no—
336C22⋊C4—21no—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—4416no—
340C42—28no—
341C42—22no—
342C42—21no—
343C42—22no—
344C42—114no—
345C42—222no—
346C42—444no—
347C42C2×C22⋊D1111yescharacteristic
348C42C2×C22⋊D1111yescharacteristic
349C42C2×C22⋊D1112yes—
350C11#2559111yescharacteristic, complemented, Sylow
351C23—21no—
352C23—448no—
353C23—444no—
354C23—442no—
355C23C22×C22⋊D1111yescharacteristic
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8—42no—
360Q8—44no—
361Q8—44no—
362D4—21no—
363D4—21no—
364D4—42no—
365D4—442no—
366D4—442no—
367D4—444no—
368D4—884no—
369D4—884no—
370C2×C4—24no—
371C2×C4—28no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—44no—
378C2×C4—224no—
379C2×C4—444no—
380C2×C4#6700612yes—
381C2×C4#6700612yes—
382C2×C4#41×D1112yes—
383C2×C4#6704212yes—
384C2×C4C22×C22⋊D1111yescharacteristic
385C2×C4C22×C22⋊D1111yescharacteristic
386C8—442no—
387C8—442no—
388C22—22no—
389C22—41no—
390C22—42no—
391C22—888no—
392C22—882no—
393C22—884no—
394C22#1062336012yes—
395C22C2×#6700611yescharacteristic
396C4—22no—
397C4—44no—
398C4—41no—
399C4—42no—
400C4—44no—
401C4—444no—
402C4#1062285814yes—
403C4#1062336111yescharacteristic
404C4#1062336311yescharacteristic
405C4#1062336512yes—
406C2—22no—
407C2—81no—
408C2—1762no—
409C2#1307223111yescharacteristic
410C2C2×#1062285812yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3509C2
socleC22×C11C2×#120
prime radical#13078096C2
hypercenter#3509D11
hypocenterC11#25591
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #13078992C2semidirect
3. #13076974C2semidirect
4. #13069636C2semidirect
5. #13069594C2semidirect
6. #13069461C2semidirect
7. #13069019C2semidirect
8. C4×#66901C2semidirect
9. C11×#3509C2semidirect
146. #3509D11semidirect
350. C11#25591semidirect

Maximal subgroups

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

subgroupindex
#130789922
#130780962
#130769742
#130696362
#130695942
#130694612
#130690192
C4×#669012
C11×#35092
#2559111