Finite Group Databasebeta

← #14926199

Subgroups — #14926199

Order 2816.

1716 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073351C214yesmaximal, complemented
2#13073282C214yesmaximal
3#13072690C214yesmaximal
4#13072591C214yesmaximal, complemented
5#13071921C211yesmaximal, characteristic, complemented
6#13071886C212yesmaximal
7C4×#66942C214yesmaximal, complemented
8C4×#66951C214yesmaximal
9#13071111C211yesmaximal, characteristic
10C4×Q8×Dic11C212yesmaximal, complemented
11C11×#2399C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2212yes—
13C2×Q8×Dic11C2214yes—
14C2×#66951C2214yes—
15C2×#66942C2214yes—
16C2×#66925C2211yescharacteristic
17C11×#398C2214yes—
18C11×#395C2214yes—
19C4×C11×C4⋊C4C2214yes—
20C11×#376C2211yescharacteristic
21#10622844C2212yes—
22#10622842C2212yes—
23#10622607C2214yes—
24#10622605C2212yes—
25#10622603C2214yes—
26#10622597C2214yes—
27#10622595C2212yes—
28#10622594C2214yes—
29#10622594C2214yes—
30#10622591C2214yes—
31#10622591C2214yes—
32C4⋊C4×Dic11C2214yes—
33C4⋊C4×Dic11C2214yes—
34C4⋊C4×Dic11C2214yes—
35#10622585C2214yes—
36C4×(C2×D11)⋊C4C2212yes—
37C4×(C2×D11)⋊C4C2214yes—
38C4×C4⋊Dic11C2212yes—
39C4×C4⋊Dic11C2214yes—
40C4×Dic11⋊C4C2212yes—
41C4×Dic11⋊C4C2214yes—
42C4×Dic11⋊C4C2214yes—
43C42×Dic11C2211yescharacteristic
44C42×Dic11C2214yes—
45#10622283C2214yes—
46#10622282C2214yes—
47#10622282C2214yes—
48#10622273C2214yes—
49#10622270C2214yes—
50#10622267C2214yes—
51#10622266C2214yes—
52#10622265C2214yes—
53#10622265C2214yes—
54#10622264C2214yes—
55#10622263C2214yes—
56#10622260C2214yes—
57C22×Q8×C11C2312yes—
58C22×C4×D11C2311yescharacteristic
59C4×Q8×C11—28no—
60C2×C11×C4⋊C4C2314yes—
61C2×C11×C4⋊C4C2314yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2314yes—
64C2×C42×C11C2314yes—
65C2×C42×C11C2312yes—
66C2×C42×C11C2311yescharacteristic
67Q8×Dic11—216no—
68C2×(C2×D11)⋊C4C2312yes—
69C2×(C2×D11)⋊C4C2314yes—
70C2×(C2×D11)⋊C4C2314yes—
71C2×(C2×D11)⋊C4C2314yes—
72C2×C4⋊Dic11C2314yes—
73C2×C4⋊Dic11C2314yes—
74C2×C4⋊Dic11C2314yes—
75C2×Dic11⋊C4C2312yes—
76C2×Dic11⋊C4C2314yes—
77C2×Dic11⋊C4C2314yes—
78C2×Dic11⋊C4C2314yes—
79C2×Dic11⋊C4C2314yes—
80C2×Dic11⋊C4C2314yes—
81C2×C4×Dic11C2311yescharacteristic
82C2×C4×Dic11C2314yes—
83C2×C4×Dic11C2314yes—
84C2×C4×Dic11C2314yes—
85C2×C4×Dic11C2314yes—
86C2×C4×Dic11C2314yes—
87C2×C4×Dic11C2312yes—
88C2×C4×Dic11C2314yes—
89#66951—216no—
90#66942—216no—
91#66925—24no—
92C11×#95C2314yes—
93C11×#95C2314yes—
94C11×#95C2314yes—
95C11⋊#95C2314yes—
96C11⋊#95C2314yes—
97C11⋊#95C2314yes—
98C11⋊#95C2314yes—
99C11⋊#95C2314yes—
100C11⋊#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2312yes—
106C11⋊#95C2312yes—
107#34973—111nomaximal, Sylow
108C23×D11C2411yescharacteristic
109C2×Q8×C11—28no—
110C2×Q8×C11—24no—
111C22×C4×C11C2414yes—
112C22×C4×C11C2414yes—
113C22×C4×C11C2412yes—
114C22×C4×C11C2414yes—
115C22×C4×C11C2411yescharacteristic
116C22×Dic11C2411yescharacteristic
117C22×Dic11C2414yes—
118C22×Dic11C2412yes—
119C22×Dic11C2414yes—
120C22×Dic11C2414yes—
121C2×C4×D11—22no—
122C2×C4×D11—24no—
123C11×C4⋊C4—28no—
124C11×C4⋊C4—28no—
125C11×C4⋊C4—28no—
126C11×C4⋊C4—24no—
127C42×C11—28no—
128C42×C11—24no—
129C42×C11#4114yes—
130(C2×D11)⋊C4—28no—
131(C2×D11)⋊C4—28no—
132(C2×D11)⋊C4—24no—
133(C2×D11)⋊C4—28no—
134C4⋊Dic11—28no—
135C4⋊Dic11—28no—
136C4⋊Dic11#41116yes—
137Dic11⋊C4—28no—
138Dic11⋊C4—28no—
139Dic11⋊C4—28no—
140Dic11⋊C4—28no—
141Dic11⋊C4—24no—
142Dic11⋊C4—28no—
143C4×Dic11—28no—
144C4×Dic11—28no—
145C4×Dic11—28no—
146C4×Dic11—28no—
147C4×Dic11—22no—
148C4×Dic11—28no—
149C4×Dic11—24no—
150C4×Dic11—28no—
151#2524—114no—
152#2519—114no—
153#2469—114no—
154#2462—114no—
155#2402—111no—
156#2399D1111yescharacteristic, complemented
157#2396—112no—
158C4×#125—114no—
159C4×#126—114no—
160#2298—111no—
161C42×Q8—112no—
162C23×C11C2511yescharacteristic
163C22×D11—24no—
164C22×D11—21no—
165C22×D11—22no—
166Q8×C11—216no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11C2×#4114yes—
177C2×C4×C11C2×#4112yes—
178C2×C4×C11C2×#4118yes—
179C2×C4×C112−1+414yes—
180C2×Dic11—24no—
181C2×Dic11—24no—
182C2×Dic11—24no—
183C2×Dic11—24no—
184C2×Dic11—22no—
185C2×Dic11—24no—
186C2×Dic11—24no—
187C2×Dic11—24no—
188C2×Dic11—21no—
189C2×Dic11—24no—
190C2×Dic11—22no—
191C2×Dic11C2×#4118yes—
192C2×Dic11C2×#4118yes—
193C4×D11—44no—
194C2×#126—114no—
195C2×#125—114no—
196C2×C4×Q8—114no—
197C2×C4×Q8C2×D1112yes—
198C2×#117—111no—
199#400—112no—
200#400—114no—
201#399—112no—
202#398—114no—
203#398—114no—
204#398C2×D1114yes—
205#396—114no—
206#395—112no—
207#395C2×D1114yes—
208#393—112no—
209#389—114no—
210#389—114no—
211#388—114no—
212#388—114no—
213#388—114no—
214#388—114no—
215#387—114no—
216#387—114no—
217#387—114no—
218#387—114no—
219#387—114no—
220#387—114no—
221#387—114no—
222#387—114no—
223#383—114no—
224#382—114no—
225C4×C4⋊C4—114no—
226C4×C4⋊C4—114no—
227C4×C4⋊C4—114no—
228C4×C4⋊C4—114no—
229C4×C4⋊C4—114no—
230C4×C4⋊C4—114no—
231C4×C4⋊C4—112no—
232C4×C4⋊C4—112no—
233C4×C4⋊C4C2×D1114yes—
234C4×C22⋊C4—114no—
235C4×C22⋊C4—112no—
236#376C2×D1111yescharacteristic
237C43—114no—
238C43—111no—
239C22×C11C22×#4111yescharacteristic
240C22×C11C22×#4114yes—
241C22×C11C2×2−1+412yes—
242C2×D11—42no—
243C2×D11—41no—
244C2×D11—44no—
245C4×C11—24no—
246C4×C11—28no—
247C4×C11—44no—
248C4×C11—44no—
249C4×C11#54114yes—
250Dic11—28no—
251Dic11—28no—
252Dic11—42no—
253Dic11—41no—
254Dic11—44no—
255C22×Q8C22×D1112yes—
256C23×C4—111no—
257#126—2216no—
258#125—2216no—
259C4×Q8—28no—
260C4×Q8—2216no—
261#117—224no—
262C2×C4⋊C4—114no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—114no—
265C2×C4⋊C4—114no—
266C2×C4⋊C4—114no—
267C2×C4⋊C4—114no—
268C2×C4⋊C4—114no—
269C2×C4⋊C4—114no—
270C2×C4⋊C4—114no—
271C2×C4⋊C4C22×D1114yes—
272C2×C4⋊C4C22×D1112yes—
273C2×C4⋊C4C22×D1114yes—
274C2×C4⋊C4C22×D1114yes—
275C2×C22⋊C4—112no—
276C2×C22⋊C4—114no—
277C2×C22⋊C4—114no—
278C2×C22⋊C4—114no—
279C2×C42—114no—
280C2×C42—114no—
281C2×C42—114no—
282C2×C42—114no—
283C2×C42—114no—
284C2×C42—111no—
285C2×C42—112no—
286C2×C42—114no—
287C2×C42C22×D1114yes—
288C2×C42C22×D1112yes—
289C2×C42C22×D1111yescharacteristic
290#95—114no—
291#95—114no—
292#95—114no—
293#95—114no—
294#95—114no—
295#95—112no—
296#95—112no—
297#95—114no—
298#95—114no—
299#95—114no—
300#95—114no—
301#95—114no—
302#95C22×D1114yes—
303#95C22×D1114yes—
304#95C22×D1114yes—
305C2×C11#344412yes—
306C2×C11C2×#54111yescharacteristic
307C2×C11#348214yes—
308D11—81no—
309C24—111no—
310C2×Q8—24no—
311C2×Q8—28no—
312C22×C4—114no—
313C22×C4—114no—
314C22×C4—111no—
315C22×C4—114no—
316C22×C4—112no—
317C22×C4—222no—
318C22×C4—224no—
319C22×C4C23×D1114yes—
320C22×C4C23×D1114yes—
321C22×C4C23×D1112yes—
322C22×C4C23×D1114yes—
323C22×C4C23×D1111yescharacteristic
324C4⋊C4—28no—
325C4⋊C4—24no—
326C4⋊C4—28no—
327C4⋊C4—28no—
328C4⋊C4—1116no—
329C4⋊C4—228no—
330C4⋊C4—228no—
331C4⋊C4—228no—
332C4⋊C4—228no—
333C4⋊C4—228no—
334C4⋊C4—228no—
335C4⋊C4—224no—
336C4⋊C4—228no—
337C22⋊C4—228no—
338C22⋊C4—228no—
339C22⋊C4—224no—
340C22⋊C4—228no—
341C42—28no—
342C42—24no—
343C42—228no—
344C42—228no—
345C42—228no—
346C42—228no—
347C42—222no—
348C42—224no—
349C42—228no—
350C42—228no—
351C42#434114yes—
352C11#3497311yescharacteristic, complemented, Sylow
353C23—221no—
354C23—222no—
355C23—224no—
356C23C24×D1111yescharacteristic
357Q8—216no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—118no—
368C2×C4—118no—
369C2×C4—224no—
370C2×C4—224no—
371C2×C4—224no—
372C2×C4—224no—
373C2×C4—222no—
374C2×C4—221no—
375C2×C4—224no—
376C2×C4—222no—
377C2×C4—224no—
378C2×C4—224no—
379C2×C4—224no—
380C2×C4—444no—
381C2×C4C2×#434114yes—
382C2×C4C2×#434112yes—
383C2×C4#6704014yes—
384C2×C4#41×D1118yes—
385C22—442no—
386C22—444no—
387C22—441no—
388C22C22×#434111yescharacteristic
389C22C2×#6704012yes—
390C22C2×#41×D1114yes—
391C4—24no—
392C4—28no—
393C4—44no—
394C4—44no—
395C4—228no—
396C4—228no—
397C4—442no—
398C4—444no—
399C4—441no—
400C4#1062326214yes—
401C2—881no—
402C2#1308190812yes—
403C2C2×#1062326211yescharacteristic
404C2#1308223414yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2399C2
prime radicalC23×D11C24
hypercenter#2399D11
hypocenterC11#34973
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2399

Complements

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

NH ≅ G/Ntype
1. #13073351C2semidirect
4. #13072591C2semidirect
5. #13071921C2semidirect
7. C4×#66942C2semidirect
10. C4×Q8×Dic11C2semidirect
11. C11×#2399C2semidirect
156. #2399D11semidirect
352. C11#34973semidirect

Maximal subgroups

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

subgroupindex
#130733512
#130732822
#130726902
#130725912
#130719212
#130718862
C4×#669422
C4×#669512
#130711112
C4×Q8×Dic112
C11×#23992
#3497311