Finite Group Databasebeta

← #14764624

Subgroups — #14764624

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071075C211yesmaximal, characteristic
2#13069412C212yesmaximal
3#13069336C212yesmaximal, complemented
4#13069228C212yesmaximal, complemented
5#13069226C212yesmaximal, complemented
6#13068687C211yesmaximal, characteristic, complemented
7#13068686C211yesmaximal, characteristic, complemented
8#13068599C211yesmaximal, characteristic, complemented
9#13068468C211yesmaximal, characteristic, complemented
10#13068363C211yesmaximal, characteristic, complemented
11C11×#1798C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13C2×C4×C22⋊D11C2211yescharacteristic
14C2×#66925C2211yescharacteristic
15C2×C11×C4⋊C8C2212yes—
16C2×C11×C22⋊C8C2212yes—
17C4×C22⋊Dic11C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2212yes—
19C2×(C2×D11)⋊C8C2212yes—
20C2×(C2×D11)⋊C8C2212yes—
21C2×#66879C2212yes—
22C2×#66879C2212yes—
23C2×Dic11⋊C8C2212yes—
24C2×Dic11⋊C8C2212yes—
25#10622603C412yes—
26#10622585C412yes—
27#10622570C412yes—
28#10622558C412yes—
29C4×(C2×D11)⋊C4C2211yescharacteristic
30C4×Dic11⋊C4C2211yescharacteristic
31C42×Dic11C2211yescharacteristic
32C11×#336C2211yescharacteristic
33C11×#336C2211yescharacteristic
34#10622188C2212yes—
35#10622188C2212yes—
36#10622162C2212yes—
37#10622162C2211yescharacteristic
38#10622162C2211yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11C2×C411yescharacteristic
41C22×C4×D11C2311yescharacteristic
42C22×C8×C11C2312yes—
43C22×C8×C11C2312yes—
44C11×#117—42no—
45C2×C11×C4⋊C4C2×C412yes—
46C2×C11×C22⋊C4C2×C412yes—
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C22⋊Dic11C2×C411yescharacteristic
50C2×C22⋊Dic11C2×C412yes—
51C4×C22⋊D11—24no—
52C2×(C2×D11)⋊C4C2×C411yescharacteristic
53C2×(C2×D11)⋊C4C2×C412yes—
54C2×(C2×D11)⋊C4C2×C412yes—
55C2×Dic11⋊C4C2×C411yescharacteristic
56C2×Dic11⋊C4C2×C412yes—
57C2×Dic11⋊C4C2×C412yes—
58C2×C4×Dic11C2×C412yes—
59C2×C4×Dic11C2×C412yes—
60C2×C4×Dic11C2311yescharacteristic
61C2×C4×Dic11C2311yescharacteristic
62C2×C4×Dic11C2311yescharacteristic
63C22×C11⋊C8C2312yes—
64C22×C11⋊C8C2312yes—
65#66925—42no—
66C11×C4⋊C8—42no—
67C11×C22⋊C8—42no—
68C11⋊#95C2×C412yes—
69C11⋊#95C2×C412yes—
70C11⋊#95C2×C412yes—
71C22⋊(C11⋊C8)—42no—
72(C2×D11)⋊C8—42no—
73(C2×D11)⋊C8—42no—
74#66879—24no—
75#66879—42no—
76Dic11⋊C8—24no—
77Dic11⋊C8—42no—
78#22015—111nomaximal, Sylow
79C24×C11C22×C411yescharacteristic
80C23×D11C22×C411yescharacteristic
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C22×C412yes—
88C22×C4×C11C2411yescharacteristic
89C2×C22⋊D11—22no—
90C2×C22⋊D11—42no—
91C22×Dic11C22×C412yes—
92C22×Dic11C22×C412yes—
93C22×Dic11C22×C411yescharacteristic
94C22×Dic11C22×C411yescharacteristic
95C22×Dic11C22×C411yescharacteristic
96C2×C4×D11—22no—
97C2×C4×D11—21no—
98C2×C4×D11—22no—
99C2×C4×D11—21no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C11×C4⋊C4—42no—
107C11×C22⋊C4—42no—
108C42×C11—22no—
109C42×C11—22no—
110C22⋊Dic11—22no—
111C22⋊Dic11—42no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115Dic11⋊C4—22no—
116Dic11⋊C4—42no—
117Dic11⋊C4—42no—
118C4×Dic11—22no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C4×Dic11—42no—
122C4×Dic11—42no—
123C4×Dic11#4114yes—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130#2293—111no—
131#1955—112no—
132#1940—112no—
133#1924—112no—
134#1924—112no—
135#1818—111no—
136#1818—111no—
137#1798—111no—
138#1798D1111yescharacteristic, complemented
139#1767—111no—
140#1745—111no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11C23×C411yescharacteristic
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—22no—
151C22×D11—22no—
152C2×C4×C11—21no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11C2×#4112yes—
164C2×C4×C11H(5,𝔽2)11yescharacteristic
165C2×C4×C11H(5,𝔽2)12yes—
166C2×C4×C112−1+411yescharacteristic
167C22⋊D11—44no—
168C2×Dic11—22no—
169C2×Dic11—22no—
170C2×Dic11—21no—
171C2×Dic11—22no—
172C2×Dic11—21no—
173C2×Dic11—22no—
174C2×Dic11—21no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11#11712yes—
180C2×Dic11#11712yes—
181C4×D11—42no—
182C4×D11—42no—
183C8×C11—42no—
184C8×C11—42no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C2×C4×D4—111no—
188C2×#117—111no—
189C2×#117C2×D1111yescharacteristic
190C2×C4⋊C8—112no—
191C2×C4⋊C8—112no—
192C2×C4⋊C8C2×D1112yes—
193C2×C22⋊C8—112no—
194C2×C22⋊C8—112no—
195C2×C22⋊C8—112no—
196C2×C22⋊C8C2×D1112yes—
197C2×#97—112no—
198C2×#97—112no—
199#390—112no—
200#389—112no—
201#388—112no—
202#388—112no—
203C4×C4⋊C4—111no—
204C4×C22⋊C4—111no—
205C4×C22⋊C4—111no—
206C43—111no—
207#336—112no—
208#336—112no—
209#336—111no—
210#336—111no—
211#336—112no—
212#336C2×D1111yescharacteristic
213#336C2×D1111yescharacteristic
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11C2×#11711yescharacteristic
220C22×C11#51811yescharacteristic
221C22×C11#52011yescharacteristic
222C22×C11#56812yes—
223C22×C11#56812yes—
224C2×D11—41no—
225C2×D11—41no—
226C2×D11—41no—
227C2×D11—42no—
228C2×D11—42no—
229C4×C11—41no—
230C4×C11—42no—
231C4×C11—42no—
232C4×C11#54012yes—
233C4×C11#54212yes—
234Dic11—22no—
235Dic11—22no—
236Dic11—41no—
237Dic11—42no—
238Dic11—42no—
239C22×D4—111no—
240C23×C4—111no—
241C23×C4C22×D1111yescharacteristic
242C22×C8—112no—
243C22×C8—112no—
244C22×C8C22×D1112yes—
245C22×C8C22×D1112yes—
246C4×D4—224no—
247#117—42no—
248#117—442no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—112no—
251C2×C4⋊C4—112no—
252C2×C4⋊C4C4×D1112yes—
253C2×C22⋊C4—111no—
254C2×C22⋊C4—111no—
255C2×C22⋊C4—112no—
256C2×C22⋊C4—112no—
257C2×C22⋊C4—112no—
258C2×C22⋊C4C4×D1112yes—
259C2×C42—111no—
260C2×C42—111no—
261C2×C42—111no—
262C2×C42—112no—
263C2×C42—112no—
264C2×C42C22×D1111yescharacteristic
265C2×C42C22×D1111yescharacteristic
266C4⋊C8—42no—
267C4⋊C8—224no—
268C4⋊C8—442no—
269C22⋊C8—42no—
270C22⋊C8—442no—
271C22⋊C8—442no—
272C22⋊C8—442no—
273#97—224no—
274#97—442no—
275#95—112no—
276#95—112no—
277#95—112no—
278C2×C11—81no—
279C2×C11#231911yescharacteristic
280C2×C11#292111yescharacteristic
281C2×C11#292311yescharacteristic
282C2×C11#298012yes—
283C2×C11#299512yes—
284D11—81no—
285C24—111no—
286C24C2×C4×D1111yescharacteristic
287C2×D4—222no—
288C2×D4—442no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—111no—
294C22×C4—111no—
295C22×C4—112no—
296C22×C4—112no—
297C22×C4—111no—
298C22×C4—221no—
299C22×C4—222no—
300C22×C4—221no—
301C22×C4—222no—
302C22×C4C2×C4×D1112yes—
303C22×C4C2×C4×D1111yescharacteristic
304C22×C4C2×C4×D1112yes—
305C22×C4C23×D1111yescharacteristic
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—222no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8—222no—
317C2×C8—222no—
318C4⋊C4—42no—
319C4⋊C4—222no—
320C4⋊C4—442no—
321C4⋊C4—442no—
322C22⋊C4—42no—
323C22⋊C4—222no—
324C22⋊C4—222no—
325C22⋊C4—442no—
326C22⋊C4—442no—
327C22⋊C4—442no—
328C42—22no—
329C42—22no—
330C42—114no—
331C42—221no—
332C42—222no—
333C42—221no—
334C42—442no—
335C42—442no—
336C11#2201511yescharacteristic, complemented, Sylow
337C23—21no—
338C23—22no—
339C23—22no—
340C23—21no—
341C23—21no—
342C23—221no—
343C23—222no—
344C23—222no—
345C23—221no—
346C23—221no—
347C23C22×C4×D1111yescharacteristic
348D4—444no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—112no—
361C2×C4—112no—
362C2×C4—222no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—221no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—222no—
371C2×C4—221no—
372C2×C4—221no—
373C2×C4—442no—
374C2×C4—442no—
375C2×C4#6703711yescharacteristic
376C2×C4#6703712yes—
377C2×C4#6704011yescharacteristic
378C2×C4#41×D1112yes—
379C8—42no—
380C8—42no—
381C8—442no—
382C8—442no—
383C22—41no—
384C22—41no—
385C22—42no—
386C22—41no—
387C22—42no—
388C22—441no—
389C22—441no—
390C22—442no—
391C22—441no—
392C22—442no—
393C22#1062301711yescharacteristic
394C22#1062303511yescharacteristic
395C22D11×#11711yescharacteristic
396C22#1062328112yes—
397C22#1062328112yes—
398C4—41no—
399C4—42no—
400C4—42no—
401C4—222no—
402C4—222no—
403C4—442no—
404C4—441no—
405C4—442no—
406C4#1062314612yes—
407C4#1062317112yes—
408C2—81no—
409C2—881no—
410C2#1307125811yescharacteristic
411C2#1307725011yescharacteristic
412C2#1307726411yescharacteristic
413C2#1307768512yes—
414C2#1307778412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1798C2
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1798D11
hypocenterC11#22015
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
3. #13069336C2semidirect
4. #13069228C2semidirect
5. #13069226C2semidirect
6. #13068687C2semidirect
7. #13068686C2semidirect
8. #13068599C2semidirect
9. #13068468C2semidirect
10. #13068363C2semidirect
11. C11×#1798C2semidirect
138. #1798D11semidirect
336. C11#22015semidirect

Maximal subgroups

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

subgroupindex
#130710752
#130694122
#130693362
#130692282
#130692262
#130686872
#130686862
#130685992
#130684682
#130683632
C11×#17982
#2201511