Finite Group Databasebeta

← #14767720

Subgroups — #14767720

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071884C211yesmaximal, characteristic
2#13069550C212yesmaximal, complemented
3#13069331C212yesmaximal, complemented
4#13069174C212yesmaximal, complemented
5#13069170C212yesmaximal, complemented
6#13068798C212yesmaximal
7#13068390C212yesmaximal
8#13068313C211yesmaximal, characteristic
9C11×#1798C211yesmaximal, characteristic
10C2×C11×#117C2211yescharacteristic
11C22×#4318C2211yescharacteristic
12C23×C11⋊C8C2211yescharacteristic
13C2×C4×Dic22C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×C22⋊C8C2212yes—
17C4×C22⋊Dic11C2212yes—
18C2×Dic11⋊C8C2212yes—
19C2×Dic11⋊C8C2212yes—
20C2×C8×Dic11C2212yes—
21C2×C8×Dic11C2212yes—
22#10622599C411yescharacteristic
23#10622597C412yes—
24#10622592C411yescharacteristic
25#10622562C411yescharacteristic
26#10622561C412yes—
27#10622560C411yescharacteristic
28C4×C4⋊Dic11C2211yescharacteristic
29C4×Dic11⋊C4C2212yes—
30C11×#336C2212yes—
31#10622188C2212yes—
32#10622188C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622162C2212yes—
36#10622162C2212yes—
37C23×C4×C11C2311yescharacteristic
38C22×Dic22C2×C411yescharacteristic
39C22×C8×C11C2312yes—
40C22×C8×C11C2312yes—
41C11×#117—41no—
42C11×#117—41no—
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4C2×C411yescharacteristic
46C2×C11×C22⋊C4C2×C411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C22⋊Dic11C2×C412yes—
50C2×C22⋊Dic11C2×C412yes—
51C2×C4⋊Dic11C2×C412yes—
52C2×C4⋊Dic11C2×C411yescharacteristic
53C2×Dic11⋊C4C2×C412yes—
54C2×Dic11⋊C4C2×C412yes—
55C2×Dic11⋊C4C2×C412yes—
56C2×C4×Dic11C2312yes—
57C2×C4×Dic11C2312yes—
58C2×#4318—22no—
59C2×#4318—41no—
60C2×#4318—41no—
61C22×C11⋊C8—41no—
62C22×C11⋊C8—41no—
63C22×C11⋊C8Q814yescomplemented
64C22×C11⋊C8C2312yes—
65C22×C11⋊C8C2312yes—
66C4×Dic22—41no—
67C4×Dic22—41no—
68C11×C4⋊C8—41no—
69C11×C4⋊C8—41no—
70C11×C22⋊C8—24no—
71C11⋊#95C2×C412yes—
72C11⋊#95C2×C412yes—
73C11⋊#95C2×C411yescharacteristic
74C11⋊#95C2×C411yescharacteristic
75C11⋊#95C2×C412yes—
76C11⋊#95C2×C412yes—
77Dic11⋊C8—42no—
78Dic11⋊C8—42no—
79C8×Dic11—42no—
80C8×Dic11—42no—
81#22288—111nomaximal, Sylow
82C24×C11C22×C411yescharacteristic
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×Q812yes—
93C22×C4×C11#4112yes—
94C22×C4×C11C2411yescharacteristic
95C22×Dic11C22×C412yes—
96C22×Dic11C22×C412yes—
97C22×Dic11C22×C412yes—
98C22×Dic11C22×C412yes—
99C2×Dic22—24no—
100C2×Dic22—41no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—21no—
112C42×C11—21no—
113C42×C11—21no—
114C42×C11—21no—
115C22⋊Dic11—24no—
116C22⋊Dic11—24no—
117C4⋊Dic11—24no—
118C4⋊Dic11—41no—
119Dic11⋊C4—24no—
120Dic11⋊C4—24no—
121Dic11⋊C4—42no—
122C4×Dic11—22no—
123C4×Dic11—22no—
124C4×Dic11—22no—
125C4×Dic11—22no—
126#4318—44no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—44no—
133C2×C11⋊C8C2×Q814yes—
134#2396—111no—
135#1984—112no—
136#1939—112no—
137#1916—112no—
138#1916—112no—
139#1851—112no—
140#1798D1111yescharacteristic
141C8×C22⋊C4—112no—
142#1729—111no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11C4×Q812yes—
148C23×C11C23×C411yescharacteristic
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11C4×Q812yes—
164C2×C4×C11C22×Q811yescharacteristic
165C2×C4×C11C2×#4111yescharacteristic
166C2×C4×C11H(5,𝔽2)11yescharacteristic
167C2×C4×C11H(5,𝔽2)11yescharacteristic
168C2×C4×C11H(5,𝔽2)11yescharacteristic
169C2×C4×C112−1+411yescharacteristic
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11#13114yes—
181C2×Dic11#13114yes—
182Dic22—44no—
183C8×C11—42no—
184C8×C11—42no—
185C11⋊C8—24no—
186C11⋊C8—42no—
187C22×M16—111no—
188C23×C8—111no—
189C2×C4×Q8—111no—
190C2×#117C2×D1111yescharacteristic
191C2×C4⋊C8—112no—
192C2×C4⋊C8—112no—
193C2×C4⋊C8C2×D1111yescharacteristic
194C2×C4⋊C8C2×D1111yescharacteristic
195C2×C22⋊C8C2×D1112yes—
196C2×C4×C8—112no—
197C2×C4×C8—112no—
198#400—111no—
199#399—111no—
200#398—112no—
201#396—112no—
202#395—111no—
203#393—111no—
204C4×C4⋊C4—112no—
205C4×C4⋊C4—111no—
206C4×C22⋊C4—112no—
207#336—112no—
208#336—112no—
209#336—112no—
210#336—112no—
211#336—112no—
212#336—112no—
213#336C2×D1112yes—
214C22×C11—22no—
215C22×C11—24no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—42no—
219C22×C11C2×C4×Q811yescharacteristic
220C22×C11#51811yescharacteristic
221C22×C11#52011yescharacteristic
222C22×C11C2×#13112yes—
223C22×C11C2×#13112yes—
224C4×C11—22no—
225C4×C11—41no—
226C4×C11—41no—
227C4×C11—41no—
228C4×C11—41no—
229C4×C11#53811yescharacteristic
230C4×C11#53911yescharacteristic
231C4×C11#54311yescharacteristic
232C4×C11#54411yescharacteristic
233Dic11—24no—
234Dic11—24no—
235Dic11—42no—
236Dic11—42no—
237C22×Q8—111no—
238C23×C4C22×D1111yescharacteristic
239C2×M16—222no—
240C2×M16—441no—
241C2×M16—441no—
242C22×C8—112no—
243C22×C8—114no—
244C22×C8—112no—
245C22×C8—441no—
246C22×C8—441no—
247C22×C8C22×D1112yes—
248C22×C8C22×D1112yes—
249C4×Q8—441no—
250C4×Q8—441no—
251#117—41no—
252#117—41no—
253C2×C4⋊C4—112no—
254C2×C4⋊C4—112no—
255C2×C4⋊C4—112no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4C4×D1111yescharacteristic
259C2×C4⋊C4C4×D1111yescharacteristic
260C2×C22⋊C4—112no—
261C2×C22⋊C4—112no—
262C2×C22⋊C4C4×D1111yescharacteristic
263C2×C22⋊C4C4×D1111yescharacteristic
264C2×C42—112no—
265C2×C42—112no—
266C2×C42C22×D1111yescharacteristic
267C2×C42C22×D1111yescharacteristic
268C4⋊C8—41no—
269C4⋊C8—41no—
270C4⋊C8—442no—
271C4⋊C8—442no—
272C22⋊C8—24no—
273C4×C8—442no—
274C4×C8—442no—
275#95—112no—
276#95—112no—
277#95—112no—
278#95—111no—
279#95—111no—
280#95—112no—
281C2×C11—42no—
282C2×C11#232911yescharacteristic
283C2×C11#296012yes—
284C2×C11#297711yescharacteristic
285C2×C11#297911yescharacteristic
286C2×C11#299412yes—
287C24C2×C4×D1111yescharacteristic
288C2×Q8—224no—
289C2×Q8—441no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—112no—
295C22×C4—112no—
296C22×C4—112no—
297C22×C4—112no—
298C22×C4C2×C4×D1111yescharacteristic
299C22×C4C2×C4×D1111yescharacteristic
300C22×C4C2×C4×D1111yescharacteristic
301C22×C4C2×C4×D1111yescharacteristic
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4#434112yes—
304C22×C4Q8×D1112yes—
305C22×C4C23×D1111yescharacteristic
306M16—444no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—114no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8—444no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—224no—
323C4⋊C4—224no—
324C4⋊C4—224no—
325C4⋊C4—442no—
326C4⋊C4—441no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—224no—
330C22⋊C4—224no—
331C42—21no—
332C42—21no—
333C42—21no—
334C42—21no—
335C42—222no—
336C42—222no—
337C42—222no—
338C42—222no—
339C11#2228811yescharacteristic, complemented, Sylow
340C23—21no—
341C23—22no—
342C23—22no—
343C23—21no—
344C23#6694012yes—
345C23C22×C4×D1111yescharacteristic
346Q8—444no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—114no—
362C2×C4—114no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4#6694012yes—
374C2×C4C2×#434111yescharacteristic
375C2×C4#6703711yescharacteristic
376C2×C4#6703711yescharacteristic
377C2×C4C2×Q8×D1111yescharacteristic
378C2×C4#6704211yescharacteristic
379C2×C4#6704311yescharacteristic
380C8—42no—
381C8—42no—
382C8—224no—
383C8—442no—
384C22—24no—
385C22—22no—
386C22—42no—
387C22—41no—
388C22—41no—
389C22#1062301711yescharacteristic
390C22C2×#6694011yescharacteristic
391C22#1062305411yescharacteristic
392C22D11×#13112yes—
393C22D11×#13112yes—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—41no—
399C4—224no—
400C4—224no—
401C4—442no—
402C4—442no—
403C4#1062313311yescharacteristic
404C4#1062314811yescharacteristic
405C4#1062315411yescharacteristic
406C4#1062316511yescharacteristic
407C2—42no—
408C2#1307134611yescharacteristic
409C2#1307754912yes—
410C2#1307766811yescharacteristic
411C2#1307768011yescharacteristic
412C2#1307777012yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1798C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1798D11
hypocenterC11#22288
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. #13069550C2semidirect
3. #13069331C2semidirect
4. #13069174C2semidirect
5. #13069170C2semidirect
63. C22×C11⋊C8Q8semidirect
339. C11#22288semidirect

Maximal subgroups

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

subgroupindex
#130718842
#130695502
#130693312
#130691742
#130691702
#130687982
#130683902
#130683132
C11×#17982
#2228811