Finite Group Databasebeta

← #14727833

Subgroups — #14727833

Order 2816.

888 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079764C212yesmaximal, complemented
2#13074437C211yesmaximal, characteristic
3#13067658C214yesmaximal, complemented
4#13067641C214yesmaximal
5#13067180C212yesmaximal, complemented
6#13066930C211yesmaximal, characteristic
7C11×#3458C211yesmaximal, characteristic
8C11×#544—22no—
9C11×#544—22no—
10C11×#544—21no—
11C11×#544C2212yes—
12C11×#543—21no—
13C11×#543C2212yes—
14C11×#533—24no—
15C11×#533—21no—
16C11×#533C2212yes—
17C2×C11×#117—21no—
18C2×C11×#117C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20#10622825—21no—
21#10622694—22no—
22#10622691—22no—
23#10622657C2218yes—
24#10622634—24no—
25#10622599C2212yes—
26#10622592—21no—
27#10622562C2212yes—
28#10622560—21no—
29#10622549C2211yescharacteristic
30#10622541—21no—
31#10622538C2212yes—
32#10622176C2218yes—
33#10622166C2212yes—
34#10622163C2212yes—
35C23×C4×C11D411yescharacteristic
36C22×Dic22—21no—
37C11×C4⋊Q8—24no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—24no—
41C11×C4⋊Q8D412yes—
42C11×C4⋊Q8D412yes—
43C11×#125—24no—
44C11×#125—22no—
45C11×#125—24no—
46C11×#125—22no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8C2314yes—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×Q8×C11D414yes—
59C11×#117—22no—
60C11×#117—22no—
61C11×#117—22no—
62C11×#117—22no—
63C11×#117—22no—
64C11×#117—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C11×C22⋊C4C2311yescharacteristic
72C2×C42×C11—22no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2312yes—
79C2×Dic11⋊C4—22no—
80#66922—22no—
81#66922—22no—
82#66899—28no—
83C11⋊#95—22no—
84C11⋊#95—21no—
85C11⋊#95—22no—
86C11⋊#95C2312yes—
87C22⋊(C11⋊C8)C2314yes—
88#66871—28no—
89C4⋊(C11⋊C8)—22no—
90C4×C11⋊C8—22no—
91#18311—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11C2×D414yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11Q1614yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—22no—
110C22×Dic11—22no—
111C2×Dic22—42no—
112C2×Dic22—82no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4C2×D414yes—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—24no—
129C11×C22⋊C4—22no—
130C11×C22⋊C4—22no—
131C42×C11—24no—
132C42×C11—24no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11C2×D412yes—
136C42×C11C2×D412yes—
137C22⋊Dic11—82no—
138C4⋊Dic11—24no—
139C4⋊Dic11—41no—
140C4⋊Dic11—41no—
141C4⋊Dic11—42no—
142Dic11⋊C4—82no—
143C2×C11⋊C8—24no—
144#3458D1111yescharacteristic
145#3230—112no—
146#2628—111no—
147#1617—114no—
148#1614—114no—
149#1518—112no—
150#1458—111no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11C2×Q1612yes—
156C23×C11C22×D411yescharacteristic
157Q8×C11—44no—
158Q8×C11—82no—
159Q8×C11—82no—
160Q8×C11—82no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—24no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—82no—
174C2×C4×C11—82no—
175C2×C4×C11#12012yes—
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11C2×Q1612yes—
179C2×C4×C11C2×Q1612yes—
180C2×C4×C11#13712yes—
181C2×C4×C11C22×D412yes—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188Dic22—84no—
189C11⋊C8—44no—
190#544—22no—
191#544—22no—
192#544—21no—
193#544C2×D1112yes—
194#543—21no—
195#543C2×D1112yes—
196#533—24no—
197#533—21no—
198#533C2×D1112yes—
199C2×C4⋊Q8—111no—
200C2×#117—21no—
201C2×#117C2×D1111yescharacteristic
202#500—222no—
203#487—222no—
204#484—118no—
205#477—224no—
206#431—112no—
207#400—112no—
208#399—112no—
209#395—221no—
210#393—221no—
211#389—221no—
212#382—111no—
213#380—221no—
214#328—118no—
215#324—112no—
216#323—112no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—22no—
220C22×C11—42no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—81no—
224C22×C11C2×#12011yescharacteristic
225C22×C11C22×Q1611yescharacteristic
226C22×C11C2×#13711yescharacteristic
227C4×C11—22no—
228C4×C11—22no—
229C4×C11—22no—
230C4×C11—41no—
231C4×C11—44no—
232C4×C11—41no—
233C4×C11—44no—
234C4×C11#45112yes—
235C4×C11#45112yes—
236Dic11—82no—
237Dic11—82no—
238C22×Q8—221no—
239C23×C4C22⋊D1111yescharacteristic
240C4⋊Q8—24no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—24no—
244C4⋊Q8—222no—
245C4⋊Q8—222no—
246C4⋊Q8C22⋊D1112yes—
247C4⋊Q8C22⋊D1112yes—
248#125—24no—
249#125—22no—
250#125—24no—
251#125—22no—
252C22⋊Q8—24no—
253C22⋊Q8—24no—
254C22⋊Q8—24no—
255C22⋊Q8—22no—
256C22⋊Q8—22no—
257C22⋊Q8—22no—
258C22⋊Q8—24no—
259C22⋊Q8C22×D1114yes—
260C4×Q8—22no—
261C4×Q8—22no—
262C4×Q8—22no—
263C4×Q8C22⋊D1114yes—
264#117—22no—
265#117—22no—
266#117—22no—
267#117—22no—
268#117—22no—
269#117—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—112no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4C22⋊D1111yescharacteristic
277C2×C4⋊C4C22×D1111yescharacteristic
278C2×C22⋊C4—22no—
279C2×C22⋊C4—222no—
280C2×C22⋊C4C22⋊D1111yescharacteristic
281C2×C22⋊C4C22×D1111yescharacteristic
282C2×C42—22no—
283C2×C42C22⋊D1111yescharacteristic
284C2×C42C22×D1111yescharacteristic
285#107—228no—
286C4⋊C8—222no—
287#103—228no—
288C22⋊C8—114no—
289C4×C8—222no—
290#95—112no—
291#95—222no—
292#95—221no—
293#95—222no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—42no—
297C2×C11C2×#45111yescharacteristic
298C2×C11#302111yescharacteristic
299C2×C11#302811yescharacteristic
300C24C2×C22⋊D1111yescharacteristic
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—442no—
305C2×Q8—882no—
306C2×Q8C2×C22⋊D1114yes—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—222no—
313C22×C4—222no—
314C22×C4#432614yes—
315C22×C4C2×C22⋊D1111yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320C22×C4C23×D1111yescharacteristic
321C2×C8—224no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—24no—
326C4⋊C4—24no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4—24no—
335C4⋊C4—224no—
336C4⋊C4—442no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C4⋊C4—882no—
340C4⋊C4C2×C22⋊D1114yes—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—882no—
346C42—24no—
347C42—24no—
348C42—21no—
349C42—21no—
350C42C2×C22⋊D1112yes—
351C42C2×C22⋊D1112yes—
352C11#1831111yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23C2×#432612yes—
358C23C22×C22⋊D1111yescharacteristic
359Q8—44no—
360Q8—82no—
361Q8—82no—
362Q8—82no—
363Q8—884no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—24no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4#6699512yes—
385C2×C4C2×#432612yes—
386C2×C4C2×#432612yes—
387C2×C4#6700612yes—
388C2×C4#6700611yescharacteristic
389C2×C4#6700611yescharacteristic
390C2×C4C22×C22⋊D1112yes—
391C8—444no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—81no—
399C22C2×#6699511yescharacteristic
400C22C22×#432611yescharacteristic
401C22C2×#6700611yescharacteristic
402C4—22no—
403C4—22no—
404C4—22no—
405C4—41no—
406C4—44no—
407C4—41no—
408C4—44no—
409C4—882no—
410C4—882no—
411C4#1062284112yes—
412C4#1062284112yes—
413C2—21no—
414C2—21no—
415C2—42no—
416C2C2×#1062284111yescharacteristic
417C2#1307798811yescharacteristic
418C2#1307802211yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3458C2
socleC22×C11C2×#120
prime radicalC24×C11C2×D4
hypercenter#3458D11
hypocenterC11#18311
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3458

Complements

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

NH ≅ G/Ntype
1. #13079764C2semidirect
3. #13067658C2semidirect
5. #13067180C2semidirect
352. C11#18311semidirect

Maximal subgroups

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

subgroupindex
#130797642
#130744372
#130676582
#130676412
#130671802
#130669302
C11×#34582
#1831111