Finite Group Databasebeta

← #14663960

Subgroups — #14663960

Order 2816.

468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074381C211yesmaximal, characteristic
2#13068347C211yesmaximal, characteristic
3#13066927C211yesmaximal, characteristic
4#13066617C211yesmaximal, characteristic
5#13066616C211yesmaximal, characteristic
6#13066615C211yesmaximal, characteristic
7C11×#1344C211yesmaximal, characteristic
8C2×#66941C411yescharacteristic, complemented
9C2×#66931—21no—
10C2×#66930—21no—
11C2×#66930C2211yescharacteristic
12C11×#397C2211yescharacteristic
13#10622593C411yescharacteristic, complemented
14#10622566C2211yescharacteristic
15#10622565—21no—
16#10622331—21no—
17#10622274C411yescharacteristic, complemented
18#10622270—21no—
19#10622263C411yescharacteristic, complemented
20#10622259—21no—
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C23×Dic11D411yescharacteristic
28C22×Dic22—21no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—41no—
42C2×Dic11⋊C4C2×C411yescharacteristic
43C2×Dic11⋊C4D411yescharacteristic
44C2×C4×Dic11—41no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47#66941—41no—
48#66941—41no—
49#66931—42no—
50#66931—42no—
51#66930—24no—
52#66930—41no—
53#66930—41no—
54#66930—42no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95C2×C411yescharacteristic
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95C2×C411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64Dic11⋊C8—41no—
65C8×Dic11—41no—
66#11694—111nomaximal, Sylow
67C24×C11C2×D411yescharacteristic
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—22no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—41no—
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11D812yes—
84C22×Dic11SD1612yes—
85C2×Dic22—41no—
86C2×Dic22—41no—
87C2×Dic22—42no—
88C2×Dic22—42no—
89C2×C8×C11—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C22⋊Dic11—22no—
97C22⋊Dic11—41no—
98C22⋊Dic11—41no—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11—42no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105Dic11⋊C4—44no—
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11—44no—
114C2×C11⋊C8—41no—
115#2621—111no—
116#1740—111no—
117#1458—111no—
118#1344—111no—
119#1344—111no—
120#1344—111no—
121#1344D1111yescharacteristic
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11C2×C22⋊C411yescharacteristic
127C23×C11C2×D811yescharacteristic
128C23×C11C2×SD1611yescharacteristic
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—22no—
147C2×Dic11—22no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161C2×Dic11#9911yescharacteristic
162C2×Dic11#9911yescharacteristic
163C2×Dic11#10212yes—
164C2×Dic11#10212yes—
165C2×Dic11#10412yes—
166Dic22—82no—
167Dic22—82no—
168C8×C11—81no—
169C11⋊C8—81no—
170C2×C4⋊Q8—111no—
171C2×C22⋊Q8—221no—
172C2×#117—111no—
173C2×#117—221no—
174#431—221no—
175#398—111no—
176#398—111no—
177#398—221no—
178#397—111no—
179#397—221no—
180#397C2×D1111yescharacteristic
181#391—221no—
182#382—111no—
183#342—111no—
184#342—221no—
185#342C2×D1111yescharacteristic
186#324—221no—
187#323—111no—
188#323C2×D1111yescharacteristic
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—81no—
198C22×C11C2×#9911yescharacteristic
199C22×C11C2×#10211yescharacteristic
200C22×C11C2×#10411yescharacteristic
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—81no—
204C4×C11—82no—
205C4×C11—81no—
206Dic11—22no—
207Dic11—41no—
208Dic11—41no—
209Dic11—81no—
210Dic11—82no—
211Dic11—81no—
212Dic11#32712yes—
213Dic11#32712yes—
214C22×Q8—221no—
215C23×C4—111no—
216C4⋊Q8—441no—
217C4⋊Q8—441no—
218C22⋊Q8—442no—
219C22⋊Q8—442no—
220#117—224no—
221#117—441no—
222#117—441no—
223#117—442no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—441no—
232C2×C4⋊C4C4×D1111yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—111no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4C22×D1111yescharacteristic
239C2×C42—111no—
240C2×C42—111no—
241C2×C42—441no—
242C4⋊C8—441no—
243C22⋊C8—21no—
244C22⋊C8—221no—
245C4×C8—441no—
246#95—21no—
247#95—111no—
248#95—221no—
249#95—221no—
250#95—221no—
251#95—221no—
252#95C4×D1111yescharacteristic
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—41no—
256C2×C11—41no—
257C2×C11C2×#32711yescharacteristic
258C2×C11#212311yescharacteristic
259C2×C11#212911yescharacteristic
260C24D4×D1111yescharacteristic
261C2×Q8—442no—
262C2×Q8—441no—
263C2×Q8—441no—
264C2×Q8—442no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—112no—
271C22×C4—112no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—222no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—441no—
280C22×C4C2×C4×D1111yescharacteristic
281C22×C4D4×D1111yescharacteristic
282C2×C8—41no—
283C2×C8—441no—
284C4⋊C4—41no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—442no—
289C4⋊C4—442no—
290C4⋊C4—442no—
291C4⋊C4—442no—
292C4⋊C4—444no—
293C22⋊C4—22no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—222no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C22⋊C4—441no—
303C42—221no—
304C42—221no—
305C42—221no—
306C42—221no—
307C42—444no—
308C11#1169411yescharacteristic, complemented, Sylow
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23C22⋊C4×D1111yescharacteristic
314C23D8×D1111yescharacteristic
315C23SD16×D1111yescharacteristic
316Q8—882no—
317Q8—882no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—111no—
332C2×C4—111no—
333C2×C4—112no—
334C2×C4—112no—
335C2×C4—112no—
336C2×C4—222no—
337C2×C4—222no—
338C2×C4—222no—
339C2×C4—222no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—442no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—881no—
354C2×C4—881no—
355C8—81no—
356C8—881no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22D11×#9911yescharacteristic
367C22D11×#10211yescharacteristic
368C22D11×#10411yescharacteristic
369C4—41no—
370C4—41no—
371C4—81no—
372C4—82no—
373C4—81no—
374C4—112no—
375C4—112no—
376C4—222no—
377C4—441no—
378C4—441no—
379C4—881no—
380C4—882no—
381C4—881no—
382C2—21no—
383C2—21no—
384C2—41no—
385C2—41no—
386C2D11×#32711yescharacteristic
387C2#1307026811yescharacteristic
388C2#1307028911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1344C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1344D11
hypocenterC11#11694
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
8. C2×#66941C4semidirect
13. #10622593C4semidirect
17. #10622274C4semidirect
19. #10622263C4semidirect
308. C11#11694semidirect

Maximal subgroups

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

subgroupindex
#130743812
#130683472
#130669272
#130666172
#130666162
#130666152
C11×#13442
#1169411