Finite Group Databasebeta

← #14649577

Subgroups — #14649577

Order 2816.

450 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077636C211yesmaximal, characteristic
2#13068426C211yesmaximal, characteristic
3#13067211C211yesmaximal, characteristic, complemented
4#13067128C211yesmaximal, characteristic, complemented
5#13066508C211yesmaximal, characteristic, complemented
6#13066487C211yesmaximal, characteristic, complemented
7C11×#3116C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C4×C11×#41C2211yescharacteristic
10C11×#485—21no—
11C11×#477C411yescharacteristic, complemented
12C11×#476C411yescharacteristic, complemented
13C11×#462C411yescharacteristic, complemented
14C11×#461C411yescharacteristic, complemented
15C11×#452—21no—
16C11×#441—21no—
17C11×#440—21no—
18C11×#432C2211yescharacteristic
19C2×#66901—21no—
20Q8×C11⋊C8—21no—
21#10622625—21no—
22#10622625—22no—
23#10622545C2211yescharacteristic
24#10622539—21no—
25#10622539C2211yescharacteristic
26C4×#4318—21no—
27C4×#4318C2211yescharacteristic
28C4×#4318C2211yescharacteristic
29#10622181—21no—
30#10622181—21no—
31#10622176—22no—
32#10622170—21no—
33C2×C11×#41D411yescharacteristic
34C2×C11×Q16—21no—
35C2×C11×SD16—21no—
36C11×C4⋊Q8C2×C411yescharacteristic
37C11×C4⋊Q8C2×C411yescharacteristic
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11C2×C411yescharacteristic
44C4×Q8×C11D411yescharacteristic
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11C2×C411yescharacteristic
48C4×D4×C11D411yescharacteristic
49C11×#117—21no—
50C11×#117—21no—
51C11×#117D411yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C4×Dic11—21no—
55C2×#4318—22no—
56C2×#4318—21no—
57C2×#4318—21no—
58C11×#107—21no—
59C11×#106—21no—
60C11×C4⋊C8C2×C411yescharacteristic
61C11×C4⋊C8C2×C411yescharacteristic
62C11×#103—21no—
63C11×#103—21no—
64C11×#103—21no—
65C11×#102—21no—
66C11×C22⋊C8—21no—
67C11×#97—21no—
68#66901—24no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C22⋊(C11⋊C8)—22no—
72C22⋊(C11⋊C8)D412yes—
73C4⋊(C11⋊C8)—22no—
74C4⋊(C11⋊C8)—21no—
75#66867—21no—
76#66867—21no—
77#66867D411yescharacteristic
78#66867D411yescharacteristic
79C4×C11⋊C8—22no—
80C4×C11⋊C8—21no—
81C4×C11⋊C8—21no—
82#9160—111nomaximal, Sylow
83C11×#41—22no—
84C11×#41—41no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11C22⋊C411yescharacteristic
88C2×D4×C11—21no—
89C2×D4×C11C22⋊C411yescharacteristic
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×Dic11—41no—
97C11×Q16—42no—
98C11×SD16—42no—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4C22⋊C411yescharacteristic
110C11×C4⋊C4C22⋊C411yescharacteristic
111C11×C22⋊C4—21no—
112C11×C22⋊C4—21no—
113C11×C22⋊C4—21no—
114C11×C22⋊C4—41no—
115C42×C11—21no—
116C42×C11—21no—
117C42×C11—21no—
118C42×C11—41no—
119C42×C11C22×C411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123C4×Dic11—22no—
124C4×Dic11—41no—
125#4318—22no—
126#4318—41no—
127#4318—42no—
128#4318—44no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—41no—
133#3116D1111yescharacteristic
134#2971—111no—
135#1759—111no—
136#1526—111no—
137#1506—111no—
138#1300—111no—
139#1291—111no—
140C23×C11—21no—
141C23×C11#12111yescharacteristic
142Q8×C11—21no—
143Q8×C11—41no—
144Q8×C11—41no—
145Q8×C11—81no—
146Q8×C11#10412yes—
147D4×C11—21no—
148D4×C11—21no—
149D4×C11—42no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—81no—
162C2×C4×C11C2×C22⋊C411yescharacteristic
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12311yescharacteristic
168C2×Dic11—42no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171C8×C11—41no—
172C8×C11—41no—
173C11⋊C8—22no—
174C11⋊C8—42no—
175C11⋊C8—41no—
176C11⋊C8—42no—
177#533C2×D1111yescharacteristic
178C4×#41C2×D1111yescharacteristic
179#485—21no—
180#477Dic1111yescharacteristic, complemented
181#476Dic1111yescharacteristic, complemented
182#462Dic1111yescharacteristic, complemented
183#461Dic1111yescharacteristic, complemented
184#452—21no—
185C8×Q8—221no—
186#441—21no—
187#440—21no—
188#436—222no—
189#436—221no—
190#432—111no—
191#432—221no—
192#432C2×D1111yescharacteristic
193C2×#104—221no—
194C4×M16—111no—
195C4×M16—111no—
196C4×M16—221no—
197#376—111no—
198#339—221no—
199#330—221no—
200#330—221no—
201#328—222no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11#38611yescharacteristic
209C4×C11—21no—
210C4×C11—22no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—41no—
216C4×C11—41no—
217C4×C11—81no—
218C4×C11—81no—
219C4×C11C2×#10411yescharacteristic
220C4×C11#42111yescharacteristic
221Dic11—82no—
222C2×#41C22⋊D1111yescharacteristic
223C2×Q16—21no—
224C2×SD16—21no—
225C2×M16—222no—
226C2×M16—221no—
227C2×M16—221no—
228C4⋊Q8C2×Dic1111yescharacteristic
229C4⋊Q8C2×Dic1111yescharacteristic
230#125—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8C2×Dic1111yescharacteristic
236C4×Q8C22⋊D1111yescharacteristic
237C4×D4—21no—
238C4×D4—21no—
239C4×D4C2×Dic1111yescharacteristic
240C4×D4C22⋊D1111yescharacteristic
241#117—21no—
242#117—21no—
243#117C22⋊D1111yescharacteristic
244C2×C42—21no—
245C2×C42—221no—
246C2×C42C22×D1111yescharacteristic
247#107—21no—
248#106—21no—
249C4⋊C8—222no—
250C4⋊C8—221no—
251C4⋊C8C2×Dic1111yescharacteristic
252C4⋊C8C2×Dic1111yescharacteristic
253#104—224no—
254#103—21no—
255#103—21no—
256#103—21no—
257#102—21no—
258C22⋊C8—21no—
259C22⋊C8—112no—
260C22⋊C8—222no—
261#97—21no—
262#97—111no—
263#97—111no—
264#97—221no—
265#97—221no—
266C4×C8—222no—
267C4×C8—221no—
268C4×C8—221no—
269#95—221no—
270#95—221no—
271C2×C11—41no—
272C2×C11—81no—
273C2×C11#187111yescharacteristic
274C2×C11#190211yescharacteristic
275C2×C11#190611yescharacteristic
276#41—22no—
277#41—41no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8C22⋊Dic1111yescharacteristic
281C2×D4—21no—
282C2×D4C22⋊Dic1111yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—441no—
287C22×C4D4×D1111yescharacteristic
288C22×C4#434111yescharacteristic
289C22×C4C2×C22⋊D1111yescharacteristic
290Q16—42no—
291SD16—42no—
292M16—222no—
293M16—442no—
294M16—444no—
295M16—441no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—221no—
299C2×C8—221no—
300C2×C8—222no—
301C2×C8—441no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4C22⋊Dic1111yescharacteristic
311C4⋊C4C22⋊Dic1111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—41no—
316C42—21no—
317C42—21no—
318C42—21no—
319C42—41no—
320C42—222no—
321C42—441no—
322C42D4×D1111yescharacteristic
323C42#434111yescharacteristic
324C42C22×Dic1111yescharacteristic
325C42C2×C22⋊D1111yescharacteristic
326C11#916011yescharacteristic, complemented, Sylow
327C23—21no—
328C23#6699211yescharacteristic
329Q8—21no—
330Q8—41no—
331Q8—41no—
332Q8—81no—
333Q8#6690112yes—
334D4—21no—
335D4—21no—
336D4—42no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—442no—
350C2×C4—881no—
351C2×C4—881no—
352C2×C4D4×Dic1111yescharacteristic
353C2×C4D4×Dic1111yescharacteristic
354C2×C4#6698811yescharacteristic
355C2×C4#6699011yescharacteristic
356C2×C4#6699211yescharacteristic
357C2×C4C2×C22⋊Dic1111yescharacteristic
358C8—41no—
359C8—41no—
360C8—222no—
361C8—441no—
362C8—442no—
363C8—442no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22#1062283311yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—882no—
382C4C2×#6690111yescharacteristic
383C4#1062284911yescharacteristic
384C2—41no—
385C2—81no—
386C2#1306891911yescharacteristic
387C2#1306909111yescharacteristic
388C2#1306911911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3116C2
socleC22×C11#386
prime radicalC2×C11×#41D4
cosocleC2×C42×C11C23
hypercenter#3116D11
hypocenterC11#9160
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3116

Complements

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

NH ≅ G/Ntype
3. #13067211C2semidirect
4. #13067128C2semidirect
5. #13066508C2semidirect
6. #13066487C2semidirect
11. C11×#477C4semidirect
12. C11×#476C4semidirect
13. C11×#462C4semidirect
14. C11×#461C4semidirect
180. #477Dic11semidirect
181. #476Dic11semidirect
182. #462Dic11semidirect
183. #461Dic11semidirect
326. C11#9160semidirect

Maximal subgroups

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

subgroupindex
#130776362
#130684262
#130672112
#130671282
#130665082
#130664872
C11×#31162
#916011