Finite Group Databasebeta

← #14663338

Subgroups — #14663338

Order 2816.

398 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 71 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#13073098C211yesmaximal, characteristic
2#13066944C211yesmaximal, characteristic
3D11×#324C211yesmaximal, characteristic
4#13066560C211yesmaximal, characteristic, complemented
5#13066549C211yesmaximal, characteristic, complemented
6#13066549C211yesmaximal, characteristic, complemented
7C11×#1324C211yesmaximal, characteristic, complemented
8C2×#66950C411yescharacteristic
9C2×C4⋊C4×D11C2211yescharacteristic
10C11×#382C2211yescharacteristic
11#10622590C411yescharacteristic
12#10622587C2211yescharacteristic
13C4×(C2×D11)⋊C4C411yescharacteristic
14#10622542C411yescharacteristic
15#10622339—21no—
16D11×C22⋊C8—21no—
17#10622277—21no—
18#10622277—21no—
19#10622273—21no—
20#10622273—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622107—21no—
26#10622107—21no—
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×Dic22C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×Dic11⋊C4D411yescharacteristic
39C2×Dic11⋊C4D411yescharacteristic
40C2×C4×Dic11C2×C411yescharacteristic
41C2×#4313—41no—
42C2×C8×D11—41no—
43#66950—41no—
44#66950—41no—
45C4⋊C4×D11—41no—
46C4⋊C4×D11—41no—
47C11×C22⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60(C2×D11)⋊C8—41no—
61(C2×D11)⋊C8—41no—
62#11551—111nomaximal, Sylow
63C23×D11C22⋊C411yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—41no—
83C2×C4×D11—42no—
84C2×C4×D11—42no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C42×C11—21no—
94C42×C11—21no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—42no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102C4×Dic11—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#4313—82no—
106C8×D11—82no—
107#2503—111no—
108#1463—111no—
109C2×#324—111no—
110#1324—111no—
111#1324D1111yescharacteristic, complemented
112#1319—111no—
113#1319—111no—
114C23×C11C2×C22⋊C411yescharacteristic
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—22no—
118C22×D11—41no—
119C22×D11#9911yescharacteristic
120C22×D11#9911yescharacteristic
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11#13111yescharacteristic
133C2×C4×C11#13111yescharacteristic
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C4×D11—41no—
148C4×D11—41no—
149C4×D11—41no—
150C4×D11—41no—
151C4×D11—42no—
152C4×D11—42no—
153C4×D11—81no—
154C4×D11—81no—
155Dic22—81no—
156Dic22—81no—
157C8×C11—81no—
158C8×C11—81no—
159C11⋊C8—81no—
160C11⋊C8—81no—
161C2×C22⋊Q8—111no—
162C22×C4⋊C4—111no—
163#407—221no—
164C2×C22⋊C8—221no—
165#400—221no—
166#400—221no—
167#391—111no—
168#391—111no—
169#382—111no—
170#382C2×D1111yescharacteristic
171#381—221no—
172#381—221no—
173C4×C22⋊C4—111no—
174#324—111no—
175#324—111no—
176#324—221no—
177#324—221no—
178#324C2×D1111yescharacteristic
179#324C2×D1111yescharacteristic
180C22×C11—21no—
181C22×C11—21no—
182C22×C11#40811yescharacteristic
183C22×C11C2×#9911yescharacteristic
184C22×C11#41311yescharacteristic
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—42no—
191C2×D11—42no—
192C2×D11#35412yes—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—81no—
198C4×C11—81no—
199Dic11—41no—
200Dic11—41no—
201Dic11—41no—
202Dic11—81no—
203Dic11—81no—
204C22×Q8—111no—
205C23×C4—111no—
206C23×C4—111no—
207C23×C4—111no—
208C2×M16—441no—
209C22×C8—441no—
210C22⋊Q8—441no—
211C22⋊Q8—441no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—441no—
217C2×C4⋊C4—441no—
218C2×C4⋊C4C4×D1111yescharacteristic
219C2×C4⋊C4C22×D1111yescharacteristic
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C42—111no—
223C2×C42C4×D1111yescharacteristic
224C22⋊C8—21no—
225C22⋊C8—21no—
226C22⋊C8—221no—
227C22⋊C8—221no—
228C22⋊C8—441no—
229C22⋊C8—441no—
230#95—21no—
231#95—21no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95—221no—
239C2×C11—21no—
240C2×C11—21no—
241C2×C11#146811yescharacteristic
242C2×C11C2×#35411yescharacteristic
243C2×C11#213311yescharacteristic
244D11—22no—
245D11—41no—
246C24—111no—
247C2×Q8—221no—
248C2×Q8—221no—
249C2×Q8—441no—
250C2×Q8—441no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—441no—
267C22×C4—442no—
268C22×C4—442no—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4D4×D1111yescharacteristic
272M16—882no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—441no—
276C2×C8—441no—
277C2×C8—882no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—442no—
284C22⋊C4—441no—
285C22⋊C4—441no—
286C22⋊C4—442no—
287C42—21no—
288C42—21no—
289C42—441no—
290C11#1155111yescharacteristic, complemented, Sylow
291C23—111no—
292C23—111no—
293C23—222no—
294C23—221no—
295C23—221no—
296C23—441no—
297C23C22⋊C4×D1111yescharacteristic
298Q8—881no—
299Q8—881no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—881no—
331C2×C4—881no—
332C2×C4#6695411yescharacteristic
333C2×C4#6696011yescharacteristic
334C8—81no—
335C8—81no—
336C8—881no—
337C8—881no—
338C22—21no—
339C22—21no—
340C22—112no—
341C22—221no—
342C22—221no—
343C22—221no—
344C22—221no—
345C22—221no—
346C22—442no—
347C22—442no—
348C22#1062234011yescharacteristic
349C22D11×#9911yescharacteristic
350C22#1062236411yescharacteristic
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4—881no—
361C4—881no—
362C2—21no—
363C2—21no—
364C2—222no—
365C2—441no—
366C2#1306696311yescharacteristic
367C2D11×#35411yescharacteristic
368C2#1307030211yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1324C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1324D11
hypocenterC11#11551
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
4. #13066560C2semidirect
5. #13066549C2semidirect
6. #13066549C2semidirect
7. C11×#1324C2semidirect
111. #1324D11semidirect
290. C11#11551semidirect

Maximal subgroups

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

subgroupindex
#130730982
#130669442
D11×#3242
#130665602
#130665492
C11×#13242
#1155111