Finite Group Databasebeta

← #14664894

Subgroups — #14664894

Order 2816.

452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 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#13073970C211yesmaximal, characteristic
2#13068604C211yesmaximal, characteristic
3#13066641C212yesmaximal, complemented
4#13066638C212yesmaximal, complemented
5C11×#1459C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×C4×Dic22C411yescharacteristic, complemented
8C2×C11×C22⋊C8—21no—
9#10622834—21no—
10C2×#66898—21no—
11#10622825—21no—
12#10622823—21no—
13#10622823—21no—
14#10622586—21no—
15#10622562C411yescharacteristic, complemented
16#10622562C2211yescharacteristic
17#10622560C411yescharacteristic, complemented
18#10622560C2211yescharacteristic
19#10622549C411yescharacteristic, complemented
20C11×#324—21no—
21C11×#323C2212yes—
22#10622164C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C22×C8×C11—41no—
28C4×D4×C11—41no—
29C4×D4×C11—41no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—41no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C4×Dic22—41no—
47C4×Dic22—41no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8—41no—
50#66898—42no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—41no—
55C11⋊#95C2×C411yescharacteristic
56C11⋊#95C2×C411yescharacteristic
57#11897—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11SD1612yes—
63C2×D4×C11Q1612yes—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—81no—
69C22×C4×C11—81no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—42no—
80C2×Dic22—41no—
81C2×Dic22—42no—
82C2×C8×C11—42no—
83C2×C8×C11—82no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C42×C11—21no—
88C42×C11—21no—
89C22⋊Dic11—42no—
90C22⋊Dic11—42no—
91C22⋊Dic11—42no—
92C22⋊Dic11—42no—
93C22⋊Dic11—81no—
94C22⋊Dic11—81no—
95C4⋊Dic11—41no—
96C4⋊Dic11—42no—
97C4⋊Dic11—82no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100Dic11⋊C4—81no—
101Dic11⋊C4—81no—
102C4×Dic11—42no—
103#2580—111no—
104#1799—111no—
105#1459D1111yescharacteristic
106#1352—112no—
107#1351—112no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11#10312yes—
117C23×C11C2×C22⋊C411yescharacteristic
118C23×C11C2×SD1611yescharacteristic
119C23×C11C2×Q1611yescharacteristic
120D4×C11—42no—
121D4×C11—42no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11#9911yescharacteristic
136C2×C4×C11#9911yescharacteristic
137C2×C4×C11#10312yes—
138C2×Dic11—22no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—82no—
151C2×Dic11—82no—
152C2×Dic11—82no—
153Dic22—42no—
154Dic22—42no—
155C8×C11—82no—
156C2×C4×Q8—111no—
157C2×C4×D4C2×D1111yescharacteristic
158C2×#99—221no—
159C2×C22⋊C8—21no—
160#399—111no—
161#399—111no—
162#393—111no—
163#393—111no—
164#390—221no—
165#389—221no—
166#385—221no—
167#385—221no—
168#382—111no—
169#380—221no—
170#342—112no—
171#324—21no—
172#323C2×D1112yes—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—22no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—42no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11C2×#9911yescharacteristic
188C22×C11C2×#10311yescharacteristic
189C22×C11#42111yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—22no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196Dic11—42no—
197Dic11—81no—
198Dic11—81no—
199Dic11—81no—
200Dic11—162no—
201C22×Q8—111no—
202C22×D4D4411yescharacteristic
203C23×C4D4411yescharacteristic
204C23×C4C22⋊D1111yescharacteristic
205C22×C8—41no—
206C4×Q8—441no—
207C4×Q8—441no—
208C4×D4—41no—
209C4×D4—41no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—441no—
216C2×C4⋊C4C22⋊D1111yescharacteristic
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—222no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4C4×D1111yescharacteristic
223C2×C22⋊C4C22×D1111yescharacteristic
224C2×C42—221no—
225C2×C42C4×D1111yescharacteristic
226#99—442no—
227C22⋊C8—22no—
228C22⋊C8—41no—
229#95—111no—
230#95—111no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95—441no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—41no—
238C2×C11—42no—
239C2×C11—41no—
240C2×C11#152011yescharacteristic
241C2×C11#212011yescharacteristic
242C2×C11#212711yescharacteristic
243C24(C2×D11)⋊C411yescharacteristic
244C24C2×D4411yescharacteristic
245C2×Q8—441no—
246C2×Q8—442no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4#431412yes—
250C2×D4Dic4412yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—442no—
262C22×C4(C2×D11)⋊C411yescharacteristic
263C22×C4(C2×D11)⋊C411yescharacteristic
264C22×C4(C2×D11)⋊C411yescharacteristic
265C22×C4C2×C4×D1111yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267C2×C8—42no—
268C2×C8—82no—
269C4⋊C4—41no—
270C4⋊C4—441no—
271C4⋊C4—442no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—881no—
275C4⋊C4—881no—
276C4⋊C4—882no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—881no—
284C22⋊C4—881no—
285C42—21no—
286C42—21no—
287C42—442no—
288C11#1189711yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#6688012yes—
298C23C2×#431411yescharacteristic
299C23C2×Dic4411yescharacteristic
300C23C2×(C2×D11)⋊C411yescharacteristic
301Q8—442no—
302Q8—442no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—222no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
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—882no—
331C2×C4—882no—
332C2×C4—882no—
333C2×C4#6687011yescharacteristic
334C2×C4#6687011yescharacteristic
335C2×C4#6688012yes—
336C8—82no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—21no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22C2×#6687011yescharacteristic
352C22C2×#6688011yescharacteristic
353C22#1062275211yescharacteristic
354C4—22no—
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—442no—
361C4—881no—
362C4—881no—
363C4—881no—
364C4—1762no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—42no—
369C2—41no—
370C2#1306718911yescharacteristic
371C2#1307025811yescharacteristic
372C2#1307028311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1459C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1459D11
hypocenterC11#11897
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13066641C2semidirect
4. #13066638C2semidirect
7. C2×C4×Dic22C4semidirect
15. #10622562C4semidirect
17. #10622560C4semidirect
19. #10622549C4semidirect
288. C11#11897semidirect

Maximal subgroups

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

subgroupindex
#130739702
#130686042
#130666412
#130666382
C11×#14592
#1189711