Finite Group Databasebeta

← #14664567

Subgroups — #14664567

Order 2816.

418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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#13074484C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066639C212yesmaximal, complemented
4#13066615C212yesmaximal, complemented
5C11×#1799C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66923C411yescharacteristic, complemented
8C2×C11×#99—21no—
9C11×#380—21no—
10#10622835—21no—
11#10622823—21no—
12#10622823—21no—
13#10622820—21no—
14#10622593—21no—
15#10622566C411yescharacteristic, complemented
16#10622566C2211yescharacteristic
17#10622562C411yescharacteristic, complemented
18#10622562C2211yescharacteristic
19#10622550C411yescharacteristic, complemented
20C11×#342C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C4×D4×C11—41no—
27C4×D4×C11—41no—
28C2×C11×C4⋊C4—41no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×#4318—41no—
45#66923—41no—
46#66923—41no—
47C11×#99—42no—
48C11×#95—41no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)—41no—
57#11827—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—42no—
69C22×C4×C11—81no—
70C22×C4×C11—81no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—82no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—42no—
85C11×C22⋊C4—42no—
86C42×C11—21no—
87C42×C11—21no—
88C22⋊Dic11—42no—
89C22⋊Dic11—41no—
90C22⋊Dic11—41no—
91C22⋊Dic11—81no—
92C22⋊Dic11—81no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—42no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—81no—
99Dic11⋊C4—81no—
100#4318—82no—
101C2×C11⋊C8—42no—
102#2633—111no—
103#1799D1111yescharacteristic
104#1465—111no—
105#1352—112no—
106#1344—112no—
107C23×C11—21no—
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×C11C2×C22⋊C411yescharacteristic
117C23×C11AGL(1,ℤ/8)11yescharacteristic
118C23×C11#13711yescharacteristic
119D4×C11—42no—
120D4×C11—42no—
121C2×C4×C11—21no—
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—82no—
136C2×C4×C11—82no—
137C2×C4×C11—82no—
138C2×C4×C11#9911yescharacteristic
139C2×C4×C11#9911yescharacteristic
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—41no—
151C2×Dic11—41no—
152C11⋊C8—82no—
153C2×#125—111no—
154C2×C4×D4C2×D1111yescharacteristic
155C2×#99—21no—
156#407—221no—
157#399—111no—
158#399—111no—
159#398—221no—
160#397—111no—
161#397—111no—
162#394—221no—
163#385—221no—
164#385—221no—
165#383—111no—
166#380—21no—
167#342C2×D1112yes—
168#324—221no—
169#323—112no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—42no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11C2×#9911yescharacteristic
185C22×C11#41711yescharacteristic
186C22×C11#42111yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—162no—
194Dic11—81no—
195Dic11—81no—
196Dic11—81no—
197Dic11—81no—
198C22×D4C22⋊D1111yescharacteristic
199C23×C4D4411yescharacteristic
200C23×C4C22⋊D1111yescharacteristic
201C2×M16—441no—
202#125—441no—
203#125—441no—
204C4×D4—41no—
205C4×D4—41no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4D4411yescharacteristic
214C2×C22⋊C4—22no—
215C2×C22⋊C4—221no—
216C2×C22⋊C4—221no—
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4C4×D1111yescharacteristic
220C2×C22⋊C4C22×D1111yescharacteristic
221C2×C42C4×D1111yescharacteristic
222#99—42no—
223C22⋊C8—222no—
224C22⋊C8—441no—
225#95—41no—
226#95—111no—
227#95—111no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—41no—
235C2×C11—41no—
236C2×C11—81no—
237C2×C11#151311yescharacteristic
238C2×C11#212311yescharacteristic
239C2×C11#212711yescharacteristic
240C24(C2×D11)⋊C411yescharacteristic
241C24C2×C22⋊D1111yescharacteristic
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—41no—
245C2×D4—41no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—42no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4(C2×D11)⋊C411yescharacteristic
259C22×C4(C2×D11)⋊C411yescharacteristic
260C22×C4C2×C4×D1111yescharacteristic
261C22×C4C2×D4411yescharacteristic
262M16—882no—
263C2×C8—442no—
264C4⋊C4—41no—
265C4⋊C4—82no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—442no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—881no—
272C4⋊C4—881no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—442no—
278C22⋊C4—441no—
279C22⋊C4—441no—
280C22⋊C4—881no—
281C22⋊C4—881no—
282C42—21no—
283C42—21no—
284C11#1182711yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23C2×(C2×D11)⋊C411yescharacteristic
295C23#6698511yescharacteristic
296C23#6699511yescharacteristic
297D4—42no—
298D4—42no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—82no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
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#6687011yescharacteristic
329C2×C4#6687011yescharacteristic
330C8—882no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22C2×#6687011yescharacteristic
346C22#1062257911yescharacteristic
347C22#1062261811yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—162no—
355C4—881no—
356C4—881no—
357C4—881no—
358C4—881no—
359C2—21no—
360C2—21no—
361C2—41no—
362C2—41no—
363C2—81no—
364C2#1306715711yescharacteristic
365C2#1307026911yescharacteristic
366C2#1307028311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1799C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1799D11
hypocenterC11#11827
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13066639C2semidirect
4. #13066615C2semidirect
7. C2×#66923C4semidirect
15. #10622566C4semidirect
17. #10622562C4semidirect
19. #10622550C4semidirect
284. C11#11827semidirect

Maximal subgroups

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

subgroupindex
#130744842
#130669542
#130666392
#130666152
C11×#17992
#1182711