Finite Group Databasebeta

← #14663409

Subgroups — #14663409

Order 2816.

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

normal subgroups only

This group has 494 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#13073583C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic, complemented
3#13066549C212yesmaximal, complemented
4#13066547C212yesmaximal, complemented
5C11×#1465C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66993C411yescharacteristic
8C2×#66989C411yescharacteristic
9C2×#66928C411yescharacteristic
10C11×#407—21no—
11#10622826—21no—
12#10622826—21no—
13C2×C22⋊(C11⋊C8)—21no—
14#10622601C2211yescharacteristic
15#10622587C2211yescharacteristic
16#10622574—21no—
17#10622574—21no—
18C4×C4⋊Dic11C411yescharacteristic
19C11×#324C2212yes—
20C11×#323—21no—
21#10622166C2212yes—
22#10622163—21no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×D44C2×C411yescharacteristic
29C22×Dic22C2×C411yescharacteristic
30C2×C11×M16—41no—
31C4×D4×C11—41no—
32C4×D4×C11—41no—
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39#66993—42no—
40#66989—42no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11—21no—
46C2×C4×Dic11C2×C411yescharacteristic
47C2×C4×Dic11C2×C411yescharacteristic
48C22×C11⋊C8—41no—
49#66928—41no—
50#66928—41no—
51C11×C22⋊C8—22no—
52C11×C22⋊C8—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11566—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C24×C11C22⋊C411yescharacteristic
61C23×D11—21no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—81no—
70C22×C4×C11—81no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—42no—
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—81no—
81C2×C22⋊D11—81no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×D44—22no—
86C2×D44—41no—
87C2×D44—41no—
88C2×Dic22—22no—
89C2×Dic22—41no—
90C2×Dic22—41no—
91C11×M16—82no—
92C2×C8×C11—42no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C42×C11—21no—
97C42×C11—21no—
98C22⋊Dic11—42no—
99C22⋊Dic11—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—81no—
104(C2×D11)⋊C4—81no—
105C4⋊Dic11—42no—
106C4×Dic11—41no—
107C4×Dic11—41no—
108C2×C11⋊C8—42no—
109C2×C11⋊C8—82no—
110#2544—111no—
111#1465D1111yescharacteristic, complemented
112#1459—111no—
113#1319—112no—
114#1318—112no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11#10012yes—
125C23×C11C2×C22⋊C411yescharacteristic
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133D4×C11—44no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11#9911yescharacteristic
148C2×C4×C11#9911yescharacteristic
149C2×C4×C11#13112yes—
150C22⋊D11—84no—
151C22⋊D11—84no—
152C2×Dic11—22no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161D44—82no—
162Dic22—82no—
163C8×C11—82no—
164C11⋊C8—82no—
165C2×#127—111no—
166C2×#124—111no—
167C2×#124—111no—
168C2×C4×D4C2×D1111yescharacteristic
169#407—21no—
170C2×C22⋊C8—221no—
171#394—221no—
172#394—221no—
173#391—111no—
174#390—111no—
175#386—221no—
176#386—221no—
177C4×C4⋊C4—111no—
178#324—112no—
179#324C2×D1112yes—
180#323—21no—
181#323—221no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—22no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11#40811yescharacteristic
195C22×C11C2×#9911yescharacteristic
196C22×C11C2×#10011yescharacteristic
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—22no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—41no—
210Dic11—42no—
211Dic11—81no—
212Dic11—81no—
213C22×Q8—111no—
214C22×D4—111no—
215C22×D4—221no—
216C22×D4—221no—
217C22×D4C4×D1111yescharacteristic
218C23×C4D4411yescharacteristic
219C23×C4C22⋊D1111yescharacteristic
220C2×M16—41no—
221C22×C8—441no—
222#127—442no—
223#124—441no—
224#124—441no—
225#124—442no—
226C4×D4—41no—
227C4×D4—41no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4C22×D1111yescharacteristic
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4D4411yescharacteristic
237C2×C22⋊C4C22⋊D1111yescharacteristic
238C2×C42—111no—
239C2×C42—111no—
240C2×C42C4×D1111yescharacteristic
241C22⋊C8—22no—
242C22⋊C8—41no—
243C22⋊C8—222no—
244C22⋊C8—441no—
245#95—221no—
246#95—221no—
247#95—221no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—42no—
251C2×C11—81no—
252C2×C11#147111yescharacteristic
253C2×C11#212711yescharacteristic
254C2×C11#213211yescharacteristic
255D11—161no—
256C24—221no—
257C24(C2×D11)⋊C411yescharacteristic
258C24(C2×D11)⋊C411yescharacteristic
259C2×Q8—222no—
260C2×Q8—441no—
261C2×Q8—441no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—222no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—442no—
269C2×D4—442no—
270C2×D4—442no—
271C2×D4—442no—
272C2×D4—881no—
273C2×D4—881no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—81no—
279C22×C4—81no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4(C2×D11)⋊C411yescharacteristic
284C22×C4(C2×D11)⋊C411yescharacteristic
285C22×C4C2×C4×D1111yescharacteristic
286C22×C4C2×D4411yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288M16—82no—
289C2×C8—42no—
290C2×C8—442no—
291C2×C8—882no—
292C4⋊C4—41no—
293C4⋊C4—442no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—442no—
297C22⋊C4—442no—
298C22⋊C4—442no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C22⋊C4—881no—
302C22⋊C4—881no—
303C42—21no—
304C42—21no—
305C42—441no—
306C42—441no—
307C11#1156611yescharacteristic, complemented, Sylow
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—441no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23—441no—
322C23—441no—
323C23—441no—
324C23#6688712yes—
325C23C2×(C2×D11)⋊C411yescharacteristic
326Q8—882no—
327D4—44no—
328D4—882no—
329D4—884no—
330D4—884no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—222no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4#6687011yescharacteristic
354C2×C4#6687011yescharacteristic
355C2×C4#6696012yes—
356C8—82no—
357C8—882no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—81no—
369C22—81no—
370C22—881no—
371C22—881no—
372C22—881no—
373C22—881no—
374C22—881no—
375C22—881no—
376C22—881no—
377C22C2×#6687011yescharacteristic
378C22#1062274211yescharacteristic
379C22C2×#6688711yescharacteristic
380C4—21no—
381C4—21no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—442no—
387C4—881no—
388C4—881no—
389C2—21no—
390C2—21no—
391C2—42no—
392C2—81no—
393C2—1761no—
394C2#1306697711yescharacteristic
395C2#1307028311yescharacteristic
396C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1465C2
socleC22×C11C2×#99
prime radicalC2×#66993C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1465D11
hypocenterC11#11566
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #13066934C2semidirect
3. #13066549C2semidirect
4. #13066547C2semidirect
5. C11×#1465C2semidirect
111. #1465D11semidirect
307. C11#11566semidirect

Maximal subgroups

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

subgroupindex
#130735832
#130669342
#130665492
#130665472
C11×#14652
#1156611