Finite Group Databasebeta

← #14657529

Subgroups — #14657529

Order 2816.

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

normal subgroups only

This group has 420 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#13078088C211yesmaximal, characteristic
2#13068631C211yesmaximal, characteristic, complemented
3#13067387C211yesmaximal, characteristic, complemented
4#13067263C211yesmaximal, characteristic
5#13067177C211yesmaximal, characteristic
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1461C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66995—21no—
10#10623008C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C2×#66899—21no—
14#10622644—21no—
15#10622641—22no—
16#10622640—21no—
17#10622579—21no—
18#10622549C2211yescharacteristic
19#10622537C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C11×#324—22no—
22#10622167—21no—
23#10622124—21no—
24#10622123—21no—
25#10622108—22no—
26#10622095—22no—
27C22×Q8×C11D411yescharacteristic
28C2×#4339—21no—
29C4×Q8×C11—21no—
30C4×Q8×C11—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C2×#4326—22no—
38#66995—42no—
39#66995—42no—
40C2×#4325—22no—
41#66983—21no—
42#66983—21no—
43C2×C4⋊Dic11—21no—
44C2×#4318—21no—
45C22×C11⋊C8—21no—
46#66928—21no—
47#66927D411yescharacteristic
48C4×D44—21no—
49C4×D44—21no—
50#66922D411yescharacteristic
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8D412yes—
55C4×C8×C11—21no—
56C4×C8×C11—21no—
57#66899—42no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60#66874—22no—
61#66873—22no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66#10467—111nomaximal, Sylow
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11SD1612yes—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C2×C22⋊D11—41no—
79C22×Dic11—41no—
80#4339—41no—
81#4339—41no—
82#4339—41no—
83#4339—41no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×Dic22—21no—
89C2×C8×C11—22no—
90C2×C8×C11—41no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C42×C11—41no—
96C42×C11—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101#4326—44no—
102#4325—44no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109#4318—41no—
110#4318—41no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#3037—111no—
116#1805—111no—
117#1570—111no—
118#1540—111no—
119#1517—111no—
120#1461D1111yescharacteristic, complemented
121#1286—111no—
122C23×C11#12111yescharacteristic
123C22×D11—41no—
124Q8×C11—22no—
125Q8×C11—22no—
126Q8×C11—41no—
127Q8×C11—41no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—81no—
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12311yescharacteristic
139C2×C4×C11#12311yescharacteristic
140C2×C4×C11#12411yescharacteristic
141C2×C4×C11C2×SD1611yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C22⋊D11—81no—
146C22⋊D11—81no—
147C2×Dic11—41no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150C2×Dic11—81no—
151D44—41no—
152D44—41no—
153D44—81no—
154D44—81no—
155C4×D11—81no—
156C4×D11—81no—
157Dic22—41no—
158Dic22—41no—
159C8×C11—42no—
160C8×C11—81no—
161C11⋊C8—42no—
162C11⋊C8—81no—
163C2×#137—221no—
164#532—111no—
165C2×C4×Q8C2×D1111yescharacteristic
166#464—222no—
167#462—221no—
168#460—221no—
169#431C2×D1111yescharacteristic
170#431C2×D1111yescharacteristic
171#423—111no—
172C2×C4⋊C8—111no—
173#417—221no—
174C2×#103—221no—
175#382—111no—
176#340—221no—
177#334—222no—
178#332—221no—
179#331—221no—
180#327—222no—
181#324—22no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11#39411yescharacteristic
185C22×C11#46511yescharacteristic
186C22×C11#46911yescharacteristic
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—42no—
195C4×C11—81no—
196C4×C11#44911yescharacteristic
197C4×C11#45011yescharacteristic
198C4×C11#48111yescharacteristic
199C4×C11#48211yescharacteristic
200Dic11—81no—
201Dic11—161no—
202C2×#41—221no—
203C22×Q8D4411yescharacteristic
204#137—442no—
205#137—442no—
206C2×Q16—222no—
207C2×SD16—222no—
208C2×M16—221no—
209C22×C8—221no—
210C4⋊Q8—111no—
211#127—111no—
212#124—221no—
213#121—221no—
214#121—221no—
215C4×Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×D4—221no—
220C4×D4—221no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4D4411yescharacteristic
224C2×C42—21no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—112no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232#103—222no—
233#103—442no—
234#102—222no—
235C22⋊C8—21no—
236C22⋊C8C22⋊D1112yes—
237C4×C8—21no—
238C4×C8—21no—
239#95—221no—
240#95—221no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11#203411yescharacteristic
244C2×C11#204911yescharacteristic
245C2×C11#205311yescharacteristic
246D11—161no—
247#41—441no—
248#41—441no—
249#41—441no—
250#41—441no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—221no—
257C2×Q8#431412yes—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—441no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—441no—
265C22×C4—441no—
266C22×C4C2×D4411yescharacteristic
267C22×C4#433911yescharacteristic
268C22×C4C2×C22⋊D1111yescharacteristic
269Q16—444no—
270SD16—444no—
271M16—441no—
272M16—441no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—222no—
276C2×C8—441no—
277C2×C8—441no—
278C2×C8—441no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C42—41no—
290C42—41no—
291C42D4×D1111yescharacteristic
292C42D4×D1111yescharacteristic
293C42#434111yescharacteristic
294C42#434111yescharacteristic
295C11#1046711yescharacteristic, complemented, Sylow
296C23—441no—
297C23#6698311yescharacteristic
298Q8—22no—
299Q8—22no—
300Q8—41no—
301Q8—41no—
302Q8—441no—
303Q8—441no—
304D4—441no—
305D4—441no—
306D4—881no—
307D4—881no—
308D4—881no—
309D4—881no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—441no—
318C2×C4—881no—
319C2×C4—881no—
320C2×C4—881no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4#6693511yescharacteristic
324C2×C4#6693611yescharacteristic
325C2×C4#6693811yescharacteristic
326C2×C4#6693911yescharacteristic
327C2×C4C2×#431411yescharacteristic
328C2×C4#6695711yescharacteristic
329C2×C4#6696111yescharacteristic
330C2×C4#6696111yescharacteristic
331C2×C4#6699111yescharacteristic
332C2×C4#6699211yescharacteristic
333C8—42no—
334C8—81no—
335C8—442no—
336C8—881no—
337C22—21no—
338C22—21no—
339C22—881no—
340C22—881no—
341C22—881no—
342C22#1062257411yescharacteristic
343C22#1062272711yescharacteristic
344C22#1062274811yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—42no—
350C4—81no—
351C4—881no—
352C4—1761no—
353C4#1062234411yescharacteristic
354C4#1062234711yescharacteristic
355C4#1062234811yescharacteristic
356C4#1062235011yescharacteristic
357C2—21no—
358C2—21no—
359C2—1761no—
360C2#1306980611yescharacteristic
361C2#1306989511yescharacteristic
362C2#1306992111yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1461C2
socleC22×C11#394
prime radical#10623008C22
hypercenter#1461D11
hypocenterC11#10467
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #13068631C2semidirect
3. #13067387C2semidirect
6. #13066475C2semidirect
7. C11×#1461C2semidirect
120. #1461D11semidirect
295. C11#10467semidirect

Maximal subgroups

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

subgroupindex
#130780882
#130686312
#130673872
#130672632
#130671772
#130664752
C11×#14612
#1046711