Finite Group Databasebeta

← #14655176

Subgroups — #14655176

Order 2816.

542 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 85 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#13078992C211yesmaximal, characteristic
2#13074562C211yesmaximal, characteristic
3#13067329C211yesmaximal, characteristic
4#13067218C211yesmaximal, characteristic, complemented
5#13067128C211yesmaximal, characteristic, complemented
6#13066508C211yesmaximal, characteristic, complemented
7C11×#3236C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C2×#66927C2211yescharacteristic
11C11×#501—21no—
12C11×#491—21no—
13C11×#484—21no—
14C11×#483—21no—
15C11×#479—22no—
16C11×#432C2211yescharacteristic
17#10622701—21no—
18#10622701—21no—
19#10622680—22no—
20#10622614—22no—
21#10622604—22no—
22#10622604—22no—
23#10622601—21no—
24#10622601—21no—
25#10622545C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622181—22no—
29#10622176—22no—
30#10622123—22no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44D412yes—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×#125—21no—
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×(C2×D11)⋊C4—24no—
52C2×(C2×D11)⋊C4—24no—
53C2×C4×Dic11—21no—
54C2×#4318—21no—
55#66927—21no—
56#66927—21no—
57#66927—21no—
58#66927—21no—
59C11×#107—22no—
60C11×#106—22no—
61C11×C4⋊C8D412yes—
62C11×#103—22no—
63C11×#103—22no—
64C11×C22⋊C8—21no—
65C11×#97—21no—
66C11⋊#95—21no—
67C11⋊#95D412yes—
68C22⋊(C11⋊C8)—21no—
69#66873—24no—
70#66873—24no—
71C4⋊(C11⋊C8)—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10097—111nomaximal, Sylow
76C23×D11—22no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—22no—
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—44no—
88C2×D44—44no—
89C2×D44—41no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—82no—
94C2×C8×C11—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115(C2×D11)⋊C4—84no—
116(C2×D11)⋊C4—84no—
117C4×Dic11—42no—
118#4318—42no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—41no—
121#3236D1111yescharacteristic, complemented
122#3138—111no—
123#2641—111no—
124#1555—111no—
125#1528—111no—
126#1506—111no—
127#1300—111no—
128C23×C11#12011yescharacteristic
129C22×D11—44no—
130C22×D11—44no—
131C22×D11—42no—
132C22×D11—44no—
133Q8×C11—42no—
134Q8×C11—81no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12711yescharacteristic
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153D44—44no—
154D44—82no—
155D44—82no—
156D44—82no—
157D44—82no—
158D44—82no—
159C8×C11—42no—
160C11⋊C8—42no—
161C11⋊C8—81no—
162#533C2×D1111yescharacteristic
163C2×#127—111no—
164C2×#125C2×D1111yescharacteristic
165#501—21no—
166#491—21no—
167#490—222no—
168#486—221no—
169#486—221no—
170#484—21no—
171#483—21no—
172#479—22no—
173#432—111no—
174#432C2×D1111yescharacteristic
175#418—222no—
176C4×M16—111no—
177#394—222no—
178#394—222no—
179#390—221no—
180#390—221no—
181#376—111no—
182#331—222no—
183#330—222no—
184#328—222no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11#39211yescharacteristic
188C22×C11#45512yes—
189C2×D11—88no—
190C2×D11—82no—
191C2×D11—82no—
192C2×D11—82no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—81no—
199C4×C11—81no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11#45412yes—
203Dic11—82no—
204C22×D4—112no—
205C22×D4—221no—
206C22×D4—221no—
207C2×M16—221no—
208C4⋊Q8C22⋊D1111yescharacteristic
209C4⋊Q8C22⋊D1111yescharacteristic
210#127—221no—
211#127—221no—
212#127—221no—
213#127—221no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—21no—
218#125—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223#117—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C22⋊D1111yescharacteristic
227C2×C4⋊C4C22⋊D1111yescharacteristic
228C2×C22⋊C4—224no—
229C2×C22⋊C4—224no—
230C2×C42—221no—
231C2×C42C22×D1111yescharacteristic
232#107—22no—
233#106—22no—
234C4⋊C8—221no—
235C4⋊C8C22⋊D1112yes—
236#103—22no—
237#103—22no—
238#102—224no—
239#102—224no—
240C22⋊C8—21no—
241C22⋊C8—221no—
242#97—21no—
243#97—112no—
244#97—221no—
245C4×C8—221no—
246#95—112no—
247#95—221no—
248C2×C11—22no—
249C2×C11#200311yescharacteristic
250C2×C11#200411yescharacteristic
251C2×C11#200811yescharacteristic
252D11—162no—
253C24—222no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×D4—222no—
257C2×D4—222no—
258C2×D4—444no—
259C2×D4—444no—
260C2×D4—441no—
261C2×D4—441no—
262C2×D4—441no—
263C2×D4—441no—
264C2×D4—882no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—222no—
268C22×C4D4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271M16—442no—
272C2×C8—22no—
273C2×C8—222no—
274C2×C8—441no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—884no—
291C22⋊C4—884no—
292C42—41no—
293C42—442no—
294C42D4×D1111yescharacteristic
295C42#434111yescharacteristic
296C42C2×C22⋊D1111yescharacteristic
297C42C2×C22⋊D1111yescharacteristic
298C11#1009711yescharacteristic, complemented, Sylow
299C23—444no—
300C23—444no—
301C23—444no—
302C23—442no—
303C23#6699011yescharacteristic
304Q8—42no—
305Q8—81no—
306D4—444no—
307D4—882no—
308D4—882no—
309D4—882no—
310D4—882no—
311D4—882no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4#6699011yescharacteristic
325C2×C4#6699111yescharacteristic
326C2×C4#6699211yescharacteristic
327C2×C4#6699211yescharacteristic
328C2×C4#6699311yescharacteristic
329C2×C4#6700611yescharacteristic
330C8—42no—
331C8—442no—
332C8—881no—
333C22—21no—
334C22—21no—
335C22—888no—
336C22—882no—
337C22—882no—
338C22—882no—
339C22#1062281512yes—
340C22#1062283611yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4—882no—
351C4#1062285812yes—
352C2—22no—
353C2—1762no—
354C2#1306963611yescharacteristic
355C2#1306964211yescharacteristic
356C2#1306966611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3236C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#3236D11
hypocenterC11#10097
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3236

Complements

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

NH ≅ G/Ntype
4. #13067218C2semidirect
5. #13067128C2semidirect
6. #13066508C2semidirect
7. C11×#3236C2semidirect
121. #3236D11semidirect
298. C11#10097semidirect

Maximal subgroups

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

subgroupindex
#130789922
#130745622
#130673292
#130672182
#130671282
#130665082
C11×#32362
#1009711