Finite Group Databasebeta

← #14667008

Subgroups — #14667008

Order 2816.

338 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 57 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#13079476C211yesmaximal, characteristic
2#13070801C211yesmaximal, characteristic, complemented
3#13070057C211yesmaximal, characteristic, complemented
4#13066632C211yesmaximal, characteristic, complemented
5#13066631C211yesmaximal, characteristic, complemented
6#13066541C211yesmaximal, characteristic, complemented
7C11×#2232C211yesmaximal, characteristic, complemented
8#10623138—21no—
9C11×#466C2211yescharacteristic
10C2×C11×#107C2211yescharacteristic, complemented
11#10622769—21no—
12#10622728C2211yescharacteristic
13#10622723C2211yescharacteristic
14#10622652—21no—
15#10622579—21no—
16#10622498—21no—
17#10622397—21no—
18#10622386—21no—
19C11×#366—21no—
20C11×#357—21no—
21C11×C22⋊C16C2211yescharacteristic, complemented
22#10622190C2211yescharacteristic, complemented
23C22⋊(C11⋊C16)C2211yescharacteristic, complemented
24#10622168—21no—
25#10622129—21no—
26#10622128—21no—
27C2×D4×D11—21no—
28C2×#4339D411yescharacteristic
29C2×C11×D8D411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31C11×#121—21no—
32C2×C11×C4⋊C4—21no—
33#66993—41no—
34#66991—21no—
35#66990—41no—
36C2×#4323—21no—
37#66983—21no—
38C2×#4318—21no—
39C2×#4318D411yescharacteristic
40C2×D88D411yescharacteristic
41#66948—21no—
42#66945—21no—
43#66938—41no—
44#66935—41no—
45C2×C11×C16—21no—
46C11×#107—21no—
47C11×#107—21no—
48C11×#107D411yescharacteristic
49C11×#102—21no—
50#66896—21no—
51#66885—21no—
52(C2×D11)⋊C8—21no—
53(C2×D11)⋊C8—21no—
54#66882D411yescharacteristic
55C2×C11⋊C16—21no—
56#66874—41no—
57#66873—21no—
58#66873—41no—
59#66872—21no—
60#12284—111nomaximal, Sylow
61C23×D11—41no—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D411yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11—41no—
68C2×C22⋊D11—41no—
69C2×C22⋊D11—41no—
70D4×D11—81no—
71D4×D11—81no—
72#4339—41no—
73#4339—41no—
74C2×D44—21no—
75C2×D44—41no—
76C2×D44D811yescharacteristic
77C2×C4×D11—21no—
78C2×Dic22D811yescharacteristic
79C11×D8—41no—
80C2×C8×C11—41no—
81C2×C8×C11C2×D411yescharacteristic
82C2×C8×C11C2×D411yescharacteristic
83C11×C4⋊C4—21no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—41no—
87C22⋊Dic11—41no—
88#4323—81no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92C4⋊Dic11—21no—
93C4×Dic11—41no—
94#4318—41no—
95#4318—41no—
96#4318—41no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—41no—
99D88—41no—
100C11×C16—41no—
101C11⋊C16—41no—
102#3199—111no—
103#2233—111no—
104#2232D1111yescharacteristic, complemented
105#2078—111no—
106#1349—111no—
107#1349—111no—
108#1315—111no—
109C23×C11—41no—
110C23×C11AGL(1,ℤ/8)11yescharacteristic
111C22×D11—21no—
112C22×D11—41no—
113C22×D11—82no—
114C22×D11—161no—
115C22×D11—161no—
116D4×C11—41no—
117D4×C11—41no—
118D4×C11—161no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—41no—
122C2×C4×C11—81no—
123C2×C4×C11—161no—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11C2×D811yescharacteristic
126C22⋊D11—81no—
127C22⋊D11—82no—
128C22⋊D11—161no—
129C22⋊D11—161no—
130C2×Dic11—21no—
131C2×Dic11—41no—
132D44—41no—
133D44—41no—
134D44—41no—
135D44—161no—
136C4×D11—41no—
137C4×D11—41no—
138Dic22—41no—
139C8×C11—21no—
140C8×C11—21no—
141C11⋊C8—41no—
142C11⋊C8—81no—
143#535—221no—
144#482—221no—
145#482—221no—
146#469—221no—
147#466—111no—
148#466C2×D1111yescharacteristic
149#447—221no—
150#447—221no—
151C2×#107C2×D1111yescharacteristic, complemented
152#417—221no—
153#408—111no—
154#367—221no—
155#366—21no—
156#357—21no—
157#357—221no—
158C22⋊C16—111no—
159C22⋊C16C2×D1111yescharacteristic, complemented
160#343—221no—
161#341—111no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—81no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11#44711yescharacteristic
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—81no—
173C2×D11—81no—
174C2×D11—81no—
175C2×D11—164no—
176C4×C11—21no—
177C4×C11—81no—
178C4×C11—161no—
179C4×C11#45511yescharacteristic
180C4×C11#45811yescharacteristic
181Dic11—41no—
182Dic11—81no—
183C2×#41—111no—
184C22×D4—221no—
185C2×D8—111no—
186C2×D8—221no—
187C2×D8C22⋊D1111yescharacteristic
188C2×M16—111no—
189C2×M16—221no—
190C22×C8C22×D1111yescharacteristic
191#127—441no—
192#124—441no—
193#121—21no—
194#121—221no—
195#121—221no—
196#121—221no—
197#120—441no—
198#120—441no—
199#117—221no—
200C2×C4⋊C4—21no—
201C2×C16—21no—
202C2×C16—221no—
203#107—21no—
204#107—21no—
205#107—111no—
206#107C22⋊D1111yescharacteristic
207#106—221no—
208#103—441no—
209#102—21no—
210#102—221no—
211#102—221no—
212#102—221no—
213#102—441no—
214C22⋊C8—221no—
215C22⋊C8—221no—
216C2×C11—41no—
217C2×C11—161no—
218C2×C11#160711yescharacteristic
219C2×C11#219211yescharacteristic
220C2×C11#219411yescharacteristic
221D11—81no—
222D11—161no—
223C24—441no—
224#41—441no—
225#41—441no—
226C2×Q8—111no—
227C2×D4—21no—
228C2×D4—41no—
229C2×D4—111no—
230C2×D4—221no—
231C2×D4—221no—
232C2×D4—441no—
233C2×D4—441no—
234C2×D4—441no—
235C2×D4—441no—
236C2×D4—881no—
237C2×D4—881no—
238C22×C4—41no—
239C22×C4—221no—
240C22×C4D4×D1111yescharacteristic
241D8—41no—
242D8—441no—
243D8—881no—
244M16—441no—
245M16—441no—
246M16—441no—
247C2×C8—41no—
248C2×C8—221no—
249C2×C8—441no—
250C2×C8D4×D1111yescharacteristic
251C2×C8C2×C22⋊D1111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—221no—
256C22⋊C4—41no—
257C22⋊C4—441no—
258C22⋊C4—441no—
259C22⋊C4—441no—
260C22⋊C4—441no—
261C42—441no—
262C16—41no—
263C16—441no—
264C11#1228411yescharacteristic, complemented, Sylow
265C23—41no—
266C23—221no—
267C23—441no—
268C23—882no—
269C23—1761no—
270C23—1761no—
271C23#6696411yescharacteristic
272Q8—441no—
273D4—41no—
274D4—41no—
275D4—161no—
276D4—441no—
277D4—441no—
278D4—441no—
279D4—881no—
280D4—882no—
281D4—1761no—
282D4—1761no—
283D4—1761no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—81no—
288C2×C4—161no—
289C2×C4—221no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4D8×D1111yescharacteristic
294C2×C4#6699011yescharacteristic
295C8—21no—
296C8—21no—
297C8—441no—
298C8—881no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—441no—
306C22—441no—
307C22—441no—
308C22—881no—
309C22—881no—
310C22—881no—
311C22—1764no—
312C22#1062276911yescharacteristic
313C4—21no—
314C4—81no—
315C4—161no—
316C4—441no—
317C4—881no—
318C4#1062266611yescharacteristic
319C4#1062281511yescharacteristic
320C2—41no—
321C2—161no—
322C2—881no—
323C2—1761no—
324C2#1306760011yescharacteristic
325C2#1307057211yescharacteristic
326C2#1307058411yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2232C2
socleC22×C11#447
prime radical#13079476C2
hypercenter#2232D11
hypocenterC11#12284
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
2. #13070801C2semidirect
3. #13070057C2semidirect
4. #13066632C2semidirect
5. #13066631C2semidirect
6. #13066541C2semidirect
7. C11×#2232C2semidirect
10. C2×C11×#107C22semidirect
21. C11×C22⋊C16C22semidirect
22. #10622190C22semidirect
23. C22⋊(C11⋊C16)C22semidirect
104. #2232D11semidirect
151. C2×#107C2×D11semidirect
159. C22⋊C16C2×D11semidirect
264. C11#12284semidirect

Maximal subgroups

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

subgroupindex
#130794762
#130708012
#130700572
#130666322
#130666312
#130665412
C11×#22322
#1228411