Finite Group Databasebeta

← #14643022

Subgroups — #14643022

Order 2816.

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

normal subgroups only

This group has 396 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#13076598C211yesmaximal, characteristic
2#13070143C211yesmaximal, characteristic
3#13070094C211yesmaximal, characteristic, complemented
4#13070024C211yesmaximal, characteristic, complemented
5#13066440C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic
7C11×#1272C211yesmaximal, characteristic, complemented
8C11×#391C2211yescharacteristic
9#10622844—21no—
10C2×#66899—21no—
11C2×#66885—21no—
12C2×#66882—21no—
13C2×#66881—21no—
14#10622603—21no—
15#10622552C2211yescharacteristic
16#10622548C2211yescharacteristic
17#10622541C2211yescharacteristic
18#10622287—21no—
19#10622285—21no—
20#10622283—21no—
21#10622268—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622189—21no—
25#10622167—21no—
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C22×C11⋊C8—21no—
48C11×#95—21no—
49C11×#95—21no—
50#66899—42no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55#66885—42no—
56#66882—42no—
57#66881—42no—
58#7820—111nomaximal, Sylow
59C23×D11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—21no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—41no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—41no—
76C2×D44—41no—
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—41no—
84C42×C11—41no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87(C2×D11)⋊C4—41no—
88(C2×D11)⋊C4—41no—
89(C2×D11)⋊C4—81no—
90(C2×D11)⋊C4—81no—
91(C2×D11)⋊C4—81no—
92(C2×D11)⋊C4—81no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105C4×Dic11—81no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#2808—111no—
110#2093—111no—
111#2084—111no—
112#2072—111no—
113#1272D1111yescharacteristic, complemented
114#1271—111no—
115#1270—111no—
116C23×C11#12011yescharacteristic
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124Q8×C11—42no—
125Q8×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11#13511yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155C2×Dic11—81no—
156D44—42no—
157D44—81no—
158C8×C11—42no—
159C8×C11—42no—
160C11⋊C8—81no—
161C2×#107—221no—
162C2×#106—221no—
163C2×#103—221no—
164C2×#102—221no—
165#397—221no—
166#394—221no—
167#393—221no—
168#391C2×D1111yescharacteristic
169#390—111no—
170#389—111no—
171#388—221no—
172#388—221no—
173#387—221no—
174#384—111no—
175#340—221no—
176#340—221no—
177#336—111no—
178#336C2×D1111yescharacteristic
179#336C2×D1111yescharacteristic
180C22×C11#44911yescharacteristic
181C22×C11#44911yescharacteristic
182C22×C11#45211yescharacteristic
183C22×C11#45311yescharacteristic
184C22×C11#45511yescharacteristic
185C22×C11#45611yescharacteristic
186C22×C11#45811yescharacteristic
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11—81no—
202Dic11—81no—
203Dic11—81no—
204Dic11—81no—
205Dic11—161no—
206C22×Q8D4411yescharacteristic
207C22×D4—111no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—221no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4D4411yescharacteristic
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225C2×C42—221no—
226C2×C42C22×D1111yescharacteristic
227#107—442no—
228#106—442no—
229#103—442no—
230#102—442no—
231#95—21no—
232#95—21no—
233#95—221no—
234#95—221no—
235#95—221no—
236#95—221no—
237C2×C11#160911yescharacteristic
238C2×C11#161211yescharacteristic
239C2×C11#161811yescharacteristic
240C2×C11#162011yescharacteristic
241C2×C11#164611yescharacteristic
242C2×C11#165211yescharacteristic
243C2×C11#166111yescharacteristic
244D11—161no—
245C24—221no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×D4—221no—
251C2×D4—221no—
252C2×D4—441no—
253C2×D4—441no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—441no—
260C22×C4C2×D4411yescharacteristic
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—441no—
270C2×C8—441no—
271C2×C8—441no—
272C4⋊C4—41no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—441no—
286C22⋊C4—441no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C22⋊C4—881no—
290C22⋊C4—881no—
291C22⋊C4—881no—
292C22⋊C4—881no—
293C42—41no—
294C42—881no—
295C11#782011yescharacteristic, complemented, Sylow
296C23—441no—
297C23—441no—
298C23—441no—
299C23—441no—
300C23—441no—
301C23—441no—
302C23—441no—
303C23#6693511yescharacteristic
304Q8—42no—
305Q8—81no—
306D4—442no—
307D4—881no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
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—441no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4—881no—
332C2×C4#6695711yescharacteristic
333C2×C4#6696111yescharacteristic
334C2×C4#6696711yescharacteristic
335C2×C4#6696911yescharacteristic
336C2×C4#6697111yescharacteristic
337C2×C4#6697211yescharacteristic
338C8—42no—
339C8—42no—
340C8—881no—
341C22—881no—
342C22—881no—
343C22—881no—
344C22—881no—
345C22—881no—
346C22—881no—
347C22—881no—
348C22#1062234711yescharacteristic
349C22#1062235511yescharacteristic
350C22#1062235911yescharacteristic
351C22#1062242311yescharacteristic
352C22#1062242411yescharacteristic
353C22#1062243511yescharacteristic
354C22#1062243911yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—81no—
362C4—81no—
363C4—881no—
364C4—881no—
365C4—881no—
366C4—1761no—
367C2—1761no—
368C2#1306761611yescharacteristic
369C2#1306763211yescharacteristic
370C2#1306766711yescharacteristic
371C2#1306767711yescharacteristic
372C2#1306784511yescharacteristic
373C2#1306788811yescharacteristic
374C2#1306793611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1272D11
hypocenterC11#7820
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
3. #13070094C2semidirect
4. #13070024C2semidirect
5. #13066440C2semidirect
7. C11×#1272C2semidirect
113. #1272D11semidirect
295. C11#7820semidirect

Maximal subgroups

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

subgroupindex
#130765982
#130701432
#130700942
#130700242
#130664402
#130664362
C11×#12722
#782011