Finite Group Databasebeta

← #14666897

Subgroups — #14666897

Order 2816.

414 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 55 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#13075885C211yesmaximal, characteristic
2#13069782C211yesmaximal, characteristic, complemented
3#13067539C211yesmaximal, characteristic
4#13066640C211yesmaximal, characteristic, complemented
5#13066614C211yesmaximal, characteristic
6#13066545C211yesmaximal, characteristic, complemented
7C11×#1614C211yesmaximal, characteristic, complemented
8C11×#543C2211yescharacteristic
9C11×#484—21no—
10C11×#399C2211yescharacteristic
11#10622659—21no—
12#10622604—21no—
13#10622603—21no—
14#10622591—21no—
15#10622573C2211yescharacteristic
16#10622571—21no—
17#10622570—21no—
18#10622556—21no—
19#10622556C2211yescharacteristic
20#10622288—21no—
21C11×#328—21no—
22C11×#323C2211yescharacteristic
23#10622176—21no—
24#10622164—21no—
25#10622164C2211yescharacteristic
26#10622163C2211yescharacteristic
27C22×C22⋊D11—21no—
28C23×Dic11D411yescharacteristic
29C22×D44D411yescharacteristic
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—41no—
33C11×C22⋊Q8—41no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11D411yescharacteristic
41C2×#4325—41no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C11×#107—41no—
50C11×#103—41no—
51C11×C22⋊C8—21no—
52C11×#95D411yescharacteristic
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—41no—
58C11⋊#95—41no—
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61#66873—41no—
62#12267—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C23×D11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—42no—
74C2×C22⋊D11—41no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—81no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84C22×Dic11—41no—
85C2×D44—41no—
86C2×D44—81no—
87C2×C8×C11—41no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—81no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—81no—
98C22⋊Dic11—41no—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101#4325—82no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—81no—
104(C2×D11)⋊C4—81no—
105(C2×D11)⋊C4—81no—
106(C2×D11)⋊C4—81no—
107Dic11⋊C4—42no—
108C4×Dic11—81no—
109C2×C11⋊C8—41no—
110#2752—111no—
111#2030—111no—
112#1614D1111yescharacteristic, complemented
113#1596—111no—
114#1352—111no—
115#1343—111no—
116#1317—111no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11#12011yescharacteristic
122C23×C11#13511yescharacteristic
123C23×C11#13711yescharacteristic
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131Q8×C11—81no—
132Q8×C11—81no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C22⋊D11—82no—
148C22⋊D11—82no—
149C2×Dic11—22no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161C2×Dic11—81no—
162C2×Dic11—81no—
163D44—42no—
164D44—81no—
165C8×C11—81no—
166C11⋊C8—81no—
167#543C2×D1111yescharacteristic
168#484—21no—
169#450—221no—
170#399C2×D1111yescharacteristic
171#397—221no—
172#394—221no—
173#392—111no—
174#390—221no—
175#388—221no—
176#387—221no—
177#386—221no—
178#381—111no—
179#381—221no—
180#342—111no—
181#342—221no—
182#328—21no—
183#328—221no—
184#323—111no—
185#323C2×D1111yescharacteristic
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—81no—
195C22×C11#45211yescharacteristic
196C22×C11#45511yescharacteristic
197C22×C11B(4,𝔽2)11yescharacteristic
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11—81no—
211Dic11—42no—
212Dic11—81no—
213Dic11—81no—
214Dic11—161no—
215C22×D4—111no—
216C22×D4—221no—
217C23×C4—111no—
218C2×SD16—441no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—41no—
222C22⋊Q8—41no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4C22⋊D1111yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—111no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4C22×D1111yescharacteristic
236C2×C42—221no—
237#107—41no—
238#103—41no—
239#102—441no—
240C22⋊C8—21no—
241C22⋊C8—221no—
242#95—111no—
243#95—221no—
244#95—221no—
245#95—221no—
246#95—221no—
247#95—441no—
248#95—441no—
249#95C22⋊D1111yescharacteristic
250C2×C11—21no—
251C2×C11—21no—
252C2×C11—41no—
253C2×C11—41no—
254C2×C11#160611yescharacteristic
255C2×C11#219811yescharacteristic
256C2×C11#220011yescharacteristic
257D11—161no—
258C24—221no—
259C24D4×D1111yescharacteristic
260C2×Q8—21no—
261C2×Q8—21no—
262C2×D4—441no—
263C2×D4—442no—
264C2×D4—441no—
265C2×D4—441no—
266C2×D4—881no—
267C2×D4—881no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—441no—
278C22×C4—441no—
279C22×C4—441no—
280C22×C4D4×D1111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282SD16—882no—
283C2×C8—41no—
284C2×C8—441no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—81no—
291C4⋊C4—442no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—81no—
296C22⋊C4—442no—
297C22⋊C4—441no—
298C22⋊C4—441no—
299C22⋊C4—441no—
300C22⋊C4—881no—
301C22⋊C4—881no—
302C22⋊C4—881no—
303C22⋊C4—881no—
304C42—881no—
305C11#1226711yescharacteristic, complemented, Sylow
306C23—21no—
307C23—21no—
308C23—41no—
309C23—41no—
310C23—441no—
311C23—441no—
312C23—441no—
313C23—441no—
314C23—441no—
315C23—441no—
316C23—441no—
317C23#6697111yescharacteristic
318C23#6697211yescharacteristic
319C23#6699011yescharacteristic
320Q8—81no—
321Q8—81no—
322D4—442no—
323D4—881no—
324D4—882no—
325D4—882no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—222no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—442no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—881no—
351C2×C4—881no—
352C2×C4—881no—
353C2×C4—881no—
354C8—81no—
355C8—881no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—81no—
365C22—881no—
366C22—881no—
367C22—881no—
368C22—881no—
369C22—881no—
370C22—881no—
371C22—881no—
372C22#1062264511yescharacteristic
373C22#1062280011yescharacteristic
374C22#1062281511yescharacteristic
375C4—41no—
376C4—41no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4—442no—
382C4—881no—
383C4—881no—
384C4—1761no—
385C2—21no—
386C2—21no—
387C2—41no—
388C2—41no—
389C2—1761no—
390C2#1306759511yescharacteristic
391C2#1307061011yescharacteristic
392C2#1307062211yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1614C2
socleC22×C11B(4,𝔽2)
prime radical#10622573C22
hypercenter#1614D11
hypocenterC11#12267
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1614

Complements

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

NH ≅ G/Ntype
2. #13069782C2semidirect
4. #13066640C2semidirect
6. #13066545C2semidirect
7. C11×#1614C2semidirect
112. #1614D11semidirect
305. C11#12267semidirect

Maximal subgroups

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

subgroupindex
#130758852
#130697822
#130675392
#130666402
#130666142
#130665452
C11×#16142
#1226711