Finite Group Databasebeta

← #14666783

Subgroups — #14666783

Order 2816.

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

normal subgroups only

This group has 386 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#13076691C211yesmaximal, characteristic
2#13069958C211yesmaximal, characteristic, complemented
3#13067556C211yesmaximal, characteristic
4#13066622C211yesmaximal, characteristic, complemented
5#13066620C211yesmaximal, characteristic
6#13066561C211yesmaximal, characteristic, complemented
7C11×#1611C211yesmaximal, characteristic, complemented
8C11×#544C2211yescharacteristic
9C2×#66951—21no—
10C11×#483—21no—
11C11×#398C2211yescharacteristic
12#10622659—21no—
13#10622608—21no—
14#10622607—21no—
15#10622607—21no—
16#10622604C2211yescharacteristic
17#10622589C2211yescharacteristic
18#10622289—21no—
19#10622285—21no—
20#10622270—21no—
21C11×#328—21no—
22C11×#324C2211yescharacteristic
23#10622176—21no—
24#10622170—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×D44D411yescharacteristic
28C11×C4⋊Q8—41no—
29C11×#125—41no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C11×#117—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×#4325—41no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11D411yescharacteristic
50C2×#4318—21no—
51#66951—42no—
52#66951—42no—
53C11×#106—41no—
54C11×#103—41no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95D411yescharacteristic
58C11⋊#95—21no—
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61#66873—41no—
62#66872—41no—
63#66871—41no—
64#12249—111nomaximal, Sylow
65C23×D11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C2×D44—41no—
77C2×D44—81no—
78C2×C8×C11—41no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C22⋊C4—41no—
90C42×C11—41no—
91#4325—82no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—81no—
97(C2×D11)⋊C4—81no—
98(C2×D11)⋊C4—81no—
99C4⋊Dic11—41no—
100C4⋊Dic11—42no—
101Dic11⋊C4—42no—
102Dic11⋊C4—81no—
103Dic11⋊C4—81no—
104Dic11⋊C4—81no—
105C4×Dic11—21no—
106C4×Dic11SD1612yescomplemented
107#4318—22no—
108#4318—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2823—111no—
112#2060—111no—
113#1611D1111yescharacteristic, complemented
114#1599—111no—
115#1346—111no—
116#1345—111no—
117#1325—111no—
118C23×C11#12011yescharacteristic
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126Q8×C11—81no—
127Q8×C11—81no—
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—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11C2×SD1611yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×Dic11—22no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153D44—42no—
154D44—81no—
155C8×C11—81no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158#544C2×D1111yescharacteristic
159C2×#126—221no—
160#483—21no—
161#450—221no—
162#428—221no—
163#398—221no—
164#398C2×D1111yescharacteristic
165#396—221no—
166#396—221no—
167#396—221no—
168#394—111no—
169#394—221no—
170#384—111no—
171#343—111no—
172#339—221no—
173#328—21no—
174#328—221no—
175#324—111no—
176#324C2×D1111yescharacteristic
177C22×C11—21no—
178C22×C11—21no—
179C22×C11#45011yescharacteristic
180C22×C11#45611yescharacteristic
181C22×C11B(4,𝔽2)11yescharacteristic
182C2×D11—81no—
183C2×D11—81no—
184C2×D11—81no—
185C2×D11—81no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197Dic11—42no—
198Dic11—81no—
199Dic11—81no—
200C22×D4—111no—
201C2×SD16—441no—
202C2×M16—221no—
203C4⋊Q8—41no—
204#126—442no—
205#126—442no—
206#125—41no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209#117—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4C22⋊D1111yescharacteristic
218C2×C4⋊C4C22×D1111yescharacteristic
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—111no—
226#107—441no—
227#106—41no—
228#106—441no—
229#103—41no—
230#102—441no—
231C22⋊C8—21no—
232C22⋊C8—221no—
233#95—21no—
234#95—111no—
235#95—221no—
236#95C22⋊D1111yescharacteristic
237C2×C11—21no—
238C2×C11—21no—
239C2×C11#160411yescharacteristic
240C2×C11#220011yescharacteristic
241C2×C11#220311yescharacteristic
242D11—161no—
243C24—221no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×D4—441no—
247C2×D4—881no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4D4×D1111yescharacteristic
254C22×C4D4×D1111yescharacteristic
255C22×C4C2×C22⋊D1111yescharacteristic
256SD16—882no—
257M16—222no—
258M16—441no—
259C2×C8—41no—
260C2×C8—441no—
261C2×C8—441no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—441no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—881no—
276C4⋊C4—881no—
277C4⋊C4—881no—
278C22⋊C4—41no—
279C22⋊C4—442no—
280C22⋊C4—442no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C22⋊C4—881no—
284C22⋊C4—881no—
285C22⋊C4—881no—
286C42—41no—
287C42—112no—
288C42—221no—
289C11#1224911yescharacteristic, complemented, Sylow
290C23—441no—
291C23—441no—
292C23—441no—
293C23—441no—
294C23—441no—
295C23—441no—
296C23—441no—
297C23#6699011yescharacteristic
298Q8—81no—
299Q8—81no—
300D4—442no—
301D4—881no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—222no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4SD16×D1111yescharacteristic
326C2×C4#6696711yescharacteristic
327C8—81no—
328C8—442no—
329C8—881no—
330C22—21no—
331C22—21no—
332C22—881no—
333C22—881no—
334C22—881no—
335C22—881no—
336C22—881no—
337C22—881no—
338C22—881no—
339C22#1062264511yescharacteristic
340C22#1062278211yescharacteristic
341C22#1062281811yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4—442no—
351C4—881no—
352C4—881no—
353C2—21no—
354C2—21no—
355C2—1761no—
356C2#1306758311yescharacteristic
357C2#1307062011yescharacteristic
358C2#1307063511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1611C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D44D4
hypercenter#1611D11
hypocenterC11#12249
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1611

Complements

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

NH ≅ G/Ntype
2. #13069958C2semidirect
4. #13066622C2semidirect
6. #13066561C2semidirect
7. C11×#1611C2semidirect
106. C4×Dic11SD16semidirect
113. #1611D11semidirect
289. C11#12249semidirect

Maximal subgroups

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

subgroupindex
#130766912
#130699582
#130675562
#130666222
#130666202
#130665612
C11×#16112
#1224911