Finite Group Databasebeta

← #14666122

Subgroups — #14666122

Order 2816.

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

normal subgroups only

This group has 398 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#13076449C211yesmaximal, characteristic, complemented
2#13069837C211yesmaximal, characteristic, complemented
3#13067653C211yesmaximal, characteristic, complemented
4#13066644C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic, complemented
6#13066561C211yesmaximal, characteristic, complemented
7C11×#1598C211yesmaximal, characteristic
8C11×#537C2211yescharacteristic
9C11×#447—21no—
10C11×#394C2211yescharacteristic
11C2×#66901—21no—
12#10622845—21no—
13#10622835—21no—
14#10622647—21no—
15#10622599C2211yescharacteristic
16#10622589C2211yescharacteristic
17#10622564—21no—
18#10622561—21no—
19#10622557—21no—
20#10622557—21no—
21#10622265—21no—
22C11×#327—21no—
23C11×#324C2211yescharacteristic
24#10622175—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C2×C11×#41—21no—
28C22×D4×C11D411yescharacteristic
29C2×C11×D8—41no—
30C11×C22⋊Q8—41no—
31C11×#121—21no—
32C11×#121—21no—
33C11×#121—41no—
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×C4⋊Dic11D411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49C11×#102—41no—
50C11×C22⋊C8—21no—
51C11×#95D411yescharacteristic
52#66901—42no—
53#66899—41no—
54#66896—41no—
55#66896—41no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95D411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66872—41no—
63#12144—111nomaximal, Sylow
64C24×C11—21no—
65C11×#41—41no—
66C11×#41—41no—
67C11×#41—41no—
68C11×#41—41no—
69C2×Q8×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—81no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C11×D8—82no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—81no—
95C22⋊Dic11—42no—
96C22⋊Dic11—42no—
97C22⋊Dic11—81no—
98C22⋊Dic11—81no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101Dic11⋊C4—42no—
102Dic11⋊C4—81no—
103Dic11⋊C4—81no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—81no—
107#4318—41no—
108#4318—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2795—111no—
112#2039—111no—
113#1616—111no—
114#1598D1111yescharacteristic
115#1353—111no—
116#1345—111no—
117#1325—111no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11#12011yescharacteristic
127Q8×C11—41no—
128Q8×C11—41no—
129D4×C11—41no—
130D4×C11—41no—
131D4×C11—42no—
132D4×C11—81no—
133D4×C11—81no—
134D4×C11—81no—
135D4×C11—81no—
136D4×C11—81no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C8×C11—81no—
164C11⋊C8—81no—
165C11⋊C8—81no—
166#537C2×D1111yescharacteristic
167#481—221no—
168#447—21no—
169C2×#104—221no—
170#417—221no—
171#400—111no—
172#396—221no—
173#394—221no—
174#394C2×D1111yescharacteristic
175#388—221no—
176#388—221no—
177#388—221no—
178#387—221no—
179#384—111no—
180#343—111no—
181#327—21no—
182#327—221no—
183#324—111no—
184#324C2×D1111yescharacteristic
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#44911yescharacteristic
198C22×C11#45411yescharacteristic
199C22×C11B(4,𝔽2)11yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—81no—
205C4×C11—81no—
206Dic11—42no—
207Dic11—81no—
208Dic11—81no—
209Dic11—81no—
210C2×#41—21no—
211C22×D4C22⋊D1111yescharacteristic
212C2×D8—41no—
213C2×M16—221no—
214C22⋊Q8—41no—
215#121—21no—
216#121—21no—
217#121—41no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4C22×D1111yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C42—111no—
231C2×C42—221no—
232#106—441no—
233#104—442no—
234#103—441no—
235#102—41no—
236#102—441no—
237#102—441no—
238C22⋊C8—21no—
239C22⋊C8—221no—
240#95—111no—
241#95—221no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95C22⋊D1111yescharacteristic
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—161no—
249C2×C11—161no—
250C2×C11#159711yescharacteristic
251C2×C11#220011yescharacteristic
252C2×C11#220411yescharacteristic
253C24—21no—
254#41—41no—
255#41—41no—
256#41—41no—
257#41—41no—
258C2×Q8—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—81no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4D4×D1111yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274D8—82no—
275M16—441no—
276M16—441no—
277C2×C8—41no—
278C2×C8—441no—
279C2×C8—441no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C4⋊C4—442no—
286C4⋊C4—881no—
287C4⋊C4—881no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—81no—
293C22⋊C4—442no—
294C22⋊C4—442no—
295C22⋊C4—881no—
296C22⋊C4—881no—
297C42—221no—
298C42—221no—
299C42—881no—
300C11#1214411yescharacteristic, complemented, Sylow
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#6699011yescharacteristic
310Q8—41no—
311Q8—41no—
312D4—41no—
313D4—41no—
314D4—42no—
315D4—81no—
316D4—81no—
317D4—81no—
318D4—81no—
319D4—81no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—222no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4#6696411yescharacteristic
345C2×C4#6696511yescharacteristic
346C8—81no—
347C8—881no—
348C8—881no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22#1062264511yescharacteristic
362C22#1062277111yescharacteristic
363C22#1062281411yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—81no—
369C4—81no—
370C4—442no—
371C4—881no—
372C4—881no—
373C4—881no—
374C2—21no—
375C2—21no—
376C2—161no—
377C2—161no—
378C2#1306754211yescharacteristic
379C2#1307062111yescharacteristic
380C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
Fitting, prime radicalC11×#1598C2
socleC22×C11B(4,𝔽2)
hypercenter#1598D11
hypocenterC11#12144
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1598

Complements

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

NH ≅ G/Ntype
1. #13076449C2semidirect
2. #13069837C2semidirect
3. #13067653C2semidirect
4. #13066644C2semidirect
5. #13066619C2semidirect
6. #13066561C2semidirect
300. C11#12144semidirect

Maximal subgroups

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

subgroupindex
#130764492
#130698372
#130676532
#130666442
#130666192
#130665612
C11×#15982
#1214411