Finite Group Databasebeta

← #14655911

Subgroups — #14655911

Order 2816.

512 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079932C211yesmaximal, characteristic
2#13079767C211yesmaximal, characteristic, complemented
3#13069560C211yesmaximal, characteristic, complemented
4#13069540C211yesmaximal, characteristic, complemented
5#13067111C211yesmaximal, characteristic
6#13066467C211yesmaximal, characteristic, complemented
7C11×#3141C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#489—22no—
12C11×#487—21no—
13C11×#486—21no—
14C11×#417—22no—
15C4×C11×M16C2211yescharacteristic
16C2×#66899—22no—
17#10622707—21no—
18#10622706—21no—
19#10622704—22no—
20#10622691—21no—
21#10622688—21no—
22#10622654—22no—
23#10622632—21no—
24#10622621—21no—
25#10622583—22no—
26C4×C4⋊Dic11C2211yescharacteristic
27#10622538C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622193—22no—
30#10622175—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C2×C11×M16D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8D411yescharacteristic
39C11×#127D411yescharacteristic
40C11×#124—21no—
41C11×#121—21no—
42C11×#121—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4324—22no—
49#66979—21no—
50C2×C4⋊Dic11—21no—
51#66977—21no—
52#66977—21no—
53C2×C4×Dic11—21no—
54C22×C11⋊C8D412yes—
55#66923—21no—
56#66922D411yescharacteristic
57#66922D411yescharacteristic
58C4×Dic22—21no—
59C4×Dic22—21no—
60C11×#103—24no—
61C11×#102—24no—
62C11×#97—21no—
63C4×C8×C11—21no—
64#66899—44no—
65#66896—22no—
66C11⋊#95—21no—
67C22⋊(C11⋊C8)D412yes—
68#66874—24no—
69#66874—22no—
70#66872—22no—
71#66871—24no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4×C11⋊C8—21no—
76#10202—111nomaximal, Sylow
77C11×#41—42no—
78C11×#41—42no—
79C2×Q8×C11—21no—
80C2×Q8×C11—22no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C2×Q8×C11—41no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×Dic11—41no—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C11×M16—22no—
97C11×M16—22no—
98C2×C8×C11—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C22⋊Dic11—41no—
112#4324—82no—
113C4⋊Dic11—22no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121C4×Dic11—41no—
122C4×Dic11—42no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—42no—
126#3246—111no—
127#3230—111no—
128#3141D1111yescharacteristic
129#1986—111no—
130#1981—111no—
131#1502—111no—
132#1283—111no—
133C23×C11—41no—
134C23×C11#12711yescharacteristic
135Q8×C11—44no—
136Q8×C11—42no—
137Q8×C11—81no—
138Q8×C11—81no—
139D4×C11—42no—
140D4×C11—41no—
141D4×C11—41no—
142D4×C11—81no—
143D4×C11—81no—
144D4×C11—81no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—82no—
151C2×C4×C11—82no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#13512yes—
159C2×C4×C11#13712yes—
160C2×Dic11—42no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165Dic22—42no—
166Dic22—41no—
167Dic22—41no—
168C8×C11—42no—
169C11⋊C8—42no—
170C11⋊C8—42no—
171#533—111no—
172#532C2×D1111yescharacteristic
173C2×C4⋊Q8C2×D1111yescharacteristic
174#500—221no—
175#489—22no—
176#487—21no—
177#487—221no—
178#486—21no—
179#484—222no—
180#477—222no—
181#476—221no—
182#475—221no—
183#465—222no—
184#461—221no—
185#460—221no—
186#431—111no—
187C2×C4⋊C8—111no—
188#417—22no—
189C2×#103—222no—
190C4×M16C2×D1111yescharacteristic
191C4×C4⋊C4—111no—
192#339—222no—
193#327—222no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11#39211yescharacteristic
200C22×C11#49511yescharacteristic
201C22×C11#49711yescharacteristic
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—82no—
206C4×C11—81no—
207C4×C11#45212yes—
208C4×C11#45311yescharacteristic
209C4×C11#45411yescharacteristic
210C4×C11#46412yes—
211Dic11—82no—
212Dic11—81no—
213Dic11—81no—
214C2×#41—21no—
215C22×Q8—21no—
216C2×SD16—222no—
217C2×M16C22⋊D1112yes—
218C22×C8—112no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—111no—
223C4⋊Q8—111no—
224C4⋊Q8C22⋊D1112yes—
225C4⋊Q8C22⋊D1111yescharacteristic
226#127C22⋊D1111yescharacteristic
227#125—221no—
228#124—21no—
229C22⋊Q8—221no—
230C22⋊Q8—221no—
231#121—21no—
232#121—21no—
233C4×Q8—221no—
234C4×Q8—221no—
235C4×D4—21no—
236C4×D4—21no—
237#117—221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—221no—
241C2×C42—221no—
242C2×C42C22×D1111yescharacteristic
243#107—224no—
244#106—222no—
245C4⋊C8—221no—
246C4⋊C8—221no—
247C4⋊C8—221no—
248#103—24no—
249#103—222no—
250#103—224no—
251#103—444no—
252#102—24no—
253#102—222no—
254C22⋊C8—112no—
255#97—21no—
256C4×C8—21no—
257C4×C8—221no—
258#95—221no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—161no—
262C2×C11#200611yescharacteristic
263C2×C11#200911yescharacteristic
264C2×C11#201511yescharacteristic
265#41—42no—
266#41—42no—
267C2×Q8—22no—
268C2×Q8—21no—
269C2×Q8—42no—
270C2×Q8—42no—
271C2×Q8—41no—
272C2×Q8—221no—
273C2×Q8—221no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—441no—
281C22×C4D4×D1111yescharacteristic
282C22×C4D4×D1111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284SD16—882no—
285M16—22no—
286M16—22no—
287C2×C8—22no—
288C2×C8—222no—
289C2×C8—222no—
290C2×C8—442no—
291C4⋊C4—21no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—222no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—441no—
308C42—441no—
309C42—442no—
310C42D4×D1111yescharacteristic
311C42#434111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C42C2×C22⋊D1111yescharacteristic
314C11#1020211yescharacteristic, complemented, Sylow
315C23—41no—
316C23#6699311yescharacteristic
317Q8—44no—
318Q8—42no—
319Q8—81no—
320Q8—81no—
321Q8—442no—
322Q8—441no—
323Q8—441no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—442no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—881no—
341C2×C4—881no—
342C2×C4#6699011yescharacteristic
343C2×C4#6699011yescharacteristic
344C2×C4#6699111yescharacteristic
345C2×C4#6699211yescharacteristic
346C2×C4#6699211yescharacteristic
347C2×C4#6700312yes—
348C2×C4#6700412yes—
349C2×C4#6700611yescharacteristic
350C8—42no—
351C8—442no—
352C8—442no—
353C22—21no—
354C22—21no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22#1062267211yescharacteristic
359C22#1062267311yescharacteristic
360C22#1062283611yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—82no—
365C4—81no—
366C4—882no—
367C4—881no—
368C4—881no—
369C4#1062266712yes—
370C4#1062281111yescharacteristic
371C4#1062281411yescharacteristic
372C4#1062285212yes—
373C2—21no—
374C2—21no—
375C2—161no—
376C2#1306965611yescharacteristic
377C2#1306967411yescharacteristic
378C2#1306971011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3141C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3141D11
hypocenterC11#10202
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #13079767C2semidirect
3. #13069560C2semidirect
4. #13069540C2semidirect
6. #13066467C2semidirect
314. C11#10202semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130797672
#130695602
#130695402
#130671112
#130664672
C11×#31412
#1020211