Finite Group Databasebeta

← #14655912

Subgroups — #14655912

Order 2816.

512 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 99 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#13079933C211yesmaximal, characteristic
2#13079767C211yesmaximal, characteristic, complemented
3#13079012C211yesmaximal, characteristic
4#13069559C211yesmaximal, characteristic, complemented
5#13067110C211yesmaximal, characteristic
6#13066466C211yesmaximal, characteristic, complemented
7C11×#1981C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623008C2211yescharacteristic
10#10623001C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×#103—22no—
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622727—22no—
15#10622706—21no—
16#10622706—21no—
17#10622704—22no—
18#10622702—22no—
19#10622701—21no—
20#10622691—21no—
21#10622583—22no—
22#10622579—22no—
23#10622538C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622464—21no—
26#10622461—21no—
27#10622455—21no—
28#10622454—21no—
29#10622161—22no—
30#10622089—22no—
31C22×Q8×C11—21no—
32C2×#4339—21no—
33C22×C8×C11D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D412yes—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
43#66983—21no—
44#66983—21no—
45#66979—21no—
46#66977—21no—
47#66977—21no—
48C2×#4318D412yes—
49C2×#4314—22no—
50#66928—21no—
51#66927D411yescharacteristic
52C4×D44—21no—
53C4×D44—21no—
54#66923—21no—
55#66922D411yescharacteristic
56#66922D411yescharacteristic
57#66922D411yescharacteristic
58C4×Dic22—21no—
59C4×Dic22—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×#103—44no—
63C11×#95—21no—
64C22⋊(C11⋊C8)D412yes—
65#66885—22no—
66#66881—22no—
67#66880—22no—
68#66874—24no—
69#66874—24no—
70#66873—24no—
71#66871—24no—
72C4⋊(C11⋊C8)—21no—
73#66867—21no—
74C4×C11⋊C8—21no—
75C4×C11⋊C8—21no—
76#10202—111nomaximal, Sylow
77C2×Q8×C11—22no—
78C2×Q8×C11—42no—
79C2×Q8×C11—42no—
80C2×Q8×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C2×C22⋊D11—41no—
87#4339—42no—
88#4339—42no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×C4×D11—41no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C2×C8×C11—22no—
97C2×C8×C11—42no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C42×C11—42no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C22⋊Dic11—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120C4×Dic11—41no—
121#4318—22no—
122#4318—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125#4314—82no—
126#3246—111no—
127#3230—111no—
128#3141—111no—
129#1986—111no—
130#1981D1111yescharacteristic, complemented
131#1502—111no—
132#1283—111no—
133C23×C11#12711yescharacteristic
134C22×D11—41no—
135Q8×C11—44no—
136Q8×C11—81no—
137Q8×C11—81no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—81no—
144C2×C4×C11—82no—
145C2×C4×C11—81no—
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#13512yes—
153C2×C4×C11#13712yes—
154C22⋊D11—81no—
155C22⋊D11—81no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159D44—42no—
160D44—41no—
161D44—41no—
162D44—81no—
163C4×D11—82no—
164Dic22—42no—
165Dic22—42no—
166Dic22—41no—
167Dic22—41no—
168C8×C11—42no—
169C11⋊C8—42no—
170C11⋊C8—42no—
171#533—111no—
172#532—111no—
173C2×C4⋊Q8C2×D1111yescharacteristic
174#500—221no—
175#489—222no—
176#487—221no—
177#487—221no—
178#486—221no—
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⋊C8C2×D1111yescharacteristic
188#417—222no—
189C2×#103—22no—
190C4×M16—111no—
191C4×C4⋊C4C2×D1111yescharacteristic
192#339—222no—
193#327—222no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11#39211yescharacteristic
197C22×C11#49511yescharacteristic
198C22×C11#49711yescharacteristic
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—82no—
206C4×C11—82no—
207C4×C11#45212yes—
208C4×C11#45311yescharacteristic
209C4×C11#45411yescharacteristic
210C4×C11#46412yes—
211Dic11—81no—
212Dic11—81no—
213Dic11—81no—
214C2×#41—221no—
215C22×Q8—21no—
216C2×SD16—222no—
217C2×M16—112no—
218C22×C8C22⋊D1112yes—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—111no—
223C4⋊Q8—111no—
224C4⋊Q8—111no—
225C4⋊Q8D4412yes—
226#127—111no—
227#125—221no—
228#124—221no—
229C22⋊Q8—221no—
230C22⋊Q8—221no—
231#121—221no—
232#121—221no—
233C4×Q8—221no—
234C4×Q8—221no—
235C4×D4—221no—
236C4×D4—221no—
237#117—221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C42—21no—
242C2×C42C22×D1111yescharacteristic
243#107—224no—
244#106—222no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—221no—
248#103—44no—
249#103—224no—
250#103—224no—
251#103—222no—
252#102—224no—
253#102—222no—
254C22⋊C8—112no—
255#97—221no—
256C4×C8—221no—
257C4×C8—221no—
258#95—21no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11#200611yescharacteristic
262C2×C11#200911yescharacteristic
263C2×C11#201511yescharacteristic
264D11—161no—
265#41—442no—
266#41—442no—
267C2×Q8—22no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×Q8—41no—
271C2×Q8—221no—
272C2×Q8—221no—
273C2×Q8—221no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—441no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—441no—
281C22×C4D4×D1111yescharacteristic
282C22×C4D4×D1111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284SD16—882no—
285M16—222no—
286M16—222no—
287C2×C8—22no—
288C2×C8—42no—
289C2×C8—222no—
290C2×C8—222no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C42—42no—
309C42—441no—
310C42C2×D4411yescharacteristic
311C42#433911yescharacteristic
312C42D4×D1111yescharacteristic
313C42D4×D1111yescharacteristic
314C11#1020211yescharacteristic, complemented, Sylow
315C23—441no—
316C23#6699311yescharacteristic
317Q8—44no—
318Q8—81no—
319Q8—81no—
320Q8—442no—
321Q8—441no—
322Q8—442no—
323Q8—441no—
324D4—441no—
325D4—442no—
326D4—441no—
327D4—881no—
328D4—881no—
329D4—881no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—882no—
342C2×C4#6693511yescharacteristic
343C2×C4#6693511yescharacteristic
344C2×C4#6693711yescharacteristic
345C2×C4#6693711yescharacteristic
346C2×C4#6696912yes—
347C2×C4#6697112yes—
348C2×C4#6698311yescharacteristic
349C2×C4#6699011yescharacteristic
350C8—42no—
351C8—442no—
352C8—442no—
353C22—21no—
354C22—21no—
355C22—881no—
356C22—881no—
357C22—881no—
358C22#1062257311yescharacteristic
359C22#1062278111yescharacteristic
360C22#1062280311yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—82no—
365C4—82no—
366C4—881no—
367C4—881no—
368C4—881no—
369C4#1062241112yes—
370C4#1062242312yes—
371C4#1062267511yescharacteristic
372C4#1062269011yescharacteristic
373C2—21no—
374C2—21no—
375C2—1761no—
376C2#1306965711yescharacteristic
377C2#1306967811yescharacteristic
378C2#1306971111yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1981C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1981D11
hypocenterC11#10202
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
2. #13079767C2semidirect
4. #13069559C2semidirect
6. #13066466C2semidirect
7. C11×#1981C2semidirect
130. #1981D11semidirect
314. C11#10202semidirect

Maximal subgroups

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

subgroupindex
#130799332
#130797672
#130790122
#130695592
#130671102
#130664662
C11×#19812
#1020211