Finite Group Databasebeta

← #14654744

Subgroups — #14654744

Order 2816.

550 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 97 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#13078961C211yesmaximal, characteristic, complemented
2#13078624C211yesmaximal, characteristic, complemented
3#13069415C211yesmaximal, characteristic, complemented
4#13067020C211yesmaximal, characteristic, complemented
5#13067015C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#3100C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#480—21no—
12C11×#474—21no—
13C11×#459—21no—
14C11×#447—21no—
15C4×C11×D8—22no—
16C11×#431C2211yescharacteristic
17#10622846—22no—
18#10622831—21no—
19C2×C22⋊(C11⋊C8)—22no—
20#10622695—21no—
21#10622684—21no—
22#10622668—21no—
23#10622668—21no—
24#10622632—21no—
25C4×#4324—22no—
26#10622621—21no—
27#10622584—21no—
28#10622538C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30C2×#66867C2211yescharacteristic
31D4⋊(C11⋊C8)—22no—
32#10622094—22no—
33C2×C11×#41—21no—
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C2×C11×D8—22no—
37C11×C4⋊Q8D411yescharacteristic
38C11×#127D411yescharacteristic
39C11×#124—21no—
40C11×#121—21no—
41C11×#121—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4324—22no—
52#66979—21no—
53#66977—21no—
54#66977—21no—
55C22×C11⋊C8—21no—
56C22×C11⋊C8D412yes—
57#66923—21no—
58#66922D411yescharacteristic
59#66922D411yescharacteristic
60C4×Dic22—21no—
61C4×Dic22—21no—
62C11×#107—22no—
63C11×C4⋊C8—21no—
64C11×#102—22no—
65C11×#102—22no—
66C11×C22⋊C8—21no—
67C4×C8×C11D412yes—
68#66899—22no—
69#66899—22no—
70#66896—22no—
71#66896—22no—
72#66896—22no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—44no—
75#66874—22no—
76#66872—22no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80#66867—21no—
81#66867—21no—
82C4×C11⋊C8D412yes—
83#10033—111nomaximal, Sylow
84C24×C11—21no—
85C11×#41—42no—
86C11×#41—42no—
87C2×Q8×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—42no—
94C2×D4×C11—41no—
95C22×C4×C11—21no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C2×Dic22—21no—
105C2×Dic22—21no—
106C11×D8—44no—
107C2×C8×C11—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C22⋊Dic11—41no—
121#4324—44no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128C4×Dic11—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—42no—
135#3135—111no—
136#3101—111no—
137#3100D1111yescharacteristic
138#1955—111no—
139#1481—111no—
140#1480—111no—
141#1275—111no—
142C23×C11—22no—
143C23×C11—41no—
144C23×C11—42no—
145C23×C11—41no—
146C23×C11—42no—
147C23×C11—41no—
148C23×C11#12111yescharacteristic
149Q8×C11—42no—
150D4×C11—22no—
151D4×C11—22no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—42no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—82no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12711yescharacteristic
174C2×C4×C11#13512yes—
175C2×C4×C11AGL(1,ℤ/8)12yes—
176C2×Dic11—41no—
177C2×Dic11—41no—
178Dic22—42no—
179Dic22—42no—
180C8×C11—42no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183C11⋊C8—81no—
184#533—111no—
185#532C2×D1111yescharacteristic
186C2×C4×D4C2×D1111yescharacteristic
187#491—221no—
188#490—221no—
189#489—221no—
190#489—221no—
191#483—221no—
192#480—21no—
193#476—221no—
194#474—21no—
195#461—221no—
196#459—21no—
197#450—221no—
198#447—21no—
199C4×SD16—222no—
200C4×D8—22no—
201#431—111no—
202#431C2×D1111yescharacteristic
203C2×C4⋊C8—111no—
204#416—222no—
205C2×C22⋊C8—222no—
206C2×#97—111no—
207Q8⋊C8—222no—
208D4⋊C8—222no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—44no—
212C22×C11—42no—
213C22×C11—82no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11#39211yescharacteristic
220C22×C11#46312yes—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11—81no—
227C4×C11#44912yes—
228C4×C11#49511yescharacteristic
229C4×C11#49611yescharacteristic
230Dic11—81no—
231Dic11—81no—
232C2×#41—21no—
233C22×D4C22⋊D1111yescharacteristic
234C23×C4—21no—
235C2×SD16—222no—
236C2×D8—22no—
237C22×C8—112no—
238C22×C8—221no—
239C4⋊Q8—111no—
240C4⋊Q8—111no—
241C4⋊Q8C22⋊D1111yescharacteristic
242#127C22⋊D1111yescharacteristic
243#125—221no—
244#124—21no—
245C22⋊Q8—221no—
246C22⋊Q8—221no—
247#121—21no—
248#121—21no—
249C4×Q8—221no—
250C4×Q8—221no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257#117—221no—
258C2×C4⋊C4C22⋊D1111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C22×D1111yescharacteristic
261#107—22no—
262#106—222no—
263C4⋊C8—21no—
264C4⋊C8—221no—
265C4⋊C8—221no—
266C4⋊C8—221no—
267#103—222no—
268#103—222no—
269#103—222no—
270#102—22no—
271#102—22no—
272#102—222no—
273#102—222no—
274#102—222no—
275C22⋊C8—21no—
276C22⋊C8—221no—
277C22⋊C8—444no—
278#97—221no—
279#97—221no—
280C4×C8—112no—
281C4×C8C22⋊D1112yes—
282C2×C11—22no—
283C2×C11—82no—
284C2×C11—161no—
285C2×C11#201011yescharacteristic
286C2×C11#201211yescharacteristic
287C2×C11#201711yescharacteristic
288C24—21no—
289#41—42no—
290#41—42no—
291C2×Q8—21no—
292C2×Q8—221no—
293C2×Q8—221no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—42no—
300C2×D4—41no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4D4×D1111yescharacteristic
308C22×C4#434111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310SD16—444no—
311D8—44no—
312C2×C8—22no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8—222no—
317C2×C8—442no—
318C2×C8—441no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—221no—
327C4⋊C4—441no—
328C4⋊C4—441no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—441no—
334C42—441no—
335C42D4×D1111yescharacteristic
336C42D4×D1111yescharacteristic
337C42C2×C22⋊D1111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C11#1003311yescharacteristic, complemented, Sylow
340C23—22no—
341C23—41no—
342C23—42no—
343C23—42no—
344C23—41no—
345C23—41no—
346C23#6699211yescharacteristic
347Q8—42no—
348Q8—442no—
349Q8—442no—
350D4—22no—
351D4—22no—
352D4—41no—
353D4—41no—
354D4—42no—
355D4—42no—
356D4—42no—
357D4—82no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—82no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4#6696412yes—
371C2×C4#6696512yes—
372C2×C4#6699011yescharacteristic
373C2×C4#6699011yescharacteristic
374C2×C4#6699111yescharacteristic
375C2×C4#6699211yescharacteristic
376C2×C4#6699311yescharacteristic
377C2×C4#6700611yescharacteristic
378C8—42no—
379C8—442no—
380C8—442no—
381C8—881no—
382C22—21no—
383C22—21no—
384C22—44no—
385C22—42no—
386C22—82no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22#1062276612yes—
393C22#1062283611yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—81no—
399C4—81no—
400C4—881no—
401C4—881no—
402C4#1062276711yescharacteristic
403C4#1062276811yescharacteristic
404C4#1062277112yes—
405C2—22no—
406C2—82no—
407C2—161no—
408C2#1306968111yescharacteristic
409C2#1306969111yescharacteristic
410C2#1306971911yescharacteristic
subgroupG/H
centerC2×C4#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3100C2
socleC22×C11#392
hypercenter#3100D11
hypocenterC11#10033
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #13078961C2semidirect
2. #13078624C2semidirect
3. #13069415C2semidirect
4. #13067020C2semidirect
5. #13067015C2semidirect
6. #13066446C2semidirect
339. C11#10033semidirect

Maximal subgroups

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

subgroupindex
#130789612
#130786242
#130694152
#130670202
#130670152
#130664462
C11×#31002
#1003311