Finite Group Databasebeta

← #14654580

Subgroups — #14654580

Order 2816.

534 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079806C211yesmaximal, characteristic
2#13078738C211yesmaximal, characteristic
3#13069534C211yesmaximal, characteristic
4#13067218C211yesmaximal, characteristic, complemented
5#13067063C211yesmaximal, characteristic, complemented
6#13066472C211yesmaximal, characteristic, complemented
7C11×#2584C211yesmaximal, characteristic, complemented
8C2×C11×#125C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#398—21no—
12C11×#395—21no—
13C11×#389—21no—
14C11×#389—21no—
15C11×#389—22no—
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622840—21no—
18#10622680—21no—
19#10622679—22no—
20#10622678—21no—
21#10622640—21no—
22#10622639—22no—
23#10622634—21no—
24#10622581—21no—
25#10622580—21no—
26#10622580—21no—
27C2×#66869—22no—
28#10622539C2211yescharacteristic
29#10622539C2211yescharacteristic
30C4×#4318C2211yescharacteristic
31#10622181—22no—
32Q8⋊(C11⋊C8)—22no—
33C22×Q8×C11D411yescharacteristic
34C2×#4339—21no—
35C11×#125—21no—
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11D412yes—
54C2×C42×C11C2311yescharacteristic
55C2×#4325—22no—
56#66983—21no—
57#66983—21no—
58C2×#4318—21no—
59#66928—21no—
60#66927D411yescharacteristic
61C4×D44—21no—
62C4×D44—21no—
63#66922D411yescharacteristic
64C11×#95—22no—
65C11×#95—22no—
66C11×#95—21no—
67#66899—22no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66873—22no—
71#66873—22no—
72#66873—22no—
73#66872—22no—
74#66871—22no—
75#66871—22no—
76#66869—44no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)D412yes—
79#66867—21no—
80#66867—21no—
81#66867D412yes—
82C4×C11⋊C8—21no—
83#10007—111nomaximal, Sylow
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—42no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C2×C22⋊D11—41no—
96#4339—42no—
97#4339—42no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×C4×D11—41no—
102C2×Dic22—21no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—44no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—82no—
118C42×C11—42no—
119C42×C11—41no—
120C42×C11—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125#4325—44no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130#4318—22no—
131#4318—41no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—41no—
135#3234—111no—
136#3112—111no—
137#2584D1111yescharacteristic, complemented
138#1980—111no—
139#1528—111no—
140#1491—111no—
141#1285—111no—
142C23×C11#12011yescharacteristic
143C22×D11—41no—
144Q8×C11—22no—
145Q8×C11—22no—
146Q8×C11—41no—
147Q8×C11—41no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12711yescharacteristic
172C22⋊D11—81no—
173C22⋊D11—81no—
174C2×Dic11—41no—
175D44—42no—
176D44—42no—
177D44—42no—
178C4×D11—82no—
179Dic22—42no—
180C11⋊C8—42no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183#532—111no—
184C2×#125C2×D1111yescharacteristic
185C2×C4×Q8C2×D1111yescharacteristic
186#501—221no—
187#490—221no—
188#481—221no—
189#480—221no—
190#480—221no—
191#478—222no—
192#477—221no—
193#460—221no—
194#448—221no—
195#440—222no—
196#432—111no—
197#432—111no—
198C2×#104—222no—
199C4×M16—111no—
200#398—21no—
201#395—21no—
202#389—21no—
203#389—21no—
204#389—22no—
205C4×C4⋊C4C2×D1111yescharacteristic
206#330—222no—
207Q8⋊C8—222no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11#39211yescharacteristic
211C22×C11#45311yescharacteristic
212C22×C11#45411yescharacteristic
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—81no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—44no—
222C4×C11—42no—
223C4×C11—81no—
224C4×C11—81no—
225C4×C11—81no—
226C4×C11#45612yes—
227Dic11—81no—
228C2×#41—221no—
229C22×Q8C22⋊D1111yescharacteristic
230C2×SD16—222no—
231C2×M16—221no—
232C4⋊Q8—111no—
233#127—111no—
234#125—21no—
235#125—21no—
236#125—21no—
237#125—21no—
238#124—221no—
239#121—221no—
240#121—221no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×D4—221no—
246C4×D4—221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4C22⋊D1111yescharacteristic
254C2×C4⋊C4C22⋊D1111yescharacteristic
255C2×C4⋊C4C22⋊D1111yescharacteristic
256C2×C42—21no—
257C2×C42C22⋊D1112yes—
258C2×C42C22×D1111yescharacteristic
259#107—222no—
260#107—222no—
261#106—222no—
262C4⋊C8—112no—
263C4⋊C8—221no—
264#104—444no—
265#103—222no—
266#102—222no—
267#102—222no—
268#102—222no—
269C22⋊C8—221no—
270C22⋊C8—221no—
271#97—112no—
272#97—221no—
273#97—221no—
274C4×C8—221no—
275#95—22no—
276#95—22no—
277#95—21no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11#200511yescharacteristic
281C2×C11#200611yescharacteristic
282C2×C11#201011yescharacteristic
283D11—161no—
284#41—442no—
285#41—442no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—42no—
289C2×Q8—221no—
290C2×D4—221no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—441no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—441no—
300C22×C4C2×C22⋊D1111yescharacteristic
301C22×C4C2×C22⋊D1111yescharacteristic
302C22×C4C2×C22⋊D1111yescharacteristic
303SD16—444no—
304M16—222no—
305M16—441no—
306C2×C8—222no—
307C2×C8—222no—
308C2×C8—441no—
309C4⋊C4—24no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—44no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—82no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C22⋊C4—441no—
327C22⋊C4—441no—
328C42—42no—
329C42—41no—
330C42—41no—
331C42D4×D1111yescharacteristic
332C42D4×D1111yescharacteristic
333C42D4×D1111yescharacteristic
334C42#434111yescharacteristic
335C11#1000711yescharacteristic, complemented, Sylow
336C23—441no—
337C23#6700611yescharacteristic
338Q8—22no—
339Q8—22no—
340Q8—41no—
341Q8—41no—
342Q8—442no—
343D4—442no—
344D4—442no—
345D4—442no—
346D4—881no—
347D4—881no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—24no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—441no—
367C2×C4—882no—
368C2×C4#6699011yescharacteristic
369C2×C4#6699011yescharacteristic
370C2×C4#6699111yescharacteristic
371C2×C4#6699211yescharacteristic
372C2×C4#6699211yescharacteristic
373C2×C4#6699311yescharacteristic
374C8—442no—
375C8—442no—
376C8—442no—
377C22—21no—
378C22—21no—
379C22—881no—
380C22—881no—
381C22—881no—
382C22#1062283611yescharacteristic
383C22#1062285411yescharacteristic
384C22#1062285811yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—44no—
391C4—42no—
392C4—81no—
393C4—81no—
394C4—81no—
395C4—881no—
396C4#1062270812yes—
397C2—21no—
398C2—21no—
399C2—1761no—
400C2#1306965211yescharacteristic
401C2#1306965811yescharacteristic
402C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2584C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#2584D11
hypocenterC11#10007
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2584

Complements

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

NH ≅ G/Ntype
4. #13067218C2semidirect
5. #13067063C2semidirect
6. #13066472C2semidirect
7. C11×#2584C2semidirect
137. #2584D11semidirect
335. C11#10007semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130787382
#130695342
#130672182
#130670632
#130664722
C11×#25842
#1000711