Finite Group Databasebeta

← #14726613

Subgroups — #14726613

Order 2816.

1198 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 183 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#13078703C212yesmaximal, complemented
2#13071899C211yesmaximal, characteristic, complemented
3#13067653C214yesmaximal, complemented
4#13067551C214yesmaximal, complemented
5#13067124C212yesmaximal, complemented
6#13066960C211yesmaximal, characteristic, complemented
7C11×#3497C211yesmaximal, characteristic, complemented
8C2×C11×2−1+4—21no—
9C11×#550—22no—
10D4×Q8×C11—22no—
11C11×#548—24no—
12C11×#537—21no—
13C11×#537C2214yes—
14C11×#532—22no—
15C11×#532C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18#10622844—21no—
19#10622697—22no—
20#10622685—22no—
21#10622649C2214yes—
22#10622647C2214yes—
23#10622627—24no—
24#10622606—21no—
25#10622604C2212yes—
26#10622599C2212yes—
27C4×(C2×D11)⋊C4—22no—
28#10622545C2211yescharacteristic
29#10622539C2212yes—
30#10622175C2218yes—
31#10622166C2214yes—
32C11×2−1+4—48no—
33C2×C11×#41—24no—
34C2×C11×#41—24no—
35C2×C11×#41—22no—
36C22×Q8×C11—24no—
37C22×Q8×C11D411yescharacteristic
38C22×D44C2311yescharacteristic
39C22×C4×D11—21no—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8D412yes—
42C11×#127—22no—
43C11×#127D412yes—
44C11×#124—24no—
45C11×#124—22no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—28no—
48C11×#121—24no—
49C11×#121—28no—
50C11×#121—22no—
51C11×#121—24no—
52C11×#121C2314yes—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×D4×C11—24no—
56C4×D4×C11—24no—
57C4×D4×C11—22no—
58C4×D4×C11D414yes—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C42×C11D412yes—
62C2×C42×C11C2311yescharacteristic
63C2×#4323—24no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4×Dic11—21no—
69C4×D44—22no—
70C4×D44—22no—
71#66896—24no—
72C11⋊#95—21no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95C2312yes—
76C22⋊(C11⋊C8)C2314yes—
77#66873—24no—
78#66872—24no—
79C4⋊(C11⋊C8)—22no—
80#66867—22no—
81#18186—111nomaximal, Sylow
82C23×D11—21no—
83C11×#41—48no—
84C11×#41—48no—
85C11×#41—416no—
86C11×#41—48no—
87C2×Q8×C11—24no—
88C2×Q8×C11—22no—
89C2×Q8×C11—22no—
90C2×Q8×C11—24no—
91C2×Q8×C11—416no—
92C2×D4×C11—24no—
93C2×D4×C11—24no—
94C2×D4×C11—24no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11C2×D414yes—
98C22×C4×C11—28no—
99C22×C4×C11—24no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—22no—
107C2×D44—22no—
108C2×D44—42no—
109C2×C4×D11—44no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4C2×D414yes—
117C11×C22⋊C4—28no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—24no—
120C42×C11—22no—
121C42×C11—22no—
122C42×C11C2×D412yes—
123C42×C11C2×D412yes—
124#4323—48no—
125(C2×D11)⋊C4—44no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—44no—
128C4⋊Dic11—22no—
129C4×Dic11—42no—
130C2×C11⋊C8—24no—
131#3497D1111yescharacteristic, complemented
132#3109—112no—
133#2398—111no—
134#1616—114no—
135#1598—114no—
136#1505—112no—
137#1467—111no—
138C23×C11—24no—
139C23×C11C22×D411yescharacteristic
140C22×D11—22no—
141C22×D11—42no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—42no—
145Q8×C11—28no—
146Q8×C11—44no—
147Q8×C11—48no—
148D4×C11—44no—
149D4×C11—44no—
150D4×C11—48no—
151D4×C11—48no—
152D4×C11—44no—
153D4×C11—84no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—41no—
161C2×C4×C11—48no—
162C2×C4×C11—416no—
163C2×C4×C11—42no—
164C2×C4×C11#12012yes—
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)14yes—
168C2×C4×C11C22×D412yes—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—41no—
173C2×Dic11—42no—
174D44—24no—
175D44—42no—
176C4×D11—82no—
177C4×D11—82no—
178C11⋊C8—44no—
179C2×2−1+4—21no—
180#550—22no—
181D4×Q8—22no—
182#548—24no—
183#537—21no—
184#537C2×D1114yes—
185#532—22no—
186#532C2×D1112yes—
187C2×C4×Q8C2×D1111yescharacteristic
188C2×C4×D4—111no—
189#481—114no—
190#476—222no—
191#459—222no—
192#447—114no—
193#442—224no—
194#432—112no—
195#400—112no—
196#397—221no—
197#394—112no—
198#393—221no—
199C4×C22⋊C4—222no—
200#376—111no—
201#327—118no—
202#324—114no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—44no—
206C22×C11—44no—
207C22×C11—44no—
208C22×C11C2×#12011yescharacteristic
209C22×C11C2×AGL(1,ℤ/8)12yes—
210C2×D11—44no—
211C2×D11—42no—
212C2×D11—82no—
213C2×D11—81no—
214C2×D11—81no—
215C4×C11—22no—
216C4×C11—24no—
217C4×C11—21no—
218C4×C11—22no—
219C4×C11—44no—
220C4×C11—42no—
221C4×C11#45412yes—
222Dic11—82no—
223Dic11—81no—
2242−1+4—48no—
225C2×#41—24no—
226C2×#41—24no—
227C2×#41—22no—
228C22×Q8—24no—
229C22×Q8C22⋊D1111yescharacteristic
230C22×D4—111no—
231C23×C4—221no—
232C2×D8—224no—
233C4⋊Q8—22no—
234C4⋊Q8C22⋊D1112yes—
235#127—22no—
236#127C22⋊D1112yes—
237#124—24no—
238#124—22no—
239C22⋊Q8—24no—
240C22⋊Q8—28no—
241#121—24no—
242#121—28no—
243#121—22no—
244#121—24no—
245#121C22×D1114yes—
246C4×Q8—22no—
247C4×Q8—22no—
248C4×D4—24no—
249C4×D4—24no—
250C4×D4—22no—
251C4×D4—222no—
252C4×D4—222no—
253C4×D4C22⋊D1114yes—
254C2×C4⋊C4—111no—
255C2×C4⋊C4C22⋊D1111yescharacteristic
256C2×C4⋊C4C22×D1112yes—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—222no—
259C2×C22⋊C4—222no—
260C2×C42—221no—
261C2×C42C22⋊D1112yes—
262C2×C42C22×D1111yescharacteristic
263#106—224no—
264C4⋊C8—222no—
265#102—224no—
266#102—224no—
267C22⋊C8—114no—
268#97—222no—
269#95—112no—
270#95—221no—
271#95—222no—
272#95—222no—
273C2×C11—22no—
274C2×C11—84no—
275C2×C11#300311yescharacteristic
276C2×C11C2×#45411yescharacteristic
277C2×C11#302511yescharacteristic
278D11—82no—
279C24—221no—
280#41—48no—
281#41—48no—
282#41—416no—
283#41—48no—
284C2×Q8—24no—
285C2×Q8—24no—
286C2×Q8—22no—
287C2×Q8—22no—
288C2×Q8—416no—
289C2×D4—24no—
290C2×D4—24no—
291C2×D4—24no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—222no—
295C2×D4—442no—
296C2×D4C2×C22⋊D1114yes—
297C22×C4—28no—
298C22×C4—24no—
299C22×C4—222no—
300C22×C4—221no—
301C22×C4—444no—
302C22×C4—441no—
303C22×C4—441no—
304C22×C4C2×C22⋊D1112yes—
305C22×C4C2×C22⋊D1111yescharacteristic
306C22×C4C2×C22⋊D1111yescharacteristic
307C22×C4C2×C22⋊D1112yes—
308C22×C4C23×D1111yescharacteristic
309D8—448no—
310C2×C8—224no—
311C4⋊C4—24no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—24no—
315C4⋊C4—222no—
316C4⋊C4C2×C22⋊D1114yes—
317C22⋊C4—28no—
318C22⋊C4—24no—
319C22⋊C4—24no—
320C22⋊C4—444no—
321C22⋊C4—444no—
322C22⋊C4—442no—
323C42—22no—
324C42—22no—
325C42—442no—
326C42C2×C22⋊D1112yes—
327C42C2×C22⋊D1112yes—
328C11#1818611yescharacteristic, complemented, Sylow
329C23—24no—
330C23—222no—
331C23—442no—
332C23—441no—
333C23—442no—
334C23—441no—
335C23C22×C22⋊D1111yescharacteristic
336Q8—28no—
337Q8—48no—
338Q8—44no—
339D4—44no—
340D4—48no—
341D4—44no—
342D4—48no—
343D4—44no—
344D4—84no—
345D4—224no—
346D4—442no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—41no—
354C2×C4—416no—
355C2×C4—48no—
356C2×C4—42no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—441no—
362C2×C4—882no—
363C2×C4—882no—
364C2×C4#6698514yes—
365C2×C4#6700611yescharacteristic
366C2×C4#6700612yes—
367C2×C4#6700611yescharacteristic
368C2×C4C22×C22⋊D1112yes—
369C8—444no—
370C22—21no—
371C22—21no—
372C22—44no—
373C22—44no—
374C22—44no—
375C22—444no—
376C22—442no—
377C22—882no—
378C22—881no—
379C22—881no—
380C22C2×#6698512yes—
381C22C2×#6700611yescharacteristic
382C4—24no—
383C4—22no—
384C4—21no—
385C4—22no—
386C4—44no—
387C4—42no—
388C4—882no—
389C4—881no—
390C4#1062285812yes—
391C2—22no—
392C2—84no—
393C2—882no—
394C2#1307784311yescharacteristic
395C2C2×#1062285811yescharacteristic
396C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3497C2
socleC22×C11C2×#120
hypercenter#3497D11
hypocenterC11#18186
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. #13078703C2semidirect
2. #13071899C2semidirect
3. #13067653C2semidirect
4. #13067551C2semidirect
5. #13067124C2semidirect
6. #13066960C2semidirect
7. C11×#3497C2semidirect
131. #3497D11semidirect
328. C11#18186semidirect

Maximal subgroups

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

subgroupindex
#130787032
#130718992
#130676532
#130675512
#130671242
#130669602
C11×#34972
#1818611