Finite Group Databasebeta

← #14726559

Subgroups — #14726559

Order 2816.

1106 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1106 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#13078711C212yesmaximal, complemented
2#13071895C211yesmaximal, characteristic
3#13067641C214yesmaximal, complemented
4#13067539C214yesmaximal, complemented
5#13067128C212yesmaximal, complemented
6#13066957C211yesmaximal, characteristic, complemented
7C11×#3501C211yesmaximal, characteristic, complemented
8C11×#554—22no—
9C11×#554—24no—
10D4×Q8×C11—22no—
11C11×#544—21no—
12C11×#543C2214yes—
13C11×#533C2212yes—
14C2×C11×C22⋊Q8—22no—
15C11×#518—21no—
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×C22⋊D11—22no—
18C2×C4×D44C2211yescharacteristic
19#10622836—21no—
20#10622700—22no—
21#10622696—22no—
22#10622659C2214yes—
23#10622657C2214yes—
24#10622639—24no—
25#10622605—21no—
26#10622573C2212yes—
27#10622562C2212yes—
28#10622545C2211yescharacteristic
29#10622539C2212yes—
30#10622176C2218yes—
31#10622163C2214yes—
32C22×Q8×C11—22no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11D412yes—
35C22×C22⋊D11—22no—
36C22×D44C2311yescharacteristic
37C22×C4×D11—21no—
38C11×C4⋊Q8—24no—
39C11×C4⋊Q8D412yescomplemented
40C11×C4⋊Q8D412yescomplemented
41C11×#125—24no—
42C11×#125—22no—
43C11×C22⋊Q8—24no—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8—28no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—28no—
49C11×C22⋊Q8C2314yes—
50C4×Q8×C11—22no—
51C4×Q8×C11D414yescomplemented
52C4×D4×C11—24no—
53C4×D4×C11—24no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C11×#117—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4C2312yes—
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64C2×#4325—24no—
65C4×C22⋊D11—48no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—22no—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11—21no—
71C4×D44—22no—
72C4×D44—22no—
73#66899—24no—
74C11⋊#95—21no—
75C11⋊#95C2312yes—
76C22⋊(C11⋊C8)C2314yes—
77#66873—24no—
78#66871—24no—
79C4⋊(C11⋊C8)—22no—
80#66867—22no—
81#18180—111nomaximal, Sylow
82C24×C11C2×D412yes—
83C23×D11—21no—
84C2×Q8×C11—24no—
85C2×Q8×C11—22no—
86C2×Q8×C11—84no—
87C2×Q8×C11C2×D414yes—
88C2×D4×C11—24no—
89C2×D4×C11—22no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—44no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2411yescharacteristic
99C2×C22⋊D11—44no—
100C2×C22⋊D11—44no—
101C2×C22⋊D11—44no—
102C22×Dic11—22no—
103C22×Dic11—21no—
104C2×D44—22no—
105C2×D44—42no—
106C2×C4×D11—44no—
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—28no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4C2×D414yes—
118C11×C22⋊C4—28no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C42×C11—24no—
122C42×C11C2×D412yes—
123C42×C11C2×D412yes—
124C22⋊Dic11—44no—
125#4325—48no—
126(C2×D11)⋊C4—44no—
127(C2×D11)⋊C4—42no—
128C4⋊Dic11—22no—
129Dic11⋊C4—44no—
130C4×Dic11—24no—
131C2×C11⋊C8—24no—
132#3501D1111yescharacteristic, complemented
133#3110—112no—
134#2397—111no—
135#1614—114no—
136#1596—114no—
137#1506—112no—
138#1466—111no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11#13714yes—
144C23×C11C22×D411yescharacteristic
145C22×D11—22no—
146C22×D11—42no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—42no—
150Q8×C11—44no—
151Q8×C11—44no—
152Q8×C11—84no—
153D4×C11—28no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11—24no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—44no—
161C2×C4×C11—42no—
162C2×C4×C11—82no—
163C2×C4×C11—84no—
164C2×C4×C11—84no—
165C2×C4×C11#12012yes—
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11C22×D412yes—
169C22⋊D11—416no—
170C2×Dic11—24no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175D44—24no—
176D44—42no—
177C4×D11—82no—
178C4×D11—82no—
179C11⋊C8—44no—
180#554—22no—
181#554—24no—
182D4×Q8—22no—
183#544—21no—
184#543C2×D1114yes—
185#533C2×D1112yes—
186C2×C22⋊Q8—22no—
187#518—21no—
188C2×C4×D4—111no—
189C2×C4×D4—222no—
190C2×C4×D4C2×D1111yescharacteristic
191#484—114no—
192#474—222no—
193#461—222no—
194#450—114no—
195#440—224no—
196#432—112no—
197#399—112no—
198#399—221no—
199#392—112no—
200#392—221no—
201#376—111no—
202#328—118no—
203#323—114no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—24no—
207C22×C11—44no—
208C22×C11—42no—
209C22×C11—42no—
210C22×C11—82no—
211C22×C11C2×#12011yescharacteristic
212C22×C11C2×#13712yes—
213C2×D11—44no—
214C2×D11—42no—
215C2×D11—82no—
216C2×D11—81no—
217C2×D11—81no—
218C4×C11—22no—
219C4×C11—21no—
220C4×C11—22no—
221C4×C11—42no—
222C4×C11—44no—
223C4×C11—44no—
224C4×C11#45312yes—
225Dic11—44no—
226Dic11—81no—
227C22×Q8—22no—
228C22×D4—111no—
229C22×D4—222no—
230C22×D4C22⋊D1111yescharacteristic
231C23×C4—221no—
232C23×C4C22⋊D1112yes—
233C2×SD16—224no—
234C4⋊Q8—24no—
235C4⋊Q8C22⋊D1112yescomplemented
236C4⋊Q8C22⋊D1112yescomplemented
237#125—24no—
238#125—22no—
239C22⋊Q8—24no—
240C22⋊Q8—24no—
241C22⋊Q8—28no—
242C22⋊Q8—22no—
243C22⋊Q8—24no—
244C22⋊Q8—28no—
245C22⋊Q8C22×D1114yes—
246C4×Q8—22no—
247C4×Q8C22⋊D1114yescomplemented
248C4×D4—24no—
249C4×D4—24no—
250C4×D4—22no—
251C4×D4—22no—
252C4×D4—222no—
253C4×D4—222no—
254C4×D4—448no—
255#117—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—222no—
260C2×C4⋊C4C22⋊D1111yescharacteristic
261C2×C22⋊C4—24no—
262C2×C22⋊C4—222no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—222no—
265C2×C22⋊C4C22×D1112yes—
266C2×C42—221no—
267C2×C42C22×D1111yescharacteristic
268#107—224no—
269C4⋊C8—222no—
270#103—224no—
271#102—224no—
272C22⋊C8—114no—
273#97—222no—
274#95—112no—
275#95—221no—
276C2×C11—22no—
277C2×C11—44no—
278C2×C11#300411yescharacteristic
279C2×C11C2×#45311yescharacteristic
280C2×C11#302511yescharacteristic
281D11—82no—
282C24—221no—
283C24C2×C22⋊D1112yes—
284C2×Q8—24no—
285C2×Q8—22no—
286C2×Q8—84no—
287C2×Q8C2×C22⋊D1114yes—
288C2×D4—24no—
289C2×D4—22no—
290C2×D4—222no—
291C2×D4—442no—
292C2×D4—444no—
293C2×D4—444no—
294C2×D4—444no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—44no—
300C22×C4—222no—
301C22×C4—221no—
302C22×C4—444no—
303C22×C4—441no—
304C22×C4—441no—
305C22×C4C2×C22⋊D1111yescharacteristic
306C22×C4C2×C22⋊D1111yescharacteristic
307C22×C4C2×C22⋊D1112yes—
308C22×C4C23×D1111yescharacteristic
309SD16—448no—
310C2×C8—224no—
311C4⋊C4—24no—
312C4⋊C4—28no—
313C4⋊C4—22no—
314C4⋊C4—24no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—24no—
319C4⋊C4—222no—
320C4⋊C4—444no—
321C4⋊C4C2×C22⋊D1114yes—
322C22⋊C4—28no—
323C22⋊C4—24no—
324C22⋊C4—24no—
325C22⋊C4—444no—
326C22⋊C4—444no—
327C22⋊C4—442no—
328C42—24no—
329C42—224no—
330C42C2×C22⋊D1112yes—
331C42C2×C22⋊D1112yes—
332C11#1818011yescharacteristic, complemented, Sylow
333C23—22no—
334C23—22no—
335C23—42no—
336C23—42no—
337C23—222no—
338C23—442no—
339C23—441no—
340C23—442no—
341C23—441no—
342C23#6699514yes—
343C23C22×C22⋊D1111yescharacteristic
344Q8—44no—
345Q8—44no—
346Q8—84no—
347D4—28no—
348D4—224no—
349D4—442no—
350D4—4416no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—44no—
358C2×C4—42no—
359C2×C4—82no—
360C2×C4—84no—
361C2×C4—84no—
362C2×C4—224no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—441no—
367C2×C4—882no—
368C2×C4—882no—
369C2×C4#6700612yes—
370C2×C4#6700611yescharacteristic
371C2×C4#6700611yescharacteristic
372C2×C4C22×C22⋊D1112yes—
373C8—444no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—44no—
378C22—42no—
379C22—42no—
380C22—82no—
381C22—444no—
382C22—442no—
383C22—882no—
384C22—881no—
385C22—881no—
386C22C2×#6699512yes—
387C22C2×#6700611yescharacteristic
388C4—22no—
389C4—21no—
390C4—22no—
391C4—42no—
392C4—44no—
393C4—44no—
394C4—444no—
395C4—881no—
396C4#1062285412yes—
397C2—22no—
398C2—44no—
399C2—882no—
400C2#1307785011yescharacteristic
401C2C2×#1062285411yescharacteristic
402C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radical#13071895C2
hypercenter#3501D11
hypocenterC11#18180
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13078711C2semidirect
3. #13067641C2semidirect
4. #13067539C2semidirect
5. #13067128C2semidirect
6. #13066957C2semidirect
7. C11×#3501C2semidirect
39. C11×C4⋊Q8D4semidirect
40. C11×C4⋊Q8D4semidirect
51. C4×Q8×C11D4semidirect
132. #3501D11semidirect
235. C4⋊Q8C22⋊D11semidirect
236. C4⋊Q8C22⋊D11semidirect
247. C4×Q8C22⋊D11semidirect
332. C11#18180semidirect

Maximal subgroups

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

subgroupindex
#130787112
#130718952
#130676412
#130675392
#130671282
#130669572
C11×#35012
#1818011