Finite Group Databasebeta

← #14649551

Subgroups — #14649551

Order 2816.

692 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 143 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#13076947C211yesmaximal, characteristic
2C2×#10622549C211yesmaximal, characteristic, complemented
3C2×#10622108C212yesmaximal
4#13066496C212yesmaximal, complemented
5C11×#1817C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×#66982—21no—
9C22×C4⋊Dic11—21no—
10C2×C11×C22⋊C8C2212yes—
11#10622826—21no—
12#10622825C2211yescharacteristic
13C2×C11⋊#95—21no—
14C2×C11⋊#95C2212yes—
15#10622553—22no—
16#10622552C412yescomplemented
17#10622549—24no—
18#10622541C412yescomplemented
19C11×#336—22no—
20#10622108—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×C22⋊D11—21no—
25C23×Dic11—22no—
26C22×D44C2×C411yescharacteristic
27C22×C8×C11—22no—
28C2×C42×C11—22no—
29C2×C42×C11—22no—
30C2×C42×C11C2×C412yes—
31C2×C42×C11D412yes—
32C2×C22⋊Dic11—21no—
33#66983—22no—
34#66983—22no—
35#66982—42no—
36#66982—42no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—22no—
39C2×(C2×D11)⋊C4—21no—
40C2×C4⋊Dic11—24no—
41C2×C4⋊Dic11—42no—
42C2×C4⋊Dic11—42no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×C4⋊Dic11C2×C412yes—
45C2×Dic11⋊C4—22no—
46C11×C22⋊C8—22no—
47C11×C22⋊C8—22no—
48C11⋊#95—24no—
49C11⋊#95—22no—
50C11⋊#95—22no—
51C11⋊#95—21no—
52C11⋊#95D414yes—
53#9156—111nomaximal, Sylow
54C24×C11C2×D411yescharacteristic
55C23×D11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11C22⋊C412yes—
65C22×C4×C11C22⋊C412yes—
66C22×C4×C11D812yes—
67C22×C4×C11SD1612yes—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D412yes—
71C22×C4×C11#4112yes—
72C2×C22⋊D11—41no—
73C2×C22⋊D11—41no—
74C2×C22⋊D11—41no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11—41no—
78C22×Dic11—21no—
79C22×Dic11—22no—
80C22×Dic11—24no—
81C22×Dic11—44no—
82C22×Dic11—44no—
83C22×Dic11—42no—
84C22×Dic11—42no—
85C2×D44—22no—
86C2×D44—42no—
87C2×C8×C11—44no—
88C2×C8×C11—42no—
89C42×C11—24no—
90C42×C11—24no—
91C22⋊Dic11—41no—
92C22⋊Dic11—41no—
93(C2×D11)⋊C4—44no—
94(C2×D11)⋊C4—44no—
95(C2×D11)⋊C4—42no—
96C4⋊Dic11—22no—
97C4⋊Dic11—42no—
98C4⋊Dic11—48no—
99Dic11⋊C4—44no—
100#2854—111no—
101C2×#382—111no—
102#1817D1111yescharacteristic, complemented
103C2×#327—112no—
104#1294—112no—
105C23×C11—22no—
106C23×C11—22no—
107C23×C11C2×C22⋊C411yescharacteristic
108C23×C11#12011yescharacteristic
109C23×C11#12311yescharacteristic
110C23×C11C2×D811yescharacteristic
111C23×C11C2×SD1611yescharacteristic
112C23×C11AGL(1,ℤ/8)11yescharacteristic
113C23×C11#13711yescharacteristic
114C22×D11—41no—
115C22×D11—42no—
116C22×D11—41no—
117C22×D11—41no—
118C22×D11—42no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11#10214yes—
135C2×C4×C11C4×D412yes—
136C2×C4×C11#12112yes—
137C22⋊D11—81no—
138C22⋊D11—81no—
139C22⋊D11—81no—
140C22⋊D11—81no—
141C2×Dic11—44no—
142C2×Dic11—44no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145C2×Dic11—41no—
146C2×Dic11—42no—
147C2×Dic11—41no—
148C2×Dic11—42no—
149C2×Dic11—44no—
150C2×Dic11—84no—
151C2×Dic11—84no—
152D44—82no—
153C8×C11—82no—
154C2×#123—221no—
155C2×#121—111no—
156C22×C4⋊C4—221no—
157C22×C42C2×D1111yescharacteristic
158C2×C22⋊C8C2×D1112yes—
159#390—112no—
160#389—112no—
161#388—222no—
162#386—221no—
163#382—224no—
164#380—111no—
165C2×#95—112no—
166C2×#95—221no—
167#336—22no—
168#327—224no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11#38611yescharacteristic
178C22×C11#41012yes—
179C22×C11C2×#10211yescharacteristic
180C22×C11#41711yescharacteristic
181C22×C11#42112yes—
182C22×C11#44711yescharacteristic
183C22×C11#44811yescharacteristic
184C22×C11#48011yescharacteristic
185C22×C11#48111yescharacteristic
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—82no—
190C2×D11—82no—
191C4×C11—24no—
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—42no—
195Dic11—84no—
196Dic11—81no—
197Dic11—82no—
198C22×D4—111no—
199C22×D4—221no—
200C23×C4—222no—
201C23×C4D4411yescharacteristic
202C23×C4D4411yescharacteristic
203C23×C4C22×D1111yescharacteristic
204C22×C8—22no—
205#123—442no—
206#123—442no—
207#121—222no—
208#121—222no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—112no—
211C2×C4⋊C4—224no—
212C2×C4⋊C4—222no—
213C2×C4⋊C4—442no—
214C2×C4⋊C4—442no—
215C2×C22⋊C4—221no—
216C2×C22⋊C4—222no—
217C2×C22⋊C4—222no—
218C2×C22⋊C4—221no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42C4×D1112yes—
222C2×C42C22⋊D1112yes—
223C22⋊C8—22no—
224C22⋊C8—22no—
225#95—114no—
226#95—224no—
227#95—222no—
228#95—222no—
229#95—221no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11#151212yes—
235C2×C11#151712yes—
236C2×C11#187411yescharacteristic
237C2×C11#189711yescharacteristic
238C2×C11#189911yescharacteristic
239D11—161no—
240C24—221no—
241C24C2×D4411yescharacteristic
242C2×D4—222no—
243C2×D4—442no—
244C2×D4—441no—
245C2×D4—441no—
246C2×D4—441no—
247C2×D4—441no—
248C2×D4—441no—
249C2×D4—441no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—224no—
259C22×C4—222no—
260C22×C4—221no—
261C22×C4—444no—
262C22×C4—444no—
263C22×C4—442no—
264C22×C4—442no—
265C22×C4#431412yes—
266C22×C4D8812yes—
267C22×C4(C2×D11)⋊C412yes—
268C22×C4(C2×D11)⋊C412yes—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4D4×D1112yes—
271C22×C4#434112yes—
272C22×C4C2×C22⋊D1111yescharacteristic
273C2×C8—44no—
274C2×C8—42no—
275C4⋊C4—222no—
276C4⋊C4—442no—
277C4⋊C4—448no—
278C4⋊C4—444no—
279C22⋊C4—444no—
280C22⋊C4—441no—
281C22⋊C4—441no—
282C22⋊C4—444no—
283C22⋊C4—442no—
284C42—24no—
285C42—24no—
286C11#915611yescharacteristic, complemented, Sylow
287C23—22no—
288C23—22no—
289C23—441no—
290C23—441no—
291C23—442no—
292C23—441no—
293C23—442no—
294C23#6693511yescharacteristic
295C23#6693911yescharacteristic
296C23C2×#431411yescharacteristic
297C23C2×D8811yescharacteristic
298C23#6696111yescharacteristic
299C23#6696211yescharacteristic
300C23C2×(C2×D11)⋊C411yescharacteristic
301D4—882no—
302D4—881no—
303D4—881no—
304D4—881no—
305D4—881no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—444no—
322C2×C4—444no—
323C2×C4—442no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—442no—
327C2×C4—441no—
328C2×C4—444no—
329C2×C4—442no—
330C2×C4—884no—
331C2×C4—884no—
332C2×C4#6688514yes—
333C2×C4(C22⋊D11)⋊C412yes—
334C2×C4#6699212yes—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—881no—
345C22—881no—
346C22—881no—
347C22—882no—
348C22—882no—
349C22#1062234511yescharacteristic
350C22#1062234811yescharacteristic
351C22#1062234911yescharacteristic
352C22#1062235111yescharacteristic
353C22#1062257111yescharacteristic
354C22#1062261912yes—
355C22C2×#6688511yescharacteristic
356C22#1062274611yescharacteristic
357C22#1062275212yes—
358C4—22no—
359C4—22no—
360C4—24no—
361C4—42no—
362C4—884no—
363C4—881no—
364C4—882no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—1761no—
370C2#1306715512yes—
371C2#1306717712yes—
372C2#1306893111yescharacteristic
373C2#1306906211yescharacteristic
374C2#1306907211yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1817C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1817D11
hypocenterC11#9156
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. C2×#10622549C2semidirect
4. #13066496C2semidirect
5. C11×#1817C2semidirect
16. #10622552C4semidirect
18. #10622541C4semidirect
102. #1817D11semidirect
286. C11#9156semidirect

Maximal subgroups

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

subgroupindex
#130769472
C2×#106225492
C2×#106221082
#130664962
C11×#18172
#915611