Finite Group Databasebeta

← #14649839

Subgroups — #14649839

Order 2816.

622 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 127 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#13074358C211yesmaximal, characteristic
2#13071234C211yesmaximal, characteristic, complemented
3#13067185C212yesmaximal
4#13066484C212yesmaximal, complemented
5C2×C11×#324C211yesmaximal, characteristic, complemented
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×#66982—21no—
9C2×#66979—21no—
10C2×C11×C22⋊C8C2212yes—
11#10622826—21no—
12#10622825—21no—
13#10622825C2211yescharacteristic
14#10622825C2212yes—
15#10622607—22no—
16#10622604C412yescomplemented
17#10622598—24no—
18#10622596C412yescomplemented
19C11×#324—22no—
20#10622108—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C22×C8×C11—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C11×C4⋊C4D412yes—
31C2×C22⋊Dic11—22no—
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—21no—
39C2×(C2×D11)⋊C4—22no—
40#66979—42no—
41#66979—42no—
42C2×C4⋊Dic11—22no—
43C2×C4⋊Dic11—22no—
44C2×C4⋊Dic11—22no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×Dic11⋊C4—22no—
48C2×C4×Dic11—22no—
49C11×C22⋊C8—22no—
50C11×C22⋊C8—22no—
51C11⋊#95—22no—
52C11⋊#95—22no—
53C11⋊#95C2×C412yes—
54C11⋊#95D414yes—
55#9204—111nomaximal, Sylow
56C24×C11C2×D411yescharacteristic
57C23×D11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—81no—
65C22×C4×C11—81no—
66C22×C4×C11C22⋊C412yes—
67C22×C4×C11C22⋊C412yes—
68C22×C4×C11D812yes—
69C22×C4×C11SD1612yes—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D412yes—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4112yes—
74C2×C22⋊D11—41no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11—41no—
79C2×C22⋊D11—41no—
80C22×Dic11—21no—
81C22×Dic11—22no—
82C22×Dic11—24no—
83C2×D44—22no—
84C2×D44—81no—
85C2×C8×C11—42no—
86C2×C8×C11—82no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—24no—
89C22⋊Dic11—42no—
90C22⋊Dic11—41no—
91C22⋊Dic11—41no—
92C22⋊Dic11—42no—
93(C2×D11)⋊C4—44no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—82no—
96C4⋊Dic11—22no—
97C4⋊Dic11—44no—
98C4⋊Dic11—82no—
99C4⋊Dic11—81no—
100C4⋊Dic11—82no—
101Dic11⋊C4—44no—
102C4×Dic11—44no—
103#2618—111no—
104#2316—111no—
105#1519—112no—
106C2×#324D1111yescharacteristic, complemented
107#1289—112no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11C2×C22⋊C411yescharacteristic
111C23×C11#12011yescharacteristic
112C23×C11#12311yescharacteristic
113C23×C11C2×D811yescharacteristic
114C23×C11C2×SD1611yescharacteristic
115C23×C11AGL(1,ℤ/8)11yescharacteristic
116C23×C11#13711yescharacteristic
117C22×D11—42no—
118C22×D11—42no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
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—42no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—81no—
136C2×C4×C11#10214yes—
137C2×C4×C11C4×D412yes—
138C2×C4×C11#12112yes—
139C22⋊D11—81no—
140C22⋊D11—81no—
141C22⋊D11—81no—
142C22⋊D11—81no—
143C2×Dic11—44no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—44no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—44no—
152D44—82no—
153C8×C11—82no—
154C2×#123—221no—
155C2×#121—111no—
156C2×#117—221no—
157C22×C4⋊C4C2×D1111yescharacteristic
158C2×C22⋊C8C2×D1112yes—
159#398—112no—
160#396—222no—
161#394—112no—
162#389—224no—
163#386—221no—
164#380—111no—
165#380—112no—
166#380—221no—
167#327—224no—
168#324—22no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11#38611yescharacteristic
180C22×C11C2×#10211yescharacteristic
181C22×C11#41711yescharacteristic
182C22×C11#44711yescharacteristic
183C22×C11#44811yescharacteristic
184C22×C11#48011yescharacteristic
185C22×C11#48111yescharacteristic
186C2×D11—82no—
187C2×D11—82no—
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C4×C11—24no—
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—42no—
195Dic11—84no—
196Dic11—82no—
197Dic11—81no—
198C22×D4—111no—
199C22×D4—221no—
200C23×C4D4411yescharacteristic
201C23×C4D4411yescharacteristic
202C23×C4C22×D1111yescharacteristic
203C22×C8—22no—
204#123—442no—
205#123—442no—
206#121—222no—
207#121—222no—
208#117—442no—
209#117—442no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—222no—
214C2×C4⋊C4—222no—
215C2×C4⋊C4—222no—
216C2×C4⋊C4—222no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4C4×D1112yes—
219C2×C4⋊C4C22⋊D1112yes—
220C2×C22⋊C4—222no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—222no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—222no—
225C2×C42—222no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228#95—112no—
229#95—114no—
230#95—222no—
231#95—222no—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11#187411yescharacteristic
239C2×C11#191211yescharacteristic
240C2×C11#191311yescharacteristic
241D11—161no—
242C24—221no—
243C24C2×D4411yescharacteristic
244C2×D4—222no—
245C2×D4—441no—
246C2×D4—441no—
247C2×D4—441no—
248C2×D4—441no—
249C2×D4—441no—
250C2×D4—441no—
251C2×D4—881no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—81no—
259C22×C4—81no—
260C22×C4—224no—
261C22×C4—222no—
262C22×C4—221no—
263C22×C4#431412yes—
264C22×C4D8812yes—
265C22×C4(C2×D11)⋊C412yes—
266C22×C4(C2×D11)⋊C412yes—
267C22×C4C2×C4×D1111yescharacteristic
268C22×C4D4×D1112yes—
269C22×C4#434112yes—
270C22×C4C2×C22⋊D1111yescharacteristic
271C2×C8—42no—
272C2×C8—82no—
273C4⋊C4—24no—
274C4⋊C4—24no—
275C4⋊C4—222no—
276C4⋊C4—444no—
277C4⋊C4—444no—
278C4⋊C4—882no—
279C4⋊C4—881no—
280C4⋊C4—882no—
281C22⋊C4—441no—
282C22⋊C4—442no—
283C22⋊C4—441no—
284C22⋊C4—442no—
285C22⋊C4—444no—
286C22⋊C4—442no—
287C22⋊C4—882no—
288C42—444no—
289C11#920411yescharacteristic, complemented, Sylow
290C23—41no—
291C23—41no—
292C23—442no—
293C23—442no—
294C23—441no—
295C23—441no—
296C23—441no—
297C23#6693511yescharacteristic
298C23#6693911yescharacteristic
299C23C2×#431411yescharacteristic
300C23C2×D8811yescharacteristic
301C23#6696111yescharacteristic
302C23#6696211yescharacteristic
303C23C2×(C2×D11)⋊C411yescharacteristic
304D4—882no—
305D4—881no—
306D4—881no—
307D4—881no—
308D4—881no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—442no—
324C2×C4—444no—
325C2×C4—444no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—444no—
332C2×C4#6688514yes—
333C2×C4(C22⋊D11)⋊C412yes—
334C2×C4#6699212yes—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—882no—
347C22—882no—
348C22—881no—
349C22—881no—
350C22—881no—
351C22#1062234511yescharacteristic
352C22#1062234811yescharacteristic
353C22#1062234911yescharacteristic
354C22#1062235111yescharacteristic
355C22#1062257111yescharacteristic
356C22C2×#6688511yescharacteristic
357C22#1062274611yescharacteristic
358C4—22no—
359C4—22no—
360C4—24no—
361C4—42no—
362C4—884no—
363C4—882no—
364C4—881no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—1761no—
372C2#1306893111yescharacteristic
373C2#1306915111yescharacteristic
374C2#1306915611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#324C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenterC2×#324D11
hypocenterC11#9204
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #13071234C2semidirect
4. #13066484C2semidirect
5. C2×C11×#324C2semidirect
16. #10622604C4semidirect
18. #10622596C4semidirect
106. C2×#324D11semidirect
289. C11#9204semidirect

Maximal subgroups

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

subgroupindex
#130743582
#130712342
#130671852
#130664842
C2×C11×#3242
#920411