Finite Group Databasebeta

← #14656225

Subgroups — #14656225

Order 2816.

524 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079762C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic
3#13073601C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic
5#13067116C211yesmaximal, characteristic
6#13066518C211yesmaximal, characteristic
7C11×#1479C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66997—21no—
10#10623001C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14#10622838—21no—
15#10622635—22no—
16#10622634—21no—
17#10622633—21no—
18#10622596—22no—
19#10622587—21no—
20#10622577—21no—
21C4×C4⋊Dic11C2211yescharacteristic
22#10622541—22no—
23#10622537C2211yescharacteristic
24#10622464—22no—
25#10622334—22no—
26#10622294—21no—
27#10622293—21no—
28C11×Q8⋊C8—22no—
29#10622124—22no—
30#10622105—22no—
31C22×Q8×C11D411yescharacteristic
32C22×Dic22—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C42×C11—21no—
40C2×C42×C11C2311yescharacteristic
41#66997—42no—
42#66997—42no—
43#66979—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11D412yes—
47#66977—21no—
48#66977—21no—
49C2×Dic11⋊C4—24no—
50C2×C4×Dic11—21no—
51C2×#4318—21no—
52#66923—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922D411yescharacteristic
58#66922D411yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C4×C8×C11—21no—
66C4×C8×C11—21no—
67#66899—22no—
68#66899—22no—
69C11⋊#95—24no—
70C11⋊#95D412yes—
71#66881—24no—
72#66880—24no—
73#66872—22no—
74#66871—22no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77#10251—111nomaximal, Sylow
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11SD1612yes—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—22no—
90C22×Dic11—22no—
91C2×Dic22—21no—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×Dic22—41no—
97C2×Dic22—41no—
98C2×Dic22—41no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C42×C11—41no—
106C42×C11—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C22⋊Dic11—41no—
112C4⋊Dic11—24no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—22no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—22no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121Dic11⋊C4—48no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124C4×Dic11—41no—
125C4×Dic11—41no—
126C4×Dic11—41no—
127#4318—41no—
128#4318—41no—
129C2×C11⋊C8—22no—
130#3229—111no—
131#3078—111no—
132#2546—111no—
133#1546—111no—
134#1503—111no—
135#1479D1111yescharacteristic
136#1303—111no—
137C23×C11#12011yescharacteristic
138Q8×C11—22no—
139Q8×C11—22no—
140Q8×C11—41no—
141Q8×C11—41no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C2×C4×C11C2×SD1611yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11#13711yescharacteristic
159C2×Dic11—24no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167Dic22—42no—
168Dic22—81no—
169Dic22—81no—
170Dic22—81no—
171Dic22—81no—
172Dic22—81no—
173C8×C11—42no—
174C8×C11—81no—
175C11⋊C8—42no—
176#533—111no—
177C2×C4⋊Q8—111no—
178C2×C4⋊Q8—221no—
179C2×C4×Q8C2×D1111yescharacteristic
180#498—221no—
181#487—221no—
182#483—222no—
183#479—222no—
184#477—221no—
185#475—221no—
186#475—222no—
187#431C2×D1111yescharacteristic
188#431C2×D1111yescharacteristic
189#428—221no—
190#423—111no—
191#419—221no—
192#398—222no—
193#391—221no—
194#389—222no—
195C4×C4⋊C4—111no—
196#332—222no—
197#328—222no—
198Q8⋊C8—22no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11#39211yescharacteristic
202C22×C11#45011yescharacteristic
203C22×C11#45211yescharacteristic
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—42no—
208C4×C11—81no—
209C4×C11#44811yescharacteristic
210C4×C11#44911yescharacteristic
211C4×C11#45612yes—
212C4×C11#46511yescharacteristic
213C4×C11#46811yescharacteristic
214Dic11—44no—
215Dic11—82no—
216Dic11—81no—
217Dic11—81no—
218C22×Q8—221no—
219C22×Q8D4411yescharacteristic
220C2×M16—221no—
221C4⋊Q8—111no—
222C4⋊Q8—111no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8—442no—
228C4⋊Q8—442no—
229#125—221no—
230C22⋊Q8—221no—
231C22⋊Q8—221no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8—221no—
237C4×Q8—221no—
238#117—221no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—112no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—224no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4D4411yescharacteristic
245C2×C42—21no—
246C2×C42—221no—
247C2×C42C22×D1111yescharacteristic
248#107—222no—
249#106—222no—
250#106—224no—
251C4⋊C8—21no—
252C4⋊C8—112no—
253C4⋊C8—221no—
254C4⋊C8C22⋊D1112yes—
255#103—224no—
256#103—222no—
257#103—222no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260C4×C8—21no—
261C4×C8—21no—
262#95—112no—
263#95—224no—
264C2×C11—21no—
265C2×C11—21no—
266C2×C11#200011yescharacteristic
267C2×C11#200511yescharacteristic
268C2×C11#200911yescharacteristic
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—221no—
275C2×Q8—221no—
276C2×Q8—441no—
277C2×Q8—441no—
278C2×Q8—441no—
279C2×Q8—441no—
280C2×Q8—441no—
281C2×Q8—441no—
282C2×Q8#431412yes—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—222no—
286C22×C4—222no—
287C22×C4C2×D4411yescharacteristic
288C22×C4D4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290M16—441no—
291M16—441no—
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—222no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—224no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—222no—
303C4⋊C4—221no—
304C4⋊C4—222no—
305C4⋊C4—221no—
306C4⋊C4—448no—
307C4⋊C4—441no—
308C4⋊C4—441no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C22⋊C4—441no—
312C42—41no—
313C42—41no—
314C42—441no—
315C42—441no—
316C42—441no—
317C42#433911yescharacteristic
318C42D4×D1111yescharacteristic
319C42D4×D1111yescharacteristic
320C42C2×C22⋊D1111yescharacteristic
321C11#1025111yescharacteristic, complemented, Sylow
322C23#6693511yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—442no—
328Q8—881no—
329Q8—881no—
330Q8—881no—
331Q8—881no—
332Q8—881no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—224no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4#6693511yescharacteristic
349C2×C4#6693711yescharacteristic
350C2×C4#6693711yescharacteristic
351C2×C4C2×#431411yescharacteristic
352C2×C4#6695711yescharacteristic
353C2×C4#6696111yescharacteristic
354C2×C4#6696211yescharacteristic
355C2×C4#6698311yescharacteristic
356C2×C4#6699011yescharacteristic
357C2×C4#6699311yescharacteristic
358C8—42no—
359C8—81no—
360C8—442no—
361C22—21no—
362C22—21no—
363C22#1062234411yescharacteristic
364C22#1062234611yescharacteristic
365C22#1062257311yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—81no—
371C4—444no—
372C4—882no—
373C4—881no—
374C4—881no—
375C4#1062234711yescharacteristic
376C4#1062235111yescharacteristic
377C4#1062272711yescharacteristic
378C4#1062274711yescharacteristic
379C4#1062281812yes—
380C2—21no—
381C2—21no—
382C2#1306962111yescharacteristic
383C2#1306965311yescharacteristic
384C2#1306967711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1479C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#1479D11
hypocenterC11#10251
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
321. C11#10251semidirect

Maximal subgroups

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

subgroupindex
#130797622
#130784212
#130736012
#130672872
#130671162
#130665182
C11×#14792
#1025111