Finite Group Databasebeta

← #14656224

Subgroups — #14656224

Order 2816.

524 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079760C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic
3#13067288C211yesmaximal, characteristic
4#13067114C211yesmaximal, characteristic
5#13067011C211yesmaximal, characteristic
6#13066519C211yesmaximal, characteristic
7C11×#2546C211yesmaximal, characteristic
8C2×C11×C4⋊Q8—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#398—22no—
13C11×#391—21no—
14C11×#389—22no—
15C4×C11×C4⋊C4C2211yescharacteristic
16#10622838—21no—
17#10622707—22no—
18#10622706—21no—
19#10622692—21no—
20#10622635—22no—
21#10622634—21no—
22#10622633—21no—
23#10622584—22no—
24#10622577—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622090—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—42no—
38C11×C4⋊Q8—42no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—24no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4D412yes—
49C2×C42×C11—21no—
50C2×C42×C11—21no—
51C2×C42×C11C2311yescharacteristic
52#66979—21no—
53#66977—21no—
54#66977—21no—
55C2×#4318—21no—
56#66923—21no—
57#66922D411yescharacteristic
58#66922D411yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×#95—24no—
62C11×#95D412yes—
63#66899—22no—
64#66899—22no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#66874—24no—
68#66872—22no—
69#66872—24no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
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×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11SD1612yes—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C2×Dic22—21no—
98C2×Dic22—21no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—48no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C42×C11—41no—
110C42×C11—41no—
111C42×C11—41no—
112C42×C11—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C22⋊Dic11—41no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124C4×Dic11—41no—
125#4318—41no—
126#4318—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130#3229—111no—
131#3078—111no—
132#2546D1111yescharacteristic
133#1546—111no—
134#1503—111no—
135#1479—111no—
136#1303—111no—
137C23×C11#12011yescharacteristic
138Q8×C11—22no—
139Q8×C11—22no—
140Q8×C11—41no—
141Q8×C11—41no—
142Q8×C11—81no—
143Q8×C11—81no—
144Q8×C11—81no—
145Q8×C11—81no—
146C2×C4×C11—22no—
147C2×C4×C11—24no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12711yescharacteristic
165C2×C4×C11C2×SD1611yescharacteristic
166C2×C4×C11#13511yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C11#13711yescharacteristic
169C2×Dic11—41no—
170C2×Dic11—41no—
171Dic22—42no—
172Dic22—81no—
173C11⋊C8—42no—
174C11⋊C8—42no—
175C11⋊C8—81no—
176#533—111no—
177C2×C4⋊Q8—21no—
178C2×C4⋊Q8C2×D1111yescharacteristic
179C2×C4×Q8C2×D1111yescharacteristic
180#498—221no—
181#487—221no—
182#483—222no—
183#479—222no—
184#477—221no—
185#475—222no—
186#475—221no—
187#431—111no—
188#431—111no—
189#428—221no—
190#423—111no—
191#419—221no—
192#398—22no—
193#391—21no—
194#389—22no—
195C4×C4⋊C4C2×D1111yescharacteristic
196#332—222no—
197#328—222no—
198Q8⋊C8—222no—
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—44no—
208C4×C11—42no—
209C4×C11—82no—
210C4×C11—81no—
211C4×C11#44811yescharacteristic
212C4×C11#44911yescharacteristic
213C4×C11#45612yes—
214C4×C11#46511yescharacteristic
215C4×C11#46811yescharacteristic
216Dic11—81no—
217Dic11—81no—
218C22×Q8—21no—
219C22×Q8C22⋊D1111yescharacteristic
220C2×M16—221no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—42no—
226C4⋊Q8—42no—
227C4⋊Q8—111no—
228C4⋊Q8—111no—
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—24no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C22⋊D1111yescharacteristic
244C2×C4⋊C4C22⋊D1112yes—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42C22×D1111yescharacteristic
248#107—222no—
249#106—222no—
250#106—224no—
251C4⋊C8—112no—
252C4⋊C8—112no—
253C4⋊C8—221no—
254C4⋊C8—221no—
255#103—224no—
256#103—222no—
257#103—222no—
258C22⋊C8—221no—
259C22⋊C8—221no—
260C4×C8—221no—
261C4×C8—221no—
262#95—24no—
263#95C22⋊D1112yes—
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—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—221no—
281C2×Q8—221no—
282C2×Q8#432412yes—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4C2×C22⋊D1111yescharacteristic
288C22×C4C2×C22⋊D1111yescharacteristic
289C22×C4C2×C22⋊D1111yescharacteristic
290M16—441no—
291M16—441no—
292C2×C8—222no—
293C2×C8—222no—
294C2×C8—441no—
295C4⋊C4—24no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—48no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C22⋊C4—441no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42—41no—
316C42—441no—
317C42D4×D1111yescharacteristic
318C42D4×D1111yescharacteristic
319C42D4×D1111yescharacteristic
320C42#434111yescharacteristic
321C11#1025111yescharacteristic, complemented, Sylow
322C23#6700611yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—81no—
328Q8—81no—
329Q8—81no—
330Q8—81no—
331Q8—442no—
332Q8—881no—
333C2×C4—22no—
334C2×C4—24no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4#6698511yescharacteristic
349C2×C4C2×#432411yescharacteristic
350C2×C4#6699011yescharacteristic
351C2×C4#6699011yescharacteristic
352C2×C4#6699111yescharacteristic
353C2×C4#6699211yescharacteristic
354C2×C4#6699211yescharacteristic
355C2×C4#6699311yescharacteristic
356C2×C4#6700311yescharacteristic
357C2×C4#6700411yescharacteristic
358C8—442no—
359C8—442no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22#1062283111yescharacteristic
364C22#1062283611yescharacteristic
365C22#1062285211yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—44no—
370C4—42no—
371C4—82no—
372C4—81no—
373C4—881no—
374C4—881no—
375C4#1062265011yescharacteristic
376C4#1062265311yescharacteristic
377C4#1062265411yescharacteristic
378C4#1062265511yescharacteristic
379C4#1062270812yes—
380C2—21no—
381C2—21no—
382C2#1306961911yescharacteristic
383C2#1306965211yescharacteristic
384C2#1306967611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2546C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#2546D11
hypocenterC11#10251
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

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
#130797602
#130784212
#130672882
#130671142
#130670112
#130665192
C11×#25462
#1025111