Finite Group Databasebeta

← #14656237

Subgroups — #14656237

Order 2816.

504 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079764C211yesmaximal, characteristic
2#13078417C211yesmaximal, characteristic
3#13073824C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic
5#13067012C211yesmaximal, characteristic
6#13066519C211yesmaximal, characteristic
7C11×#1503C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622707—21no—
14#10622704—21no—
15#10622694—21no—
16#10622691—21no—
17#10622676—22no—
18#10622657—22no—
19#10622634—22no—
20#10622617—21no—
21#10622608—21no—
22#10622598—22no—
23#10622548—21no—
24#10622542—21no—
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622269—22no—
28C11×#328—22no—
29#10622120—22no—
30#10622094—22no—
31C22×Dic22—21no—
32C22×Dic22D411yescharacteristic
33C11×C4⋊Q8D411yescharacteristic
34C11×C4⋊Q8D411yescharacteristic
35C11×#125—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C11×#117—21no—
41C2×C11×C4⋊C4—21no—
42C2×C42×C11—21no—
43C2×C42×C11C2311yescharacteristic
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—24no—
46C2×C4⋊Dic11D411yescharacteristic
47C2×C4⋊Dic11D412yes—
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C2×#4318—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C4×Dic22—21no—
58C4×Dic22—21no—
59C11×C4⋊C8—21no—
60C11×C22⋊C8—21no—
61C4×C8×C11—21no—
62C11×#95D412yes—
63#66899—24no—
64C11⋊#95—24no—
65C22⋊(C11⋊C8)—21no—
66#66874—22no—
67#66874—22no—
68#66872—22no—
69#66871—22no—
70#66871—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73C4⋊(C11⋊C8)D412yes—
74C4×C11⋊C8—21no—
75#10253—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C22×C4×C11—22no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—22no—
84C22×Dic11—21no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×Dic22—82no—
93C2×Dic22Q1612yes—
94C2×C8×C11—41no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11—41no—
104C42×C11—41no—
105C42×C11—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C4⋊Dic11—21no—
111C4⋊Dic11—22no—
112C4⋊Dic11—21no—
113C4⋊Dic11—22no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—84no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119C4×Dic11—41no—
120C4×Dic11—41no—
121#4318—41no—
122#4318—41no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125#3230—111no—
126#3078—111no—
127#2567—111no—
128#1549—111no—
129#1503D1111yescharacteristic
130#1479—111no—
131#1303—111no—
132C23×C11#12011yescharacteristic
133Q8×C11—42no—
134Q8×C11—81no—
135C2×C4×C11—22no—
136C2×C4×C11—24no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12711yescharacteristic
148C2×C4×C11C2×Q1611yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×Dic11—22no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—42no—
156C2×Dic11—44no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159Dic22—22no—
160Dic22—22no—
161Dic22—41no—
162Dic22—41no—
163Dic22—82no—
164Dic22—82no—
165C8×C11—81no—
166C11⋊C8—42no—
167C11⋊C8—42no—
168#533C2×D1111yescharacteristic
169C2×C4⋊Q8—111no—
170C2×C4×Q8—111no—
171#500—221no—
172#487—221no—
173#484—222no—
174#479—222no—
175#477—222no—
176#477—221no—
177#475—221no—
178#431—111no—
179#431C2×D1111yescharacteristic
180#428—221no—
181#423—111no—
182#419—221no—
183#395—222no—
184#391—221no—
185#389—222no—
186#384—221no—
187C4×C4⋊C4C2×D1111yescharacteristic
188#332—222no—
189#328—22no—
190Q8⋊C8—222no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11#39211yescharacteristic
194C22×C11#45111yescharacteristic
195C22×C11#45211yescharacteristic
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—44no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11#45111yescharacteristic
203C4×C11#45211yescharacteristic
204C4×C11#45612yes—
205C4×C11#46711yescharacteristic
206C4×C11#47011yescharacteristic
207Dic11—42no—
208Dic11—82no—
209Dic11—81no—
210C22×Q8—111no—
211C22×Q8—221no—
212C2×M16—221no—
213C4⋊Q8—221no—
214C4⋊Q8—221no—
215C4⋊Q8—221no—
216C4⋊Q8—221no—
217C4⋊Q8D4411yescharacteristic
218C4⋊Q8D4411yescharacteristic
219#125—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—221no—
225C4×Q8—221no—
226C4×Q8—221no—
227C4×Q8—221no—
228#117—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—112no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—224no—
235C2×C42—21no—
236C2×C42—221no—
237C2×C42C22×D1111yescharacteristic
238#107—222no—
239#107—224no—
240#106—222no—
241C4⋊C8—21no—
242C4⋊C8—112no—
243C4⋊C8—112no—
244C4⋊C8—221no—
245#103—222no—
246#103—222no—
247#103—224no—
248C22⋊C8—21no—
249C22⋊C8—221no—
250C4×C8—21no—
251C4×C8—221no—
252#95—224no—
253#95C22⋊D1112yes—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11#200111yescharacteristic
257C2×C11#200511yescharacteristic
258C2×C11#200811yescharacteristic
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—112no—
262C2×Q8—221no—
263C2×Q8—221no—
264C2×Q8—221no—
265C2×Q8—221no—
266C2×Q8—221no—
267C2×Q8—441no—
268C2×Q8—441no—
269C2×Q8—882no—
270C22×C4—22no—
271C22×C4—221no—
272C22×C4—222no—
273C22×C4—221no—
274C22×C4D4×D1111yescharacteristic
275C22×C4D4×D1111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277M16—441no—
278M16—441no—
279C2×C8—41no—
280C2×C8—222no—
281C2×C8—222no—
282C4⋊C4—24no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—222no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—222no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C4⋊C4—884no—
298C22⋊C4—41no—
299C42—41no—
300C42—41no—
301C42—41no—
302C42—441no—
303C42—441no—
304C42C2×D4411yescharacteristic
305C42#433911yescharacteristic
306C42D4×D1111yescharacteristic
307C42D4×D1111yescharacteristic
308C11#1025311yescharacteristic, complemented, Sylow
309C23#6699011yescharacteristic
310Q8—42no—
311Q8—81no—
312Q8—222no—
313Q8—222no—
314Q8—441no—
315Q8—441no—
316Q8—882no—
317Q8—882no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—222no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—442no—
329C2×C4—444no—
330C2×C4—441no—
331C2×C4—442no—
332C2×C4#6693511yescharacteristic
333C2×C4#6693511yescharacteristic
334C2×C4#6693711yescharacteristic
335C2×C4#6693711yescharacteristic
336C2×C4#6696811yescharacteristic
337C2×C4#6696911yescharacteristic
338C2×C4Q16×D1111yescharacteristic
339C2×C4#6697111yescharacteristic
340C2×C4#6698311yescharacteristic
341C2×C4#6699311yescharacteristic
342C8—81no—
343C8—442no—
344C8—442no—
345C22—21no—
346C22—21no—
347C22#1062257311yescharacteristic
348C22#1062278611yescharacteristic
349C22#1062279911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—44no—
354C4—81no—
355C4—81no—
356C4—442no—
357C4—882no—
358C4—881no—
359C4#1062242111yescharacteristic
360C4#1062242311yescharacteristic
361C4#1062242611yescharacteristic
362C4#1062242911yescharacteristic
363C4#1062243912yes—
364C2—21no—
365C2—21no—
366C2#1306962511yescharacteristic
367C2#1306965111yescharacteristic
368C2#1306966811yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1503C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#1503D11
hypocenterC11#10253
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
308. C11#10253semidirect

Maximal subgroups

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

subgroupindex
#130797642
#130784172
#130738242
#130673002
#130670122
#130665192
C11×#15032
#1025311