Finite Group Databasebeta

← #14655903

Subgroups — #14655903

Order 2816.

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

normal subgroups only

This group has 528 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#13079932C211yesmaximal, characteristic
2#13079158C211yesmaximal, characteristic, complemented
3#13069540C211yesmaximal, characteristic, complemented
4#13069536C211yesmaximal, characteristic
5#13067116C211yesmaximal, characteristic, complemented
6#13066465C211yesmaximal, characteristic, complemented
7C11×#3227C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#498—21no—
12C11×#486—21no—
13C11×#481—22no—
14C11×#476—22no—
15C11×#431C2211yescharacteristic
16C2×#66901—22no—
17C2×#66899—22no—
18#10622707—21no—
19#10622693—22no—
20#10622692—21no—
21#10622691—21no—
22#10622688—21no—
23#10622654—22no—
24#10622632—21no—
25#10622621—21no—
26#10622577—22no—
27C4×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30#10622105—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D412yes—
38C11×#127D411yescharacteristic
39C11×#124—21no—
40C11×#121—21no—
41C11×#121—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4324—22no—
48#66979—21no—
49C2×C4⋊Dic11—21no—
50#66977—21no—
51#66977—21no—
52C2×C4×Dic11—21no—
53C2×#4318D412yes—
54C22×C11⋊C8D412yes—
55#66923—21no—
56#66922D411yescharacteristic
57#66922D411yescharacteristic
58C4×Dic22—21no—
59C4×Dic22—21no—
60C11×#106—24no—
61C11×C4⋊C8—21no—
62C11×#102—24no—
63C11×C22⋊C8D412yes—
64C4×C8×C11—21no—
65#66901—44no—
66#66899—44no—
67#66896—22no—
68C11⋊#95—21no—
69#66874—22no—
70#66872—24no—
71#66872—22no—
72#66871—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75#66867—21no—
76C4×C11⋊C8—21no—
77#10201—111nomaximal, Sylow
78C11×#41—42no—
79C11×#41—42no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—42no—
83C2×Q8×C11—42no—
84C2×Q8×C11—41no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11—41no—
95C2×Dic22—21no—
96C2×Dic22—21no—
97C2×C8×C11—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C22⋊Dic11—41no—
111#4324—82no—
112C4⋊Dic11—22no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—41no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120C4×Dic11—41no—
121C4×Dic11—42no—
122#4318—22no—
123#4318SD1614yescomplemented
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—42no—
127#3246—111no—
128#3227D1111yescharacteristic
129#3165—111no—
130#1981—111no—
131#1980—111no—
132#1503—111no—
133#1283—111no—
134C23×C11—41no—
135C23×C11#12711yescharacteristic
136Q8×C11—44no—
137Q8×C11—42no—
138Q8×C11—81no—
139Q8×C11—81no—
140D4×C11—42no—
141D4×C11—41no—
142D4×C11—41no—
143D4×C11—42no—
144D4×C11—81no—
145D4×C11—81no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—82no—
152C2×C4×C11—82no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11C2×SD1612yes—
160C2×C4×C11#13712yes—
161C2×Dic11—42no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—81no—
165C2×Dic11—81no—
166Dic22—41no—
167Dic22—41no—
168Dic22—81no—
169C8×C11—42no—
170C11⋊C8—24no—
171C11⋊C8—42no—
172#533—111no—
173#532C2×D1111yescharacteristic
174C2×C4⋊Q8C2×D1111yescharacteristic
175#501—222no—
176#500—221no—
177#498—21no—
178#498—221no—
179#486—21no—
180#481—22no—
181#476—22no—
182#476—221no—
183#475—221no—
184#465—222no—
185#461—221no—
186#460—221no—
187#431C2×D1111yescharacteristic
188#428—222no—
189C2×C4⋊C8—111no—
190C2×#104—222no—
191C2×#103—222no—
192C4×M16—111no—
193C4×C4⋊C4—111no—
194#328—222no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11#39211yescharacteristic
201C22×C11#49211yescharacteristic
202C22×C11#49711yescharacteristic
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—82no—
207C4×C11—81no—
208C4×C11#44812yes—
209C4×C11#45311yescharacteristic
210C4×C11#45411yescharacteristic
211C4×C11#46112yes—
212Dic11—82no—
213Dic11—81no—
214Dic11—81no—
215C2×#41—21no—
216C22×Q8—21no—
217C2×SD16—222no—
218C2×M16—112no—
219C22×C8—112no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—111no—
224C4⋊Q8—111no—
225C4⋊Q8C22⋊D1112yes—
226C4⋊Q8C22⋊D1111yescharacteristic
227#127C22⋊D1111yescharacteristic
228#125—221no—
229#124—21no—
230C22⋊Q8—221no—
231C22⋊Q8—221no—
232#121—21no—
233#121—21no—
234C4×Q8—221no—
235C4×Q8—221no—
236C4×D4—21no—
237C4×D4—21no—
238#117—221no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—221no—
242C2×C42—221no—
243C2×C42C22×D1111yescharacteristic
244#107—224no—
245#106—24no—
246#106—224no—
247#106—222no—
248C4⋊C8—21no—
249C4⋊C8—221no—
250C4⋊C8—221no—
251#104—444no—
252#103—222no—
253#103—444no—
254#102—24no—
255#102—222no—
256C22⋊C8C22⋊D1112yes—
257#97—221no—
258C4×C8—21no—
259C4×C8—221no—
260#95—221no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—161no—
264C2×C11#200611yescharacteristic
265C2×C11#200911yescharacteristic
266C2×C11#201311yescharacteristic
267#41—42no—
268#41—42no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×Q8—221no—
275C2×Q8—221no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—441no—
283C22×C4D4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286SD16—882no—
287M16—114no—
288M16—222no—
289C2×C8—22no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8—442no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—222no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—441no—
310C42—441no—
311C42—442no—
312C42D4×D1111yescharacteristic
313C42#434111yescharacteristic
314C42C2×C22⋊D1111yescharacteristic
315C42C2×C22⋊D1111yescharacteristic
316C11#1020111yescharacteristic, complemented, Sylow
317C23—41no—
318C23#6699311yescharacteristic
319Q8—44no—
320Q8—42no—
321Q8—81no—
322Q8—81no—
323Q8—441no—
324Q8—441no—
325Q8—881no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—41no—
330D4—81no—
331D4—81no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—442no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—881no—
343C2×C4—881no—
344C2×C4SD16×D1112yes—
345C2×C4#6696812yes—
346C2×C4#6699011yescharacteristic
347C2×C4#6699011yescharacteristic
348C2×C4#6699111yescharacteristic
349C2×C4#6699211yescharacteristic
350C2×C4#6699211yescharacteristic
351C2×C4#6700611yescharacteristic
352C8—42no—
353C8—224no—
354C8—442no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1062278011yescharacteristic
361C22#1062278811yescharacteristic
362C22#1062283611yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—882no—
369C4—881no—
370C4—881no—
371C4#1062277512yes—
372C4#1062278312yes—
373C4#1062281111yescharacteristic
374C4#1062281411yescharacteristic
375C2—21no—
376C2—21no—
377C2—161no—
378C2#1306965611yescharacteristic
379C2#1306967611yescharacteristic
380C2#1306969711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3227C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3227D11
hypocenterC11#10201
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. #13079158C2semidirect
3. #13069540C2semidirect
5. #13067116C2semidirect
6. #13066465C2semidirect
123. #4318SD16semidirect
316. C11#10201semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130791582
#130695402
#130695362
#130671162
#130664652
C11×#32272
#1020111