Finite Group Databasebeta

← #14655906

Subgroups — #14655906

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#13079741C211yesmaximal, characteristic
2#13079163C211yesmaximal, characteristic, complemented
3#13069538C211yesmaximal, characteristic, complemented
4#13069536C211yesmaximal, characteristic
5#13067115C211yesmaximal, characteristic, complemented
6#13066466C211yesmaximal, characteristic, complemented
7C11×#3246C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#476—21no—
12C11×#475—21no—
13C11×#465—22no—
14C11×#461—21no—
15C11×#460—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×#66901—22no—
18C2×#66880—22no—
19#10622692—21no—
20#10622692—21no—
21#10622691—21no—
22#10622683—21no—
23#10622678—22no—
24#10622647—22no—
25#10622621—22no—
26#10622608—22no—
27C4×C4⋊Dic11C2211yescharacteristic
28#10622538C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30#10622176—22no—
31C2×C11×#41—21no—
32C22×Dic22—21no—
33C2×C11×SD16—22no—
34C22×C8×C11D412yes—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#127D411yescharacteristic
39C11×#125—21no—
40C11×#124—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×#121—21no—
44C11×#121—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C11×#117—21no—
50C2×C42×C11C2311yescharacteristic
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4×Dic11—21no—
55C2×#4318D412yes—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922D412yes—
60C11×#106—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×#103—22no—
64C11×#102—22no—
65#66901—44no—
66#66896—24no—
67C11⋊#95—21no—
68C22⋊(C11⋊C8)D412yes—
69#66880—44no—
70#66872—24no—
71#66872—24no—
72#66871—24no—
73C4⋊(C11⋊C8)—21no—
74#66867—21no—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10201—111nomaximal, Sylow
78C11×#41—42no—
79C11×#41—42no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×Dic11—41no—
92C22×Dic11—41no—
93C2×Dic22—22no—
94C2×Dic22—42no—
95C2×Dic22—42no—
96C2×Dic22—41no—
97C11×SD16—82no—
98C2×C8×C11—22no—
99C2×C8×C11—42no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C4⋊Dic11—22no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4×Dic11—42no—
123#4318—22no—
124#4318SD1614yescomplemented
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127#3246D1111yescharacteristic
128#3227—111no—
129#3165—111no—
130#1981—111no—
131#1980—111no—
132#1503—111no—
133#1283—111no—
134C23×C11—41no—
135C23×C11#12711yescharacteristic
136Q8×C11—41no—
137Q8×C11—41no—
138Q8×C11—42no—
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—41no—
151C2×C4×C11—41no—
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—42no—
163C2×Dic11—82no—
164C2×Dic11—81no—
165C2×Dic11—81no—
166Dic22—44no—
167Dic22—81no—
168Dic22—81no—
169C8×C11—42no—
170C11⋊C8—24no—
171C11⋊C8—42no—
172#533C2×D1111yescharacteristic
173#532C2×D1111yescharacteristic
174C2×C4⋊Q8—111no—
175#501—222no—
176#500—221no—
177#498—221no—
178#498—221no—
179#486—221no—
180#481—222no—
181#476—21no—
182#476—222no—
183#475—21no—
184#465—22no—
185#461—21no—
186#460—21no—
187#431—111no—
188#428—222no—
189C2×C4⋊C8C2×D1111yescharacteristic
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—81no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11#44812yes—
210C4×C11#45311yescharacteristic
211C4×C11#45411yescharacteristic
212C4×C11#46112yes—
213Dic11—82no—
214Dic11—82no—
215C2×#41—21no—
216C22×Q8—221no—
217C2×SD16—22no—
218C2×M16—112no—
219C22×C8C22⋊D1112yes—
220C4⋊Q8—112no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224C4⋊Q8C22⋊D1111yescharacteristic
225C4⋊Q8C22⋊D1111yescharacteristic
226C4⋊Q8C22⋊D1111yescharacteristic
227#127C22⋊D1111yescharacteristic
228#125—21no—
229#124—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232#121—21no—
233#121—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—21no—
237C4×D4—21no—
238#117—21no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C42—221no—
243C2×C42C22×D1111yescharacteristic
244#107—224no—
245#106—22no—
246#106—224no—
247#106—224no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—221no—
251#104—444no—
252#103—22no—
253#103—444no—
254#102—22no—
255#102—224no—
256C22⋊C8—112no—
257#97—221no—
258C4×C8—221no—
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—21no—
271C2×Q8—21no—
272C2×Q8—222no—
273C2×Q8—442no—
274C2×Q8—442no—
275C2×Q8—441no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C22×C4—41no—
281C22×C4—441no—
282C22×C4—441no—
283C22×C4D4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286SD16—82no—
287M16—114no—
288M16—222no—
289C2×C8—22no—
290C2×C8—42no—
291C2×C8—222no—
292C2×C8—222no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—222no—
302C4⋊C4—222no—
303C4⋊C4—222no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C42—41no—
311C42—442no—
312C42D4×D1111yescharacteristic
313C42#434111yescharacteristic
314C42C2×C22⋊D1111yescharacteristic
315C42C2×C22⋊D1111yescharacteristic
316C11#1020111yescharacteristic, complemented, Sylow
317C23—41no—
318C23#6699311yescharacteristic
319Q8—42no—
320Q8—41no—
321Q8—41no—
322Q8—81no—
323Q8—444no—
324Q8—881no—
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—41no—
337C2×C4—41no—
338C2×C4—82no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—882no—
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—81no—
367C4—81no—
368C4—81no—
369C4—882no—
370C4—882no—
371C4#1062277512yes—
372C4#1062278312yes—
373C4#1062285411yescharacteristic
374C4#1062285811yescharacteristic
375C2—21no—
376C2—21no—
377C2—161no—
378C2#1306965811yescharacteristic
379C2#1306967311yescharacteristic
380C2#1306969711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3246C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3246D11
hypocenterC11#10201
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3246

Complements

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

NH ≅ G/Ntype
2. #13079163C2semidirect
3. #13069538C2semidirect
5. #13067115C2semidirect
6. #13066466C2semidirect
124. #4318SD16semidirect
316. C11#10201semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130791632
#130695382
#130695362
#130671152
#130664662
C11×#32462
#1020111