Finite Group Databasebeta

← #14655864

Subgroups — #14655864

Order 2816.

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

normal subgroups only

This group has 554 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#13079554C211yesmaximal, characteristic
2#13078992C211yesmaximal, characteristic
3#13069561C211yesmaximal, characteristic, complemented
4#13069542C211yesmaximal, characteristic
5#13067115C211yesmaximal, characteristic, complemented
6#13066466C211yesmaximal, characteristic, complemented
7C11×#3249C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C11×#533C2211yescharacteristic
10C2×#66927C2211yescharacteristic
11C11×#477—21no—
12C11×#477—21no—
13C11×#467—22no—
14C11×#462—21no—
15C11×#462—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×#66885—22no—
18#10622701—21no—
19#10622701—21no—
20#10622701—21no—
21#10622698—21no—
22#10622680—22no—
23#10622659—22no—
24#10622640—22no—
25#10622614—22no—
26C4×C4⋊Dic11C2211yescharacteristic
27#10622538C2211yescharacteristic
28C4×#4318C2211yescharacteristic
29#10622176—22no—
30#10622170—22no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44—21no—
34C2×C11×Q16—22no—
35C22×C8×C11D412yes—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
40C11×#125—21no—
41C11×#125—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C11×#117—21no—
51C11×#117—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4325—24no—
54C2×C4⋊Dic11—21no—
55C2×C4×Dic11—21no—
56C2×#4318D412yes—
57#66927—21no—
58#66927—21no—
59#66927—21no—
60#66927D412yes—
61C11×#107—22no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×#103—22no—
65C11×#103—22no—
66C11⋊#95—21no—
67C22⋊(C11⋊C8)D412yes—
68#66885—44no—
69#66873—24no—
70#66873—24no—
71#66873—24no—
72C4⋊(C11⋊C8)—21no—
73#66867—21no—
74C4×C11⋊C8—21no—
75C4×C11⋊C8—21no—
76#10195—111nomaximal, Sylow
77C23×D11—41no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—41no—
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—42no—
90C2×D44—42no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—42no—
95C2×D44—42no—
96C2×D44—82no—
97C11×Q16—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—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11—41no—
115C42×C11—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120#4325—84no—
121C4⋊Dic11—22no—
122C4⋊Dic11—41no—
123C4×Dic11—42no—
124#4318—22no—
125#4318—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128#3249D1111yescharacteristic, complemented
129#3208—111no—
130#3138—111no—
131#1986—111no—
132#1982—111no—
133#1503—111no—
134#1283—111no—
135C23×C11#12711yescharacteristic
136C22×D11—42no—
137C22×D11—82no—
138C22×D11—82no—
139C22×D11—81no—
140C22×D11—81no—
141Q8×C11—42no—
142Q8×C11—41no—
143Q8×C11—41no—
144Q8×C11—41no—
145Q8×C11—41no—
146Q8×C11—81no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#13512yes—
161C2×C4×C11#13712yes—
162C2×Dic11—42no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165D44—44no—
166D44—44no—
167D44—44no—
168D44—82no—
169D44—81no—
170D44—81no—
171D44—82no—
172C8×C11—42no—
173C11⋊C8—42no—
174C11⋊C8—42no—
175#533C2×D1111yescharacteristic
176#533C2×D1111yescharacteristic
177C2×#127—111no—
178#492—221no—
179#490—222no—
180#486—221no—
181#486—221no—
182#486—221no—
183#477—21no—
184#477—21no—
185#467—22no—
186#462—21no—
187#462—21no—
188#460—222no—
189#450—222no—
190#431—111no—
191C2×C4⋊C8C2×D1111yescharacteristic
192#418—222no—
193C2×#102—222no—
194C4×M16—111no—
195C4×C4⋊C4—111no—
196#339—222no—
197#328—222no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11#39211yescharacteristic
201C22×C11#49511yescharacteristic
202C22×C11#49711yescharacteristic
203C2×D11—82no—
204C2×D11—82no—
205C2×D11—82no—
206C2×D11—162no—
207C2×D11—162no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—81no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11#45212yes—
216C4×C11#45311yescharacteristic
217C4×C11#45411yescharacteristic
218C4×C11#46412yes—
219Dic11—82no—
220C22×D4—221no—
221C22×D4—221no—
222C22×D4—221no—
223C2×Q16—22no—
224C2×SD16—224no—
225C2×M16—112no—
226C22×C8C22⋊D1112yes—
227C4⋊Q8C22⋊D1111yescharacteristic
228C4⋊Q8C22⋊D1111yescharacteristic
229C4⋊Q8C22⋊D1111yescharacteristic
230C4⋊Q8C22⋊D1111yescharacteristic
231#127—112no—
232#127—221no—
233#127—221no—
234#127—221no—
235#125—21no—
236#125—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245#117—21no—
246#117—21no—
247C2×C4⋊C4—221no—
248C2×C42—221no—
249C2×C42C22×D1111yescharacteristic
250#107—22no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—221no—
254#103—22no—
255#103—22no—
256#102—224no—
257#102—224no—
258#102—224no—
259#102—444no—
260C22⋊C8—112no—
261#97—221no—
262C4×C8—221no—
263C4×C8—221no—
264#95—221no—
265C2×C11—21no—
266C2×C11—21no—
267C2×C11#200611yescharacteristic
268C2×C11#200811yescharacteristic
269C2×C11#201511yescharacteristic
270D11—162no—
271C24—441no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×D4—222no—
277C2×D4—222no—
278C2×D4—222no—
279C2×D4—442no—
280C2×D4—442no—
281C2×D4—442no—
282C2×D4—442no—
283C2×D4—441no—
284C2×D4—441no—
285C2×D4—441no—
286C2×D4—882no—
287C22×C4—441no—
288C22×C4D4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290C22×C4C2×C22⋊D1111yescharacteristic
291Q16—82no—
292SD16—884no—
293M16—222no—
294M16—222no—
295C2×C8—22no—
296C2×C8—42no—
297C2×C8—222no—
298C2×C8—222no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—222no—
312C4⋊C4—441no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C42—41no—
316C42—41no—
317C42—442no—
318C42D4×D1111yescharacteristic
319C42#434111yescharacteristic
320C42C2×C22⋊D1111yescharacteristic
321C42C2×C22⋊D1111yescharacteristic
322C11#1019511yescharacteristic, complemented, Sylow
323C23—442no—
324C23—882no—
325C23—882no—
326C23—881no—
327C23—881no—
328C23#6699311yescharacteristic
329Q8—42no—
330Q8—41no—
331Q8—41no—
332Q8—41no—
333Q8—41no—
334Q8—81no—
335D4—444no—
336D4—444no—
337D4—444no—
338D4—882no—
339D4—882no—
340D4—881no—
341D4—881no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—442no—
350C2×C4—881no—
351C2×C4—881no—
352C2×C4#6697112yes—
353C2×C4#6697212yes—
354C2×C4#6699011yescharacteristic
355C2×C4#6699011yescharacteristic
356C2×C4#6699111yescharacteristic
357C2×C4#6699211yescharacteristic
358C2×C4#6699211yescharacteristic
359C2×C4#6700611yescharacteristic
360C8—42no—
361C8—442no—
362C8—442no—
363C22—21no—
364C22—21no—
365C22—882no—
366C22—882no—
367C22—882no—
368C22—1762no—
369C22—1762no—
370C22#1062280311yescharacteristic
371C22#1062280411yescharacteristic
372C22#1062283611yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—882no—
381C4#1062279812yes—
382C4#1062280012yes—
383C4#1062285411yescharacteristic
384C4#1062285811yescharacteristic
385C2—21no—
386C2—21no—
387C2—1762no—
388C2#1306965811yescharacteristic
389C2#1306966611yescharacteristic
390C2#1306970711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3249C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#3249D11
hypocenterC11#10195
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
3. #13069561C2semidirect
5. #13067115C2semidirect
6. #13066466C2semidirect
7. C11×#3249C2semidirect
128. #3249D11semidirect
322. C11#10195semidirect

Maximal subgroups

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

subgroupindex
#130795542
#130789922
#130695612
#130695422
#130671152
#130664662
C11×#32492
#1019511