Finite Group Databasebeta

← #14649780

Subgroups — #14649780

Order 2816.

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

normal subgroups only

This group has 458 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#13077253C211yesmaximal, characteristic
2#13074440C211yesmaximal, characteristic
3#13067298C211yesmaximal, characteristic, complemented
4#13067296C211yesmaximal, characteristic, complemented
5#13066928C211yesmaximal, characteristic
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×#66925C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#382C2211yescharacteristic
13#10622739—21no—
14M16×Dic11—21no—
15#10622600—21no—
16#10622598—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622453—22no—
20#10622453—22no—
21#10622290—21no—
22#10622286C412yes—
23#10622272—21no—
24#10622269C412yes—
25#10622119—22no—
26#10622119—22no—
27#10622107—21no—
28#10622106—21no—
29C22×C4×D11D411yescharacteristic
30C22×Dic22C2×C412yes—
31C2×C11×M16—21no—
32C2×C11×C4⋊C4—21no—
33C2×C42×C11C2311yescharacteristic
34C2×(C2×D11)⋊C4—22no—
35C2×(C2×D11)⋊C4C2×C411yescharacteristic
36C2×(C2×D11)⋊C4D411yescharacteristic
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—22no—
40C2×Dic11⋊C4C2×C411yescharacteristic
41C2×Dic11⋊C4D411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×#4318—21no—
44#66925—21no—
45#66925—21no—
46#66925—21no—
47#66925—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8D412yes—
55C11×C22⋊C8—21no—
56C4×C8×C11—21no—
57C11×#95—21no—
58C11×#95C2×C412yes—
59C11⋊#95—22no—
60C11⋊#95—22no—
61C22⋊(C11⋊C8)—21no—
62(C2×D11)⋊C8—24no—
63#66879—22no—
64C8×Dic11—22no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68C4×C11⋊C8—21no—
69#9192—111nomaximal, Sylow
70C23×D11C22⋊C411yescharacteristic
71C22×C4×C11—22no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—22no—
76C22×Dic11C22⋊C411yescharacteristic
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×Dic22—22no—
86C2×Dic22—22no—
87C2×Dic22—82no—
88C11×M16—41no—
89C11×M16—41no—
90C2×C8×C11—22no—
91C2×C8×C11—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97C42×C11#4111yescharacteristic
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—82no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—82no—
108Dic11⋊C4—21no—
109Dic11⋊C4—21no—
110Dic11⋊C4—21no—
111Dic11⋊C4—21no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114#4318—41no—
115#4318—41no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118#2921—111no—
119#2628—111no—
120#1548—111no—
121#1548—111no—
122#1458—111no—
123#1286—111no—
124#1286D1111yescharacteristic, complemented
125C23×C11C2×C22⋊C411yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—41no—
130C22×D11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11#13511yescharacteristic
144C2×C4×C11#13711yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C4×D11—41no—
157C4×D11—41no—
158C4×D11—41no—
159C4×D11—41no—
160Dic22—82no—
161Dic22—82no—
162C8×C11—42no—
163C8×C11—81no—
164C11⋊C8—42no—
165C11⋊C8—81no—
166C2×C4⋊Q8—111no—
167C2×#117—111no—
168#433—222no—
169#433—222no—
170#431—111no—
171#431C2×D1111yescharacteristic
172#423—111no—
173#423C2×D1111yescharacteristic
174#407—221no—
175C4×M16—221no—
176#400—221no—
177#399—221no—
178#395—112no—
179#393—112no—
180#389—221no—
181#382C2×D1111yescharacteristic
182#380—221no—
183#333—222no—
184#333—222no—
185#324—221no—
186#323—221no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11#38611yescharacteristic
190C22×C11#41611yescharacteristic
191C22×C11#41911yescharacteristic
192C2×D11—42no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—81no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—82no—
202C4×C11#45211yescharacteristic
203C4×C11#45211yescharacteristic
204C4×C11#48511yescharacteristic
205C4×C11#48511yescharacteristic
206Dic11—41no—
207Dic11—41no—
208Dic11—41no—
209Dic11—82no—
210C22×Q8—112no—
211C23×C4—111no—
212C2×M16—21no—
213C2×M16—221no—
214C4⋊Q8—221no—
215C4⋊Q8—221no—
216C4⋊Q8—221no—
217C4⋊Q8—221no—
218#117—221no—
219#117—221no—
220#117—221no—
221#117—221no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—222no—
228C2×C22⋊C4—111no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4—222no—
231C2×C42—111no—
232C2×C42C22×D1111yescharacteristic
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—112no—
236C4⋊C8—221no—
237C4⋊C8—221no—
238C4⋊C8D4412yes—
239C22⋊C8—21no—
240C22⋊C8—224no—
241C22⋊C8—221no—
242#97—222no—
243C4×C8—21no—
244C4×C8—222no—
245C4×C8—221no—
246#95—21no—
247#95—222no—
248#95—222no—
249#95C4×D1112yes—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11#187311yescharacteristic
253C2×C11#190911yescharacteristic
254C2×C11#191411yescharacteristic
255D11—81no—
256C24—111no—
257C2×Q8—222no—
258C2×Q8—222no—
259C2×Q8—882no—
260C22×C4—22no—
261C22×C4—111no—
262C22×C4—111no—
263C22×C4—111no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—222no—
271C22×C4C2×C4×D1111yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4D4×D1111yescharacteristic
274M16—41no—
275M16—41no—
276M16—441no—
277M16—441no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—222no—
281C2×C8—441no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—882no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—882no—
298C42—221no—
299C42—221no—
300C42C2×D4411yescharacteristic
301C42#433911yescharacteristic
302C42D4×D1111yescharacteristic
303C42#434311yescharacteristic
304C11#919211yescharacteristic, complemented, Sylow
305C23—221no—
306C23—221no—
307C23—221no—
308C23—441no—
309C23—441no—
310C23C22⋊C4×D1111yescharacteristic
311Q8—882no—
312Q8—882no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4C4×D4411yescharacteristic
333C2×C4#6693511yescharacteristic
334C2×C4#6693711yescharacteristic
335C2×C4#6694611yescharacteristic
336C2×C4#6694711yescharacteristic
337C2×C4#6694811yescharacteristic
338C2×C4#6696511yescharacteristic
339C2×C4#6696811yescharacteristic
340C2×C4#6696911yescharacteristic
341C2×C4#6697111yescharacteristic
342C8—42no—
343C8—81no—
344C8—442no—
345C8—881no—
346C22—21no—
347C22—21no—
348C22—442no—
349C22—441no—
350C22—441no—
351C22—441no—
352C22—881no—
353C22#1062227811yescharacteristic
354C22#1062238511yescharacteristic
355C22#1062241511yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—441no—
362C4—441no—
363C4—441no—
364C4—882no—
365C4#1062239611yescharacteristic
366C4#1062242311yescharacteristic
367C4#1062248011yescharacteristic
368C4#1062250111yescharacteristic
369C2—21no—
370C2—21no—
371C2—881no—
372C2#1306892711yescharacteristic
373C2#1306913711yescharacteristic
374C2#1306916211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#386
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#9192
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
3. #13067298C2semidirect
4. #13067296C2semidirect
6. #13066474C2semidirect
7. C11×#1286C2semidirect
124. #1286D11semidirect
304. C11#9192semidirect

Maximal subgroups

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

subgroupindex
#130772532
#130744402
#130672982
#130672962
#130669282
#130664742
C11×#12862
#919211