Finite Group Databasebeta

← #14645613

Subgroups — #14645613

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic
2#13068600C211yesmaximal, characteristic
3#13067271C212yesmaximal, complemented
4#13067020C212yesmaximal, complemented
5C11×#1458C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×#66979—21no—
8#10623050—22no—
9#10623050—22no—
10#10623048—24no—
11#10623031—21no—
12#10623031C412yes—
13#10623014—21no—
14#10623014C412yes—
15#10623001—21no—
16#10623001C2212yes—
17C11×#431C2212yes—
18C2×C22⋊(C11⋊C8)—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C11×#324—21no—
22C11×#323—21no—
23#10622162—21no—
24#10622120—22no—
25#10622119—22no—
26#10622094—24no—
27C23×C4×C11D411yescharacteristic
28C11×#117—22no—
29C11×#117—22no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×C22⋊Dic11—22no—
37#66979—22no—
38#66979—22no—
39#66979—22no—
40#66979—22no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43#66977—22no—
44#66977—22no—
45#66977—22no—
46#66977C2×C414yes—
47C2×C4×Dic11—22no—
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50#66943—24no—
51#66943—24no—
52#66941—24no—
53#66941—24no—
54#66931—24no—
55#66931—24no—
56#66931—24no—
57#66931—24no—
58#66923—22no—
59#66923—22no—
60#66922—21no—
61#66922—21no—
62#66922D412yes—
63#66922D412yes—
64C4×Dic22—22no—
65C4×Dic22—22no—
66C4×Dic22—22no—
67C4×Dic22D414yes—
68C11×C4⋊C8—22no—
69C11×C22⋊C8—22no—
70C4×C8×C11—22no—
71C22⋊(C11⋊C8)—42no—
72C4⋊(C11⋊C8)—22no—
73C4⋊(C11⋊C8)—22no—
74#8410—111nomaximal, Sylow
75C24×C11C22⋊C411yescharacteristic
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11SD1612yes—
84C22×C4×C11Q1612yes—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×Dic11—22no—
89C22×Dic11—22no—
90C2×Dic22—22no—
91C2×Dic22—22no—
92C2×Dic22—22no—
93C2×Dic22C22⋊C414yes—
94C2×C8×C11—42no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—22no—
99C42×C11—21no—
100C42×C11—21no—
101C42×C11C2×D412yes—
102C42×C11C2×D412yes—
103C22⋊Dic11—24no—
104C22⋊Dic11—24no—
105C4⋊Dic11—22no—
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11C22⋊C414yes—
113Dic11⋊C4—24no—
114Dic11⋊C4—24no—
115Dic11⋊C4—24no—
116Dic11⋊C4—24no—
117C4×Dic11—24no—
118C4×Dic11—24no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125#3458—111no—
126#1798—111no—
127#1542—112no—
128#1481—112no—
129#1458D1111yescharacteristic
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11#10312yes—
135C23×C11C2×C22⋊C411yescharacteristic
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11#10312yes—
149C2×C4×C11C2×C22⋊C412yes—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12012yes—
153C2×C4×C11C2×SD1611yescharacteristic
154C2×C4×C11C2×Q1611yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×Dic11—24no—
158C2×Dic11—24no—
159C2×Dic11—82no—
160C2×Dic11—82no—
161Dic22—44no—
162Dic22—82no—
163Dic22—82no—
164Dic22—82no—
165C8×C11—82no—
166C11⋊C8—81no—
167C11⋊C8—81no—
168#544—112no—
169#544—222no—
170#544—222no—
171#544—221no—
172#543—112no—
173#543—221no—
174#533—112no—
175#533—224no—
176#533—221no—
177C2×#117—221no—
178C2×#117C2×D1111yescharacteristic
179#431C2×D1112yes—
180C2×C4⋊C8—111no—
181C2×C4⋊C8—111no—
182C2×C22⋊C8—221no—
183#336—221no—
184#333—222no—
185#332—222no—
186Q8⋊C8—224no—
187#324—21no—
188#323—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—22no—
192C22×C11—42no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—81no—
196C22×C11#37911yescharacteristic
197C22×C11C2×#10311yescharacteristic
198C22×C11#41911yescharacteristic
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11#44811yescharacteristic
205C4×C11#44811yescharacteristic
206C4×C11#45111yescharacteristic
207C4×C11#45111yescharacteristic
208Dic11—44no—
209Dic11—44no—
210C23×C4D4411yescharacteristic
211C22×C8—221no—
212C22×C8—221no—
213C4⋊Q8—112no—
214C4⋊Q8—112no—
215C4⋊Q8—221no—
216C4⋊Q8—221no—
217C4⋊Q8—224no—
218C4⋊Q8—224no—
219#125—222no—
220#125—224no—
221#125—224no—
222#125—222no—
223C22⋊Q8—114no—
224C22⋊Q8—224no—
225C22⋊Q8—224no—
226C22⋊Q8—224no—
227C22⋊Q8—224no—
228C22⋊Q8—222no—
229C22⋊Q8—222no—
230C22⋊Q8—222no—
231C4×Q8—114no—
232C4×Q8—222no—
233C4×Q8—222no—
234C4×Q8—222no—
235#117—22no—
236#117—22no—
237#117—222no—
238#117—222no—
239#117—222no—
240#117—222no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4C4×D1111yescharacteristic
244C2×C4⋊C4C22⋊D1111yescharacteristic
245C2×C22⋊C4—222no—
246C2×C22⋊C4C4×D1111yescharacteristic
247C2×C22⋊C4C22⋊D1111yescharacteristic
248C2×C42—222no—
249C2×C42D4411yescharacteristic
250C2×C42C22×D1111yescharacteristic
251C4⋊C8—22no—
252C4⋊C8—222no—
253C4⋊C8—222no—
254C22⋊C8—22no—
255C22⋊C8—442no—
256C4×C8—22no—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11—42no—
260C2×C11#178711yescharacteristic
261C2×C11#179111yescharacteristic
262C2×C11#179411yescharacteristic
263C24(C2×D11)⋊C411yescharacteristic
264C2×Q8—114no—
265C2×Q8—222no—
266C2×Q8—222no—
267C2×Q8—222no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—222no—
273C22×C4—222no—
274C22×C4#431412yes—
275C22×C4Dic4412yes—
276C22×C4(C2×D11)⋊C411yescharacteristic
277C22×C4(C2×D11)⋊C411yescharacteristic
278C22×C4(C2×D11)⋊C411yescharacteristic
279C22×C4C2×C4×D1111yescharacteristic
280C22×C4C2×D4411yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282C2×C8—42no—
283C2×C8—441no—
284C2×C8—441no—
285C2×C8—441no—
286C2×C8—441no—
287C2×C8—441no—
288C2×C8—441no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—114no—
292C4⋊C4—222no—
293C4⋊C4—222no—
294C4⋊C4—224no—
295C4⋊C4—224no—
296C4⋊C4—222no—
297C4⋊C4—222no—
298C4⋊C4—224no—
299C4⋊C4—222no—
300C4⋊C4—222no—
301C4⋊C4—224no—
302C4⋊C4—222no—
303C22⋊C4—22no—
304C22⋊C4—22no—
305C22⋊C4—224no—
306C22⋊C4—224no—
307C42—21no—
308C42—21no—
309C42—224no—
310C42—224no—
311C42D4×D1112yes—
312C42D4×D1112yes—
313C11#841011yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23#6688012yes—
319C23C2×(C2×D11)⋊C411yescharacteristic
320Q8—444no—
321Q8—882no—
322Q8—882no—
323Q8—882no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—224no—
337C2×C4—224no—
338C2×C4—882no—
339C2×C4—882no—
340C2×C4#6688012yes—
341C2×C4C22⋊C4×D1112yes—
342C2×C4#6693511yescharacteristic
343C2×C4#6693511yescharacteristic
344C2×C4C2×#431411yescharacteristic
345C2×C4C2×Dic4411yescharacteristic
346C2×C4#6696211yescharacteristic
347C2×C4#6696211yescharacteristic
348C2×C4#6699012yes—
349C8—82no—
350C8—881no—
351C8—881no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22#1062256811yescharacteristic
360C22C2×#6688011yescharacteristic
361C22#1062273311yescharacteristic
362C4—22no—
363C4—22no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—444no—
368C4—444no—
369C4#1062235111yescharacteristic
370C4#1062235111yescharacteristic
371C4#1062235211yescharacteristic
372C4#1062235211yescharacteristic
373C2—21no—
374C2—21no—
375C2—42no—
376C2#1306855211yescharacteristic
377C2#1306856511yescharacteristic
378C2#1306858211yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1458C2
socleC22×C11#379
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1458D11
hypocenterC11#8410
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #13067271C2semidirect
4. #13067020C2semidirect
313. C11#8410semidirect

Maximal subgroups

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

subgroupindex
#130820212
#130686002
#130672712
#130670202
C11×#14582
#841011