Finite Group Databasebeta

← #14739058

Subgroups — #14739058

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079543C211yesmaximal, characteristic
2C2×#10622633C211yesmaximal, characteristic, complemented
3#13078088C211yesmaximal, characteristic
4#13068046C214yesmaximal, complemented
5#13067964C214yesmaximal, complemented
6#13067387C211yesmaximal, characteristic, complemented
7#13067300C211yesmaximal, characteristic, complemented
8#13067263C211yesmaximal, characteristic
9C11×#2982C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66995—21no—
12#10623008C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C8×Q8×C11—22no—
15C8×Q8×C11C2214yes—
16C11×#431—22no—
17C11×#431C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C2×#66899—21no—
20#10622644C2212yes—
21#10622641—22no—
22#10622640C2212yes—
23#10622633—22no—
24#10622633C2214yes—
25#10622579—21no—
26C2×#66872—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622454—22no—
30#10622351—22no—
31#10622306C2212yes—
32#10622294C2212yes—
33#10622124C2212yes—
34#10622123C2212yes—
35#10622120C2214yes—
36#10622095C2214yes—
37C22×Q8×C11D411yescharacteristic
38C2×#4339—21no—
39C22×Dic22—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11D412yes—
43C4×Q8×C11C2312yes—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C42×C11—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4326—22no—
49#66995—44no—
50C2×#4325—22no—
51#66983—21no—
52#66983—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×#4318—21no—
56C22×C11⋊C8—21no—
57C2×#4314—24no—
58#66928—21no—
59#66927C2311yescharacteristic
60C4×D44—21no—
61C4×D44—21no—
62#66922—21no—
63#66922—21no—
64#66922—21no—
65#66922C2312yes—
66#66922C2311yescharacteristic
67C11×C4⋊C8—24no—
68C11×C4⋊C8D412yes—
69C11×C4⋊C8C2312yes—
70C11×C22⋊C8—21no—
71C11×C22⋊C8D412yes—
72C4×C8×C11—24no—
73C4×C8×C11—21no—
74C4×C8×C11C2312yes—
75#66899—24no—
76#66880—24no—
77#66874—22no—
78#66873—22no—
79#66872—24no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)C2312yes—
83C4⋊(C11⋊C8)C2312yes—
84#19397—111nomaximal, Sylow
85C2×Q8×C11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11SD1614yescomplemented
88C2×Q8×C11C2×D412yes—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C2×C22⋊D11—41no—
95C22×Dic11—41no—
96#4339—42no—
97#4339—42no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×C4×D11—41no—
102C2×Dic22—21no—
103C2×Dic22—22no—
104C2×Dic22—41no—
105C2×Dic22—82no—
106C2×C8×C11—22no—
107C2×C8×C11C2×D414yes—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4C2×D412yes—
112C42×C11—22no—
113C42×C11—22no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11C2411yescharacteristic
118#4326—44no—
119#4325—44no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122C4⋊Dic11—22no—
123C4⋊Dic11—21no—
124C4⋊Dic11—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128#4318—42no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132#4314—84no—
133#3206—111no—
134C2×#475—111no—
135#3037—111no—
136#2982D1111yescharacteristic, complemented
137#1680—114no—
138#1666—114no—
139#1570—111no—
140#1549—111no—
141#1540—111no—
142C23×C11#12111yescharacteristic
143C22×D11—41no—
144Q8×C11—22no—
145Q8×C11—24no—
146Q8×C11C2×SD1614yes—
147C2×C4×C11—22no—
148C2×C4×C11—24no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—81no—
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11C2×SD1612yes—
157C2×C4×C11#13512yes—
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C22⋊D11—82no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—82no—
165D44—41no—
166D44—41no—
167D44—42no—
168D44—81no—
169C4×D11—82no—
170Dic22—41no—
171Dic22—41no—
172Dic22—44no—
173Dic22—82no—
174C8×C11—24no—
175C8×C11—42no—
176C11⋊C8—42no—
177C11⋊C8—42no—
178C2×#137—221no—
179#532—111no—
180C2×C4⋊Q8—111no—
181C2×C4×Q8C2×D1111yescharacteristic
182#492—112no—
183#487—112no—
184#475—114no—
185#475—222no—
186#464—222no—
187#462—112no—
188#461—222no—
189#460—112no—
190#448—222no—
191C8×Q8—22no—
192C8×Q8C2×D1114yes—
193#431—22no—
194#431C2×D1111yescharacteristic
195#431C2×D1111yescharacteristic
196C2×#106—221no—
197#423—111no—
198C2×C4⋊C8—111no—
199#417—221no—
200C2×#103—221no—
201#334—114no—
202#332—112no—
203#332—114no—
204#331—112no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11#46512yes—
208C22×C11C2×#12111yescharacteristic
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—81no—
212C4×C11—21no—
213C4×C11—24no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—42no—
217C4×C11#46512yes—
218C4×C11C22×SD1611yescharacteristic
219C4×C11C2×#13511yescharacteristic
220C4×C11#57712yes—
221Dic11—82no—
222Dic11—81no—
223C2×#41—221no—
224C22×Q8—221no—
225C22×Q8D4411yescharacteristic
226#137—444no—
227C2×Q16—222no—
228C2×SD16—222no—
229C2×SD16—224no—
230C2×M16—221no—
231C22×C8—221no—
232C4⋊Q8—112no—
233C4⋊Q8—111no—
234C4⋊Q8—221no—
235C4⋊Q8—221no—
236C4⋊Q8—221no—
237#127—111no—
238#124—221no—
239#121—221no—
240#121—221no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8D4412yes—
244C4×Q8C22×D1112yes—
245C4×D4—221no—
246C4×D4—221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4D4411yescharacteristic
251C2×C42—21no—
252C2×C42C22×D1111yescharacteristic
253#106—224no—
254C4⋊C8—24no—
255C4⋊C8—112no—
256C4⋊C8—112no—
257C4⋊C8—221no—
258C4⋊C8—221no—
259C4⋊C8C22⋊D1112yes—
260C4⋊C8C22×D1112yes—
261#103—224no—
262#103—224no—
263#103—222no—
264#102—222no—
265C22⋊C8—21no—
266C22⋊C8C22⋊D1112yes—
267C4×C8—24no—
268C4×C8—21no—
269C4×C8C22×D1112yes—
270C2×C11—22no—
271C2×C11#304311yescharacteristic
272C2×C11C2×#46511yescharacteristic
273C2×C11#306911yescharacteristic
274D11—161no—
275#41—442no—
276#41—442no—
277C2×Q8—22no—
278C2×Q8—21no—
279C2×Q8—221no—
280C2×Q8—222no—
281C2×Q8—441no—
282C2×Q8—882no—
283C2×Q8#431414yescomplemented
284C2×Q8C2×D4412yes—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—441no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4C2×D4411yescharacteristic
294C22×C4#433911yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296Q16—444no—
297SD16—444no—
298SD16—884no—
299M16—442no—
300C2×C8—22no—
301C2×C8—222no—
302C2×C8—222no—
303C2×C8—442no—
304C2×C8C2×C22⋊D1114yes—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—222no—
309C4⋊C4—222no—
310C4⋊C4—221no—
311C4⋊C4—221no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C4⋊C4C2×D4412yes—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C42—22no—
318C42—22no—
319C42C2×D4411yescharacteristic
320C42#433911yescharacteristic
321C42C2×C22⋊D1111yescharacteristic
322C42C23×D1111yescharacteristic
323C11#1939711yescharacteristic, complemented, Sylow
324C23—441no—
325C23#6698311yescharacteristic
326Q8—24no—
327Q8—22no—
328Q8—441no—
329Q8—441no—
330Q8—444no—
331Q8—882no—
332Q8C2×#431414yes—
333D4—441no—
334D4—441no—
335D4—442no—
336D4—881no—
337D4—882no—
338C2×C4—24no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—441no—
345C2×C4—442no—
346C2×C4—882no—
347C2×C4—882no—
348C2×C4C2×#431412yes—
349C2×C4#6695712yes—
350C2×C4#6698311yescharacteristic
351C2×C4#6698311yescharacteristic
352C2×C4#6698311yescharacteristic
353C2×C4C22×D4411yescharacteristic
354C2×C4C2×#433911yescharacteristic
355C2×C4C22×C22⋊D1111yescharacteristic
356C8—24no—
357C8—42no—
358C8—442no—
359C8—442no—
360C22—21no—
361C22—21no—
362C22—881no—
363C22—881no—
364C22—881no—
365C22#1062272712yes—
366C22C2×#6698311yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—24no—
371C4—42no—
372C4—882no—
373C4—881no—
374C4#1062272712yes—
375C4C22×#431411yescharacteristic
376C4C2×#6695711yescharacteristic
377C4#1062336812yes—
378C2—22no—
379C2—1761no—
380C2#1307813711yescharacteristic
381C2C2×#1062272711yescharacteristic
382C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2982C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#2982D11
hypocenterC11#19397
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. C2×#10622633C2semidirect
4. #13068046C2semidirect
5. #13067964C2semidirect
6. #13067387C2semidirect
7. #13067300C2semidirect
9. C11×#2982C2semidirect
87. C2×Q8×C11SD16semidirect
136. #2982D11semidirect
283. C2×Q8#4314semidirect
323. C11#19397semidirect

Maximal subgroups

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

subgroupindex
#130795432
C2×#106226332
#130780882
#130680462
#130679642
#130673872
#130673002
#130672632
C11×#29822
#1939711