Finite Group Databasebeta

← #14739116

Subgroups — #14739116

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079746C211yesmaximal, characteristic
2C2×#10622634C211yesmaximal, characteristic, complemented
3#13078088C211yesmaximal, characteristic
4#13068032C214yesmaximal, complemented
5#13067998C214yesmaximal, complemented
6#13067387C211yesmaximal, characteristic, complemented
7#13067296C211yesmaximal, 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#10622634—22no—
24#10622634C2214yes—
25#10622579—21no—
26C2×#66871—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622455—22no—
30#10622348—22no—
31#10622307C2212yes—
32#10622293C2212yes—
33#10622124C2212yes—
34#10622123C2212yes—
35#10622119C2214yes—
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—
57#66928—21no—
58#66927C2311yescharacteristic
59C4×D44—21no—
60C4×D44—21no—
61#66922—21no—
62#66922—21no—
63#66922—21no—
64#66922C2312yes—
65#66922C2311yescharacteristic
66C11×C4⋊C8—24no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8C2312yes—
69C11×C22⋊C8—21no—
70C11×C22⋊C8D412yes—
71C4×C8×C11—24no—
72C4×C8×C11—21no—
73C4×C8×C11C2312yes—
74#66899—24no—
75#66885—24no—
76#66881—24no—
77#66874—22no—
78#66873—22no—
79#66871—24no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)C2312yes—
83C4⋊(C11⋊C8)C2312yes—
84#19403—111nomaximal, Sylow
85C2×Q8×C11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11SD1614yes—
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#3227—111no—
133C2×#477—111no—
134#3037—111no—
135#2982D1111yescharacteristic, complemented
136#1678—114no—
137#1672—114no—
138#1570—111no—
139#1548—111no—
140#1540—111no—
141C23×C11#12111yescharacteristic
142C22×D11—41no—
143Q8×C11—22no—
144Q8×C11—24no—
145Q8×C11C2×SD1614yes—
146C2×C4×C11—22no—
147C2×C4×C11—24no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11C2×SD1612yes—
156C2×C4×C11#13512yes—
157C2×C4×C11C22×D411yescharacteristic
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C2×#4111yescharacteristic
160C22⋊D11—82no—
161C2×Dic11—42no—
162C2×Dic11—41no—
163C2×Dic11—82no—
164D44—41no—
165D44—41no—
166D44—42no—
167D44—81no—
168C4×D11—82no—
169Dic22—41no—
170Dic22—41no—
171Dic22—82no—
172Dic22—82no—
173C8×C11—24no—
174C8×C11—42no—
175C11⋊C8—42no—
176C11⋊C8—42no—
177C2×#137—221no—
178#532—111no—
179C2×C4⋊Q8—111no—
180C2×C4×Q8C2×D1111yescharacteristic
181#498—112no—
182#486—112no—
183#481—222no—
184#477—114no—
185#477—222no—
186#476—222no—
187#464—222no—
188#462—112no—
189#460—112no—
190C8×Q8—22no—
191C8×Q8C2×D1114yes—
192#431—22no—
193#431C2×D1111yescharacteristic
194#431C2×D1111yescharacteristic
195C2×#107—221no—
196#423—111no—
197C2×C4⋊C8—111no—
198#417—221no—
199C2×#103—221no—
200#334—114no—
201#333—114no—
202#332—112no—
203#331—112no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11#46512yes—
207C22×C11C2×#12111yescharacteristic
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C4×C11—21no—
212C4×C11—24no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11#46512yes—
217C4×C11C22×SD1611yescharacteristic
218C4×C11C2×#13511yescharacteristic
219C4×C11#57812yes—
220Dic11—81no—
221Dic11—82no—
222C2×#41—221no—
223C22×Q8—221no—
224C22×Q8D4411yescharacteristic
225#137—444no—
226C2×Q16—222no—
227C2×SD16—222no—
228C2×M16—221no—
229C22×C8—221no—
230C4⋊Q8—112no—
231C4⋊Q8—111no—
232C4⋊Q8—221no—
233C4⋊Q8—221no—
234C4⋊Q8—221no—
235#127—111no—
236#124—221no—
237#121—221no—
238#121—221no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8D4412yes—
242C4×Q8C22×D1112yes—
243C4×D4—221no—
244C4×D4—221no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4D4411yescharacteristic
249C2×C42—21no—
250C2×C42C22×D1111yescharacteristic
251#107—224no—
252#106—224no—
253C4⋊C8—24no—
254C4⋊C8—112no—
255C4⋊C8—112no—
256C4⋊C8—221no—
257C4⋊C8—221no—
258C4⋊C8C22⋊D1112yes—
259C4⋊C8C22×D1112yes—
260#103—224no—
261#103—222no—
262#102—224no—
263#102—222no—
264C22⋊C8—21no—
265C22⋊C8C22⋊D1112yes—
266C4×C8—24no—
267C4×C8—21no—
268C4×C8C22×D1112yes—
269C2×C11—22no—
270C2×C11#304411yescharacteristic
271C2×C11C2×#46511yescharacteristic
272C2×C11#306811yescharacteristic
273D11—161no—
274#41—442no—
275#41—442no—
276C2×Q8—22no—
277C2×Q8—21no—
278C2×Q8—221no—
279C2×Q8—222no—
280C2×Q8—441no—
281C2×Q8—882no—
282C2×Q8#431414yes—
283C2×Q8C2×D4412yes—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—441no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—441no—
291C22×C4—441no—
292C22×C4C2×D4411yescharacteristic
293C22×C4#433911yescharacteristic
294C22×C4C2×C22⋊D1111yescharacteristic
295Q16—444no—
296SD16—444no—
297M16—442no—
298C2×C8—22no—
299C2×C8—222no—
300C2×C8—222no—
301C2×C8—442no—
302C2×C8C2×C22⋊D1114yes—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—222no—
307C4⋊C4—221no—
308C4⋊C4—222no—
309C4⋊C4—221no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C4⋊C4C2×D4412yes—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C42—22no—
316C42—22no—
317C42C2×D4411yescharacteristic
318C42#433911yescharacteristic
319C42C2×C22⋊D1111yescharacteristic
320C42C23×D1111yescharacteristic
321C11#1940311yescharacteristic, complemented, Sylow
322C23—441no—
323C23#6698311yescharacteristic
324Q8—24no—
325Q8—22no—
326Q8—441no—
327Q8—441no—
328Q8—882no—
329Q8—882no—
330Q8C2×#431414yes—
331D4—441no—
332D4—441no—
333D4—442no—
334D4—881no—
335D4—882no—
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—441no—
343C2×C4—442no—
344C2×C4—882no—
345C2×C4—882no—
346C2×C4C2×#431412yes—
347C2×C4#6695712yes—
348C2×C4#6698311yescharacteristic
349C2×C4#6698311yescharacteristic
350C2×C4#6698311yescharacteristic
351C2×C4C22×D4411yescharacteristic
352C2×C4C2×#433911yescharacteristic
353C2×C4C22×C22⋊D1111yescharacteristic
354C8—24no—
355C8—42no—
356C8—442no—
357C8—442no—
358C22—21no—
359C22—21no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22#1062272712yes—
364C22C2×#6698311yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—24no—
369C4—42no—
370C4—882no—
371C4—881no—
372C4#1062272712yes—
373C4C22×#431411yescharacteristic
374C4C2×#6695711yescharacteristic
375C4#1062336912yes—
376C2—22no—
377C2—1761no—
378C2#1307814611yescharacteristic
379C2C2×#1062272711yescharacteristic
380C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2982C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#2982D11
hypocenterC11#19403
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×#10622634C2semidirect
4. #13068032C2semidirect
5. #13067998C2semidirect
6. #13067387C2semidirect
7. #13067296C2semidirect
9. C11×#2982C2semidirect
135. #2982D11semidirect
321. C11#19403semidirect

Maximal subgroups

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

subgroupindex
#130797462
C2×#106226342
#130780882
#130680322
#130679982
#130673872
#130672962
#130672632
C11×#29822
#1940311