Finite Group Databasebeta

← #14737757

Subgroups — #14737757

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622706C211yesmaximal, characteristic, complemented
2#13078432C211yesmaximal, characteristic
3#13078425C211yesmaximal, characteristic
4#13077572C211yesmaximal, characteristic
5#13068077C214yesmaximal, complemented
6#13068070C214yesmaximal, complemented
7#13067374C211yesmaximal, characteristic, complemented
8#13067300C211yesmaximal, characteristic, complemented
9C11×#1548C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C4×#4339C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#423C2211yescharacteristic
15#10622746—21no—
16#10622734—21no—
17#10622707—21no—
18#10622706—21no—
19#10622706—21no—
20#10622706C2214yes—
21#10622704C2212yes—
22#10622700—21no—
23#10622697C2212yes—
24C2×#66874—22no—
25#10622579—21no—
26#10622577—21no—
27#10622537C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622464C2212yes—
30#10622463—21no—
31#10622459C2212yes—
32#10622455—21no—
33#10622447C2212yes—
34#10622443C2212yes—
35(C22⋊D11)⋊C8—22no—
36#10622298—21no—
37C4×C8×D11—21no—
38C11×#333C2214yes—
39#10622120C2214yes—
40#10622117C2214yes—
41C22×Q8×C11—21no—
42C2×#4339D411yescharacteristic
43C22×Dic22—21no—
44C2×C11×M16—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52C4×C22⋊D11—21no—
53C4×C22⋊D11—21no—
54#66979D411yescharacteristic
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×#4318—21no—
58C22×C11⋊C8D412yes—
59C2×C8×D11—22no—
60C4×D44D411yescharacteristic
61C4×D44C2311yescharacteristic
62#66925—21no—
63C42×D11—21no—
64#66922—21no—
65#66922—21no—
66#66922—21no—
67#66922C2312yes—
68C4×Dic22D411yescharacteristic
69C4×Dic22C2311yescharacteristic
70C11×C4⋊C8—21no—
71C11×C4⋊C8C2312yes—
72C11×C4⋊C8C2312yes—
73C11×C22⋊C8—21no—
74C4×C8×C11—21no—
75#66885—22no—
76(C2×D11)⋊C8—22no—
77#66882—22no—
78#66881—22no—
79#66880—22no—
80Dic11⋊C8—22no—
81C8×Dic11—22no—
82#66874—22no—
83#66874—24no—
84#66874—24no—
85#66873—22no—
86#66872—22no—
87#66871—22no—
88C4⋊(C11⋊C8)—21no—
89C4⋊(C11⋊C8)C2312yes—
90C4×C11⋊C8D411yescharacteristic
91C4×C11⋊C8D411yescharacteristic
92C4×C11⋊C8C2312yes—
93#19277—111nomaximal, Sylow
94C2×Q8×C11—22no—
95C2×Q8×C11—41no—
96C2×Q8×C11—82no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C2×C22⋊D11—21no—
102C22×Dic11—41no—
103#4339—22no—
104#4339Q1614yes—
105C2×D44C2×D411yescharacteristic
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×Dic22—22no—
110C2×Dic22—44no—
111C2×Dic22—41no—
112C2×Dic22C2×D411yescharacteristic
113C11×M16—42no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123C42×C11C2411yescharacteristic
124C22⋊Dic11—21no—
125(C2×D11)⋊C4—21no—
126(C2×D11)⋊C4—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131C4⋊Dic11C2×D411yescharacteristic
132C4⋊Dic11C2×D411yescharacteristic
133Dic11⋊C4—21no—
134Dic11⋊C4—21no—
135C4×Dic11—21no—
136C4×Dic11—21no—
137C4×Dic11—21no—
138#4318—42no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—42no—
141C2×C11⋊C8C2×D412yes—
142C2×C11⋊C8C2×D412yes—
143C8×D11—44no—
144C2×#487—111no—
145#3079—111no—
146#3079—111no—
147C8×#41—111no—
148#1684—114no—
149#1683—114no—
150#1567—111no—
151#1549—111no—
152#1548D1111yescharacteristic, complemented
153C23×C11#12111yescharacteristic
154C22×D11—21no—
155Q8×C11—82no—
156Q8×C11—82no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—42no—
160C2×C4×C11—82no—
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11C2×Q1612yes—
165C2×C4×C11#13512yes—
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C2×#4111yescharacteristic
169C22⋊D11—24no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—42no—
174C2×Dic11—82no—
175D44—21no—
176D44C2×Q1612yes—
177C4×D11—24no—
178C4×D11—42no—
179C4×D11—42no—
180Dic22—21no—
181Dic22—44no—
182Dic22—82no—
183Dic22C2×Q1612yes—
184C8×C11—42no—
185C8×C11—42no—
186C11⋊C8—22no—
187C11⋊C8—22no—
188C11⋊C8—42no—
189C2×C4⋊Q8—111no—
190C2×C4⋊Q8C2×D1111yescharacteristic
191C4×#41—111no—
192#487—114no—
193#487—221no—
194#487—221no—
195#477—112no—
196#477—221no—
197#476—112no—
198#476—221no—
199#475—112no—
200#475—221no—
201#474—112no—
202#474—221no—
203C8×Q8—112no—
204C8×D4—112no—
205C8×D4—222no—
206#431—221no—
207#431C2×D1111yescharacteristic
208#428—221no—
209#428—221no—
210#423—111no—
211#423C2×D1111yescharacteristic
212#417—221no—
213#417—221no—
214C2×#103—222no—
215C2×C4×C8—111no—
216C2×C4×C8—221no—
217#335—114no—
218#333C2×D1114yes—
219#332—114no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11#46712yes—
223C22×C11C2×#12111yescharacteristic
224C2×D11—22no—
225C2×D11—41no—
226C2×D11—41no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—82no—
230C4×C11#46712yes—
231C4×C11#47112yes—
232C4×C11C22×Q1611yescharacteristic
233C4×C11C2×#13511yescharacteristic
234C4×C11#57512yes—
235Dic11—22no—
236Dic11—41no—
237Dic11—41no—
238Dic11—82no—
239C2×#41—111no—
240C22×Q8—21no—
241C22×Q8—221no—
242C2×M16—21no—
243C2×M16—221no—
244C22×C8—112no—
245C22×C8—222no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—112no—
250C4⋊Q8—221no—
251C4⋊Q8—221no—
252C4⋊Q8—221no—
253C4⋊Q8C22×D1112yes—
254C4×Q8—111no—
255C4×Q8—111no—
256C4×D4—111no—
257C4×D4—111no—
258C4×D4—221no—
259C4×D4—221no—
260#117—111no—
261#117—221no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C42—221no—
267C2×C42C22×D1111yescharacteristic
268#107—222no—
269#107—222no—
270#106—222no—
271#106—222no—
272C4⋊C8—21no—
273C4⋊C8—112no—
274C4⋊C8—222no—
275C4⋊C8—221no—
276C4⋊C8C22×D1112yes—
277C4⋊C8C22×D1112yes—
278#103—224no—
279#103—224no—
280#103—222no—
281#103—222no—
282#102—222no—
283#102—222no—
284C22⋊C8—21no—
285C22⋊C8—222no—
286C4×C8—21no—
287C4×C8—111no—
288C4×C8—111no—
289C4×C8—112no—
290C4×C8—222no—
291C2×C11—22no—
292C2×C11#304011yescharacteristic
293C2×C11C2×#46711yescharacteristic
294C2×C11C2×#47111yescharacteristic
295D11—42no—
296#41—114no—
297#41—222no—
298C2×Q8—22no—
299C2×Q8—41no—
300C2×Q8—82no—
301C2×Q8—111no—
302C2×Q8—222no—
303C2×Q8—444no—
304C2×Q8—441no—
305C2×D4—111no—
306C2×D4—221no—
307C22×C4—41no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—221no—
311C22×C4—441no—
312C22×C4#433911yescharacteristic
313C22×C4D4×D1111yescharacteristic
314C22×C4D4×D1111yescharacteristic
315M16—42no—
316M16—442no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—112no—
320C2×C8—112no—
321C2×C8—222no—
322C2×C8—444no—
323C2×C8—442no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—111no—
329C4⋊C4—111no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—222no—
333C4⋊C4—222no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C22⋊C4—221no—
337C22⋊C4—221no—
338C22⋊C4—221no—
339C42—221no—
340C42—221no—
341C42—221no—
342C42#433911yescharacteristic
343C42D4×D1111yescharacteristic
344C42D4×D1111yescharacteristic
345C42C23×D1111yescharacteristic
346C11#1927711yescharacteristic, complemented, Sylow
347C23—221no—
348C23#6693711yescharacteristic
349Q8—82no—
350Q8—82no—
351Q8—112no—
352Q8—221no—
353Q8—444no—
354Q8—882no—
355D4—112no—
356D4—224no—
357D4—221no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—42no—
361C2×C4—82no—
362C2×C4—221no—
363C2×C4—224no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—882no—
370C2×C4#6693711yescharacteristic
371C2×C4#6693711yescharacteristic
372C2×C4#6693711yescharacteristic
373C2×C4#6696912yes—
374C2×C4Q16×D1112yes—
375C2×C4C2×#433911yescharacteristic
376C2×C4C2×D4×D1111yescharacteristic
377C2×C4C2×D4×D1111yescharacteristic
378C8—42no—
379C8—42no—
380C8—222no—
381C8—222no—
382C8—442no—
383C22—21no—
384C22—21no—
385C22—222no—
386C22—441no—
387C22—441no—
388C22#1062242612yes—
389C22C2×#6693711yescharacteristic
390C4—21no—
391C4—21no—
392C4—82no—
393C4—222no—
394C4—441no—
395C4—441no—
396C4—882no—
397C4#1062236112yes—
398C4#1062242612yes—
399C4C2×#6696911yescharacteristic
400C4C2×Q16×D1111yescharacteristic
401C4#1062330812yes—
402C2—22no—
403C2—442no—
404C2#1307811311yescharacteristic
405C2C2×#1062242611yescharacteristic
406C2C2×#1062236111yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1548C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#1548D11
hypocenterC11#19277
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
1. C2×#10622706C2semidirect
5. #13068077C2semidirect
6. #13068070C2semidirect
7. #13067374C2semidirect
8. #13067300C2semidirect
9. C11×#1548C2semidirect
152. #1548D11semidirect
346. C11#19277semidirect

Maximal subgroups

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

subgroupindex
C2×#106227062
#130784322
#130784252
#130775722
#130680772
#130680702
#130673742
#130673002
C11×#15482
#1927711