Finite Group Databasebeta

← #14737674

Subgroups — #14737674

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622705C211yesmaximal, characteristic, complemented
2#13078432C211yesmaximal, characteristic
3#13078425C211yesmaximal, characteristic
4#13077572C211yesmaximal, characteristic
5#13067985C214yesmaximal, complemented
6#13067980C214yesmaximal, complemented
7#13067374C211yesmaximal, characteristic, complemented
8#13067300C211yesmaximal, characteristic, complemented
9C11×#1549C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C22×#4326—22no—
12C4×#4339C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16#10622746—21no—
17#10622734—21no—
18#10622707C2212yes—
19#10622705—21no—
20#10622705—21no—
21#10622705C2214yes—
22#10622704—21no—
23#10622700C2212yes—
24#10622697—21no—
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×#332C2214yes—
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
52C2×#4326—24no—
53C2×#4326—24no—
54C2×#4326—48no—
55C4×C22⋊D11—21no—
56C4×C22⋊D11—21no—
57#66979D411yescharacteristic
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×#4318—21no—
61C22×C11⋊C8D412yes—
62C2×C8×D11—22no—
63C4×D44D411yescharacteristic
64C4×D44C2311yescharacteristic
65#66925—21no—
66C42×D11—21no—
67#66922—21no—
68#66922—21no—
69#66922—21no—
70#66922C2312yes—
71C4×Dic22D411yescharacteristic
72C4×Dic22C2311yescharacteristic
73C11×C4⋊C8—21no—
74C11×C4⋊C8C2312yes—
75C11×C4⋊C8C2312yes—
76C11×C22⋊C8—21no—
77C4×C8×C11—21no—
78#66885—22no—
79(C2×D11)⋊C8—22no—
80#66882—22no—
81#66881—22no—
82#66880—22no—
83Dic11⋊C8—22no—
84C8×Dic11—22no—
85#66874—22no—
86#66873—22no—
87#66872—22no—
88#66871—22no—
89C4⋊(C11⋊C8)—21no—
90C4⋊(C11⋊C8)C2312yes—
91C4×C11⋊C8D411yescharacteristic
92C4×C11⋊C8D411yescharacteristic
93C4×C11⋊C8C2312yes—
94#19268—111nomaximal, Sylow
95C2×Q8×C11—22no—
96C2×Q8×C11—44no—
97C2×Q8×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C2×C22⋊D11—21no—
103C22×Dic11—41no—
104#4339—22no—
105#4339Q1614yescomplemented
106C2×D44C2×D411yescharacteristic
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×Dic22—22no—
111C2×Dic22—44no—
112C2×Dic22—41no—
113C2×Dic22C2×D411yescharacteristic
114C11×M16—42no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11C2411yescharacteristic
125C22⋊Dic11—21no—
126#4326—48no—
127#4326—48no—
128(C2×D11)⋊C4—21no—
129(C2×D11)⋊C4—21no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134C4⋊Dic11C2×D411yescharacteristic
135C4⋊Dic11C2×D411yescharacteristic
136Dic11⋊C4—21no—
137Dic11⋊C4—21no—
138C4×Dic11—21no—
139C4×Dic11—21no—
140C4×Dic11—21no—
141#4318—42no—
142C2×C11⋊C8—24no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8C2×D412yes—
145C2×C11⋊C8C2×D412yes—
146C8×D11—44no—
147C2×#494—111no—
148#3079—111no—
149#3079—111no—
150C8×#41—111no—
151#1670—114no—
152#1669—114no—
153#1567—111no—
154#1549—111no—
155#1549D1111yescharacteristic, complemented
156C23×C11#12111yescharacteristic
157C22×D11—21no—
158Q8×C11—44no—
159Q8×C11—82no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11C2×Q1612yes—
168C2×C4×C11#13512yes—
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C22×D411yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172C22⋊D11—24no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—42no—
177C2×Dic11—82no—
178D44—21no—
179D44C2×Q1612yescomplemented
180C4×D11—24no—
181C4×D11—42no—
182C4×D11—42no—
183Dic22—21no—
184Dic22—44no—
185Dic22—82no—
186Dic22C2×Q1612yescomplemented
187C8×C11—42no—
188C8×C11—42no—
189C11⋊C8—22no—
190C11⋊C8—42no—
191C11⋊C8AGL(1,ℤ/8)14yes—
192C22×Q16—222no—
193C2×C4⋊Q8—111no—
194C2×C4⋊Q8C2×D1111yescharacteristic
195C4×#41—111no—
196#494—114no—
197#494—221no—
198#494—221no—
199#477—221no—
200#477—221no—
201#476—221no—
202#476—221no—
203#475—112no—
204#475—112no—
205#474—112no—
206#474—112no—
207C8×Q8—112no—
208C8×D4—112no—
209C8×D4—222no—
210#431—221no—
211#431C2×D1111yescharacteristic
212#428—221no—
213#428—221no—
214#423—111no—
215#423C2×D1111yescharacteristic
216#417—221no—
217#417—221no—
218C2×C4×C8—111no—
219C2×C4×C8—221no—
220#335—114no—
221#332—114no—
222#332C2×D1114yes—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11#46712yes—
226C22×C11C2×#12111yescharacteristic
227C2×D11—22no—
228C2×D11—41no—
229C2×D11—41no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—82no—
233C4×C11#46712yes—
234C4×C11#47312yes—
235C4×C11C22×Q1611yescharacteristic
236C4×C11C2×#13511yescharacteristic
237C4×C11C2×AGL(1,ℤ/8)12yes—
238Dic11—22no—
239Dic11—41no—
240Dic11—41no—
241Dic11—82no—
242C2×#41—111no—
243C22×Q8—21no—
244C22×Q8—221no—
245C2×Q16—224no—
246C2×Q16—224no—
247C2×Q16—448no—
248C2×M16—21no—
249C2×M16—221no—
250C22×C8—112no—
251C22×C8—222no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—112no—
256C4⋊Q8—221no—
257C4⋊Q8—221no—
258C4⋊Q8—221no—
259C4⋊Q8C22×D1112yes—
260C4×Q8—111no—
261C4×Q8—111no—
262C4×D4—111no—
263C4×D4—111no—
264C4×D4—221no—
265C4×D4—221no—
266#117—111no—
267#117—221no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C42—221no—
273C2×C42C22×D1111yescharacteristic
274#107—222no—
275#107—222no—
276#106—222no—
277#106—222no—
278C4⋊C8—21no—
279C4⋊C8—112no—
280C4⋊C8—222no—
281C4⋊C8—221no—
282C4⋊C8C22×D1112yes—
283C4⋊C8C22×D1112yes—
284#103—222no—
285#103—222no—
286#102—222no—
287#102—222no—
288C22⋊C8—21no—
289C22⋊C8—222no—
290C4×C8—21no—
291C4×C8—111no—
292C4×C8—111no—
293C4×C8—112no—
294C4×C8—222no—
295C2×C11—22no—
296C2×C11#303811yescharacteristic
297C2×C11C2×#46711yescharacteristic
298C2×C11C2×#47311yescharacteristic
299D11—42no—
300#41—114no—
301#41—222no—
302C2×Q8—22no—
303C2×Q8—44no—
304C2×Q8—41no—
305C2×Q8—111no—
306C2×Q8—222no—
307C2×Q8—444no—
308C2×Q8—441no—
309C2×D4—111no—
310C2×D4—221no—
311C22×C4—41no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—441no—
316C22×C4#433911yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4D4×D1111yescharacteristic
319Q16—448no—
320Q16—448no—
321M16—42no—
322M16—442no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—112no—
326C2×C8—112no—
327C2×C8—224no—
328C2×C8—222no—
329C2×C8—444no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—111no—
335C4⋊C4—111no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C4⋊C4—222no—
339C4⋊C4—222no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C22⋊C4—221no—
343C22⋊C4—221no—
344C22⋊C4—221no—
345C42—221no—
346C42—221no—
347C42—221no—
348C42#433911yescharacteristic
349C42D4×D1111yescharacteristic
350C42D4×D1111yescharacteristic
351C42C23×D1111yescharacteristic
352C11#1926811yescharacteristic, complemented, Sylow
353C23—221no—
354C23#6693711yescharacteristic
355Q8—44no—
356Q8—82no—
357Q8—112no—
358Q8—221no—
359Q8—444no—
360Q8—882no—
361D4—112no—
362D4—224no—
363D4—221no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—82no—
368C2×C4—221no—
369C2×C4—224no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4—442no—
375C2×C4—882no—
376C2×C4#6693711yescharacteristic
377C2×C4#6693711yescharacteristic
378C2×C4#6693711yescharacteristic
379C2×C4#6696912yes—
380C2×C4Q16×D1112yes—
381C2×C4C2×#433911yescharacteristic
382C2×C4C2×D4×D1111yescharacteristic
383C2×C4C2×D4×D1111yescharacteristic
384C8—42no—
385C8—42no—
386C8—114no—
387C8—222no—
388C8—442no—
389C22—21no—
390C22—21no—
391C22—222no—
392C22—441no—
393C22—441no—
394C22#1062242612yes—
395C22C2×#6693711yescharacteristic
396C4—21no—
397C4—21no—
398C4—82no—
399C4—222no—
400C4—441no—
401C4—441no—
402C4—882no—
403C4#1062236812yes—
404C4#1062242612yes—
405C4C2×#6696911yescharacteristic
406C4C2×Q16×D1111yescharacteristic
407C4D11×AGL(1,ℤ/8)12yes—
408C2—22no—
409C2—442no—
410C2#1307809511yescharacteristic
411C2C2×#1062242611yescharacteristic
412C2C2×#1062236811yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1549C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#1549D11
hypocenterC11#19268
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
1. C2×#10622705C2semidirect
5. #13067985C2semidirect
6. #13067980C2semidirect
7. #13067374C2semidirect
8. #13067300C2semidirect
9. C11×#1549C2semidirect
105. #4339Q16semidirect
155. #1549D11semidirect
179. D44C2×Q16semidirect
186. Dic22C2×Q16semidirect
352. C11#19268semidirect

Maximal subgroups

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

subgroupindex
C2×#106227052
#130784322
#130784252
#130775722
#130679852
#130679802
#130673742
#130673002
C11×#15492
#1926811