Finite Group Databasebeta

← #14737694

Subgroups — #14737694

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622293C211yesmaximal, characteristic, complemented
2#13078432C211yesmaximal, characteristic
3#13078104C211yesmaximal, characteristic
4C8×#4339C211yesmaximal, characteristic
5#13067999C214yesmaximal, complemented
6#13067992C214yesmaximal, complemented
7#13067298C211yesmaximal, characteristic, complemented
8#13067289C211yesmaximal, characteristic, complemented
9C11×#1566C211yesmaximal, characteristic, complemented
10C2×#66962—21no—
11C4×#4339C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#423C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17#10622746—21no—
18#10622734—21no—
19#10622733—21no—
20C8×C22⋊D11—22no—
21C2×#66881—22no—
22#10622538C2211yescharacteristic
23#10622464—21no—
24#10622463C2212yes—
25#10622462—21no—
26#10622462C2212yes—
27#10622459—21no—
28#10622455C2212yes—
29#10622454—21no—
30#10622454C2212yes—
31C8×D44C2212yes—
32#10622298—21no—
33C4×C8×D11—21no—
34#10622293—21no—
35#10622293—21no—
36#10622293C2214yes—
37C8×Dic22C2212yes—
38C11×#334C2214yes—
39#10622120C2214yes—
40#10622119C2214yes—
41C2×#4339D411yescharacteristic
42C22×Dic22—21no—
43C22×Dic22—21no—
44C2×C11×M16—21no—
45C2×C11×M16—21no—
46C22×C8×C11D412yes—
47C2×C42×C11C2311yescharacteristic
48C4×C22⋊D11—21no—
49C4×C22⋊D11—21no—
50#66979D411yescharacteristic
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55#66962—44no—
56C2×Dic44—22no—
57C2×#4314—22no—
58C2×C8×D11—22no—
59C4×D44D411yescharacteristic
60C4×D44C2311yescharacteristic
61#66925—21no—
62C42×D11—21no—
63#66922—21no—
64#66922—21no—
65#66922—21no—
66#66922—21no—
67#66922—21no—
68#66922—21no—
69#66922C2312yes—
70#66922C2312yes—
71C4×Dic22D411yescharacteristic
72C4×Dic22C2311yescharacteristic
73C11×C4⋊C8—21no—
74C11×C4⋊C8—21no—
75C11×C4⋊C8C2312yes—
76C11×C4⋊C8C2312yes—
77C4×C8×C11D411yescharacteristic
78C4×C8×C11D411yescharacteristic
79C4×C8×C11C2312yes—
80C22⋊(C11⋊C8)—21no—
81#66885—22no—
82(C2×D11)⋊C8—22no—
83#66882—22no—
84#66881—24no—
85#66881—24no—
86#66881—22no—
87#66880—22no—
88#66880—22no—
89#66880—22no—
90Dic11⋊C8—22no—
91C8×Dic11—22no—
92C4⋊(C11⋊C8)C2312yes—
93C4×C11⋊C8—21no—
94#19270—111nomaximal, Sylow
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C2×C22⋊D11—21no—
99C22×Dic11—41no—
100C22×Dic11—41no—
101#4339—22no—
102#4339SD1614yes—
103C2×D44C2×D411yescharacteristic
104C2×C4×D11—21no—
105C2×C4×D11—21no—
106C2×C4×D11—21no—
107C2×Dic22—22no—
108C2×Dic22—22no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×Dic22—42no—
112C2×Dic22—42no—
113C2×Dic22—82no—
114C2×Dic22C2×D411yescharacteristic
115C11×M16—42no—
116C11×M16—42no—
117C2×C8×C11—24no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11C2×D412yes—
121C2×C8×C11C2×D412yes—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125C42×C11C2411yescharacteristic
126C22⋊Dic11—21no—
127(C2×D11)⋊C4—21no—
128(C2×D11)⋊C4—21no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135C4⋊Dic11—41no—
136C4⋊Dic11—41no—
137C4⋊Dic11C2×D411yescharacteristic
138C4⋊Dic11C2×D411yescharacteristic
139Dic11⋊C4—21no—
140Dic11⋊C4—21no—
141C4×Dic11—21no—
142C4×Dic11—21no—
143C4×Dic11—21no—
144C2×C11⋊C8—22no—
145Dic44—44no—
146#4314—44no—
147C8×D11—44no—
148C2×#498—111no—
149#3079—111no—
150#3039—111no—
151C8×#41—111no—
152#1672—114no—
153#1671—114no—
154#1566D1111yescharacteristic, complemented
155#1548—111no—
156#1546—111no—
157C23×C11#12111yescharacteristic
158C22×D11—21no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11C2×SD1612yes—
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—42no—
175C2×Dic11—82no—
176C2×Dic11—82no—
177D44—21no—
178D44C2×SD1612yes—
179C4×D11—24no—
180C4×D11—42no—
181C4×D11—42no—
182Dic22—21no—
183Dic22—42no—
184Dic22—42no—
185Dic22—82no—
186Dic22—82no—
187Dic22—82no—
188Dic22C2×SD1612yes—
189C8×C11—22no—
190C8×C11—42no—
191C8×C11—42no—
192C8×C11#13714yescomplemented
193C11⋊C8—42no—
194C2×#137—221no—
195C2×C4⋊Q8—111no—
196C2×C4⋊Q8—111no—
197C4×#41—111no—
198#498—114no—
199#498—221no—
200#498—221no—
201#477—112no—
202#476—112no—
203#475—221no—
204#474—221no—
205#462—112no—
206#462—221no—
207#461—112no—
208#461—221no—
209C8×Q8—112no—
210C8×D4—112no—
211C8×D4—222no—
212#431—111no—
213#431—221no—
214#428—221no—
215C2×#106—222no—
216#423C2×D1111yescharacteristic
217#423C2×D1111yescharacteristic
218#419—221no—
219#417—221no—
220C2×C4×C8—221no—
221C2×C4×C8C2×D1111yescharacteristic
222#334C2×D1114yes—
223#333—114no—
224#332—114no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11#46512yes—
228C22×C11C2×#12111yescharacteristic
229C2×D11—22no—
230C2×D11—41no—
231C2×D11—41no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11#46512yes—
235C4×C11#47112yes—
236C4×C11C22×SD1611yescharacteristic
237C4×C11C2×#13511yescharacteristic
238C4×C11C2×#13712yes—
239Dic11—22no—
240Dic11—41no—
241Dic11—41no—
242Dic11—82no—
243Dic11—82no—
244C2×#41—111no—
245C22×Q8—221no—
246C22×Q8—221no—
247#137—444no—
248C2×Q16—222no—
249C2×SD16—222no—
250C2×M16—21no—
251C2×M16—21no—
252C22×C8—222no—
253C22×C8D4412yes—
254C4⋊Q8—112no—
255C4⋊Q8—112no—
256C4⋊Q8—221no—
257C4⋊Q8—221no—
258C4⋊Q8—221no—
259C4⋊Q8—221no—
260C4⋊Q8—221no—
261C4⋊Q8—221no—
262C4×Q8—111no—
263C4×Q8—111no—
264C4×D4—111no—
265C4×D4—111no—
266C4×D4—221no—
267C4×D4—221no—
268#117—111no—
269#117—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C42—221no—
275C2×C42C22×D1111yescharacteristic
276#107—222no—
277#106—222no—
278#106—224no—
279#106—224no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—112no—
283C4⋊C8—222no—
284C4⋊C8C22×D1112yes—
285C4⋊C8C22×D1112yes—
286#103—222no—
287#103—222no—
288#103—222no—
289#102—222no—
290C22⋊C8—221no—
291C22⋊C8—222no—
292C4×C8—222no—
293C4×C8—221no—
294C4×C8D4411yescharacteristic
295C4×C8D4411yescharacteristic
296C4×C8C22×D1112yes—
297C2×C11—22no—
298C2×C11#303911yescharacteristic
299C2×C11C2×#46511yescharacteristic
300C2×C11C2×#47111yescharacteristic
301D11—42no—
302#41—114no—
303#41—222no—
304C2×Q8—111no—
305C2×Q8—222no—
306C2×Q8—222no—
307C2×Q8—441no—
308C2×Q8—441no—
309C2×Q8—442no—
310C2×Q8—442no—
311C2×Q8—882no—
312C2×D4—111no—
313C2×D4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—441no—
318C22×C4—441no—
319C22×C4C2×D4411yescharacteristic
320C22×C4D4×D1111yescharacteristic
321C22×C4#434311yescharacteristic
322Q16—444no—
323SD16—444no—
324M16—42no—
325M16—42no—
326C2×C8—24no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—222no—
330C2×C8—444no—
331C2×C8C2×D4412yes—
332C2×C8C2×D4412yes—
333C4⋊C4—111no—
334C4⋊C4—111no—
335C4⋊C4—221no—
336C4⋊C4—221no—
337C4⋊C4—222no—
338C4⋊C4—222no—
339C4⋊C4—222no—
340C4⋊C4—222no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C22⋊C4—221no—
346C22⋊C4—221no—
347C22⋊C4—221no—
348C42—221no—
349C42—221no—
350C42—221no—
351C42C2×D4411yescharacteristic
352C42D4×D1111yescharacteristic
353C42#434311yescharacteristic
354C42C23×D1111yescharacteristic
355C11#1927011yescharacteristic, complemented, Sylow
356C23—221no—
357C23#6694811yescharacteristic
358Q8—112no—
359Q8—221no—
360Q8—442no—
361Q8—442no—
362Q8—882no—
363Q8—882no—
364Q8—882no—
365D4—112no—
366D4—224no—
367D4—221no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—221no—
371C2×C4—224no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—882no—
379C2×C4—882no—
380C2×C4#6694811yescharacteristic
381C2×C4#6694811yescharacteristic
382C2×C4#6694811yescharacteristic
383C2×C4SD16×D1112yes—
384C2×C4#6696912yes—
385C2×C4C22×D4411yescharacteristic
386C2×C4C2×D4×D1111yescharacteristic
387C2×C4C2×#434311yescharacteristic
388C8—22no—
389C8—42no—
390C8—42no—
391C8—442no—
392C8#6696214yescomplemented
393C22—21no—
394C22—21no—
395C22—222no—
396C22—441no—
397C22—441no—
398C22#1062247712yes—
399C22C2×#6694811yescharacteristic
400C4—21no—
401C4—21no—
402C4—222no—
403C4—441no—
404C4—441no—
405C4—882no—
406C4—882no—
407C4#1062247712yes—
408C4#1062251112yes—
409C4C2×#6696212yes—
410C4C2×SD16×D1111yescharacteristic
411C4C2×#6696911yescharacteristic
412C2—22no—
413C2—442no—
414C2#1307810411yescharacteristic
415C2C2×#1062247711yescharacteristic
416C2C2×#1062251111yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1566C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#1566D11
hypocenterC11#19270
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
1. C2×#10622293C2semidirect
5. #13067999C2semidirect
6. #13067992C2semidirect
7. #13067298C2semidirect
8. #13067289C2semidirect
9. C11×#1566C2semidirect
154. #1566D11semidirect
192. C8×C11#137semidirect
355. C11#19270semidirect
392. C8#66962semidirect

Maximal subgroups

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

subgroupindex
C2×#106222932
#130784322
#130781042
C8×#43392
#130679992
#130679922
#130672982
#130672892
C11×#15662
#1927011