Finite Group Databasebeta

← #14737696

Subgroups — #14737696

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×#10622692C211yesmaximal, characteristic, complemented
2#13078425C211yesmaximal, characteristic
3#13078104C211yesmaximal, characteristic
4#13077572C211yesmaximal, characteristic
5#13068001C214yesmaximal, complemented
6#13067994C214yesmaximal, complemented
7#13067371C211yesmaximal, characteristic, complemented
8#13067287C211yesmaximal, characteristic, complemented
9C11×#1548C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66962—21no—
12C4×#4339C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16#10622733—21no—
17#10622707—21no—
18#10622704C2212yes—
19#10622700—21no—
20#10622697C2212yes—
21#10622692—21no—
22#10622692—21no—
23#10622692C2214yes—
24#10622579—21no—
25#10622577—21no—
26C2×#66872—22no—
27#10622537C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622462—21no—
30#10622462C2212yes—
31#10622454—21no—
32#10622454C2212yes—
33#10622447C2212yes—
34#10622443C2212yes—
35(C22⋊D11)⋊C8—22no—
36#10622298—21no—
37C4×C8×D11—21no—
38C11×#333C2214yes—
39#10622124C2214yes—
40#10622118C2214yes—
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—
59#66962—44no—
60C2×Dic44—22no—
61C2×#4314—22no—
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(C2×D11)⋊C8—22no—
79#66880—22no—
80#66880—22no—
81Dic11⋊C8—22no—
82C8×Dic11—22no—
83#66874—22no—
84#66873—22no—
85#66872—22no—
86#66872—24no—
87#66872—24no—
88#66871—22no—
89C4⋊(C11⋊C8)—21no—
90C4⋊(C11⋊C8)C2312yes—
91C4×C11⋊C8D411yescharacteristic
92C4×C11⋊C8D411yescharacteristic
93C4×C11⋊C8C2312yes—
94#19270—111nomaximal, Sylow
95C2×Q8×C11—22no—
96C2×Q8×C11—41no—
97C2×Q8×C11—82no—
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#4339SD1614yes—
106C2×D44C2×D411yescharacteristic
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×Dic22—22no—
111C2×Dic22—41no—
112C2×Dic22—42no—
113C2×Dic22—42no—
114C2×Dic22C2×D411yescharacteristic
115C11×M16—42no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
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—41no—
132C4⋊Dic11—41no—
133C4⋊Dic11C2×D411yescharacteristic
134C4⋊Dic11C2×D411yescharacteristic
135Dic11⋊C4—21no—
136Dic11⋊C4—21no—
137C4×Dic11—21no—
138C4×Dic11—21no—
139C4×Dic11—21no—
140#4318—42no—
141C2×C11⋊C8—24no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8C2×D412yes—
144C2×C11⋊C8C2×D412yes—
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#1566—111no—
155#1548D1111yescharacteristic, complemented
156#1546—111no—
157C23×C11#12111yescharacteristic
158C22×D11—21no—
159Q8×C11—82no—
160Q8×C11—82no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—42no—
164C2×C4×C11—82no—
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11C2×SD1612yes—
169C2×C4×C11#13512yes—
170C2×C4×C11C22×D411yescharacteristic
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C2×#4111yescharacteristic
173C22⋊D11—24no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—42no—
178C2×Dic11—82no—
179D44—21no—
180D44C2×SD1612yes—
181C4×D11—24no—
182C4×D11—42no—
183C4×D11—42no—
184Dic22—21no—
185Dic22—42no—
186Dic22—42no—
187Dic22—82no—
188Dic22C2×SD1612yes—
189C8×C11—42no—
190C8×C11—42no—
191C11⋊C8—22no—
192C11⋊C8—42no—
193C11⋊C8#13714yescomplemented
194C2×#137—221no—
195C2×C4⋊Q8—111no—
196C2×C4⋊Q8C2×D1111yescharacteristic
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—221no—
213#431C2×D1111yescharacteristic
214#428—221no—
215C2×#106—222no—
216#423—111no—
217#423C2×D1111yescharacteristic
218#419—221no—
219#417—221no—
220C2×C4×C8—111no—
221C2×C4×C8—221no—
222#334—114no—
223#333C2×D1114yes—
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—82no—
235C4×C11#46512yes—
236C4×C11#47112yes—
237C4×C11C22×SD1611yescharacteristic
238C4×C11C2×#13511yescharacteristic
239C4×C11C2×#13712yes—
240Dic11—22no—
241Dic11—41no—
242Dic11—41no—
243Dic11—82no—
244C2×#41—111no—
245C22×Q8—21no—
246C22×Q8—221no—
247#137—444no—
248C2×Q16—222no—
249C2×SD16—222no—
250C2×M16—21no—
251C2×M16—221no—
252C22×C8—112no—
253C22×C8—222no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—112no—
258C4⋊Q8—221no—
259C4⋊Q8—221no—
260C4⋊Q8—221no—
261C4⋊Q8C22×D1112yes—
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—21no—
271C2×C4⋊C4—21no—
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—112no—
282C4⋊C8—222no—
283C4⋊C8—221no—
284C4⋊C8C22×D1112yes—
285C4⋊C8C22×D1112yes—
286#103—222no—
287#103—222no—
288#103—222no—
289#102—222no—
290C22⋊C8—21no—
291C22⋊C8—222no—
292C4×C8—21no—
293C4×C8—111no—
294C4×C8—111no—
295C4×C8—112no—
296C4×C8—222no—
297C2×C11—22no—
298C2×C11#303911yescharacteristic
299C2×C11C2×#46511yescharacteristic
300C2×C11C2×#47111yescharacteristic
301D11—42no—
302#41—114no—
303#41—222no—
304C2×Q8—22no—
305C2×Q8—41no—
306C2×Q8—82no—
307C2×Q8—111no—
308C2×Q8—222no—
309C2×Q8—441no—
310C2×Q8—442no—
311C2×Q8—442no—
312C2×D4—111no—
313C2×D4—221no—
314C22×C4—41no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—441no—
319C22×C4#433911yescharacteristic
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322Q16—444no—
323SD16—444no—
324M16—42no—
325M16—442no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—112no—
329C2×C8—112no—
330C2×C8—224no—
331C2×C8—222no—
332C2×C8—444no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—111no—
338C4⋊C4—111no—
339C4⋊C4—221no—
340C4⋊C4—221no—
341C4⋊C4—222no—
342C4⋊C4—222no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C22⋊C4—221no—
346C22⋊C4—221no—
347C22⋊C4—221no—
348C42—221no—
349C42—221no—
350C42—221no—
351C42#433911yescharacteristic
352C42D4×D1111yescharacteristic
353C42D4×D1111yescharacteristic
354C42C23×D1111yescharacteristic
355C11#1927011yescharacteristic, complemented, Sylow
356C23—221no—
357C23#6693711yescharacteristic
358Q8—82no—
359Q8—82no—
360Q8—112no—
361Q8—221no—
362Q8—442no—
363Q8—442no—
364Q8—882no—
365D4—112no—
366D4—224no—
367D4—221no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—42no—
371C2×C4—82no—
372C2×C4—221no—
373C2×C4—224no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—882no—
380C2×C4#6693711yescharacteristic
381C2×C4#6693711yescharacteristic
382C2×C4#6693711yescharacteristic
383C2×C4SD16×D1112yes—
384C2×C4#6697212yes—
385C2×C4C2×#433911yescharacteristic
386C2×C4C2×D4×D1111yescharacteristic
387C2×C4C2×D4×D1111yescharacteristic
388C8—42no—
389C8—42no—
390C8—114no—
391C8—222no—
392C8—442no—
393C22—21no—
394C22—21no—
395C22—222no—
396C22—441no—
397C22—441no—
398C22#1062242012yes—
399C22C2×#6693711yescharacteristic
400C4—21no—
401C4—21no—
402C4—82no—
403C4—222no—
404C4—441no—
405C4—441no—
406C4—882no—
407C4#1062236112yes—
408C4#1062242012yes—
409C4C2×SD16×D1111yescharacteristic
410C4C2×#6697211yescharacteristic
411C4D11×#13712yes—
412C2—22no—
413C2—442no—
414C2#1307810211yescharacteristic
415C2C2×#1062242011yescharacteristic
416C2C2×#1062236111yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1548C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#1548D11
hypocenterC11#19270
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×#10622692C2semidirect
5. #13068001C2semidirect
6. #13067994C2semidirect
7. #13067371C2semidirect
8. #13067287C2semidirect
9. C11×#1548C2semidirect
155. #1548D11semidirect
193. C11⋊C8#137semidirect
355. C11#19270semidirect

Maximal subgroups

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

subgroupindex
C2×#106226922
#130784252
#130781042
#130775722
#130680012
#130679942
#130673712
#130672872
C11×#15482
#1927011