Finite Group Databasebeta

← #14736921

Subgroups — #14736921

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079737C211yesmaximal, characteristic
2#13079543C211yesmaximal, characteristic
3C2×#10622694C211yesmaximal, characteristic, complemented
4#13077327C211yesmaximal, characteristic
5#13068162C214yesmaximal, complemented
6#13068038C214yesmaximal, complemented
7#13067362C211yesmaximal, characteristic, complemented
8#13067302C211yesmaximal, characteristic, complemented
9C11×#1546C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66960—21no—
12#10623008C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C2×#66899—21no—
17C2×#66899—21no—
18#10622742—21no—
19#10622701—21no—
20#10622700C2214yes—
21#10622694—21no—
22#10622694—21no—
23#10622694C2212yes—
24#10622694C2212yes—
25#10622691—21no—
26#10622580—22no—
27#10622538C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622454C2214yes—
30#10622451—21no—
31#10622451C2212yes—
32#10622447—21no—
33#10622447C2212yes—
34#10622351—22no—
35#10622306—21no—
36#10622294—21no—
37C11×#332C2214yes—
38#10622124C2214yes—
39#10622118C2212yes—
40#10622117C2212yes—
41C22×Q8×C11—21no—
42C2×#4339—21no—
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
52#66983—21no—
53#66983D412yes—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C22×C11⋊C8D411yescharacteristic
57C22×C11⋊C8D411yescharacteristic
58#66960—44no—
59C2×#4314—24no—
60C2×#4313—22no—
61C2×C8×D11—22no—
62#66928—21no—
63#66927D411yescharacteristic
64C4×D44—21no—
65C4×D44C2312yes—
66#66922—21no—
67#66922—21no—
68#66922—21no—
69#66922D411yescharacteristic
70#66922C2312yes—
71C11×C4⋊C8—21no—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C22⋊C8—21no—
75C4×C8×C11—21no—
76#66899—22no—
77#66899—22no—
78#66899—22no—
79#66899—22no—
80C22⋊(C11⋊C8)—21no—
81(C2×D11)⋊C8—22no—
82(C2×D11)⋊C8—22no—
83#66880—24no—
84#66873—24no—
85#66871—24no—
86C4⋊(C11⋊C8)C2312yes—
87C4×C11⋊C8—21no—
88C4×C11⋊C8D411yescharacteristic
89C4×C11⋊C8D411yescharacteristic
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92#19197—111nomaximal, Sylow
93C2×Q8×C11—22no—
94C2×Q8×C11—41no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C2×C22⋊D11—22no—
102C22×Dic11—41no—
103#4339—42no—
104#4339—42no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44C2×D412yes—
108C2×C4×D11—22no—
109C2×Dic22—21no—
110C2×Dic22—22no—
111C2×Dic22—41no—
112C2×Dic22—82no—
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
124(C2×D11)⋊C4—22no—
125(C2×D11)⋊C4—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131C4⋊Dic11C2×D412yes—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137C2×C11⋊C8C2×D411yescharacteristic
138C2×C11⋊C8C2×D411yescharacteristic
139#4314—84no—
140#4313—44no—
141C8×D11—44no—
142#3226—111no—
143#3206—111no—
144C2×#487—111no—
145#2931—111no—
146#1699—114no—
147#1679—114no—
148#1564—111no—
149#1549—111no—
150#1546D1111yescharacteristic, complemented
151C23×C11#12111yescharacteristic
152C22×D11—22no—
153Q8×C11—42no—
154Q8×C11—42no—
155Q8×C11—82no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—42no—
159C2×C4×C11—82no—
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#13512yes—
164C2×C4×C11AGL(1,ℤ/8)12yes—
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C22⋊D11—44no—
169C2×Dic11—22no—
170C2×Dic11—42no—
171C2×Dic11—82no—
172D44—24no—
173D44—42no—
174D44—42no—
175C4×D11—42no—
176C4×D11—42no—
177Dic22—42no—
178Dic22—44no—
179Dic22—82no—
180C8×C11—42no—
181C8×C11—42no—
182C11⋊C8—21no—
183C11⋊C8—21no—
184C11⋊C8—21no—
185C11⋊C8—21no—
186C11⋊C8—42no—
187C2×#131—221no—
188#532—111no—
189C2×C4⋊Q8—111no—
190C2×C4⋊Q8C2×D1111yescharacteristic
191#500—221no—
192#492—221no—
193#487—112no—
194#487—112no—
195#487—221no—
196#487—221no—
197#487—221no—
198#486—221no—
199#480—222no—
200#474—114no—
201#461—114no—
202#448—222no—
203#436—112no—
204#436—221no—
205C8×D4—112no—
206C8×D4—221no—
207#431—111no—
208#431C2×D1111yescharacteristic
209#423C2×D1111yescharacteristic
210C2×#103—221no—
211C2×#103—221no—
212#408—221no—
213C2×C4×C8—111no—
214#335—112no—
215#334—112no—
216#332—114no—
217#332C2×D1114yes—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11#46312yes—
221C22×C11C2×#12111yescharacteristic
222C2×D11—42no—
223C2×D11—42no—
224C2×D11—42no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—82no—
228C4×C11#46312yes—
229C4×C11#47312yes—
230C4×C11C2×#13511yescharacteristic
231C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
232C4×C11#57712yes—
233Dic11—42no—
234Dic11—82no—
235C2×#41—221no—
236C22×Q8—21no—
237C22×Q8—221no—
238C2×SD16—224no—
239#131—444no—
240C2×M16—21no—
241C2×M16—222no—
242C22×C8—111no—
243C22×C8—111no—
244C22×C8—222no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—111no—
249C4⋊Q8—112no—
250C4⋊Q8—221no—
251C4⋊Q8—221no—
252C4⋊Q8—221no—
253C4⋊Q8C22×D1112yes—
254#127—111no—
255#124—221no—
256#121—112no—
257#121—221no—
258C4×D4—112no—
259C4×D4—221no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C42C22×D1111yescharacteristic
265#107—224no—
266C4⋊C8—21no—
267C4⋊C8—112no—
268C4⋊C8C22×D1112yes—
269C4⋊C8C22×D1112yes—
270#103—224no—
271#103—222no—
272#103—222no—
273#103—222no—
274#103—222no—
275#102—224no—
276C22⋊C8—21no—
277C22⋊C8—222no—
278C22⋊C8—222no—
279C22⋊C8—221no—
280C4×C8—21no—
281C4×C8—111no—
282C4×C8—111no—
283C4×C8—111no—
284C4×C8—111no—
285C4×C8—221no—
286C2×C11—22no—
287C2×C11C2×#46311yescharacteristic
288C2×C11#305711yescharacteristic
289C2×C11C2×#47311yescharacteristic
290D11—82no—
291#41—442no—
292#41—442no—
293C2×Q8—22no—
294C2×Q8—41no—
295C2×Q8—42no—
296C2×Q8—42no—
297C2×Q8—221no—
298C2×Q8—222no—
299C2×Q8—441no—
300C2×Q8—882no—
301C2×D4—112no—
302C2×D4—222no—
303C2×D4—221no—
304C2×D4—221no—
305C22×C4—41no—
306C22×C4—222no—
307C22×C4—441no—
308C22×C4#433911yescharacteristic
309C22×C4D4×D1111yescharacteristic
310C22×C4D4×D1111yescharacteristic
311SD16—884no—
312M16—42no—
313M16—444no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—111no—
317C2×C8—111no—
318C2×C8—111no—
319C2×C8—111no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—444no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—112no—
329C4⋊C4—221no—
330C4⋊C4—222no—
331C4⋊C4—222no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C22⋊C4—222no—
335C22⋊C4—222no—
336C42#433911yescharacteristic
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C42C23×D1111yescharacteristic
340C11#1919711yescharacteristic, complemented, Sylow
341C23—222no—
342C23#6693711yescharacteristic
343Q8—42no—
344Q8—42no—
345Q8—82no—
346Q8—442no—
347Q8—444no—
348Q8—882no—
349D4—224no—
350D4—444no—
351D4—442no—
352D4—442no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—42no—
356C2×C4—82no—
357C2×C4—222no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—882no—
362C2×C4#6693711yescharacteristic
363C2×C4#6693711yescharacteristic
364C2×C4#6693711yescharacteristic
365C2×C4#6696412yes—
366C2×C4#6696912yes—
367C2×C4C2×#433911yescharacteristic
368C2×C4C2×D4×D1111yescharacteristic
369C2×C4C2×D4×D1111yescharacteristic
370C8—42no—
371C8—42no—
372C8—221no—
373C8—221no—
374C8—221no—
375C8—221no—
376C8—442no—
377C22—21no—
378C22—21no—
379C22—442no—
380C22—442no—
381C22—442no—
382C22#1062240012yes—
383C22C2×#6693711yescharacteristic
384C4—21no—
385C4—21no—
386C4—82no—
387C4—442no—
388C4—882no—
389C4#1062236812yes—
390C4#1062240012yes—
391C4C2×#6696411yescharacteristic
392C4C2×#6696911yescharacteristic
393C4#1062330912yes—
394C2—22no—
395C2—882no—
396C2C2×#1062240011yescharacteristic
397C2#1307825811yescharacteristic
398C2C2×#1062236811yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1546C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#1546D11
hypocenterC11#19197
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. C2×#10622694C2semidirect
5. #13068162C2semidirect
6. #13068038C2semidirect
7. #13067362C2semidirect
8. #13067302C2semidirect
9. C11×#1546C2semidirect
150. #1546D11semidirect
340. C11#19197semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130795432
C2×#106226942
#130773272
#130681622
#130680382
#130673622
#130673022
C11×#15462
#1919711