Finite Group Databasebeta

← #14739014

Subgroups — #14739014

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078409C211yesmaximal, characteristic
2C2×#10622697C211yesmaximal, characteristic
3#13077639C211yesmaximal, characteristic
4#13068064C214yesmaximal, complemented
5#13068012C214yesmaximal, complemented
6#13067391C211yesmaximal, characteristic, complemented
7#13067297C211yesmaximal, characteristic, complemented
8#13067273C211yesmaximal, characteristic, complemented
9C11×#3230C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×D44C2211yescharacteristic
13C11×#500C2212yescomplemented
14C11×#487C2212yescomplemented
15C11×#484—22no—
16C11×#477—22no—
17C11×#431C2211yescharacteristic
18#10622700C2212yes—
19#10622697—22no—
20#10622697C2214yes—
21#10622697C2212yes—
22#10622679—22no—
23#10622614—21no—
24#10622608—21no—
25C2×#66873—21no—
26C2×#66872—21no—
27#10622538C2211yescharacteristic
28#10622537C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622447—22no—
31D11×C22⋊C8—22no—
32C8×D44C2214yes—
33#10622185C2212yescomplemented
34#10622184C2212yescomplemented
35#10622184C2214yescomplemented
36#10622096C2214yescomplemented
37C22×Q8×C11—21no—
38C22×D44D411yescharacteristic
39C22×C4×D11—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8C2311yescharacteristic
44C11×C4⋊Q8C2312yes—
45C11×C4⋊Q8C2311yescharacteristic
46C11×#125—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C11×#117—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—21no—
56C2×C4⋊Dic11D411yescharacteristic
57C2×#4318—21no—
58C22×C11⋊C8—21no—
59C2×C8×D11—24no—
60C4×D44—21no—
61C4×D44—21no—
62C4×D44D412yes—
63C4×D44C2312yes—
64C11×#107—24no—
65C11×C4⋊C8D412yes—
66C11×#103—24no—
67C11×C22⋊C8D412yes—
68C4×C8×C11C2312yes—
69C22⋊(C11⋊C8)—21no—
70(C2×D11)⋊C8—24no—
71#66873—24no—
72#66873—22no—
73#66873—22no—
74#66872—24no—
75#66872—22no—
76#66871—22no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)C2312yes—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83#19393—111nomaximal, Sylow
84C23×D11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—22no—
88C2×Q8×C11—41no—
89C2×Q8×C11—82no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—21no—
95C2×D44—21no—
96C2×D44—22no—
97C2×D44Q1614yes—
98C2×D44C2×D412yes—
99C2×C4×D11—22no—
100C2×C4×D11—22no—
101C2×C4×D11—82no—
102C2×C8×C11C2×D414yes—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C42×C11C2411yescharacteristic
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11C2×D412yes—
123#4318—42no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—42no—
128C8×D11—84no—
129#3230D1111yescharacteristic, complemented
130#3077—111no—
131C2×#476—111no—
132#2972—111no—
133#1683—114no—
134#1675—114no—
135#1571—111no—
136#1548—111no—
137#1542—111no—
138C23×C11#12111yescharacteristic
139C22×D11—22no—
140C22×D11—24no—
141C22×D11—81no—
142C22×D11—81no—
143Q8×C11—42no—
144Q8×C11—81no—
145Q8×C11—82no—
146Q8×C11—82no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—82no—
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11C2×Q1612yes—
157C2×C4×C11#13512yes—
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C2×Dic11—22no—
162C2×Dic11—81no—
163D44—22no—
164D44—24no—
165D44C2×Q1614yes—
166C4×D11—44no—
167C4×D11—82no—
168C8×C11—24no—
169C11⋊C8—42no—
170C11⋊C8—42no—
171C11⋊C8—42no—
172#533C2×D1111yescharacteristic
173C2×C4⋊Q8C2×D1111yescharacteristic
174C2×C4×D4—111no—
175#500C2×D1112yescomplemented
176#487C2×D1112yescomplemented
177#484—22no—
178#478—222no—
179#477—22no—
180#476—112no—
181#476—114no—
182#476—222no—
183#474—112no—
184C8×D4—114no—
185C8×D4—222no—
186#431—111no—
187#431C2×D1111yescharacteristic
188#428—221no—
189C2×#106—221no—
190#423—111no—
191C2×C4⋊C8—111no—
192#418—221no—
193C2×#102—221no—
194C2×C22⋊C8—222no—
195#335—114no—
196#333—112no—
197#333—114no—
198#332—112no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11#46712yes—
202C22×C11C2×#12111yescharacteristic
203C2×D11—24no—
204C2×D11—42no—
205C2×D11—42no—
206C2×D11—84no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—81no—
211C4×C11—82no—
212C4×C11—81no—
213C4×C11#46712yes—
214C4×C11C22×Q1611yescharacteristic
215C4×C11C2×#13511yescharacteristic
216C4×C11#57712yes—
217Dic11—42no—
218C22×Q8—21no—
219C22×D4—111no—
220C23×C4—221no—
221C2×M16—221no—
222C22×C8—221no—
223C22×C8—224no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8C22×D1112yes—
228C4⋊Q8C22×D1111yescharacteristic
229C4⋊Q8C22×D1111yescharacteristic
230#125—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—112no—
236C4×D4—112no—
237C4×D4—221no—
238C4×D4—221no—
239#117—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—111no—
243C2×C22⋊C4—221no—
244C2×C42C22×D1111yescharacteristic
245#107—24no—
246#107—222no—
247#106—224no—
248#106—222no—
249C4⋊C8—112no—
250C4⋊C8—112no—
251C4⋊C8—112no—
252C4⋊C8—221no—
253C4⋊C8—221no—
254C4⋊C8C22⋊D1112yes—
255#103—24no—
256#102—224no—
257#102—222no—
258#102—222no—
259C22⋊C8—221no—
260C22⋊C8—224no—
261C22⋊C8C22⋊D1112yes—
262C4×C8—221no—
263C4×C8C22×D1112yes—
264C2×C11—22no—
265C2×C11#304211yescharacteristic
266C2×C11C2×#46711yescharacteristic
267C2×C11#306811yescharacteristic
268D11—44no—
269C24—221no—
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—82no—
275C2×D4—114no—
276C2×D4—112no—
277C2×D4—222no—
278C2×D4—221no—
279C22×C4—41no—
280C22×C4—221no—
281C22×C4—222no—
282C22×C4—222no—
283C22×C4—882no—
284C22×C4D4×D1111yescharacteristic
285C22×C4#434111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287M16—442no—
288C2×C8—222no—
289C2×C8—222no—
290C2×C8—222no—
291C2×C8—442no—
292C2×C8—884no—
293C2×C8C2×C22⋊D1114yes—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—112no—
305C4⋊C4—221no—
306C22⋊C4—41no—
307C22⋊C4—222no—
308C22⋊C4—222no—
309C42—41no—
310C42D4×D1111yescharacteristic
311C42#434111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C42C23×D1111yescharacteristic
314C11#1939311yescharacteristic, complemented, Sylow
315C23—222no—
316C23—224no—
317C23—881no—
318C23—881no—
319C23#6699111yescharacteristic
320Q8—42no—
321Q8—81no—
322Q8—82no—
323Q8—82no—
324D4—114no—
325D4—222no—
326D4—224no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—222no—
334C2×C4—444no—
335C2×C4—882no—
336C2×C4—881no—
337C2×C4Q16×D1112yes—
338C2×C4#6697212yes—
339C2×C4#6699111yescharacteristic
340C2×C4#6699111yescharacteristic
341C2×C4#6699111yescharacteristic
342C2×C4C2×D4×D1111yescharacteristic
343C2×C4C2×#434111yescharacteristic
344C2×C4C22×C22⋊D1111yescharacteristic
345C8—24no—
346C8—442no—
347C8—442no—
348C8—442no—
349C22—21no—
350C22—21no—
351C22—224no—
352C22—442no—
353C22—442no—
354C22—884no—
355C22#1062280112yes—
356C22C2×#6699111yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—81no—
362C4—81no—
363C4—442no—
364C4#1062280112yes—
365C4C2×Q16×D1111yescharacteristic
366C4C2×#6697211yescharacteristic
367C4#1062336812yes—
368C2—22no—
369C2—444no—
370C2#1307812411yescharacteristic
371C2C2×#1062280111yescharacteristic
372C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3230C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#3230D11
hypocenterC11#19393
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
4. #13068064C2semidirect
5. #13068012C2semidirect
6. #13067391C2semidirect
7. #13067297C2semidirect
8. #13067273C2semidirect
9. C11×#3230C2semidirect
13. C11×#500C22semidirect
14. C11×#487C22semidirect
33. #10622185C22semidirect
34. #10622184C22semidirect
35. #10622184C22semidirect
36. #10622096C22semidirect
129. #3230D11semidirect
175. #500C2×D11semidirect
176. #487C2×D11semidirect
314. C11#19393semidirect

Maximal subgroups

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

subgroupindex
#130784092
C2×#106226972
#130776392
#130680642
#130680122
#130673912
#130672972
#130672732
C11×#32302
#1939311