Finite Group Databasebeta

← #14757270

Subgroups — #14757270

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622577C211yesmaximal, characteristic
2C2×#10622715C211yesmaximal, characteristic
3#13071240C211yesmaximal, characteristic
4#13070973C211yesmaximal, characteristic
5#13069385C214yesmaximal, complemented
6#13069376C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic
8#13068333C211yesmaximal, characteristic
9C22×C11×#106C211yesmaximal, characteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C2×C11×#106—24no—
18C2×C11×#106C2214yes—
19#10622823—22no—
20C4×C22⋊Dic11—22no—
21#10622715C418yescomplemented
22C2×Dic11⋊C8C2214yes—
23#10622590C2212yes—
24#10622589C2212yes—
25C4⋊C4×Dic11—22no—
26C4⋊C4×Dic11C2214yes—
27#10622586—22no—
28#10622577—24no—
29C2×#66872C2212yes—
30C2×#66871C2212yes—
31#10622189C2212yes—
32#10622189C2212yes—
33#10622167C2214yes—
34C23×C4×C11—21no—
35C23×C4×C11—21no—
36C23×C4×C11C2311yescharacteristic
37C22×C8×C11—22no—
38C22×C8×C11—22no—
39C22×C8×C11C2×C414yes—
40C22×C8×C11C2312yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D414yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11D412yes—
52#66979—22no—
53#66979—22no—
54#66979—22no—
55#66979C2×C414yes—
56#66979Q814yes—
57#66979Q814yes—
58C2×C4⋊Dic11D412yes—
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2312yes—
62C2×Dic11⋊C4—24no—
63C2×C4×Dic11—21no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—24no—
66C2×C4×Dic11C2312yes—
67C2×#4318—22no—
68C2×#4318—22no—
69C2×#4318C2×C414yes—
70C22×C11⋊C8C2312yes—
71C11×#106—28no—
72C11⋊#95—24no—
73C11⋊#95—24no—
74Dic11⋊C8C2×C4116yescomplemented
75#66872—24no—
76#66871—24no—
77#21174—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C22×C4×C11—22no—
80C22×C4×C11—24no—
81C22×C4×C11—22no—
82C22×C4×C11—42no—
83C22×C4×C11—82no—
84C22×C4×C11—82no—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×Q812yes—
89C22×C4×C11C2×Q812yes—
90C22×C4×C11#4112yes—
91C22×C4×C11#4112yes—
92C22×C4×C11C2411yescharacteristic
93C22×Dic11—22no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11C2×D414yes—
97C2×C8×C11—28no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11C22×C414yes—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—42no—
106C11×C4⋊C4C2×D414yes—
107C22⋊Dic11—24no—
108C22⋊Dic11—42no—
109C22⋊Dic11C4⋊C418yes—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—22no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11C4⋊C418yes—
116C4⋊Dic11C2×Q814yes—
117Dic11⋊C4—84no—
118C4×Dic11—24no—
119C4×Dic11—42no—
120C4×Dic11—84no—
121C4×Dic11C22×C414yes—
122C4×Dic11C2×Q814yes—
123#4318—28no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8C22×C414yes—
127C2×#428—111no—
128C22×#106D1111yescharacteristic
129C2×#424—111no—
130#2317—111no—
131#2274—111no—
132#1949—114no—
133#1948—114no—
134#1736—111no—
135#1735—111no—
136C23×C11—22no—
137C23×C11—22no—
138C23×C11C2×C4⋊C412yes—
139C23×C11#12112yes—
140C23×C11C22⋊Q812yes—
141C23×C11C22×D411yescharacteristic
142C2×C4×C11—24no—
143C2×C4×C11—44no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
146C2×C4×C11—84no—
147C2×C4×C11—84no—
148C2×C4×C11C2×C4⋊C412yes—
149C2×C4×C11C4×D414yes—
150C2×C4×C11C4×Q814yes—
151C2×C4×C11#12112yes—
152C2×C4×C11C22⋊Q812yes—
153C2×C4×C11#12514yes—
154C2×C4×C11C4⋊Q814yes—
155C2×C4×C11C23×C411yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C22×Q811yescharacteristic
158C2×C4×C11C22×Q811yescharacteristic
159C2×C4×C11C2×#4111yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C2×Dic11—24no—
162C2×Dic11—24no—
163C2×Dic11—24no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11C2×C4⋊C418yes—
171C8×C11—24no—
172C11⋊C8—24no—
173C22×M16—111no—
174C23×C8C2×D1111yescharacteristic
175C2×#117—111no—
176C2×#117—111no—
177C2×#117—111no—
178C22×C4⋊C4C2×D1111yescharacteristic
179C22×C4⋊C4C2×D1111yescharacteristic
180#428—224no—
181C2×#107—112no—
182C2×#106—24no—
183C2×#106—112no—
184C2×#106C2×D1114yes—
185#424—118no—
186C2×C4⋊C8—114no—
187#389—222no—
188#385—222no—
189#384—112no—
190#382—112no—
191C4×C4⋊C4—114no—
192C4×C4⋊C4—222no—
193C4×C22⋊C4—222no—
194#340—112no—
195#340—112no—
196#340—114no—
197C22×C11—24no—
198C22×C11—24no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11#38914yes—
202C22×C11C22×C4⋊C411yescharacteristic
203C22×C11C2×#12111yescharacteristic
204C22×C11C2×C22⋊Q811yescharacteristic
205C22×C11#57712yes—
206C22×C11#57712yes—
207C4×C11—44no—
208C4×C11—82no—
209C4×C11#38914yes—
210C4×C11C2×C4×D411yescharacteristic
211C4×C11C2×C4×Q811yescharacteristic
212C4×C11C2×#12511yescharacteristic
213C4×C11C2×C4⋊Q811yescharacteristic
214Dic11—28no—
215Dic11—44no—
216Dic11—81no—
217Dic11—81no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4C22×D1111yescharacteristic
221C2×M16—114no—
222C2×M16—222no—
223C2×M16—222no—
224C22×C8—22no—
225C22×C8—22no—
226C22×C8—112no—
227C22×C8C4×D1114yes—
228C22×C8C22×D1112yes—
229#117—114no—
230#117—114no—
231#117—114no—
232#117—222no—
233#117—222no—
234#117—222no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—112no—
241C2×C4⋊C4—112no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—224no—
245C2×C4⋊C4C22⋊D1114yes—
246C2×C4⋊C4C22×D1112yes—
247C2×C4⋊C4C22×D1112yes—
248C2×C22⋊C4—112no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C42—112no—
252C2×C42—221no—
253C2×C42—221no—
254C2×C42—224no—
255#107—224no—
256#106—28no—
257#106—224no—
258C4⋊C8—1116no—
259#95—224no—
260#95—224no—
261C2×C11—24no—
262C2×C11C2×#38911yescharacteristic
263C2×C11#291212yes—
264C2×C11#304211yescharacteristic
265C2×C11#304311yescharacteristic
266C2×C11#308412yes—
267C24D4×D1111yescharacteristic
268C22×C4—22no—
269C22×C4—24no—
270C22×C4—22no—
271C22×C4—42no—
272C22×C4—82no—
273C22×C4—82no—
274C22×C4—114no—
275C22×C4—222no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4C2×C4×D1112yes—
279C22×C4#433912yes—
280C22×C4D4×D1111yescharacteristic
281C22×C4#434112yes—
282C22×C4Q8×D1112yes—
283C22×C4Q8×D1112yes—
284C22×C4C2×C22⋊D1112yes—
285C22×C4C23×D1111yescharacteristic
286M16—228no—
287C2×C8—28no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—114no—
291C2×C8—222no—
292C2×C8—222no—
293C2×C8C2×C4×D1114yes—
294C4⋊C4—24no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—42no—
299C4⋊C4—118no—
300C4⋊C4—114no—
301C4⋊C4—222no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—884no—
307C4⋊C4C2×C22⋊D1114yes—
308C22⋊C4—118no—
309C22⋊C4—224no—
310C22⋊C4—442no—
311C42—114no—
312C42—114no—
313C42—224no—
314C42—442no—
315C42—884no—
316C11#2117411yescharacteristic, complemented, Sylow
317C23—22no—
318C23—22no—
319C23C4⋊C4×D1112yes—
320C23#6694912yes—
321C23#6699212yes—
322C23C2×D4×D1111yescharacteristic
323C2×C4—24no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4—84no—
328C2×C4—84no—
329C2×C4—118no—
330C2×C4—224no—
331C2×C4—224no—
332C2×C4—224no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4#6694014yes—
340C2×C4#6694214yes—
341C2×C4C4⋊C4×D1112yes—
342C2×C4#6694912yes—
343C2×C4C4×C22⋊D1114yes—
344C2×C4#6699212yes—
345C2×C4#6699714yes—
346C2×C4C22×C4×D1111yescharacteristic
347C2×C4C2×#433911yescharacteristic
348C2×C4C2×#434111yescharacteristic
349C2×C4C2×Q8×D1111yescharacteristic
350C2×C4C2×Q8×D1111yescharacteristic
351C2×C4C22×C22⋊D1111yescharacteristic
352C8—24no—
353C8—224no—
354C22—22no—
355C22—22no—
356C22—24no—
357C22—24no—
358C22#1062258514yes—
359C22C2×C4⋊C4×D1111yescharacteristic
360C22C2×#6694911yescharacteristic
361C22#1062329312yes—
362C22#1062329312yes—
363C22C2×#6699211yescharacteristic
364C4—44no—
365C4—82no—
366C4—228no—
367C4—444no—
368C4—881no—
369C4—881no—
370C4#1062258514yes—
371C4C2×#6694011yescharacteristic
372C4C2×#6694211yescharacteristic
373C4C2×C4×C22⋊D1111yescharacteristic
374C4C2×#6699711yescharacteristic
375C2—24no—
376C2C2×#1062258511yescharacteristic
377C2#1307720712yes—
378C2#1307812511yescharacteristic
379C2#1307813411yescharacteristic
380C2#1307848312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#106C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC22×#106D11
hypocenterC11#21174
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
5. #13069385C2semidirect
6. #13069376C2semidirect
21. #10622715C4semidirect
74. Dic11⋊C8C2×C4semidirect
316. C11#21174semidirect

Maximal subgroups

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

subgroupindex
C2×#106225772
C2×#106227152
#130712402
#130709732
#130693852
#130693762
#130683352
#130683332
C22×C11×#1062
#2117411