Finite Group Databasebeta

← #15617556

Subgroups — #15617556

Order 2816.

2122 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic11C211yesmaximal, characteristic
2#13077278C2116yesmaximal, complemented
3#13077251C214yesmaximal, complemented
4#13077245C214yesmaximal, complemented
5C2×#10622731C212yesmaximal, complemented
6#13077061C211yesmaximal, characteristic
7#13077034C212yesmaximal, complemented
8C11×#2879C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C22×C11×M16C2212yes—
11#41×Dic11C414yes—
12#41×Dic11C414yes—
13#41×Dic11C2218yes—
14C2×Q8×Dic11C412yes—
15C2×D4×Dic11C414yes—
16C2×D4×Dic11C412yes—
17C2×#66979C2212yes—
18C2×#66979C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C22×#4318C2212yes—
22C11×#408C2218yes—
23C11×#407C2214yes—
24#10622847C2218yes—
25#10622820C2214yes—
26#10622735C2218yescomplemented
27#10622731C2214yes—
28#10622731C2214yes—
29#10622731C2218yescomplemented
30M16×Dic11C2218yes—
31#10622714C2218yescomplemented
32C2×Dic11⋊C8C2218yescomplemented
33#10622333C22132yescomplemented
34#10622332C22116yescomplemented
35#10622331C22116yescomplemented
36C2×C11×#41—28no—
37C2×C11×#41C2×C414yes—
38C2×C11×#41C2314yes—
39C22×Q8×C11C2×C411yescharacteristic
40C22×D4×C11C2×C412yes—
41C22×D4×C11C2×C411yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2×C414yes—
45C23×Dic11C2×C412yes—
46C2×C11×M16—28no—
47C2×C11×M16C2314yes—
48C2×C11×M16C2314yes—
49C22×C8×C11C2314yes—
50C2×C22⋊Dic11C2×C414yes—
51C2×C22⋊Dic11C2×C412yes—
52Q8×Dic11C2×C418yes—
53Q8×Dic11C2×C418yes—
54D4×Dic11C2×C4116yes—
55D4×Dic11C2×C418yes—
56D4×Dic11C2×C4116yes—
57D4×Dic11C2×C418yes—
58#66979C2×C418yes—
59#66979C2×C414yes—
60#66979C2314yes—
61#66979C2318yes—
62C2×C4⋊Dic11C2×C414yes—
63C2×C4⋊Dic11C2×C412yes—
64C2×C4×Dic11C2×C414yes—
65C2×C4×Dic11C2×C412yes—
66C2×C4×Dic11C2×C414yes—
67C2×C4×Dic11C2×C412yes—
68C2×C4×Dic11C2×C414yes—
69C2×C4×Dic11C2×C412yes—
70C2×C4×Dic11C2312yes—
71C2×C4×Dic11C2311yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C2×C4×Dic11C2314yes—
74C2×C4×Dic11C2318yes—
75C2×#4318—28no—
76C2×#4318C2314yes—
77C2×#4318C2314yes—
78C22×C11⋊C8C2314yes—
79C11×C22⋊C8C23116yes—
80C22⋊(C11⋊C8)C23116yes—
81#66879C23116yes—
82Dic11⋊C8C23116yes—
83Dic11⋊C8C23116yes—
84C8×Dic11C23116yes—
85#60125—111nomaximal, Sylow
86C24×C11C22×C412yes—
87C24×C11C22×C411yescharacteristic
88C11×#41—216no—
89C11×#41—28no—
90C11×#41—28no—
91C2×Q8×C11—24no—
92C2×Q8×C11C22×C414yes—
93C2×D4×C11—28no—
94C2×D4×C11—24no—
95C2×D4×C11C22×C418yes—
96C2×D4×C11C22×C414yes—
97C22×C4×C11—28no—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C414yes—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C22×C412yes—
102C22×C4×C11#4118yes—
103C22×C4×C11C2414yes—
104C22×C4×C11C2412yes—
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—44no—
107C22×Dic11—48no—
108C22×Dic11C22×C412yes—
109C22×Dic11C22×C418yes—
110C22×Dic11C22×C414yes—
111C22×Dic11C22×C414yes—
112C22×Dic11C22×C412yes—
113C22×Dic11C22×C418yes—
114C22×Dic11C22×C414yes—
115C11×M16—28no—
116C11×M16—28no—
117C2×C8×C11—28no—
118C2×C8×C11C2418yes—
119C22⋊Dic11C22×C4116yes—
120C22⋊Dic11C22×C418yes—
121C4⋊Dic11C22×C4116yes—
122C4⋊Dic11C22×C418yes—
123C4×Dic11C22×C411yescharacteristic
124C4×Dic11C22×C411yescharacteristic
125C4×Dic11C22×C414yes—
126C4×Dic11C22×C412yes—
127C4×Dic11C22×C418yes—
128C4×Dic11C22×C418yes—
129C4×Dic11C22×C414yes—
130C4×Dic11C22×C414yes—
131C4×Dic11C2414yes—
132C4×Dic11C2412yes—
133C4×Dic11C2412yes—
134#4318—28no—
135#4318—28no—
136C2×C11⋊C8—28no—
137C2×C11⋊C8C2418yes—
138C2×C4×#41—111no—
139#2925—1116no—
140#2921—114no—
141#2920—114no—
142C2×#423—112no—
143#2879—111no—
144#2879D1111yescharacteristic
145#2873—112no—
146C23×C11—24no—
147C23×C11—42no—
148C23×C11—44no—
149C23×C11#11714yes—
150C23×C11C23×C414yes—
151C23×C11C23×C412yes—
152C23×C11C23×C411yescharacteristic
153Q8×C11—28no—
154D4×C11—216no—
155D4×C11—28no—
156C2×C4×C11—24no—
157C2×C4×C11—28no—
158C2×C4×C11—28no—
159C2×C4×C11#11714yes—
160C2×C4×C11#11718yes—
161C2×C4×C11C23×C414yes—
162C2×C4×C11C23×C411yescharacteristic
163C2×C4×C11C23×C412yes—
164C2×C4×C11C2×#4114yes—
165C2×C4×C11C2×#4114yes—
166C2×C4×C11C2×#4114yes—
167C2×C4×C11C2511yescharacteristic
168C2×Dic11—24no—
169C2×Dic11—28no—
170C2×Dic11—216no—
171C2×Dic11—44no—
172C2×Dic11—48no—
173C2×Dic11—44no—
174C2×Dic11—42no—
175C2×Dic11C23×C412yes—
176C2×Dic11C23×C418yes—
177C2×Dic11C23×C414yes—
178C2×Dic11C23×C412yes—
179C8×C11—28no—
180C11⋊C8—28no—
181C22×#41C2×D1111yescharacteristic
182C22×M16—112no—
183C22×M16C2×D1112yes—
184C4×#41—118no—
185C4×#41—114no—
186C4×#41—114no—
187C2×C4×Q8—112no—
188C2×C4×D4—114no—
189C2×C4×D4—112no—
190C2×#117—111no—
191C2×#117—112no—
192C22×C42—111no—
193C22×C42—112no—
194#433—1132no—
195#432—1116no—
196#431—1116no—
197#423—114no—
198#423—114no—
199#423—118no—
200C2×C4⋊C8—118no—
201#408—118no—
202#408C2×D1118yes—
203#407—114no—
204#407C2×D1114yes—
205#405—118no—
206#405—118no—
207C4×M16—118no—
208C22×C11—22no—
209C22×C11—24no—
210C22×C11—24no—
211C22×C11—28no—
212C22×C11—44no—
213C22×C11—48no—
214C22×C11C2×#11712yes—
215C22×C11C2×#11714yes—
216C22×C11C24×C411yescharacteristic
217C4×C11—24no—
218C4×C11C2×#11712yes—
219C4×C11C2×#11714yes—
220C4×C11C22×#4112yes—
221Dic11—22no—
222Dic11—24no—
223Dic11—28no—
224Dic11#56814yes—
225C2×#41—28no—
226C2×#41C4×D1114yes—
227C2×#41C22×D1114yes—
228C22×Q8C4×D1111yescharacteristic
229C22×D4C4×D1112yes—
230C22×D4C4×D1111yescharacteristic
231C23×C4—114no—
232C23×C4—112no—
233C23×C4C22×D1112yes—
234C23×C4C22×D1111yescharacteristic
235C2×M16—28no—
236C2×M16—114no—
237C2×M16—114no—
238C2×M16—228no—
239C2×M16C22×D1114yes—
240C2×M16C22×D1114yes—
241C22×C8—114no—
242C22×C8C22×D1114yes—
243C4×Q8—118no—
244C4×Q8—118no—
245C4×D4—1116no—
246C4×D4—118no—
247C4×D4—1116no—
248C4×D4—118no—
249#117—118no—
250#117—114no—
251#117—114no—
252#117—118no—
253C2×C4⋊C4—114no—
254C2×C4⋊C4—112no—
255C2×C22⋊C4—114no—
256C2×C22⋊C4—112no—
257C2×C42—114no—
258C2×C42—112no—
259C2×C42—114no—
260C2×C42—112no—
261C2×C42—114no—
262C2×C42—112no—
263C2×C42—112no—
264C2×C42—111no—
265C2×C42—114no—
266C2×C42—118no—
267C2×C42—111no—
268C4⋊C8—1116no—
269C4⋊C8—1116no—
270C22⋊C8—1116no—
271C22⋊C8C22×D11116yes—
272#97—1116no—
273C4×C8—1116no—
274C2×C11—22no—
275C2×C11—24no—
276C2×C11—44no—
277C2×C11C22×#11711yescharacteristic
278C2×C11C2×#56812yes—
279C24C2×C4×D1112yes—
280C24C2×C4×D1111yescharacteristic
281#41—216no—
282#41—28no—
283#41—28no—
284C2×Q8—24no—
285C2×Q8C2×C4×D1114yes—
286C2×D4—28no—
287C2×D4—24no—
288C2×D4C2×C4×D1118yes—
289C2×D4C2×C4×D1114yes—
290C22×C4—28no—
291C22×C4—112no—
292C22×C4—118no—
293C22×C4—114no—
294C22×C4—114no—
295C22×C4—112no—
296C22×C4—118no—
297C22×C4—114no—
298C22×C4—444no—
299C22×C4—448no—
300C22×C4C2×C4×D1112yes—
301C22×C4C2×C4×D1114yes—
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4C2×C4×D1112yes—
304C22×C4#434118yes—
305C22×C4C23×D1114yes—
306C22×C4C23×D1111yescharacteristic
307C22×C4C23×D1112yes—
308M16—28no—
309M16—28no—
310M16—228no—
311M16—228no—
312C2×C8—28no—
313C2×C8—118no—
314C2×C8—228no—
315C2×C8C23×D1118yes—
316C4⋊C4—1116no—
317C4⋊C4—118no—
318C22⋊C4—1116no—
319C22⋊C4—118no—
320C42—111no—
321C42—111no—
322C42—114no—
323C42—112no—
324C42—118no—
325C42—114no—
326C42—118no—
327C42—114no—
328C42—114no—
329C42—112no—
330C42—112no—
331C11#6012511yescharacteristic, complemented, Sylow
332C23—24no—
333C23—42no—
334C23—44no—
335C23#6693014yes—
336C23C22×C4×D1114yes—
337C23C22×C4×D1112yes—
338C23C22×C4×D1111yescharacteristic
339Q8—28no—
340D4—216no—
341D4—28no—
342C2×C4—24no—
343C2×C4—28no—
344C2×C4—28no—
345C2×C4—112no—
346C2×C4—112no—
347C2×C4—118no—
348C2×C4—114no—
349C2×C4—224no—
350C2×C4—228no—
351C2×C4—2216no—
352C2×C4—444no—
353C2×C4—448no—
354C2×C4—444no—
355C2×C4—442no—
356C2×C4#6693014yes—
357C2×C4#6693018yes—
358C2×C4C22×C4×D1114yes—
359C2×C4C22×C4×D1111yescharacteristic
360C2×C4C22×C4×D1112yes—
361C2×C4C2×#434114yes—
362C2×C4C2×#434114yes—
363C2×C4C2×#434114yes—
364C2×C4C24×D1111yescharacteristic
365C8—28no—
366C8—228no—
367C22—22no—
368C22—24no—
369C22—24no—
370C22—28no—
371C22—44no—
372C22—48no—
373C22C2×#6693012yes—
374C22C2×#6693014yes—
375C22C23×C4×D1111yescharacteristic
376C4—24no—
377C4—114no—
378C4—222no—
379C4—228no—
380C4—224no—
381C4C2×#6693012yes—
382C4C2×#6693014yes—
383C4C22×#434112yes—
384C2—22no—
385C2—24no—
386C2—44no—
387C2C22×#6693011yescharacteristic
388C2D11×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2879C2
prime radicalC22×C11×#41C22
cosocleC2×C4×C11C25
hypercenter#2879D11
hypocenterC11#60125
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2879

Complements

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

NH ≅ G/Ntype
2. #13077278C2semidirect
3. #13077251C2semidirect
4. #13077245C2semidirect
5. C2×#10622731C2semidirect
7. #13077034C2semidirect
26. #10622735C22semidirect
29. #10622731C22semidirect
31. #10622714C22semidirect
32. C2×Dic11⋊C8C22semidirect
33. #10622333C22semidirect
34. #10622332C22semidirect
35. #10622331C22semidirect
331. C11#60125semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic112
#130772782
#130772512
#130772452
C2×#106227312
#130770612
#130770342
C11×#28792
#6012511