Finite Group Databasebeta

← #14959881

Subgroups — #14959881

Order 2816.

2502 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C212yesmaximal
2#13077013C212yesmaximal, complemented
3#13076992C212yesmaximal, complemented
4#13076978C212yesmaximal, complemented
5#13076977C212yesmaximal, complemented
6#13076966C218yesmaximal
7C4×#66941C218yesmaximal, complemented
8#13071023C211yesmaximal, characteristic
9#13071019C212yesmaximal
10C2×C42×Dic11C211yesmaximal, characteristic
11C11×#2285C211yesmaximal, characteristic
12C2×C11×#117C2212yes—
13C22×C42×C11C2211yescharacteristic
14C2×#66979C2212yes—
15C22×C4×Dic11C2214yes—
16C22×C4×Dic11C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18#10623048—216no—
19C2×#66943C2214yes—
20C2×#66941C2214yes—
21C2×#66941C2218yes—
22C2×#66931C2218yes—
23C2×C4×Dic22C2218yes—
24C11×#384C2212yes—
25C11×#382C2212yes—
26C11×#380C2214yes—
27C4×C11×C4⋊C4C2214yes—
28#10622825C2214yes—
29#10622598C2218yes—
30#10622590C2214yes—
31#10622589C2218yes—
32#10622589C2214yes—
33#10622586C2218yes—
34#10622555C2218yes—
35#10622549C2212yes—
36#10622548C2212yes—
37C4×C4⋊Dic11C2214yes—
38C4×Dic11⋊C4C2218yes—
39C42×Dic11C2211yescharacteristic
40C42×Dic11C2211yescharacteristic
41C42×Dic11C2214yes—
42C42×Dic11C2211yescharacteristic
43C42×Dic11C2211yescharacteristic
44#10622260C22116yes—
45#10622259C22116yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C22×Dic22C2318yes—
51C11×#117—28no—
52C2×C11×C4⋊C4C2314yes—
53C2×C11×C4⋊C4C2318yes—
54C2×C11×C22⋊C4C2314yes—
55C2×C42×C11Q818yescomplemented
56C2×C42×C11C2314yes—
57C2×C42×C11C2312yes—
58C2×C42×C11C2311yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11C2314yes—
61#66979—28no—
62C2×C4⋊Dic11C2318yes—
63C2×C4⋊Dic11C2314yes—
64C2×C4⋊Dic11C2318yes—
65C2×Dic11⋊C4C2318yes—
66C2×Dic11⋊C4C2318yes—
67C2×Dic11⋊C4C23116yes—
68C2×C4×Dic11—216no—
69C2×C4×Dic11D418yes—
70C2×C4×Dic11Q818yescomplemented
71C2×C4×Dic11C2314yes—
72C2×C4×Dic11C2314yes—
73C2×C4×Dic11C2314yes—
74C2×C4×Dic11C2314yes—
75C2×C4×Dic11C2312yes—
76C2×C4×Dic11C2311yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C2×C4×Dic11C2312yes—
79C2×C4×Dic11C2311yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C2×C4×Dic11C2314yes—
82#66943—216no—
83#66941—216no—
84#66941—232no—
85#66931—232no—
86C4×Dic22—232no—
87C11×#95C2318yes—
88C11⋊#95C2318yes—
89C11⋊#95C23116yes—
90#36645—111nomaximal, Sylow
91C24×C11C2411yescharacteristic
92C22×C4×C11—28no—
93C22×C4×C11C2×D414yes—
94C22×C4×C11C2×Q818yes—
95C22×C4×C11C2×Q814yes—
96C22×C4×C11C2×Q814yes—
97C22×C4×C11C2418yes—
98C22×C4×C11C2412yes—
99C22×C4×C11C2411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×C4×C11C2412yes—
102C22×Dic11—28no—
103C22×Dic11—28no—
104C22×Dic11C2×D418yes—
105C22×Dic11C2×Q818yes—
106C22×Dic11C2418yes—
107C22×Dic11C2412yes—
108C22×Dic11C2412yes—
109C22×Dic11C2412yes—
110C22×Dic11C2412yes—
111C2×Dic22—216no—
112C2×Dic22—232no—
113C11×C4⋊C4—28no—
114C11×C4⋊C4—216no—
115C11×C22⋊C4—28no—
116C42×C11—28no—
117C42×C11C2×Q814yes—
118C42×C11C2×Q818yes—
119C42×C11C2×Q814yes—
120C22⋊Dic11—28no—
121C4⋊Dic11—216no—
122C4⋊Dic11—28no—
123C4⋊Dic11—216no—
124Dic11⋊C4—216no—
125Dic11⋊C4—216no—
126Dic11⋊C4—232no—
127C4×Dic11—28no—
128C4×Dic11—28no—
129C4×Dic11—28no—
130C4×Dic11—28no—
131C4×Dic11C2×D418yes—
132C4×Dic11C2×D414yes—
133C4×Dic11C2×D414yes—
134C4×Dic11C2×Q814yes—
135C4×Dic11C2×Q818yes—
136C4×Dic11C2×Q814yes—
137C4×Dic11#41116yes—
138C2×#533—112no—
139#2868—112no—
140#2862—112no—
141#2859—112no—
142#2859—112no—
143#2857—118no—
144C4×C4⋊Q8—118no—
145#2285—111no—
146#2285—112no—
147#2285D1111yescharacteristic
148C2×C43—111no—
149C23×C11—24no—
150C23×C11C22×D412yes—
151C23×C11C22×Q812yes—
152C23×C11C22×Q812yes—
153C23×C11C2511yescharacteristic
154C2×C4×C11—24no—
155C2×C4×C11—216no—
156C2×C4×C11—28no—
157C2×C4×C11—216no—
158C2×C4×C11C4⋊Q8116yescomplemented
159C2×C4×C11C22×D412yes—
160C2×C4×C11C22×D412yes—
161C2×C4×C11C22×Q814yes—
162C2×C4×C11C22×Q812yes—
163C2×C4×C11C22×Q812yes—
164C2×C4×C11C22×Q814yes—
165C2×C4×C11C22×Q812yes—
166C2×C4×C11C22×Q812yes—
167C2×C4×C11C2×#4118yes—
168C2×Dic11—24no—
169C2×Dic11—24no—
170C2×Dic11—216no—
171C2×Dic11—216no—
172C2×Dic11—28no—
173C2×Dic11—216no—
174C2×Dic11C22×D414yes—
175C2×Dic11C22×D414yes—
176C2×Dic11C22×Q814yes—
177C2×Dic11C22×Q814yes—
178C2×Dic11C2×#4118yes—
179C2×Dic11C2×#4118yes—
180Dic22—432no—
181#533—2216no—
182C2×C4⋊Q8—118no—
183C2×C4⋊Q8—114no—
184C2×#125—114no—
185C2×C22⋊Q8—118no—
186C2×C4×Q8—118no—
187C2×#117—112no—
188C2×#117C2×D1112yes—
189C22×C42—111no—
190C22×C42—111no—
191C22×C42—114no—
192C22×C42C2×D1111yescharacteristic
193#391—1116no—
194#389—118no—
195#389—118no—
196#389—1116no—
197#384—118no—
198#384—114no—
199#384—112no—
200#384C2×D1112yes—
201#382—114no—
202#382—112no—
203#382C2×D1112yes—
204#380—114no—
205#380—118no—
206#380C2×D1114yes—
207C4×C4⋊C4—118no—
208C4×C4⋊C4—114no—
209C4×C4⋊C4C2×D1114yes—
210C43—114no—
211C43—111no—
212C43—111no—
213C43—111no—
214C43—111no—
215C22×C11—24no—
216C22×C11—24no—
217C22×C11—24no—
218C22×C11C2×C4⋊Q814yes—
219C22×C11C23×D411yescharacteristic
220C22×C11C23×Q811yescharacteristic
221C22×C11C23×Q811yescharacteristic
222C22×C11C22×#4114yes—
223C4×C11—24no—
224C4×C11—48no—
225C4×C11C2×C4⋊Q814yes—
226C4×C11C2×C4⋊Q814yes—
227C4×C11#53318yescomplemented
228Dic11—24no—
229Dic11—24no—
230Dic11—48no—
231Dic11#53218yes—
232Dic11#53318yescomplemented
233C22×Q8—118no—
234C23×C4—112no—
235C23×C4—112no—
236C23×C4C22×D1112yes—
237C23×C4C22×D1111yescharacteristic
238C4⋊Q8—2216no—
239C4⋊Q8—2232no—
240#125—2216no—
241C22⋊Q8—2232no—
242C4×Q8—2232no—
243#117—28no—
244#117—228no—
245C2×C4⋊C4—114no—
246C2×C4⋊C4—118no—
247C2×C4⋊C4—118no—
248C2×C4⋊C4—118no—
249C2×C4⋊C4—1116no—
250C2×C4⋊C4—118no—
251C2×C4⋊C4C22×D1114yes—
252C2×C4⋊C4C22×D1118yes—
253C2×C22⋊C4—114no—
254C2×C22⋊C4C22×D1114yes—
255C2×C42—118no—
256C2×C42—118no—
257C2×C42—111no—
258C2×C42—111no—
259C2×C42—114no—
260C2×C42—111no—
261C2×C42—111no—
262C2×C42—112no—
263C2×C42—112no—
264C2×C42—114no—
265C2×C42—114no—
266C2×C42—114no—
267C2×C42—114no—
268C2×C42—2216no—
269C2×C42Dic2218yescomplemented
270C2×C42C22×D1114yes—
271C2×C42C22×D1111yescharacteristic
272C2×C42C22×D1111yescharacteristic
273C2×C42C22×D1112yes—
274#95—1116no—
275#95—118no—
276#95C22×D1118yes—
277C2×C11—24no—
278C2×C11C22×C4⋊Q811yescharacteristic
279C2×C11C2×#53212yes—
280C2×C11C2×#53312yes—
281C2×C11C2×#53312yes—
282C24C23×D1111yescharacteristic
283C2×Q8—2216no—
284C2×Q8—2232no—
285C22×C4—28no—
286C22×C4—112no—
287C22×C4—112no—
288C22×C4—118no—
289C22×C4—118no—
290C22×C4—112no—
291C22×C4—112no—
292C22×C4—118no—
293C22×C4—228no—
294C22×C4—228no—
295C22×C4C2×Dic2218yes—
296C22×C4C2×Dic2214yes—
297C22×C4D4×D1114yes—
298C22×C4Q8×D1114yes—
299C22×C4C23×D1118yes—
300C22×C4C23×D1112yes—
301C22×C4C23×D1111yescharacteristic
302C22×C4C23×D1112yes—
303C22×C4C23×D1111yescharacteristic
304C4⋊C4—28no—
305C4⋊C4—216no—
306C4⋊C4—2216no—
307C4⋊C4—2216no—
308C4⋊C4—2216no—
309C4⋊C4—2232no—
310C4⋊C4—228no—
311C4⋊C4—2216no—
312C22⋊C4—28no—
313C22⋊C4—228no—
314C42—28no—
315C42—118no—
316C42—114no—
317C42—114no—
318C42—114no—
319C42—118no—
320C42—114no—
321C42—1116no—
322C42—228no—
323C42—228no—
324C42—228no—
325C42—228no—
326C42C2×Dic2214yes—
327C42C2×Dic2218yes—
328C42C2×Dic2214yes—
329C11#3664511yescharacteristic, complemented, Sylow
330C23—24no—
331C23C22×Dic2212yes—
332C23C2×D4×D1112yes—
333C23C2×Q8×D1112yes—
334C23C24×D1111yescharacteristic
335Q8—4432no—
336C2×C4—24no—
337C2×C4—216no—
338C2×C4—28no—
339C2×C4—216no—
340C2×C4—114no—
341C2×C4—114no—
342C2×C4—118no—
343C2×C4—118no—
344C2×C4—114no—
345C2×C4—114no—
346C2×C4—2216no—
347C2×C4—2216no—
348C2×C4—224no—
349C2×C4—224no—
350C2×C4—228no—
351C2×C4—2216no—
352C2×C4#66941116yescomplemented
353C2×C4C22×Dic2214yes—
354C2×C4C22×Dic2212yes—
355C2×C4C22×Dic2212yes—
356C2×C4C22×Dic2214yes—
357C2×C4C2×D4×D1112yes—
358C2×C4C2×D4×D1112yes—
359C2×C4C2×Q8×D1112yes—
360C2×C4C2×Q8×D1112yes—
361C2×C4#41×D1118yes—
362C22—24no—
363C22—24no—
364C22—24no—
365C22C2×#6694114yes—
366C22C23×Dic2211yescharacteristic
367C22C22×D4×D1111yescharacteristic
368C22C22×Q8×D1111yescharacteristic
369C22C2×#41×D1114yes—
370C4—24no—
371C4—48no—
372C4—118no—
373C4—118no—
374C4—224no—
375C4—224no—
376C4—448no—
377C4C2×#6694114yes—
378C4C2×#6694114yes—
379C4#1062304818yescomplemented
380C2—24no—
381C2C22×#6694111yescharacteristic
382C2D11×#53212yes—
383C2D11×#53312yes—
384C2C2×#1062304812yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2285C2
prime radicalC24×C11C24
hypercenter#2285D11
hypocenterC11#36645
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #13077013C2semidirect
3. #13076992C2semidirect
4. #13076978C2semidirect
5. #13076977C2semidirect
7. C4×#66941C2semidirect
55. C2×C42×C11Q8semidirect
70. C2×C4×Dic11Q8semidirect
158. C2×C4×C11C4⋊Q8semidirect
227. C4×C11#533semidirect
232. Dic11#533semidirect
269. C2×C42Dic22semidirect
329. C11#36645semidirect
352. C2×C4#66941semidirect
379. C4#10623048semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
#130770132
#130769922
#130769782
#130769772
#130769662
C4×#669412
#130710232
#130710192
C2×C42×Dic112
C11×#22852
#3664511