Finite Group Databasebeta

← #14914017

Subgroups — #14914017

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4343C211yesmaximal, characteristic
2#13071585C216yesmaximal, complemented
3#13071534C212yesmaximal, complemented
4#13071497C216yesmaximal, complemented
5#13071454C212yesmaximal
6#13071260C213yesmaximal, complemented
7#13071254C213yesmaximal, complemented
8#13071012C213yesmaximal, complemented
9#13071008C213yesmaximal, complemented
10#13070981C211yesmaximal, characteristic, complemented
11C11×#2276C211yesmaximal, characteristic, complemented
12C22×#4343C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×Q8×Dic11C2212yes—
16C2×Q8×Dic11C2211yescharacteristic
17C4×#4343C4116yescomplemented
18C2×#66946C2213yes—
19C2×#66945C2213yes—
20C2×C4×D44C2213yes—
21C2×C42×D11C2213yes—
22C4×C11×C4⋊C4C2216yes—
23C4×C11×C4⋊C4C2213yes—
24C11×#376C2213yes—
25#10622601C2216yes—
26#10622600C2216yes—
27#10622590C2216yes—
28C4⋊C4×Dic11C2216yes—
29#10622586C2216yes—
30#10622553C22112yes—
31#10622552C2216yes—
32C4×(C2×D11)⋊C4C2216yes—
33C4×(C2×D11)⋊C4C2216yes—
34C4×C4⋊Dic11C2213yes—
35#10622545C2213yes—
36#10622545C2216yes—
37C4×Dic11⋊C4C2216yes—
38#10622541C2216yes—
39#10622282C22112yes—
40#10622280C2213yes—
41#10622280C2213yes—
42#10622277C2216yes—
43#10622277C2216yes—
44#10622264C2211yescharacteristic
45#10622264C2213yes—
46#10622263C2216yes—
47C22×Q8×C11C2311yescharacteristic
48C2×#4343—28no—
49C2×#4343C2×C418yes—
50C22×D44C2313yes—
51C22×C4×D11C2313yes—
52C22×C4×D11C2313yes—
53C22×C4×D11C2313yes—
54C4×Q8×C11—28no—
55C4×Q8×C11C2×C418yes—
56C2×C11×C4⋊C4C2316yes—
57C2×C11×C4⋊C4C2313yes—
58C2×C42×C11C2316yes—
59C2×C42×C11C2316yes—
60C2×C42×C11C2313yes—
61Q8×Dic11—28no—
62Q8×Dic11C2×C418yes—
63C2×(C2×D11)⋊C4C2316yes—
64C2×(C2×D11)⋊C4C2316yes—
65C2×(C2×D11)⋊C4C23112yes—
66C2×(C2×D11)⋊C4C2316yes—
67C2×C4⋊Dic11C2316yes—
68C2×C4⋊Dic11C2313yes—
69C2×Dic11⋊C4C2316yes—
70C2×Dic11⋊C4C2316yes—
71C2×C4×Dic11C2316yes—
72C2×C4×Dic11C2316yes—
73C2×C4×Dic11C2311yescharacteristic
74C2×C4×Dic11C2313yes—
75C2×C4×Dic11C2313yes—
76#66946C2×C4124yes—
77#66945C2×C4124yes—
78C4×D44C2×C4124yes—
79C42×D11C2×C4124yes—
80C11×#95C2316yes—
81C11×#95C2313yes—
82C11×#95C2311yescharacteristic
83C11⋊#95C2312yes—
84C11⋊#95C2316yes—
85C11⋊#95C2316yes—
86C11⋊#95C2312yes—
87C11⋊#95C2313yes—
88C11⋊#95C2316yes—
89C11⋊#95C2311yescharacteristic
90C11⋊#95C23112yes—
91#34197—111nomaximal, Sylow
92C23×D11C2413yes—
93C2×Q8×C11C22×C414yes—
94C2×Q8×C11#4118yes—
95C22×C4×C11C2416yes—
96C22×C4×C11C2412yes—
97C22×C4×C11C2411yescharacteristic
98C22×C4×C11C2413yes—
99C22×C4×C11C2413yes—
100C22×Dic11C2412yes—
101C22×Dic11C2416yes—
102C22×Dic11C2411yescharacteristic
103C22×Dic11C2411yescharacteristic
104C22×Dic11C2413yes—
105#4343—232no—
106C2×D44—212no—
107C2×D44C22×C4112yes—
108C2×C4×D11—212no—
109C2×C4×D11—43no—
110C2×C4×D11—43no—
111C2×C4×D11—46no—
112C2×C4×D11C22×C4112yes—
113C2×C4×D11C22×C4112yes—
114C2×C4×D11C22×C4112yes—
115C11×C4⋊C4—212no—
116C11×C4⋊C4C22×C4112yes—
117C42×C11—212no—
118C42×C11—46no—
119C42×C11C22×C4112yes—
120(C2×D11)⋊C4—412no—
121(C2×D11)⋊C4—46no—
122(C2×D11)⋊C4—46no—
123(C2×D11)⋊C4C22×C4124yes—
124C4⋊Dic11—212no—
125C4⋊Dic11C22×C4112yes—
126Dic11⋊C4—46no—
127Dic11⋊C4—46no—
128C4×Dic11—212no—
129C4×Dic11—46no—
130C4×Dic11C22×C414yes—
131C4×Dic11C22×C4112yes—
132C4×Dic11C22×C4112yes—
133C2×C4×#41—111no—
134#2357—116no—
135#2351—112no—
136#2346—116no—
137#2341—112no—
138#2319—113no—
139#2319—113no—
140#2283—113no—
141#2283—113no—
142#2276—111no—
143#2276D1111yescharacteristic, complemented
144C23×C11C2511yescharacteristic
145C22×D11—26no—
146C22×D11—23no—
147C22×D11—23no—
148C22×D11—26no—
149C22×D11C23×C416yes—
150Q8×C11#117116yes—
151C2×C4×C11—23no—
152C2×C4×C11—23no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—26no—
156C2×C4×C11—22no—
157C2×C4×C11—26no—
158C2×C4×C11—22no—
159C2×C4×C11—26no—
160C2×C4×C11C23×C416yes—
161C2×C4×C11C23×C412yes—
162C2×C4×C11C23×C416yes—
163C2×C4×C11C2×#41112yes—
164C2×Dic11—22no—
165C2×Dic11—26no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—22no—
169C2×Dic11—26no—
170C2×Dic11—26no—
171C2×Dic11—22no—
172C2×Dic11—26no—
173C2×Dic11—22no—
174C2×Dic11C23×C412yes—
175C2×Dic11C23×C412yes—
176C2×Dic11C23×C416yes—
177D44—224no—
178C4×D11—224no—
179C4×D11—412no—
180C4×D11—412no—
181C22×#41—111no—
182C4×#41—1116no—
183C2×C4×Q8—111no—
184C2×C4×Q8—112no—
185C2×C4×Q8C2×D1112yes—
186C2×C4×Q8C2×D1111yescharacteristic
187C2×C4×D4—113no—
188C2×C4×D4—113no—
189C2×#117—113no—
190C22×C42—113no—
191#390—116no—
192#390—116no—
193#389—116no—
194#389—116no—
195#388—1112no—
196#388—1112no—
197#383—111no—
198#383—113no—
199#382—116no—
200#382—116no—
201#381—116no—
202#381—116no—
203#380—116no—
204#380—113no—
205#380—113no—
206C4×C4⋊C4—116no—
207C4×C4⋊C4—113no—
208C4×C4⋊C4—116no—
209C4×C4⋊C4C2×D1113yes—
210C4×C4⋊C4C2×D1116yes—
211C4×C22⋊C4—116no—
212C4×C22⋊C4—116no—
213#376—113no—
214#376—116no—
215#376C2×D1113yes—
216C22×C11C24×C411yescharacteristic
217C22×C11C22×#4112yes—
218C22×C11#58511yescharacteristic
219C22×C11#58512yes—
220C22×C11#58511yescharacteristic
221C2×D11—26no—
222C2×D11—26no—
223C2×D11—26no—
224C2×D11—46no—
225C2×D11—46no—
226C4×C11—26no—
227C4×C11—22no—
228C4×C11—46no—
229C4×C11—42no—
230C4×C11C2×#117112yes—
231Dic11—22no—
232Dic11—22no—
233Dic11—26no—
234Dic11—42no—
235Dic11—46no—
236C2×#41—118no—
237C2×#41—228no—
238C22×Q8C22×D1111yescharacteristic
239C22×D4—113no—
240C23×C4—113no—
241C23×C4—113no—
242C23×C4—113no—
243C4×Q8—28no—
244C4×Q8—118no—
245C4×Q8—228no—
246C4×Q8C4×D1118yes—
247C4×D4—1124no—
248C4×D4—1124no—
249#117—1124no—
250C2×C4⋊C4—113no—
251C2×C4⋊C4—116no—
252C2×C4⋊C4—116no—
253C2×C4⋊C4—116no—
254C2×C4⋊C4C22×D1116yes—
255C2×C4⋊C4C22×D1113yes—
256C2×C22⋊C4—116no—
257C2×C22⋊C4—116no—
258C2×C22⋊C4—1112no—
259C2×C22⋊C4—116no—
260C2×C42—113no—
261C2×C42—113no—
262C2×C42—111no—
263C2×C42—1124no—
264C2×C42—116no—
265C2×C42—116no—
266C2×C42C22×D1116yes—
267C2×C42C22×D1116yes—
268C2×C42C22×D1113yes—
269#95—111no—
270#95—116no—
271#95—113no—
272#95—116no—
273#95—1112no—
274#95—112no—
275#95—116no—
276#95—112no—
277#95C22×D1111yescharacteristic
278#95C22×D1113yes—
279#95C22×D1116yes—
280C2×C11C22×#11711yescharacteristic
281C2×C11#342811yescharacteristic
282C2×C11#342811yescharacteristic
283C2×C11#352412yes—
284C2×C11#352412yes—
285D11—46no—
286C24—113no—
287#41—2232no—
288C2×Q8C2×C4×D1114yes—
289C2×Q8#433918yes—
290C2×D4—1112no—
291C2×D4—2212no—
292C22×C4—111no—
293C22×C4—111no—
294C22×C4—113no—
295C22×C4—1112no—
296C22×C4—1112no—
297C22×C4—1112no—
298C22×C4—112no—
299C22×C4—116no—
300C22×C4—2212no—
301C22×C4—443no—
302C22×C4—443no—
303C22×C4—446no—
304C22×C4C23×D1116yes—
305C22×C4C23×D1112yes—
306C22×C4C23×D1111yescharacteristic
307C22×C4C23×D1113yes—
308C22×C4C23×D1113yes—
309C4⋊C4—212no—
310C4⋊C4—1112no—
311C4⋊C4—2212no—
312C4⋊C4—446no—
313C4⋊C4—446no—
314C4⋊C4C2×C4×D11112yes—
315C22⋊C4—1124no—
316C22⋊C4—446no—
317C22⋊C4—446no—
318C22⋊C4—4412no—
319C42—212no—
320C42—46no—
321C42—114no—
322C42—1112no—
323C42—1112no—
324C42—2212no—
325C42—446no—
326C42C2×C4×D11112yes—
327C11#3419711yescharacteristic, complemented, Sylow
328C23—116no—
329C23—226no—
330C23—223no—
331C23—223no—
332C23—226no—
333C23C24×D1111yescharacteristic
334Q8#66925116yes—
335D4—2224no—
336C2×C4—23no—
337C2×C4—23no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—26no—
341C2×C4—26no—
342C2×C4—22no—
343C2×C4—26no—
344C2×C4—22no—
345C2×C4—112no—
346C2×C4—112no—
347C2×C4—116no—
348C2×C4—222no—
349C2×C4—221no—
350C2×C4—226no—
351C2×C4—221no—
352C2×C4—2224no—
353C2×C4—222no—
354C2×C4—226no—
355C2×C4—222no—
356C2×C4—226no—
357C2×C4—226no—
358C2×C4—222no—
359C2×C4—4412no—
360C2×C4—4412no—
361C2×C4C22×C4×D1112yes—
362C2×C4C22×C4×D1116yes—
363C2×C4C22×C4×D1116yes—
364C2×C4C2×#4339112yes—
365C22—226no—
366C22—226no—
367C22—226no—
368C22—446no—
369C22—446no—
370C22C23×C4×D1111yescharacteristic
371C22C22×#433912yes—
372C22#1062345511yescharacteristic
373C22#1062345712yes—
374C22#1062345711yescharacteristic
375C4—26no—
376C4—22no—
377C4—46no—
378C4—42no—
379C4—222no—
380C4—222no—
381C4—226no—
382C4—442no—
383C4—446no—
384C4C2×#66925112yes—
385C2—446no—
386C2C22×#6692511yescharacteristic
387C2#1308181611yescharacteristic
388C2#1308181811yescharacteristic
389C2#1308271712yes—
390C2#1308272712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2276C2
socle, cosocleC23×C11C25
prime radicalC22×#4343C22
hypercenter#2276D11
hypocenterC11#34197
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2276

Complements

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

NH ≅ G/Ntype
2. #13071585C2semidirect
3. #13071534C2semidirect
4. #13071497C2semidirect
6. #13071260C2semidirect
7. #13071254C2semidirect
8. #13071012C2semidirect
9. #13071008C2semidirect
10. #13070981C2semidirect
11. C11×#2276C2semidirect
17. C4×#4343C4semidirect
143. #2276D11semidirect
327. C11#34197semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43432
#130715852
#130715342
#130714972
#130714542
#130712602
#130712542
#130710122
#130710082
#130709812
C11×#22762
#3419711