Finite Group Databasebeta

← #14913963

Subgroups — #14913963

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic
2#13071583C213yesmaximal, complemented
3#13071579C213yesmaximal, complemented
4#13071537C211yesmaximal, characteristic, complemented
5#13071492C216yesmaximal
6Q8×(C2×D11)⋊C4C212yesmaximal
7#13071263C216yesmaximal, complemented
8#13071012C213yesmaximal
9#13071009C213yesmaximal
10#13070981C212yesmaximal, complemented
11C11×#2351C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×Q8×Dic11C2212yes—
16C2×Q8×Dic11C2211yescharacteristic
17C4×Q8×D11C4116yescomplemented
18C2×C4⋊C4×D11C2213yes—
19C2×#66940C2213yes—
20C2×C42×D11C2213yes—
21C2×C4×Dic22C2213yes—
22C11×#389C2216yes—
23C11×#382C2213yes—
24C4×C11×C4⋊C4C2213yes—
25#10622600C2216yes—
26#10622600C2216yes—
27#10622598C2216yes—
28#10622591C22112yes—
29#10622590C2216yes—
30C4⋊C4×Dic11C2216yes—
31C4⋊C4×Dic11C2216yes—
32#10622587C2216yes—
33C4×(C2×D11)⋊C4C2216yes—
34#10622549C2213yes—
35C4×C4⋊Dic11C2216yes—
36C4×C4⋊Dic11C2213yes—
37#10622545C2216yes—
38#10622542C2216yes—
39#10622279C2216yes—
40#10622277C2213yes—
41#10622277C2211yescharacteristic
42#10622268C22112yes—
43#10622264C2216yes—
44#10622264C2213yes—
45#10622264C2213yes—
46#10622261C2216yes—
47C22×Q8×C11C2311yescharacteristic
48C2×Q8×D11—24no—
49C2×Q8×D11—24no—
50C2×Q8×D11C2×C418yes—
51C22×C4×D11C2311yescharacteristic
52C22×C4×D11C2313yes—
53C22×C4×D11C2313yes—
54C22×Dic22C2313yes—
55C4×Q8×C11—28no—
56C4×Q8×C11C2×C418yes—
57C2×C11×C4⋊C4C2316yes—
58C2×C11×C4⋊C4C2316yes—
59C2×C11×C4⋊C4C2313yes—
60C2×C42×C11C2316yes—
61C2×C42×C11C2313yes—
62Q8×Dic11—28no—
63Q8×Dic11C2×C418yes—
64C2×(C2×D11)⋊C4C2316yes—
65C2×(C2×D11)⋊C4C2312yes—
66C2×C4⋊Dic11C2316yes—
67C2×C4⋊Dic11C2316yes—
68C2×C4⋊Dic11C2313yes—
69C2×Dic11⋊C4C2316yes—
70C2×C4×Dic11C2316yes—
71C2×C4×Dic11C23112yes—
72C2×C4×Dic11C2313yes—
73C2×C4×Dic11C2313yes—
74C2×C4×Dic11C2313yes—
75C4⋊C4×D11C2×C4124yes—
76#66940C2×C4124yes—
77C42×D11C2×C4124yes—
78C4×Dic22C2×C4124yes—
79C11×#95C2313yes—
80C11×#95C2311yescharacteristic
81C11×#95C2316yes—
82C11⋊#95C2313yes—
83C11⋊#95C23112yes—
84C11⋊#95C2311yescharacteristic
85C11⋊#95C2316yes—
86C11⋊#95C2316yes—
87C11⋊#95C2316yes—
88C11⋊#95C2316yes—
89C11⋊#95C2316yes—
90C11⋊#95C2316yes—
91C11⋊#95C2312yes—
92#34192—111nomaximal, Sylow
93C23×D11C2411yescharacteristic
94C2×Q8×C11C22×C414yes—
95C2×Q8×C11#4114yes—
96C2×Q8×C11#4114yes—
97C22×C4×C11C2412yes—
98C22×C4×C11C2416yes—
99C22×C4×C11C2411yescharacteristic
100C22×C4×C11C2413yes—
101C22×C4×C11C2413yes—
102C22×Dic11C2412yes—
103C22×Dic11C2416yes—
104C22×Dic11C2411yescharacteristic
105C22×Dic11C2413yes—
106C22×Dic11C2413yes—
107Q8×D11—232no—
108C2×C4×D11—24no—
109C2×C4×D11—26no—
110C2×C4×D11—26no—
111C2×C4×D11—46no—
112C2×C4×D11C22×C414yes—
113C2×C4×D11C22×C4112yes—
114C2×C4×D11C22×C4112yes—
115C2×Dic22—26no—
116C2×Dic22—26no—
117C2×Dic22C22×C4112yes—
118C11×C4⋊C4—212no—
119C11×C4⋊C4—46no—
120C11×C4⋊C4C22×C4112yes—
121C42×C11—212no—
122C42×C11C22×C4112yes—
123(C2×D11)⋊C4—212no—
124(C2×D11)⋊C4—24no—
125C4⋊Dic11—212no—
126C4⋊Dic11—46no—
127C4⋊Dic11C22×C4112yes—
128Dic11⋊C4C22×C4124yes—
129C4×Dic11—212no—
130C4×Dic11—412no—
131C4×Dic11C22×C4112yes—
132C4×Dic11C22×C4112yes—
133C4×Dic11C22×C4112yes—
134C22×C4×Q8—111no—
135#2356—113no—
136#2356—113no—
137#2351—111no—
138#2351D1111yescharacteristic, complemented
139#2345—116no—
140Q8×C22⋊C4—112no—
141#2320—116no—
142#2283—113no—
143#2283—113no—
144#2276—112no—
145C23×C11C2511yescharacteristic
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—22no—
149C22×D11C23×C412yes—
150C22×D112−1+414yes—
151Q8×C11#117116yes—
152C2×C4×C11—22no—
153C2×C4×C11—26no—
154C2×C4×C11—22no—
155C2×C4×C11—26no—
156C2×C4×C11—22no—
157C2×C4×C11—26no—
158C2×C4×C11—26no—
159C2×C4×C11—22no—
160C2×C4×C11C23×C412yes—
161C2×C4×C11C23×C416yes—
162C2×C4×C11C23×C416yes—
163C2×C4×C11C2×#4116yes—
164C2×C4×C11C2×#4116yes—
165C2×Dic11—23no—
166C2×Dic11—23no—
167C2×Dic11—22no—
168C2×Dic11—26no—
169C2×Dic11—22no—
170C2×Dic11—26no—
171C2×Dic11—22no—
172C2×Dic11—26no—
173C2×Dic11—26no—
174C2×Dic11—22no—
175C2×Dic11C23×C412yes—
176C2×Dic11C23×C416yes—
177C2×Dic11C23×C416yes—
178C4×D11—28no—
179C4×D11—224no—
180C4×D11—412no—
181Dic22—224no—
182C23×Q8—111no—
183C2×C4×Q8—111no—
184C2×C4×Q8—1116no—
185C2×C4×Q8—112no—
186C2×C4×Q8—113no—
187C2×C4×Q8—113no—
188C2×C4×Q8C2×D1112yes—
189C2×C4×Q8C2×D1111yescharacteristic
190C22×C4⋊C4—113no—
191C22×C42—113no—
192#391—116no—
193#391—116no—
194#389—116no—
195#389C2×D1116yes—
196#387—1112no—
197#387—1112no—
198#383—116no—
199#383—113no—
200#383—113no—
201#382—116no—
202#382—113no—
203#382C2×D1113yes—
204#381—111no—
205#381—113no—
206#380—116no—
207#380—116no—
208C4×C4⋊C4—116no—
209C4×C4⋊C4—116no—
210C4×C4⋊C4—116no—
211C4×C4⋊C4—113no—
212C4×C4⋊C4C2×D1113yes—
213C4×C22⋊C4—116no—
214C4×C22⋊C4—116no—
215#376—116no—
216#376—116no—
217C22×C11C24×C411yescharacteristic
218C22×C11C22×#4111yescharacteristic
219C22×C11C22×#4111yescharacteristic
220C22×C11C2×2−1+412yes—
221C22×C11#58512yes—
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—24no—
225C2×D11—24no—
226C2×D11#51914yes—
227C4×C11—22no—
228C4×C11—26no—
229C4×C11—42no—
230C4×C11—46no—
231C4×C11C2×#117112yes—
232Dic11—26no—
233Dic11—22no—
234Dic11—26no—
235Dic11—42no—
236Dic11—46no—
237C22×Q8—118no—
238C22×Q8—113no—
239C22×Q8—224no—
240C22×Q8—224no—
241C22×Q8C22×D1111yescharacteristic
242C23×C4—113no—
243C23×C4—111no—
244C23×C4—113no—
245C4×Q8—28no—
246C4×Q8—118no—
247C4×Q8—1124no—
248C4×Q8—1124no—
249C4×Q8—228no—
250C4×Q8C4×D1118yes—
251C2×C4⋊C4—113no—
252C2×C4⋊C4—116no—
253C2×C4⋊C4—1124no—
254C2×C4⋊C4—116no—
255C2×C4⋊C4—116no—
256C2×C4⋊C4C22×D1116yes—
257C2×C4⋊C4C22×D1116yes—
258C2×C4⋊C4C22×D1113yes—
259C2×C22⋊C4—112no—
260C2×C22⋊C4—116no—
261C2×C42—113no—
262C2×C42—113no—
263C2×C42—113no—
264C2×C42—1124no—
265C2×C42—116no—
266C2×C42—1112no—
267C2×C42C22×D1116yes—
268C2×C42C22×D1113yes—
269#95—112no—
270#95—113no—
271#95—116no—
272#95—116no—
273#95—116no—
274#95—1112no—
275#95—116no—
276#95—116no—
277#95—116no—
278#95—111no—
279#95C22×D1113yes—
280#95C22×D1116yes—
281#95C22×D1111yescharacteristic
282C2×C11C22×#11711yescharacteristic
283C2×C11C2×#51911yescharacteristic
284C2×C11#342811yescharacteristic
285C2×C11#351612yes—
286C2×C11#351612yes—
287D11—24no—
288C24—111no—
289C2×Q8—1112no—
290C2×Q8—2232no—
291C2×Q8—226no—
292C2×Q8—226no—
293C2×Q8C2×C4×D1114yes—
294C2×Q8#434114yes—
295C2×Q8#434314yes—
296C22×C4—111no—
297C22×C4—113no—
298C22×C4—113no—
299C22×C4—114no—
300C22×C4—1112no—
301C22×C4—1112no—
302C22×C4—112no—
303C22×C4—116no—
304C22×C4—224no—
305C22×C4—226no—
306C22×C4—226no—
307C22×C4—446no—
308C22×C4C23×D1112yes—
309C22×C4C23×D1116yes—
310C22×C4C23×D1111yescharacteristic
311C22×C4C23×D1113yes—
312C22×C4C23×D1113yes—
313C4⋊C4—212no—
314C4⋊C4—46no—
315C4⋊C4—1124no—
316C4⋊C4—1112no—
317C4⋊C4—2212no—
318C4⋊C4—446no—
319C4⋊C4C2×C4×D11112yes—
320C22⋊C4—224no—
321C22⋊C4—2212no—
322C42—212no—
323C42—1112no—
324C42—1112no—
325C42—1112no—
326C42—2212no—
327C42—4412no—
328C42C2×C4×D11112yes—
329C11#3419211yescharacteristic, complemented, Sylow
330C23—112no—
331C23—114no—
332C23—221no—
333C23—221no—
334C23—222no—
335C23C24×D1111yescharacteristic
336Q8—2224no—
337Q8#66945116yes—
338C2×C4—26no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—26no—
342C2×C4—26no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—26no—
346C2×C4—112no—
347C2×C4—116no—
348C2×C4—116no—
349C2×C4—228no—
350C2×C4—223no—
351C2×C4—223no—
352C2×C4—226no—
353C2×C4—222no—
354C2×C4—2224no—
355C2×C4—222no—
356C2×C4—226no—
357C2×C4—226no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—226no—
361C2×C4—4412no—
362C2×C4C22×C4×D1112yes—
363C2×C4C22×C4×D1116yes—
364C2×C4C22×C4×D1116yes—
365C2×C4C2×#434116yes—
366C2×C4C2×#434316yes—
367C22—114no—
368C22—222no—
369C22—222no—
370C22—224no—
371C22—224no—
372C22C23×C4×D1111yescharacteristic
373C22C22×#434111yescharacteristic
374C22C22×#434311yescharacteristic
375C22#1062345312yes—
376C22D11×2−1+412yes—
377C4—22no—
378C4—26no—
379C4—42no—
380C4—46no—
381C4—226no—
382C4—222no—
383C4—226no—
384C4—442no—
385C4—446no—
386C4C2×#66945112yes—
387C2—224no—
388C2C22×#6694511yescharacteristic
389C2D11×#51911yescharacteristic
390C2#1308181511yescharacteristic
391C2#1308260212yes—
392C2#1308261212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2351C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2351D11
hypocenterC11#34192
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. #13071583C2semidirect
3. #13071579C2semidirect
4. #13071537C2semidirect
7. #13071263C2semidirect
10. #13070981C2semidirect
11. C11×#2351C2semidirect
17. C4×Q8×D11C4semidirect
138. #2351D11semidirect
329. C11#34192semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
#130715832
#130715792
#130715372
#130714922
Q8×(C2×D11)⋊C42
#130712632
#130710122
#130710092
#130709812
C11×#23512
#3419211