Finite Group Databasebeta

← #14913244

Subgroups — #14913244

Order 2816.

2446 conjugacy classes of subgroups.

The subgroup lattice has 402 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#13071484C216yesmaximal
6Q8×(C2×D11)⋊C4C212yesmaximal
7#13071087C216yesmaximal, complemented
8#13071009C213yesmaximal
9C4×Q8×Dic11C212yesmaximal, complemented
10C4×#66945C213yesmaximal
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×#66945C2216yes—
19C2×C4⋊C4×D11C2213yes—
20C2×#66940C2213yes—
21C2×C42×D11C2213yes—
22C2×C4×Dic22C2213yes—
23C11×#389C2216yes—
24C11×#382C2213yes—
25C4×C11×C4⋊C4C2213yes—
26#10622600C2216yes—
27#10622598C2216yes—
28#10622591C22112yes—
29C4⋊C4×Dic11C2216yes—
30C4⋊C4×Dic11C2216yes—
31C4⋊C4×Dic11C2216yes—
32#10622587C2216yes—
33C4×(C2×D11)⋊C4C2216yes—
34#10622549C2213yes—
35C4×C4⋊Dic11C2213yes—
36C4×C4⋊Dic11C2216yes—
37C42×Dic11C2216yes—
38#10622542C2216yes—
39#10622279C2211yescharacteristic
40#10622279C2213yes—
41#10622277C2216yes—
42#10622268C22112yes—
43#10622264C2216yes—
44#10622261C2213yes—
45#10622261C2213yes—
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×Dic11C2316yes—
72C2×C4×Dic11C2316yes—
73C2×C4×Dic11C2312yes—
74C2×C4×Dic11C2316yes—
75C2×C4×Dic11C2313yes—
76C2×C4×Dic11C2313yes—
77C2×C4×Dic11C2313yes—
78#66945—224no—
79C4⋊C4×D11C2×C4124yes—
80#66940C2×C4124yes—
81C42×D11C2×C4124yes—
82C4×Dic22C2×C4124yes—
83C11×#95C2311yescharacteristic
84C11×#95C2313yes—
85C11×#95C2316yes—
86C11⋊#95C2311yescharacteristic
87C11⋊#95C2313yes—
88C11⋊#95C23112yes—
89C11⋊#95C2316yes—
90C11⋊#95C2316yes—
91C11⋊#95C2316yes—
92C11⋊#95C23112yes—
93#34128—111nomaximal, Sylow
94C23×D11C2411yescharacteristic
95C2×Q8×C11C22×C414yes—
96C2×Q8×C11#4114yes—
97C2×Q8×C11#4114yes—
98C22×C4×C11C2416yes—
99C22×C4×C11C2411yescharacteristic
100C22×C4×C11C2413yes—
101C22×C4×C11C2412yes—
102C22×C4×C11C2413yes—
103C22×Dic11C2416yes—
104C22×Dic11C2413yes—
105C22×Dic11C2413yes—
106C22×Dic11C2412yes—
107C22×Dic11C2411yescharacteristic
108Q8×D11—232no—
109C2×C4×D11—24no—
110C2×C4×D11—212no—
111C2×C4×D11—26no—
112C2×C4×D11—26no—
113C2×C4×D11C22×C414yes—
114C2×C4×D11C22×C4112yes—
115C2×C4×D11C22×C4112yes—
116C2×Dic22—26no—
117C2×Dic22—26no—
118C2×Dic22C22×C4112yes—
119C11×C4⋊C4—212no—
120C11×C4⋊C4—212no—
121C11×C4⋊C4C22×C4112yes—
122C42×C11—212no—
123C42×C11C22×C4112yes—
124(C2×D11)⋊C4—212no—
125(C2×D11)⋊C4#4118yes—
126C4⋊Dic11—212no—
127C4⋊Dic11—212no—
128C4⋊Dic11C22×C4112yes—
129Dic11⋊C4C22×C4124yes—
130C4×Dic11—212no—
131C4×Dic11—24no—
132C4×Dic11—212no—
133C4×Dic11—212no—
134C4×Dic11—212no—
135C4×Dic11C22×C4112yes—
136C4×Dic11C22×C4112yes—
137C4×Dic11C22×C4112yes—
138C22×C4×Q8—111no—
139#2356—113no—
140#2356—113no—
141#2351—111no—
142#2351D1111yescharacteristic, complemented
143#2344—116no—
144Q8×C22⋊C4—112no—
145#2295—116no—
146#2283—113no—
147C42×Q8—112no—
148C4×#117—113no—
149C23×C11C2511yescharacteristic
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—22no—
153C22×D11C23×C412yes—
154C22×D11C2×#4114yes—
155Q8×C11#117116yescomplemented
156C2×C4×C11—26no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—26no—
161C2×C4×C11—26no—
162C2×C4×C11—26no—
163C2×C4×C11C23×C412yes—
164C2×C4×C11C23×C416yes—
165C2×C4×C11C23×C416yes—
166C2×C4×C11C2×#4116yes—
167C2×C4×C11C2×#4116yes—
168C2×C4×C11C2×#4114yes—
169C2×Dic11—22no—
170C2×Dic11—26no—
171C2×Dic11—23no—
172C2×Dic11—23no—
173C2×Dic11—22no—
174C2×Dic11—26no—
175C2×Dic11—26no—
176C2×Dic11—26no—
177C2×Dic11C23×C416yes—
178C2×Dic11C23×C416yes—
179C2×Dic11C23×C412yes—
180C2×Dic11C2×#4114yes—
181C2×Dic112−1+414yes—
182C4×D11—224no—
183C4×D11—224no—
184C4×D11—28no—
185Dic22—224no—
186C23×Q8—111no—
187C2×C4×Q8—111no—
188C2×C4×Q8—1116no—
189C2×C4×Q8—112no—
190C2×C4×Q8—113no—
191C2×C4×Q8—113no—
192C2×C4×Q8C2×D1112yes—
193C2×C4×Q8C2×D1111yescharacteristic
194C2×#117—116no—
195C22×C4⋊C4—113no—
196C22×C42—113no—
197#391—116no—
198#391—116no—
199#389—116no—
200#389C2×D1116yes—
201#387—1112no—
202#387—1112no—
203#383—116no—
204#382—113no—
205#382C2×D1113yes—
206#381—116no—
207#380—116no—
208C4×C4⋊C4—116no—
209C4×C4⋊C4—116no—
210C4×C4⋊C4—116no—
211C4×C4⋊C4—116no—
212C4×C4⋊C4—113no—
213C4×C4⋊C4C2×D1113yes—
214C4×C22⋊C4—116no—
215C4×C22⋊C4—111no—
216C4×C22⋊C4—113no—
217#376—113no—
218#376—113no—
219#376—116no—
220C43—116no—
221C22×C11C24×C411yescharacteristic
222C22×C11C22×#4111yescharacteristic
223C22×C11C22×#4111yescharacteristic
224C22×C11C22×#4112yes—
225C22×C11C2×2−1+412yes—
226C2×D11—22no—
227C2×D11—22no—
228C2×D11—24no—
229C2×D11—24no—
230C2×D11C4×#4114yes—
231C4×C11—26no—
232C4×C11—22no—
233C4×C11—24no—
234C4×C11—46no—
235C4×C11C2×#117112yes—
236Dic11—26no—
237Dic11—26no—
238Dic11—24no—
239Dic11—46no—
240Dic11#51914yes—
241C22×Q8—118no—
242C22×Q8—113no—
243C22×Q8—224no—
244C22×Q8—224no—
245C22×Q8C22×D1111yescharacteristic
246C23×C4—113no—
247C23×C4—113no—
248C23×C4—111no—
249C4×Q8—28no—
250C4×Q8—118no—
251C4×Q8—1124no—
252C4×Q8—1124no—
253C4×Q8—228no—
254C4×Q8C4×D1118yes—
255#117—2224no—
256C2×C4⋊C4—113no—
257C2×C4⋊C4—116no—
258C2×C4⋊C4—1124no—
259C2×C4⋊C4—116no—
260C2×C4⋊C4—116no—
261C2×C4⋊C4C22×D1116yes—
262C2×C4⋊C4C22×D1116yes—
263C2×C4⋊C4C22×D1113yes—
264C2×C22⋊C4—112no—
265C2×C22⋊C4—116no—
266C2×C42—113no—
267C2×C42—113no—
268C2×C42—113no—
269C2×C42—1124no—
270C2×C42—116no—
271C2×C42—116no—
272C2×C42—116no—
273C2×C42—112no—
274C2×C42—116no—
275C2×C42C22×D1116yes—
276C2×C42C22×D1113yes—
277#95—111no—
278#95—113no—
279#95—116no—
280#95—116no—
281#95—1112no—
282#95—116no—
283#95—1112no—
284#95C22×D1111yescharacteristic
285#95C22×D1113yes—
286#95C22×D1116yes—
287C2×C11C22×#11711yescharacteristic
288C2×C11C2×C4×#4111yescharacteristic
289C2×C11C2×#51911yescharacteristic
290C2×C11#348212yes—
291C2×C11#348212yes—
292D11—24no—
293C24—111no—
294C2×Q8—1112no—
295C2×Q8—2232no—
296C2×Q8—226no—
297C2×Q8—226no—
298C2×Q8C2×C4×D1114yes—
299C2×Q8#434114yes—
300C2×Q8#434314yes—
301C22×C4—111no—
302C22×C4—113no—
303C22×C4—112no—
304C22×C4—113no—
305C22×C4—114no—
306C22×C4—1112no—
307C22×C4—1112no—
308C22×C4—116no—
309C22×C4—224no—
310C22×C4—2212no—
311C22×C4—226no—
312C22×C4—226no—
313C22×C4C23×D1116yes—
314C22×C4C23×D1111yescharacteristic
315C22×C4C23×D1113yes—
316C22×C4C23×D1112yes—
317C22×C4C23×D1113yes—
318C4⋊C4—212no—
319C4⋊C4—212no—
320C4⋊C4—1124no—
321C4⋊C4—1112no—
322C4⋊C4—2212no—
323C4⋊C4—2212no—
324C4⋊C4C2×C4×D11112yes—
325C22⋊C4—118no—
326C22⋊C4—2212no—
327C42—212no—
328C42—1112no—
329C42—1112no—
330C42—1112no—
331C42—2212no—
332C42—224no—
333C42—2212no—
334C42—2212no—
335C42—2212no—
336C42C2×C4×D11112yes—
337C11#3412811yescharacteristic, complemented, Sylow
338C23—112no—
339C23—114no—
340C23—221no—
341C23—221no—
342C23—222no—
343C23C24×D1111yescharacteristic
344Q8—2224no—
345Q8#66945116yescomplemented
346C2×C4—22no—
347C2×C4—26no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—26no—
351C2×C4—26no—
352C2×C4—26no—
353C2×C4—112no—
354C2×C4—114no—
355C2×C4—116no—
356C2×C4—116no—
357C2×C4—114no—
358C2×C4—228no—
359C2×C4—2224no—
360C2×C4—223no—
361C2×C4—222no—
362C2×C4—223no—
363C2×C4—226no—
364C2×C4—222no—
365C2×C4—2224no—
366C2×C4—226no—
367C2×C4—226no—
368C2×C4—226no—
369C2×C4C22×C4×D1112yes—
370C2×C4C22×C4×D1116yes—
371C2×C4C22×C4×D1116yes—
372C2×C4C2×#434116yes—
373C2×C4C2×#434316yes—
374C2×C4#41×D1114yes—
375C22—114no—
376C22—224no—
377C22—224no—
378C22—222no—
379C22—222no—
380C22C23×C4×D1111yescharacteristic
381C22C22×#434111yescharacteristic
382C22C22×#434311yescharacteristic
383C22C2×#41×D1112yes—
384C22D11×2−1+412yes—
385C4—24no—
386C4—26no—
387C4—22no—
388C4—46no—
389C4—114no—
390C4—224no—
391C4—226no—
392C4—226no—
393C4—446no—
394C4C2×#66945112yes—
395C2—224no—
396C2C22×#6694511yescharacteristic
397C2C4×#41×D1111yescharacteristic
398C2D11×#51911yescharacteristic
399C2#1308223212yes—
400C2#1308223612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2351C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2351D11
hypocenterC11#34128
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. #13071087C2semidirect
9. C4×Q8×Dic11C2semidirect
11. C11×#2351C2semidirect
17. C4×Q8×D11C4semidirect
142. #2351D11semidirect
155. Q8×C11#117semidirect
337. C11#34128semidirect
345. Q8#66945semidirect

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
#130714842
Q8×(C2×D11)⋊C42
#130710872
#130710092
C4×Q8×Dic112
C4×#669452
C11×#23512
#3412811