Finite Group Databasebeta

← #14914008

Subgroups — #14914008

Order 2816.

2350 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#13071569C216yesmaximal, complemented
3Q8×Dic11⋊C4C212yesmaximal, complemented
4#13071481C216yesmaximal
5Q8×(C2×D11)⋊C4C212yesmaximal
6#13071268C213yesmaximal, complemented
7#13071262C213yesmaximal, complemented
8#13071020C213yesmaximal
9#13071008C213yesmaximal
10#13070981C211yesmaximal, characteristic, complemented
11C11×#2276C211yesmaximal, 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×#66925C2216yes—
21C2×C42×D11C2213yes—
22C2×C4×Dic22C2213yes—
23C4×C11×C4⋊C4C2216yes—
24C4×C11×C4⋊C4C2213yes—
25C11×#376C2213yes—
26#10622600C2216yes—
27#10622589C2216yes—
28C4⋊C4×Dic11C2216yes—
29#10622587C2216yes—
30#10622586C2216yes—
31C4×(C2×D11)⋊C4C2216yes—
32C4×C4⋊Dic11C2213yes—
33#10622546C22112yes—
34#10622545C2213yes—
35C4×Dic11⋊C4C2216yes—
36C4×Dic11⋊C4C2216yes—
37#10622542C2216yes—
38#10622541C2216yes—
39#10622280C2211yescharacteristic
40#10622280C2213yes—
41#10622277C2216yes—
42#10622265C22112yes—
43#10622264C2213yes—
44#10622264C2213yes—
45#10622263C2216yes—
46#10622263C2216yes—
47C22×Q8×C11C2311yescharacteristic
48C2×Q8×D11—28no—
49C2×Q8×D11C2×C418yes—
50C22×C4×D11C2311yescharacteristic
51C22×C4×D11C2313yes—
52C22×C4×D11C2313yes—
53C22×Dic22C2313yes—
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)⋊C4C2312yes—
65C2×C4⋊Dic11C2316yes—
66C2×C4⋊Dic11C2313yes—
67C2×Dic11⋊C4C2312yes—
68C2×Dic11⋊C4C2316yes—
69C2×Dic11⋊C4C23112yes—
70C2×Dic11⋊C4C2316yes—
71C2×C4×Dic11C2316yes—
72C2×C4×Dic11C2316yes—
73C2×C4×Dic11C2313yes—
74C2×C4×Dic11C2313yes—
75C2×C4×Dic11C2313yes—
76C4⋊C4×D11C2×C4124yes—
77#66940C2×C4124yes—
78#66925—412no—
79C42×D11C2×C4124yes—
80C4×Dic22C2×C4124yes—
81C11×#95C2313yes—
82C11×#95C2316yes—
83C11×#95C2311yescharacteristic
84C11⋊#95C2313yes—
85C11⋊#95C2316yes—
86C11⋊#95C2316yes—
87C11⋊#95C23112yes—
88C11⋊#95C2316yes—
89C11⋊#95C2311yescharacteristic
90C11⋊#95C2316yes—
91C11⋊#95C2316yes—
92#34196—111nomaximal, Sylow
93C23×D11C2411yescharacteristic
94C2×Q8×C11C22×C414yes—
95C2×Q8×C11#4118yes—
96C22×C4×C11C2412yes—
97C22×C4×C11C2416yes—
98C22×C4×C11C2411yescharacteristic
99C22×C4×C11C2413yes—
100C22×C4×C11C2413yes—
101C22×Dic11C2412yes—
102C22×Dic11C2416yes—
103C22×Dic11C2413yes—
104C22×Dic11C2413yes—
105C22×Dic11C2411yescharacteristic
106Q8×D11—232no—
107C2×C4×D11—24no—
108C2×C4×D11—26no—
109C2×C4×D11—26no—
110C2×C4×D11—212no—
111C2×C4×D11C22×C414yes—
112C2×C4×D11C22×C4112yes—
113C2×C4×D11C22×C4112yes—
114C2×Dic22—212no—
115C2×Dic22C22×C4112yes—
116C11×C4⋊C4—212no—
117C11×C4⋊C4C22×C4112yes—
118C42×C11—212no—
119C42×C11—46no—
120C42×C11C22×C4112yes—
121(C2×D11)⋊C4—212no—
122(C2×D11)⋊C4—24no—
123C4⋊Dic11—212no—
124C4⋊Dic11C22×C4112yes—
125Dic11⋊C4—24no—
126Dic11⋊C4—212no—
127Dic11⋊C4—412no—
128Dic11⋊C4C22×C4124yes—
129C4×Dic11—212no—
130C4×Dic11—46no—
131C4×Dic11C22×C4112yes—
132C4×Dic11C22×C4112yes—
133C4×Dic11C22×C4112yes—
134C22×C4×Q8—111no—
135#2355—116no—
136Q8×C4⋊C4—112no—
137#2344—116no—
138Q8×C22⋊C4—112no—
139#2320—113no—
140#2320—113no—
141#2285—113no—
142#2283—113no—
143#2276—111no—
144#2276D1111yescharacteristic, complemented
145C23×C11C2511yescharacteristic
146C22×D11—22no—
147C22×D11—22no—
148C22×D11C23×C412yes—
149C22×D11H(5,𝔽2)12yes—
150C22×D112−1+412yes—
151Q8×C11#117116yescomplemented
152C2×C4×C11—23no—
153C2×C4×C11—22no—
154C2×C4×C11—23no—
155C2×C4×C11—22no—
156C2×C4×C11—26no—
157C2×C4×C11—26no—
158C2×C4×C11—26no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11C23×C412yes—
162C2×C4×C11C23×C416yes—
163C2×C4×C11C23×C416yes—
164C2×C4×C11C2×#41112yes—
165C2×Dic11—26no—
166C2×Dic11—23no—
167C2×Dic11—23no—
168C2×Dic11—22no—
169C2×Dic11—26no—
170C2×Dic11—26no—
171C2×Dic11—26no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11C23×C416yes—
175C2×Dic11C23×C416yes—
176C2×Dic11C23×C412yes—
177C2×Dic112−1+414yes—
178C4×D11—224no—
179C4×D11—224no—
180C4×D11—28no—
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
190C2×#117—116no—
191C22×C4⋊C4—113no—
192C22×C42—113no—
193#391—116no—
194#391—116no—
195#389—116no—
196#389—116no—
197#387—1112no—
198#387—1112no—
199#384—116no—
200#383—113no—
201#383—113no—
202#382—116no—
203#382—116no—
204#381—116no—
205#380—116no—
206#380—111no—
207#380—113no—
208C4×C4⋊C4—116no—
209C4×C4⋊C4—113no—
210C4×C4⋊C4—116no—
211C4×C4⋊C4—116no—
212C4×C4⋊C4C2×D1113yes—
213C4×C4⋊C4C2×D1116yes—
214C4×C22⋊C4—116no—
215#376—113no—
216#376C2×D1113yes—
217C22×C11C24×C411yescharacteristic
218C22×C11C22×#4112yes—
219C22×C11C2×H(5,𝔽2)11yescharacteristic
220C22×C11C2×2−1+412yes—
221C22×C11C2×2−1+411yescharacteristic
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—24no—
225C2×D11—24no—
226C2×D11#52014yes—
227C4×C11—22no—
228C4×C11—26no—
229C4×C11—46no—
230C4×C11—42no—
231C4×C11C2×#117112yes—
232Dic11—26no—
233Dic11—26no—
234Dic11—46no—
235Dic11—42no—
236Dic11#51914yes—
237C22×Q8—118no—
238C22×Q8—113no—
239C22×Q8—228no—
240C22×Q8C22×D1111yescharacteristic
241C23×C4—113no—
242C23×C4—113no—
243C23×C4—111no—
244C4×Q8—28no—
245C4×Q8—118no—
246C4×Q8—1124no—
247C4×Q8—1124no—
248C4×Q8—228no—
249C4×Q8C4×D1118yes—
250#117—4412no—
251C2×C4⋊C4—116no—
252C2×C4⋊C4—113no—
253C2×C4⋊C4—1124no—
254C2×C4⋊C4—116no—
255C2×C4⋊C4—112no—
256C2×C4⋊C4—116no—
257C2×C4⋊C4—1112no—
258C2×C4⋊C4C22×D1116yes—
259C2×C4⋊C4C22×D1113yes—
260C2×C22⋊C4—116no—
261C2×C22⋊C4—112no—
262C2×C42—113no—
263C2×C42—113no—
264C2×C42—113no—
265C2×C42—1124no—
266C2×C42—116no—
267C2×C42—116no—
268C2×C42C22×D1116yes—
269C2×C42C22×D1116yes—
270C2×C42C22×D1113yes—
271#95—111no—
272#95—113no—
273#95—116no—
274#95—116no—
275#95—116no—
276#95—1112no—
277#95—116no—
278#95—116no—
279#95C22×D1111yescharacteristic
280#95C22×D1113yes—
281#95C22×D1116yes—
282C2×C11C22×#11711yescharacteristic
283C2×C11C2×#51911yescharacteristic
284C2×C11C2×#52011yescharacteristic
285C2×C11#352212yes—
286C2×C11#352312yes—
287D11—24no—
288C24—111no—
289C2×Q8—1112no—
290C2×Q8—2232no—
291C2×Q8—2212no—
292C2×Q8C2×C4×D1114yes—
293C2×Q8#433918yes—
294C22×C4—111no—
295C22×C4—113no—
296C22×C4—113no—
297C22×C4—114no—
298C22×C4—1112no—
299C22×C4—1112no—
300C22×C4—112no—
301C22×C4—116no—
302C22×C4—224no—
303C22×C4—226no—
304C22×C4—226no—
305C22×C4—2212no—
306C22×C4C23×D1112yes—
307C22×C4C23×D1116yes—
308C22×C4C23×D1111yescharacteristic
309C22×C4C23×D1113yes—
310C22×C4C23×D1113yes—
311C4⋊C4—212no—
312C4⋊C4—1124no—
313C4⋊C4—1112no—
314C4⋊C4—224no—
315C4⋊C4—2212no—
316C4⋊C4—2212no—
317C4⋊C4—4412no—
318C4⋊C4C2×C4×D11112yes—
319C22⋊C4—2212no—
320C22⋊C4—224no—
321C42—212no—
322C42—46no—
323C42—1112no—
324C42—1112no—
325C42—1112no—
326C42—2212no—
327C42—446no—
328C42C2×C4×D11112yes—
329C11#3419611yescharacteristic, complemented, Sylow
330C23—112no—
331C23—112no—
332C23—112no—
333C23—222no—
334C23—222no—
335C23C24×D1111yescharacteristic
336Q8—2224no—
337Q8#66925116yescomplemented
338C2×C4—23no—
339C2×C4—22no—
340C2×C4—23no—
341C2×C4—22no—
342C2×C4—26no—
343C2×C4—26no—
344C2×C4—22no—
345C2×C4—26no—
346C2×C4—22no—
347C2×C4—112no—
348C2×C4—114no—
349C2×C4—116no—
350C2×C4—116no—
351C2×C4—228no—
352C2×C4—2224no—
353C2×C4—226no—
354C2×C4—223no—
355C2×C4—223no—
356C2×C4—2224no—
357C2×C4—222no—
358C2×C4—226no—
359C2×C4—226no—
360C2×C4—222no—
361C2×C4—226no—
362C2×C4—222no—
363C2×C4C22×C4×D1112yes—
364C2×C4C22×C4×D1116yes—
365C2×C4C22×C4×D1116yes—
366C2×C4C2×#4339112yes—
367C22—114no—
368C22—224no—
369C22—224no—
370C22—222no—
371C22—222no—
372C22C23×C4×D1111yescharacteristic
373C22C22×#433912yes—
374C22D11×H(5,𝔽2)11yescharacteristic
375C22D11×2−1+412yes—
376C22D11×2−1+411yescharacteristic
377C4—22no—
378C4—26no—
379C4—46no—
380C4—42no—
381C4—114no—
382C4—226no—
383C4—226no—
384C4—446no—
385C4—442no—
386C4C2×#66925112yes—
387C2—224no—
388C2C22×#6692511yescharacteristic
389C2D11×#51911yescharacteristic
390C2D11×#52011yescharacteristic
391C2#1308269512yes—
392C2#1308270612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2276C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2276D11
hypocenterC11#34196
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2276

Complements

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

NH ≅ G/Ntype
2. #13071569C2semidirect
3. Q8×Dic11⋊C4C2semidirect
6. #13071268C2semidirect
7. #13071262C2semidirect
10. #13070981C2semidirect
11. C11×#2276C2semidirect
17. C4×Q8×D11C4semidirect
144. #2276D11semidirect
151. Q8×C11#117semidirect
329. C11#34196semidirect
337. Q8#66925semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
#130715692
Q8×Dic11⋊C42
#130714812
Q8×(C2×D11)⋊C42
#130712682
#130712622
#130710202
#130710082
#130709812
C11×#22762
#3419611