Finite Group Databasebeta

← #14913962

Subgroups — #14913962

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic
2#13071577C216yesmaximal, complemented
3#13071534C212yesmaximal, complemented
4#13071489C216yesmaximal
5Q8×(C2×D11)⋊C4C212yesmaximal
6#13071268C213yesmaximal, complemented
7#13071262C213yesmaximal, complemented
8#13071012C213yesmaximal
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×C42×D11C2213yes—
21C2×C4×Dic22C2213yes—
22C4×C11×C4⋊C4C2216yes—
23C4×C11×C4⋊C4C2213yes—
24C11×#376C2213yes—
25#10622600C2216yes—
26#10622590C2216yes—
27C4⋊C4×Dic11C2216yes—
28#10622587C2216yes—
29#10622586C2216yes—
30C4×(C2×D11)⋊C4C2216yes—
31C4×(C2×D11)⋊C4C2216yes—
32C4×C4⋊Dic11C2213yes—
33#10622546C22112yes—
34#10622545C2213yes—
35#10622545C2216yes—
36C4×Dic11⋊C4C2216yes—
37#10622542C2216yes—
38#10622541C2216yes—
39#10622280C2216yes—
40#10622277C2211yescharacteristic
41#10622277C2213yes—
42#10622265C22112yes—
43#10622264C2216yes—
44#10622264C2216yes—
45#10622263C2213yes—
46#10622263C2213yes—
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)⋊C4C2312yes—
64C2×(C2×D11)⋊C4C2316yes—
65C2×C4⋊Dic11C2316yes—
66C2×C4⋊Dic11C2313yes—
67C2×Dic11⋊C4C2316yes—
68C2×Dic11⋊C4C2316yes—
69C2×Dic11⋊C4C2316yes—
70C2×C4×Dic11C2316yes—
71C2×C4×Dic11C2316yes—
72C2×C4×Dic11C2313yes—
73C2×C4×Dic11C2313yes—
74C2×C4×Dic11C2313yes—
75C4⋊C4×D11C2×C4124yes—
76#66940C2×C4124yes—
77C42×D11C2×C4124yes—
78C4×Dic22C2×C4124yes—
79C11×#95C2311yescharacteristic
80C11×#95C2313yes—
81C11×#95C2316yes—
82C11⋊#95C2311yescharacteristic
83C11⋊#95C2313yes—
84C11⋊#95C2316yes—
85C11⋊#95C2316yes—
86C11⋊#95C2312yes—
87C11⋊#95C23112yes—
88C11⋊#95C23112yes—
89C11⋊#95C2316yes—
90C11⋊#95C2316yes—
91#34192—111nomaximal, Sylow
92C23×D11C2411yescharacteristic
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×Dic11C2413yes—
104C22×Dic11C2413yes—
105Q8×D11—232no—
106C2×C4×D11—24no—
107C2×C4×D11—212no—
108C2×C4×D11—43no—
109C2×C4×D11—43no—
110C2×C4×D11C22×C414yes—
111C2×C4×D11C22×C4112yes—
112C2×C4×D11C22×C4112yes—
113C2×Dic22—212no—
114C2×Dic22C22×C4112yes—
115C11×C4⋊C4—212no—
116C11×C4⋊C4C22×C4112yes—
117C42×C11—212no—
118C42×C11—46no—
119C42×C11C22×C4112yes—
120(C2×D11)⋊C4—24no—
121(C2×D11)⋊C4—212no—
122C4⋊Dic11—212no—
123C4⋊Dic11C22×C4112yes—
124Dic11⋊C4—46no—
125Dic11⋊C4—46no—
126Dic11⋊C4C22×C4124yes—
127C4×Dic11—212no—
128C4×Dic11—46no—
129C4×Dic11C22×C4112yes—
130C4×Dic11C22×C4112yes—
131C4×Dic11C22×C4112yes—
132C22×C4×Q8—111no—
133#2356—116no—
134#2351—112no—
135#2345—116no—
136Q8×C22⋊C4—112no—
137#2320—113no—
138#2320—113no—
139#2283—113no—
140#2283—113no—
141#2276—111no—
142#2276D1111yescharacteristic, complemented
143C23×C11C2511yescharacteristic
144C22×D11—22no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11C23×C412yes—
148C22×D112−1+414yes—
149Q8×C11#117116yes—
150C2×C4×C11—22no—
151C2×C4×C11—23no—
152C2×C4×C11—23no—
153C2×C4×C11—22no—
154C2×C4×C11—26no—
155C2×C4×C11—26no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—26no—
159C2×C4×C11C23×C412yes—
160C2×C4×C11C23×C416yes—
161C2×C4×C11C23×C416yes—
162C2×C4×C11C2×#41112yes—
163C2×Dic11—26no—
164C2×Dic11—22no—
165C2×Dic11—23no—
166C2×Dic11—23no—
167C2×Dic11—22no—
168C2×Dic11—26no—
169C2×Dic11—22no—
170C2×Dic11—26no—
171C2×Dic11—26no—
172C2×Dic11—22no—
173C2×Dic11C23×C412yes—
174C2×Dic11C23×C416yes—
175C2×Dic11C23×C416yes—
176C4×D11—28no—
177C4×D11—224no—
178C4×D11—412no—
179Dic22—224no—
180C23×Q8—111no—
181C2×C4×Q8—111no—
182C2×C4×Q8—1116no—
183C2×C4×Q8—112no—
184C2×C4×Q8—113no—
185C2×C4×Q8—113no—
186C2×C4×Q8C2×D1112yes—
187C2×C4×Q8C2×D1111yescharacteristic
188C22×C4⋊C4—113no—
189C22×C42—113no—
190#391—116no—
191#391—116no—
192#389—116no—
193#389—116no—
194#387—1112no—
195#387—1112no—
196#383—116no—
197#383—116no—
198#382—116no—
199#382—113no—
200#382—113no—
201#381—111no—
202#381—113no—
203#380—116no—
204#380—116no—
205C4×C4⋊C4—116no—
206C4×C4⋊C4—113no—
207C4×C4⋊C4—116no—
208C4×C4⋊C4C2×D1113yes—
209C4×C4⋊C4C2×D1116yes—
210C4×C22⋊C4—116no—
211C4×C22⋊C4—116no—
212#376—113no—
213#376—116no—
214#376C2×D1113yes—
215C22×C11C24×C411yescharacteristic
216C22×C11C22×#4112yes—
217C22×C11C2×2−1+412yes—
218C22×C11#58511yescharacteristic
219C22×C11#58511yescharacteristic
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—24no—
223C2×D11—24no—
224C2×D11#51914yes—
225C4×C11—22no—
226C4×C11—26no—
227C4×C11—46no—
228C4×C11—42no—
229C4×C11C2×#117112yes—
230Dic11—26no—
231Dic11—22no—
232Dic11—26no—
233Dic11—42no—
234Dic11—46no—
235C22×Q8—118no—
236C22×Q8—113no—
237C22×Q8—228no—
238C22×Q8C22×D1111yescharacteristic
239C23×C4—113no—
240C23×C4—111no—
241C23×C4—113no—
242C4×Q8—28no—
243C4×Q8—118no—
244C4×Q8—1124no—
245C4×Q8—1124no—
246C4×Q8—228no—
247C4×Q8C4×D1118yes—
248C2×C4⋊C4—116no—
249C2×C4⋊C4—113no—
250C2×C4⋊C4—1124no—
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—112no—
258C2×C42—113no—
259C2×C42—113no—
260C2×C42—113no—
261C2×C42—1124no—
262C2×C42—116no—
263C2×C42—116no—
264C2×C42C22×D1116yes—
265C2×C42C22×D1116yes—
266C2×C42C22×D1113yes—
267#95—111no—
268#95—116no—
269#95—116no—
270#95—113no—
271#95—1112no—
272#95—1112no—
273#95—116no—
274#95—116no—
275#95—112no—
276#95C22×D1111yescharacteristic
277#95C22×D1116yes—
278#95C22×D1113yes—
279C2×C11C22×#11711yescharacteristic
280C2×C11C2×#51911yescharacteristic
281C2×C11#342811yescharacteristic
282C2×C11#351612yes—
283C2×C11#351612yes—
284D11—24no—
285C24—111no—
286C2×Q8—1112no—
287C2×Q8—2232no—
288C2×Q8—2212no—
289C2×Q8C2×C4×D1114yes—
290C2×Q8#433918yes—
291C22×C4—111no—
292C22×C4—113no—
293C22×C4—113no—
294C22×C4—114no—
295C22×C4—1112no—
296C22×C4—1112no—
297C22×C4—112no—
298C22×C4—116no—
299C22×C4—224no—
300C22×C4—2212no—
301C22×C4—443no—
302C22×C4—443no—
303C22×C4C23×D1116yes—
304C22×C4C23×D1112yes—
305C22×C4C23×D1111yescharacteristic
306C22×C4C23×D1113yes—
307C22×C4C23×D1113yes—
308C4⋊C4—212no—
309C4⋊C4—1124no—
310C4⋊C4—1112no—
311C4⋊C4—2212no—
312C4⋊C4—446no—
313C4⋊C4—446no—
314C4⋊C4C2×C4×D11112yes—
315C22⋊C4—2212no—
316C22⋊C4—224no—
317C42—212no—
318C42—46no—
319C42—1112no—
320C42—1112no—
321C42—1112no—
322C42—2212no—
323C42—446no—
324C42C2×C4×D11112yes—
325C11#3419211yescharacteristic, complemented, Sylow
326C23—112no—
327C23—114no—
328C23—222no—
329C23—221no—
330C23—221no—
331C23C24×D1111yescharacteristic
332Q8—2224no—
333Q8#66925116yes—
334C2×C4—23no—
335C2×C4—22no—
336C2×C4—23no—
337C2×C4—22no—
338C2×C4—26no—
339C2×C4—26no—
340C2×C4—26no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—112no—
344C2×C4—116no—
345C2×C4—116no—
346C2×C4—228no—
347C2×C4—226no—
348C2×C4—223no—
349C2×C4—222no—
350C2×C4—223no—
351C2×C4—2224no—
352C2×C4—222no—
353C2×C4—226no—
354C2×C4—222no—
355C2×C4—222no—
356C2×C4—226no—
357C2×C4—226no—
358C2×C4—4412no—
359C2×C4C22×C4×D1112yes—
360C2×C4C22×C4×D1116yes—
361C2×C4C22×C4×D1116yes—
362C2×C4C2×#4339112yes—
363C22—114no—
364C22—222no—
365C22—222no—
366C22—224no—
367C22—224no—
368C22C23×C4×D1111yescharacteristic
369C22C22×#433912yes—
370C22#1062345511yescharacteristic
371C22D11×2−1+412yes—
372C22#1062345711yescharacteristic
373C4—22no—
374C4—26no—
375C4—46no—
376C4—42no—
377C4—226no—
378C4—222no—
379C4—226no—
380C4—442no—
381C4—446no—
382C4C2×#66925112yes—
383C2—224no—
384C2C22×#6692511yescharacteristic
385C2D11×#51911yescharacteristic
386C2#1308181611yescharacteristic
387C2#1308260112yes—
388C2#1308261112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2276C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2276D11
hypocenterC11#34192
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2276

Complements

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

NH ≅ G/Ntype
2. #13071577C2semidirect
3. #13071534C2semidirect
6. #13071268C2semidirect
7. #13071262C2semidirect
10. #13070981C2semidirect
11. C11×#2276C2semidirect
17. C4×Q8×D11C4semidirect
142. #2276D11semidirect
325. 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
#130715772
#130715342
#130714892
Q8×(C2×D11)⋊C42
#130712682
#130712622
#130710122
#130710082
#130709812
C11×#22762
#3419211