Finite Group Databasebeta

← #14913207

Subgroups — #14913207

Order 2816.

2510 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4343C211yesmaximal, characteristic
2#13071591C213yesmaximal, complemented
3#13071587C213yesmaximal, complemented
4#13071537C211yesmaximal, characteristic, complemented
5#13071508C216yesmaximal, complemented
6#13071454C212yesmaximal
7#13071074C216yesmaximal, complemented
8#13071009C213yesmaximal, complemented
9C4×Q8×Dic11C212yesmaximal, complemented
10C4×#66945C213yesmaximal, complemented
11C11×#2351C211yesmaximal, characteristic, complemented
12C22×#4343C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×Q8×Dic11C2212yes—
16C2×Q8×Dic11C2211yescharacteristic
17C4×#4343C4116yescomplemented
18C2×#66946C2213yes—
19C2×#66945C2216yes—
20C2×#66945C2213yes—
21C2×C4×D44C2213yes—
22C2×C42×D11C2213yes—
23C11×#389C2216yes—
24C11×#382C2213yes—
25C4×C11×C4⋊C4C2213yes—
26#10622603C22112yes—
27#10622601C2216yes—
28#10622600C2216yes—
29#10622598C2216yes—
30C4⋊C4×Dic11C2216yes—
31C4⋊C4×Dic11C2216yes—
32C4⋊C4×Dic11C2216yes—
33#10622552C2216yes—
34C4×(C2×D11)⋊C4C2216yes—
35#10622549C2213yes—
36C4×C4⋊Dic11C2213yes—
37C4×C4⋊Dic11C2216yes—
38C42×Dic11C2216yes—
39#10622283C22112yes—
40#10622279C2213yes—
41#10622279C2213yes—
42#10622279C2216yes—
43#10622277C2216yes—
44#10622264C2216yes—
45#10622261C2211yescharacteristic
46#10622261C2213yes—
47C22×Q8×C11C2311yescharacteristic
48C2×#4343—24no—
49C2×#4343—24no—
50C2×#4343C2×C418yes—
51C22×D44C2313yes—
52C22×C4×D11C2313yes—
53C22×C4×D11C2313yes—
54C22×C4×D11C2313yes—
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)⋊C4C2316yes—
66C2×(C2×D11)⋊C4C23112yes—
67C2×(C2×D11)⋊C4C2316yes—
68C2×C4⋊Dic11C2316yes—
69C2×C4⋊Dic11C2316yes—
70C2×C4⋊Dic11C2313yes—
71C2×C4×Dic11C2316yes—
72C2×C4×Dic11C2316yes—
73C2×C4×Dic11C2316yes—
74C2×C4×Dic11C2316yes—
75C2×C4×Dic11C2311yescharacteristic
76C2×C4×Dic11C2313yes—
77C2×C4×Dic11C2313yes—
78C2×C4×Dic11C2312yes—
79#66946C2×C4124yes—
80#66945—224no—
81#66945C2×C4124yes—
82C4×D44C2×C4124yes—
83C42×D11C2×C4124yes—
84C11×#95C2313yes—
85C11×#95C2311yescharacteristic
86C11×#95C2316yes—
87C11⋊#95C2316yes—
88C11⋊#95C2313yes—
89C11⋊#95C2311yescharacteristic
90C11⋊#95C2312yes—
91C11⋊#95C23112yes—
92C11⋊#95C2316yes—
93#34125—111nomaximal, Sylow
94C23×D11C2413yes—
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×Dic11C2411yescharacteristic
105C22×Dic11C2413yes—
106C22×Dic11C2412yes—
107C22×Dic11C2411yescharacteristic
108#4343—232no—
109C2×D44—26no—
110C2×D44—26no—
111C2×D44C22×C4112yes—
112C2×C4×D11—212no—
113C2×C4×D11—26no—
114C2×C4×D11—26no—
115C2×C4×D11—46no—
116C2×C4×D11C22×C4112yes—
117C2×C4×D11C22×C4112yes—
118C2×C4×D11C22×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—212no—
126(C2×D11)⋊C4—412no—
127(C2×D11)⋊C4C22×C4124yes—
128C4⋊Dic11—212no—
129C4⋊Dic11—212no—
130C4⋊Dic11C22×C4112yes—
131C4×Dic11—212no—
132C4×Dic11—212no—
133C4×Dic11—46no—
134C4×Dic11—46no—
135C4×Dic11C22×C414yes—
136C4×Dic11C22×C4112yes—
137C4×Dic11C22×C4112yes—
138C4×Dic11#4118yescomplemented
139C2×C4×#41—111no—
140#2357—113no—
141#2357—113no—
142#2351—111no—
143#2351D1111yescharacteristic, complemented
144#2347—116no—
145#2341—112no—
146#2293—116no—
147#2283—113no—
148C42×Q8—112no—
149C4×#117—113no—
150C23×C11C2511yescharacteristic
151C22×D11—26no—
152C22×D11—23no—
153C22×D11—23no—
154C22×D11—26no—
155C22×D11C23×C416yes—
156Q8×C11#117116yescomplemented
157C2×C4×C11—26no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—26no—
162C2×C4×C11—26no—
163C2×C4×C11—26no—
164C2×C4×C11C23×C416yes—
165C2×C4×C11C23×C412yes—
166C2×C4×C11C23×C416yes—
167C2×C4×C11C2×#4116yes—
168C2×C4×C11C2×#4116yes—
169C2×C4×C11C2×#4114yes—
170C2×Dic11—22no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—22no—
174C2×Dic11—26no—
175C2×Dic11—26no—
176C2×Dic11—26no—
177C2×Dic11—26no—
178C2×Dic11C23×C412yes—
179C2×Dic11C23×C416yes—
180C2×Dic11C23×C412yes—
181C2×Dic11C2×#4114yes—
182C2×Dic11C2×#4114yes—
183D44—224no—
184C4×D11—224no—
185C4×D11—224no—
186C4×D11—412no—
187C22×#41—111no—
188C4×#41—1116no—
189C2×C4×Q8—111no—
190C2×C4×Q8—112no—
191C2×C4×Q8C2×D1112yes—
192C2×C4×Q8C2×D1111yescharacteristic
193C2×C4×D4—113no—
194C2×C4×D4—113no—
195C2×#117—113no—
196C2×#117—116no—
197C22×C42—113no—
198#390—116no—
199#390—116no—
200#389—116no—
201#389C2×D1116yes—
202#388—1112no—
203#388—1112no—
204#383—116no—
205#382—113no—
206#382C2×D1113yes—
207#381—116no—
208#380—116no—
209C4×C4⋊C4—116no—
210C4×C4⋊C4—116no—
211C4×C4⋊C4—116no—
212C4×C4⋊C4—116no—
213C4×C4⋊C4—113no—
214C4×C4⋊C4C2×D1113yes—
215C4×C22⋊C4—116no—
216C4×C22⋊C4—113no—
217C4×C22⋊C4—113no—
218C4×C22⋊C4—116no—
219#376—111no—
220#376—113no—
221C43—116no—
222C22×C11C24×C411yescharacteristic
223C22×C11C22×#4111yescharacteristic
224C22×C11C22×#4111yescharacteristic
225C22×C11C22×#4112yes—
226C22×C11#58512yes—
227C2×D11—26no—
228C2×D11—26no—
229C2×D11—26no—
230C2×D11—46no—
231C2×D11—46no—
232C4×C11—26no—
233C4×C11—22no—
234C4×C11—24no—
235C4×C11—46no—
236C4×C11C2×#117112yes—
237Dic11—22no—
238Dic11—26no—
239Dic11—24no—
240Dic11—46no—
241Dic11C4×#4114yes—
242C2×#41—118no—
243C2×#41—224no—
244C2×#41—224no—
245C22×Q8C22×D1111yescharacteristic
246C22×D4—113no—
247C23×C4—113no—
248C23×C4—113no—
249C23×C4—113no—
250C4×Q8—28no—
251C4×Q8—118no—
252C4×Q8—228no—
253C4×Q8C4×D1118yes—
254C4×D4—1124no—
255C4×D4—1124no—
256#117—1124no—
257#117—2224no—
258C2×C4⋊C4—113no—
259C2×C4⋊C4—116no—
260C2×C4⋊C4—116no—
261C2×C4⋊C4C22×D1116yes—
262C2×C4⋊C4C22×D1116yes—
263C2×C4⋊C4C22×D1113yes—
264C2×C22⋊C4—116no—
265C2×C22⋊C4—116no—
266C2×C22⋊C4—116no—
267C2×C22⋊C4—1112no—
268C2×C42—112no—
269C2×C42—113no—
270C2×C42—113no—
271C2×C42—111no—
272C2×C42—1124no—
273C2×C42—116no—
274C2×C42—116no—
275C2×C42—116no—
276C2×C42—116no—
277C2×C42C22×D1116yes—
278C2×C42C22×D1113yes—
279#95—112no—
280#95—111no—
281#95—116no—
282#95—113no—
283#95—116no—
284#95—1112no—
285#95C22×D1111yescharacteristic
286#95C22×D1113yes—
287#95C22×D1116yes—
288C2×C11C22×#11711yescharacteristic
289C2×C11C2×C4×#4111yescharacteristic
290C2×C11#342811yescharacteristic
291C2×C11#348012yes—
292C2×C11#348012yes—
293D11—46no—
294C24—113no—
295#41—2232no—
296C2×Q8C2×C4×D1114yes—
297C2×Q8#434114yes—
298C2×Q8#434314yes—
299C2×D4—1112no—
300C2×D4—226no—
301C2×D4—226no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—113no—
305C22×C4—112no—
306C22×C4—1112no—
307C22×C4—1112no—
308C22×C4—1112no—
309C22×C4—116no—
310C22×C4—2212no—
311C22×C4—226no—
312C22×C4—226no—
313C22×C4—446no—
314C22×C4C23×D1116yes—
315C22×C4C23×D1111yescharacteristic
316C22×C4C23×D1113yes—
317C22×C4C23×D1112yes—
318C22×C4C23×D1113yes—
319C4⋊C4—212no—
320C4⋊C4—212no—
321C4⋊C4—1112no—
322C4⋊C4—2212no—
323C4⋊C4—2212no—
324C4⋊C4C2×C4×D11112yes—
325C22⋊C4—1124no—
326C22⋊C4—2212no—
327C22⋊C4—2212no—
328C22⋊C4—4412no—
329C42—212no—
330C42—114no—
331C42—1112no—
332C42—1112no—
333C42—118no—
334C42—2212no—
335C42—2212no—
336C42—446no—
337C42—446no—
338C42C2×C4×D11112yes—
339C11#3412511yescharacteristic, complemented, Sylow
340C23—116no—
341C23—223no—
342C23—223no—
343C23—226no—
344C23—226no—
345C23C24×D1111yescharacteristic
346Q8#66945116yescomplemented
347D4—2224no—
348C2×C4—22no—
349C2×C4—26no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—26no—
353C2×C4—26no—
354C2×C4—26no—
355C2×C4—112no—
356C2×C4—114no—
357C2×C4—112no—
358C2×C4—116no—
359C2×C4—114no—
360C2×C4—2224no—
361C2×C4—221no—
362C2×C4—222no—
363C2×C4—221no—
364C2×C4—222no—
365C2×C4—226no—
366C2×C4—2224no—
367C2×C4—226no—
368C2×C4—226no—
369C2×C4—226no—
370C2×C4—4412no—
371C2×C4C22×C4×D1112yes—
372C2×C4C22×C4×D1116yes—
373C2×C4C22×C4×D1116yes—
374C2×C4C2×#434116yes—
375C2×C4C2×#434316yes—
376C2×C4#41×D1114yes—
377C22—226no—
378C22—226no—
379C22—226no—
380C22—446no—
381C22—446no—
382C22C23×C4×D1111yescharacteristic
383C22C22×#434111yescharacteristic
384C22C22×#434311yescharacteristic
385C22C2×#41×D1112yes—
386C22#1062345712yes—
387C4—24no—
388C4—26no—
389C4—22no—
390C4—46no—
391C4—114no—
392C4—224no—
393C4—222no—
394C4—226no—
395C4—446no—
396C4C2×#66945112yes—
397C2—446no—
398C2C22×#6694511yescharacteristic
399C2C4×#41×D1111yescharacteristic
400C2#1308181811yescharacteristic
401C2#1308220612yes—
402C2#1308221612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2351C2
socle, cosocleC23×C11C25
prime radicalC22×#4343C22
hypercenter#2351D11
hypocenterC11#34125
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. #13071591C2semidirect
3. #13071587C2semidirect
4. #13071537C2semidirect
5. #13071508C2semidirect
7. #13071074C2semidirect
8. #13071009C2semidirect
9. C4×Q8×Dic11C2semidirect
10. C4×#66945C2semidirect
11. C11×#2351C2semidirect
17. C4×#4343C4semidirect
138. C4×Dic11#41semidirect
143. #2351D11semidirect
156. Q8×C11#117semidirect
339. C11#34125semidirect
346. Q8#66945semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43432
#130715912
#130715872
#130715372
#130715082
#130714542
#130710742
#130710092
C4×Q8×Dic112
C4×#669452
C11×#23512
#3412511