Finite Group Databasebeta

← #14913249

Subgroups — #14913249

Order 2816.

2610 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×#41×Dic11C211yesmaximal, characteristic
2#13071564C216yesmaximal, complemented
3Q8×Dic11⋊C4C212yesmaximal, complemented
4#13071503C213yesmaximal, complemented
5#13071499C213yesmaximal, complemented
6#13071457C211yesmaximal, characteristic
7#13071078C216yesmaximal, complemented
8#13071018C213yesmaximal, complemented
9C4×Q8×Dic11C212yesmaximal, complemented
10C4×#66930C213yesmaximal, complemented
11C11×#2341C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14#41×Dic11C4116yescomplemented
15C2×Q8×Dic11C2212yes—
16C2×Q8×Dic11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×D4×Dic11C2213yes—
19C2×D4×Dic11C2213yes—
20C2×#66979C2213yes—
21C22×C4×Dic11C2213yes—
22C2×#66930C2216yes—
23C2×#66930C2216yes—
24C11×#390C2216yes—
25C11×#380C2213yes—
26C4×C11×C22⋊C4C2213yes—
27#10622834C2216yes—
28#10622825C2213yes—
29C4×C22⋊Dic11C2213yes—
30#10622589C2216yes—
31C4⋊C4×Dic11C2216yes—
32C4⋊C4×Dic11C2216yes—
33#10622586C2216yes—
34#10622558C22112yes—
35#10622557C22112yes—
36#10622555C2216yes—
37C22⋊C4×Dic11C2216yes—
38C4×C4⋊Dic11C2216yes—
39C4×Dic11⋊C4C2216yes—
40C42×Dic11C2216yes—
41#10622541C2216yes—
42#10622263C2216yes—
43#10622262C2211yescharacteristic
44#10622262C2213yes—
45#10622261C2213yes—
46#10622261C2213yes—
47C2×C11×#41—28no—
48C2×C11×#41C2×C418yes—
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11C2313yes—
51C23×C4×C11C2313yes—
52C23×Dic11C2313yes—
53C23×Dic11C2313yes—
54C4×Q8×C11—28no—
55C2×C11×C4⋊C4C2316yes—
56C2×C11×C22⋊C4C2316yes—
57C2×C11×C22⋊C4C2316yes—
58C2×C42×C11C2316yes—
59C2×C22⋊Dic11C2316yes—
60C2×C22⋊Dic11C2316yes—
61C2×C22⋊Dic11C2316yes—
62Q8×Dic11—28no—
63Q8×Dic11C2×C418yes—
64Q8×Dic11C2×C418yes—
65D4×Dic11C2×C4124yes—
66D4×Dic11C2×C4124yes—
67#66979C2×C4124yes—
68C2×C4⋊Dic11C2316yes—
69C2×C4⋊Dic11C2313yes—
70C2×C4⋊Dic11C2313yes—
71C2×Dic11⋊C4C2316yes—
72C2×Dic11⋊C4C23112yes—
73C2×Dic11⋊C4C2312yes—
74C2×C4×Dic11C2×C4124yes—
75C2×C4×Dic11C2316yes—
76C2×C4×Dic11C2316yes—
77C2×C4×Dic11C2316yes—
78C2×C4×Dic11C2312yes—
79C2×C4×Dic11C2316yes—
80C2×C4×Dic11C2313yes—
81C2×C4×Dic11C2311yescharacteristic
82C2×C4×Dic11C2313yes—
83C2×C4×Dic11C2313yes—
84#66930—224no—
85#66930—412no—
86C11×#95C2311yescharacteristic
87C11×#95C2313yes—
88C11⋊#95C2311yescharacteristic
89C11⋊#95C2313yes—
90C11⋊#95C2316yes—
91C11⋊#95C2316yes—
92C11⋊#95C23112yes—
93#34129—111nomaximal, Sylow
94C24×C11C2413yes—
95C11×#41—232no—
96C2×Q8×C11C22×C414yes—
97C2×Q8×C11#4118yes—
98C2×D4×C11—212no—
99C2×D4×C11C22×C4112yes—
100C22×C4×C11—212no—
101C22×C4×C11C22×C4112yes—
102C22×C4×C11C2416yes—
103C22×C4×C11C2411yescharacteristic
104C22×C4×C11C2412yes—
105C22×C4×C11C2413yes—
106C22×Dic11—212no—
107C22×Dic11—26no—
108C22×Dic11—26no—
109C22×Dic11C22×C4112yes—
110C22×Dic11C22×C4112yes—
111C22×Dic11C2416yes—
112C22×Dic11C2413yes—
113C22×Dic11C2413yes—
114C22×Dic11C2412yes—
115C22×Dic11C2411yescharacteristic
116C22×Dic11C2411yescharacteristic
117C11×C4⋊C4—212no—
118C11×C22⋊C4—212no—
119C11×C22⋊C4—46no—
120C42×C11—212no—
121C22⋊Dic11—212no—
122C22⋊Dic11—46no—
123C22⋊Dic11C22×C4124yes—
124C4⋊Dic11—212no—
125C4⋊Dic11C22×C4112yes—
126C4⋊Dic11C22×C4112yes—
127Dic11⋊C4—212no—
128Dic11⋊C4—412no—
129Dic11⋊C4#4118yescomplemented
130C4×Dic11—212no—
131C4×Dic11—212no—
132C4×Dic11—24no—
133C4×Dic11—212no—
134C4×Dic11—212no—
135C4×Dic11C22×C414yes—
136C4×Dic11C22×C4112yes—
137C4×Dic11C22×C4112yes—
138C4×Dic11C22×C4112yes—
139C2×C4×#41—111no—
140#2354—116no—
141Q8×C4⋊C4—112no—
142#2346—113no—
143#2346—113no—
144#2341—111no—
145#2341D1111yescharacteristic
146#2293—116no—
147#2285—113no—
148C42×Q8—112no—
149C4×#117—113no—
150C23×C11—26no—
151C23×C11—26no—
152C23×C11—23no—
153C23×C11—23no—
154C23×C11C23×C416yes—
155C23×C11C2511yescharacteristic
156Q8×C11#117116yescomplemented
157D4×C11—224no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—224no—
162C2×C4×C11—26no—
163C2×C4×C11—26no—
164C2×C4×C11—26no—
165C2×C4×C11C23×C412yes—
166C2×C4×C11C23×C416yes—
167C2×C4×C11C2×#41112yes—
168C2×C4×C11C2×#4114yes—
169C2×Dic11—22no—
170C2×Dic11—26no—
171C2×Dic11—23no—
172C2×Dic11—22no—
173C2×Dic11—23no—
174C2×Dic11—224no—
175C2×Dic11—224no—
176C2×Dic11—26no—
177C2×Dic11—26no—
178C2×Dic11—26no—
179C2×Dic11C23×C416yes—
180C2×Dic11C23×C416yes—
181C2×Dic11C23×C412yes—
182C2×Dic11C23×C412yes—
183C2×Dic11C2×#4114yes—
184C2×Dic11C2×#4114yes—
185C2×Dic11H(5,𝔽2)12yes—
186C2×Dic112−1+412yes—
187C22×#41C2×D1111yescharacteristic
188C4×#41—1116no—
189C2×C4×Q8—111no—
190C2×C4×Q8—111no—
191C2×C4×Q8—112no—
192C2×C4×Q8C2×D1112yes—
193C2×C4×D4—113no—
194C2×C4×D4—113no—
195C2×#117—113no—
196C2×#117—116no—
197C2×#117—116no—
198C22×C42—113no—
199#390—116no—
200#390C2×D1116yes—
201#389—116no—
202#389—116no—
203#388—1112no—
204#388—1112no—
205#384—116no—
206#382—116no—
207#380—113no—
208#380—116no—
209#380C2×D1113yes—
210C4×C4⋊C4—116no—
211C4×C4⋊C4—116no—
212C4×C4⋊C4—116no—
213C4×C4⋊C4—116no—
214C4×C4⋊C4—111no—
215C4×C4⋊C4—113no—
216C4×C22⋊C4—113no—
217C4×C22⋊C4—116no—
218C4×C22⋊C4C2×D1113yes—
219#376—113no—
220#376—113no—
221C43—116no—
222C22×C11—26no—
223C22×C11—26no—
224C22×C11—26no—
225C22×C11—46no—
226C22×C11—46no—
227C22×C11C24×C411yescharacteristic
228C22×C11C22×#4112yes—
229C22×C11C22×#4112yes—
230C22×C11C2×H(5,𝔽2)11yescharacteristic
231C22×C11C2×2−1+411yescharacteristic
232C4×C11—22no—
233C4×C11—24no—
234C4×C11—46no—
235C4×C11C2×#117112yes—
236Dic11—26no—
237Dic11—26no—
238Dic11—24no—
239Dic11—46no—
240Dic11C4×#4114yes—
241Dic11#52014yes—
242C2×#41—28no—
243C2×#41C4×D1118yes—
244C22×Q8C22×D1111yescharacteristic
245C22×D4C22×D1113yes—
246C23×C4—113no—
247C23×C4—113no—
248C23×C4C22×D1113yes—
249C4×Q8—28no—
250C4×Q8—118no—
251C4×Q8—118no—
252C4×Q8—228no—
253C4×D4—1124no—
254C4×D4—1124no—
255#117—1124no—
256#117—2224no—
257#117—4412no—
258C2×C4⋊C4—112no—
259C2×C4⋊C4—113no—
260C2×C4⋊C4—113no—
261C2×C4⋊C4—116no—
262C2×C4⋊C4—116no—
263C2×C4⋊C4—1112no—
264C2×C4⋊C4C22×D1116yes—
265C2×C22⋊C4—116no—
266C2×C22⋊C4—116no—
267C2×C22⋊C4—116no—
268C2×C22⋊C4C22×D1116yes—
269C2×C22⋊C4C22×D1116yes—
270C2×C42—1124no—
271C2×C42—113no—
272C2×C42—113no—
273C2×C42—113no—
274C2×C42—111no—
275C2×C42—116no—
276C2×C42—116no—
277C2×C42—116no—
278C2×C42—116no—
279C2×C42—112no—
280C2×C42C22×D1116yes—
281#95—111no—
282#95—113no—
283#95—116no—
284#95—116no—
285#95—1112no—
286#95C22×D1111yescharacteristic
287#95C22×D1113yes—
288C2×C11—46no—
289C2×C11C22×#11711yescharacteristic
290C2×C11C2×C4×#4111yescharacteristic
291C2×C11C2×#52011yescharacteristic
292C2×C11#348212yes—
293C2×C11#348312yes—
294C24C23×D1113yes—
295#41—232no—
296C2×Q8C2×C4×D1114yes—
297C2×Q8#434118yes—
298C2×D4—212no—
299C2×D4C2×C4×D11112yes—
300C22×C4—212no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—1112no—
304C22×C4—1112no—
305C22×C4—112no—
306C22×C4—113no—
307C22×C4—113no—
308C22×C4—116no—
309C22×C4—2212no—
310C22×C4—226no—
311C22×C4—226no—
312C22×C4C2×C4×D11112yes—
313C22×C4C23×D1116yes—
314C22×C4C23×D1111yescharacteristic
315C22×C4C23×D1112yes—
316C22×C4C23×D1113yes—
317C4⋊C4—212no—
318C4⋊C4—1112no—
319C4⋊C4—1112no—
320C4⋊C4—118no—
321C4⋊C4—2212no—
322C4⋊C4—2212no—
323C4⋊C4—4412no—
324C22⋊C4—212no—
325C22⋊C4—46no—
326C22⋊C4—1124no—
327C22⋊C4—2212no—
328C22⋊C4—446no—
329C42—212no—
330C42—114no—
331C42—1112no—
332C42—1112no—
333C42—1112no—
334C42—2212no—
335C42—2212no—
336C42—224no—
337C42—2212no—
338C42—2212no—
339C11#3412911yescharacteristic, complemented, Sylow
340C23—26no—
341C23—26no—
342C23—23no—
343C23—23no—
344C23C22×C4×D1116yes—
345C23C24×D1111yescharacteristic
346Q8#66930116yescomplemented
347D4—224no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—224no—
352C2×C4—26no—
353C2×C4—26no—
354C2×C4—26no—
355C2×C4—112no—
356C2×C4—112no—
357C2×C4—114no—
358C2×C4—112no—
359C2×C4—112no—
360C2×C4—116no—
361C2×C4—116no—
362C2×C4—114no—
363C2×C4—2224no—
364C2×C4—2224no—
365C2×C4—222no—
366C2×C4—226no—
367C2×C4—223no—
368C2×C4—222no—
369C2×C4—223no—
370C2×C4—226no—
371C2×C4—226no—
372C2×C4—226no—
373C2×C4C22×C4×D1112yes—
374C2×C4C22×C4×D1116yes—
375C2×C4C2×#4341112yes—
376C2×C4#41×D1114yes—
377C22—26no—
378C22—26no—
379C22—26no—
380C22—46no—
381C22—46no—
382C22C23×C4×D1111yescharacteristic
383C22C22×#434112yes—
384C22C2×#41×D1112yes—
385C22D11×H(5,𝔽2)11yescharacteristic
386C22D11×2−1+411yescharacteristic
387C4—24no—
388C4—22no—
389C4—46no—
390C4—114no—
391C4—114no—
392C4—224no—
393C4—226no—
394C4—226no—
395C4—446no—
396C4C2×#66930112yes—
397C2—46no—
398C2C22×#6693011yescharacteristic
399C2C4×#41×D1111yescharacteristic
400C2D11×#52011yescharacteristic
401C2#1308223212yes—
402C2#1308223912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2341C2
socle, cosocleC23×C11C25
prime radicalC22×C11×#41C22
hypercenter#2341D11
hypocenterC11#34129
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. #13071564C2semidirect
3. Q8×Dic11⋊C4C2semidirect
4. #13071503C2semidirect
5. #13071499C2semidirect
7. #13071078C2semidirect
8. #13071018C2semidirect
9. C4×Q8×Dic11C2semidirect
10. C4×#66930C2semidirect
14. #41×Dic11C4semidirect
129. Dic11⋊C4#41semidirect
156. Q8×C11#117semidirect
339. C11#34129semidirect
346. Q8#66930semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic112
#130715642
Q8×Dic11⋊C42
#130715032
#130714992
#130714572
#130710782
#130710182
C4×Q8×Dic112
C4×#669302
C11×#23412
#3412911