Finite Group Databasebeta

← #14920090

Subgroups — #14920090

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071924C213yesmaximal, complemented
2#13071917C216yesmaximal, complemented
3#13071899C213yesmaximal, complemented
4#13071886C213yesmaximal, complemented
5#13071879C216yesmaximal, complemented
6#13071856C213yesmaximal
7C42×D44C213yesmaximal, complemented
8C4×#66925C213yesmaximal, complemented
9C42×Q8×C11C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2213yes—
11C2×C4×D44C2216yes—
12C2×C4×D44C2213yes—
13C2×#66925C2213yes—
14C2×#66925C2213yes—
15C2×C42×D11C2213yes—
16C4×C11×C4⋊C4C2216yes—
17C4×C11×C4⋊C4C2213yes—
18C43×C11C2213yes—
19#10622844C2213yes—
20#10622842C2211yescharacteristic
21#10622607C2216yes—
22#10622606C2216yes—
23#10622605C2213yes—
24#10622604C2216yes—
25#10622599C2216yes—
26#10622597C2216yes—
27#10622595C2213yes—
28C4×(C2×D11)⋊C4C2216yes—
29C4×(C2×D11)⋊C4C2216yes—
30C4×(C2×D11)⋊C4C2216yes—
31C4×(C2×D11)⋊C4C2216yes—
32C4×(C2×D11)⋊C4C2216yes—
33C4×C4⋊Dic11C2213yes—
34C4×C4⋊Dic11C2216yes—
35#10622545C2213yes—
36#10622545C2213yes—
37C4×Dic11⋊C4C2216yes—
38C4×Dic11⋊C4C2216yes—
39C42×Dic11C2211yescharacteristic
40#10622288C2216yes—
41#10622287C2213yes—
42#10622285C2213yes—
43#10622284C2211yescharacteristic
44C11⋊#401C2212yes—
45#10622274C2213yes—
46#10622273C2216yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D44C2313yes—
49C22×C4×D11C2316yes—
50C22×C4×D11C2313yes—
51C4×Q8×C11—212no—
52C2×C11×C4⋊C4C2313yes—
53C2×C11×C4⋊C4C2316yes—
54C2×C42×C11C2313yes—
55C2×C42×C11C2316yes—
56C2×C42×C11C2316yes—
57C2×C42×C11C2313yes—
58C2×C42×C11C2311yescharacteristic
59C2×(C2×D11)⋊C4C2313yes—
60C2×(C2×D11)⋊C4C2316yes—
61C2×(C2×D11)⋊C4C2313yes—
62C2×(C2×D11)⋊C4C2316yes—
63C2×(C2×D11)⋊C4C2316yes—
64C2×(C2×D11)⋊C4C2316yes—
65C2×C4⋊Dic11C2316yes—
66C2×C4⋊Dic11C2313yes—
67C2×Dic11⋊C4C2316yes—
68C2×Dic11⋊C4C2313yes—
69C2×Dic11⋊C4C2313yes—
70C2×C4×Dic11C2316yes—
71C2×C4×Dic11C2313yes—
72C2×C4×Dic11C2313yes—
73C2×C4×Dic11C2313yes—
74C4×D44—224no—
75C4×D44—212no—
76#66925—212no—
77#66925—212no—
78C42×D11—212no—
79C11×#95C2313yes—
80C11×#95C2311yescharacteristic
81C11×#95C2312yes—
82C11⋊#95C2316yes—
83C11⋊#95C2316yes—
84C11⋊#95C2316yes—
85C11⋊#95C2316yes—
86C11⋊#95C2316yes—
87C11⋊#95C2316yes—
88C11⋊#95C2313yes—
89C11⋊#95C2313yes—
90#34551—111nomaximal, Sylow
91C23×D11C2413yes—
92C2×Q8×C11—26no—
93C22×C4×C11C2416yes—
94C22×C4×C11C2413yes—
95C22×C4×C11C2413yes—
96C22×C4×C11C2413yes—
97C22×Dic11C2416yes—
98C22×Dic11C2413yes—
99C22×Dic11C2411yescharacteristic
100C22×Dic11C2413yes—
101C2×D44—212no—
102C2×D44—26no—
103C2×C4×D11—26no—
104C2×C4×D11—26no—
105C2×C4×D11—212no—
106C2×C4×D11—212no—
107C2×C4×D11—212no—
108C2×C4×D11#41112yes—
109C11×C4⋊C4—212no—
110C11×C4⋊C4—26no—
111C42×C11—26no—
112C42×C11—212no—
113C42×C11—212no—
114C42×C11#41112yes—
115C42×C11#4114yes—
116(C2×D11)⋊C4—212no—
117(C2×D11)⋊C4—212no—
118(C2×D11)⋊C4—212no—
119(C2×D11)⋊C4—26no—
120(C2×D11)⋊C4—26no—
121(C2×D11)⋊C4—212no—
122C4⋊Dic11—212no—
123C4⋊Dic11—26no—
124Dic11⋊C4—212no—
125Dic11⋊C4—26no—
126Dic11⋊C4—26no—
127C4×Dic11—212no—
128C4×Dic11—26no—
129C4×Dic11—26no—
130C4×Dic11—26no—
131#2402—113no—
132#2401—116no—
133#2398—113no—
134#2396—113no—
135#2395—116no—
136#2392—113no—
137C42×Q8D1111yescharacteristic, complemented
138C42×D4—113no—
139C4×#117—113no—
140C23×C11C2511yescharacteristic
141C22×D11—23no—
142C22×D11—26no—
143C22×D11—26no—
144C22×D11—23no—
145C22×D11C2×#4116yes—
146Q8×C11—28no—
147C2×C4×C11—26no—
148C2×C4×C11—26no—
149C2×C4×C11—26no—
150C2×C4×C11—26no—
151C2×C4×C11—26no—
152C2×C4×C11C2×#4116yes—
153C2×C4×C11C2×#4116yes—
154C2×C4×C11C2×#4116yes—
155C2×C4×C11C2×#4116yes—
156C2×C4×C11C2×#4116yes—
157C2×Dic11—23no—
158C2×Dic11—23no—
159C2×Dic11—26no—
160C2×Dic11—23no—
161C2×Dic11—23no—
162C2×Dic11—26no—
163C2×Dic11—26no—
164C2×Dic11—26no—
165C2×Dic11C2×#4116yes—
166D44—224no—
167C4×D11—224no—
168C4×D11—424no—
169C2×C4×Q8C2×D1113yes—
170C2×C4×D4—116no—
171C2×C4×D4—113no—
172C2×#117—113no—
173C2×#117—113no—
174C22×C42—113no—
175#401—112no—
176#400—113no—
177#400—116no—
178#400—116no—
179#399—113no—
180#398—116no—
181#398—113no—
182#397—116no—
183#397—113no—
184#397—116no—
185#396—116no—
186#395—111no—
187#394—116no—
188#394—113no—
189#393—113no—
190#392—111no—
191C4×C4⋊C4—116no—
192C4×C4⋊C4—116no—
193C4×C4⋊C4—113no—
194C4×C4⋊C4—116no—
195C4×C4⋊C4C2×D1113yes—
196C4×C4⋊C4C2×D1116yes—
197C4×C22⋊C4—116no—
198C4×C22⋊C4—116no—
199C4×C22⋊C4—116no—
200C4×C22⋊C4—116no—
201C4×C22⋊C4—116no—
202#376—113no—
203#376—113no—
204C43—111no—
205C43C2×D1113yes—
206C22×C11C22×#4113yes—
207C22×C11C22×#4111yescharacteristic
208C22×C11C22×#4113yes—
209C2×D11—26no—
210C2×D11—212no—
211C2×D11—46no—
212C2×D11—43no—
213C2×D11—43no—
214C4×C11—26no—
215C4×C11—26no—
216C4×C11—46no—
217C4×C11#529112yes—
218Dic11—26no—
219Dic11—46no—
220Dic11—43no—
221Dic11—41no—
222C22×Q8C22×D1111yescharacteristic
223C22×D4—113no—
224C23×C4—113no—
225C23×C4—116no—
226C4×Q8—212no—
227C4×D4—2224no—
228C4×D4—2212no—
229#117—2212no—
230#117—2212no—
231C2×C4⋊C4—113no—
232C2×C4⋊C4—113no—
233C2×C4⋊C4—116no—
234C2×C4⋊C4—116no—
235C2×C4⋊C4—113no—
236C2×C4⋊C4C22×D1116yes—
237C2×C4⋊C4C22×D1113yes—
238C2×C22⋊C4—113no—
239C2×C22⋊C4—113no—
240C2×C22⋊C4—116no—
241C2×C22⋊C4—116no—
242C2×C22⋊C4—116no—
243C2×C22⋊C4—116no—
244C2×C42—113no—
245C2×C42—113no—
246C2×C42—113no—
247C2×C42—116no—
248C2×C42—2212no—
249C2×C42C22×D1113yes—
250C2×C42C22×D1116yes—
251C2×C42C22×D1116yes—
252C2×C42C22×D1113yes—
253C2×C42C22×D1111yescharacteristic
254#95—116no—
255#95—116no—
256#95—116no—
257#95—116no—
258#95—113no—
259#95—113no—
260#95—116no—
261#95—116no—
262#95C22×D1111yescharacteristic
263#95C22×D1113yes—
264#95C22×D1112yes—
265C2×C11C2×#52913yes—
266C2×C11#344413yes—
267C2×C11#344411yescharacteristic
268D11—46no—
269C24—113no—
270C2×Q8—26no—
271C2×D4—2212no—
272C2×D4—226no—
273C22×C4—113no—
274C22×C4—1112no—
275C22×C4—116no—
276C22×C4—111no—
277C22×C4—113no—
278C22×C4—226no—
279C22×C4—226no—
280C22×C4—2212no—
281C22×C4—2212no—
282C22×C4—2212no—
283C22×C4C23×D1116yes—
284C22×C4C23×D1113yes—
285C22×C4C23×D1113yes—
286C22×C4C23×D1113yes—
287C4⋊C4—212no—
288C4⋊C4—26no—
289C4⋊C4—2212no—
290C4⋊C4—2212no—
291C4⋊C4—226no—
292C4⋊C4—226no—
293C4⋊C4—226no—
294C22⋊C4—2212no—
295C22⋊C4—2212no—
296C22⋊C4—2212no—
297C22⋊C4—226no—
298C22⋊C4—226no—
299C22⋊C4—2212no—
300C42—212no—
301C42—26no—
302C42—212no—
303C42—226no—
304C42—2212no—
305C42—226no—
306C42—226no—
307C42#4339112yes—
308C42#434314yes—
309C11#3455111yescharacteristic, complemented, Sylow
310C23—116no—
311C23—223no—
312C23—226no—
313C23—223no—
314C23—226no—
315C23C24×D1111yescharacteristic
316Q8—28no—
317D4—2224no—
318C2×C4—26no—
319C2×C4—26no—
320C2×C4—26no—
321C2×C4—26no—
322C2×C4—26no—
323C2×C4—116no—
324C2×C4—223no—
325C2×C4—223no—
326C2×C4—2224no—
327C2×C4—223no—
328C2×C4—223no—
329C2×C4—226no—
330C2×C4—226no—
331C2×C4—226no—
332C2×C4—226no—
333C2×C4—4424no—
334C2×C4C2×#433916yes—
335C2×C4C2×#433916yes—
336C2×C4C2×#433916yes—
337C2×C4C2×#434316yes—
338C2×C4#41×D1116yes—
339C22—226no—
340C22—2212no—
341C22—446no—
342C22—443no—
343C22—443no—
344C22C22×#433913yes—
345C22C22×#434311yescharacteristic
346C22C2×#41×D1113yes—
347C4—26no—
348C4—26no—
349C4—46no—
350C4—226no—
351C4—446no—
352C4—443no—
353C4—441no—
354C4#10623111112yes—
355C2—446no—
356C2C2×#1062311113yes—
357C2#1308190913yes—
358C2#1308191211yescharacteristic
subgroupG/H
centerC2×C42C22×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC42×Q8×C11C2
prime radical#10622284C22
hypercenterC42×Q8D11
hypocenterC11#34551
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C2×C42 ◁ C42×Q8

Complements

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

NH ≅ G/Ntype
1. #13071924C2semidirect
2. #13071917C2semidirect
3. #13071899C2semidirect
4. #13071886C2semidirect
5. #13071879C2semidirect
7. C42×D44C2semidirect
8. C4×#66925C2semidirect
9. C42×Q8×C11C2semidirect
137. C42×Q8D11semidirect
309. C11#34551semidirect

Maximal subgroups

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

subgroupindex
#130719242
#130719172
#130718992
#130718862
#130718792
#130718562
C42×D442
C4×#669252
C42×Q8×C112
#3455111