Finite Group Databasebeta

← #25262914

Subgroups — #25262914

Order 11008.

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#19137903C213yesmaximal, complemented
2#19137896C216yesmaximal, complemented
3#19137878C213yesmaximal, complemented
4#19137865C213yesmaximal, complemented
5#19137858C216yesmaximal, complemented
6#19137835C213yesmaximal
7C42×D172C213yesmaximal, complemented
8C4×#13063282C213yesmaximal, complemented
9C42×Q8×C43C211yesmaximal, characteristic, complemented
10C2×C4×D172C2216yes—
11C2×C4×D172C2213yes—
12C2×#13063282C2213yes—
13C2×#13063282C2213yes—
14C2×C42×D43C2213yes—
15C43⋊#401C2212yes—
16#14582841C2216yes—
17#14582838C2216yes—
18#14582837C2213yes—
19#14582834C2213yes—
20#14582832C2216yes—
21#14582831C2213yes—
22#14582828C2216yes—
23#14582826C2213yes—
24#14582825C2216yes—
25#14582821C2216yes—
26#14582818C2211yescharacteristic
27#14582817C2213yes—
28#14582816C2216yes—
29#14582810C2213yes—
30#14582809C2211yescharacteristic
31C4×Dic43⋊C4C2216yes—
32C4×Dic43⋊C4C2216yes—
33C4×C4⋊Dic43C2213yes—
34C4×C4⋊Dic43C2216yes—
35C4×(C2×D43)⋊C4C2216yes—
36C4×(C2×D43)⋊C4C2216yes—
37C4×(C2×D43)⋊C4C2216yes—
38C4×(C2×D43)⋊C4C2216yes—
39C4×(C2×D43)⋊C4C2216yes—
40#14582745C2213yes—
41#14582745C2213yes—
42C42×Dic43C2211yescharacteristic
43C2×C4×Q8×C43C2213yes—
44C4×C4⋊C4×C43C2213yes—
45C4×C4⋊C4×C43C2216yes—
46C43×C43C2213yes—
47C22×D172C2313yes—
48C22×C4×D43C2316yes—
49C22×C4×D43C2313yes—
50C4×D172—224no—
51C4×D172—212no—
52#13063282—212no—
53#13063282—212no—
54C2×C4⋊Dic43C2316yes—
55C2×C4⋊Dic43C2313yes—
56C2×Dic43⋊C4C2313yes—
57C2×Dic43⋊C4C2313yes—
58C2×Dic43⋊C4C2316yes—
59C2×(C2×D43)⋊C4C2313yes—
60C2×(C2×D43)⋊C4C2313yes—
61C2×(C2×D43)⋊C4C2316yes—
62C2×(C2×D43)⋊C4C2316yes—
63C2×(C2×D43)⋊C4C2316yes—
64C2×(C2×D43)⋊C4C2316yes—
65C2×C4×Dic43C2313yes—
66C2×C4×Dic43C2316yes—
67C2×C4×Dic43C2313yes—
68C2×C4×Dic43C2313yes—
69C42×D43—212no—
70C43⋊#95C2316yes—
71C43⋊#95C2313yes—
72C43⋊#95C2316yes—
73C43⋊#95C2313yes—
74C43⋊#95C2316yes—
75C43⋊#95C2316yes—
76C43⋊#95C2316yes—
77C43⋊#95C2316yes—
78C22×Q8×C43C2311yescharacteristic
79C4×Q8×C43—212no—
80C2×C4⋊C4×C43C2316yes—
81C2×C4⋊C4×C43C2313yes—
82C2×C42×C43C2316yes—
83C2×C42×C43C2313yes—
84C2×C42×C43C2316yes—
85C2×C42×C43C2313yes—
86C2×C42×C43C2311yescharacteristic
87#95×C43C2311yescharacteristic
88#95×C43C2313yes—
89#95×C43C2312yes—
90C23×D43C2413yes—
91C2×Q8×C43—26no—
92C22×C4×C43C2416yes—
93C22×C4×C43C2413yes—
94C22×C4×C43C2413yes—
95C22×C4×C43C2413yes—
96C22×Dic43C2416yes—
97C22×Dic43C2413yes—
98C22×Dic43C2411yescharacteristic
99C22×Dic43C2413yes—
100C2×D172—26no—
101C2×D172—212no—
102C2×C4×D43—26no—
103C2×C4×D43—26no—
104C2×C4×D43—212no—
105C2×C4×D43—212no—
106C2×C4×D43—212no—
107C2×C4×D43#41112yes—
108C4⋊C4×C43—212no—
109C4⋊C4×C43—26no—
110C42×C43—212no—
111C42×C43—26no—
112C42×C43—212no—
113C42×C43#41112yes—
114C42×C43#4114yes—
115(C2×D43)⋊C4—26no—
116(C2×D43)⋊C4—26no—
117(C2×D43)⋊C4—212no—
118(C2×D43)⋊C4—212no—
119(C2×D43)⋊C4—212no—
120(C2×D43)⋊C4—212no—
121C4⋊Dic43—26no—
122C4⋊Dic43—212no—
123Dic43⋊C4—26no—
124Dic43⋊C4—26no—
125Dic43⋊C4—212no—
126C4×Dic43—212no—
127C4×Dic43—26no—
128C4×Dic43—26no—
129C4×Dic43—26no—
130C23×C43C2511yescharacteristic
131C22×D43—23no—
132C22×D43—26no—
133C22×D43—26no—
134C22×D43—23no—
135C22×D43C2×#4116yes—
136Q8×C43—28no—
137C2×C4×C43—26no—
138C2×C4×C43—26no—
139C2×C4×C43—26no—
140C2×C4×C43—26no—
141C2×C4×C43—26no—
142C2×C4×C43C2×#4116yes—
143C2×C4×C43C2×#4116yes—
144C2×C4×C43C2×#4116yes—
145C2×C4×C43C2×#4116yes—
146C2×C4×C43C2×#4116yes—
147C2×Dic43—23no—
148C2×Dic43—23no—
149C2×Dic43—26no—
150C2×Dic43—26no—
151C2×Dic43—23no—
152C2×Dic43—23no—
153C2×Dic43—26no—
154C2×Dic43—26no—
155C2×Dic43C2×#4116yes—
156D172—224no—
157C4×D43—224no—
158C4×D43—424no—
159#34551—431nomaximal, Sylow
160C22×C43C22×#4113yes—
161C22×C43C22×#4113yes—
162C22×C43C22×#4111yescharacteristic
163C2×D43—26no—
164C2×D43—212no—
165C2×D43—46no—
166C2×D43—43no—
167C2×D43—43no—
168C4×C43—26no—
169C4×C43—26no—
170C4×C43—46no—
171C4×C43#529112yes—
172Dic43—26no—
173Dic43—46no—
174Dic43—43no—
175Dic43—41no—
176#2402—433no—
177#2401—436no—
178#2398—433no—
179#2396—433no—
180#2395—436no—
181#2392—433no—
182C42×Q8D4311yescharacteristic, complemented
183C42×D4—433no—
184C4×#117—433no—
185C2×C43C2×#52913yes—
186C2×C43#344413yes—
187C2×C43#344411yescharacteristic
188D43—46no—
189C2×C4×Q8C2×D4313yes—
190C2×C4×D4—436no—
191C2×C4×D4—433no—
192C2×#117—433no—
193C2×#117—433no—
194C22×C42—433no—
195#401—432no—
196#400—433no—
197#400—436no—
198#400—436no—
199#399—433no—
200#398—436no—
201#398—433no—
202#397—436no—
203#397—433no—
204#397—436no—
205#396—436no—
206#395—431no—
207#394—436no—
208#394—433no—
209#393—433no—
210#392—431no—
211C4×C4⋊C4—436no—
212C4×C4⋊C4—436no—
213C4×C4⋊C4—433no—
214C4×C4⋊C4—436no—
215C4×C4⋊C4C2×D4313yes—
216C4×C4⋊C4C2×D4316yes—
217C4×C22⋊C4—436no—
218C4×C22⋊C4—436no—
219C4×C22⋊C4—436no—
220C4×C22⋊C4—436no—
221C4×C22⋊C4—436no—
222#376—433no—
223#376—433no—
224C43—431no—
225C43C2×D4313yes—
226C43#3455111yescharacteristic, complemented, Sylow
227C22×Q8C22×D4311yescharacteristic
228C22×D4—433no—
229C23×C4—433no—
230C23×C4—436no—
231C4×Q8—212no—
232C4×D4—8624no—
233C4×D4—8612no—
234#117—8612no—
235#117—8612no—
236C2×C4⋊C4—433no—
237C2×C4⋊C4—433no—
238C2×C4⋊C4—436no—
239C2×C4⋊C4—436no—
240C2×C4⋊C4—433no—
241C2×C4⋊C4C22×D4316yes—
242C2×C4⋊C4C22×D4313yes—
243C2×C22⋊C4—433no—
244C2×C22⋊C4—433no—
245C2×C22⋊C4—436no—
246C2×C22⋊C4—436no—
247C2×C22⋊C4—436no—
248C2×C22⋊C4—436no—
249C2×C42—433no—
250C2×C42—433no—
251C2×C42—433no—
252C2×C42—436no—
253C2×C42—8612no—
254C2×C42C22×D4313yes—
255C2×C42C22×D4316yes—
256C2×C42C22×D4316yes—
257C2×C42C22×D4313yes—
258C2×C42C22×D4311yescharacteristic
259#95—436no—
260#95—436no—
261#95—436no—
262#95—436no—
263#95—433no—
264#95—433no—
265#95—436no—
266#95—436no—
267#95C22×D4311yescharacteristic
268#95C22×D4313yes—
269#95C22×D4312yes—
270C24—433no—
271C2×Q8—26no—
272C2×D4—8612no—
273C2×D4—866no—
274C22×C4—433no—
275C22×C4—4312no—
276C22×C4—436no—
277C22×C4—433no—
278C22×C4—431no—
279C22×C4—866no—
280C22×C4—866no—
281C22×C4—8612no—
282C22×C4—8612no—
283C22×C4—8612no—
284C22×C4C23×D4316yes—
285C22×C4C23×D4313yes—
286C22×C4C23×D4313yes—
287C22×C4C23×D4313yes—
288C4⋊C4—212no—
289C4⋊C4—26no—
290C4⋊C4—8612no—
291C4⋊C4—8612no—
292C4⋊C4—866no—
293C4⋊C4—866no—
294C4⋊C4—866no—
295C22⋊C4—8612no—
296C22⋊C4—8612no—
297C22⋊C4—8612no—
298C22⋊C4—866no—
299C22⋊C4—866no—
300C22⋊C4—8612no—
301C42—26no—
302C42—212no—
303C42—212no—
304C42—866no—
305C42—866no—
306C42—8612no—
307C42—866no—
308C42#10621898112yes—
309C42#1062190214yes—
310C23—436no—
311C23—866no—
312C23—863no—
313C23—866no—
314C23—863no—
315C23C24×D4311yescharacteristic
316Q8—28no—
317D4—8624no—
318C2×C4—26no—
319C2×C4—26no—
320C2×C4—26no—
321C2×C4—26no—
322C2×C4—26no—
323C2×C4—436no—
324C2×C4—863no—
325C2×C4—863no—
326C2×C4—8624no—
327C2×C4—866no—
328C2×C4—866no—
329C2×C4—863no—
330C2×C4—863no—
331C2×C4—866no—
332C2×C4—866no—
333C2×C4—17224no—
334C2×C4#41×D4316yes—
335C2×C4C2×#1062189816yes—
336C2×C4C2×#1062189816yes—
337C2×C4C2×#1062189816yes—
338C2×C4C2×#1062190216yes—
339C22—866no—
340C22—8612no—
341C22—1726no—
342C22—1723no—
343C22—1723no—
344C22C2×#41×D4313yes—
345C22C22×#1062189813yes—
346C22C22×#1062190211yescharacteristic
347C4—26no—
348C4—26no—
349C4—46no—
350C4—866no—
351C4—1726no—
352C4—1723no—
353C4—1721no—
354C4#14583436112yes—
355C2—1726no—
356C2C2×#1458343613yes—
357C2#1914788813yes—
358C2#1914789111yescharacteristic
subgroupG/H
centerC2×C42C22×D43
commutator, socle, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC42×Q8×C43C2
prime radical#14582809C22
hypercenterC42×Q8D43
hypocenterC43#34551
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C42×Q8

Complements

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

NH ≅ G/Ntype
1. #19137903C2semidirect
2. #19137896C2semidirect
3. #19137878C2semidirect
4. #19137865C2semidirect
5. #19137858C2semidirect
7. C42×D172C2semidirect
8. C4×#13063282C2semidirect
9. C42×Q8×C43C2semidirect
182. C42×Q8D43semidirect
226. C43#34551semidirect

Maximal subgroups

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

subgroupindex
#191379032
#191378962
#191378782
#191378652
#191378582
#191378352
C42×D1722
C4×#130632822
C42×Q8×C432
#3455143