Finite Group Databasebeta

← #25017678

Subgroups — #25017678

Order 11008.

2598 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D43)⋊C4C213yesmaximal
2C2×#14582746C213yesmaximal
3C2×#95×D43C211yesmaximal, characteristic
4C4×C43⋊#95C213yesmaximal, complemented
5#95×Dic43C211yesmaximal, characteristic, complemented
6#95×Dic43C213yesmaximal, complemented
7C4×#95×C43C211yesmaximal, characteristic, complemented
8C23×C4×D43C2213yes—
9C22×(C2×D43)⋊C4C2213yes—
10C22×(C2×D43)⋊C4C2211yescharacteristic
11C22×C4×Dic43C2213yes—
12C22×C4×Dic43C2216yes—
13C4×(C2×D43)⋊C4C4124yescomplemented
14#14582746C4124yescomplemented
15C2×C43⋊#95C2213yes—
16C2×C43⋊#95C2213yes—
17C2×C43⋊#95C2213yes—
18C2×C43⋊#95C2213yes—
19#95×D43C418yescomplemented
20C22×C42×C43C2213yes—
21C2×#95×C43C2211yescharacteristic
22C2×#95×C43C2213yes—
23C24×D43C2311yescharacteristic
24C23×Dic43C2311yescharacteristic
25C23×Dic43C2313yes—
26C23×Dic43C2313yes—
27C22×C4×D43—46no—
28C22×C4×D43—46no—
29C22×C4×D43C2×C4112yes—
30C22×C4×D43C2×C4112yes—
31C22×C4×D43C2×C4112yes—
32C2×(C2×D43)⋊C4C2×C4124yes—
33C2×(C2×D43)⋊C4C2×C4112yes—
34C2×(C2×D43)⋊C4C2×C4112yes—
35C2×C4×Dic43—46no—
36C2×C4×Dic43—46no—
37C2×C4×Dic43—46no—
38C2×C4×Dic43C2×C4124yescomplemented
39C2×C4×Dic43C2×C4112yescomplemented
40C43⋊#95C2×C4112yes—
41C43⋊#95C2×C4112yescomplemented
42C43⋊#95C2×C4112yescomplemented
43C43⋊#95C2×C4112yescomplemented
44C23×C4×C43C2311yescharacteristic
45C23×C4×C43C2313yes—
46C23×C4×C43C2313yes—
47C2×C42×C43—46no—
48C2×C42×C43C2×C4112yescomplemented
49#95×C43C2×C414yes—
50#95×C43C2×C4112yescomplemented
51C24×C43C2411yescharacteristic
52C23×D43—23no—
53C23×D43—23no—
54C23×D43—21no—
55C23×D43—21no—
56C23×D43C22×C416yes—
57C23×D43C22×C416yes—
58C23×D43C22×C412yes—
59C22×C4×C43—23no—
60C22×C4×C43—26no—
61C22×C4×C43—26no—
62C22×C4×C43—23no—
63C22×C4×C43—26no—
64C22×C4×C43—23no—
65C22×C4×C43—21no—
66C22×C4×C43C22×C416yes—
67C22×C4×C43C22×C416yes—
68C22×C4×C43C22×C4112yes—
69C22×C4×C43C22×C416yes—
70C22×C4×C43C22×C416yes—
71C22×C4×C43C22×C416yes—
72C22×Dic43—23no—
73C22×Dic43—26no—
74C22×Dic43—23no—
75C22×Dic43—26no—
76C22×Dic43—26no—
77C22×Dic43—21no—
78C22×Dic43—23no—
79C22×Dic43C22×C416yes—
80C22×Dic43C22×C416yes—
81C22×Dic43C22×C4112yes—
82C22×Dic43C22×C416yes—
83C22×Dic43C22×C416yes—
84C22×Dic43C22×C416yes—
85C2×C4×D43—424no—
86C2×C4×D43—424no—
87C2×C4×D43—412no—
88C2×C4×D43—412no—
89C2×C4×D43C42148yescomplemented
90C42×C43—412no—
91(C2×D43)⋊C4C42148yescomplemented
92(C2×D43)⋊C4C42116yescomplemented
93C4×Dic43—424no—
94C4×Dic43—412no—
95C23×C43C23×C411yescharacteristic
96C23×C43C23×C413yes—
97C23×C43C23×C413yes—
98C23×C43H(5,𝔽2)13yes—
99C23×C43H(5,𝔽2)13yes—
100C23×C432−1+411yescharacteristic
101C23×C432−1+411yescharacteristic
102C22×D43—26no—
103C22×D43—212no—
104C22×D43—26no—
105C22×D43—26no—
106C22×D43—22no—
107C22×D43—26no—
108C22×D43—26no—
109C22×D43—26no—
110C22×D43—26no—
111C22×D43C2×C4214yes—
112C22×D43C2×C42112yes—
113C22×D43C2×C42112yes—
114C2×C4×C43—26no—
115C2×C4×C43—212no—
116C2×C4×C43—26no—
117C2×C4×C43—26no—
118C2×C4×C43—26no—
119C2×C4×C43—212no—
120C2×C4×C43—212no—
121C2×C4×C43—212no—
122C2×C4×C43—26no—
123C2×C4×C43—26no—
124C2×C4×C43C2×C42112yes—
125C2×C4×C43C2×C4214yes—
126C2×C4×C43C2×C42112yes—
127C2×Dic43—212no—
128C2×Dic43—212no—
129C2×Dic43—26no—
130C2×Dic43—26no—
131C2×Dic43—212no—
132C2×Dic43—26no—
133C2×Dic43—26no—
134C2×Dic43—26no—
135C2×Dic43—26no—
136C2×Dic43—212no—
137C2×Dic43C2×C42112yes—
138C2×Dic43C2×C4214yes—
139C2×Dic43C2×C42112yes—
140C4×D43—448no—
141#13749—431nomaximal, Sylow
142C22×C43C22×C4213yes—
143C22×C43C22×C4211yescharacteristic
144C22×C43C22×C4213yes—
145C22×C43#51813yes—
146C22×C43#51816yes—
147C22×C43#51813yes—
148C22×C43#51813yes—
149C22×C43#51911yescharacteristic
150C22×C43#52013yes—
151C22×C43#52013yes—
152C22×C43#52013yes—
153C22×C43#52013yes—
154C2×D43—212no—
155C2×D43—212no—
156C2×D43—24no—
157C2×D43—212no—
158C2×D43—212no—
159C2×D43—24no—
160C2×D43C4318yes—
161C4×C43—212no—
162C4×C43—24no—
163C4×C43—212no—
164Dic43—212no—
165Dic43—212no—
166Dic43—24no—
167C2×C4×C22⋊C4—433no—
168C2×C4×C22⋊C4—433no—
169C22×#95—431no—
170C4×#95—433no—
171C4×#95—433no—
172C4×#95—431no—
173C4×#95D4311yescharacteristic, complemented
174C2×C43C2×C4311yescharacteristic
175C2×C43#227313yes—
176C2×C43#227413yes—
177C2×C43#227511yescharacteristic
178C2×C43#227513yes—
179C2×C43#227513yes—
180C2×C43#227511yescharacteristic
181D43—28no—
182C24×C4—433no—
183C22×C22⋊C4—431no—
184C22×C22⋊C4—433no—
185C22×C42—433no—
186C22×C42—436no—
187C22×C42C2×D4313yes—
188C4×C22⋊C4—4324no—
189C4×C22⋊C4—4324no—
190C2×#95—433no—
191C2×#95—433no—
192C2×#95—433no—
193C2×#95—433no—
194C2×#95—438no—
195C2×#95C2×D4311yescharacteristic
196C2×#95C2×D4313yes—
197C43#1374911yescharacteristic, complemented, Sylow
198C25—431no—
199C23×C4—433no—
200C23×C4—431no—
201C23×C4—433no—
202C23×C4—4312no—
203C23×C4—4312no—
204C23×C4—4312no—
205C23×C4—1726no—
206C23×C4—1726no—
207C23×C4C22×D4311yescharacteristic
208C23×C4C22×D4313yes—
209C23×C4C22×D4313yes—
210C2×C22⋊C4—4312no—
211C2×C22⋊C4—4312no—
212C2×C22⋊C4—4324no—
213C2×C42—46no—
214C2×C42—4312no—
215C2×C42—4324no—
216C2×C42—1726no—
217C2×C42—1726no—
218C2×C42—1726no—
219C2×C42C4×D43112yescomplemented
220#95—4312no—
221#95—4312no—
222#95—4312no—
223#95—4312no—
224#95C4×D4314yes—
225#95C4×D43112yescomplemented
226C24—436no—
227C24—436no—
228C24—432no—
229C24—863no—
230C24—863no—
231C24—861no—
232C24—861no—
233C24C23×D4311yescharacteristic
234C22×C4—23no—
235C22×C4—26no—
236C22×C4—26no—
237C22×C4—23no—
238C22×C4—26no—
239C22×C4—23no—
240C22×C4—21no—
241C22×C4—436no—
242C22×C4—436no—
243C22×C4—4312no—
244C22×C4—436no—
245C22×C4—436no—
246C22×C4—436no—
247C22×C4—4348no—
248C22×C4—863no—
249C22×C4—866no—
250C22×C4—866no—
251C22×C4—863no—
252C22×C4—866no—
253C22×C4—861no—
254C22×C4—863no—
255C22×C4—17224no—
256C22×C4—17224no—
257C22×C4—17212no—
258C22×C4—17212no—
259C22×C4C2×C4×D4316yes—
260C22×C4C2×C4×D4316yes—
261C22×C4C2×C4×D4316yes—
262C22×C4C2×C4×D4316yes—
263C22×C4C2×C4×D43112yes—
264C22×C4C2×C4×D4316yes—
265C22⋊C4—4348no—
266C22⋊C4—4316no—
267C42—412no—
268C42—17224no—
269C42—17212no—
270C23—434no—
271C23—4312no—
272C23—4312no—
273C23—866no—
274C23—8612no—
275C23—866no—
276C23—866no—
277C23—862no—
278C23—866no—
279C23—866no—
280C23—866no—
281C23—866no—
282C23C22×C4×D4311yescharacteristic
283C23C22×C4×D4313yes—
284C23C22×C4×D4313yes—
285C23#1306337013yes—
286C23#1306337113yes—
287C23#1306337211yescharacteristic
288C23#1306337311yescharacteristic
289C2×C4—212no—
290C2×C4—212no—
291C2×C4—212no—
292C2×C4—26no—
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—26no—
296C2×C4—212no—
297C2×C4—26no—
298C2×C4—26no—
299C2×C4—4312no—
300C2×C4—434no—
301C2×C4—4312no—
302C2×C4—8612no—
303C2×C4—8612no—
304C2×C4—8612no—
305C2×C4—866no—
306C2×C4—866no—
307C2×C4—866no—
308C2×C4—866no—
309C2×C4—866no—
310C2×C4—866no—
311C2×C4—8612no—
312C2×C4—17248no—
313C2×C4C42×D4314yes—
314C2×C4C42×D43112yes—
315C2×C4C42×D43112yes—
316C22—438no—
317C22—8612no—
318C22—8612no—
319C22—864no—
320C22—8612no—
321C22—8612no—
322C22—864no—
323C22C2×C42×D4313yes—
324C22C2×C42×D4311yescharacteristic
325C22C2×C42×D4313yes—
326C22#1458337113yes—
327C22#1458337116yes—
328C22#1458337213yes—
329C22#1458337313yes—
330C22#1458337511yescharacteristic
331C22#1458337813yes—
332C22#1458337913yes—
333C22#1458338013yes—
334C22#1458338113yes—
335C4—212no—
336C4—24no—
337C4—212no—
338C4—8612no—
339C4—8612no—
340C4—864no—
341C2—868no—
342C2C43×D4311yescharacteristic
343C2#1913694713yes—
344C2#1913694913yes—
345C2#1913695311yescharacteristic
346C2#1913695413yes—
347C2#1913695513yes—
348C2#1913695711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC2×C43C2×C43
FittingC4×#95×C43C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC4×#95D43
hypocenterC43#13749
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
4. C4×C43⋊#95C2semidirect
5. #95×Dic43C2semidirect
6. #95×Dic43C2semidirect
7. C4×#95×C43C2semidirect
13. C4×(C2×D43)⋊C4C4semidirect
14. #14582746C4semidirect
19. #95×D43C4semidirect
38. C2×C4×Dic43C2×C4semidirect
39. C2×C4×Dic43C2×C4semidirect
41. C43⋊#95C2×C4semidirect
42. C43⋊#95C2×C4semidirect
43. C43⋊#95C2×C4semidirect
48. C2×C42×C43C2×C4semidirect
50. #95×C43C2×C4semidirect
89. C2×C4×D43C42semidirect
91. (C2×D43)⋊C4C42semidirect
92. (C2×D43)⋊C4C42semidirect
173. C4×#95D43semidirect
197. C43#13749semidirect
219. C2×C42C4×D43semidirect
225. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D43)⋊C42
C2×#145827462
C2×#95×D432
C4×C43⋊#952
#95×Dic432
C4×#95×C432
#1374943