Finite Group Databasebeta

← #25960296

Subgroups — #25960296

Order 11008.

2564 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583664C211yesmaximal, characteristic
2#568×D43C212yesmaximal
3#19143206C211yesmaximal, characteristic, complemented
4#19143205C216yesmaximal, complemented
5#19143204C212yesmaximal, complemented
6#19143203C216yesmaximal, complemented
7C2×#14582946C216yesmaximal, complemented
8#430×D43C216yesmaximal, complemented
9C43×#2916C211yesmaximal, characteristic, complemented
10C2×#41×D43C2211yescharacteristic
11#14583666C2212yes—
12#14583665C22112yes—
13#14583664—28no—
14#14583664C4116yes—
15C2×#13063333C2213yes—
16C2×#13063332C2211yescharacteristic
17C2×#13063331C2213yes—
18#131×D43—28no—
19C22×#10621872C2213yes—
20C2×M16×D43C22112yes—
21C2×M16×D43C2213yes—
22#14582948C2216yescomplemented
23#14582947C22112yescomplemented
24#14582946C22112yes—
25#14582946C2214yes—
26#14582946C22112yescomplemented
27#14582946C22112yescomplemented
28C2×#13063261C2216yescomplemented
29C2×#13063260C22112yescomplemented
30#108×D43C22124yescomplemented
31C43×#568C2212yes—
32C2×#131×C43C2211yescharacteristic
33C43×#430C2216yescomplemented
34C2×#108×C43C2216yescomplemented
35C2×#10621902Q811yescharacteristic
36C2×#10621898C2313yes—
37C2×#10621900Q813yes—
38#41×D43C2×C418yes—
39#41×D43D418yes—
40C2×Q8×D43Q811yescharacteristic
41C2×D4×D43Q813yes—
42C22×C4×D43C2313yes—
43#13063333—224no—
44#13063333C2×C4124yes—
45#13063332—28no—
46#13063332C2×C418yes—
47#13063331—224no—
48#13063331C2×C4124yes—
49C2×#10621877C23112yes—
50C2×#10621877C2313yes—
51C2×#10621872—212no—
52C2×#10621872C2×C4124yes—
53C2×#10621872C2313yes—
54C2×#10621872C2311yescharacteristic
55C2×#10621872C2313yes—
56C2×#10621872C2313yes—
57M16×D43—212no—
58M16×D43—212no—
59M16×D43C2×C4124yes—
60M16×D43C2318yes—
61M16×D43C23124yes—
62C22×C43⋊C8C2313yes—
63C2×C8×D43—212no—
64C2×C8×D43C2316yes—
65#13063261C23112yes—
66#13063261C2314yes—
67#13063260C23124yes—
68#13063260C2318yes—
69C2×#41×C43C2311yescharacteristic
70#131×C43—28no—
71#131×C43C2×C418yes—
72C2×M16×C43C23112yes—
73C2×M16×C43C2313yes—
74C22×C8×C43C2313yes—
75#108×C43C23112yes—
76#108×C43C2314yes—
77C23×D43C2×Q813yes—
78#41×C43C22×C414yes—
79#41×C43C2×D414yes—
80C2×Q8×C43C2×Q811yescharacteristic
81C2×D4×C43C2×Q813yes—
82C22×C4×C43C2413yes—
83C2×C22⋊D43C2×Q816yes—
84C22×Dic43C2×Q813yes—
85#10621902C4⋊C418yes—
86Q8×D43C4⋊C418yes—
87#10621900C4⋊C4124yes—
88D4×D43C4⋊C4124yes—
89#10621898C22×C4112yes—
90#10621898C2×D4112yes—
91C2×D172C2×Q813yes—
92C2×C4×D43C22×C4112yes—
93C2×C4×D43C2×D4112yes—
94C2×C4×D43C2×Q813yes—
95C2×C4×D43C2×Q813yes—
96C2×C4×D43C2413yes—
97C2×C4×D43C2411yescharacteristic
98C2×Dic86C2×Q813yes—
99M16×C43—212no—
100M16×C43C22×C4112yes—
101M16×C43C2418yes—
102C2×C8×C43—212no—
103C2×C8×C43C22×C4112yes—
104C2×C8×C43C2411yescharacteristic
105C2×C8×C43C2413yes—
106#10621877—212no—
107#10621877C22×C4112yes—
108#10621877C2418yes—
109C2×C43⋊C8—212no—
110C2×C43⋊C8C22×C4112yes—
111C2×C43⋊C8C2413yes—
112C2×C43⋊C8C2411yescharacteristic
113#10621872—28no—
114#10621872—224no—
115#10621872C22×C4112yes—
116#10621872C22×C414yes—
117#10621872C22×C4112yes—
118#10621872C22×C4112yes—
119C8×D43—28no—
120C8×D43—224no—
121C8×D43C22×C4124yes—
122C23×C43C22×Q813yes—
123C22×D43—83no—
124C22×D43C2×C4⋊C4112yes—
125C22×D43C22×Q811yescharacteristic
126C22×D43C22×Q813yes—
127Q8×C43C2×C4⋊C414yes—
128D4×C43C2×C4⋊C4112yes—
129C2×C4×C43C23×C416yes—
130C2×C4×C43C22×D416yes—
131C2×C4×C43C22×Q813yes—
132C2×C4×C43C2511yescharacteristic
133C22⋊D43C2×C4⋊C4124yes—
134C2×Dic43C2×C4⋊C4112yes—
135C2×Dic43C22×Q813yes—
136C2×Dic43C22×Q811yescharacteristic
137D172C2×C4⋊C4112yes—
138C4×D43C2×C4⋊C4112yes—
139C4×D43C2×C4⋊C4112yes—
140C4×D43C23×C416yes—
141C4×D43C23×C412yes—
142C4×D43C22×D412yes—
143C4×D43C22×D416yes—
144Dic86C2×C4⋊C4112yes—
145C8×C43—28no—
146C8×C43C23×C416yes—
147C8×C43C23×C412yes—
148C43⋊C8—28no—
149C43⋊C8C23×C416yes—
150C43⋊C8C23×C412yes—
151#60113—431nomaximal, Sylow
152C22×C43—43no—
153C22×C43C22×C4⋊C416yes—
154C22×C43C23×Q811yescharacteristic
155C2×D43—41no—
156C2×D43—412no—
157C2×D43—43no—
158C2×D43C22×C4⋊C412yes—
159C2×D43C22×C4⋊C416yes—
160C4×C43C22×C4⋊C416yes—
161C4×C43C24×C411yescharacteristic
162C4×C43C23×D411yescharacteristic
163Dic43C22×C4⋊C416yes—
164Dic43C22×C4⋊C412yes—
165C2×#568—431no—
166C2×#568—432no—
167#2916—436no—
168#2916—436no—
169#2916—432no—
170#2916—431no—
171#2916D4311yescharacteristic, complemented
172C2×#430—436no—
173C2×#430—436no—
174C2×C43—21no—
175C2×C43—26no—
176C2×C43C23×C4⋊C411yescharacteristic
177D43—22no—
178D43—26no—
179C22×#41—431no—
180#568—4316no—
181#568—432no—
182#568—4312no—
183#568—868no—
184#568C2×D4312yes—
185C2×#131—431no—
186C2×#131—433no—
187C2×#131—433no—
188C2×#131—868no—
189C2×#131C2×D4311yescharacteristic
190C22×M16—433no—
191C22×M16—433no—
192C22×M16—4312no—
193#430—4312no—
194#430—436no—
195#430—4312no—
196#430—434no—
197#430—4312no—
198#430—4312no—
199#430C2×D4316yescomplemented
200C2×#108—4312no—
201C2×#108—436no—
202C2×#108—4324no—
203C2×#108C2×D4316yescomplemented
204C43#6011311yescharacteristic, complemented, Sylow
205C2×#41—438no—
206C2×#41—438no—
207C2×#41—431no—
208C2×#41—433no—
209C2×#41—433no—
210C2×#41C22×D4311yescharacteristic
211C22×Q8—431no—
212C22×D4—433no—
213C23×C4—433no—
214#131—28no—
215#131—438no—
216#131—4324no—
217#131—4324no—
218#131—8624no—
219#131—8624no—
220#131—868no—
221#131C4×D4318yes—
222C2×M16—433no—
223C2×M16—4324no—
224C2×M16—4324no—
225C2×M16—433no—
226C2×M16—431no—
227C2×M16—433no—
228C2×M16—433no—
229C2×M16—4312no—
230C2×M16—438no—
231C2×M16—4324no—
232C2×M16—8612no—
233C2×M16—8612no—
234C2×M16—8612no—
235C2×M16C22×D43112yes—
236C2×M16C22×D4313yes—
237C22×C8—433no—
238C22×C8—436no—
239C22×C8—8612no—
240C22×C8C22×D4313yes—
241#108—4324no—
242#108—438no—
243#108—4312no—
244#108—434no—
245#108C22×D43112yes—
246#108C22×D4314yes—
247C24—433no—
248#41—438no—
249#41—4324no—
250#41—4312no—
251#41—4312no—
252#41C2×C4×D4314yes—
253#41D4×D4314yes—
254C2×Q8—438no—
255C2×Q8—433no—
256C2×Q8Q8×D4311yescharacteristic
257C2×D4—436no—
258C2×D4—4324no—
259C2×D4—433no—
260C2×D4Q8×D4313yes—
261C22×C4—433no—
262C22×C4—4312no—
263C22×C4—4312no—
264C22×C4—433no—
265C22×C4—433no—
266C22×C4—433no—
267C22×C4—431no—
268C22×C4C23×D4313yes—
269M16—212no—
270M16—4312no—
271M16—4312no—
272M16—434no—
273M16—4312no—
274M16—4312no—
275M16—438no—
276M16—868no—
277M16—8624no—
278M16—8612no—
279M16C2×C4×D43112yes—
280M16C23×D4318yes—
281C2×C8—212no—
282C2×C8—4312no—
283C2×C8—431no—
284C2×C8—433no—
285C2×C8—4324no—
286C2×C8—868no—
287C2×C8—8624no—
288C2×C8—8612no—
289C2×C8C2×C4×D43112yes—
290C2×C8C23×D4313yes—
291C2×C8C23×D4311yescharacteristic
292C23—4312no—
293C23—431no—
294C23—433no—
295C23—3443no—
296C23C2×Q8×D4313yes—
297Q8—4312no—
298Q8C4⋊C4×D4314yes—
299D4—4324no—
300D4—4312no—
301D4C4⋊C4×D43112yes—
302C2×C4—4312no—
303C2×C4—431no—
304C2×C4—433no—
305C2×C4—4312no—
306C2×C4—4312no—
307C2×C4—436no—
308C2×C4—432no—
309C2×C4—432no—
310C2×C4—436no—
311C2×C4C22×C4×D4316yes—
312C2×C4C2×D4×D4316yes—
313C2×C4C2×Q8×D4313yes—
314C2×C4C24×D4311yescharacteristic
315C8—28no—
316C8—432no—
317C8—436no—
318C8—868no—
319C8C22×C4×D4316yes—
320C8C22×C4×D4312yes—
321C22—43no—
322C22—432no—
323C22—436no—
324C22—1721no—
325C22—1723no—
326C22—17212no—
327C22C2×C4⋊C4×D4316yes—
328C22C22×Q8×D4311yescharacteristic
329C4—432no—
330C4—436no—
331C4C2×C4⋊C4×D4316yes—
332C4C23×C4×D4311yescharacteristic
333C4C22×D4×D4311yescharacteristic
334C2—21no—
335C2—26no—
336C2—862no—
337C2—866no—
338C2C22×C4⋊C4×D4311yescharacteristic
subgroupG/H
centerC4C22×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC43×#2916C2
socleC2×C43C23×C4⋊C4
prime radicalC2×#41×D43C22
cosocleC2×C4×C43C25
hypercenter#2916D43
hypocenterC43#60113
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×#41 ◁ #2916

Complements

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

NH ≅ G/Ntype
3. #19143206C2semidirect
4. #19143205C2semidirect
5. #19143204C2semidirect
6. #19143203C2semidirect
7. C2×#14582946C2semidirect
8. #430×D43C2semidirect
9. C43×#2916C2semidirect
22. #14582948C22semidirect
23. #14582947C22semidirect
26. #14582946C22semidirect
27. #14582946C22semidirect
28. C2×#13063261C22semidirect
29. C2×#13063260C22semidirect
30. #108×D43C22semidirect
33. C43×#430C22semidirect
34. C2×#108×C43C22semidirect
171. #2916D43semidirect
199. #430C2×D43semidirect
203. C2×#108C2×D43semidirect
204. C43#60113semidirect

Maximal subgroups

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

subgroupindex
C2×#145836642
#568×D432
#191432062
#191432052
#191432042
#191432032
C2×#145829462
#430×D432
C43×#29162
#6011343