Finite Group Databasebeta

← #25249946

Subgroups — #25249946

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583339C211yesmaximal, characteristic
2#19143464C211yesmaximal, characteristic, complemented
3#19136464C212yesmaximal, complemented
4#19136459C212yesmaximal, complemented
5C4×#13063271C212yesmaximal, complemented
6C4×#13063269C212yesmaximal, complemented
7#19136381C211yesmaximal, characteristic, complemented
8#19136302C211yesmaximal, characteristic
9C2×#14582702C211yesmaximal, characteristic, complemented
10#19136192C211yesmaximal, characteristic, complemented
11C43×#2951C211yesmaximal, characteristic
12C22×Dic172C2211yescharacteristic
13#14583376—21no—
14#14583339C418yescomplemented
15C2×#13063271C2212yes—
16C2×#13063269C2212yes—
17C2×#13063265C2211yescharacteristic
18C22×C43⋊C16C2211yescharacteristic
19#14583007—22no—
20C4×Dic172C2212yes—
21C4×Dic172C2212yes—
22#14582937C2211yescharacteristic
23#14582909—21no—
24#14582726C2212yes—
25#14582724C2212yes—
26#14582703C2211yescharacteristic
27#14582703C2211yescharacteristic
28#14582702C2212yes—
29#14582702C2212yes—
30#14582700C2211yescharacteristic
31#14582700C2211yescharacteristic
32#14582675C2212yes—
33C4×C43⋊C16C2212yes—
34C2×#135×C43C2211yescharacteristic
35C43×#520—21no—
36C43×#440—22no—
37C4×Q16×C43C2212yes—
38C4×D8×C43C2212yes—
39C2×#107×C43C2211yescharacteristic
40C43×#417—21no—
41C43×#405C2211yescharacteristic
42C22×Dic86—21no—
43C2×Dic172—21no—
44C2×Dic172—22no—
45C2×Dic172C2×C414yescomplemented
46C2×Dic172C2312yes—
47C4×Dic86—22no—
48C4×Dic86—22no—
49#13063290—41no—
50#13063290—41no—
51#13063284—21no—
52#13063281—42no—
53#13063271C2×C418yescomplemented
54#13063269C2×C418yescomplemented
55#13063265C2×C414yescomplemented
56C2×C43⋊C16—22no—
57C2×C43⋊C16C2311yescharacteristic
58C2×C43⋊C16C2311yescharacteristic
59C2×C43⋊C16C2312yes—
60#13063259C2311yescharacteristic
61#13063259C2311yescharacteristic
62#13063257—21no—
63#13063250—22no—
64#13063250—22no—
65C2×#41×C43—21no—
66#135×C43—22no—
67#135×C43C2×C414yes—
68C2×Q16×C43C2311yescharacteristic
69C2×SD16×C43—21no—
70C2×D8×C43C2311yescharacteristic
71C2×M16×C43D411yescharacteristic
72C22×C8×C43C2311yescharacteristic
73C4×Q8×C43—22no—
74C4×D4×C43—22no—
75C4×D4×C43—42no—
76#117×C43—41no—
77#117×C43D411yescharacteristic
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—41no—
80#107×C43—21no—
81#107×C43C2312yes—
82#103×C43—22no—
83#102×C43—22no—
84#97×C43D412yes—
85C4×C8×C43C2312yes—
86#41×C43—24no—
87#41×C43—42no—
88C2×Q8×C43—21no—
89C2×D4×C43—21no—
90C2×D4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—42no—
93C22×C4×C43—41no—
94C22×C4×C43C2×D411yescharacteristic
95C22×Dic43—41no—
96C2×Dic86—24no—
97C2×Dic86—22no—
98C2×Dic86—41no—
99C2×Dic86—42no—
100Q16×C43—21no—
101Q16×C43C22×C412yes—
102SD16×C43—24no—
103D8×C43—21no—
104D8×C43C22×C412yes—
105M16×C43—22no—
106C2×C8×C43C22×C412yes—
107C2×C8×C43C2×D412yes—
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43#4112yes—
110C2×C8×C43C2411yescharacteristic
111C4⋊C4×C43—22no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—42no—
114C4⋊C4×C43D811yescharacteristic
115C4⋊C4×C43D811yescharacteristic
116C22⋊C4×C43—42no—
117C22⋊C4×C43D812yes—
118C42×C43—42no—
119C42×C43C2×D412yes—
120C22⋊Dic43—41no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123Dic43⋊C4—42no—
124Dic43⋊C4—42no—
125C4×Dic43—42no—
126C4×Dic43—42no—
127C4×Dic43—41no—
128Dic172—24no—
129Dic172—22no—
130Dic172C22×C414yes—
131C43⋊C16—21no—
132C43⋊C16—21no—
133C43⋊C16C22×C414yes—
134C23×C43—41no—
135C23×C43C2×D811yescharacteristic
136Q8×C43—22no—
137Q8×C43—41no—
138D4×C43—22no—
139D4×C43—44no—
140D4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—44no—
143C2×C4×C43—42no—
144C2×C4×C43—162no—
145C2×C4×C43—161no—
146C2×C4×C43C4×D412yes—
147C2×C4×C43C2×D812yes—
148C2×C4×C43C2×D812yes—
149C2×C4×C43C2×D811yescharacteristic
150C2×C4×C43#13512yes—
151C2×C4×C43C22×D411yescharacteristic
152C2×Dic43—42no—
153C2×Dic43—44no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156Dic86—24no—
157Dic86—42no—
158Dic86—44no—
159C8×C43—22no—
160C8×C43C4×D412yes—
161C8×C43C23×C411yescharacteristic
162C8×C43C2×#4111yescharacteristic
163#33455—431nomaximal, Sylow
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—42no—
167C22×C43—81no—
168C22×C43—81no—
169C22×C43C4×D812yes—
170C22×C43C22×D811yescharacteristic
171C4×C43—22no—
172C4×C43—22no—
173C4×C43—42no—
174C4×C43—82no—
175C4×C43C4×D812yes—
176C4×C43C2×C4×D411yescharacteristic
177C4×C43C2×#13511yescharacteristic
178Dic43—44no—
179Dic43—81no—
180Dic43—81no—
181C2×#510—431no—
182#2951D4311yescharacteristic
183#2950—431no—
184#2176—432no—
185#2175—432no—
186C4×Q32—432no—
187C4×SD32—432no—
188#2159—431no—
189#2138—431no—
190C2×#358—431no—
191#2108—431no—
192C2×C43—22no—
193C2×C43—82no—
194C2×C43C2×C4×D811yescharacteristic
195C2×C43#341611yescharacteristic
196C2×C43#341711yescharacteristic
197C2×#135C2×D4311yescharacteristic
198C22×Q16—431no—
199#520—21no—
200#519—861no—
201#510—438no—
202C2×Q32—432no—
203C2×SD32—432no—
204C2×M32—431no—
205C22×C16—431no—
206#441—862no—
207#440—22no—
208C4×Q16—432no—
209C4×Q16—432no—
210C4×Q16C2×D4312yes—
211C4×D8C2×D4312yes—
212#427—431no—
213C2×#107C2×D4311yescharacteristic
214#419—861no—
215#417—21no—
216#405C2×D4311yescharacteristic
217#367—432no—
218#366—432no—
219#358—431no—
220#358—431no—
221#358—432no—
222#358—432no—
223#357—431no—
224#357—431no—
225#346—432no—
226C4×C16—432no—
227C43#3345511yescharacteristic, complemented, Sylow
228C2×#41—21no—
229C22×Q8—861no—
230#135—22no—
231#135C4×D4314yes—
232C2×Q16—434no—
233C2×Q16—432no—
234C2×Q16—862no—
235C2×Q16—861no—
236C2×Q16C22×D4311yescharacteristic
237C2×SD16—21no—
238C2×D8C22×D4311yescharacteristic
239C2×M16C22⋊D4311yescharacteristic
240C22×C8C22×D4311yescharacteristic
241C4×Q8—22no—
242C4×Q8—862no—
243C4×Q8—862no—
244C4×Q8—1721no—
245C4×Q8—1721no—
246C4×D4—22no—
247C4×D4—42no—
248#117—41no—
249#117—861no—
250#117—1722no—
251#117C22⋊D4311yescharacteristic
252C2×C4⋊C4—21no—
253C2×C4⋊C4—41no—
254Q32—438no—
255SD32—438no—
256M32—434no—
257C2×C16—432no—
258C2×C16—431no—
259C2×C16—431no—
260C2×C16—862no—
261#107—21no—
262#107—431no—
263#107—431no—
264#107C22×D4312yes—
265#106—861no—
266#103—22no—
267#103—862no—
268#103—862no—
269#102—22no—
270#97C22⋊D4312yes—
271C4×C8C22×D4312yes—
272#41—24no—
273#41—42no—
274C2×Q8—21no—
275C2×Q8—864no—
276C2×Q8—862no—
277C2×Q8—1721no—
278C2×Q8—1722no—
279C2×D4—21no—
280C2×D4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—1721no—
285C22×C4C2×C22⋊D4311yescharacteristic
286Q16—21no—
287Q16—434no—
288Q16—864no—
289Q16—862no—
290Q16C2×C4×D4312yes—
291SD16—24no—
292D8—21no—
293D8C2×C4×D4312yes—
294M16—22no—
295C2×C8C2×C4×D4312yes—
296C2×C8#1062189812yes—
297C2×C8C2×C22⋊D4312yes—
298C2×C8C2×C22⋊D4311yescharacteristic
299C2×C8C23×D4311yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—42no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4—1722no—
306C4⋊C4—1722no—
307C4⋊C4#1062188211yescharacteristic
308C4⋊C4#1062188211yescharacteristic
309C22⋊C4—42no—
310C22⋊C4—1721no—
311C22⋊C4#1062188212yes—
312C42—42no—
313C42—1721no—
314C42—1722no—
315C42—1722no—
316C42C2×C22⋊D4312yes—
317C16—434no—
318C16—861no—
319C16—861no—
320C23—41no—
321C23C2×#1062188211yescharacteristic
322Q8—22no—
323Q8—41no—
324Q8—864no—
325Q8—1722no—
326Q8—1724no—
327D4—22no—
328D4—44no—
329D4—41no—
330C2×C4—41no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—162no—
334C2×C4—161no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1722no—
338C2×C4—1724no—
339C2×C4C4×C22⋊D4312yes—
340C2×C4C2×#1062188212yes—
341C2×C4C2×#1062188212yes—
342C2×C4C2×#1062188211yescharacteristic
343C2×C4#1306334512yes—
344C2×C4C22×C22⋊D4311yescharacteristic
345C8—22no—
346C8C4×C22⋊D4312yes—
347C8C22×C4×D4311yescharacteristic
348C8C2×#1062189811yescharacteristic
349C22—21no—
350C22—21no—
351C22—42no—
352C22—81no—
353C22—81no—
354C22C4×#1062188212yes—
355C22C22×#1062188211yescharacteristic
356C4—22no—
357C4—22no—
358C4—42no—
359C4—82no—
360C4—3441no—
361C4—3441no—
362C4—1724no—
363C4C4×#1062188212yes—
364C4C2×C4×C22⋊D4311yescharacteristic
365C4C2×#1306334511yescharacteristic
366C2—22no—
367C2—82no—
368C2C2×C4×#1062188211yescharacteristic
369C2#1914774211yescharacteristic
370C2#1914774611yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2951C2
socleC22×C43C22×D8
prime radicalC2×#135×C43C22
cosocleC2×C8×C43C24
hypercenter#2951D43
hypocenterC43#33455
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
2. #19143464C2semidirect
3. #19136464C2semidirect
4. #19136459C2semidirect
5. C4×#13063271C2semidirect
6. C4×#13063269C2semidirect
7. #19136381C2semidirect
9. C2×#14582702C2semidirect
10. #19136192C2semidirect
14. #14583339C4semidirect
45. C2×Dic172C2×C4semidirect
53. #13063271C2×C4semidirect
54. #13063269C2×C4semidirect
55. #13063265C2×C4semidirect
227. C43#33455semidirect

Maximal subgroups

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

subgroupindex
C2×#145833392
#191434642
#191364642
#191364592
C4×#130632712
C4×#130632692
#191363812
#191363022
C2×#145827022
#191361922
C43×#29512
#3345543