Finite Group Databasebeta

← #25249939

Subgroups — #25249939

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583335C211yesmaximal, characteristic
2#19143472C211yesmaximal, characteristic, complemented
3#19136469C212yesmaximal, complemented
4#19136459C212yesmaximal, complemented
5C4×#13063269C212yesmaximal, complemented
6C4×#13063266C212yesmaximal, complemented
7#19136384C211yesmaximal, characteristic, complemented
8#19136300C211yesmaximal, characteristic, complemented
9C2×#14582700C211yesmaximal, characteristic, complemented
10#19136192C211yesmaximal, characteristic, complemented
11C43×#2948C211yesmaximal, characteristic, complemented
12C2×#13063347C2211yescharacteristic
13#14583379—21no—
14#14583335C418yescomplemented
15C2×#13063269C2212yes—
16C2×#13063266C2212yes—
17C2×#13063265C2211yescharacteristic
18C22×C43⋊C16C2211yescharacteristic
19#14583001—22no—
20C4×Dic172C2212yescomplemented
21C4×D344C2212yescomplemented
22C2×#13063259C2211yescharacteristic
23#14582901—21no—
24#14582726C2212yescomplemented
25#14582724C2212yescomplemented
26#14582702C2211yescharacteristic, complemented
27#14582702C2211yescharacteristic, complemented
28#14582700C2212yes—
29#14582700C2212yes—
30#14582699C2211yescharacteristic, complemented
31#14582699C2211yescharacteristic, complemented
32#14582675C2212yescomplemented
33C4×C43⋊C16C2212yescomplemented
34C22×D8×C43C2211yescharacteristic
35C43×#518—21no—
36C43×#442—22no—
37C4×D8×C43C2212yes—
38C4×D8×C43C2212yes—
39C43×#427C2211yescharacteristic
40C43×#418—21no—
41C43×#405C2211yescharacteristic
42C2×#10621898—21no—
43#13063347—22no—
44#13063347C2×C414yescomplemented
45C2×Dic172C2311yescharacteristic
46C2×#10621873—21no—
47C2×D344C2311yescharacteristic
48C4×Dic86—22no—
49C4×D172—22no—
50(C22⋊D43)⋊C4—42no—
51#13063283—41no—
52C2×C4⋊Dic43—21no—
53C4⋊C4×D43—41no—
54#13063269C2×C418yescomplemented
55#13063266C2×C418yescomplemented
56#13063265C2×C414yescomplemented
57C2×C43⋊C16—22no—
58C2×C43⋊C16C2311yescharacteristic
59C2×C43⋊C16C2311yescharacteristic
60C2×C43⋊C16C2312yes—
61#13063259—21no—
62#13063259C2312yes—
63#13063250—22no—
64#13063247—22no—
65C22×D4×C43—21no—
66C2×D8×C43—21no—
67C2×D8×C43—22no—
68C2×D8×C43C2×C414yescomplemented
69C2×D8×C43C2312yes—
70C2×M16×C43D411yescharacteristic
71C22×C8×C43C2311yescharacteristic
72C4×D4×C43—22no—
73C4×D4×C43—22no—
74C4×D4×C43—41no—
75C4×D4×C43—41no—
76#117×C43—21no—
77#117×C43D411yescharacteristic
78C2×C22⋊C4×C43—42no—
79#107×C43C2311yescharacteristic
80#107×C43C2311yescharacteristic
81#106×C43—21no—
82#102×C43—22no—
83#102×C43—22no—
84#97×C43D412yes—
85C4×C8×C43C2312yes—
86C24×C43—41no—
87C2×D4×C43—24no—
88C2×D4×C43—22no—
89C2×D4×C43—41no—
90C2×D4×C43—42no—
91C22×C4×C43—42no—
92C22×C4×C43—42no—
93C22×C4×C43C2×D411yescharacteristic
94C2×C22⋊D43—41no—
95C22×Dic43—41no—
96#10621898—24no—
97#10621898—42no—
98C2×D172—21no—
99C2×C4×D43—41no—
100C2×C4×D43—42no—
101C2×Dic86—21no—
102D8×C43—24no—
103D8×C43—22no—
104D8×C43C22×C414yes—
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—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43D811yescharacteristic
114C4⋊C4×C43D811yescharacteristic
115C22⋊C4×C43—42no—
116C22⋊C4×C43—42no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43D812yes—
119C42×C43—41no—
120C42×C43C2×D412yes—
121(C2×D43)⋊C4—42no—
122C4⋊Dic43—22no—
123C4⋊Dic43—41no—
124Dic43⋊C4—42no—
125C4×Dic43—42no—
126Dic172—21no—
127Dic172C22×C412yes—
128D344—21no—
129D344C22×C412yes—
130#10621873—24no—
131C43⋊C16—21no—
132C43⋊C16—21no—
133C43⋊C16C22×C414yes—
134C23×C43—42no—
135C23×C43—44no—
136C23×C43—161no—
137C23×C43—161no—
138C23×C43C2×D811yescharacteristic
139C22×D43—41no—
140D4×C43—24no—
141D4×C43—42no—
142D4×C43—44no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—162no—
146C2×C4×C43—162no—
147C2×C4×C43C4×D412yes—
148C2×C4×C43C2×D812yes—
149C2×C4×C43C2×D812yes—
150C2×C4×C43C2×D811yescharacteristic
151C2×C4×C43#13512yes—
152C2×C4×C43C22×D411yescharacteristic
153C22⋊D43—44no—
154C2×Dic43—41no—
155C2×Dic43—42no—
156C2×Dic43—161no—
157D172—22no—
158D172—41no—
159C4×D43—44no—
160C4×D43—162no—
161Dic86—22no—
162Dic86—41no—
163C8×C43—22no—
164C8×C43C4×D412yes—
165C8×C43C23×C411yescharacteristic
166C8×C43C2×#4111yescharacteristic
167#33454—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—44no—
171C22×C43—82no—
172C22×C43—82no—
173C22×C43—164no—
174C22×C43C4×D812yes—
175C22×C43C22×D811yescharacteristic
176C2×D43—42no—
177C2×D43—81no—
178C2×D43—81no—
179C4×C43—22no—
180C4×C43—22no—
181C4×C43—81no—
182C4×C43—81no—
183C4×C43C4×D812yes—
184C4×C43C2×C4×D411yescharacteristic
185C4×C43C2×#13511yescharacteristic
186Dic43—42no—
187Dic43—82no—
188C2×#509—431no—
189#2951—431no—
190#2948D4311yescharacteristic, complemented
191#2177—432no—
192#2175—432no—
193C4×SD32—432no—
194C4×D16—432no—
195#2159—431no—
196#2138—431no—
197C2×#357—431no—
198#2108—431no—
199C2×C43—22no—
200C2×C43—84no—
201C2×C43C2×C4×D811yescharacteristic
202C2×C43#341511yescharacteristic
203C2×C43#341611yescharacteristic
204D43—82no—
205C2×#135—431no—
206C22×D8C2×D4311yescharacteristic
207#520—861no—
208#518—21no—
209#509—438no—
210C2×SD32—432no—
211C2×D16—432no—
212C2×M32—431no—
213C22×C16—431no—
214#442—22no—
215#440—862no—
216C4×Q16—432no—
217C4×D8—432no—
218C4×D8C2×D4312yes—
219C4×D8C2×D4312yes—
220#427C2×D4311yescharacteristic
221C2×#107—431no—
222#418—21no—
223#417—861no—
224#405C2×D4311yescharacteristic
225#367—432no—
226#366—432no—
227#358—431no—
228#358—431no—
229#357—432no—
230#357—432no—
231#357—431no—
232#357—431no—
233#346—432no—
234C4×C16—432no—
235C43#3345411yescharacteristic, complemented, Sylow
236C2×#41—861no—
237C22×D4—21no—
238#135—434no—
239#135—862no—
240C2×Q16—431no—
241C2×SD16—861no—
242C2×D8—22no—
243C2×D8—21no—
244C2×D8—431no—
245C2×D8C4×D4314yescomplemented
246C2×D8C22×D4312yes—
247C2×M16C22⋊D4311yescharacteristic
248C22×C8C22×D4311yescharacteristic
249C4×Q8—862no—
250C4×D4—22no—
251C4×D4—22no—
252C4×D4—41no—
253C4×D4—41no—
254C4×D4—862no—
255C4×D4—1722no—
256#117—21no—
257#117—1721no—
258#117C22⋊D4311yescharacteristic
259C2×C4⋊C4—861no—
260C2×C4⋊C4—1721no—
261C2×C22⋊C4—42no—
262SD32—438no—
263D16—438no—
264M32—434no—
265C2×C16—432no—
266C2×C16—431no—
267C2×C16—431no—
268C2×C16—862no—
269#107—432no—
270#107—861no—
271#107C22×D4311yescharacteristic
272#107C22×D4311yescharacteristic
273#106—21no—
274#103—862no—
275#102—22no—
276#102—22no—
277#102—862no—
278#97C22⋊D4312yes—
279C4×C8C22×D4312yes—
280C24—41no—
281#41—864no—
282#41—1722no—
283C2×Q8—861no—
284C2×D4—24no—
285C2×D4—22no—
286C2×D4—41no—
287C2×D4—42no—
288C2×D4—861no—
289C2×D4—1721no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—1721no—
293C22×C4—1721no—
294C22×C4—1722no—
295C22×C4C2×C22⋊D4311yescharacteristic
296Q16—432no—
297Q16—861no—
298SD16—864no—
299D8—24no—
300D8—22no—
301D8—432no—
302D8—861no—
303D8C2×C4×D4314yes—
304M16—22no—
305C2×C8C2×C4×D4312yes—
306C2×C8#1062189812yes—
307C2×C8C2×C22⋊D4312yes—
308C2×C8C2×C22⋊D4311yescharacteristic
309C2×C8C23×D4311yescharacteristic
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—862no—
313C4⋊C4—1721no—
314C4⋊C4—1722no—
315C4⋊C4#1062188211yescharacteristic
316C4⋊C4#1062188211yescharacteristic
317C22⋊C4—41no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—1722no—
321C22⋊C4#1062188212yes—
322C42—41no—
323C42—1722no—
324C42C2×C22⋊D4312yes—
325C16—434no—
326C16—861no—
327C16—861no—
328C23—42no—
329C23—44no—
330C23—161no—
331C23—161no—
332C23—1721no—
333C23C2×#1062188211yescharacteristic
334Q8—862no—
335Q8—1721no—
336D4—24no—
337D4—42no—
338D4—44no—
339D4—862no—
340D4—1724no—
341D4—1721no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—162no—
345C2×C4—162no—
346C2×C4—1722no—
347C2×C4—1721no—
348C2×C4—1724no—
349C2×C4—6882no—
350C2×C4—6881no—
351C2×C4C4×C22⋊D4312yes—
352C2×C4C2×#1062188212yes—
353C2×C4C2×#1062188212yes—
354C2×C4C2×#1062188211yescharacteristic
355C2×C4#1306334512yes—
356C2×C4C22×C22⋊D4311yescharacteristic
357C8—22no—
358C8C4×C22⋊D4312yes—
359C8C22×C4×D4311yescharacteristic
360C8C2×#1062189811yescharacteristic
361C22—21no—
362C22—21no—
363C22—44no—
364C22—82no—
365C22—82no—
366C22—164no—
367C22—3441no—
368C22—3441no—
369C22—1722no—
370C22C4×#1062188212yes—
371C22C22×#1062188211yescharacteristic
372C4—22no—
373C4—22no—
374C4—81no—
375C4—81no—
376C4—3442no—
377C4—1722no—
378C4C4×#1062188212yes—
379C4C2×C4×C22⋊D4311yescharacteristic
380C4C2×#1306334511yescharacteristic
381C2—22no—
382C2—84no—
383C2—3442no—
384C2C2×C4×#1062188211yescharacteristic
385C2#1914773411yescharacteristic
386C2#1914774211yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2948C2
socleC22×C43C22×D8
prime radicalC2×#14583335C2
cosocleC2×C8×C43C24
hypercenter#2948D43
hypocenterC43#33454
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2948

Complements

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

NH ≅ G/Ntype
2. #19143472C2semidirect
3. #19136469C2semidirect
4. #19136459C2semidirect
5. C4×#13063269C2semidirect
6. C4×#13063266C2semidirect
7. #19136384C2semidirect
8. #19136300C2semidirect
9. C2×#14582700C2semidirect
10. #19136192C2semidirect
11. C43×#2948C2semidirect
14. #14583335C4semidirect
20. C4×Dic172C22semidirect
21. C4×D344C22semidirect
24. #14582726C22semidirect
25. #14582724C22semidirect
26. #14582702C22semidirect
27. #14582702C22semidirect
30. #14582699C22semidirect
31. #14582699C22semidirect
32. #14582675C22semidirect
33. C4×C43⋊C16C22semidirect
44. #13063347C2×C4semidirect
54. #13063269C2×C4semidirect
55. #13063266C2×C4semidirect
56. #13063265C2×C4semidirect
68. C2×D8×C43C2×C4semidirect
190. #2948D43semidirect
235. C43#33454semidirect
245. C2×D8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833352
#191434722
#191364692
#191364592
C4×#130632692
C4×#130632662
#191363842
#191363002
C2×#145827002
#191361922
C43×#29482
#3345443