Finite Group Databasebeta

← #25249935

Subgroups — #25249935

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×#14583334C211yesmaximal, characteristic
2#19143448C211yesmaximal, characteristic, complemented
3#19136469C212yesmaximal, complemented
4#19136457C212yesmaximal, complemented
5C4×#13063268C212yesmaximal, complemented
6C4×#13063266C212yesmaximal, complemented
7#19136381C211yesmaximal, characteristic, complemented
8#19136302C211yesmaximal, characteristic, complemented
9C2×#14582699C211yesmaximal, characteristic, complemented
10#19136192C211yesmaximal, characteristic, complemented
11C43×#2951C211yesmaximal, characteristic, complemented
12C22×D344C2211yescharacteristic
13#14583373—21no—
14#14583334C418yescomplemented
15C2×#13063268C2212yes—
16C2×#13063266C2212yes—
17C2×#13063265C2211yescharacteristic
18C22×C43⋊C16C2211yescharacteristic
19#14583012—22no—
20C4×D344C2212yes—
21C4×D344C2212yes—
22#14582937C2211yescharacteristic
23#14582905—21no—
24#14582726C2212yescomplemented
25#14582724C2212yescomplemented
26#14582703C2211yescharacteristic, complemented
27#14582703C2211yescharacteristic, complemented
28#14582700C2211yescharacteristic, complemented
29#14582700C2211yescharacteristic, complemented
30#14582699C2212yes—
31#14582699C2212yes—
32#14582675C2212yescomplemented
33C4×C43⋊C16C2212yescomplemented
34C2×#135×C43C2211yescharacteristic
35C43×#520—21no—
36C43×#440—22no—
37C4×Q16×C43C2212yescomplemented
38C4×D8×C43C2212yescomplemented
39C2×#107×C43C2211yescharacteristic
40C43×#417—21no—
41C43×#405C2211yescharacteristic
42C22×D172—21no—
43C2×D344—21no—
44C2×D344—22no—
45C2×D344C2×C414yescomplemented
46C2×D344C2312yes—
47C4×D172—22no—
48C4×D172—22no—
49#13063287—41no—
50#13063287—41no—
51#13063284—21no—
52C22⋊C4×D43—42no—
53#13063268C2×C418yescomplemented
54#13063266C2×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#13063247—22no—
64#13063247—22no—
65C2×#41×C43—21no—
66#135×C43—22no—
67#135×C43C2×C414yescomplemented
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—
86C23×D43—41no—
87#41×C43—24no—
88#41×C43—42no—
89C2×Q8×C43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—42no—
94C22×C4×C43—41no—
95C22×C4×C43C2×D411yescharacteristic
96C2×D172—24no—
97C2×D172—22no—
98C2×D172—41no—
99C2×D172—42no—
100C2×C4×D43—42no—
101C2×C4×D43—42no—
102Q16×C43—21no—
103Q16×C43C22×C412yes—
104SD16×C43—24no—
105D8×C43—21no—
106D8×C43C22×C412yes—
107M16×C43—22no—
108C2×C8×C43C22×C412yes—
109C2×C8×C43C2×D412yes—
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43#4112yes—
112C2×C8×C43C2411yescharacteristic
113C4⋊C4×C43—22no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—42no—
116C4⋊C4×C43D811yescharacteristic
117C4⋊C4×C43D811yescharacteristic
118C22⋊C4×C43—42no—
119C22⋊C4×C43D812yes—
120C42×C43—42no—
121C42×C43C2×D412yes—
122C22⋊Dic43—41no—
123(C2×D43)⋊C4—42no—
124(C2×D43)⋊C4—42no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127C4×Dic43—41no—
128D344—24no—
129D344—22no—
130D344C22×C414yes—
131C43⋊C16—21no—
132C43⋊C16—21no—
133C43⋊C16C22×C414yes—
134C23×C43—41no—
135C23×C43C2×D811yescharacteristic
136C22×D43—42no—
137C22×D43—44no—
138C22×D43—161no—
139C22×D43—161no—
140Q8×C43—22no—
141Q8×C43—41no—
142D4×C43—22no—
143D4×C43—44no—
144D4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—44no—
147C2×C4×C43—42no—
148C2×C4×C43—162no—
149C2×C4×C43—161no—
150C2×C4×C43C4×D412yes—
151C2×C4×C43C2×D812yes—
152C2×C4×C43C2×D812yes—
153C2×C4×C43C2×D811yescharacteristic
154C2×C4×C43#13512yes—
155C2×C4×C43C22×D411yescharacteristic
156C2×Dic43—41no—
157C2×Dic43—41no—
158D172—24no—
159D172—42no—
160D172—44no—
161C4×D43—162no—
162C4×D43—162no—
163C8×C43—22no—
164C8×C43C4×D412yes—
165C8×C43C23×C411yescharacteristic
166C8×C43C2×#4111yescharacteristic
167#33454—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—42no—
171C22×C43—81no—
172C22×C43—81no—
173C22×C43C4×D812yes—
174C22×C43C22×D811yescharacteristic
175C2×D43—44no—
176C2×D43—82no—
177C2×D43—82no—
178C2×D43—164no—
179C4×C43—22no—
180C4×C43—22no—
181C4×C43—42no—
182C4×C43—82no—
183C4×C43C4×D812yes—
184C4×C43C2×C4×D411yescharacteristic
185C4×C43C2×#13511yescharacteristic
186Dic43—81no—
187Dic43—81no—
188C2×#509—431no—
189#2951D4311yescharacteristic, complemented
190#2948—431no—
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—82no—
201C2×C43C2×C4×D811yescharacteristic
202C2×C43#341511yescharacteristic
203C2×C43#341611yescharacteristic
204D43—84no—
205C2×#135C2×D4311yescharacteristic
206C22×D8—431no—
207#520—21no—
208#518—861no—
209#509—438no—
210C2×SD32—432no—
211C2×D16—432no—
212C2×M32—431no—
213C22×C16—431no—
214#442—862no—
215#440—22no—
216C4×Q16C2×D4312yescomplemented
217C4×D8—432no—
218C4×D8—432no—
219C4×D8C2×D4312yescomplemented
220#427—431no—
221C2×#107C2×D4311yescharacteristic
222#418—861no—
223#417—21no—
224#405C2×D4311yescharacteristic
225#367—432no—
226#366—432no—
227#358—431no—
228#358—431no—
229#357—431no—
230#357—431no—
231#357—432no—
232#357—432no—
233#346—432no—
234C4×C16—432no—
235C43#3345411yescharacteristic, complemented, Sylow
236C2×#41—21no—
237C22×D4—861no—
238#135—22no—
239#135C4×D4314yescomplemented
240C2×Q16C22×D4311yescharacteristic
241C2×SD16—21no—
242C2×D8—434no—
243C2×D8—432no—
244C2×D8—862no—
245C2×D8—861no—
246C2×D8C22×D4311yescharacteristic
247C2×M16C22⋊D4311yescharacteristic
248C22×C8C22×D4311yescharacteristic
249C4×Q8—22no—
250C4×D4—22no—
251C4×D4—42no—
252C4×D4—862no—
253C4×D4—862no—
254C4×D4—1721no—
255C4×D4—1721no—
256#117—41no—
257#117—861no—
258#117C22⋊D4311yescharacteristic
259C2×C4⋊C4—21no—
260C2×C4⋊C4—41no—
261C2×C22⋊C4—1722no—
262SD32—438no—
263D16—438no—
264M32—434no—
265C2×C16—432no—
266C2×C16—431no—
267C2×C16—431no—
268C2×C16—862no—
269#107—21no—
270#107—431no—
271#107—431no—
272#107C22×D4312yes—
273#106—861no—
274#103—22no—
275#102—22no—
276#102—862no—
277#102—862no—
278#97C22⋊D4312yes—
279C4×C8C22×D4312yes—
280C24—1721no—
281#41—24no—
282#41—42no—
283C2×Q8—21no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—864no—
287C2×D4—862no—
288C2×D4—1721no—
289C2×D4—1722no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—42no—
293C22×C4—1722no—
294C22×C4—1722no—
295C22×C4C2×C22⋊D4311yescharacteristic
296Q16—21no—
297Q16C2×C4×D4312yes—
298SD16—24no—
299D8—21no—
300D8—434no—
301D8—864no—
302D8—862no—
303D8C2×C4×D4312yes—
304M16—22no—
305C2×C8C2×C4×D4312yes—
306C2×C8#1062189812yes—
307C2×C8C2×C22⋊D4312yes—
308C2×C8C2×C22⋊D4311yescharacteristic
309C2×C8C23×D4311yescharacteristic
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—42no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C4⋊C4#1062188211yescharacteristic
316C4⋊C4#1062188211yescharacteristic
317C22⋊C4—42no—
318C22⋊C4—1721no—
319C22⋊C4—1722no—
320C22⋊C4—1722no—
321C22⋊C4#1062188212yes—
322C42—42no—
323C42—1721no—
324C42C2×C22⋊D4312yes—
325C16—434no—
326C16—861no—
327C16—861no—
328C23—41no—
329C23—1722no—
330C23—1724no—
331C23—6881no—
332C23—6881no—
333C23C2×#1062188211yescharacteristic
334Q8—22no—
335Q8—41no—
336D4—22no—
337D4—44no—
338D4—41no—
339D4—864no—
340D4—1722no—
341D4—1724no—
342C2×C4—41no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—162no—
346C2×C4—161no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—6882no—
350C2×C4—6882no—
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—42no—
364C22—81no—
365C22—81no—
366C22—3442no—
367C22—3442no—
368C22—1724no—
369C22—6884no—
370C22C4×#1062188212yes—
371C22C22×#1062188211yescharacteristic
372C4—22no—
373C4—22no—
374C4—42no—
375C4—82no—
376C4—3441no—
377C4—3441no—
378C4C4×#1062188212yes—
379C4C2×C4×C22⋊D4311yescharacteristic
380C4C2×#1306334511yescharacteristic
381C2—22no—
382C2—82no—
383C2—3444no—
384C2C2×C4×#1062188211yescharacteristic
385C2#1914773411yescharacteristic
386C2#1914773911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2951C2
socleC22×C43C22×D8
prime radicalC2×#14583334C2
cosocleC2×C8×C43C24
hypercenter#2951D43
hypocenterC43#33454
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. #19143448C2semidirect
3. #19136469C2semidirect
4. #19136457C2semidirect
5. C4×#13063268C2semidirect
6. C4×#13063266C2semidirect
7. #19136381C2semidirect
8. #19136302C2semidirect
9. C2×#14582699C2semidirect
10. #19136192C2semidirect
11. C43×#2951C2semidirect
14. #14583334C4semidirect
24. #14582726C22semidirect
25. #14582724C22semidirect
26. #14582703C22semidirect
27. #14582703C22semidirect
28. #14582700C22semidirect
29. #14582700C22semidirect
32. #14582675C22semidirect
33. C4×C43⋊C16C22semidirect
37. C4×Q16×C43C22semidirect
38. C4×D8×C43C22semidirect
45. C2×D344C2×C4semidirect
53. #13063268C2×C4semidirect
54. #13063266C2×C4semidirect
55. #13063265C2×C4semidirect
67. #135×C43C2×C4semidirect
189. #2951D43semidirect
216. C4×Q16C2×D43semidirect
219. C4×D8C2×D43semidirect
235. C43#33454semidirect
239. #135C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833342
#191434482
#191364692
#191364572
C4×#130632682
C4×#130632662
#191363812
#191363022
C2×#145826992
#191361922
C43×#29512
#3345443