Finite Group Databasebeta

← #25250005

Subgroups — #25250005

Order 11008.

652 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
1#19147728C211yesmaximal, characteristic
2#443×D43C212yesmaximal, complemented
3#19136481C211yesmaximal, characteristic, complemented
4#19136480C211yesmaximal, characteristic, complemented
5#19136478C212yesmaximal, complemented
6#19136477C211yesmaximal, characteristic, complemented
7#19136474C212yesmaximal, complemented
8#19136388C211yesmaximal, characteristic, complemented
9#19136321C212yesmaximal, complemented
10C4×#13063264C211yesmaximal, characteristic, complemented
11C43×#2178C211yesmaximal, characteristic, complemented
12#135×D43C2212yes—
13#131×D43—22no—
14#14583341C412yescomplemented
15#14583338C412yescomplemented
16#14583336C412yescomplemented
17#14583333C412yescomplemented
18#14583331C2211yescharacteristic
19#14583329C2212yes—
20C2×#13063264C2211yescharacteristic
21C2×#13063264C2211yescharacteristic
22#14583017C2212yescomplemented
23#14583016C2212yescomplemented
24#14583015C2212yescomplemented
25#14583014—22no—
26#14583013—22no—
27#108×D43C2212yes—
28#104×D43—22no—
29C4×C8×D43C2211yescharacteristic
30#14582729C2211yescharacteristic, complemented
31#14582728C2212yescomplemented
32#14582707C2212yescomplemented
33#14582706C2212yescomplemented
34#14582705C2212yescomplemented
35#14582674C2211yescharacteristic, complemented
36#14582674C2211yescharacteristic, complemented
37C4×C43⋊C16C2211yescharacteristic, complemented
38C43×#508C2211yescharacteristic
39C43×#443C2212yescomplemented
40C43×#368C2211yescharacteristic, complemented
41C43×#359C2212yescomplemented
42C4×C16×C43C2211yescharacteristic, complemented
43#41×D43—22no—
44#13063348C2×C412yes—
45#13063347C2312yes—
46#13063346—22no—
47#13063345—22no—
48#13063344C2×C412yes—
49Q16×D43C2×C412yes—
50SD16×D43—22no—
51D8×D43C2×C412yes—
52#13063333—22no—
53#13063333—42no—
54#13063332—22no—
55#13063331—22no—
56#13063331—42no—
57M16×D43—22no—
58M16×D43—42no—
59C2×C8×D43—42no—
60C2×C8×D43D411yescharacteristic
61C2×C8×D43C2311yescharacteristic
62C42×D43D411yescharacteristic
63Dic344C2×C411yescharacteristic, complemented
64#13063271C2×C412yescomplemented
65#13063270C2×C412yescomplemented
66#13063269C2×C412yescomplemented
67#13063268C2×C412yescomplemented
68D688C2×C411yescharacteristic, complemented
69#13063266C2×C412yescomplemented
70#13063264—22no—
71#13063264C2×C412yes—
72#13063264C2×C412yes—
73C2×C43⋊C16C2311yescharacteristic
74C2×C43⋊C16C2311yescharacteristic
75#13063261C2312yes—
76#13063260—22no—
77#13063253—22no—
78#13063252—22no—
79#13063251—22no—
80C4×C43⋊C8D411yescharacteristic
81C8×Dic43D411yescharacteristic
82C8×Dic43C2311yescharacteristic
83#135×C43C2312yes—
84#131×C43—22no—
85Q32×C43C2×C411yescharacteristic, complemented
86SD32×C43C2×C412yescomplemented
87D16×C43C2×C411yescharacteristic, complemented
88C2×C16×C43C2311yescharacteristic
89C2×C16×C43C2311yescharacteristic
90#108×C43C2312yes—
91#104×C43—22no—
92C4×C8×C43C2311yescharacteristic
93#41×C43—22no—
94#10621902—22no—
95Q8×D43—22no—
96#10621900—22no—
97#10621900—42no—
98D4×D43—22no—
99D4×D43—42no—
100#10621898—22no—
101#10621898—42no—
102C2×C4×D43—21no—
103C2×C4×D43—42no—
104C2×C4×D43C2×D411yescharacteristic
105Q16×C43C22×C412yes—
106SD16×C43—22no—
107D8×C43C22×C412yes—
108M16×C43—22no—
109M16×C43—42no—
110C2×C8×C43—42no—
111C2×C8×C43C2×D411yescharacteristic
112C2×C8×C43C2411yescharacteristic
113C42×C43C2×D411yescharacteristic
114#10621885—22no—
115#10621884—22no—
116#10621883—22no—
117#10621882—22no—
118C4×Dic43—21no—
119C4×Dic43C2×D411yescharacteristic
120#10621877—22no—
121#10621877—42no—
122C2×C43⋊C8—42no—
123C2×C43⋊C8C2×D411yescharacteristic
124C2×C43⋊C8C2×D411yescharacteristic
125Dic172C22×C412yes—
126D344C22×C412yes—
127#10621873—22no—
128#10621872—42no—
129#10621872—42no—
130#10621872—42no—
131C8×D43—42no—
132C8×D43—42no—
133C8×D43—42no—
134C8×D43D812yes—
135C8×D43D812yes—
136C8×D43C22×C412yes—
137C8×D43#4112yes—
138C16×C43—21no—
139C16×C43C22×C411yescharacteristic
140C16×C43C22×C411yescharacteristic
141C43⋊C16—21no—
142C43⋊C16C22×C412yes—
143C22×D43—42no—
144C22×D43#13511yescharacteristic
145Q8×C43—22no—
146D4×C43—22no—
147D4×C43—42no—
148C2×C4×C43—21no—
149C2×C4×C43—42no—
150C2×C4×C43C22×D411yescharacteristic
151C22⋊D43—42no—
152C22⋊D43—42no—
153C22⋊D43—42no—
154C2×Dic43—21no—
155C2×Dic43—42no—
156C2×Dic43#13511yescharacteristic
157D172—22no—
158D172—42no—
159C4×D43—42no—
160C4×D43—42no—
161C4×D43—42no—
162C4×D43—42no—
163C4×D43C4×D412yes—
164C4×D43C2×D812yes—
165Dic86—22no—
166Dic86—42no—
167C8×C43—42no—
168C8×C43C2×D811yescharacteristic
169C8×C43C2×D811yescharacteristic
170C8×C43C23×C411yescharacteristic
171C8×C43C2×#4111yescharacteristic
172C43⋊C8—42no—
173C43⋊C8C4×D412yes—
174C43⋊C8C2×D812yes—
175#33463—431nomaximal, Sylow
176C22×C43—42no—
177C22×C43C2×#13511yescharacteristic
178C2×D43—41no—
179C2×D43—42no—
180C2×D43—84no—
181C2×D43C4×D812yes—
182C4×C43—22no—
183C4×C43—42no—
184C4×C43C2×C4×D411yescharacteristic
185C4×C43C22×D811yescharacteristic
186Dic43—41no—
187Dic43—42no—
188Dic43C4×D812yes—
189#3414—431no—
190C2×#443—432no—
191#2179—431no—
192#2179—431no—
193#2179—432no—
194#2178—432no—
195#2178—431no—
196#2178D4311yescharacteristic, complemented
197#2161—431no—
198#2143—432no—
199C4×M32—431no—
200C2×C43—21no—
201C2×C43—82no—
202C2×C43C2×C4×D811yescharacteristic
203D43—22no—
204D43—82no—
205C2×#135—432no—
206C2×#131—862no—
207#510—432no—
208#510—432no—
209#509—432no—
210#509—432no—
211#508—432no—
212#508—431no—
213#508C2×D4311yescharacteristic
214C2×M32—431no—
215C2×M32—431no—
216#443—432no—
217#443—432no—
218#443—432no—
219#443—862no—
220#443—862no—
221#443C2×D4312yescomplemented
222C2×#108—432no—
223C2×#104—862no—
224C2×C4×C8—431no—
225#368—431no—
226#368—432no—
227#368C2×D4311yescharacteristic, complemented
228#359—432no—
229#359—432no—
230#359—432no—
231#359C2×D4312yescomplemented
232#346—431no—
233#346—431no—
234C4×C16—431no—
235C4×C16C2×D4311yescharacteristic, complemented
236C43#3346311yescharacteristic, complemented, Sylow
237C2×#41—862no—
238#135—432no—
239#135—432no—
240#135—432no—
241#135—862no—
242#135—862no—
243#135C22×D4312yes—
244C2×Q16—432no—
245C2×SD16—862no—
246C2×D8—432no—
247#131—22no—
248#131—862no—
249#131—862no—
250#131—862no—
251#131—1722no—
252#131—1722no—
253C2×M16—862no—
254C2×M16—1722no—
255C22×C8—431no—
256C22×C8—431no—
257C22×C8—1722no—
258C2×C42—431no—
259Q32—432no—
260Q32—431no—
261Q32C4×D4311yescharacteristic, complemented
262SD32—432no—
263SD32—432no—
264SD32—432no—
265SD32C4×D4312yescomplemented
266D16—432no—
267D16—431no—
268D16C4×D4311yescharacteristic, complemented
269M32—432no—
270M32—432no—
271M32—862no—
272C2×C16—431no—
273C2×C16—431no—
274C2×C16C22×D4311yescharacteristic
275C2×C16C22×D4311yescharacteristic
276#108—432no—
277#108—862no—
278#108C22×D4312yes—
279#104—22no—
280#104—862no—
281#104—862no—
282#104—862no—
283C4×C8—431no—
284C4×C8—431no—
285C4×C8—431no—
286C4×C8C22×D4311yescharacteristic
287#41—22no—
288#41—862no—
289#41—862no—
290#41—862no—
291#41—1722no—
292#41—1722no—
293C2×Q8—862no—
294C2×D4—862no—
295C2×D4—1722no—
296C22×C4—431no—
297C22×C4—861no—
298C22×C4—1722no—
299Q16—432no—
300Q16—862no—
301Q16C2×C4×D4312yes—
302SD16—22no—
303SD16—862no—
304SD16—862no—
305SD16—862no—
306D8—432no—
307D8—862no—
308D8C2×C4×D4312yes—
309M16—22no—
310M16—42no—
311M16—862no—
312M16—1722no—
313M16—1722no—
314M16—1722no—
315M16—1722no—
316C2×C8—42no—
317C2×C8—431no—
318C2×C8—431no—
319C2×C8—432no—
320C2×C8—432no—
321C2×C8—432no—
322C2×C8—432no—
323C2×C8—1722no—
324C2×C8—1722no—
325C2×C8—1722no—
326C2×C8—1722no—
327C2×C8D4×D4311yescharacteristic
328C2×C8C23×D4311yescharacteristic
329C42—431no—
330C42—861no—
331C42D4×D4311yescharacteristic
332C16—21no—
333C16—432no—
334C16—861no—
335C16C2×C4×D4311yescharacteristic
336C16C2×C4×D4311yescharacteristic
337C23—431no—
338C23—1722no—
339Q8—22no—
340Q8—862no—
341Q8—1722no—
342D4—22no—
343D4—42no—
344D4—862no—
345D4—1722no—
346D4—1722no—
347D4—1722no—
348D4—1722no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—431no—
352C2×C4—432no—
353C2×C4—432no—
354C2×C4—861no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4—1722no—
359C2×C4—1722no—
360C2×C4C2×D4×D4311yescharacteristic
361C8—42no—
362C8—432no—
363C8—432no—
364C8—1722no—
365C8D8×D4311yescharacteristic
366C8D8×D4311yescharacteristic
367C8C22×C4×D4311yescharacteristic
368C8#41×D4311yescharacteristic
369C22—42no—
370C22—432no—
371C22—3444no—
372C22—1721no—
373C22—1722no—
374C22#135×D4311yescharacteristic
375C4—22no—
376C4—42no—
377C4—432no—
378C4—1721no—
379C4—1722no—
380C4C4×D4×D4311yescharacteristic
381C4C2×D8×D4311yescharacteristic
382C2—21no—
383C2—82no—
384C2—862no—
385C2—3442no—
386C2C4×D8×D4311yescharacteristic
subgroupG/H
centerC8D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2178C2
socleC2×C43C2×C4×D8
prime radical#19147728C2
cosocleC2×C8×C43C24
hypercenter#2178D43
hypocenterC43#33463
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C8 ◁ C2×C8 ◁ C4×C8 ◁ #2178

Complements

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

NH ≅ G/Ntype
2. #443×D43C2semidirect
3. #19136481C2semidirect
4. #19136480C2semidirect
5. #19136478C2semidirect
6. #19136477C2semidirect
7. #19136474C2semidirect
8. #19136388C2semidirect
9. #19136321C2semidirect
10. C4×#13063264C2semidirect
11. C43×#2178C2semidirect
14. #14583341C4semidirect
15. #14583338C4semidirect
16. #14583336C4semidirect
17. #14583333C4semidirect
22. #14583017C22semidirect
23. #14583016C22semidirect
24. #14583015C22semidirect
30. #14582729C22semidirect
31. #14582728C22semidirect
32. #14582707C22semidirect
33. #14582706C22semidirect
34. #14582705C22semidirect
35. #14582674C22semidirect
36. #14582674C22semidirect
37. C4×C43⋊C16C22semidirect
39. C43×#443C22semidirect
40. C43×#368C22semidirect
41. C43×#359C22semidirect
42. C4×C16×C43C22semidirect
63. Dic344C2×C4semidirect
64. #13063271C2×C4semidirect
65. #13063270C2×C4semidirect
66. #13063269C2×C4semidirect
67. #13063268C2×C4semidirect
68. D688C2×C4semidirect
69. #13063266C2×C4semidirect
85. Q32×C43C2×C4semidirect
86. SD32×C43C2×C4semidirect
87. D16×C43C2×C4semidirect
196. #2178D43semidirect
221. #443C2×D43semidirect
227. #368C2×D43semidirect
231. #359C2×D43semidirect
235. C4×C16C2×D43semidirect
236. C43#33463semidirect
261. Q32C4×D43semidirect
265. SD32C4×D43semidirect
268. D16C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191477282
#443×D432
#191364812
#191364802
#191364782
#191364772
#191364742
#191363882
#191363212
C4×#130632642
C43×#21782
#3346343