Finite Group Databasebeta

← #25081835

Subgroups — #25081835

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145713C211yesmaximal, characteristic, complemented
2C2×#14583104C211yesmaximal, characteristic, complemented
3#19143619C211yesmaximal, characteristic, complemented
4#19134030C214yesmaximal, complemented
5#19133982C214yesmaximal, complemented
6#19133371C211yesmaximal, characteristic, complemented
7#19133268C211yesmaximal, characteristic, complemented
8#19133244C211yesmaximal, characteristic, complemented
9C43×#3036C211yesmaximal, characteristic
10C22×#10621883—21no—
11C2×#13063325C2211yescharacteristic
12#14583302C2212yescomplemented
13#14583245C2212yescomplemented
14#14583210—22no—
15#14583179—22no—
16#14583104—22no—
17#14583104C2214yes—
18D4×C43⋊C8—22no—
19D4×C43⋊C8C2214yes—
20#14582952C2211yescharacteristic
21#14582952C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×#13063248—21no—
24C2×C22⋊(C43⋊C8)—22no—
25#14582651C2214yescomplemented
26#14582646C2214yescomplemented
27#14582645C2212yescomplemented
28#14582643C2212yescomplemented
29C2×AGL(1,ℤ/8)×C43—21no—
30C43×#532C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C43×#463—22no—
33C43×#461C2212yes—
34C43×#459C2212yes—
35C43×#423C2211yescharacteristic
36C43×#417—21no—
37C22×Dic86—21no—
38C2×#10621883—24no—
39C2×#10621883—44no—
40C22×C43⋊C8—21no—
41C22×C43⋊C8—24no—
42#13063325—21no—
43#13063325—21no—
44#13063325—21no—
45#13063325C2312yes—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—21no—
48#13063258—24no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)D412yes—
51C4⋊(C43⋊C8)C2312yes—
52C4⋊(C43⋊C8)C2312yes—
53#13063248—24no—
54#13063246—24no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—24no—
57C22⋊(C43⋊C8)D412yes—
58C4×C43⋊C8—21no—
59C4×C43⋊C8C2312yes—
60C2×#41×C43—21no—
61C22×D4×C43D411yescharacteristic
62C23×C4×C43—21no—
63AGL(1,ℤ/8)×C43—44no—
64C2×SD16×C43—22no—
65C2×D8×C43—22no—
66C2×M16×C43—21no—
67C4⋊Q8×C43C2311yescharacteristic
68#127×C43C2311yescharacteristic
69#124×C43—21no—
70#121×C43—21no—
71#121×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43—21no—
75C4×D4×C43—21no—
76C4×D4×C43D412yes—
77C4×D4×C43C2312yes—
78C2×C4⋊C4×C43D411yescharacteristic
79C2×C22⋊C4×C43—21no—
80C2×C42×C43C2311yescharacteristic
81C4⋊C8×C43—21no—
82C4⋊C8×C43C2312yes—
83#103×C43—22no—
84#102×C43—22no—
85C24×C43—21no—
86#41×C43—42no—
87#41×C43—42no—
88C2×Q8×C43—21no—
89C2×D4×C43—21no—
90C2×D4×C43—22no—
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—41no—
95C2×D4×C43D814yes—
96C2×D4×C43C2×D412yes—
97C22×C4×C43—22no—
98C22×C4×C43—22no—
99C22×C4×C43—21no—
100C22×C4×C43—41no—
101C22×C4×C43—82no—
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×Dic43—41no—
106C2×Dic86—22no—
107C2×Dic86—42no—
108C2×Dic86—42no—
109C2×Dic86—41no—
110SD16×C43—44no—
111D8×C43—44no—
112M16×C43—42no—
113C2×C8×C43—22no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43C2×D412yes—
118C22⋊C4×C43—22no—
119C22⋊C4×C43—22no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C42×C43C2×D411yescharacteristic
123C42×C43C2×D411yescharacteristic
124C42×C43#4111yescharacteristic
125C42×C43C2411yescharacteristic
126#10621883—48no—
127C4⋊Dic43—22no—
128C4⋊Dic43—22no—
129C4⋊Dic43—41no—
130C4⋊Dic43—41no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8—42no—
134C2×C43⋊C8—84no—
135C2×C43⋊C8C2×D414yes—
136C23×C43—22no—
137C23×C43—24no—
138C23×C43—41no—
139C23×C43—81no—
140C23×C43—81no—
141C23×C43#12111yescharacteristic
142Q8×C43—41no—
143Q8×C43—41no—
144D4×C43—22no—
145D4×C43—24no—
146D4×C43—41no—
147D4×C43—41no—
148D4×C43—42no—
149D4×C43—81no—
150D4×C43—82no—
151D4×C43C2×D814yes—
152C2×C4×C43—22no—
153C2×C4×C43—22no—
154C2×C4×C43—41no—
155C2×C4×C43—44no—
156C2×C4×C43—41no—
157C2×C4×C43—82no—
158C2×C4×C43—81no—
159C2×C4×C43—82no—
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43C2×D812yes—
164C2×C4×C43#13512yes—
165C2×C4×C43C22×D411yescharacteristic
166C2×C4×C43C22×D411yescharacteristic
167C2×C4×C43C2×#4111yescharacteristic
168C2×Dic43—42no—
169C2×Dic43—82no—
170Dic86—42no—
171Dic86—42no—
172Dic86—82no—
173C8×C43—42no—
174C43⋊C8—24no—
175C43⋊C8—42no—
176C43⋊C8—42no—
177#19392—431nomaximal, Sylow
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—24no—
181C22×C43—42no—
182C22×C43—42no—
183C22×C43—84no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43—81no—
187C22×C43#46612yes—
188C22×C43C2×#12111yescharacteristic
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—42no—
193C4×C43—81no—
194C4×C43#46612yes—
195C4×C43C22×D811yescharacteristic
196C4×C43C2×#13511yescharacteristic
197C4×C43#57712yes—
198Dic43—82no—
199#3226—431no—
200#3036D4311yescharacteristic
201C2×#461—431no—
202#2972—431no—
203#1681—434no—
204#1673—434no—
205#1571—431no—
206#1546—431no—
207#1540—431no—
208C2×C43—22no—
209C2×C43—44no—
210C2×C43—161no—
211C2×C43#304211yescharacteristic
212C2×C43C2×#46611yescharacteristic
213C2×C43#306911yescharacteristic
214C2×AGL(1,ℤ/8)—21no—
215C22×SD16—861no—
216#532C2×D4311yescharacteristic
217C2×C4⋊Q8—431no—
218C2×C4×D4C2×D4311yescharacteristic
219#500—432no—
220#486—432no—
221#480—862no—
222#474—862no—
223#463—22no—
224#461—434no—
225#461—862no—
226#461C2×D4312yes—
227#459C2×D4312yes—
228C8×D4—434no—
229C8×D4—862no—
230#431—431no—
231#431—431no—
232#423C2×D4311yescharacteristic
233C2×C4⋊C8—431no—
234#417—21no—
235C2×#103—861no—
236C2×C22⋊C8—862no—
237#335—434no—
238#332—432no—
239#332—434no—
240#331—432no—
241C43#1939211yescharacteristic, complemented, Sylow
242C2×#41—21no—
243C22×Q8—861no—
244C22×D4C22⋊D4311yescharacteristic
245C23×C4—21no—
246AGL(1,ℤ/8)—44no—
247C2×SD16—22no—
248C2×SD16—864no—
249C2×SD16—1724no—
250C2×D8—22no—
251C2×M16—21no—
252C22×C8—864no—
253C22×C8—861no—
254C4⋊Q8—432no—
255C4⋊Q8—861no—
256C4⋊Q8—861no—
257C4⋊Q8—861no—
258C4⋊Q8C22×D4311yescharacteristic
259#127C22×D4311yescharacteristic
260#124—21no—
261#121—21no—
262#121—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4C22⋊D4312yes—
268C4×D4C22×D4312yes—
269C2×C4⋊C4—861no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4C22⋊D4311yescharacteristic
272C2×C22⋊C4—21no—
273C2×C42C22×D4311yescharacteristic
274#107—864no—
275C4⋊C8—21no—
276C4⋊C8—432no—
277C4⋊C8—432no—
278C4⋊C8—432no—
279C4⋊C8—861no—
280C4⋊C8C22×D4312yes—
281#103—22no—
282#103—864no—
283#102—22no—
284#102—864no—
285C22⋊C8—432no—
286C22⋊C8—864no—
287C22⋊C8—861no—
288C4×C8—432no—
289C4×C8—861no—
290C24—21no—
291#41—42no—
292#41—42no—
293C2×Q8—21no—
294C2×Q8—862no—
295C2×Q8—1722no—
296C2×Q8—1722no—
297C2×Q8—1721no—
298C2×D4—21no—
299C2×D4—22no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4#1062188214yes—
305C2×D4C2×C22⋊D4312yes—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—41no—
310C22×C4—82no—
311C22×C4—1721no—
312C22×C4D4×D4311yescharacteristic
313C22×C4#1062190011yescharacteristic
314C22×C4C2×C22⋊D4311yescharacteristic
315SD16—44no—
316SD16—1728no—
317D8—44no—
318M16—42no—
319C2×C8—22no—
320C2×C8—434no—
321C2×C8—862no—
322C2×C8—862no—
323C2×C8—3444no—
324C2×C8—1722no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—862no—
329C4⋊C4—862no—
330C4⋊C4—1721no—
331C4⋊C4—1721no—
332C4⋊C4C2×C22⋊D4312yes—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42D4×D4311yescharacteristic
338C42#1062190011yescharacteristic
339C42C2×C22⋊D4311yescharacteristic
340C42C23×D4311yescharacteristic
341C23—22no—
342C23—24no—
343C23—41no—
344C23—81no—
345C23—81no—
346C23#1306329711yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—3442no—
350Q8—1722no—
351Q8—1722no—
352D4—24no—
353D4—22no—
354D4—41no—
355D4—41no—
356D4—42no—
357D4—81no—
358D4—82no—
359D4C2×#1062188214yes—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—44no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—82no—
368C2×C4—3442no—
369C2×C4—1722no—
370C2×C4#1306329711yescharacteristic
371C2×C4#1306329711yescharacteristic
372C2×C4#1306329711yescharacteristic
373C2×C4C2×#1062188212yes—
374C2×C4#1306334512yes—
375C2×C4C2×D4×D4311yescharacteristic
376C2×C4C22×C22⋊D4311yescharacteristic
377C2×C4C2×#1062190011yescharacteristic
378C8—42no—
379C8—864no—
380C8—1722no—
381C8—1722no—
382C22—21no—
383C22—21no—
384C22—24no—
385C22—42no—
386C22—42no—
387C22—84no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22#1458313312yes—
392C22C2×#1306329711yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—81no—
398C4—3442no—
399C4#1458313312yes—
400C4C22×#1062188211yescharacteristic
401C4C2×#1306334511yescharacteristic
402C4#1458370912yes—
403C2—22no—
404C2—44no—
405C2—161no—
406C2#1914410911yescharacteristic
407C2C2×#1458313311yescharacteristic
408C2#1914433411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3036C2
socleC22×C43C2×#121
hypercenter#3036D43
hypocenterC43#19392
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #19145713C2semidirect
2. C2×#14583104C2semidirect
3. #19143619C2semidirect
4. #19134030C2semidirect
5. #19133982C2semidirect
6. #19133371C2semidirect
7. #19133268C2semidirect
8. #19133244C2semidirect
12. #14583302C22semidirect
13. #14583245C22semidirect
25. #14582651C22semidirect
26. #14582646C22semidirect
27. #14582645C22semidirect
28. #14582643C22semidirect
241. C43#19392semidirect

Maximal subgroups

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

subgroupindex
#191457132
C2×#145831042
#191436192
#191340302
#191339822
#191333712
#191332682
#191332442
C43×#30362
#1939243