Finite Group Databasebeta

← #25011844

Subgroups — #25011844

Order 11008.

466 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143366C211yesmaximal, characteristic
2C2×#14582710C211yesmaximal, characteristic
3C2×#14582708C211yesmaximal, characteristic
4M32×Dic43C211yesmaximal, characteristic, complemented
5#106×Dic43C211yesmaximal, characteristic, complemented
6#19132700C211yesmaximal, characteristic, complemented
7C43×#1386C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9#14583367—21no—
10C2×#13063265C2211yescharacteristic
11#14582993C411yescharacteristic, complemented
12#14582993C411yescharacteristic, complemented
13#14582986—21no—
14#14582986—21no—
15#14582981C411yescharacteristic, complemented
16#14582981C411yescharacteristic, complemented
17C2×#13063257C2211yescharacteristic
18#14582893—21no—
19C2×C8×Dic43C2211yescharacteristic
20C4⋊C4×Dic43—21no—
21#14582710C414yescomplemented
22#14582708C414yescomplemented
23#14582674—21no—
24C16×Dic43—21no—
25#14582661—21no—
26C2×M32×C43C2211yescharacteristic
27C43×#427C2211yescharacteristic
28C2×#106×C43C2211yescharacteristic
29C2×#10621898—21no—
30#13063347—21no—
31#13063347—21no—
32#13063347C2×C412yes—
33#13063347C2×C412yes—
34C2×Dic172C2×C411yescharacteristic
35C2×#10621873—21no—
36C2×D344C2×C411yescharacteristic
37C22×C43⋊C8D411yescharacteristic
38#13063290—21no—
39#13063290—21no—
40#13063287—21no—
41#13063287—21no—
42(C22⋊D43)⋊C4—41no—
43(C22⋊D43)⋊C4—41no—
44#13063282—41no—
45C2×C4⋊Dic43—21no—
46C2×C4×Dic43—41no—
47C2×C4×Dic43D411yescharacteristic
48C42×D43—41no—
49#13063265—21no—
50#13063265C2×C412yescomplemented
51C2×C43⋊C16—21no—
52#13063257—21no—
53#13063257C2×C412yescomplemented
54#13063248—21no—
55#13063248—21no—
56#13063245—21no—
57#13063245—21no—
58C8×Dic43C2×C411yescharacteristic
59C8×Dic43C2×C411yescharacteristic
60C8×Dic43D411yescharacteristic
61C8×Dic43D411yescharacteristic
62C43⋊#95—41no—
63C22×C8×C43C2311yescharacteristic
64#117×C43—21no—
65C2×C4⋊C4×C43—21no—
66M32×C43—21no—
67M32×C43C2×C412yescomplemented
68C2×C16×C43—21no—
69#107×C43C2×C411yescharacteristic
70#107×C43C2×C411yescharacteristic
71#106×C43—21no—
72#106×C43—21no—
73#106×C43C2×C412yescomplemented
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C2×C22⋊D43—41no—
77C22×Dic43—41no—
78C22×Dic43D811yescharacteristic
79C22×Dic43D811yescharacteristic
80#10621898—22no—
81#10621898—22no—
82#10621898—41no—
83#10621898—41no—
84C2×D172—21no—
85C2×C4×D43—41no—
86C2×C4×D43—41no—
87C2×C4×D43—41no—
88C2×Dic86—21no—
89C2×C8×C43C22×C411yescharacteristic
90C2×C8×C43C22×C411yescharacteristic
91C2×C8×C43C22×C411yescharacteristic
92C2×C8×C43C2×D411yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C2×C8×C43#4111yescharacteristic
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C42×C43—41no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—41no—
103C4⋊Dic43—22no—
104C4⋊Dic43—41no—
105Dic43⋊C4—41no—
106Dic43⋊C4—41no—
107C4×Dic43—41no—
108C4×Dic43—41no—
109C4×Dic43—82no—
110C4×Dic43C22⋊C411yescharacteristic
111C4×Dic43C22⋊C411yescharacteristic
112C4×Dic43SD1611yescharacteristic
113C4×Dic43SD1611yescharacteristic
114C2×C43⋊C8—21no—
115C2×C43⋊C8—21no—
116C2×C43⋊C8C22⋊C411yescharacteristic
117C2×C43⋊C8C22⋊C411yescharacteristic
118Dic172—21no—
119Dic172C4212yescomplemented
120D344—21no—
121D344C4212yescomplemented
122#10621873—22no—
123#10621873—22no—
124C16×C43—22no—
125C43⋊C16—22no—
126C23×C43C2×D811yescharacteristic
127C22×D43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—42no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43C2×C22⋊C411yescharacteristic
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43C4×D411yescharacteristic
136C2×C4×C43C2×SD1611yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43#13511yescharacteristic
139C22⋊D43—42no—
140C22⋊D43—42no—
141C2×Dic43—22no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—42no—
145C2×Dic43—81no—
146C2×Dic43—81no—
147C2×Dic43#10211yescharacteristic
148C2×Dic43#10211yescharacteristic
149C2×Dic43#10211yescharacteristic
150C2×Dic43#10211yescharacteristic
151D172—22no—
152D172—41no—
153C4×D43—42no—
154C4×D43—42no—
155C4×D43—82no—
156C4×D43—82no—
157Dic86—22no—
158Dic86—41no—
159C8×C43C2×C4211yescharacteristic
160C8×C43#11711yescharacteristic
161C8×C43C4×D411yescharacteristic
162C8×C43C4×D411yescharacteristic
163C43⋊C8—21no—
164C43⋊C8—21no—
165C4×#360—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43C2×#10211yescharacteristic
169C22×C43C4×D811yescharacteristic
170C22×C43C4×D811yescharacteristic
171C2×D43—42no—
172C2×D43—81no—
173C2×D43—81no—
174C4×C43—82no—
175C4×C43—81no—
176C4×C43—81no—
177C4×C43C4×C22⋊C411yescharacteristic
178C4×C43#41611yescharacteristic
179C4×C43C4×SD1611yescharacteristic
180C4×C43C4×SD1611yescharacteristic
181Dic43—21no—
182Dic43—21no—
183Dic43—21no—
184Dic43—42no—
185Dic43—82no—
186Dic43#36012yescomplemented
187C4×#135—431no—
188C2×#360—431no—
189C2×#360—431no—
190C4×M32—431no—
191C4×#106—431no—
192#1386—431no—
193#1386D4311yescharacteristic, complemented
194C2×C43—21no—
195C2×C43—21no—
196C2×C43C4×#10211yescharacteristic
197C2×C43C2×#36011yescharacteristic
198C2×C43#214511yescharacteristic
199D43—82no—
200C2×#135—431no—
201C4×#41—861no—
202C2×M32—431no—
203C2×M32C2×D4311yescharacteristic
204C4×Q16—431no—
205C4×Q16—431no—
206C4×SD16—861no—
207C4×SD16—861no—
208C4×D8—431no—
209C4×D8—431no—
210#427C2×D4311yescharacteristic
211C2×#106—431no—
212C2×#106C2×D4311yescharacteristic
213#416—861no—
214C2×C4×C8—431no—
215C4×C4⋊C4—861no—
216#360—434no—
217#360—434no—
218#346—861no—
219C4×C16—861no—
220#340—861no—
221C43C4×#36011yescharacteristic, complemented, Sylow
222C2×#41—861no—
223#135—432no—
224#135—432no—
225#135—861no—
226#135—861no—
227C2×Q16—431no—
228C2×SD16—861no—
229C2×D8—431no—
230C22×C8—431no—
231C22×C8C22×D4311yescharacteristic
232C4×Q8—861no—
233C4×Q8—861no—
234C4×D4—861no—
235C4×D4—861no—
236C4×D4—1721no—
237C4×D4—1721no—
238#117—21no—
239#117—1721no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—861no—
242C2×C42—431no—
243C2×C42—1721no—
244C2×C42—1721no—
245M32—21no—
246M32—432no—
247M32—861no—
248M32C4×D4312yescomplemented
249C2×C16—21no—
250C2×C16—861no—
251#107C4×D4311yescharacteristic
252#107C4×D4311yescharacteristic
253#106—21no—
254#106—21no—
255#106—432no—
256#106—861no—
257#106C4×D4312yescomplemented
258#103—861no—
259#103—861no—
260#102—861no—
261#102—861no—
262C4×C8—431no—
263C4×C8—431no—
264C4×C8—431no—
265C4×C8—431no—
266#95—1721no—
267#41—862no—
268#41—862no—
269#41—1721no—
270#41—1721no—
271C2×Q8—861no—
272C2×D4—861no—
273C2×D4—1721no—
274C22×C4—41no—
275C22×C4—431no—
276C22×C4—431no—
277C22×C4—1721no—
278C22×C4—1721no—
279C22×C4—1721no—
280C22×C4—1721no—
281C22×C4D4×D4311yescharacteristic
282Q16—432no—
283Q16—861no—
284SD16—862no—
285SD16—862no—
286D8—432no—
287D8—861no—
288C2×C8—431no—
289C2×C8—431no—
290C2×C8—861no—
291C2×C8—861no—
292C2×C8C2×C4×D4311yescharacteristic
293C2×C8C2×C4×D4311yescharacteristic
294C2×C8C2×C4×D4311yescharacteristic
295C2×C8D4×D4311yescharacteristic
296C2×C8#1062190011yescharacteristic
297C2×C8#1062190211yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—862no—
303C4⋊C4—1721no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C22⋊C4—41no—
307C22⋊C4—1721no—
308C22⋊C4—1721no—
309C42—41no—
310C42—431no—
311C42—431no—
312C42—431no—
313C42—431no—
314C42—3442no—
315C42—1721no—
316C42—1721no—
317C16—22no—
318C16—862no—
319C23—1721no—
320C23D8×D4311yescharacteristic
321Q8—862no—
322Q8—1721no—
323D4—862no—
324D4—1722no—
325D4—1722no—
326D4—1721no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—431no—
333C2×C4—431no—
334C2×C4—431no—
335C2×C4—431no—
336C2×C4—862no—
337C2×C4—3442no—
338C2×C4—3442no—
339C2×C4—3441no—
340C2×C4—3441no—
341C2×C4—1721no—
342C2×C4—1722no—
343C2×C4—1721no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4C22⋊C4×D4311yescharacteristic
347C2×C4(C22⋊D43)⋊C411yescharacteristic
348C2×C4#1306328711yescharacteristic
349C2×C4SD16×D4311yescharacteristic
350C2×C4#1306334611yescharacteristic
351C2×C4#1306334811yescharacteristic
352C8—861no—
353C8—861no—
354C8C42×D4311yescharacteristic
355C8#1306328311yescharacteristic
356C8(C22⋊D43)⋊C411yescharacteristic
357C8#1306328711yescharacteristic
358C22—21no—
359C22—21no—
360C22—3441no—
361C22—3441no—
362C22—1722no—
363C22#102×D4311yescharacteristic
364C22#1458297911yescharacteristic
365C22#1458298111yescharacteristic
366C4—82no—
367C4—81no—
368C4—81no—
369C4—432no—
370C4—861no—
371C4—861no—
372C4—861no—
373C4—3442no—
374C4—1722no—
375C4#1458274611yescharacteristic
376C4#1458289411yescharacteristic
377C4#1458298411yescharacteristic
378C4#1458298611yescharacteristic
379C2—21no—
380C2—21no—
381C2—3442no—
382C2#1913440911yescharacteristic
383C2#360×D4311yescharacteristic
384C2#1913632911yescharacteristic
subgroupG/H
centerC22#102×D43
commutatorC8×C43C2×C42
FrattiniC22×C8C22×D43
FittingC43×#1386C2
socleC22×C43C2×#102
prime radicalC2×#13063347C22
cosocleC22×C8×C43C23
hypercenter#1386D43
hypocenterC43C4×#360
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
4. M32×Dic43C2semidirect
5. #106×Dic43C2semidirect
6. #19132700C2semidirect
7. C43×#1386C2semidirect
11. #14582993C4semidirect
12. #14582993C4semidirect
15. #14582981C4semidirect
16. #14582981C4semidirect
21. #14582710C4semidirect
22. #14582708C4semidirect
50. #13063265C2×C4semidirect
53. #13063257C2×C4semidirect
67. M32×C43C2×C4semidirect
73. #106×C43C2×C4semidirect
119. Dic172C42semidirect
121. D344C42semidirect
186. Dic43#360semidirect
193. #1386D43semidirect
221. C43C4×#360semidirect
248. M32C4×D43semidirect
257. #106C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191433662
C2×#145827102
C2×#145827082
M32×Dic432
#106×Dic432
#191327002
C43×#13862
C4×#36043