Finite Group Databasebeta

← #25017005

Subgroups — #25017005

Order 11008.

336 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145660C211yesmaximal, characteristic
2#19136265C211yesmaximal, characteristic
3#19136261C211yesmaximal, characteristic
4#19132765C211yesmaximal, characteristic, complemented
5#19132765C211yesmaximal, characteristic, complemented
6#19132760C211yesmaximal, characteristic, complemented
7C43×#1409C211yesmaximal, characteristic, complemented
8#14583510C411yescharacteristic, complemented
9#14583462C2211yescharacteristic
10#14583291C411yescharacteristic, complemented
11#14583263C2211yescharacteristic
12#14583254C411yescharacteristic, complemented
13#14583119—21no—
14#14583097—21no—
15#14583058—21no—
16#14583048—21no—
17#14582958C411yescharacteristic, complemented
18#14582871—21no—
19#99×D43—21no—
20#14582693—21no—
21#14582692C2211yescharacteristic
22#14582692C2211yescharacteristic
23#14582691—21no—
24C43×#492C2211yescharacteristic
25C43×#353C2211yescharacteristic
26C43×#353C2211yescharacteristic
27C2×#10621900D411yescharacteristic
28C2×D4×D43D411yescharacteristic
29C2×#10621885—21no—
30C2×#10621884—21no—
31#13063321D411yescharacteristic
32#13063320—41no—
33#13063317C2×C411yescharacteristic, complemented
34#13063315—41no—
35#13063313C2×C411yescharacteristic
36#13063312D411yescharacteristic
37#13063301—21no—
38#13063297—41no—
39#13063293—41no—
40Q8×Dic43—21no—
41#13063282C2×C411yescharacteristic
42#13063281—41no—
43C22⋊C4×D43—41no—
44Dic43⋊C8—21no—
45#13063250—21no—
46#13063247—21no—
47#13063246—21no—
48#13063246—21no—
49#13063240—21no—
50#13063240—21no—
51#13063239—41no—
52#13063239—41no—
53(C2×D43)⋊C8—21no—
54#13063236C2×C411yescharacteristic, complemented
55C2×SD16×C43—21no—
56C2×SD16×C43—21no—
57C4⋊Q8×C43C2×C411yescharacteristic, complemented
58#127×C43C2311yescharacteristic
59#99×C43—21no—
60#99×C43—21no—
61C4×C8×C43C2×C411yescharacteristic, complemented
62C23×D43—21no—
63C2×Q8×C43—21no—
64C2×D4×C43—41no—
65C2×D4×C43C2×D411yescharacteristic
66C2×D4×C43C2×D411yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—41no—
70C22×Dic43—21no—
71#10621900—81no—
72D4×D43—81no—
73C2×D172C22⋊C411yescharacteristic
74C2×C4×D43—81no—
75C2×C4×D43C22⋊C411yescharacteristic
76C2×Dic86C22⋊C411yescharacteristic
77SD16×C43—81no—
78SD16×C43—81no—
79C2×C8×C43—21no—
80C4⋊C4×C43—41no—
81C22⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C42×C43C22×C411yescharacteristic
84C22⋊Dic43—41no—
85C22⋊Dic43—41no—
86C22⋊Dic43—41no—
87#10621885—81no—
88#10621884—81no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—41no—
91(C2×D43)⋊C4—41no—
92(C2×D43)⋊C4—81no—
93C4⋊Dic43—21no—
94C4⋊Dic43—41no—
95Dic43⋊C4—21no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—81no—
99C4×Dic43—41no—
100C4×Dic43—81no—
101C4×Dic43C22⋊C411yescharacteristic
102C2×C43⋊C8—21no—
103C23×C43—21no—
104C23×C43—21no—
105C22×D43—21no—
106C22×D43—41no—
107C22×D43—41no—
108C22×D43—161no—
109C22×D43#9911yescharacteristic
110Q8×C43—41no—
111Q8×C43—41no—
112D4×C43—41no—
113D4×C43—41no—
114D4×C43—161no—
115C2×C4×C43—21no—
116C2×C4×C43—41no—
117C2×C4×C43—81no—
118C2×C4×C43—81no—
119C2×C4×C43C2×C22⋊C411yescharacteristic
120C22⋊D43—81no—
121C22⋊D43—81no—
122C22⋊D43—161no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—81no—
129C2×Dic43—81no—
130C2×Dic43#9911yescharacteristic
131D172—41no—
132C4×D43—41no—
133C4×D43—162no—
134Dic86—41no—
135C8×C43—41no—
136C43⋊C8—41no—
137#13610—431nomaximal, Sylow
138C22×C43—41no—
139C22×C43—41no—
140C22×C43—81no—
141C22×C43—81no—
142C22×C43C2×#9911yescharacteristic
143C2×D43—21no—
144C2×D43—41no—
145C2×D43—41no—
146C2×D43—82no—
147C2×D43—81no—
148C2×D43—161no—
149C4×C43—21no—
150C4×C43—41no—
151C4×C43—81no—
152C4×C43—161no—
153C4×C43—161no—
154Dic43—21no—
155Dic43—41no—
156Dic43—41no—
157Dic43—81no—
158Dic43—161no—
159Dic43—161no—
160#3222—431no—
161#2128—431no—
162#2127—431no—
163#1412—431no—
164#1412—431no—
165#1409—431no—
166#1409D4311yescharacteristic, complemented
167C2×C43—21no—
168C2×C43—81no—
169C2×C43—81no—
170C2×C43#212711yescharacteristic
171D43—41no—
172D43—81no—
173#541—431no—
174#535—431no—
175#497—431no—
176#492C2×D4311yescharacteristic
177#490—431no—
178#488—431no—
179#464—861no—
180#460—861no—
181#452—861no—
182#450—861no—
183#433—431no—
184#410—861no—
185C2×#99—861no—
186#354—861no—
187#353—431no—
188#353—431no—
189#353—861no—
190#353C2×D4311yescharacteristic
191#353C2×D4311yescharacteristic
192C43#1361011yescharacteristic, complemented, Sylow
193C2×#41—431no—
194C22×D4—431no—
195C2×Q16—861no—
196C2×SD16—21no—
197C2×SD16—21no—
198C2×SD16—861no—
199C4⋊Q8C4×D4311yescharacteristic, complemented
200#127—431no—
201#127C22×D4311yescharacteristic
202#126—1721no—
203#125—431no—
204#125—1721no—
205#124—431no—
206#124—431no—
207C22⋊Q8—861no—
208#121—1721no—
209#120—1721no—
210C4×Q8—861no—
211#117—431no—
212#117—1721no—
213C2×C22⋊C4—1721no—
214C4⋊C8—861no—
215#103—861no—
216#102—861no—
217#102—861no—
218#102—861no—
219#99—21no—
220#99—21no—
221#99—861no—
222#99—861no—
223#99—1721no—
224#99—1721no—
225C22⋊C8—861no—
226#97—431no—
227C4×C8C4×D4311yescharacteristic, complemented
228C24—861no—
229#41—3441no—
230C2×Q8—21no—
231C2×Q8—431no—
232C2×D4—41no—
233C2×D4—431no—
234C2×D4—861no—
235C2×D4—861no—
236C2×D4—3441no—
237C2×D4—1721no—
238C2×D4D4×D4311yescharacteristic
239C2×D4D4×D4311yescharacteristic
240C22×C4—431no—
241C22×C4—861no—
242C22×C4—3441no—
243Q16—3441no—
244SD16—81no—
245SD16—81no—
246SD16—3441no—
247C2×C8—21no—
248C2×C8—861no—
249C4⋊C4—41no—
250C4⋊C4—861no—
251C4⋊C4—861no—
252C4⋊C4—3441no—
253C4⋊C4—1721no—
254C4⋊C4—1721no—
255C4⋊C4—1721no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—861no—
259C22⋊C4—3441no—
260C22⋊C4—1721no—
261C22⋊C4—1721no—
262C22⋊C4—1721no—
263C22⋊C4—1721no—
264C22⋊C4—1721no—
265C42—431no—
266C42—3441no—
267C42—1721no—
268C42C2×C4×D4311yescharacteristic
269C23—21no—
270C23—21no—
271C23—431no—
272C23—861no—
273C23—1721no—
274C23—1721no—
275C23—6881no—
276Q8—41no—
277Q8—41no—
278Q8—1721no—
279D4—41no—
280D4—41no—
281D4—161no—
282D4—3441no—
283D4—3441no—
284D4—1721no—
285D4—6881no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—431no—
291C2×C4—861no—
292C2×C4—861no—
293C2×C4—3441no—
294C2×C4—3441no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—6882no—
300C2×C4C22⋊C4×D4311yescharacteristic
301C8—41no—
302C8—1721no—
303C22—41no—
304C22—41no—
305C22—81no—
306C22—81no—
307C22—861no—
308C22—3441no—
309C22—3442no—
310C22—1721no—
311C22—1721no—
312C22—6881no—
313C22#99×D4311yescharacteristic
314C4—21no—
315C4—41no—
316C4—81no—
317C4—161no—
318C4—161no—
319C4—861no—
320C4—3441no—
321C4—1721no—
322C4—1721no—
323C4—6881no—
324C4—6881no—
325C2—21no—
326C2—81no—
327C2—81no—
328C2—3441no—
329C2—1721no—
330C2#1913626111yescharacteristic
subgroupG/H
centerC2#19136261
commutatorC42×C43C22×C4
Frattini#127C22×D43
FittingC43×#1409C2
socleC2×C43#2127
prime radical#14583462C22
cosocle#127×C43C23
hypercenter#1409D43
hypocenterC43#13610
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #1409

Complements

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

NH ≅ G/Ntype
4. #19132765C2semidirect
5. #19132765C2semidirect
6. #19132760C2semidirect
7. C43×#1409C2semidirect
8. #14583510C4semidirect
10. #14583291C4semidirect
12. #14583254C4semidirect
17. #14582958C4semidirect
33. #13063317C2×C4semidirect
54. #13063236C2×C4semidirect
57. C4⋊Q8×C43C2×C4semidirect
61. C4×C8×C43C2×C4semidirect
166. #1409D43semidirect
192. C43#13610semidirect
199. C4⋊Q8C4×D43semidirect
227. C4×C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191456602
#191362652
#191362612
#191327652
#191327602
C43×#14092
#1361043