Finite Group Databasebeta

← #25000932

Subgroups — #25000932

Order 11008.

364 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 99 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#19145137C211yesmaximal, characteristic
2#19135371C211yesmaximal, characteristic
3#19133283C211yesmaximal, characteristic
4#19133276C211yesmaximal, characteristic
5#19132997C211yesmaximal, characteristic
6#19132445C211yesmaximal, characteristic
7C2×C43×#332C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583305—22no—
10#14583302—21no—
11#14583295—21no—
12#14582952C2211yescharacteristic
13C2×#13063261—21no—
14#14582939—21no—
15#14582939—21no—
16#14582923C2211yescharacteristic
17C4×#10621877C2211yescharacteristic
18#14582664—21no—
19#14582648—22no—
20#14582647—21no—
21#14582646—21no—
22#14582629—22no—
23C2×C4⋊Q8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C43×#332—22no—
27C2×#10621877—21no—
28C2×#10621877D411yescharacteristic
29C2×#10621877D411yescharacteristic
30#13063325D411yescharacteristic
31#13063325D411yescharacteristic
32#13063317—21no—
33#13063304—21no—
34#13063304—21no—
35C4×Dic86—21no—
36C4×Dic86—21no—
37#13063284—21no—
38#13063261—42no—
39#13063258—22no—
40#13063258—22no—
41#13063256—22no—
42#13063256—22no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46C22⋊(C43⋊C8)—21no—
47#13063236—21no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C22×Q8×C43—21no—
51C22×C8×C43—21no—
52C22×C8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43—21no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43D412yes—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C42×C43C2311yescharacteristic
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43D412yes—
64C2×Q8×C43—22no—
65C2×Q8×C43—41no—
66C2×Q8×C43—81no—
67C2×Q8×C43—81no—
68C22×C4×C43—41no—
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43#4111yescharacteristic
71C22×C4×C43#4111yescharacteristic
72C2×Dic86—21no—
73C2×Dic86—21no—
74C2×C8×C43—22no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—81no—
79C4⋊C4×C43—22no—
80C4⋊C4×C43—22no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C42×C43C2×D411yescharacteristic
84C42×C43C2×D411yescharacteristic
85C42×C43C2×D411yescharacteristic
86C42×C43#4111yescharacteristic
87C22⋊Dic43—41no—
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94C4×Dic43—41no—
95#10621877—21no—
96#10621877—21no—
97#10621877—41no—
98#10621877—41no—
99#10621877SD1612yes—
100#10621877Q1612yes—
101C2×C43⋊C8—21no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C23×C43#12411yescharacteristic
106Q8×C43—82no—
107Q8×C43—81no—
108Q8×C43—81no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—41no—
112C2×C4×C43—42no—
113C2×C4×C43—82no—
114C2×C4×C43#12011yescharacteristic
115C2×C4×C43#12111yescharacteristic
116C2×C4×C43#12111yescharacteristic
117C2×C4×C43#12111yescharacteristic
118C2×C4×C43#12311yescharacteristic
119C2×C4×C43#12311yescharacteristic
120C2×C4×C43C2×SD1611yescharacteristic
121C2×C4×C43C2×Q1611yescharacteristic
122C2×C4×C43#13711yescharacteristic
123C2×C4×C43#13711yescharacteristic
124C2×Dic43—41no—
125C2×Dic43—41no—
126Dic86—41no—
127Dic86—41no—
128Dic86—81no—
129C8×C43—42no—
130C8×C43—81no—
131C43⋊C8—22no—
132C43⋊C8—22no—
133C43⋊C8—81no—
134C43⋊C8—81no—
135#10556—431nomaximal, Sylow
136C22×C43—21no—
137C22×C43—21no—
138C22×C43#39411yescharacteristic
139C22×C43#48711yescharacteristic
140C22×C43#49111yescharacteristic
141C4×C43—21no—
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—82no—
145C4×C43#44811yescharacteristic
146C4×C43#45111yescharacteristic
147C4×C43#46111yescharacteristic
148C4×C43#46211yescharacteristic
149C4×C43#47111yescharacteristic
150C4×C43#47211yescharacteristic
151Dic43—81no—
152Dic43—81no—
153#3165—431no—
154#1950—431no—
155#1550—431no—
156#1548—431no—
157C2×#332D4311yescharacteristic
158#1481—431no—
159#1283—431no—
160C2×C43—21no—
161C2×C43—21no—
162C2×C43#204311yescharacteristic
163C2×C43#204911yescharacteristic
164C2×C43#205111yescharacteristic
165#533—431no—
166C2×C4⋊Q8C2×D4311yescharacteristic
167#501—862no—
168#500—861no—
169#498—861no—
170#431—431no—
171C2×#108—861no—
172#428—861no—
173#428—861no—
174#423—431no—
175C2×C4⋊C8C2×D4311yescharacteristic
176C2×C4⋊C8C2×D4311yescharacteristic
177C4×M16—431no—
178#341—861no—
179#333—861no—
180#333—862no—
181#332—22no—
182#332—861no—
183Q8⋊C8—862no—
184C43#1055611yescharacteristic, complemented, Sylow
185C22×Q8—21no—
186C2×M16—431no—
187C2×M16—431no—
188C2×M16—861no—
189C22×C8—21no—
190C22×C8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—431no—
195C4⋊Q8—431no—
196C4⋊Q8D17212yes—
197#125—861no—
198C22⋊Q8—861no—
199C22⋊Q8—861no—
200C4×Q8—861no—
201C4×Q8—861no—
202#117—861no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C42C22×D4311yescharacteristic
206#108—1722no—
207#107—862no—
208#107—862no—
209#106—862no—
210#106—862no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—861no—
215C4⋊C8—861no—
216C4⋊C8—861no—
217C4⋊C8C22⋊D4312yes—
218C22⋊C8—861no—
219#97—861no—
220C4×C8—861no—
221C4×C8—861no—
222C2×Q8—22no—
223C2×Q8—41no—
224C2×Q8—81no—
225C2×Q8—81no—
226C2×Q8—861no—
227C2×Q8—861no—
228C22×C4—41no—
229C22×C4#1062189811yescharacteristic
230C22×C4D4×D4311yescharacteristic
231C22×C4#1062190011yescharacteristic
232M16—432no—
233M16—432no—
234M16—861no—
235M16—861no—
236M16—1721no—
237M16—1721no—
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—81no—
243C2×C8—861no—
244C2×C8—861no—
245C2×C8—1721no—
246C2×C8—1721no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4—1721no—
256C4⋊C4—1721no—
257C22⋊C4—1721no—
258C42—1721no—
259C42C2×D17211yescharacteristic
260C42D4×D4311yescharacteristic
261C42#1062190011yescharacteristic
262C42C2×C22⋊D4311yescharacteristic
263C23#1306331111yescharacteristic
264Q8—82no—
265Q8—81no—
266Q8—81no—
267Q8—3441no—
268Q8—1721no—
269Q8—1721no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—82no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4#1306329511yescharacteristic
278C2×C4#1306329611yescharacteristic
279C2×C4#1306329711yescharacteristic
280C2×C4#1306329911yescharacteristic
281C2×C4#1306330711yescharacteristic
282C2×C4#1306330911yescharacteristic
283C2×C4SD16×D4311yescharacteristic
284C2×C4Q16×D4311yescharacteristic
285C2×C4#1306335411yescharacteristic
286C2×C4#1306335711yescharacteristic
287C8—42no—
288C8—81no—
289C8—862no—
290C8—862no—
291C8—3441no—
292C8—3441no—
293C22—21no—
294C22—21no—
295C22#1458281511yescharacteristic
296C22#1458324811yescharacteristic
297C22#1458326611yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—82no—
302C4—3441no—
303C4—3441no—
304C4#1458303911yescharacteristic
305C4#1458305611yescharacteristic
306C4#1458310211yescharacteristic
307C4#1458310711yescharacteristic
308C4#1458315911yescharacteristic
309C4#1458316611yescharacteristic
310C2—21no—
311C2—21no—
312C2#1913584011yescharacteristic
313C2#1913587411yescharacteristic
314C2#1913588811yescharacteristic
subgroupG/H
centerC22#14582815
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#332C2
socleC22×C43#394
prime radicalC23×C43#124
hypercenterC2×#332D43
hypocenterC43#10556
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
184. C43#10556semidirect

Maximal subgroups

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

subgroupindex
#191451372
#191353712
#191332832
#191332762
#191329972
#191324452
C2×C43×#3322
#1055643