Finite Group Databasebeta

← #24997563

Subgroups — #24997563

Order 11008.

636 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 103 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#19145041C211yesmaximal, characteristic, complemented
2#19144595C212yesmaximal, complemented
3#19132993C212yesmaximal, complemented
4#19132426C211yesmaximal, characteristic, complemented
5C43×#1955C211yesmaximal, characteristic, complemented
6C2×#13063347—22no—
7#14583449C2212yes—
8#14583293—22no—
9#14583288—22no—
10#14583212—22no—
11#14583179—22no—
12#14583094—22no—
13#14583033—22no—
14C4×#10621882—24no—
15#14582952C2212yes—
16#14582626—24no—
17C2×C4×D4×C43C2211yescharacteristic
18C2×C4⋊C8×C43C2211yescharacteristic
19C2×C22⋊C8×C43—22no—
20C2×#97×C43C2211yescharacteristic
21C2×#10621898—22no—
22#13063347—44no—
23#13063347—44no—
24C2×Dic172—22no—
25C2×#10621873—24no—
26C2×D344—22no—
27C2×#10621882—24no—
28#13063325D412yes—
29#13063322D412yes—
30#13063313—22no—
31#13063299—22no—
32#13063299—22no—
33C4×D172—22no—
34C4×D172—22no—
35#13063258—24no—
36C4⋊(C43⋊C8)—22no—
37#13063246—24no—
38#13063245—24no—
39C22⋊(C43⋊C8)—22no—
40C4×C43⋊C8D414yes—
41C22×D4×C43D411yescharacteristic
42C23×C4×C43—21no—
43C22×C8×C43—21no—
44C22×C8×C43D412yes—
45C4×D4×C43—22no—
46C4×D4×C43—22no—
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C22⋊C4×C43—21no—
49C2×C42×C43C2311yescharacteristic
50C4⋊C8×C43—22no—
51C22⋊C8×C43—44no—
52#97×C43—22no—
53C24×C43—21no—
54C2×D4×C43—22no—
55C2×D4×C43—42no—
56C22×C4×C43—21no—
57C22×C4×C43—41no—
58C22×C4×C43—41no—
59C22×C4×C43—42no—
60C22×C4×C43—42no—
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43#4111yescharacteristic
64C2×C22⋊D43—42no—
65#10621898—44no—
66#10621898—44no—
67C2×D172—22no—
68C2×D172—22no—
69C2×D172—22no—
70C2×C4×D43—42no—
71C2×Dic86—22no—
72C2×C8×C43—22no—
73C2×C8×C43—22no—
74C2×C8×C43—41no—
75C2×C8×C43—42no—
76C2×C8×C43D814yescomplemented
77C4⋊C4×C43—22no—
78C22⋊C4×C43—42no—
79C42×C43C2×D412yes—
80C42×C43C2×D412yes—
81#10621882—48no—
82(C2×D43)⋊C4—42no—
83(C2×D43)⋊C4—42no—
84C4⋊Dic43—22no—
85C4⋊Dic43—22no—
86C2×C43⋊C8—24no—
87Dic172—44no—
88D344—44no—
89#10621873—48no—
90C23×C43—22no—
91C23×C43—41no—
92C23×C43—42no—
93C23×C43—41no—
94C23×C43—42no—
95C23×C43#12111yescharacteristic
96C22×D43—42no—
97D4×C43—24no—
98D4×C43—42no—
99C2×C4×C43—41no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43—42no—
103C2×C4×C43—82no—
104C2×C4×C43—81no—
105C2×C4×C43—81no—
106C2×C4×C43#12011yescharacteristic
107C2×C4×C43#12012yes—
108C2×C4×C43#12112yes—
109C2×C4×C43#12711yescharacteristic
110C2×C4×C43C2×D812yes—
111C2×C4×C43AGL(1,ℤ/8)12yes—
112C22⋊D43—84no—
113C2×Dic43—42no—
114D172—44no—
115D172—44no—
116D172—44no—
117C4×D43—82no—
118C4×D43—82no—
119Dic86—44no—
120C8×C43—24no—
121C8×C43—81no—
122C43⋊C8—44no—
123#10032—431nomaximal, Sylow
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—44no—
127C22×C43—42no—
128C22×C43—82no—
129C22×C43—81no—
130C22×C43—81no—
131C22×C43#39211yescharacteristic
132C22×C43#45912yes—
133C2×D43—82no—
134C2×D43—82no—
135C2×D43—82no—
136C4×C43—22no—
137C4×C43—22no—
138C4×C43—81no—
139C4×C43#44712yes—
140C4×C43#49311yescharacteristic
141C4×C43#49611yescharacteristic
142Dic43—82no—
143#3150—431no—
144#3100—432no—
145#1955D4311yescharacteristic, complemented
146#1480—432no—
147#1275—431no—
148C2×C43—22no—
149C2×C43—82no—
150C2×C43#201011yescharacteristic
151C2×C43#201111yescharacteristic
152C2×C43#201711yescharacteristic
153D43—162no—
154C2×#135—862no—
155#532—432no—
156C2×C4×D4C2×D4311yescharacteristic
157#497—862no—
158#496—862no—
159#480—862no—
160#474—862no—
161#459—862no—
162#447—862no—
163C4×D8—864no—
164#431—432no—
165C2×C4⋊C8C2×D4311yescharacteristic
166C2×C22⋊C8—22no—
167C2×#97C2×D4311yescharacteristic
168D4⋊C8—864no—
169C43#1003211yescharacteristic, complemented, Sylow
170C2×#41—862no—
171C22×D4D17211yescharacteristic
172C23×C4—21no—
173#135—1724no—
174#135—1724no—
175C2×Q16—862no—
176C2×SD16—864no—
177C2×D8—862no—
178C2×D8—864no—
179C22×C8—21no—
180C22×C8C22⋊D4312yes—
181C4⋊Q8—432no—
182#127—432no—
183#124—862no—
184#121—862no—
185#121—862no—
186C4×D4—22no—
187C4×D4—22no—
188C4×D4—862no—
189C4×D4—862no—
190C2×C4⋊C4D17211yescharacteristic
191C2×C22⋊C4—21no—
192C2×C42C22×D4311yescharacteristic
193#107—864no—
194C4⋊C8—22no—
195C4⋊C8—862no—
196#102—864no—
197#102—864no—
198C22⋊C8—44no—
199C22⋊C8—862no—
200#97—22no—
201C4×C8—434no—
202C24—21no—
203#41—1724no—
204#41—1724no—
205C2×Q8—862no—
206C2×D4—22no—
207C2×D4—42no—
208C2×D4—862no—
209C2×D4—862no—
210C2×D4—862no—
211C2×D4—1722no—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—1722no—
218C22×C4C2×D17211yescharacteristic
219C22×C4#1062189811yescharacteristic
220C22×C4C2×C22⋊D4311yescharacteristic
221Q16—1724no—
222SD16—1728no—
223D8—1724no—
224D8—1728no—
225C2×C8—22no—
226C2×C8—22no—
227C2×C8—41no—
228C2×C8—42no—
229C2×C8—864no—
230C2×C8#1062188214yescomplemented
231C4⋊C4—22no—
232C4⋊C4—862no—
233C4⋊C4—862no—
234C22⋊C4—42no—
235C22⋊C4—1722no—
236C22⋊C4—1722no—
237C42D4×D4312yes—
238C42D4×D4312yes—
239C23—22no—
240C23—41no—
241C23—42no—
242C23—41no—
243C23—42no—
244C23—1722no—
245C23#1306329911yescharacteristic
246Q8—1724no—
247D4—24no—
248D4—42no—
249D4—3444no—
250D4—1724no—
251D4—1724no—
252D4—1724no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—81no—
258C2×C4—82no—
259C2×C4—81no—
260C2×C4—3442no—
261C2×C4—3442no—
262C2×C4—1722no—
263C2×C4#1306329311yescharacteristic
264C2×C4#1306329512yes—
265C2×C4#1306329812yes—
266C2×C4#1306332111yescharacteristic
267C2×C4C2×#1062188212yes—
268C2×C4#1306335012yes—
269C8—24no—
270C8—81no—
271C8—1724no—
272C22—21no—
273C22—21no—
274C22—44no—
275C22—42no—
276C22—82no—
277C22—81no—
278C22—81no—
279C22—3442no—
280C22—3442no—
281C22—3442no—
282C22#1458280811yescharacteristic
283C22#1458309412yes—
284C4—22no—
285C4—22no—
286C4—81no—
287C4—3442no—
288C4#1458303212yes—
289C4#1458327511yescharacteristic
290C4#1458328911yescharacteristic
291C2—22no—
292C2—82no—
293C2—6882no—
294C2#1913566211yescharacteristic
295C2#1913566511yescharacteristic
296C2#1913569911yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1955C2
socleC22×C43#392
hypercenter#1955D43
hypocenterC43#10032
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #19145041C2semidirect
2. #19144595C2semidirect
3. #19132993C2semidirect
4. #19132426C2semidirect
5. C43×#1955C2semidirect
76. C2×C8×C43D8semidirect
145. #1955D43semidirect
169. C43#10032semidirect
230. C2×C8#10621882semidirect

Maximal subgroups

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

subgroupindex
#191450412
#191445952
#191329932
#191324262
C43×#19552
#1003243