Finite Group Databasebeta

← #24997561

Subgroups — #24997561

Order 11008.

636 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 105 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#19144591C212yesmaximal, complemented
2#19135393C211yesmaximal, characteristic, complemented
3#19132994C212yesmaximal, complemented
4#19132426C211yesmaximal, characteristic, complemented
5C43×#3150C211yesmaximal, characteristic, complemented
6C2×C4×D172C2211yescharacteristic
7#14583210—22no—
8#14583176—22no—
9#14583091—22no—
10#14583032—22no—
11C4×#10621882—24no—
12#14582952C2212yes—
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×(C2×D43)⋊C8—22no—
15D4⋊(C43⋊C8)—24no—
16C2×#135×C43—22no—
17C43×#532C2212yes—
18C43×#497—22no—
19C43×#496—22no—
20C2×#97×C43C2211yescharacteristic
21C22×D172D411yescharacteristic
22C22×C4×D43—21no—
23C2×#10621882—24no—
24C22×C43⋊C8—21no—
25C4×D172—22no—
26C4×D172—22no—
27C2×C4⋊Dic43D411yescharacteristic
28C2×(C2×D43)⋊C4—21no—
29#13063258—24no—
30C4⋊(C43⋊C8)—22no—
31C4⋊(C43⋊C8)—22no—
32#13063246—24no—
33#13063245—24no—
34C22⋊(C43⋊C8)—22no—
35(C2×D43)⋊C8—44no—
36C4×C43⋊C8D414yes—
37C2×#41×C43—22no—
38#135×C43—44no—
39#135×C43—44no—
40C2×Q16×C43—22no—
41C2×SD16×C43—24no—
42C2×D8×C43—22no—
43C22×C8×C43D412yes—
44C4⋊Q8×C43D412yes—
45#127×C43D412yes—
46#124×C43—22no—
47#121×C43—22no—
48#121×C43—22no—
49C4×D4×C43—22no—
50C4×D4×C43—22no—
51C2×C42×C43C2311yescharacteristic
52#97×C43—22no—
53C23×D43—21no—
54#41×C43—44no—
55#41×C43—44no—
56C2×Q8×C43—22no—
57C2×D4×C43—22no—
58C2×D4×C43—22no—
59C2×D4×C43—22no—
60C2×D4×C43—42no—
61C22×C4×C43—42no—
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43#4111yescharacteristic
65C22×Dic43—21no—
66C2×D172—22no—
67C2×D172—42no—
68C2×C4×D43—41no—
69C2×C4×D43—41no—
70C2×C4×D43—42no—
71C2×C4×D43—42no—
72Q16×C43—44no—
73SD16×C43—48no—
74D8×C43—44no—
75C2×C8×C43—22no—
76C2×C8×C43—22no—
77C2×C8×C43D814yescomplemented
78C4⋊C4×C43—22no—
79C4⋊C4×C43—22no—
80C22⋊C4×C43—42no—
81C22⋊C4×C43—42no—
82C42×C43C2×D412yes—
83C42×C43C2×D412yes—
84#10621882—48no—
85(C2×D43)⋊C4—42no—
86C4⋊Dic43—22no—
87C2×C43⋊C8—24no—
88C2×C43⋊C8—41no—
89C2×C43⋊C8—42no—
90C23×C43—42no—
91C23×C43#12111yescharacteristic
92C22×D43—22no—
93C22×D43—41no—
94C22×D43—42no—
95C22×D43—41no—
96C22×D43—42no—
97Q8×C43—44no—
98D4×C43—44no—
99D4×C43—44no—
100D4×C43—44no—
101D4×C43—84no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—42no—
105C2×C4×C43—82no—
106C2×C4×C43—82no—
107C2×C4×C43#12012yes—
108C2×C4×C43#12011yescharacteristic
109C2×C4×C43#12112yes—
110C2×C4×C43#12711yescharacteristic
111C2×C4×C43C2×D812yes—
112C2×C4×C43AGL(1,ℤ/8)12yes—
113C2×Dic43—41no—
114C2×Dic43—42no—
115D172—24no—
116D172—42no—
117C4×D43—82no—
118C4×D43—81no—
119C4×D43—81no—
120C8×C43—24no—
121C43⋊C8—44no—
122C43⋊C8—81no—
123#10032—431nomaximal, Sylow
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—82no—
127C22×C43—82no—
128C22×C43—82no—
129C22×C43#39211yescharacteristic
130C22×C43#45912yes—
131C2×D43—44no—
132C2×D43—42no—
133C2×D43—82no—
134C2×D43—81no—
135C2×D43—81no—
136C4×C43—22no—
137C4×C43—22no—
138C4×C43—82no—
139C4×C43#44712yes—
140C4×C43#49311yescharacteristic
141C4×C43#49611yescharacteristic
142Dic43—81no—
143#3150D4311yescharacteristic, complemented
144#3100—432no—
145#1955—431no—
146#1480—432no—
147#1275—431no—
148C2×C43—22no—
149C2×C43—162no—
150C2×C43#201011yescharacteristic
151C2×C43#201111yescharacteristic
152C2×C43#201711yescharacteristic
153D43—82no—
154C2×#135—22no—
155#532C2×D4312yes—
156C2×C4×D4—431no—
157#497—22no—
158#496—22no—
159#480—862no—
160#474—862no—
161#459—862no—
162#447—862no—
163C4×D8—864no—
164#431—432no—
165C2×C4⋊C8—431no—
166C2×C22⋊C8—862no—
167C2×#97C2×D4311yescharacteristic
168D4⋊C8—864no—
169C43#1003211yescharacteristic, complemented, Sylow
170C2×#41—22no—
171C22×D4—431no—
172C23×C4—861no—
173#135—44no—
174#135—44no—
175C2×Q16—22no—
176C2×SD16—24no—
177C2×D8—22no—
178C2×D8—864no—
179C22×C8—861no—
180C22×C8C22⋊D4312yes—
181C4⋊Q8C22⋊D4312yes—
182#127C22⋊D4312yes—
183#124—22no—
184#121—22no—
185#121—22no—
186C4×D4—22no—
187C4×D4—22no—
188C4×D4—862no—
189C4×D4—862no—
190C2×C4⋊C4—431no—
191C2×C22⋊C4—861no—
192C2×C42C22×D4311yescharacteristic
193#107—864no—
194C4⋊C8—862no—
195C4⋊C8—862no—
196#102—864no—
197#102—864no—
198C22⋊C8—862no—
199C22⋊C8—1724no—
200#97—22no—
201C4×C8—434no—
202C24—861no—
203#41—44no—
204#41—44no—
205C2×Q8—22no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—42no—
210C2×D4—862no—
211C2×D4—1722no—
212C22×C4—42no—
213C22×C4—861no—
214C22×C4—1721no—
215C22×C4—1721no—
216C22×C4—1722no—
217C22×C4—1722no—
218C22×C4D4×D4311yescharacteristic
219C22×C4#1062190011yescharacteristic
220C22×C4C2×C22⋊D4311yescharacteristic
221Q16—44no—
222SD16—48no—
223D8—44no—
224D8—1728no—
225C2×C8—22no—
226C2×C8—22no—
227C2×C8—864no—
228C2×C8—1721no—
229C2×C8—1722no—
230C2×C8#1062188214yescomplemented
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—862no—
234C22⋊C4—42no—
235C22⋊C4—42no—
236C22⋊C4—1722no—
237C42D4×D4312yes—
238C42C2×C22⋊D4312yes—
239C23—42no—
240C23—862no—
241C23—1721no—
242C23—1722no—
243C23—1721no—
244C23—1722no—
245C23#1306329611yescharacteristic
246Q8—44no—
247D4—44no—
248D4—44no—
249D4—44no—
250D4—84no—
251D4—864no—
252D4—1722no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—3441no—
259C2×C4—3441no—
260C2×C4—3442no—
261C2×C4—1721no—
262C2×C4—1722no—
263C2×C4#1306329312yes—
264C2×C4#1306329411yescharacteristic
265C2×C4#1306329712yes—
266C2×C4#1306332111yescharacteristic
267C2×C4C2×#1062188212yes—
268C2×C4#1306335112yes—
269C8—24no—
270C8—3441no—
271C8—1724no—
272C22—21no—
273C22—21no—
274C22—82no—
275C22—82no—
276C22—82no—
277C22—3442no—
278C22—3441no—
279C22—3441no—
280C22—1724no—
281C22—1722no—
282C22#1458280711yescharacteristic
283C22#1458309112yes—
284C4—22no—
285C4—22no—
286C4—82no—
287C4—3441no—
288C4#1458303312yes—
289C4#1458327511yescharacteristic
290C4#1458328611yescharacteristic
291C2—22no—
292C2—162no—
293C2—3442no—
294C2#1913565911yescharacteristic
295C2#1913566611yescharacteristic
296C2#1913569811yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3150C2
socleC22×C43#392
hypercenter#3150D43
hypocenterC43#10032
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3150

Complements

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

NH ≅ G/Ntype
1. #19144591C2semidirect
2. #19135393C2semidirect
3. #19132994C2semidirect
4. #19132426C2semidirect
5. C43×#3150C2semidirect
77. C2×C8×C43D8semidirect
143. #3150D43semidirect
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
#191445912
#191353932
#191329942
#191324262
C43×#31502
#1003243