Finite Group Databasebeta

← #24991000

Subgroups — #24991000

Order 11008.

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

normal subgroups only

This group has 392 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#19135428C211yesmaximal, characteristic
2#19133363C212yesmaximal, complemented
3#19133187C211yesmaximal, characteristic
4#19132487C212yesmaximal, complemented
5C43×#2980C211yesmaximal, characteristic
6#14582923C2211yescharacteristic
7C2×#13063252—21no—
8C2×#13063252—21no—
9C4×#10621877C2212yes—
10#14582745C2211yescharacteristic
11#14582651—22no—
12#14582649—22no—
13#14582639C411yescharacteristic, complemented
14#14582639C412yescomplemented
15#14582639C411yescharacteristic, complemented
16C43×#532C2211yescharacteristic
17C43×#435—22no—
18C43×#435—22no—
19C43×#432C2212yes—
20C43×#408—21no—
21C43×#408—21no—
22C2×#10621877—22no—
23C2×#10621877—21no—
24C2×C4×Dic43—21no—
25C4⋊(C43⋊C8)—22no—
26#13063252—42no—
27#13063252—42no—
28#13063236C2×C412yes—
29#13063236C2×C412yes—
30C4×C43⋊C8—22no—
31C43⋊#95—22no—
32C2×#41×C43D411yescharacteristic
33C2×#41×C43D411yescharacteristic
34C2×M16×C43—21no—
35C2×M16×C43—21no—
36C22×C8×C43—21no—
37C22×C8×C43—21no—
38C4⋊Q8×C43Q811yescharacteristic
39#127×C43Q811yescharacteristic
40#124×C43C2×C411yescharacteristic
41#124×C43C2×C411yescharacteristic
42#121×C43—22no—
43C4×D4×C43—22no—
44C2×C42×C43C2311yescharacteristic
45C4⋊C8×C43D412yes—
46C4⋊C8×C43D412yes—
47C22⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49C22⋊C8×C43—22no—
50#97×C43—22no—
51#41×C43—41no—
52#41×C43—41no—
53#41×C43—41no—
54#41×C43—41no—
55C2×Q8×C43C4⋊C411yescharacteristic
56C2×Q8×C43C4⋊C411yescharacteristic
57C2×D4×C43—22no—
58C2×D4×C43—21no—
59C2×D4×C43—21no—
60C2×D4×C43C4⋊C411yescharacteristic
61C2×D4×C43C4⋊C411yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43#4112yes—
66C22×Dic43—41no—
67M16×C43—81no—
68M16×C43—81no—
69C2×C8×C43—22no—
70C2×C8×C43—22no—
71C2×C8×C43—81no—
72C2×C8×C43—81no—
73C4⋊C4×C43—22no—
74C22⋊C4×C43—22no—
75C22⋊C4×C43—22no—
76C42×C43C22×C411yescharacteristic
77C42×C43C2×D412yes—
78C42×C43C2×Q811yescharacteristic
79C4×Dic43—22no—
80C4×Dic43—41no—
81#10621877—44no—
82#10621877—41no—
83#10621877—41no—
84C2×C43⋊C8—22no—
85C2×C43⋊C8—22no—
86C2×C43⋊C8—41no—
87C23×C43—21no—
88C23×C43—21no—
89C23×C43#12311yescharacteristic
90Q8×C43—41no—
91Q8×C43—41no—
92D4×C43—41no—
93D4×C43—41no—
94D4×C43—82no—
95D4×C43—81no—
96D4×C43—81no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—42no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43C2×C4⋊C411yescharacteristic
107C2×C4×C43C4×D412yes—
108C2×C4×C43#12011yescharacteristic
109C2×C4×C43C22⋊Q812yes—
110C2×Dic43—42no—
111C2×Dic43—82no—
112C8×C43—42no—
113C8×C43—42no—
114C43⋊C8—24no—
115C43⋊C8—42no—
116C43⋊C8—81no—
117#8918—431nomaximal, Sylow
118C22×C43—21no—
119C22×C43—22no—
120C22×C43—41no—
121C22×C43—41no—
122C22×C43—42no—
123C22×C43—42no—
124C22×C43#38511yescharacteristic
125C4×C43—21no—
126C4×C43—22no—
127C4×C43—22no—
128C4×C43—41no—
129C4×C43—41no—
130C4×C43#45311yescharacteristic
131C4×C43#45511yescharacteristic
132Dic43—82no—
133#2980D4311yescharacteristic
134#1963—431no—
135#1569—432no—
136#1525—431no—
137#1300—432no—
138C2×C43—41no—
139C2×C43—81no—
140C2×C43—81no—
141C2×C43#185611yescharacteristic
142C2×C43#186112yes—
143#532C2×D4311yescharacteristic
144#435—22no—
145#435—22no—
146#432C2×D4312yes—
147#423—431no—
148C2×#104—861no—
149C2×#104—861no—
150#408—21no—
151#408—21no—
152C4×M16—432no—
153#376—431no—
154#335—862no—
155#334—862no—
156#329—431no—
157#329—432no—
158#329—431no—
159C43#891811yescharacteristic, complemented, Sylow
160C2×#41C22⋊D4311yescharacteristic
161C2×#41C22⋊D4311yescharacteristic
162C2×M16—21no—
163C2×M16—21no—
164C2×M16—862no—
165C2×M16—861no—
166C22×C8—21no—
167C22×C8—21no—
168C4⋊Q8Dic8611yescharacteristic
169#127Dic8611yescharacteristic
170#124C4×D4311yescharacteristic
171#124C4×D4311yescharacteristic
172#121—22no—
173C4×D4—22no—
174C2×C42—861no—
175C2×C42C22×D4311yescharacteristic
176C4⋊C8—862no—
177C4⋊C8C22⋊D4312yes—
178C4⋊C8C22⋊D4312yes—
179#104—1722no—
180#104—1722no—
181C22⋊C8—22no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184#97—22no—
185#97—432no—
186#97—432no—
187C4×C8—862no—
188#95—862no—
189#41—41no—
190#41—41no—
191#41—41no—
192#41—41no—
193C2×Q8Dic43⋊C411yescharacteristic
194C2×Q8Dic43⋊C411yescharacteristic
195C2×D4—21no—
196C2×D4—21no—
197C2×D4—22no—
198C2×D4Dic43⋊C411yescharacteristic
199C2×D4Dic43⋊C411yescharacteristic
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—1721no—
203C22×C4#1062189812yes—
204C22×C4C2×C22⋊D4311yescharacteristic
205M16—81no—
206M16—81no—
207M16—1724no—
208M16—1721no—
209M16—1721no—
210C2×C8—22no—
211C2×C8—22no—
212C2×C8—81no—
213C2×C8—81no—
214C2×C8—862no—
215C2×C8—862no—
216C2×C8—1721no—
217C4⋊C4—22no—
218C22⋊C4—22no—
219C22⋊C4—22no—
220C42—862no—
221C42—1721no—
222C42C2×Dic8611yescharacteristic
223C42C2×C4×D4311yescharacteristic
224C42C2×C22⋊D4312yes—
225C23—21no—
226C23—21no—
227C23#1306330811yescharacteristic
228Q8—41no—
229Q8—41no—
230D4—41no—
231D4—41no—
232D4—82no—
233D4—81no—
234D4—81no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—3442no—
245C2×C4—1722no—
246C2×C4C2×Dic43⋊C411yescharacteristic
247C2×C4C4×C22⋊D4312yes—
248C2×C4#1306329411yescharacteristic
249C2×C4#1306330412yes—
250C8—42no—
251C8—42no—
252C8—864no—
253C8—3441no—
254C8—1722no—
255C22—21no—
256C22—22no—
257C22—41no—
258C22—41no—
259C22—42no—
260C22—42no—
261C22#1458277211yescharacteristic
262C4—21no—
263C4—22no—
264C4—22no—
265C4—41no—
266C4—41no—
267C4—3442no—
268C4#1458306711yescharacteristic
269C4#1458307711yescharacteristic
270C2—41no—
271C2—81no—
272C2—81no—
273C2#1913480511yescharacteristic
274C2#1913483512yes—
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2980C2
socleC22×C43#385
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#2980D43
hypocenterC43#8918
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2980

Complements

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

NH ≅ G/Ntype
2. #19133363C2semidirect
4. #19132487C2semidirect
13. #14582639C4semidirect
14. #14582639C4semidirect
15. #14582639C4semidirect
159. C43#8918semidirect

Maximal subgroups

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

subgroupindex
#191354282
#191333632
#191331872
#191324872
C43×#29802
#891843