Finite Group Databasebeta

← #24990634

Subgroups — #24990634

Order 11008.

418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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#19135394C211yesmaximal, characteristic
2#19133381C212yesmaximal, complemented
3#19132916C211yesmaximal, characteristic
4#19132493C212yesmaximal, complemented
5C43×#2973C211yesmaximal, characteristic
6#14582952C2212yes—
7C2×C4⋊(C43⋊C8)C2211yescharacteristic
8C2×C22⋊(C43⋊C8)—21no—
9C2×C22⋊(C43⋊C8)—21no—
10C2×#13063236C2211yescharacteristic
11#14582651—22no—
12#14582649—22no—
13#14582623C412yes—
14#14582623C412yes—
15C2×C4×D4×C43C2211yescharacteristic
16C43×#435—22no—
17C43×#435—22no—
18C43×#432C2212yes—
19C43×#407—21no—
20C2×C22⋊C8×C43—21no—
21C22×C43⋊C8—21no—
22C22×C43⋊C8—21no—
23C4⋊(C43⋊C8)—22no—
24C4⋊(C43⋊C8)—22no—
25C22⋊(C43⋊C8)—42no—
26C22⋊(C43⋊C8)—42no—
27C22⋊(C43⋊C8)C2×C414yes—
28#13063236—22no—
29C4×C43⋊C8—22no—
30C22×D4×C43Q811yescharacteristic
31C23×C4×C43D411yescharacteristic
32C23×C4×C43D411yescharacteristic
33C2×M16×C43—21no—
34C2×M16×C43—21no—
35C22×C8×C43—21no—
36C22×C8×C43—21no—
37C4×D4×C43—22no—
38C4×D4×C43—22no—
39C2×C4⋊C4×C43Q811yescharacteristic
40C2×C22⋊C4×C43C2×C411yescharacteristic
41C2×C22⋊C4×C43C2×C411yescharacteristic
42C2×C42×C43C2311yescharacteristic
43C4⋊C8×C43D412yes—
44C4⋊C8×C43D412yes—
45C22⋊C8×C43—22no—
46C22⋊C8×C43—22no—
47C22⋊C8×C43—22no—
48#97×C43—22no—
49C24×C43C4⋊C411yescharacteristic
50C24×C43C4⋊C411yescharacteristic
51C2×D4×C43—22no—
52C2×D4×C43—22no—
53C2×D4×C43—41no—
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—41no—
59C22×C4×C43—41no—
60C22×C4×C43—41no—
61C22×C4×C43—41no—
62C22×C4×C43C4⋊C411yescharacteristic
63C22×C4×C43C4⋊C411yescharacteristic
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×Q811yescharacteristic
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×C43C2×D412yes—
77C42×C43#4112yes—
78C2×C43⋊C8—22no—
79C2×C43⋊C8—24no—
80C2×C43⋊C8—41no—
81C2×C43⋊C8—41no—
82C2×C43⋊C8—41no—
83C2×C43⋊C8—41no—
84C2×C43⋊C8—41no—
85C23×C43—21no—
86C23×C43—21no—
87C23×C43—21no—
88C23×C43—21no—
89C23×C43—21no—
90C23×C43—41no—
91C23×C43—41no—
92C23×C43—41no—
93C23×C43—41no—
94C23×C43#10812yes—
95C23×C43C2×C4⋊C411yescharacteristic
96D4×C43—44no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—81no—
111C2×C4×C43—81no—
112C2×C4×C43C4×D412yes—
113C2×C4×C43#12011yescharacteristic
114C2×C4×C43C22⋊Q812yes—
115C2×C4×C43#12311yescharacteristic
116C8×C43—42no—
117C8×C43—42no—
118C43⋊C8—44no—
119C43⋊C8—42no—
120C43⋊C8—81no—
121#8864—431nomaximal, Sylow
122C22×C43—21no—
123C22×C43—21no—
124C22×C43—22no—
125C22×C43—42no—
126C22×C43—42no—
127C22×C43—41no—
128C22×C43—41no—
129C22×C43—41no—
130C22×C43—41no—
131C22×C43—41no—
132C22×C43—81no—
133C22×C43—81no—
134C22×C43#38511yescharacteristic
135C22×C43C2×#10811yescharacteristic
136C22×C43#43011yescharacteristic
137C4×C43—22no—
138C4×C43—21no—
139C4×C43—22no—
140C4×C43—41no—
141C4×C43—41no—
142C4×C43#45311yescharacteristic
143C4×C43#45511yescharacteristic
144#2973D4311yescharacteristic
145#1955—431no—
146#1573—432no—
147#1460—431no—
148#1302—432no—
149C2×C43—21no—
150C2×C43—21no—
151C2×C43—42no—
152C2×C43—81no—
153C2×C43#185511yescharacteristic
154C2×C43#185611yescharacteristic
155C2×C43#186811yescharacteristic
156C2×C4×D4C2×D4311yescharacteristic
157#435—22no—
158#435—22no—
159#432C2×D4312yes—
160#431—432no—
161C2×C4⋊C8—431no—
162#407—21no—
163C2×C22⋊C8—21no—
164C2×C22⋊C8—861no—
165C2×C22⋊C8—861no—
166C2×#97—431no—
167#335—862no—
168#334—862no—
169#323—432no—
170#323—432no—
171C43#886411yescharacteristic, complemented, Sylow
172C22×D4Dic8611yescharacteristic
173C23×C4C22⋊D4311yescharacteristic
174C23×C4C22⋊D4311yescharacteristic
175C2×M16—21no—
176C2×M16—21no—
177C22×C8—21no—
178C22×C8—21no—
179C22×C8—861no—
180C22×C8—861no—
181C4×D4—22no—
182C4×D4—22no—
183C2×C4⋊C4Dic8611yescharacteristic
184C2×C22⋊C4C4×D4311yescharacteristic
185C2×C22⋊C4C4×D4311yescharacteristic
186C2×C42C22×D4311yescharacteristic
187C4⋊C8—862no—
188C4⋊C8—862no—
189C4⋊C8C22⋊D4312yes—
190C4⋊C8C22⋊D4312yes—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—434no—
195C22⋊C8—1722no—
196C22⋊C8—1722no—
197#97—22no—
198#97—862no—
199C4×C8—862no—
200C24Dic43⋊C411yescharacteristic
201C24Dic43⋊C411yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4Dic43⋊C411yescharacteristic
214C22×C4Dic43⋊C411yescharacteristic
215C22×C4C2×Dic8611yescharacteristic
216C22×C4C2×C4×D4311yescharacteristic
217C22×C4C2×C22⋊D4311yescharacteristic
218M16—81no—
219M16—81no—
220C2×C8—22no—
221C2×C8—22no—
222C2×C8—81no—
223C2×C8—81no—
224C2×C8—862no—
225C2×C8—864no—
226C2×C8—1721no—
227C2×C8—1721no—
228C2×C8—1721no—
229C2×C8—1721no—
230C2×C8—1721no—
231C4⋊C4—22no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C42#1062189812yes—
235C42C2×C22⋊D4312yes—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23#1306326012yes—
246C23C2×Dic43⋊C411yescharacteristic
247D4—44no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4C4×C22⋊D4312yes—
264C2×C4#1306329411yescharacteristic
265C2×C4#1306330412yes—
266C2×C4#1306330811yescharacteristic
267C8—42no—
268C8—42no—
269C8—3441no—
270C8—1722no—
271C8—1724no—
272C22—21no—
273C22—21no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—81no—
283C22—81no—
284C22#1458277211yescharacteristic
285C22C2×#1306326011yescharacteristic
286C22#1458294711yescharacteristic
287C4—22no—
288C4—21no—
289C4—22no—
290C4—41no—
291C4—41no—
292C4#1458306711yescharacteristic
293C4#1458307711yescharacteristic
294C2—21no—
295C2—21no—
296C2—42no—
297C2—81no—
298C2#1913480011yescharacteristic
299C2#1913480511yescharacteristic
300C2#1913488111yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2973C2
socleC22×C43#385
prime radicalC22×D4×C43Q8
cosocleC2×C42×C43C23
hypercenter#2973D43
hypocenterC43#8864
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #19133381C2semidirect
4. #19132493C2semidirect
171. C43#8864semidirect

Maximal subgroups

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

subgroupindex
#191353942
#191333812
#191329162
#191324932
C43×#29732
#886443