Finite Group Databasebeta

← #25005711

Subgroups — #25005711

Order 11008.

526 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 93 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#19137178C211yesmaximal, characteristic
2#19132908C212yesmaximal
3#19132529C211yesmaximal, characteristic, complemented
4#19132528C212yesmaximal, complemented
5C43×#1319C211yesmaximal, characteristic, complemented
6C22×Q8×D43C411yescharacteristic
7C2×#13063283C2211yescharacteristic
8C2×#13063282C411yescharacteristic
9#14582949—22no—
10#14582806C411yescharacteristic
11#14582805C411yescharacteristic
12#14582804C2211yescharacteristic
13#14582803—22no—
14#14582761—22no—
15#14582625C2212yes—
16#14582622—22no—
17C43×#391C2211yescharacteristic
18C43×#324C2212yes—
19C22×Dic86—21no—
20C22×Dic86C2×C411yescharacteristic
21C2×Q8×D43—22no—
22C2×Q8×D43—42no—
23C2×Q8×D43—42no—
24C2×Q8×D43C814yescomplemented
25C22×C4×D43—21no—
26C22×C4×D43C2×C411yescharacteristic
27#13063283—42no—
28#13063282—42no—
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4D412yes—
33C2×C4×Dic43C2×C411yescharacteristic
34C2×C4×Dic43D412yes—
35Dic43⋊C8—42no—
36C22⋊(C43⋊C8)—22no—
37C8×Dic43—42no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C22×Q8×C43C2×C411yescharacteristic
42C2×C4⋊C4×C43C2311yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C22⋊C8×C43—22no—
45#95×C43—22no—
46C23×D43C22⋊C411yescharacteristic
47C2×Q8×C43—21no—
48C2×Q8×C43—41no—
49C2×Q8×C43—41no—
50C2×Q8×C43C2×C812yes—
51C22×C4×C43—21no—
52C22×C4×C43—21no—
53C22×C4×C43C22×C411yescharacteristic
54C22×C4×C43C2×D412yes—
55C22×Dic43—21no—
56C22×Dic43—21no—
57C22×Dic43C22⋊C412yes—
58C22×Dic43C22⋊C411yescharacteristic
59Q8×D43—48no—
60Q8×D43—48no—
61C2×C4×D43—22no—
62C2×C4×D43—22no—
63C2×C4×D43—24no—
64C2×C4×D43—42no—
65C2×C4×D43—42no—
66C2×C4×D43C2×C812yes—
67C2×C4×D43M1612yes—
68C2×Dic86—21no—
69C2×Dic86—24no—
70C2×Dic86—42no—
71C2×Dic86—42no—
72C2×Dic86—41no—
73C2×Dic86—41no—
74C2×Dic86C2×C812yes—
75C2×C8×C43—42no—
76C4⋊C4×C43—41no—
77C42×C43—41no—
78(C2×D43)⋊C4—42no—
79(C2×D43)⋊C4—42no—
80C4⋊Dic43—41no—
81Dic43⋊C4—42no—
82C4×Dic43—22no—
83C4×Dic43—22no—
84C4×Dic43—41no—
85C2×C43⋊C8—42no—
86C23×C43C2×C22⋊C411yescharacteristic
87C22×D43—21no—
88C22×D43—21no—
89C22×D43—41no—
90C22×D43—41no—
91C22×D43C22⋊C812yes—
92Q8×C43—42no—
93Q8×C43—42no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—41no—
99C2×C4×C43—41no—
100C2×C4×C43—42no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43C22×C811yescharacteristic
105C2×C4×C43C2×M1611yescharacteristic
106C2×Dic43—22no—
107C2×Dic43—22no—
108C2×Dic43—41no—
109C2×Dic43—41no—
110C2×Dic43—42no—
111C2×Dic43—41no—
112C2×Dic43—41no—
113C2×Dic43—41no—
114C2×Dic43C22⋊C812yes—
115C2×Dic43#9912yes—
116C2×Dic43#10012yes—
117C4×D43—24no—
118C4×D43—24no—
119C4×D43—48no—
120Dic86—42no—
121Dic86—48no—
122Dic86—42no—
123C8×C43—82no—
124C43⋊C8—82no—
125#11434—431nomaximal, Sylow
126C22×C43—21no—
127C22×C43—21no—
128C22×C43C2×C22⋊C811yescharacteristic
129C22×C43C2×#9911yescharacteristic
130C22×C43C2×#10011yescharacteristic
131C2×D43—22no—
132C2×D43—42no—
133C2×D43—41no—
134C2×D43—41no—
135C2×D43—42no—
136C4×C43—21no—
137C4×C43—21no—
138C4×C43—42no—
139C4×C43—42no—
140C4×C43—81no—
141Dic43—42no—
142Dic43—42no—
143Dic43—81no—
144Dic43#32314yes—
145#2310—431no—
146#1458—432no—
147#1319—431no—
148#1319—432no—
149#1319D4311yescharacteristic, complemented
150C2×C43—21no—
151C2×C43—21no—
152C2×C43C2×#32311yescharacteristic
153C2×C43#212911yescharacteristic
154C2×C43#213511yescharacteristic
155D43—42no—
156C23×Q8—431no—
157C2×#117—431no—
158C2×#117—431no—
159#431—862no—
160#391—431no—
161#391—431no—
162#391—431no—
163#391—862no—
164#391C2×D4311yescharacteristic
165#381—862no—
166#324—432no—
167#324C2×D4312yes—
168#323—862no—
169C43#1143411yescharacteristic, complemented, Sylow
170C22×Q8—434no—
171C22×Q8—431no—
172C22×Q8—861no—
173C22×Q8—862no—
174C22×Q8—1722no—
175C22×Q8—1722no—
176C22×Q8C4×D4311yescharacteristic
177C23×C4—431no—
178C23×C4—861no—
179#117—1722no—
180#117—1722no—
181C2×C4⋊C4—431no—
182C2×C4⋊C4—861no—
183C2×C4⋊C4C22×D4311yescharacteristic
184C2×C22⋊C4—432no—
185C2×C22⋊C4—861no—
186C2×C42—432no—
187C2×C42—431no—
188C2×C42C4×D4311yescharacteristic
189C4⋊C8—1722no—
190C22⋊C8—22no—
191C22⋊C8—862no—
192C4×C8—1722no—
193#95—22no—
194#95—862no—
195#95—862no—
196#95—862no—
197C24—431no—
198C2×Q8—21no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8—432no—
202C2×Q8—864no—
203C2×Q8—861no—
204C2×Q8—1721no—
205C2×Q8—1721no—
206C2×Q8—1722no—
207C2×Q8—1722no—
208C2×Q8—1728no—
209C2×Q8—1728no—
210C2×Q8C8×D4312yes—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—431no—
214C22×C4—432no—
215C22×C4—432no—
216C22×C4—432no—
217C22×C4—862no—
218C22×C4—862no—
219C22×C4—864no—
220C22×C4—861no—
221C22×C4—861no—
222C22×C4—1722no—
223C22×C4—1722no—
224C22×C4C2×C4×D4311yescharacteristic
225C22×C4D4×D4312yes—
226C2×C8—42no—
227C2×C8—1722no—
228C4⋊C4—41no—
229C4⋊C4—1721no—
230C4⋊C4—1722no—
231C22⋊C4—1722no—
232C22⋊C4—1722no—
233C42—41no—
234C42—862no—
235C42—862no—
236C42—1721no—
237C23—432no—
238C23—861no—
239C23—861no—
240C23—1721no—
241C23—1721no—
242C23C22⋊C4×D4311yescharacteristic
243Q8—42no—
244Q8—42no—
245Q8—1722no—
246Q8—1722no—
247Q8—1728no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—432no—
259C2×C4—432no—
260C2×C4—432no—
261C2×C4—864no—
262C2×C4—864no—
263C2×C4—862no—
264C2×C4—862no—
265C2×C4—1728no—
266C2×C4—1721no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4—1722no—
272C2×C4C2×C8×D4311yescharacteristic
273C2×C4M16×D4311yescharacteristic
274C8—82no—
275C8—3442no—
276C22—21no—
277C22—21no—
278C22—862no—
279C22—1722no—
280C22—1722no—
281C22—1721no—
282C22—1721no—
283C22C22⋊C8×D4311yescharacteristic
284C22#99×D4311yescharacteristic
285C22#100×D4311yescharacteristic
286C4—21no—
287C4—21no—
288C4—42no—
289C4—42no—
290C4—81no—
291C4—434no—
292C4—3441no—
293C4—1722no—
294C4—1722no—
295C2—21no—
296C2—21no—
297C2—1722no—
298C2#323×D4311yescharacteristic
299C2#1913626811yescharacteristic
300C2#1913628811yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1319C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1319D43
hypocenterC43#11434
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
3. #19132529C2semidirect
4. #19132528C2semidirect
5. C43×#1319C2semidirect
24. C2×Q8×D43C8semidirect
149. #1319D43semidirect
169. C43#11434semidirect

Maximal subgroups

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

subgroupindex
#191371782
#191329082
#191325292
#191325282
C43×#13192
#1143443