Finite Group Databasebeta

← #25015284

Subgroups — #25015284

Order 11008.

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

normal subgroups only

This group has 420 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#19139800C211yesmaximal, characteristic
2#19134591C211yesmaximal, characteristic
3#19132721C214yesmaximal
4C4×#101×C43C211yesmaximal, characteristic
5C2×#13063325C411yescharacteristic
6#14582923—21no—
7C2×#13063244C2212yes—
8#14582819—21no—
9#14582819—21no—
10#14582806C2212yes—
11#14582797—21no—
12#14582797—21no—
13#14582768C412yes—
14C4×C4⋊Dic43C411yescharacteristic
15#14582668—21no—
16C2×C4×Q8×C43C2211yescharacteristic
17C2×#101×C43C2212yes—
18C4×M16×C43—21no—
19C43×#343—21no—
20C22×Dic86—21no—
21C2×#10621877—22no—
22#13063325—41no—
23#13063325—41no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43C2×C412yes—
27C2×Dic43⋊C4—22no—
28C2×Dic43⋊C4—22no—
29C2×C4×Dic43C2×C412yes—
30C4⋊(C43⋊C8)—41no—
31C4⋊(C43⋊C8)—41no—
32#13063244—24no—
33C43⋊#95—21no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C22×Q8×C43C2311yescharacteristic
37C2×M16×C43—22no—
38C4×Q8×C43—41no—
39C4×Q8×C43—41no—
40C2×C4⋊C4×C43C2×C411yescharacteristic
41C2×C4⋊C4×C43D411yescharacteristic
42C2×C4⋊C4×C43D411yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43D411yescharacteristic
45C2×C42×C43D411yescharacteristic
46#101×C43—22no—
47#101×C43Q814yescomplemented
48#97×C43—41no—
49C4×C8×C43—41no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×Q8×C43C2×Q812yes—
53C2×Q8×C43#4112yes—
54C22×C4×C43C22⋊C411yescharacteristic
55C22×C4×C43C22⋊C411yescharacteristic
56C22×C4×C43C22⋊C411yescharacteristic
57C22×C4×C43C22⋊C411yescharacteristic
58C22×C4×C43C22×C411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×Dic43—22no—
62C22×Dic43—22no—
63C2×Dic86—42no—
64C2×Dic86—82no—
65M16×C43—24no—
66M16×C43—42no—
67C2×C8×C43—42no—
68C4⋊C4×C43—41no—
69C4⋊C4×C43—41no—
70C4⋊C4×C43—41no—
71C42×C43—21no—
72C42×C43—21no—
73C42×C43—21no—
74C42×C43—21no—
75C42×C43—21no—
76C42×C43—21no—
77C4⋊Dic43—24no—
78C4⋊Dic43—41no—
79C4⋊Dic43—41no—
80C4⋊Dic43—42no—
81Dic43⋊C4—82no—
82Dic43⋊C4—82no—
83C4×Dic43—42no—
84#10621877—42no—
85#10621877—42no—
86C2×C43⋊C8—42no—
87C23×C43C2×C22⋊C411yescharacteristic
88Q8×C43—42no—
89Q8×C43—42no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—22no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43#9911yescharacteristic
104C2×C4×C43#9911yescharacteristic
105C2×C4×C43C4×Q812yes—
106C2×C4×C43C22⋊Q812yes—
107C2×C4×C43#12411yescharacteristic
108C2×C4×C43C4⋊Q811yescharacteristic
109C2×Dic43—24no—
110C2×Dic43—42no—
111C2×Dic43—42no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—42no—
115Dic86—84no—
116C8×C43—44no—
117C43⋊C8—82no—
118#13302—431nomaximal, Sylow
119C22×C43—21no—
120C22×C43—21no—
121C22×C43#39111yescharacteristic
122C22×C43C2×#9911yescharacteristic
123C22×C43#41011yescharacteristic
124C4×C43—21no—
125C4×C43—21no—
126C4×C43—22no—
127C4×C43—22no—
128C4×C43—21no—
129C4×C43—41no—
130C4×C43—41no—
131C4×C43—41no—
132C4×C43#35612yes—
133Dic43—44no—
134Dic43—82no—
135#2567—431no—
136#1801—431no—
137C4×#101D4311yescharacteristic
138#1394—434no—
139C2×C43—21no—
140C2×C43—21no—
141C2×C43#199611yescharacteristic
142C2×C43C2×#35611yescharacteristic
143C2×C43#213411yescharacteristic
144C2×C4⋊Q8—431no—
145C2×C4×Q8C2×D4311yescharacteristic
146#423—861no—
147C2×#101—432no—
148C2×#101C2×D4312yes—
149C4×M16—21no—
150#395—861no—
151#395—861no—
152#391—432no—
153#389—861no—
154#389—861no—
155#384—432no—
156C4×C4⋊C4—431no—
157#343—21no—
158#343—861no—
159C43#1330211yescharacteristic, complemented, Sylow
160C22×Q8—861no—
161C22×Q8C22×D4311yescharacteristic
162C2×M16—22no—
163C2×M16—862no—
164C4⋊Q8—1721no—
165C4⋊Q8—1721no—
166C4×Q8—41no—
167C4×Q8—41no—
168C2×C4⋊C4—432no—
169C2×C4⋊C4—861no—
170C2×C4⋊C4—862no—
171C2×C4⋊C4—862no—
172C2×C4⋊C4—861no—
173C2×C4⋊C4C4×D4311yescharacteristic
174C2×C4⋊C4D17211yescharacteristic
175C2×C4⋊C4C22⋊D4311yescharacteristic
176C2×C42—432no—
177C2×C42C4×D4311yescharacteristic
178C2×C42D17211yescharacteristic
179C2×C42C22⋊D4311yescharacteristic
180C4⋊C8—1721no—
181C4⋊C8—1721no—
182#101—22no—
183#101—864no—
184#101Dic8614yescomplemented
185#97—41no—
186C4×C8—41no—
187#95—861no—
188#95—862no—
189#95—862no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—3442no—
193C2×Q8—1722no—
194C2×Q8C2×Dic8612yes—
195C2×Q8#1062189812yes—
196C22×C4—862no—
197C22×C4—862no—
198C22×C4(C2×D43)⋊C411yescharacteristic
199C22×C4(C2×D43)⋊C411yescharacteristic
200C22×C4(C2×D43)⋊C411yescharacteristic
201C22×C4(C2×D43)⋊C411yescharacteristic
202C22×C4C2×C4×D4311yescharacteristic
203C22×C4C2×D17211yescharacteristic
204C22×C4C2×C22⋊D4311yescharacteristic
205M16—24no—
206M16—42no—
207M16—1722no—
208M16—1722no—
209C2×C8—42no—
210C2×C8—1722no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—864no—
215C4⋊C4—3442no—
216C4⋊C4—3442no—
217C4⋊C4—1722no—
218C4⋊C4—1721no—
219C4⋊C4—1721no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—1722no—
227C23C2×(C2×D43)⋊C411yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—3444no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—864no—
245C2×C4—1722no—
246C2×C4—1722no—
247C2×C4—1722no—
248C2×C4—1722no—
249C2×C4—1722no—
250C2×C4#1306323911yescharacteristic
251C2×C4#1306323911yescharacteristic
252C2×C4C4×Dic8612yes—
253C2×C4#1306330412yes—
254C2×C4#1306331311yescharacteristic
255C2×C4#1306332511yescharacteristic
256C8—44no—
257C8—3442no—
258C22—21no—
259C22—21no—
260C22#1458280511yescharacteristic
261C22C2×#1306323911yescharacteristic
262C22#1458287211yescharacteristic
263C4—21no—
264C4—22no—
265C4—21no—
266C4—22no—
267C4—21no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—3442no—
272C4—1724no—
273C4#1458269712yes—
274C2—21no—
275C2—21no—
276C2#1913558011yescharacteristic
277C2C2×#1458269711yescharacteristic
278C2#1913628611yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC4×#101×C43C2
socleC22×C43C2×#99
prime radicalC23×C43C2×C22⋊C4
cosocleC22×Q8×C43C23
hypercenterC4×#101D43
hypocenterC43#13302
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
47. #101×C43Q8semidirect
159. C43#13302semidirect
184. #101Dic86semidirect

Maximal subgroups

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

subgroupindex
#191398002
#191345912
#191327212
C4×#101×C432
#1330243