Finite Group Databasebeta

← #25000549

Subgroups — #25000549

Order 11008.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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#19145746C211yesmaximal, characteristic
2#19135585C211yesmaximal, characteristic
3#19133384C211yesmaximal, characteristic
4#19133332C211yesmaximal, characteristic
5#19133015C211yesmaximal, characteristic
6#19132484C211yesmaximal, characteristic
7C43×#1546C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583302—21no—
10#14583251—21no—
11#14583234—22no—
12#14583191—21no—
13#14583191—21no—
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16C4×#10621877C2211yescharacteristic
17#14582668—22no—
18#14582652—21no—
19#14582650—21no—
20#14582646—21no—
21#14582644—21no—
22#14582629—22no—
23C2×C4⋊Q8×C43C2211yescharacteristic
24C43×#431C2211yescharacteristic
25C43×#423C2211yescharacteristic
26C43×#332—22no—
27C2×#10621877—21no—
28C2×#10621877—21no—
29#13063325D411yescharacteristic
30#13063325D411yescharacteristic
31#13063317—21no—
32#13063304—21no—
33#13063304—21no—
34C4×Dic86—21no—
35C4×Dic86—21no—
36#13063284—21no—
37#13063258—22no—
38#13063258—22no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)D411yescharacteristic
42C4⋊(C43⋊C8)D411yescharacteristic
43#13063248—22no—
44#13063248—22no—
45C22⋊(C43⋊C8)—21no—
46#13063236—21no—
47C4×C43⋊C8—21no—
48C4×C43⋊C8—21no—
49C22×Q8×C43—21no—
50C2×M16×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D412yes—
57C2×C42×C43C2311yescharacteristic
58C4⋊C8×C43—21no—
59C4⋊C8×C43—21no—
60C4⋊C8×C43D412yes—
61C22⋊C8×C43—21no—
62C4×C8×C43—21no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43—81no—
66C2×Q8×C43—81no—
67C22×C4×C43—22no—
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43#4111yescharacteristic
70C22×C4×C43#4111yescharacteristic
71C2×Dic86—21no—
72C2×Dic86—21no—
73M16×C43—81no—
74C2×C8×C43—22no—
75C2×C8×C43—41no—
76C4⋊C4×C43—22no—
77C4⋊C4×C43—22no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C42×C43C2×D411yescharacteristic
81C42×C43C2×D411yescharacteristic
82C42×C43C2×D411yescharacteristic
83C42×C43#4111yescharacteristic
84C22⋊Dic43—41no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43—21no—
89Dic43⋊C4—41no—
90Dic43⋊C4—41no—
91C4×Dic43—41no—
92#10621877—22no—
93#10621877—41no—
94#10621877—42no—
95C2×C43⋊C8—21no—
96C2×C43⋊C8—21no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C23×C43#12311yescharacteristic
100Q8×C43—82no—
101Q8×C43—81no—
102Q8×C43—81no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—42no—
109C2×C4×C43—82no—
110C2×C4×C43#12011yescharacteristic
111C2×C4×C43#12111yescharacteristic
112C2×C4×C43#12111yescharacteristic
113C2×C4×C43#12111yescharacteristic
114C2×C4×C43#12311yescharacteristic
115C2×C4×C43#12411yescharacteristic
116C2×Dic43—41no—
117C2×Dic43—41no—
118Dic86—41no—
119Dic86—41no—
120Dic86—41no—
121Dic86—41no—
122C8×C43—42no—
123C8×C43—81no—
124C43⋊C8—42no—
125C43⋊C8—41no—
126C43⋊C8—41no—
127C43⋊C8—81no—
128#10495—431nomaximal, Sylow
129C22×C43—21no—
130C22×C43—21no—
131C22×C43—21no—
132C22×C43#39411yescharacteristic
133C4×C43—21no—
134C4×C43—21no—
135C4×C43—21no—
136C4×C43—82no—
137C4×C43#45411yescharacteristic
138C4×C43#45611yescharacteristic
139C4×C43#47111yescharacteristic
140C4×C43#47211yescharacteristic
141C4×C43#47312yes—
142Dic43—81no—
143Dic43—81no—
144#3230—431no—
145#1997—431no—
146#1574—431no—
147#1561—431no—
148#1546D4311yescharacteristic
149#1485—431no—
150#1299—431no—
151C2×C43—41no—
152C2×C43#203811yescharacteristic
153C2×C43#204711yescharacteristic
154C2×C43#205111yescharacteristic
155#533—431no—
156C2×C4⋊Q8C2×D4311yescharacteristic
157#500—861no—
158#487—861no—
159#484—862no—
160#477—861no—
161#477—861no—
162#431—431no—
163#431C2×D4311yescharacteristic
164#423—431no—
165#423C2×D4311yescharacteristic
166C4×M16—431no—
167#343—862no—
168#335—861no—
169#334—861no—
170#332—22no—
171#332—861no—
172#332—861no—
173Q8⋊C8—862no—
174C43#1049511yescharacteristic, complemented, Sylow
175C22×Q8—21no—
176C2×M16—21no—
177C2×M16—861no—
178C2×M16—861no—
179C4⋊Q8—21no—
180C4⋊Q8—21no—
181C4⋊Q8—21no—
182C4⋊Q8—21no—
183C4⋊Q8—431no—
184C4⋊Q8—431no—
185#125—861no—
186C22⋊Q8—861no—
187C22⋊Q8—861no—
188C4×Q8—861no—
189C4×Q8—861no—
190#117—861no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4D17212yes—
193C2×C42C22×D4311yescharacteristic
194#107—862no—
195#107—862no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—431no—
199C4⋊C8—431no—
200C4⋊C8—861no—
201C4⋊C8—861no—
202C4⋊C8C22⋊D4312yes—
203#103—862no—
204#103—862no—
205C22⋊C8—21no—
206C22⋊C8—861no—
207#97—861no—
208C4×C8—21no—
209C4×C8—861no—
210C4×C8—861no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—81no—
214C2×Q8—81no—
215C2×Q8—861no—
216C2×Q8—861no—
217C22×C4—22no—
218C22×C4C2×D17211yescharacteristic
219C22×C4#1062190011yescharacteristic
220C22×C4#1062190011yescharacteristic
221M16—81no—
222M16—862no—
223M16—1722no—
224M16—1721no—
225C2×C8—22no—
226C2×C8—41no—
227C2×C8—861no—
228C2×C8—861no—
229C2×C8—1721no—
230C2×C8—1721no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—861no—
236C4⋊C4—861no—
237C4⋊C4—861no—
238C4⋊C4—861no—
239C4⋊C4—1721no—
240C4⋊C4—1721no—
241C22⋊C4—1721no—
242C42—1721no—
243C42#1062189811yescharacteristic
244C42D4×D4311yescharacteristic
245C42D4×D4311yescharacteristic
246C42C2×C22⋊D4311yescharacteristic
247C23#1306330911yescharacteristic
248Q8—82no—
249Q8—81no—
250Q8—81no—
251Q8—1721no—
252Q8—1721no—
253Q8—1721no—
254Q8—1721no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—1721no—
263C2×C4—1721no—
264C2×C4#1306329511yescharacteristic
265C2×C4#1306329611yescharacteristic
266C2×C4#1306329711yescharacteristic
267C2×C4#1306329911yescharacteristic
268C2×C4#1306330711yescharacteristic
269C2×C4#1306331111yescharacteristic
270C8—42no—
271C8—81no—
272C8—3441no—
273C8—1722no—
274C8—1721no—
275C8—1721no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22#1458281511yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—82no—
284C4—3441no—
285C4—3441no—
286C4#1458307411yescharacteristic
287C4#1458308411yescharacteristic
288C4#1458315911yescharacteristic
289C4#1458316611yescharacteristic
290C4#1458317212yes—
291C2—41no—
292C2#1913581311yescharacteristic
293C2#1913586211yescharacteristic
294C2#1913588811yescharacteristic
subgroupG/H
centerC22#14582815
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1546C2
socleC22×C43#394
prime radicalC23×C43#123
hypercenter#1546D43
hypocenterC43#10495
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
174. C43#10495semidirect

Maximal subgroups

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

subgroupindex
#191457462
#191355852
#191333842
#191333322
#191330152
#191324842
C43×#15462
#1049543