Finite Group Databasebeta

← #25000532

Subgroups — #25000532

Order 11008.

372 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 81 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#19145540C211yesmaximal, characteristic
2#19135438C211yesmaximal, characteristic
3#19133386C211yesmaximal, characteristic
4#19133277C211yesmaximal, characteristic
5#19133016C211yesmaximal, characteristic
6#19132484C211yesmaximal, characteristic
7C43×#1561C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583278—21no—
10#14583251—21no—
11#14583109—21no—
12#14583109—21no—
13#14583054—22no—
14#14582952C2211yescharacteristic
15#14582952C2211yescharacteristic
16C2×#13063243—22no—
17C4×#10621877C2211yescharacteristic
18#14582651—21no—
19#14582649—21no—
20#14582647—22no—
21Q8⋊(C43⋊C8)—22no—
22C43×#533C2211yescharacteristic
23C43×#423C2211yescharacteristic
24C43×#423C2211yescharacteristic
25C43×#332—21no—
26C43×#332—21no—
27C22×Dic86D412yes—
28C2×#10621885—22no—
29C2×#10621885—22no—
30C2×#10621877—21no—
31#13063325—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43—21no—
37C4⋊(C43⋊C8)D411yescharacteristic
38C4⋊(C43⋊C8)D411yescharacteristic
39C4⋊(C43⋊C8)D412yes—
40#13063248—22no—
41#13063248—22no—
42#13063243—44no—
43C22⋊(C43⋊C8)—21no—
44C22⋊(C43⋊C8)—21no—
45#13063236—21no—
46C4×C43⋊C8—21no—
47C4×C43⋊C8—21no—
48C4×C43⋊C8—21no—
49C2×M16×C43—21no—
50C2×M16×C43—21no—
51C4⋊Q8×C43D411yescharacteristic
52C4⋊Q8×C43D411yescharacteristic
53#125×C43—21no—
54C22⋊Q8×C43—21no—
55C22⋊Q8×C43—21no—
56C4×Q8×C43—21no—
57C4×Q8×C43—21no—
58#117×C43—21no—
59C2×C42×C43C2311yescharacteristic
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64C2×Q8×C43—21no—
65C2×Q8×C43—21no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43#4111yescharacteristic
68C22×C4×C43#4111yescharacteristic
69C22×Dic43—22no—
70C2×Dic86—22no—
71C2×Dic86—22no—
72C2×Dic86—42no—
73C2×Dic86—42no—
74M16×C43—42no—
75M16×C43—81no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C42×C43—41no—
86C42×C43C2×D411yescharacteristic
87C42×C43C2×D411yescharacteristic
88C42×C43C2×D411yescharacteristic
89C42×C43#4111yescharacteristic
90#10621885—82no—
91#10621885—82no—
92C4⋊Dic43—41no—
93C4⋊Dic43—41no—
94C4⋊Dic43—41no—
95C4⋊Dic43—41no—
96#10621877—22no—
97#10621877—41no—
98C2×C43⋊C8—21no—
99C2×C43⋊C8—21no—
100C2×C43⋊C8—22no—
101C2×C43⋊C8—41no—
102C23×C43#12311yescharacteristic
103Q8×C43—41no—
104Q8×C43—41no—
105Q8×C43—41no—
106Q8×C43—41no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—22no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43#12011yescharacteristic
115C2×C4×C43#12111yescharacteristic
116C2×C4×C43#12111yescharacteristic
117C2×C4×C43#12111yescharacteristic
118C2×C4×C43#12311yescharacteristic
119C2×C4×C43#12411yescharacteristic
120C2×Dic43—44no—
121C2×Dic43—42no—
122Dic86—42no—
123Dic86—42no—
124Dic86—82no—
125C8×C43—81no—
126C8×C43—81no—
127C43⋊C8—42no—
128C43⋊C8—41no—
129C43⋊C8—41no—
130C43⋊C8—42no—
131#10493—431nomaximal, Sylow
132C22×C43—21no—
133C22×C43—21no—
134C22×C43—21no—
135C22×C43#39411yescharacteristic
136C4×C43—21no—
137C4×C43—21no—
138C4×C43—21no—
139C4×C43—81no—
140C4×C43—81no—
141C4×C43#45311yescharacteristic
142C4×C43#45511yescharacteristic
143C4×C43#47111yescharacteristic
144C4×C43#47311yescharacteristic
145C4×C43#47312yes—
146Dic43—82no—
147#3209—431no—
148#1966—431no—
149#1574—431no—
150#1561D4311yescharacteristic
151#1548—431no—
152#1485—431no—
153#1299—431no—
154C2×C43—41no—
155C2×C43#203711yescharacteristic
156C2×C43#204711yescharacteristic
157C2×C43#205211yescharacteristic
158#533C2×D4311yescharacteristic
159C2×C4⋊Q8—431no—
160#494—861no—
161#487—861no—
162#462—861no—
163#462—861no—
164#451—862no—
165#431—431no—
166#431—431no—
167#423C2×D4311yescharacteristic
168#423C2×D4311yescharacteristic
169C2×#101—862no—
170C4×M16—431no—
171#335—861no—
172#334—861no—
173#333—862no—
174#332—21no—
175#332—21no—
176Q8⋊C8—862no—
177C43#1049311yescharacteristic, complemented, Sylow
178C22×Q8—432no—
179C2×Q16—862no—
180C2×Q16—862no—
181C2×M16—21no—
182C2×M16—21no—
183C2×M16—861no—
184C4⋊Q8—861no—
185C4⋊Q8—861no—
186C4⋊Q8—861no—
187C4⋊Q8—861no—
188C4⋊Q8C22⋊D4311yescharacteristic
189C4⋊Q8C22⋊D4311yescharacteristic
190#125—21no—
191C22⋊Q8—21no—
192C22⋊Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195#117—21no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4—861no—
198C2×C42C22×D4311yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—432no—
204C4⋊C8—431no—
205C4⋊C8—431no—
206#103—862no—
207#103—862no—
208#101—1724no—
209C22⋊C8—861no—
210C22⋊C8—861no—
211#97—861no—
212C4×C8—861no—
213C4×C8—861no—
214C4×C8—861no—
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—862no—
218C2×Q8—862no—
219C2×Q8—1722no—
220C2×Q8—1722no—
221C22×C4—862no—
222C22×C4#1062189811yescharacteristic
223C22×C4D4×D4311yescharacteristic
224C22×C4#1062190011yescharacteristic
225Q16—3442no—
226Q16—3442no—
227M16—42no—
228M16—81no—
229M16—862no—
230M16—1721no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—861no—
234C2×C8—861no—
235C2×C8—862no—
236C2×C8—1721no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—1721no—
244C4⋊C4—1721no—
245C4⋊C4—1721no—
246C4⋊C4—1721no—
247C22⋊C4—41no—
248C42—41no—
249C42#1062189811yescharacteristic
250C42D4×D4311yescharacteristic
251C42D4×D4311yescharacteristic
252C42C2×C22⋊D4311yescharacteristic
253C23#1306330711yescharacteristic
254Q8—41no—
255Q8—41no—
256Q8—41no—
257Q8—41no—
258Q8—3442no—
259Q8—1722no—
260Q8—1722no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—1724no—
269C2×C4—1722no—
270C2×C4#1306329311yescharacteristic
271C2×C4#1306329711yescharacteristic
272C2×C4#1306329811yescharacteristic
273C2×C4#1306329811yescharacteristic
274C2×C4#1306330811yescharacteristic
275C2×C4#1306331111yescharacteristic
276C8—81no—
277C8—81no—
278C8—1722no—
279C8—1721no—
280C8—1721no—
281C8—1722no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22#1458281411yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—81no—
290C4—81no—
291C4—3442no—
292C4#1458306511yescharacteristic
293C4#1458307511yescharacteristic
294C4#1458316011yescharacteristic
295C4#1458317211yescharacteristic
296C4#1458317312yes—
297C2—41no—
298C2#1913580311yescharacteristic
299C2#1913586111yescharacteristic
300C2#1913589211yescharacteristic
subgroupG/H
centerC22#14582814
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1561C2
socleC22×C43#394
prime radicalC23×C43#123
hypercenter#1561D43
hypocenterC43#10493
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1561

Complements

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

NH ≅ G/Ntype
177. C43#10493semidirect

Maximal subgroups

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

subgroupindex
#191455402
#191354382
#191333862
#191332772
#191330162
#191324842
C43×#15612
#1049343