Finite Group Databasebeta

← #25000536

Subgroups — #25000536

Order 11008.

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

normal subgroups only

This group has 372 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#19145545C211yesmaximal, characteristic
2#19135438C211yesmaximal, characteristic
3#19133332C211yesmaximal, characteristic
4#19133275C211yesmaximal, characteristic
5#19133015C211yesmaximal, characteristic
6#19132486C211yesmaximal, characteristic
7C43×#1574C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063325C2211yescharacteristic
10#14583279—21no—
11#14583250—21no—
12#14583110—21no—
13#14583110—21no—
14#14583057—22no—
15#14582923C2211yescharacteristic
16C2×#13063243—22no—
17C4×#10621877C2211yescharacteristic
18#14582647—22no—
19#14582646—21no—
20#14582644—21no—
21#14582629—22no—
22C43×#431C2211yescharacteristic
23C43×#431C2211yescharacteristic
24C43×#423C2211yescharacteristic
25C43×#335—21no—
26C43×#334—21no—
27C22×Dic86D412yes—
28C2×Dic172—22no—
29C2×Dic172—22no—
30C2×#10621877—21no—
31C2×#10621877—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325D411yescharacteristic
37#13063325D411yescharacteristic
38#13063317—21no—
39#13063304—21no—
40#13063304—21no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43#13063284—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48#13063250—22no—
49#13063250—22no—
50#13063243—44no—
51#13063236—21no—
52C4×C43⋊C8—21no—
53C2×M16×C43—21no—
54C2×C42×C43C2311yescharacteristic
55C4⋊C8×C43—21no—
56C4⋊C8×C43—21no—
57C4⋊C8×C43D412yes—
58C4⋊C8×C43D411yescharacteristic
59C4⋊C8×C43D411yescharacteristic
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62C4×C8×C43—21no—
63C4×C8×C43—21no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43#4111yescharacteristic
66C22×C4×C43#4111yescharacteristic
67C22×Dic43—22no—
68C2×Dic86—22no—
69C2×Dic86—21no—
70C2×Dic86—21no—
71C2×Dic86—22no—
72C2×Dic86—42no—
73C2×Dic86—42no—
74M16×C43—42no—
75C2×C8×C43—21no—
76C2×C8×C43—21no—
77C2×C8×C43—22no—
78C2×C8×C43—41no—
79C42×C43C2×D411yescharacteristic
80C42×C43C2×D411yescharacteristic
81C42×C43C2×D411yescharacteristic
82C42×C43#4111yescharacteristic
83C22⋊Dic43—41no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43—41no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94C4×Dic43—41no—
95#10621877—22no—
96#10621877—41no—
97#10621877—81no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100Dic172—82no—
101Dic172—82no—
102C23×C43#12311yescharacteristic
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—22no—
107C2×C4×C43—21no—
108C2×C4×C43#12011yescharacteristic
109C2×C4×C43#12111yescharacteristic
110C2×C4×C43#12111yescharacteristic
111C2×C4×C43#12111yescharacteristic
112C2×C4×C43#12311yescharacteristic
113C2×C4×C43#12411yescharacteristic
114C2×Dic43—44no—
115C2×Dic43—41no—
116C2×Dic43—41no—
117C2×Dic43—42no—
118Dic86—41no—
119Dic86—42no—
120Dic86—41no—
121Dic86—42no—
122Dic86—41no—
123Dic86—41no—
124Dic86—82no—
125C8×C43—41no—
126C8×C43—41no—
127C8×C43—42no—
128C8×C43—81no—
129C43⋊C8—42no—
130C43⋊C8—81no—
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#45311yescharacteristic
140C4×C43#45511yescharacteristic
141C4×C43#47111yescharacteristic
142C4×C43#47312yes—
143C4×C43#47311yescharacteristic
144Dic43—81no—
145Dic43—82no—
146Dic43—81no—
147#3209—431no—
148#1966—431no—
149#1574D4311yescharacteristic
150#1561—431no—
151#1548—431no—
152#1485—431no—
153#1299—431no—
154C2×C43—41no—
155C2×C43#203711yescharacteristic
156C2×C43#204711yescharacteristic
157C2×C43#205211yescharacteristic
158#533—431no—
159C2×C4⋊Q8—431no—
160#494—861no—
161#487—861no—
162#462—861no—
163#462—861no—
164#451—862no—
165#431C2×D4311yescharacteristic
166#431C2×D4311yescharacteristic
167#423—431no—
168#423C2×D4311yescharacteristic
169C2×#101—862no—
170C4×M16—431no—
171#335—21no—
172#334—21no—
173#333—862no—
174#332—861no—
175#332—861no—
176Q8⋊C8—862no—
177C43#1049311yescharacteristic, complemented, Sylow
178C22×Q8—432no—
179C2×Q16—862no—
180C2×Q16—862no—
181C2×M16—21no—
182C2×M16—861no—
183C2×M16—861no—
184C4⋊Q8—431no—
185C4⋊Q8—431no—
186C4⋊Q8—861no—
187C4⋊Q8—861no—
188C4⋊Q8—861no—
189C4⋊Q8—861no—
190#125—861no—
191C22⋊Q8—861no—
192C22⋊Q8—861no—
193C4×Q8—861no—
194C4×Q8—861no—
195#117—861no—
196C2×C4⋊C4—861no—
197C2×C4⋊C4—861no—
198C2×C42C22×D4311yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—861no—
202C4⋊C8—861no—
203C4⋊C8D17212yes—
204C4⋊C8C22⋊D4311yescharacteristic
205C4⋊C8C22⋊D4311yescharacteristic
206#103—862no—
207#103—862no—
208#101—1724no—
209C22⋊C8—21no—
210C22⋊C8—21no—
211#97—861no—
212C4×C8—21no—
213C4×C8—21no—
214C4×C8—861no—
215C2×Q8—862no—
216C2×Q8—861no—
217C2×Q8—862no—
218C2×Q8—861no—
219C2×Q8—1722no—
220C2×Q8—1722no—
221C22×C4—862no—
222C22×C4#1062189811yescharacteristic
223C22×C4D4×D4311yescharacteristic
224C22×C4#1062190211yescharacteristic
225Q16—3442no—
226Q16—3442no—
227M16—42no—
228M16—862no—
229M16—3441no—
230M16—1721no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—22no—
234C2×C8—41no—
235C2×C8—1721no—
236C2×C8—1721no—
237C4⋊C4—861no—
238C4⋊C4—861no—
239C4⋊C4—861no—
240C4⋊C4—861no—
241C4⋊C4—1721no—
242C4⋊C4—1721no—
243C4⋊C4—1721no—
244C4⋊C4—1721no—
245C4⋊C4—1721no—
246C4⋊C4—1721no—
247C22⋊C4—1721no—
248C42—1721no—
249C42C2×D17211yescharacteristic
250C42D4×D4311yescharacteristic
251C42#1062190211yescharacteristic
252C42C2×C22⋊D4311yescharacteristic
253C23#1306331011yescharacteristic
254Q8—3442no—
255Q8—1721no—
256Q8—1722no—
257Q8—1721no—
258Q8—1722no—
259Q8—1721no—
260Q8—1721no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—1724no—
267C2×C4—1721no—
268C2×C4—1721no—
269C2×C4—1722no—
270C2×C4#1306329311yescharacteristic
271C2×C4#1306329911yescharacteristic
272C2×C4#1306330011yescharacteristic
273C2×C4#1306330011yescharacteristic
274C2×C4#1306331011yescharacteristic
275C2×C4#1306331411yescharacteristic
276C8—41no—
277C8—41no—
278C8—42no—
279C8—81no—
280C8—3441no—
281C8—1722no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22#1458281611yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—3442no—
290C4—3441no—
291C4—3441no—
292C4#1458306511yescharacteristic
293C4#1458307511yescharacteristic
294C4#1458316311yescharacteristic
295C4#1458317412yes—
296C4#1458317511yescharacteristic
297C2—41no—
298C2#1913580711yescharacteristic
299C2#1913586311yescharacteristic
300C2#1913589611yescharacteristic
subgroupG/H
centerC22#14582816
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1574C2
socleC22×C43#394
prime radicalC23×C43#123
hypercenter#1574D43
hypocenterC43#10493
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1574

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
#191455452
#191354382
#191333322
#191332752
#191330152
#191324862
C43×#15742
#1049343