Finite Group Databasebeta

← #25008711

Subgroups — #25008711

Order 11008.

476 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 71 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#19136511C212yesmaximal, complemented
2#19135605C211yesmaximal, characteristic, complemented
3#19132604C212yesmaximal, complemented
4#19132519C211yesmaximal, characteristic, complemented
5C43×#3186C211yesmaximal, characteristic
6C22×Dic172C2211yescharacteristic, complemented
7C2×#13063304—21no—
8C2×#13063269—22no—
9C2×#13063250—21no—
10#14582702—22no—
11C22⋊(C43⋊C16)C2212yescomplemented
12#14582662C2211yescharacteristic, complemented
13C2×#121×C43—21no—
14C43×#480—22no—
15C43×#466—21no—
16C43×#466C2212yes—
17C43×#447—22no—
18C2×C22⋊C8×C43C2211yescharacteristic
19C22×Dic86—21no—
20C2×Dic172—22no—
21C2×Dic172—42no—
22#13063304—42no—
23#13063304—42no—
24C2×C4⋊Dic43—21no—
25C2×Dic43⋊C4—41no—
26C2×C22⋊Dic43—41no—
27#13063269—44no—
28C2×C43⋊C16—22no—
29#13063250—42no—
30C22×D4×C43—21no—
31C22×D4×C43—41no—
32C23×C4×C43D411yescharacteristic
33C2×D8×C43—21no—
34C2×D8×C43D412yes—
35C22×C8×C43D411yescharacteristic
36C22×C8×C43C2311yescharacteristic
37#121×C43—22no—
38#121×C43—22no—
39#121×C43—41no—
40#121×C43—41no—
41C2×C4⋊C4×C43—21no—
42C2×C22⋊C4×C43—41no—
43#107×C43—21no—
44#107×C43D412yes—
45#102×C43—22no—
46#102×C43—22no—
47C22⋊C8×C43—22no—
48C24×C43—41no—
49C24×C43D811yescharacteristic
50C2×D4×C43—22no—
51C2×D4×C43—42no—
52C2×D4×C43—41no—
53C2×D4×C43—42no—
54C2×D4×C43—82no—
55C2×D4×C43—81no—
56C2×D4×C43—81no—
57C2×D4×C43—82no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43—41no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43D811yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×Dic43—41no—
66C22×Dic43—41no—
67C2×Dic86—22no—
68C2×Dic86—41no—
69C2×Dic86—41no—
70C2×Dic86—41no—
71C2×Dic86—41no—
72C2×Dic86—41no—
73D8×C43—42no—
74D8×C43—81no—
75C2×C8×C43—21no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43C2×D412yes—
79C4⋊C4×C43—22no—
80C4⋊C4×C43—41no—
81C22⋊C4×C43—42no—
82C22⋊C4×C43—42no—
83C22⋊Dic43—44no—
84C4⋊Dic43—22no—
85C4⋊Dic43—41no—
86Dic43⋊C4—44no—
87Dic172—24no—
88Dic172—42no—
89C43⋊C16—42no—
90C23×C43—21no—
91C23×C43—21no—
92C23×C43—41no—
93C23×C43—41no—
94C23×C43—42no—
95C23×C43—82no—
96C23×C43—82no—
97C23×C43—82no—
98C23×C43SD3212yescomplemented
99C23×C43C2×D811yescharacteristic
100D4×C43—42no—
101D4×C43—42no—
102D4×C43—82no—
103D4×C43—84no—
104D4×C43—82no—
105D4×C43—82no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—42no—
113C2×C4×C43—81no—
114C2×C4×C43—82no—
115C2×C4×C43#12011yescharacteristic
116C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
117C2×Dic43—42no—
118C2×Dic43—42no—
119C2×Dic43—81no—
120C2×Dic43—81no—
121C2×Dic43—81no—
122C2×Dic43—81no—
123Dic86—42no—
124Dic86—42no—
125Dic86—81no—
126Dic86—81no—
127C8×C43—22no—
128C8×C43—41no—
129#12105—431nomaximal, Sylow
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—22no—
133C22×C43—42no—
134C22×C43—41no—
135C22×C43—41no—
136C22×C43—81no—
137C22×C43—82no—
138C22×C43—82no—
139C22×C43—82no—
140C22×C43—164no—
141C22×C43#44711yescharacteristic
142C22×C43C2×SD3211yescharacteristic
143C22×C43#50911yescharacteristic
144C4×C43—21no—
145C4×C43—41no—
146C4×C43—82no—
147C4×C43#45311yescharacteristic
148C4×C43B(4,𝔽2)11yescharacteristic
149Dic43—82no—
150Dic43—82no—
151#3186D4311yescharacteristic
152#2185—432no—
153#2001—431no—
154#1347—432no—
155#1314—431no—
156C2×C43—21no—
157C2×C43—21no—
158C2×C43—42no—
159C2×C43—162no—
160C2×C43#159511yescharacteristic
161C2×C43#218711yescharacteristic
162C2×C43#219111yescharacteristic
163C22×Q16—431no—
164C2×C22⋊Q8—861no—
165C2×#121—21no—
166C2×SD32—862no—
167#480—22no—
168#466—21no—
169#466C2×D4312yes—
170#447—22no—
171C2×#103—861no—
172C2×C22⋊C8C2×D4311yescharacteristic
173#358—862no—
174C22⋊C16—432no—
175#340—431no—
176C43#1210511yescharacteristic, complemented, Sylow
177C22×Q8—861no—
178C22×D4—21no—
179C22×D4—41no—
180C23×C4C22⋊D4311yescharacteristic
181C2×Q16—862no—
182C2×Q16—1722no—
183C2×D8—21no—
184C2×D8C22⋊D4312yes—
185C22×C8C22⋊D4311yescharacteristic
186C22×C8C22×D4311yescharacteristic
187C22⋊Q8—1722no—
188C22⋊Q8—1722no—
189#121—22no—
190#121—22no—
191#121—41no—
192#121—41no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—861no—
195C2×C4⋊C4—1721no—
196C2×C22⋊C4—41no—
197C2×C22⋊C4—1721no—
198SD32—1724no—
199C2×C16—862no—
200#107—21no—
201#107C22⋊D4312yes—
202#103—1722no—
203#102—22no—
204#102—22no—
205C22⋊C8—22no—
206C24—41no—
207C24#1062188211yescharacteristic
208C2×Q8—862no—
209C2×Q8—1721no—
210C2×Q8—1721no—
211C2×Q8—1721no—
212C2×Q8—1721no—
213C2×Q8—1721no—
214C2×D4—22no—
215C2×D4—41no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—81no—
219C2×D4—81no—
220C2×D4—82no—
221C2×D4—82no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—1721no—
228C22×C4—1721no—
229C22×C4#1062188211yescharacteristic
230C22×C4C2×C22⋊D4311yescharacteristic
231Q16—864no—
232Q16—1722no—
233D8—42no—
234D8—81no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8C2×C22⋊D4312yes—
239C4⋊C4—22no—
240C4⋊C4—41no—
241C4⋊C4—862no—
242C4⋊C4—1721no—
243C4⋊C4—1724no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—1724no—
247C16—1722no—
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—42no—
253C23—82no—
254C23—82no—
255C23—82no—
256C23#1306326912yescomplemented
257C23C2×#1062188211yescharacteristic
258Q8—3441no—
259Q8—3441no—
260Q8—1722no—
261Q8—1722no—
262D4—42no—
263D4—42no—
264D4—82no—
265D4—84no—
266D4—82no—
267D4—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—81no—
276C2×C4—82no—
277C2×C4—3441no—
278C2×C4—3441no—
279C2×C4—3441no—
280C2×C4—3441no—
281C2×C4—1722no—
282C2×C4—1722no—
283C2×C4#1306329411yescharacteristic
284C2×C4#1306335111yescharacteristic
285C8—22no—
286C8—41no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22—164no—
298C22#1458303311yescharacteristic
299C22C2×#1306326911yescharacteristic
300C22#1458333511yescharacteristic
301C4—21no—
302C4—41no—
303C4—82no—
304C4—3442no—
305C4—3442no—
306C4#1458306711yescharacteristic
307C4#1458308611yescharacteristic
308C2—21no—
309C2—21no—
310C2—42no—
311C2—162no—
312C2#1913351311yescharacteristic
313C2#1913652411yescharacteristic
314C2#1913654611yescharacteristic
subgroupG/H
centerC22#14583033
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
Fitting, prime radicalC43×#3186C2
socleC22×C43#447
hypercenter#3186D43
hypocenterC43#12105
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #3186

Complements

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

NH ≅ G/Ntype
1. #19136511C2semidirect
2. #19135605C2semidirect
3. #19132604C2semidirect
4. #19132519C2semidirect
6. C22×Dic172C22semidirect
11. C22⋊(C43⋊C16)C22semidirect
12. #14582662C22semidirect
98. C23×C43SD32semidirect
176. C43#12105semidirect
256. C23#13063269semidirect

Maximal subgroups

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

subgroupindex
#191365112
#191356052
#191326042
#191325192
C43×#31862
#1210543