Finite Group Databasebeta

← #24997159

Subgroups — #24997159

Order 11008.

804 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#14583057C212yesmaximal
2#19140709C211yesmaximal, characteristic
3C2×#14582637C212yesmaximal
4#19132865C211yesmaximal, characteristic
5C43×#1280C211yesmaximal, characteristic
6C23×Dic86C2211yescharacteristic
7C22×Dic172—22no—
8C2×#13063304C2212yes—
9#14583057—24no—
10#14583057—24no—
11C2×#13063250—22no—
12#14582831—22no—
13#14582820—22no—
14#14582759—22no—
15C2×C43⋊#95—22no—
16C2×C43⋊#95C2211yescharacteristic
17#14582637—24no—
18C2×C22⋊C8×C43C2212yes—
19C2×#95×C43C2211yescharacteristic
20C22×Dic86—22no—
21C22×Dic86—22no—
22C22×Dic86—21no—
23C22×Dic86—44no—
24C22×Dic86D412yes—
25C22×Dic86D412yes—
26C23×Dic43—21no—
27C23×Dic43—21no—
28C2×Dic172—28no—
29C2×Dic172—48no—
30#13063304—22no—
31#13063304—22no—
32#13063304—22no—
33#13063304—22no—
34C2×C4⋊Dic43—22no—
35C2×C4⋊Dic43—22no—
36C2×C4⋊Dic43D412yes—
37C2×Dic43⋊C4—22no—
38C2×C22⋊Dic43—22no—
39#13063250—28no—
40C43⋊#95—24no—
41C43⋊#95—22no—
42C43⋊#95—44no—
43C23×C4×C43D412yes—
44C23×C4×C43C2311yescharacteristic
45C22×C8×C43—22no—
46C22⋊C8×C43—22no—
47C22⋊C8×C43D414yes—
48#95×C43—22no—
49C24×C43C2×D411yescharacteristic
50C22×C4×C43—22no—
51C22×C4×C43—22no—
52C22×C4×C43—42no—
53C22×C4×C43—42no—
54C22×C4×C43—42no—
55C22×C4×C43Q1614yescomplemented
56C22×C4×C43C2×D412yes—
57C22×C4×C43C2×D411yescharacteristic
58C22×C4×C43C2×D412yes—
59C22×C4×C43#4111yescharacteristic
60C22×Dic43—24no—
61C22×Dic43—22no—
62C22×Dic43—22no—
63C22×Dic43—22no—
64C22×Dic43—22no—
65C22×Dic43—42no—
66C22×Dic43—42no—
67C22×Dic43—41no—
68C22×Dic43—41no—
69C22×Dic43—41no—
70C22×Dic43—41no—
71C22×Dic43—42no—
72C2×Dic86—28no—
73C2×Dic86—24no—
74C2×Dic86—22no—
75C2×Dic86—22no—
76C2×Dic86—44no—
77C2×Dic86—48no—
78C2×Dic86—44no—
79C2×Dic86—44no—
80C2×Dic86—42no—
81C2×Dic86—44no—
82C2×C8×C43—24no—
83C2×C8×C43—44no—
84C22⋊Dic43—42no—
85C22⋊Dic43—42no—
86C4⋊Dic43—22no—
87C4⋊Dic43—22no—
88C4⋊Dic43—82no—
89C4⋊Dic43—82no—
90Dic43⋊C4—42no—
91Dic43⋊C4—42no—
92Dic172—416no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43—22no—
96C23×C43#12011yescharacteristic
97C23×C43#12111yescharacteristic
98C23×C43#12711yescharacteristic
99C23×C43C2×Q1612yes—
100C23×C43#13712yes—
101C2×C4×C43—24no—
102C2×C4×C43—24no—
103C2×C4×C43—42no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43—44no—
109C2×C4×C43—82no—
110C2×C4×C43#12012yes—
111C2×C4×C43#12112yes—
112C2×Dic43—24no—
113C2×Dic43—42no—
114C2×Dic43—44no—
115C2×Dic43—42no—
116C2×Dic43—44no—
117C2×Dic43—44no—
118C2×Dic43—42no—
119C2×Dic43—42no—
120C2×Dic43—42no—
121C2×Dic43—42no—
122C2×Dic43—42no—
123C2×Dic43—44no—
124C2×Dic43—82no—
125C2×Dic43—81no—
126C2×Dic43—81no—
127Dic86—28no—
128Dic86—44no—
129Dic86—48no—
130Dic86—44no—
131Dic86—82no—
132C8×C43—44no—
133#9967—431nomaximal, Sylow
134C22×C43—22no—
135C22×C43—22no—
136C22×C43—22no—
137C22×C43—22no—
138C22×C43—21no—
139C22×C43—21no—
140C22×C43—21no—
141C22×C43—21no—
142C22×C43#39211yescharacteristic
143C22×C43#45112yes—
144C22×C43#45511yescharacteristic
145C22×C43#45611yescharacteristic
146C22×C43B(4,𝔽2)12yes—
147C22×C43#46212yes—
148C22×C43#49411yescharacteristic
149C22×C43#49711yescharacteristic
150C4×C43—22no—
151C4×C43—22no—
152C4×C43—44no—
153Dic43—44no—
154Dic43—82no—
155Dic43—82no—
156Dic43—82no—
157C2×#451—432no—
158#2659—431no—
159C2×#328—432no—
160#1446—431no—
161#1280D4311yescharacteristic
162C2×C43—21no—
163C2×C43—22no—
164C2×C43—21no—
165C2×C43#160212yes—
166C2×C43#160512yes—
167C2×C43#200711yescharacteristic
168C2×C43#201611yescharacteristic
169C2×C43#202111yescharacteristic
170C23×Q8—431no—
171C22×Q16—862no—
172C2×C22⋊Q8—432no—
173#451—864no—
174#451—864no—
175C2×#103—862no—
176C2×C22⋊C8C2×D4312yes—
177#398—862no—
178#395—862no—
179#380—862no—
180C2×#95—431no—
181C2×#95—862no—
182C2×#95C2×D4311yescharacteristic
183#328—864no—
184C43#996711yescharacteristic, complemented, Sylow
185C22×Q8—432no—
186C22×Q8—432no—
187C22×Q8—861no—
188C22×Q8—862no—
189C22×Q8—862no—
190C22×Q8—1724no—
191C23×C4—861no—
192C23×C4—861no—
193C23×C4D17212yes—
194C23×C4C22×D4311yescharacteristic
195C2×Q16—868no—
196C2×Q16—1728no—
197C22×C8—22no—
198C22⋊Q8—862no—
199C22⋊Q8—862no—
200C22⋊Q8—862no—
201C22⋊Q8—862no—
202C2×C4⋊C4—432no—
203C2×C4⋊C4—862no—
204C2×C4⋊C4—862no—
205C2×C4⋊C4—862no—
206C2×C22⋊C4—862no—
207#103—868no—
208C22⋊C8—22no—
209C22⋊C8D17214yes—
210#95—22no—
211#95—864no—
212#95—862no—
213#95—1724no—
214C24C2×D17211yescharacteristic
215C2×Q8—868no—
216C2×Q8—864no—
217C2×Q8—862no—
218C2×Q8—862no—
219C2×Q8—1724no—
220C2×Q8—1724no—
221C2×Q8—1724no—
222C2×Q8—1724no—
223C2×Q8—1728no—
224C2×Q8—1722no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—864no—
231C22×C4—862no—
232C22×C4—862no—
233C22×C4—862no—
234C22×C4—862no—
235C22×C4—1722no—
236C22×C4—1721no—
237C22×C4—1721no—
238C22×C4—1722no—
239C22×C4—1722no—
240C22×C4—1721no—
241C22×C4—1721no—
242C22×C4Dic17214yescomplemented
243C22×C4C2×D17212yes—
244C22×C4D4×D4312yes—
245C22×C4D4×D4311yescharacteristic
246C22×C4#1062190211yescharacteristic
247Q16—17216no—
248C2×C8—24no—
249C2×C8—44no—
250C4⋊C4—862no—
251C4⋊C4—862no—
252C4⋊C4—3442no—
253C4⋊C4—3442no—
254C4⋊C4—1722no—
255C4⋊C4—1722no—
256C22⋊C4—1722no—
257C22⋊C4—1722no—
258C23—21no—
259C23—21no—
260C23—22no—
261C23#1306329511yescharacteristic
262C23#1306330011yescharacteristic
263C23#1306332211yescharacteristic
264C23C2×Dic17212yes—
265C23#1306335812yes—
266Q8—868no—
267Q8—3442no—
268Q8—1724no—
269Q8—1724no—
270Q8—1728no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—44no—
279C2×C4—82no—
280C2×C4—864no—
281C2×C4—3442no—
282C2×C4—3441no—
283C2×C4—3441no—
284C2×C4—1724no—
285C2×C4—1722no—
286C2×C4—1722no—
287C2×C4—1722no—
288C2×C4—1722no—
289C2×C4—1722no—
290C2×C4—1724no—
291C2×C4—1722no—
292C2×C4—1724no—
293C2×C4—1722no—
294C2×C4—1724no—
295C2×C4#1306329512yes—
296C2×C4#1306330012yes—
297C8—44no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22#1458280911yescharacteristic
307C22#1458305712yes—
308C22#1458307911yescharacteristic
309C22#1458308411yescharacteristic
310C22#1458308712yes—
311C22#1458311012yes—
312C22#1458327911yescharacteristic
313C22#1458329311yescharacteristic
314C4—22no—
315C4—22no—
316C4—44no—
317C4—3442no—
318C4—3442no—
319C4—3442no—
320C4—1724no—
321C2—21no—
322C2—22no—
323C2—21no—
324C2#1913355412yes—
325C2#1913357112yes—
326C2#1913564411yescharacteristic
327C2#1913569711yescharacteristic
328C2#1913572211yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1280C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenter#1280D43
hypocenterC43#9967
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
55. C22×C4×C43Q16semidirect
184. C43#9967semidirect
242. C22×C4Dic172semidirect

Maximal subgroups

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

subgroupindex
C2×#145830572
#191407092
C2×#145826372
#191328652
C43×#12802
#996743