Finite Group Databasebeta

← #24985318

Subgroups — #24985318

Order 11008.

604 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 95 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#19135829C212yesmaximal, complemented
2#19135665C211yesmaximal, characteristic
3#19132418C212yesmaximal, complemented
4#19132416C211yesmaximal, characteristic, complemented
5C43×#2683C211yesmaximal, characteristic, complemented
6C22×#10621882—21no—
7C2×#13063322C2211yescharacteristic
8C2×#13063245—22no—
9C2×#13063245—22no—
10C2×#13063245—21no—
11#14582654C2212yes—
12#14582654C2211yescharacteristic
13C2×C22⋊Q8×C43—22no—
14C43×#396—22no—
15C43×#395—21no—
16C43×#390C2211yescharacteristic
17C43×#389C2212yes—
18C43×#386—21no—
19C22×D172—22no—
20C22×D172—21no—
21C2×#10621882—42no—
22C2×#10621882—42no—
23C2×#10621882—42no—
24C22×C43⋊C8—21no—
25C22×C43⋊C8—22no—
26#13063322—42no—
27#13063245—42no—
28#13063245—44no—
29#13063245—44no—
30C22×Q8×C43—21no—
31C22×D4×C43D411yescharacteristic
32C23×C4×C43—21no—
33C22⋊Q8×C43—44no—
34C22⋊Q8×C43—44no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43D412yes—
38C2×C4⋊C4×C43D412yes—
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C22⋊C4×C43—22no—
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—21no—
43C2×C42×C43C2311yescharacteristic
44#95×C43—21no—
45#95×C43—22no—
46C24×C43—21no—
47C23×D43—41no—
48C2×Q8×C43—44no—
49C2×Q8×C43—81no—
50C2×D4×C43—21no—
51C2×D4×C43—41no—
52C2×D4×C43—41no—
53C2×D4×C43SD1612yes—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—21no—
57C22×C4×C43—44no—
58C22×C4×C43—81no—
59C22×C4×C43C2×D412yes—
60C22×C4×C43C2×D411yescharacteristic
61C2×D172—24no—
62C2×D172—22no—
63C2×D172—42no—
64C2×D172—41no—
65C2×D172—41no—
66C2×D172—41no—
67C2×D172—42no—
68C2×D172—42no—
69C2×D172—42no—
70C2×D172—41no—
71C2×D172—42no—
72C2×D172—41no—
73C4⋊C4×C43—22no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—42no—
76C4⋊C4×C43—44no—
77C4⋊C4×C43—42no—
78C4⋊C4×C43—42no—
79C4⋊C4×C43D814yescomplemented
80C22⋊C4×C43—44no—
81C22⋊C4×C43—42no—
82C22⋊C4×C43—42no—
83C22⋊C4×C43—81no—
84C42×C43—41no—
85#10621882—48no—
86C2×C43⋊C8—22no—
87C2×C43⋊C8—41no—
88C2×C43⋊C8—41no—
89C2×C43⋊C8—42no—
90C2×C43⋊C8—42no—
91C2×C43⋊C8—42no—
92C23×C43—22no—
93C23×C43—42no—
94C23×C43—41no—
95C23×C43—42no—
96C23×C43—41no—
97C23×C43#12011yescharacteristic
98C22×D43—42no—
99C22×D43—82no—
100C22×D43—81no—
101C22×D43—81no—
102C22×D43—82no—
103Q8×C43—84no—
104D4×C43—42no—
105D4×C43—81no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—22no—
109C2×C4×C43—21no—
110C2×C4×C43—24no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—42no—
114C2×C4×C43—42no—
115C2×C4×C43—41no—
116C2×C4×C43—42no—
117C2×C4×C43—42no—
118C2×C4×C43—84no—
119C2×C4×C43C2×D812yes—
120C2×C4×C43C2×SD1611yescharacteristic
121C2×C4×C43AGL(1,ℤ/8)12yes—
122C2×C4×C43#13711yescharacteristic
123D172—42no—
124D172—42no—
125D172—44no—
126D172—44no—
127D172—81no—
128D172—81no—
129D172—82no—
130D172—82no—
131C43⋊C8—42no—
132C43⋊C8—82no—
133#7738—431nomaximal, Sylow
134C22×C43—42no—
135C22×C43—44no—
136C22×C43—82no—
137C22×C43—81no—
138C22×C43—81no—
139C22×C43#44712yes—
140C22×C43#44811yescharacteristic
141C22×C43#45311yescharacteristic
142C22×C43#45412yes—
143C22×C43B(4,𝔽2)11yescharacteristic
144C2×D43—82no—
145C2×D43—84no—
146C2×D43—161no—
147C2×D43—162no—
148C2×D43—161no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—22no—
152C4×C43—22no—
153C4×C43—44no—
154C4×C43—82no—
155C4×C43—81no—
156#2683D4311yescharacteristic, complemented
157#2041—432no—
158#2011—431no—
159#1271—432no—
160#1270—431no—
161C2×C43—82no—
162C2×C43#159611yescharacteristic
163C2×C43#159812yes—
164C2×C43#161911yescharacteristic
165C2×C43#162712yes—
166C2×C43#165711yescharacteristic
167D43—162no—
168C22×D8—861no—
169C2×#127—431no—
170C2×C22⋊Q8—22no—
171C2×#102—861no—
172C2×#102—862no—
173C2×#102—862no—
174#396—22no—
175#395—21no—
176#390C2×D4311yescharacteristic
177#389C2×D4312yes—
178#386—21no—
179#336—431no—
180#336—432no—
181C43#773811yescharacteristic, complemented, Sylow
182C22×Q8—21no—
183C22×D4—861no—
184C22×D4—862no—
185C22×D4C22⋊D4311yescharacteristic
186C23×C4—21no—
187C2×D8—1722no—
188C2×D8—1722no—
189C2×D8—1722no—
190C22×C8—861no—
191C22×C8—862no—
192#127—1722no—
193C22⋊Q8—44no—
194C22⋊Q8—44no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4C22⋊D4312yes—
198C2×C4⋊C4C22⋊D4312yes—
199C2×C4⋊C4C22⋊D4311yescharacteristic
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—21no—
203C2×C42C22×D4311yescharacteristic
204#102—1722no—
205#102—1724no—
206#102—1724no—
207#95—21no—
208#95—22no—
209C24—21no—
210C24—1721no—
211C2×Q8—44no—
212C2×Q8—81no—
213C2×D4—21no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4—864no—
217C2×D4—862no—
218C2×D4—1722no—
219C2×D4—1721no—
220C2×D4—1721no—
221C2×D4—1721no—
222C2×D4—1722no—
223C2×D4—1722no—
224C2×D4—1722no—
225C2×D4—1721no—
226C2×D4—1722no—
227C2×D4—1721no—
228C2×D4#1062188412yes—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—44no—
233C22×C4—81no—
234C22×C4C2×C22⋊D4312yes—
235C22×C4C2×C22⋊D4311yescharacteristic
236D8—1728no—
237C2×C8—862no—
238C2×C8—1722no—
239C2×C8—1722no—
240C2×C8—1722no—
241C2×C8—1721no—
242C2×C8—1721no—
243C4⋊C4—22no—
244C4⋊C4—41no—
245C4⋊C4—42no—
246C4⋊C4—44no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4#1062188214yescomplemented
250C22⋊C4—44no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—81no—
254C42—41no—
255C23—22no—
256C23—41no—
257C23—42no—
258C23—41no—
259C23—42no—
260C23—3441no—
261C23—3442no—
262C23—3442no—
263C23—3441no—
264C23—1722no—
265C23#1306329411yescharacteristic
266Q8—84no—
267D4—42no—
268D4—81no—
269D4—3441no—
270D4—3441no—
271D4—3442no—
272D4—3442no—
273D4—1722no—
274D4—1722no—
275D4—1724no—
276D4—1724no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—24no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—84no—
290C2×C4C2×#1062188212yes—
291C2×C4C2×#1062188411yescharacteristic
292C2×C4#1306335112yes—
293C2×C4#1306335611yescharacteristic
294C8—3442no—
295C8—1722no—
296C22—44no—
297C22—42no—
298C22—82no—
299C22—81no—
300C22—81no—
301C22—3442no—
302C22—3444no—
303C22—6882no—
304C22—6881no—
305C22—6881no—
306C22#1458303312yes—
307C22#1458303811yescharacteristic
308C22#1458306711yescharacteristic
309C22#1458307212yes—
310C22#1458308611yescharacteristic
311C4—21no—
312C4—21no—
313C4—22no—
314C4—22no—
315C4—44no—
316C4—82no—
317C4—81no—
318C2—82no—
319C2—6882no—
320C2#1913351811yescharacteristic
321C2#1913353012yes—
322C2#1913364911yescharacteristic
323C2#1913369812yes—
324C2#1913389311yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2683C2
socleC23×C43#120
prime radical#19135665C2
hypercenter#2683D43
hypocenterC43#7738
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2683

Complements

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

NH ≅ G/Ntype
1. #19135829C2semidirect
3. #19132418C2semidirect
4. #19132416C2semidirect
5. C43×#2683C2semidirect
79. C4⋊C4×C43D8semidirect
156. #2683D43semidirect
181. C43#7738semidirect
249. C4⋊C4#10621882semidirect

Maximal subgroups

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

subgroupindex
#191358292
#191356652
#191324182
#191324162
C43×#26832
#773843