Finite Group Databasebeta

← #24994349

Subgroups — #24994349

Order 11008.

726 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 107 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#19138249C211yesmaximal, characteristic
2#19137181C211yesmaximal, characteristic, complemented
3#19133125C212yesmaximal
4#19132449C212yesmaximal, complemented
5C43×#1784C211yesmaximal, characteristic, complemented
6C2×#13063314C412yescomplemented
7C2×#13063299C2211yescharacteristic
8C2×#13063284—21no—
9#14582810—22no—
10#14582806—24no—
11#14582806C412yescomplemented
12#14582778—21no—
13#14582778—21no—
14#14582762—21no—
15#14582762C2212yes—
16C4×C22⋊Dic43C2211yescharacteristic
17#14582634—24no—
18C23×Q8×C43C2211yescharacteristic
19C2×#101×C43—22no—
20C43×#407C2212yes—
21C22×D172C2×C411yescharacteristic
22C22×C22⋊D43—21no—
23#13063314—44no—
24#13063299—22no—
25#13063299—22no—
26#13063284—44no—
27C2×C4⋊Dic43—22no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×C22⋊Dic43—22no—
30C2×C22⋊Dic43—21no—
31C2×(C2×D43)⋊C4—22no—
32C2×(C2×D43)⋊C4—22no—
33C2×(C2×D43)⋊C4—21no—
34C2×C4×Dic43—22no—
35C2×C4×Dic43C2×C412yes—
36C43⋊#95—24no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95—21no—
41C43⋊#95D414yes—
42C22×Q8×C43—22no—
43C22×Q8×C43—22no—
44C22×Q8×C43—44no—
45C22×Q8×C43C2×C412yes—
46C22×Q8×C43D412yes—
47C23×C4×C43D411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C23×C4×C43C2311yescharacteristic
50C2×M16×C43—22no—
51#101×C43—44no—
52C22⋊C8×C43—22no—
53C22⋊C8×C43—22no—
54C24×C43C2×D411yescharacteristic
55C23×D43—21no—
56C2×Q8×C43—24no—
57C2×Q8×C43—24no—
58C2×Q8×C43—24no—
59C2×Q8×C43—24no—
60C2×Q8×C43—42no—
61C2×Q8×C43—42no—
62C2×Q8×C43—44no—
63C2×Q8×C43—44no—
64C2×Q8×C43—48no—
65C22×C4×C43—24no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—42no—
71C22×C4×C43—42no—
72C22×C4×C43C22⋊C412yes—
73C22×C4×C43C22⋊C412yes—
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D412yes—
77C22×C4×C43#4112yes—
78C2×C22⋊D43—44no—
79C2×C22⋊D43—41no—
80C2×C22⋊D43—41no—
81C22×Dic43—21no—
82C22×Dic43—22no—
83C22×Dic43—24no—
84C2×D172—22no—
85C2×D172—42no—
86M16×C43—44no—
87C2×C8×C43—42no—
88C22⋊Dic43—42no—
89C22⋊Dic43—44no—
90(C2×D43)⋊C4—44no—
91(C2×D43)⋊C4—44no—
92(C2×D43)⋊C4—42no—
93C4⋊Dic43—22no—
94C4⋊Dic43—44no—
95C4×Dic43—44no—
96C4×Dic43—42no—
97C23×C43—22no—
98C23×C43—22no—
99C23×C43—41no—
100C23×C43C2×C22⋊C411yescharacteristic
101C23×C43#12011yescharacteristic
102C23×C43#12311yescharacteristic
103C22×D43—42no—
104C22×D43—42no—
105C22×D43—41no—
106C22×D43—42no—
107Q8×C43—48no—
108Q8×C43—48no—
109C2×C4×C43—22no—
110C2×C4×C43—22no—
111C2×C4×C43—24no—
112C2×C4×C43—22no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43—22no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43#9914yes—
124C2×C4×C43C4×D412yes—
125C2×C4×C43#12112yes—
126C22⋊D43—82no—
127C22⋊D43—82no—
128C2×Dic43—44no—
129C2×Dic43—42no—
130C2×Dic43—42no—
131C2×Dic43—44no—
132C2×Dic43—42no—
133C2×Dic43—41no—
134C2×Dic43—42no—
135C2×Dic43—44no—
136D172—82no—
137C8×C43—82no—
138#9466—431nomaximal, Sylow
139C22×C43—21no—
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—44no—
147C22×C43#38611yescharacteristic
148C22×C43C2×#9912yes—
149C22×C43#45412yes—
150C2×D43—84no—
151C2×D43—81no—
152C2×D43—81no—
153C2×D43—81no—
154C4×C43—22no—
155C4×C43—22no—
156C4×C43—24no—
157C4×C43—42no—
158Dic43—84no—
159Dic43—82no—
160Dic43—81no—
161#2436—431no—
162#2310—431no—
163#1784D4311yescharacteristic, complemented
164#1510—432no—
165#1284—432no—
166C2×C43—22no—
167C2×C43—22no—
168C2×C43—41no—
169C2×C43#188811yescharacteristic
170C2×C43#189811yescharacteristic
171C2×C43#191211yescharacteristic
172D43—161no—
173C23×Q8C2×D4311yescharacteristic
174C2×#124—432no—
175C2×#121—431no—
176C2×#117—861no—
177C2×#101—22no—
178#407C2×D4312yes—
179#393—862no—
180#391—432no—
181#391—864no—
182#386—861no—
183#386—861no—
184#381—432no—
185#381—861no—
186C4×C22⋊C4—431no—
187#327—864no—
188C43#946611yescharacteristic, complemented, Sylow
189C22×Q8—22no—
190C22×Q8—22no—
191C22×Q8—44no—
192C22×Q8C4×D4312yes—
193C22×Q8C22⋊D4312yes—
194C22×D4—431no—
195C22×D4—861no—
196C23×C4D17211yescharacteristic
197C23×C4D17211yescharacteristic
198C23×C4C22×D4311yescharacteristic
199C2×M16—22no—
200#124—1724no—
201#121—862no—
202#121—862no—
203#117—1724no—
204C2×C4⋊C4—431no—
205C2×C4⋊C4—862no—
206C2×C22⋊C4—862no—
207C2×C22⋊C4—861no—
208C2×C22⋊C4—862no—
209C2×C22⋊C4—862no—
210C2×C22⋊C4—861no—
211C2×C42—432no—
212C2×C42—862no—
213#101—44no—
214C22⋊C8—22no—
215C22⋊C8—22no—
216#95—434no—
217#95—864no—
218#95—862no—
219#95—862no—
220#95—862no—
221#95—861no—
222C24—861no—
223C24C2×D17211yescharacteristic
224C2×Q8—24no—
225C2×Q8—24no—
226C2×Q8—24no—
227C2×Q8—24no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—44no—
231C2×Q8—44no—
232C2×Q8—48no—
233C2×D4—862no—
234C2×D4—1722no—
235C2×D4—1724no—
236C2×D4—1721no—
237C2×D4—1721no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—24no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—861no—
246C22×C4—862no—
247C22×C4—864no—
248C22×C4(C2×D43)⋊C412yes—
249C22×C4(C2×D43)⋊C412yes—
250C22×C4C2×C4×D4311yescharacteristic
251C22×C4D4×D4312yes—
252C22×C4#1062190012yes—
253C22×C4C2×C22⋊D4311yescharacteristic
254M16—44no—
255C2×C8—42no—
256C4⋊C4—862no—
257C4⋊C4—1724no—
258C22⋊C4—1724no—
259C22⋊C4—1724no—
260C22⋊C4—1722no—
261C22⋊C4—1724no—
262C22⋊C4—1722no—
263C42—1722no—
264C42—1724no—
265C23—22no—
266C23—22no—
267C23—41no—
268C23—1722no—
269C23—1722no—
270C23—1722no—
271C23—1721no—
272C23C2×(C2×D43)⋊C411yescharacteristic
273C23#1306329511yescharacteristic
274C23#1306330911yescharacteristic
275Q8—48no—
276Q8—48no—
277D4—3442no—
278D4—3442no—
279D4—3442no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—1724no—
295C2×C4—1722no—
296C2×C4—1722no—
297C2×C4—1724no—
298C2×C4—1722no—
299C2×C4—1724no—
300C2×C4—1722no—
301C2×C4—1721no—
302C2×C4#1306323914yes—
303C2×C4(C22⋊D43)⋊C412yes—
304C2×C4#1306329712yes—
305C8—82no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—44no—
314C22—3444no—
315C22—3441no—
316C22—3441no—
317C22—3441no—
318C22#1458277611yescharacteristic
319C22C2×#1306323912yes—
320C22#1458307412yes—
321C4—22no—
322C4—24no—
323C4—22no—
324C4—42no—
325C4—3444no—
326C4—3442no—
327C4—3441no—
328C2—22no—
329C2—22no—
330C2—41no—
331C2—6881no—
332C2#1913499611yescharacteristic
333C2#1913504611yescharacteristic
334C2#1913513011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1784C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1784D43
hypocenterC43#9466
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

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

NH ≅ G/Ntype
2. #19137181C2semidirect
4. #19132449C2semidirect
5. C43×#1784C2semidirect
6. C2×#13063314C4semidirect
11. #14582806C4semidirect
163. #1784D43semidirect
188. C43#9466semidirect

Maximal subgroups

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

subgroupindex
#191382492
#191371812
#191331252
#191324492
C43×#17842
#946643