Finite Group Databasebeta

← #24994419

Subgroups — #24994419

Order 11008.

726 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 99 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#19137930C211yesmaximal, characteristic
2#19137198C211yesmaximal, characteristic, complemented
3#19134538C212yesmaximal
4#19132449C212yesmaximal, complemented
5C43×#1463C211yesmaximal, characteristic, complemented
6C22×#10621898C2211yescharacteristic
7C2×#13063308—21no—
8C2×#13063251—24no—
9#14582819C412yescomplemented
10#14582816C412yescomplemented
11#14582785—24no—
12#14582778—21no—
13#14582770—22no—
14#14582762—21no—
15#14582762C2211yescharacteristic
16#14582759—21no—
17C4×C22⋊Dic43C2212yes—
18C22×C4⋊C4×C43C2211yescharacteristic
19C43×#407C2212yes—
20C43×#324—22no—
21C2×#10621898—22no—
22C2×#10621898—22no—
23C2×#10621898—44no—
24C22×Dic86C2×C411yescharacteristic
25C22×D172C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C22×C4×D43—21no—
28#13063308—44no—
29C2×C4⋊Dic43—22no—
30C2×Dic43⋊C4—22no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—22no—
33C2×(C2×D43)⋊C4—22no—
34C2×(C2×D43)⋊C4—22no—
35C2×C4×Dic43D414yes—
36#13063251—48no—
37C43⋊#95—22no—
38C43⋊#95—24no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C43⋊#95—21no—
42C43⋊#95C2×C412yes—
43C23×C4×C43D411yescharacteristic
44C23×C4×C43D411yescharacteristic
45C23×C4×C43C2311yescharacteristic
46C2×M16×C43—22no—
47C2×C4⋊C4×C43—22no—
48C2×C4⋊C4×C43—22no—
49C2×C4⋊C4×C43C2×C412yes—
50C2×C4⋊C4×C43D412yes—
51C22⋊C8×C43—22no—
52C22⋊C8×C43—22no—
53C24×C43C2×D411yescharacteristic
54C23×D43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—42no—
60C22×C4×C43—42no—
61C22×C4×C43—42no—
62C22×C4×C43C22⋊C412yes—
63C22×C4×C43C22⋊C412yes—
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D412yes—
67C22×C4×C43#4112yes—
68C2×C22⋊D43—24no—
69C2×C22⋊D43—42no—
70C2×C22⋊D43—41no—
71C2×C22⋊D43—41no—
72C22×Dic43—21no—
73C22×Dic43—22no—
74C22×Dic43—24no—
75#10621898—28no—
76#10621898—44no—
77#10621898—44no—
78#10621898—44no—
79C2×D172—22no—
80C2×D172—42no—
81C2×C4×D43—42no—
82C2×C4×D43—42no—
83C2×C4×D43—42no—
84C2×Dic86—22no—
85C2×Dic86—42no—
86M16×C43—44no—
87C2×C8×C43—42no—
88C4⋊C4×C43—24no—
89C4⋊C4×C43—24no—
90C22⋊Dic43—44no—
91C22⋊Dic43—42no—
92(C2×D43)⋊C4—44no—
93(C2×D43)⋊C4—44no—
94C4⋊Dic43—82no—
95Dic43⋊C4—44no—
96C4×Dic43—44no—
97C23×C43—22no—
98C23×C43—22no—
99C23×C43—41no—
100C23×C43C2×C22⋊C411yescharacteristic
101C23×C43#12011yescharacteristic
102C23×C43#12311yescharacteristic
103C22×D43—22no—
104C22×D43—41no—
105C22×D43—42no—
106C22×D43—41no—
107C22×D43—42no—
108C2×C4×C43—24no—
109C2×C4×C43—22no—
110C2×C4×C43—22no—
111C2×C4×C43—22no—
112C2×C4×C43—22no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—42no—
116C2×C4×C43—42no—
117C2×C4×C43—42no—
118C2×C4×C43—42no—
119C2×C4×C43—42no—
120C2×C4×C43—81no—
121C2×C4×C43C4×D412yes—
122C2×C4×C43#12112yes—
123C22⋊D43—44no—
124C22⋊D43—44no—
125C2×Dic43—22no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—42no—
129C2×Dic43—44no—
130C2×Dic43—42no—
131C2×Dic43—44no—
132C2×Dic43—42no—
133C2×Dic43—44no—
134D172—24no—
135D172—42no—
136C4×D43—48no—
137Dic86—24no—
138Dic86—42no—
139C8×C43—82no—
140#9480—431nomaximal, Sylow
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—44no—
149C22×C43#38611yescharacteristic
150C22×C43#42112yes—
151C22×C43B(4,𝔽2)12yes—
152C2×D43—44no—
153C2×D43—42no—
154C2×D43—82no—
155C2×D43—81no—
156C2×D43—81no—
157C4×C43—22no—
158C4×C43—22no—
159C4×C43—42no—
160C4×C43—42no—
161Dic43—42no—
162Dic43—84no—
163Dic43—82no—
164#2406—431no—
165#2313—431no—
166#1789—432no—
167#1463D4311yescharacteristic, complemented
168#1284—432no—
169C2×C43—22no—
170C2×C43—22no—
171C2×C43—41no—
172C2×C43#188911yescharacteristic
173C2×C43#189711yescharacteristic
174C2×C43#191211yescharacteristic
175D43—82no—
176C22×#41—431no—
177C2×#123—861no—
178C22×C4⋊C4C2×D4311yescharacteristic
179C2×#104—864no—
180#407C2×D4312yes—
181#395—432no—
182#394—432no—
183#387—864no—
184#386—861no—
185#385—862no—
186#381—431no—
187#381—861no—
188#380—861no—
189C4×C22⋊C4—432no—
190#324—22no—
191C43#948011yescharacteristic, complemented, Sylow
192C2×#41—862no—
193C2×#41—862no—
194C2×#41—1724no—
195C22×Q8—431no—
196C22×D4—431no—
197C22×D4—861no—
198C23×C4—861no—
199C23×C4D17211yescharacteristic
200C23×C4D17211yescharacteristic
201C23×C4C22×D4311yescharacteristic
202C2×M16—22no—
203#123—1724no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—862no—
207C2×C4⋊C4—862no—
208C2×C4⋊C4C4×D4312yes—
209C2×C4⋊C4C22⋊D4312yes—
210C2×C22⋊C4—861no—
211C2×C22⋊C4—862no—
212C2×C22⋊C4—862no—
213C2×C22⋊C4—862no—
214C2×C42—434no—
215#104—1728no—
216C22⋊C8—22no—
217C22⋊C8—22no—
218#95—432no—
219#95—862no—
220#95—864no—
221#95—862no—
222#95—862no—
223#95—861no—
224C24—861no—
225C24C2×D17211yescharacteristic
226#41—868no—
227#41—1724no—
228#41—1724no—
229#41—1724no—
230C2×Q8—862no—
231C2×Q8—1722no—
232C2×D4—864no—
233C2×D4—862no—
234C2×D4—1722no—
235C2×D4—1722no—
236C2×D4—1721no—
237C2×D4—1721no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—861no—
246C22×C4—862no—
247C22×C4—864no—
248C22×C4—1722no—
249C22×C4—1722no—
250C22×C4—1722no—
251C22×C4(C2×D43)⋊C412yes—
252C22×C4(C2×D43)⋊C412yes—
253C22×C4C2×C4×D4311yescharacteristic
254C22×C4D4×D4312yes—
255C22×C4#1062190012yes—
256C22×C4C2×C22⋊D4311yescharacteristic
257M16—44no—
258C2×C8—42no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—3442no—
262C4⋊C4—1724no—
263C22⋊C4—1724no—
264C22⋊C4—1724no—
265C22⋊C4—1722no—
266C22⋊C4—1724no—
267C42—1724no—
268C23—22no—
269C23—22no—
270C23—41no—
271C23—862no—
272C23—1721no—
273C23—1722no—
274C23—1722no—
275C23—1721no—
276C23C2×(C2×D43)⋊C411yescharacteristic
277C23#1306329511yescharacteristic
278C23#1306330911yescharacteristic
279Q8—864no—
280Q8—1722no—
281D4—864no—
282D4—1722no—
283D4—1724no—
284D4—1724no—
285C2×C4—24no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—862no—
299C2×C4—1728no—
300C2×C4—1722no—
301C2×C4—1724no—
302C2×C4—1724no—
303C2×C4—1722no—
304C2×C4—1724no—
305C2×C4—1722no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4(C22⋊D43)⋊C412yes—
309C2×C4#1306329712yes—
310C8—82no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—44no—
319C22—3442no—
320C22—3441no—
321C22—3441no—
322C22—1724no—
323C22—1722no—
324C22#1458277611yescharacteristic
325C22#1458291512yes—
326C22#1458308712yes—
327C4—22no—
328C4—22no—
329C4—42no—
330C4—42no—
331C4—3444no—
332C4—3442no—
333C4—1722no—
334C2—22no—
335C2—22no—
336C2—41no—
337C2—3442no—
338C2#1913500111yescharacteristic
339C2#1913504111yescharacteristic
340C2#1913513011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1463C2
socleC22×C43#386
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1463D43
hypocenterC43#9480
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #19137198C2semidirect
4. #19132449C2semidirect
5. C43×#1463C2semidirect
9. #14582819C4semidirect
10. #14582816C4semidirect
167. #1463D43semidirect
191. C43#9480semidirect

Maximal subgroups

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

subgroupindex
#191379302
#191371982
#191345382
#191324492
C43×#14632
#948043