Finite Group Databasebeta

← #24984840

Subgroups — #24984840

Order 11008.

730 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 105 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#19137084C211yesmaximal, characteristic
2#19134287C212yesmaximal, complemented
3#19132421C211yesmaximal, characteristic, complemented
4#19132415C212yesmaximal, complemented
5C43×#1272C211yesmaximal, characteristic, complemented
6C22×#10621902C411yescharacteristic
7C22×#10621872—22no—
8C2×#13063283C411yescharacteristic
9C2×C42×D43C2211yescharacteristic
10#14582806C411yescharacteristic
11#14582801C2211yescharacteristic
12#14582800C411yescharacteristic
13#14582777—22no—
14#14582746—22no—
15#14582654C2212yes—
16#14582653—22no—
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C2×#10621902—22no—
20C2×#10621902—22no—
21C2×#10621902—42no—
22C2×#10621902—42no—
23C22×D172—21no—
24C22×D172C2×C411yescharacteristic
25C22×C4×D43—21no—
26C22×C4×D43C2×C411yescharacteristic
27C22×C4×D43D412yes—
28C2×#10621872—28no—
29C2×#10621872—44no—
30C2×#10621872—44no—
31C22×C43⋊C8—22no—
32#13063283—42no—
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—22no—
36C2×(C2×D43)⋊C4—22no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43C2×C411yescharacteristic
39C2×C4×Dic43D412yes—
40C42×D43—42no—
41C43⋊#95—22no—
42C22×Q8×C43C2×C411yescharacteristic
43C22×C8×C43—22no—
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C42×C43C2311yescharacteristic
46#95×C43—22no—
47C23×D43—21no—
48C23×D43C22⋊C411yescharacteristic
49C2×Q8×C43—21no—
50C2×Q8×C43—41no—
51C2×Q8×C43—41no—
52C2×Q8×C43M1612yescomplemented
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43C22×C411yescharacteristic
56C22×C4×C43C2×D412yes—
57C22×Dic43—21no—
58C22×Dic43C22⋊C411yescharacteristic
59C22×Dic43C22⋊C412yes—
60#10621902—48no—
61#10621902—48no—
62C2×D172—24no—
63C2×D172—21no—
64C2×D172—42no—
65C2×D172—42no—
66C2×D172—41no—
67C2×D172—41no—
68C2×D172M1612yescomplemented
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43—22no—
72C2×C4×D43—22no—
73C2×C4×D43—22no—
74C2×C4×D43—24no—
75C2×C4×D43—24no—
76C2×C4×D43—24no—
77C2×C4×D43—22no—
78C2×C4×D43—42no—
79C2×C4×D43—42no—
80C2×C8×C43—24no—
81C2×C8×C43—42no—
82C2×C8×C43—42no—
83C4⋊C4×C43—41no—
84C42×C43—41no—
85(C2×D43)⋊C4—42no—
86(C2×D43)⋊C4—42no—
87(C2×D43)⋊C4—42no—
88(C2×D43)⋊C4—44no—
89C4⋊Dic43—41no—
90C4×Dic43—41no—
91C4×Dic43—42no—
92C4×Dic43—42no—
93C2×C43⋊C8—24no—
94C2×C43⋊C8—42no—
95C2×C43⋊C8—42no—
96#10621872—416no—
97C23×C43C2×C22⋊C411yescharacteristic
98C22×D43—21no—
99C22×D43—21no—
100C22×D43—22no—
101C22×D43—22no—
102C22×D43—22no—
103C22×D43—41no—
104C22×D43—41no—
105C22×D43—42no—
106C22×D43—42no—
107C22×D43#9912yes—
108Q8×C43—42no—
109Q8×C43—42no—
110C2×C4×C43—22no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—22no—
114C2×C4×C43—22no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—42no—
119C2×C4×C43C2×M1611yescharacteristic
120C2×C4×C43C2×M1611yescharacteristic
121C2×C4×C43AGL(1,ℤ/8)12yes—
122C2×C4×C43#13712yes—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—22no—
126C2×Dic43—22no—
127C2×Dic43—41no—
128C2×Dic43—42no—
129C2×Dic43#10012yes—
130C2×Dic43#10414yes—
131D172—42no—
132D172—42no—
133D172—48no—
134C4×D43—28no—
135C4×D43—28no—
136C4×D43—24no—
137C4×D43—24no—
138C4×D43—48no—
139C8×C43—44no—
140C43⋊C8—44no—
141#7631—431nomaximal, Sylow
142C22×C43#40711yescharacteristic
143C22×C43C2×#9911yescharacteristic
144C22×C43C2×#10011yescharacteristic
145C22×C43#41712yes—
146C22×C43C2×#10412yes—
147C2×D43—22no—
148C2×D43—24no—
149C2×D43—41no—
150C2×D43—42no—
151C2×D43—41no—
152C2×D43—42no—
153C2×D43—44no—
154C2×D43—81no—
155C2×D43—82no—
156C2×D43—81no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—22no—
160C4×C43—22no—
161C4×C43—42no—
162C4×C43—81no—
163Dic43—22no—
164Dic43—24no—
165Dic43—81no—
166#2297—431no—
167#1728—432no—
168#1272—431no—
169#1272D4311yescharacteristic, complemented
170#1270—432no—
171C2×C43#146211yescharacteristic
172C2×C43#148912yes—
173C2×C43#150412yes—
174C2×C43#152511yescharacteristic
175C2×C43#156011yescharacteristic
176D43—42no—
177D43—82no—
178C22×#41—431no—
179C22×M16—862no—
180C2×#117—431no—
181C22×C42—431no—
182#391—431no—
183#391C2×D4311yescharacteristic
184#390—431no—
185#390—431no—
186#386—862no—
187C4×C22⋊C4—862no—
188#336—432no—
189#336—862no—
190#336C2×D4312yes—
191C43#763111yescharacteristic, complemented, Sylow
192C2×#41—862no—
193C2×#41—862no—
194C2×#41—1722no—
195C2×#41—1722no—
196C22×Q8C4×D4311yescharacteristic
197C22×D4—431no—
198C22×D4—861no—
199C23×C4—431no—
200C23×C4—432no—
201C23×C4—861no—
202C2×M16—868no—
203C2×M16—1724no—
204C2×M16—1724no—
205C22×C8—22no—
206C22×C8—862no—
207#117—1722no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4C4×D4311yescharacteristic
210C2×C22⋊C4—862no—
211C2×C22⋊C4—861no—
212C2×C22⋊C4—862no—
213C2×C42—431no—
214C2×C42—432no—
215C2×C42—861no—
216C2×C42—1722no—
217C2×C42C22×D4311yescharacteristic
218#95—22no—
219#95—862no—
220C24—431no—
221C24—861no—
222#41—1728no—
223#41—1728no—
224C2×Q8—21no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8#1062187212yescomplemented
228C2×D4—432no—
229C2×D4—864no—
230C2×D4—861no—
231C2×D4—1721no—
232C2×D4—1721no—
233C2×D4—1722no—
234C2×D4—1722no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—432no—
238C22×C4—431no—
239C22×C4—862no—
240C22×C4—864no—
241C22×C4—864no—
242C22×C4—862no—
243C22×C4—864no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—862no—
247C22×C4—862no—
248C22×C4—861no—
249C22×C4—1722no—
250C22×C4—1722no—
251C22×C4C2×C4×D4311yescharacteristic
252C22×C4D4×D4312yes—
253M16—17216no—
254C2×C8—24no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—864no—
258C2×C8—1722no—
259C2×C8—1722no—
260C4⋊C4—41no—
261C4⋊C4—1721no—
262C22⋊C4—1724no—
263C22⋊C4—1722no—
264C22⋊C4—1722no—
265C22⋊C4—1722no—
266C42—41no—
267C42—1722no—
268C42—1721no—
269C42—1722no—
270C23—432no—
271C23—861no—
272C23—861no—
273C23—862no—
274C23—862no—
275C23—862no—
276C23—1721no—
277C23—1721no—
278C23—1722no—
279C23—1722no—
280C23C22⋊C4×D4311yescharacteristic
281Q8—42no—
282Q8—42no—
283D4—1722no—
284D4—1722no—
285D4—1728no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—432no—
296C2×C4—434no—
297C2×C4—868no—
298C2×C4—864no—
299C2×C4—864no—
300C2×C4—868no—
301C2×C4—861no—
302C2×C4—861no—
303C2×C4—862no—
304C2×C4—862no—
305C2×C4—1728no—
306C2×C4—1721no—
307C2×C4—1722no—
308C2×C4M16×D4311yescharacteristic
309C2×C4C2×#1062187211yescharacteristic
310C2×C4#1306335212yes—
311C2×C4#1306335712yes—
312C8—44no—
313C8—1724no—
314C22—864no—
315C22—862no—
316C22—3441no—
317C22—3441no—
318C22—3442no—
319C22—1724no—
320C22—1722no—
321C22—1721no—
322C22—1722no—
323C22—1721no—
324C22#1458286111yescharacteristic
325C22#99×D4311yescharacteristic
326C22#100×D4311yescharacteristic
327C22#1458289912yes—
328C22#104×D4312yes—
329C4—22no—
330C4—22no—
331C4—21no—
332C4—21no—
333C4—42no—
334C4—81no—
335C4—864no—
336C4—862no—
337C4—3441no—
338C2—3442no—
339C2—1722no—
340C2#1913292011yescharacteristic
341C2#1913303312yes—
342C2#1913309812yes—
343C2#1913318511yescharacteristic
344C2#1913332911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socleC23×C43C2×C22⋊C4
prime radicalC22×#10621902C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43#7631
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #19134287C2semidirect
3. #19132421C2semidirect
4. #19132415C2semidirect
5. C43×#1272C2semidirect
52. C2×Q8×C43M16semidirect
68. C2×D172M16semidirect
169. #1272D43semidirect
191. C43#7631semidirect
227. C2×Q8#10621872semidirect

Maximal subgroups

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

subgroupindex
#191370842
#191342872
#191324212
#191324152
C43×#12722
#763143