Finite Group Databasebeta

← #24994521

Subgroups — #24994521

Order 11008.

660 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 103 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#19138873C211yesmaximal, characteristic
2#19134669C211yesmaximal, characteristic
3#19134667C212yesmaximal
4C43⋊#1304C212yesmaximal
5C43×#2312C211yesmaximal, characteristic
6C22×C22⋊Dic43C2211yescharacteristic
7#14582827—22no—
8#14582772—21no—
9#14582771C412yescomplemented
10#14582762—21no—
11#14582760C412yescomplemented
12#14582755C2212yes—
13#14582755C2211yescharacteristic
14#14582666—22no—
15#14582665—24no—
16C22×C22⋊C4×C43C2211yescharacteristic
17C43×#388—24no—
18C43×#380—21no—
19C43×#379C2212yes—
20C4×C22⋊C4×C43—21no—
21C23×Dic43C2×C411yescharacteristic
22C23×Dic43C2×C411yescharacteristic
23C2×Dic43⋊C4—22no—
24C2×C22⋊Dic43—21no—
25C2×C22⋊Dic43—22no—
26C2×C22⋊Dic43—21no—
27C2×C22⋊Dic43—21no—
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—22no—
30C2×C22⋊Dic43—22no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—22no—
33C2×C22⋊Dic43C2×C412yes—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C25×C43C2311yescharacteristic
38C23×C4×C43D411yescharacteristic
39C23×C4×C43D411yescharacteristic
40C2×C4⋊C4×C43—22no—
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—22no—
43C2×C22⋊C4×C43—22no—
44C2×C22⋊C4×C43—22no—
45C2×C22⋊C4×C43C2×C412yes—
46C2×C22⋊C4×C43D412yes—
47C2×C22⋊C4×C43D414yes—
48C2×C42×C43—22no—
49#95×C43—22no—
50#95×C43—22no—
51C24×C43—42no—
52C24×C43—42no—
53C24×C43—81no—
54C24×C43C22×C411yescharacteristic
55C24×C43C2×D411yescharacteristic
56C24×C43C2×D411yescharacteristic
57C24×C43C2×D412yes—
58C24×C43#4112yes—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—24no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—42no—
65C22×C4×C43—81no—
66C22×C4×C43C22⋊C412yes—
67C22×C4×C43C22⋊C412yes—
68C22×Dic43—21no—
69C22×Dic43—22no—
70C22×Dic43—21no—
71C22×Dic43—22no—
72C22×Dic43—22no—
73C22×Dic43—42no—
74C22×Dic43—42no—
75C22×Dic43—81no—
76C4⋊C4×C43—82no—
77C22⋊C4×C43—24no—
78C22⋊C4×C43—24no—
79C22⋊C4×C43—44no—
80C22⋊C4×C43—44no—
81C22⋊C4×C43—82no—
82C42×C43—82no—
83C22⋊Dic43—42no—
84C22⋊Dic43—42no—
85C22⋊Dic43—44no—
86C22⋊Dic43—44no—
87C22⋊Dic43—41no—
88C22⋊Dic43—42no—
89C22⋊Dic43—41no—
90C22⋊Dic43—81no—
91C22⋊Dic43—82no—
92Dic43⋊C4—82no—
93C23×C43—22no—
94C23×C43—22no—
95C23×C43—22no—
96C23×C43—22no—
97C23×C43—24no—
98C23×C43—41no—
99C23×C43—41no—
100C23×C43—41no—
101C23×C43—41no—
102C23×C43—42no—
103C23×C43—42no—
104C23×C43—41no—
105C23×C43—42no—
106C23×C43—42no—
107C23×C43—42no—
108C23×C43—88no—
109C23×C43C2×C22⋊C411yescharacteristic
110C23×C43C4×D412yes—
111C23×C43#12011yescharacteristic
112C23×C43#12112yes—
113C23×C43#12311yescharacteristic
114C2×C4×C43—22no—
115C2×C4×C43—22no—
116C2×C4×C43—42no—
117C2×C4×C43—42no—
118C2×C4×C43—42no—
119C2×C4×C43—42no—
120C2×C4×C43—44no—
121C2×C4×C43—44no—
122C2×C4×C43—44no—
123C2×C4×C43—81no—
124C2×C4×C43—81no—
125C2×Dic43—42no—
126C2×Dic43—42no—
127C2×Dic43—42no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—42no—
131C2×Dic43—42no—
132C2×Dic43—82no—
133C2×Dic43—82no—
134C2×Dic43—82no—
135C2×Dic43—82no—
136C2×Dic43—82no—
137#9500—431nomaximal, Sylow
138C22×C43—21no—
139C22×C43—21no—
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—22no—
143C22×C43—22no—
144C22×C43—21no—
145C22×C43—22no—
146C22×C43—22no—
147C22×C43—21no—
148C22×C43—22no—
149C22×C43—22no—
150C22×C43—21no—
151C22×C43—44no—
152C22×C43—44no—
153C22×C43—82no—
154C22×C43—84no—
155C22×C43—84no—
156C22×C43#38611yescharacteristic
157C22×C43#41012yes—
158C22×C43#45812yes—
159C4×C43—42no—
160C4×C43—42no—
161C4×C43—84no—
162Dic43—82no—
163Dic43—81no—
164Dic43—81no—
165Dic43—162no—
166#2483—431no—
167#2312D4311yescharacteristic
168#1819—432no—
169#1819—431no—
170#1304—432no—
171C2×C43—22no—
172C2×C43—22no—
173C2×C43—42no—
174C2×C43—42no—
175C2×C43—41no—
176C2×C43#189011yescharacteristic
177C2×C43#189911yescharacteristic
178C2×C43#191311yescharacteristic
179C22×C22⋊C4—431no—
180C22×C22⋊C4C2×D4311yescharacteristic
181#397—862no—
182#388—24no—
183#385—432no—
184#385—861no—
185#381—432no—
186#381—861no—
187#380—21no—
188#379—431no—
189#379—432no—
190#379C2×D4312yes—
191C4×C22⋊C4—21no—
192#342—862no—
193#342—864no—
194C43#950011yescharacteristic, complemented, Sylow
195C25C22×D4311yescharacteristic
196C23×C4—431no—
197C23×C4—431no—
198C23×C4C22⋊D4311yescharacteristic
199C23×C4C22⋊D4311yescharacteristic
200C2×C4⋊C4—22no—
201C2×C4⋊C4—862no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—432no—
207C2×C22⋊C4—861no—
208C2×C22⋊C4—862no—
209C2×C22⋊C4—861no—
210C2×C22⋊C4—862no—
211C2×C22⋊C4—862no—
212C2×C22⋊C4—861no—
213C2×C22⋊C4—861no—
214C2×C22⋊C4—862no—
215C2×C22⋊C4—862no—
216C2×C22⋊C4C4×D4312yes—
217C2×C22⋊C4D17212yes—
218C2×C22⋊C4C22⋊D4314yes—
219C2×C42—22no—
220#95—22no—
221#95—22no—
222#95—862no—
223#95—862no—
224#95—862no—
225C24—42no—
226C24—42no—
227C24—81no—
228C24C2×C4×D4311yescharacteristic
229C24C2×D17211yescharacteristic
230C24#1062189812yes—
231C24C2×C22⋊D4311yescharacteristic
232C24C2×C22⋊D4312yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—24no—
238C22×C4—42no—
239C22×C4—81no—
240C22×C4—862no—
241C22×C4—862no—
242C22×C4—861no—
243C22×C4—862no—
244C22×C4—861no—
245C22×C4—3441no—
246C22×C4—1722no—
247C22×C4—1722no—
248C22×C4(C2×D43)⋊C412yes—
249C22×C4(C2×D43)⋊C412yes—
250C4⋊C4—82no—
251C4⋊C4—3442no—
252C22⋊C4—24no—
253C22⋊C4—24no—
254C22⋊C4—44no—
255C22⋊C4—44no—
256C22⋊C4—82no—
257C22⋊C4—3442no—
258C22⋊C4—3441no—
259C22⋊C4—1724no—
260C22⋊C4—1724no—
261C22⋊C4—1722no—
262C22⋊C4—1721no—
263C22⋊C4—1722no—
264C22⋊C4—1721no—
265C22⋊C4—1722no—
266C42—82no—
267C23—22no—
268C23—22no—
269C23—22no—
270C23—24no—
271C23—22no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—42no—
276C23—41no—
277C23—42no—
278C23—41no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—88no—
283C23C2×(C2×D43)⋊C411yescharacteristic
284C23C4×C22⋊D4312yes—
285C23#1306329411yescharacteristic
286C23#1306329912yes—
287C23#1306330811yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—3442no—
300C2×C4—3442no—
301C2×C4—3442no—
302C2×C4—3442no—
303C2×C4—3442no—
304C2×C4—1722no—
305C2×C4—1722no—
306C2×C4—1722no—
307C2×C4—1722no—
308C2×C4—1722no—
309C2×C4—1721no—
310C2×C4—1721no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—44no—
325C22—44no—
326C22—84no—
327C22—82no—
328C22—84no—
329C22#1458277811yescharacteristic
330C22#1458287212yes—
331C22#1458308912yes—
332C4—42no—
333C4—42no—
334C4—84no—
335C4—3442no—
336C4—3441no—
337C4—3441no—
338C4—6882no—
339C2—22no—
340C2—22no—
341C2—42no—
342C2—41no—
343C2—42no—
344C2#1913500811yescharacteristic
345C2#1913505311yescharacteristic
346C2#1913513711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC43×#2312C2
socleC22×C43#386
prime radical, cosocleC25×C43C23
hypercenter#2312D43
hypocenterC43#9500
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #2312

Complements

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

NH ≅ G/Ntype
9. #14582771C4semidirect
11. #14582760C4semidirect
194. C43#9500semidirect

Maximal subgroups

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

subgroupindex
#191388732
#191346692
#191346672
C43⋊#13042
C43×#23122
#950043