Finite Group Databasebeta

← #24996159

Subgroups — #24996159

Order 11008.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19133358C211yesmaximal, characteristic, complemented
2#19133197C211yesmaximal, characteristic, complemented
3#19133193C211yesmaximal, characteristic
4#19132951C211yesmaximal, characteristic, complemented
5#19132947C211yesmaximal, characteristic
6#19132884C211yesmaximal, characteristic, complemented
7C2×C43×#488C211yesmaximal, characteristic
8#14582956C2211yescharacteristic
9#14582956C2211yescharacteristic
10#14582952C2211yescharacteristic
11C4×#10621877C2211yescharacteristic
12#14582652—21no—
13#14582650—21no—
14#14582641—22no—
15#14582639—22no—
16#14582625—22no—
17#14582623—22no—
18#14582621—21no—
19#14582620—21no—
20C2×#125×C43C2211yescharacteristic
21C2×#124×C43C2211yescharacteristic
22C43×#488—21no—
23C43×#488—21no—
24C43×#488—21no—
25C43×#488—21no—
26C2×#103×C43C411yescharacteristic
27C2×#103×C43C411yescharacteristic
28C2×#102×C43C411yescharacteristic
29C2×#102×C43C411yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C2×#10621877—21no—
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C22⋊(C43⋊C8)—21no—
36C22⋊(C43⋊C8)—21no—
37C22⋊(C43⋊C8)D412yes—
38#13063236—21no—
39#13063236—21no—
40#13063236D412yes—
41C4×C43⋊C8—21no—
42C4×C43⋊C8—21no—
43C22×Q8×C43C2×C411yescharacteristic
44C22×D4×C43C2×C411yescharacteristic
45C22×C8×C43C2×C411yescharacteristic
46C22×C8×C43C2×C411yescharacteristic
47#125×C43—21no—
48#125×C43—21no—
49#125×C43—21no—
50#125×C43—21no—
51#124×C43—21no—
52#124×C43—21no—
53#124×C43—21no—
54#124×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C42×C43C2311yescharacteristic
62#103×C43—21no—
63#103×C43—21no—
64#103×C43—21no—
65#103×C43—21no—
66#102×C43—21no—
67#102×C43—21no—
68#102×C43—21no—
69#102×C43—21no—
70C4×C8×C43D411yescharacteristic
71C4×C8×C43D411yescharacteristic
72C4×C8×C43D411yescharacteristic
73C4×C8×C43D411yescharacteristic
74C24×C43—21no—
75C2×Q8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—41no—
78C2×Q8×C43—41no—
79C2×D4×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—41no—
82C2×D4×C43—41no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43C22×C411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C2×C8×C43C22⋊C411yescharacteristic
92C2×C8×C43C22⋊C411yescharacteristic
93C2×C8×C43C22⋊C411yescharacteristic
94C2×C8×C43C22⋊C411yescharacteristic
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C42×C43C2×D411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43C2×D411yescharacteristic
110C42×C43#4111yescharacteristic
111#10621877—42no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—22no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C23×C43—41no—
117C23×C43—42no—
118C23×C43—81no—
119C23×C43—81no—
120C23×C43C4×D411yescharacteristic
121Q8×C43—41no—
122Q8×C43—41no—
123Q8×C43—81no—
124D4×C43—41no—
125D4×C43—41no—
126D4×C43—81no—
127C2×C4×C43—22no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43C2×C22⋊C411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#12411yescharacteristic
142C2×C4×C43#12711yescharacteristic
143C8×C43—21no—
144C8×C43—21no—
145C8×C43—21no—
146C8×C43—21no—
147C43⋊C8—42no—
148C43⋊C8—42no—
149C43⋊C8—81no—
150C43⋊C8—81no—
151#9790—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—81no—
155C22×C43—81no—
156C22×C43—81no—
157C22×C43—162no—
158C22×C43#39011yescharacteristic
159C22×C43#44412yes—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—81no—
166C4×C43—81no—
167C4×C43—81no—
168C4×C43#41311yescharacteristic
169C4×C43#41311yescharacteristic
170C2×#488D4311yescharacteristic
171#1568—431no—
172#1528—431no—
173#1527—431no—
174#1470—431no—
175#1469—431no—
176#1451—431no—
177C2×C43—22no—
178C2×C43—161no—
179C2×C43#196711yescharacteristic
180C2×C43#197511yescharacteristic
181C2×C43#197611yescharacteristic
182C2×#125C2×D4311yescharacteristic
183C2×#124C2×D4311yescharacteristic
184#488—21no—
185#488—21no—
186#488—21no—
187#488—21no—
188#432—431no—
189#432—431no—
190#431—431no—
191C2×#103Dic4311yescharacteristic
192C2×#103Dic4311yescharacteristic
193C2×#102Dic4311yescharacteristic
194C2×#102Dic4311yescharacteristic
195C4×M16—431no—
196C2×C4×C8C2×D4311yescharacteristic
197#335—861no—
198#334—861no—
199#330—862no—
200#329—862no—
201#324—862no—
202#323—862no—
203#322—861no—
204#322—861no—
205C43#979011yescharacteristic, complemented, Sylow
206C22×Q8C2×Dic4311yescharacteristic
207C22×D4C2×Dic4311yescharacteristic
208C2×M16—861no—
209C22×C8C2×Dic4311yescharacteristic
210C22×C8C2×Dic4311yescharacteristic
211#125—21no—
212#125—21no—
213#125—21no—
214#125—21no—
215#124—21no—
216#124—21no—
217#124—21no—
218#124—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×Dic4311yescharacteristic
222C2×C4⋊C4C2×Dic4311yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C42C22×D4311yescharacteristic
226C4⋊C8—861no—
227C4⋊C8—861no—
228C4⋊C8—861no—
229#103—21no—
230#103—21no—
231#103—21no—
232#103—21no—
233#102—21no—
234#102—21no—
235#102—21no—
236#102—21no—
237C22⋊C8—432no—
238C22⋊C8—861no—
239C22⋊C8—861no—
240#97—432no—
241#97—861no—
242#97—861no—
243C4×C8—861no—
244C4×C8—861no—
245C4×C8C22⋊D4311yescharacteristic
246C4×C8C22⋊D4311yescharacteristic
247C4×C8C22⋊D4311yescharacteristic
248C4×C8C22⋊D4311yescharacteristic
249C24—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—41no—
257C2×D4—41no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4D4×D4311yescharacteristic
262C22×C4#1062190011yescharacteristic
263C22×C4C22×Dic4311yescharacteristic
264M16—1722no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—862no—
268C2×C8—862no—
269C2×C8—1721no—
270C2×C8—1721no—
271C2×C8C22⋊Dic4311yescharacteristic
272C2×C8C22⋊Dic4311yescharacteristic
273C2×C8C22⋊Dic4311yescharacteristic
274C2×C8C22⋊Dic4311yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42D4×D4311yescharacteristic
288C42#1062190011yescharacteristic
289C42C2×C22⋊D4311yescharacteristic
290C42C2×C22⋊D4311yescharacteristic
291C23—41no—
292C23—42no—
293C23—81no—
294C23—81no—
295C23D4×Dic4311yescharacteristic
296Q8—41no—
297Q8—41no—
298Q8—81no—
299D4—41no—
300D4—41no—
301D4—81no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4C2×C22⋊Dic4311yescharacteristic
313C2×C4D4×Dic4311yescharacteristic
314C2×C4#1306329611yescharacteristic
315C2×C4#1306329611yescharacteristic
316C2×C4#1306331211yescharacteristic
317C2×C4#1306332111yescharacteristic
318C8—21no—
319C8—21no—
320C8—21no—
321C8—21no—
322C8—3441no—
323C8—3441no—
324C8—1722no—
325C8—1722no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—162no—
332C22#1458280211yescharacteristic
333C22#1458302112yes—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4#1458288311yescharacteristic
343C4#1458288311yescharacteristic
344C2—22no—
345C2—161no—
346C2#1913544511yescharacteristic
347C2#1913548911yescharacteristic
348C2#1913549411yescharacteristic
subgroupG/H
centerC22#14582802
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#488C2
socleC22×C43#390
prime radicalC22×D4×C43C2×C4
cosocleC2×C42×C43C23
hypercenterC2×#488D43
hypocenterC43#9790
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. #19133358C2semidirect
2. #19133197C2semidirect
4. #19132951C2semidirect
6. #19132884C2semidirect
205. C43#9790semidirect

Maximal subgroups

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

subgroupindex
#191333582
#191331972
#191331932
#191329512
#191329472
#191328842
C2×C43×#4882
#979043