Finite Group Databasebeta

← #24990965

Subgroups — #24990965

Order 11008.

412 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#19135565C211yesmaximal, characteristic
2#19134764C211yesmaximal, characteristic
3#19134728C211yesmaximal, characteristic
4C2×#14582641C211yesmaximal, characteristic
5#19132476C211yesmaximal, characteristic
6#19132476C211yesmaximal, characteristic
7C43×#2382C211yesmaximal, characteristic
8C2×#13063258—21no—
9C2×#13063256—21no—
10C2×#13063236C2211yescharacteristic
11C2×#13063236C2211yescharacteristic
12C2×#13063236C2211yescharacteristic
13#14582769C2211yescharacteristic
14#14582661—21no—
15#14582661—21no—
16#14582661—21no—
17#14582661—21no—
18#14582641C414yescomplemented
19C2×#125×C43C2211yescharacteristic
20C43×#389—21no—
21C43×#389—21no—
22C43×#387—21no—
23C43×#387—21no—
24C43×#387—21no—
25C43×#387—21no—
26C43×#382C2211yescharacteristic
27C43×#382C2211yescharacteristic
28C22×C43⋊C8—21no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34#13063258—42no—
35#13063256—42no—
36#13063236—21no—
37#13063236—21no—
38#13063236—21no—
39#13063236—21no—
40#13063236C2×C412yes—
41#13063236C2×C412yes—
42#125×C43—21no—
43#125×C43—21no—
44#125×C43C2×C412yes—
45#125×C43Q812yes—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C42×C43—21no—
57C2×C42×C43—21no—
58C2×C42×C43C2311yescharacteristic
59#95×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62#95×C43—21no—
63#95×C43—21no—
64#95×C43—21no—
65#95×C43—21no—
66#95×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—41no—
77C4⋊C4×C43—22no—
78C4⋊C4×C43—22no—
79C4⋊C4×C43—22no—
80C4⋊C4×C43—22no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—81no—
88C4⋊C4×C43—81no—
89C4⋊C4×C43C4⋊C412yes—
90C4⋊C4×C43C4⋊C412yes—
91C42×C43—81no—
92C42×C43—81no—
93C42×C43C22×C411yescharacteristic
94C42×C43C2×Q811yescharacteristic
95C42×C43#4111yescharacteristic
96C42×C43#4111yescharacteristic
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99C4⋊Dic43—42no—
100C4⋊Dic43—42no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—22no—
104C2×C43⋊C8—22no—
105C2×C43⋊C8—22no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C23×C43#12011yescharacteristic
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43C2×C4⋊C411yescharacteristic
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43C22⋊Q811yescharacteristic
139C2×C4×C43C22⋊Q811yescharacteristic
140C2×C4×C43#12311yescharacteristic
141C2×Dic43—81no—
142C2×Dic43—81no—
143C2×Dic43—81no—
144C43⋊C8—24no—
145C43⋊C8—42no—
146C43⋊C8—42no—
147#8912—431nomaximal, Sylow
148C22×C43#38511yescharacteristic
149C22×C43#45311yescharacteristic
150C22×C43#45411yescharacteristic
151C22×C43#45411yescharacteristic
152C22×C43#45511yescharacteristic
153C22×C43#45611yescharacteristic
154C22×C43#45611yescharacteristic
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—42no—
162C4×C43—42no—
163C4×C43—81no—
164C4×C43—81no—
165C4×C43—81no—
166C4×C43—81no—
167Dic43—161no—
168#2382D4311yescharacteristic
169#1992—431no—
170#1847—431no—
171#1836—431no—
172C2×#330—431no—
173#1295—431no—
174#1295—431no—
175C2×C43#165711yescharacteristic
176C2×C43#166111yescharacteristic
177C2×C43#166311yescharacteristic
178C2×C43#166411yescharacteristic
179C2×C43#185711yescharacteristic
180C2×C43#185911yescharacteristic
181C2×C43#186011yescharacteristic
182C2×#125C2×D4311yescharacteristic
183C2×#107—861no—
184C2×#106—861no—
185C2×#97—431no—
186C2×#97—431no—
187C2×#97—431no—
188#389—21no—
189#389—21no—
190#387—21no—
191#387—21no—
192#387—21no—
193#387—21no—
194#384—431no—
195#382C2×D4311yescharacteristic
196#382C2×D4311yescharacteristic
197#340—861no—
198#340—861no—
199#340—861no—
200#340—861no—
201#330—434no—
202C43#891211yescharacteristic, complemented, Sylow
203C22×C8—861no—
204C22×C8—861no—
205C22×C8—861no—
206#125—21no—
207#125—21no—
208#125Dic8612yes—
209#125C4×D4312yes—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4—861no—
217C2×C4⋊C4C22⋊D4311yescharacteristic
218C2×C4⋊C4C22⋊D4311yescharacteristic
219C2×C4⋊C4C22⋊D4311yescharacteristic
220C2×C4⋊C4C22⋊D4311yescharacteristic
221C2×C4⋊C4C22⋊D4311yescharacteristic
222C2×C4⋊C4C22⋊D4311yescharacteristic
223C2×C42—21no—
224C2×C42—21no—
225C2×C42C22×D4311yescharacteristic
226#107—1722no—
227#106—1722no—
228#97—432no—
229#97—432no—
230#97—861no—
231#97—861no—
232#97—861no—
233#97—861no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—1721no—
249C22×C4C2×C22⋊D4311yescharacteristic
250C22×C4C2×C22⋊D4311yescharacteristic
251C22×C4C2×C22⋊D4311yescharacteristic
252C2×C8—862no—
253C2×C8—862no—
254C2×C8—862no—
255C2×C8—862no—
256C2×C8—862no—
257C2×C8—1721no—
258C2×C8—1721no—
259C2×C8—1721no—
260C2×C8—1721no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C4⋊C4—1722no—
276C4⋊C4—1722no—
277C4⋊C4Dic43⋊C412yes—
278C4⋊C4Dic43⋊C412yes—
279C42—81no—
280C42—81no—
281C42C2×Dic8611yescharacteristic
282C42C2×C4×D4311yescharacteristic
283C42#1062189811yescharacteristic
284C42#1062189811yescharacteristic
285C23#1306329411yescharacteristic
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—3441no—
311C2×C4—3441no—
312C2×C4—3441no—
313C2×C4C2×Dic43⋊C411yescharacteristic
314C2×C4C4×C22⋊D4311yescharacteristic
315C2×C4C4×C22⋊D4311yescharacteristic
316C2×C4#1306330411yescharacteristic
317C2×C4#1306330411yescharacteristic
318C2×C4#1306330811yescharacteristic
319C8—864no—
320C8—1722no—
321C8—1722no—
322C22#1458277211yescharacteristic
323C22#1458306711yescharacteristic
324C22#1458307211yescharacteristic
325C22#1458307211yescharacteristic
326C22#1458307711yescharacteristic
327C22#1458308211yescharacteristic
328C22#1458308211yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—42no—
336C4—42no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—6881no—
342C2#1913389311yescharacteristic
343C2#1913391211yescharacteristic
344C2#1913392311yescharacteristic
345C2#1913392911yescharacteristic
346C2#1913481011yescharacteristic
347C2#1913482111yescharacteristic
348C2#1913482811yescharacteristic
subgroupG/H
centerC23#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2382C2
socle, prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#2382D43
hypocenterC43#8912
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2382

Complements

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

NH ≅ G/Ntype
18. #14582641C4semidirect
202. C43#8912semidirect

Maximal subgroups

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

subgroupindex
#191355652
#191347642
#191347282
C2×#145826412
#191324762
C43×#23822
#891243