Finite Group Databasebeta

← #25105125

Subgroups — #25105125

Order 11008.

1014 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583277C211yesmaximal, characteristic
2C2×#14583003C212yesmaximal
3C2×Q16×Dic43C211yesmaximal, characteristic
4C2×#14582993C211yesmaximal, characteristic
5#19137313C212yesmaximal
6#19135465C212yesmaximal
7#19135456C211yesmaximal, characteristic
8#19135413C212yesmaximal
9#19134758C211yesmaximal, characteristic
10#19134281C211yesmaximal, characteristic
11C43×#1969C211yesmaximal, characteristic
12C22×Dic172C2211yescharacteristic
13C22×#10621885C2212yes—
14C2×#13063323C2212yes—
15C2×Q8×Dic43C2212yes—
16C2×#13063290C2212yes—
17#14583277C418yescomplemented
18#14583003—28no—
19Q16×Dic43—24no—
20#14582993—24no—
21C2×#13063259C2211yescharacteristic
22C2×#13063256C2212yes—
23C2×#13063250C2212yes—
24C2×#13063249C2212yes—
25C2×#13063248C2212yes—
26C2×#13063236C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582805C2212yes—
32#14582786—24no—
33#14582781—24no—
34#14582764C2212yes—
35#14582745C2211yescharacteristic
36C22×Q16×C43C2211yescharacteristic
37C2×#107×C43C2211yescharacteristic
38C2×#103×C43C2212yes—
39C2×C4×C8×C43C2211yescharacteristic
40C43×#391C2212yes—
41C22×Dic86C2312yes—
42C2×Dic172—22no—
43C2×Dic172—22no—
44C2×Dic172C2×C414yes—
45C2×#10621885—24no—
46C2×#10621885—24no—
47C2×#10621885C2×C418yes—
48C22×C43⋊C8C2311yescharacteristic
49C22×C43⋊C8C2311yescharacteristic
50#13063323—24no—
51#13063323C2×C418yes—
52Q8×Dic43—24no—
53Q8×Dic43—24no—
54#13063290—24no—
55#13063290—24no—
56C2×C4⋊Dic43—22no—
57C2×C4⋊Dic43C2312yes—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—22no—
60C2×C4×Dic43—22no—
61C2×C4×Dic43—22no—
62C2×C4×Dic43C2311yescharacteristic
63C2×C4×Dic43C2311yescharacteristic
64#13063259—22no—
65#13063256—24no—
66#13063250—24no—
67#13063249—24no—
68#13063248—24no—
69#13063236—22no—
70#13063235—22no—
71#13063235D414yes—
72C8×Dic43C2×C414yes—
73C8×Dic43D414yes—
74C43⋊#95—24no—
75C43⋊#95—24no—
76C43⋊#95D412yes—
77C43⋊#95D412yes—
78C22×Q8×C43C2312yes—
79C2×Q16×C43—22no—
80C2×Q16×C43—22no—
81C2×Q16×C43C2×C414yes—
82C22×C8×C43C2311yescharacteristic
83C22×C8×C43C2311yescharacteristic
84C2×C4⋊C4×C43C2312yes—
85C2×C42×C43C2311yescharacteristic
86#107×C43—22no—
87#103×C43—24no—
88C4×C8×C43—22no—
89#95×C43—24no—
90C2×Q8×C43—22no—
91C2×Q8×C43—22no—
92C2×Q8×C43—22no—
93C2×Q8×C43—22no—
94C2×Q8×C43—22no—
95C2×Q8×C43C22×C414yes—
96C22×C4×C43—22no—
97C22×C4×C43—22no—
98C22×C4×C43C2×D412yes—
99C22×C4×C43C2411yescharacteristic
100C22×Dic43—22no—
101C22×Dic43—22no—
102C22×Dic43C2×D412yes—
103C22×Dic43C2×D411yescharacteristic
104C22×Dic43C2×D411yescharacteristic
105C2×Dic86—22no—
106C2×Dic86—22no—
107C2×Dic86—22no—
108C2×Dic86—22no—
109C2×Dic86—22no—
110C2×Dic86C22×C414yes—
111Q16×C43—28no—
112C2×C8×C43—21no—
113C2×C8×C43—21no—
114C2×C8×C43C22×C412yes—
115C2×C8×C43C2×D412yes—
116C2×C8×C43C2×D412yes—
117C2×C8×C43#4112yes—
118C4⋊C4×C43—22no—
119C4⋊C4×C43—22no—
120C42×C43—21no—
121C42×C43—21no—
122#10621885—216no—
123C4⋊Dic43—22no—
124C4⋊Dic43—22no—
125C4⋊Dic43—44no—
126Dic43⋊C4—216no—
127Dic43⋊C4—44no—
128C4×Dic43—44no—
129C4×Dic43—44no—
130C4×Dic43C22×C412yes—
131C4×Dic43C2×D412yes—
132C4×Dic43C2×D412yes—
133C4×Dic43#4112yes—
134C2×C43⋊C8—21no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8C22×C412yes—
137C2×C43⋊C8C2×D412yes—
138C2×C43⋊C8C2×D412yes—
139C2×C43⋊C8#4112yes—
140Dic172—28no—
141C23×C43C22×D411yescharacteristic
142Q8×C43—24no—
143Q8×C43—24no—
144Q8×C43—42no—
145Q8×C43—42no—
146C2×C4×C43—24no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—22no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—42no—
153C2×C4×C43—44no—
154C2×C4×C43C23×C411yescharacteristic
155C2×C4×C43C22×D411yescharacteristic
156C2×C4×C43C22×D411yescharacteristic
157C2×C4×C43C2×#4111yescharacteristic
158C2×C4×C43C2×#4111yescharacteristic
159C2×C4×C43C2×#4111yescharacteristic
160C2×Dic43—22no—
161C2×Dic43—22no—
162C2×Dic43—22no—
163C2×Dic43—22no—
164C2×Dic43—24no—
165C2×Dic43—42no—
166C2×Dic43—42no—
167C2×Dic43—42no—
168C2×Dic43—44no—
169C2×Dic43C4×D414yes—
170C2×Dic43#12712yes—
171C2×Dic43#12712yes—
172Dic86—24no—
173Dic86—24no—
174Dic86—42no—
175Dic86—42no—
176C8×C43—22no—
177C8×C43C4×D414yes—
178C43⋊C8—22no—
179C43⋊C8C4×D414yes—
180#21698—431nomaximal, Sylow
181C22×C43C2×C4×D411yescharacteristic
182C22×C43C2×#12711yescharacteristic
183C22×C43#53211yescharacteristic
184C22×C43#57812yes—
185C22×C43#57812yes—
186C4×C43—44no—
187C4×C43—42no—
188C4×C43—82no—
189C4×C43C2×C4×D411yescharacteristic
190C4×C43C2×C4×D411yescharacteristic
191C4×C43#53211yescharacteristic
192C4×C43#53211yescharacteristic
193Dic43—22no—
194Dic43—22no—
195Dic43—24no—
196Dic43—44no—
197Dic43—82no—
198C2×#494—431no—
199C2×#441—432no—
200C2×C4×Q16—431no—
201C2×C4×Q16—431no—
202#2327—432no—
203#1971—432no—
204#1969—431no—
205#1969D4311yescharacteristic
206#1960—432no—
207#1846—431no—
208#1726—431no—
209C2×C43C4×#12711yescharacteristic
210C2×C43#295012yes—
211C2×C43#315611yescharacteristic
212C2×C43#315611yescharacteristic
213C2×C43#317712yes—
214C22×Q16—432no—
215C22×Q16—431no—
216C22×Q16C2×D4311yescharacteristic
217C2×C4⋊Q8—432no—
218C2×C4×Q8—432no—
219C2×C4×Q8—432no—
220#494—438no—
221#441—868no—
222C4×Q16—864no—
223C4×Q16—864no—
224C2×#107—431no—
225C2×#107C2×D4311yescharacteristic
226C2×#106—432no—
227C2×#103—432no—
228C2×#103—432no—
229C2×#103—432no—
230C2×#103C2×D4312yes—
231C2×#97—431no—
232C2×#97—431no—
233C2×#97—431no—
234C2×C4×C8—431no—
235C2×C4×C8—431no—
236C2×C4×C8C2×D4311yescharacteristic
237#391—432no—
238#391C2×D4312yes—
239#387—864no—
240#387—864no—
241#382—432no—
242#376—431no—
243C43#2169811yescharacteristic, complemented, Sylow
244C22×Q8—432no—
245C22×Q8C22×D4312yes—
246C2×Q16—22no—
247C2×Q16—22no—
248C2×Q16—438no—
249C2×Q16—434no—
250C2×Q16—864no—
251C2×Q16—864no—
252C2×Q16—862no—
253C2×Q16—862no—
254C2×Q16C4×D4314yes—
255C22×C8—431no—
256C22×C8—431no—
257C22×C8C22×D4311yescharacteristic
258C22×C8C22×D4311yescharacteristic
259C4⋊Q8—438no—
260C4⋊Q8—864no—
261C4×Q8—864no—
262C4×Q8—864no—
263C4×Q8—864no—
264C4×Q8—864no—
265C2×C4⋊C4—432no—
266C2×C4⋊C4—864no—
267C2×C4⋊C4—862no—
268C2×C4⋊C4—862no—
269C2×C4⋊C4C22×D4312yes—
270C2×C42—431no—
271C2×C42—431no—
272C2×C42—862no—
273C2×C42—862no—
274C2×C42C22×D4311yescharacteristic
275#107—22no—
276#107—862no—
277#106—864no—
278#103—24no—
279#103—864no—
280#103—864no—
281#103—864no—
282#97—434no—
283#97—862no—
284#97—862no—
285C4×C8—22no—
286C4×C8—434no—
287C4×C8—434no—
288#95—24no—
289#95—432no—
290#95—432no—
291#95—864no—
292#95—864no—
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—434no—
299C2×Q8—862no—
300C2×Q8—862no—
301C2×Q8—862no—
302C2×Q8—862no—
303C2×Q8—862no—
304C2×Q8C2×C4×D4314yes—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—432no—
308C22×C4—431no—
309C22×C4—431no—
310C22×C4—862no—
311C22×C4—862no—
312C22×C4D4×D4312yes—
313C22×C4C23×D4311yescharacteristic
314Q16—28no—
315Q16—8616no—
316Q16—868no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—432no—
320C2×C8—432no—
321C2×C8—432no—
322C2×C8—432no—
323C2×C8—861no—
324C2×C8—861no—
325C2×C8C2×C4×D4312yes—
326C2×C8D4×D4312yes—
327C2×C8D4×D4312yes—
328C2×C8#1062190012yes—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—8616no—
332C4⋊C4—862no—
333C4⋊C4—862no—
334C4⋊C4—1724no—
335C4⋊C4—1724no—
336C42—21no—
337C42—21no—
338C42—432no—
339C42—432no—
340C42—432no—
341C42—432no—
342C42—1724no—
343C42—1724no—
344C23C2×D4×D4311yescharacteristic
345Q8—24no—
346Q8—24no—
347Q8—42no—
348Q8—42no—
349Q8—864no—
350Q8—864no—
351Q8—1722no—
352Q8—1722no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—434no—
362C2×C4—432no—
363C2×C4—432no—
364C2×C4—862no—
365C2×C4—862no—
366C2×C4—862no—
367C2×C4—862no—
368C2×C4—864no—
369C2×C4—1722no—
370C2×C4—1724no—
371C2×C4—1722no—
372C2×C4—1722no—
373C2×C4C22×C4×D4311yescharacteristic
374C2×C4C2×D4×D4311yescharacteristic
375C2×C4C2×D4×D4311yescharacteristic
376C2×C4#41×D4311yescharacteristic
377C2×C4#41×D4311yescharacteristic
378C2×C4C2×#1062190011yescharacteristic
379C8—22no—
380C8—434no—
381C8—862no—
382C8(C22⋊D43)⋊C414yes—
383C22C4×D4×D4311yescharacteristic
384C22#127×D4311yescharacteristic
385C22#1458344411yescharacteristic
386C22#1458371212yes—
387C22#1458371312yes—
388C4—42no—
389C4—44no—
390C4—82no—
391C4—864no—
392C4—862no—
393C4—862no—
394C4—3442no—
395C4—1724no—
396C4C4×D4×D4311yescharacteristic
397C4C2×(C22⋊D43)⋊C411yescharacteristic
398C4#1458344411yescharacteristic
399C4#1458344811yescharacteristic
400C2#1913715911yescharacteristic
401C2#1914345812yes—
402C2#1914508311yescharacteristic
403C2#1914508511yescharacteristic
404C2#1914524712yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1969C2
socle, prime radicalC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenter#1969D43
hypocenterC43#21698
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1969

Complements

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

NH ≅ G/Ntype
17. #14583277C4semidirect
243. C43#21698semidirect

Maximal subgroups

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

subgroupindex
C2×#145832772
C2×#145830032
C2×Q16×Dic432
C2×#145829932
#191373132
#191354652
#191354562
#191354132
#191347582
#191342812
C43×#19692
#2169843