Finite Group Databasebeta

← #25079798

Subgroups — #25079798

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145739C211yesmaximal, characteristic, complemented
2#19145538C211yesmaximal, characteristic
3C2×#14583273C211yesmaximal, characteristic
4#19143525C211yesmaximal, characteristic, complemented
5#19134070C214yesmaximal, complemented
6#19133946C214yesmaximal, complemented
7#19133341C211yesmaximal, characteristic, complemented
8#19133264C211yesmaximal, characteristic
9C43×#1546C211yesmaximal, characteristic, complemented
10C22×#10621884—21no—
11C22×#10621884—21no—
12#14583456C2211yescharacteristic
13C2×#13063322C2211yescharacteristic
14#14583295—21no—
15#14583273—21no—
16#14583273—21no—
17#14583273C2212yes—
18#14583273C2212yes—
19#14583272—21no—
20#14583251—21no—
21#14583246—21no—
22#14583229—22no—
23#14583181C2214yescomplemented
24#14583100C2214yes—
25#14583052—22no—
26#14583026—21no—
27#14583026C2212yescomplemented
28#14583023—21no—
29#14583023C2212yescomplemented
30#14582952C2211yescharacteristic
31#14582927—21no—
32#14582857—21no—
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582651C2212yescomplemented
35#14582649C2212yescomplemented
36#14582642C2214yes—
37C2×C4⋊Q8×C43C2211yescharacteristic
38C43×#431C2211yescharacteristic
39C43×#423C2211yescharacteristic
40C43×#332C2214yescomplemented
41C22×D172—21no—
42C22×D172—21no—
43C22×D172—21no—
44C2×#10621873—24no—
45C2×#10621884—22no—
46C2×#10621884—22no—
47C2×#10621884—22no—
48C2×#10621884—22no—
49C2×#10621884—44no—
50C2×#10621884—44no—
51C22×C43⋊C8D411yescharacteristic
52C22×C43⋊C8D411yescharacteristic
53#13063325D411yescharacteristic
54#13063325D411yescharacteristic
55#13063322—21no—
56#13063322—21no—
57#13063322—21no—
58#13063322C2312yes—
59#13063317—21no—
60#13063304—21no—
61#13063304D412yes—
62C4×Dic86—21no—
63C4×Dic86C2312yes—
64#13063284—21no—
65#13063256—24no—
66C4⋊(C43⋊C8)C2312yes—
67Dic43⋊C8—22no—
68Dic43⋊C8—22no—
69#13063248—24no—
70#13063247—24no—
71C22⋊(C43⋊C8)—21no—
72#13063235—22no—
73C4×C43⋊C8—21no—
74C4×C43⋊C8D411yescharacteristic
75C4×C43⋊C8D411yescharacteristic
76C4×C43⋊C8C2311yescharacteristic
77C4×C43⋊C8C2311yescharacteristic
78C8×Dic43—22no—
79C22×Q8×C43—21no—
80C2×M16×C43—21no—
81C4⋊Q8×C43—21no—
82C4⋊Q8×C43—21no—
83C4⋊Q8×C43—21no—
84C4⋊Q8×C43C2312yes—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C42×C43C2311yescharacteristic
88C4⋊C8×C43—21no—
89C4⋊C8×C43C2312yes—
90C4⋊C8×C43C2312yes—
91C22⋊C8×C43—21no—
92C4×C8×C43—21no—
93C23×D43—41no—
94C2×Q8×C43—22no—
95C2×Q8×C43—41no—
96C2×Q8×C43—42no—
97C2×Q8×C43—42no—
98C22×C4×C43—41no—
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43#4111yescharacteristic
102C2×D172—22no—
103C2×D172—22no—
104C2×D172—22no—
105C2×D172—41no—
106C2×D172—41no—
107C2×D172—41no—
108C2×D172—42no—
109C2×D172—42no—
110C2×D172—82no—
111C2×D172—82no—
112C2×Dic86—21no—
113C2×Dic86C2×D412yes—
114M16×C43—42no—
115C2×C8×C43—22no—
116C2×C8×C43—22no—
117C4⋊C4×C43—22no—
118C4⋊C4×C43—22no—
119C4⋊C4×C43—41no—
120C4⋊C4×C43—41no—
121C42×C43C2×D411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43#4111yescharacteristic
124C42×C43C2411yescharacteristic
125C22⋊Dic43—22no—
126#10621884—44no—
127#10621884—44no—
128#10621884—44no—
129#10621884—44no—
130C4⋊Dic43—21no—
131C4⋊Dic43—21no—
132C4⋊Dic43—21no—
133C4⋊Dic43C2×D412yes—
134Dic43⋊C4—22no—
135Dic43⋊C4—22no—
136C4×Dic43—22no—
137C2×C43⋊C8—22no—
138C2×C43⋊C8—22no—
139C2×C43⋊C8SD1614yescomplemented
140C2×C43⋊C8C2×D411yescharacteristic
141C2×C43⋊C8C2×D411yescharacteristic
142C2×C43⋊C8C2×D411yescharacteristic
143C2×C43⋊C8C2×D411yescharacteristic
144#10621873—84no—
145C23×C43#12111yescharacteristic
146C22×D43—42no—
147C22×D43—82no—
148C22×D43—82no—
149C22×D43—82no—
150Q8×C43—42no—
151Q8×C43—42no—
152Q8×C43—82no—
153C2×C4×C43—22no—
154C2×C4×C43—22no—
155C2×C4×C43—42no—
156C2×C4×C43—82no—
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43C2×SD1612yes—
161C2×C4×C43AGL(1,ℤ/8)12yes—
162C2×C4×C43C22×D411yescharacteristic
163C2×C4×C43C22×D411yescharacteristic
164C2×C4×C43C2×#4111yescharacteristic
165C2×Dic43—22no—
166C2×Dic43—22no—
167D172—42no—
168D172—42no—
169D172—44no—
170D172—82no—
171D172—82no—
172D172—82no—
173D172—82no—
174Dic86—24no—
175Dic86—42no—
176C8×C43—42no—
177C8×C43—42no—
178C43⋊C8—21no—
179C43⋊C8—21no—
180C43⋊C8—42no—
181C43⋊C8C2×SD1612yes—
182C43⋊C8C2×SD1612yes—
183#19202—431nomaximal, Sylow
184C22×C43—21no—
185C22×C43—21no—
186C22×C43#46012yes—
187C22×C43C2×#12111yescharacteristic
188C2×D43—82no—
189C2×D43—82no—
190C2×D43—82no—
191C2×D43—164no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—82no—
195C4×C43#46012yes—
196C4×C43#47112yes—
197C4×C43C22×SD1611yescharacteristic
198C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
199C4×C43#57712yes—
200Dic43—42no—
201Dic43—42no—
202#3229—431no—
203#3208—431no—
204C2×#492—431no—
205#2960—431no—
206#1686—434no—
207#1666—434no—
208#1564—431no—
209#1546D4311yescharacteristic, complemented
210#1545—431no—
211C2×C43—22no—
212C2×C43C2×#46011yescharacteristic
213C2×C43#305711yescharacteristic
214C2×C43C2×#47111yescharacteristic
215D43—162no—
216C22×SD16—861no—
217C22×SD16—861no—
218#533—431no—
219C2×C4⋊Q8C2×D4311yescharacteristic
220C2×#127—431no—
221#498—861no—
222#492—432no—
223#492—432no—
224#492—861no—
225#492—861no—
226#492—861no—
227#487—861no—
228#486—861no—
229#483—862no—
230#475—434no—
231#460—434no—
232#450—862no—
233#446—432no—
234#446—861no—
235C8×Q8—432no—
236C8×Q8—861no—
237#431—431no—
238#431C2×D4311yescharacteristic
239#424—861no—
240#423C2×D4311yescharacteristic
241#405—861no—
242C2×C4×C8—431no—
243#335—432no—
244#334—432no—
245#332C2×D4314yescomplemented
246#331—434no—
247C43#1920211yescharacteristic, complemented, Sylow
248C22×Q8—21no—
249C22×D4—861no—
250C22×D4—861no—
251C22×D4—861no—
252C2×SD16—864no—
253C2×SD16—862no—
254C2×SD16—862no—
255C2×SD16—862no—
256C2×SD16—862no—
257C2×SD16—1724no—
258C2×SD16—1724no—
259C2×M16—21no—
260C22×C8—431no—
261C22×C8—431no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—431no—
266C4⋊Q8—431no—
267C4⋊Q8C22×D4312yes—
268#127—432no—
269#127—861no—
270#127—861no—
271#127—861no—
272#125—861no—
273C22⋊Q8—432no—
274C22⋊Q8—861no—
275C4×Q8—432no—
276C4×Q8—861no—
277#117—861no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C42C22×D4311yescharacteristic
281#106—864no—
282C4⋊C8—21no—
283C4⋊C8—432no—
284C4⋊C8—862no—
285C4⋊C8—862no—
286C4⋊C8C22×D4312yes—
287C4⋊C8C22×D4312yes—
288#103—864no—
289#102—864no—
290C22⋊C8—21no—
291C22⋊C8—861no—
292#97—862no—
293C4×C8—21no—
294C4×C8—431no—
295C4×C8—431no—
296C4×C8—431no—
297C4×C8—431no—
298C4×C8—862no—
299C4×C8—861no—
300C24—1721no—
301C2×Q8—22no—
302C2×Q8—41no—
303C2×Q8—42no—
304C2×Q8—42no—
305C2×Q8—432no—
306C2×Q8—861no—
307C2×D4—862no—
308C2×D4—862no—
309C2×D4—862no—
310C2×D4—3442no—
311C2×D4—3442no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4—1721no—
315C2×D4—1722no—
316C2×D4—1722no—
317C22×C4—41no—
318C22×C4#1062189811yescharacteristic
319C22×C4D4×D4311yescharacteristic
320C22×C4D4×D4311yescharacteristic
321SD16—3444no—
322SD16—1724no—
323SD16—1724no—
324SD16—1724no—
325SD16—1724no—
326M16—42no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—434no—
330C2×C8—431no—
331C2×C8—431no—
332C2×C8—431no—
333C2×C8—431no—
334C2×C8—862no—
335C2×C8—862no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—432no—
341C4⋊C4—861no—
342C4⋊C4—861no—
343C4⋊C4—862no—
344C4⋊C4—861no—
345C4⋊C4—862no—
346C22⋊C4—862no—
347C42—862no—
348C42#1062189811yescharacteristic
349C42D4×D4311yescharacteristic
350C42D4×D4311yescharacteristic
351C42C23×D4311yescharacteristic
352C23—3442no—
353C23—3442no—
354C23—3442no—
355C23—1722no—
356C23#1306329811yescharacteristic
357Q8—42no—
358Q8—42no—
359Q8—82no—
360Q8—864no—
361Q8—1722no—
362D4—3442no—
363D4—3442no—
364D4—3442no—
365D4—3442no—
366D4—1722no—
367D4—1722no—
368D4—1724no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—42no—
372C2×C4—82no—
373C2×C4—862no—
374C2×C4—862no—
375C2×C4#1306329811yescharacteristic
376C2×C4#1306329811yescharacteristic
377C2×C4#1306329811yescharacteristic
378C2×C4SD16×D4312yes—
379C2×C4#1306334912yes—
380C2×C4C2×D4×D4311yescharacteristic
381C2×C4C2×D4×D4311yescharacteristic
382C2×C4C2×#1062189811yescharacteristic
383C8—42no—
384C8—42no—
385C8—432no—
386C8—432no—
387C8—861no—
388C8—861no—
389C8—1722no—
390C22—21no—
391C22—21no—
392C22—3442no—
393C22—3442no—
394C22—3442no—
395C22—6884no—
396C22#1458309812yes—
397C22C2×#1306329811yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—1722no—
402C4—1722no—
403C4#1458309812yes—
404C4#1458316512yes—
405C4C2×SD16×D4311yescharacteristic
406C4C2×#1306334911yescharacteristic
407C4#1458370812yes—
408C2—22no—
409C2—6882no—
410C2C2×#1458309811yescharacteristic
411C2#1914423711yescharacteristic
412C2C2×#1458316511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1546C2
socleC22×C43C2×#121
prime radicalC2×#13063322C22
hypercenter#1546D43
hypocenterC43#19202
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
1. #19145739C2semidirect
4. #19143525C2semidirect
5. #19134070C2semidirect
6. #19133946C2semidirect
7. #19133341C2semidirect
9. C43×#1546C2semidirect
23. #14583181C22semidirect
27. #14583026C22semidirect
29. #14583023C22semidirect
34. #14582651C22semidirect
35. #14582649C22semidirect
40. C43×#332C22semidirect
139. C2×C43⋊C8SD16semidirect
209. #1546D43semidirect
245. #332C2×D43semidirect
247. C43#19202semidirect

Maximal subgroups

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

subgroupindex
#191457392
#191455382
C2×#145832732
#191435252
#191340702
#191339462
#191333412
#191332642
C43×#15462
#1920243