Finite Group Databasebeta

← #25104581

Subgroups — #25104581

Order 11008.

858 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583256C211yesmaximal, characteristic
2#125×Dic43C211yesmaximal, characteristic, complemented
3#19137134C211yesmaximal, characteristic
4#19135406C211yesmaximal, characteristic
5#19135279C212yesmaximal
6#19135272C212yesmaximal, complemented
7#19134725C211yesmaximal, characteristic, complemented
8#19134414C212yesmaximal, complemented
9#19134409C212yesmaximal
10C4×C8×Dic43C211yesmaximal, characteristic, complemented
11C43×#1991C211yesmaximal, characteristic, complemented
12C2×#13063313C2211yescharacteristic
13C2×#13063290C2211yescharacteristic
14C2×#13063287C2211yescharacteristic
15#14583256C418yescomplemented
16C2×#13063250C2212yes—
17C2×#13063248C2212yes—
18C2×#13063247C2212yes—
19C2×#13063245C2212yes—
20C2×C4×C43⋊C8C2211yescharacteristic
21C2×C8×Dic43C2212yes—
22C2×C8×Dic43C2212yes—
23#14582804C2211yescharacteristic
24#14582800C2211yescharacteristic
25#14582798C2212yes—
26#14582788—22no—
27#14582785—22no—
28#14582765C2211yescharacteristic
29C4⋊C4×Dic43—22no—
30C4⋊C4×Dic43C2212yes—
31#14582746—22no—
32C42×Dic43C2211yescharacteristic
33#14582661C2212yes—
34#14582661C2212yes—
35C2×#125×C43C2211yescharacteristic
36C2×C4×C8×C43C2211yescharacteristic
37C43×#382C2211yescharacteristic
38C43×#340C2212yes—
39C43×#340C2212yes—
40C22×Dic86C2311yescharacteristic
41C22×D172C2311yescharacteristic
42C22×C4×D43—21no—
43C22×C43⋊C8C2312yes—
44#13063313—22no—
45#13063313C2×C414yes—
46#13063290—24no—
47#13063287—24no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43C2312yes—
50C2×Dic43⋊C4—21no—
51C2×(C2×D43)⋊C4—22no—
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—22no—
54C2×C4×Dic43—21no—
55C2×C4×Dic43—22no—
56C2×C4×Dic43D412yes—
57C2×C4×Dic43D412yes—
58C2×C4×Dic43C2311yescharacteristic
59C2×C4×Dic43C2311yescharacteristic
60#13063250—24no—
61#13063248C2×C418yescomplemented
62#13063247—24no—
63#13063245C2×C418yes—
64C4×C43⋊C8C2×C414yescomplemented
65C8×Dic43—24no—
66C8×Dic43—24no—
67C43⋊#95—22no—
68C43⋊#95—22no—
69C43⋊#95—22no—
70C43⋊#95—22no—
71C22×C8×C43C2312yes—
72#125×C43—22no—
73#125×C43C2×C414yescomplemented
74C2×C4⋊C4×C43—22no—
75C2×C4⋊C4×C43C2311yescharacteristic
76C2×C4⋊C4×C43C2311yescharacteristic
77C2×C4⋊C4×C43C2312yes—
78C2×C42×C43C2311yescharacteristic
79C4×C8×C43—22no—
80#95×C43—22no—
81C23×D43—21no—
82C22×C4×C43—22no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2411yescharacteristic
87C22×Dic43—21no—
88C22×Dic43—22no—
89C22×Dic43C2×D411yescharacteristic
90C22×Dic43C2×D412yes—
91C22×Dic43C2×D411yescharacteristic
92C2×D172—21no—
93C2×D172—22no—
94C2×D172—22no—
95C2×D172C22×C412yes—
96C2×C4×D43—42no—
97C2×C4×D43—44no—
98C2×Dic86—22no—
99C2×Dic86—22no—
100C2×Dic86—21no—
101C2×Dic86C22×C412yes—
102C2×C8×C43—22no—
103C2×C8×C43—22no—
104C2×C8×C43#4114yes—
105C4⋊C4×C43—28no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43C22×C414yes—
110C42×C43C22×C412yes—
111C42×C43#4112yes—
112(C2×D43)⋊C4—28no—
113(C2×D43)⋊C4—42no—
114(C2×D43)⋊C4—44no—
115C4⋊Dic43—22no—
116C4⋊Dic43—22no—
117C4⋊Dic43—44no—
118Dic43⋊C4—42no—
119C4×Dic43—22no—
120C4×Dic43—24no—
121C4×Dic43—24no—
122C4×Dic43—42no—
123C4×Dic43—44no—
124C4×Dic43#4114yes—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8C22×C414yes—
128C23×C43C22×D411yescharacteristic
129C22×D43—22no—
130C22×D43—41no—
131C22×D43—41no—
132C22×D43—42no—
133C22×D43—42no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—24no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43C4×D414yes—
144C2×C4×C43C23×C411yescharacteristic
145C2×C4×C43C2×#4112yes—
146C2×C4×C43C2×#4111yescharacteristic
147C2×C4×C43C2×#4112yes—
148C2×Dic43—22no—
149C2×Dic43—22no—
150C2×Dic43—22no—
151C2×Dic43—22no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43#12412yes—
158C2×Dic43#12412yes—
159C2×Dic43#13514yes—
160C2×Dic43#13514yes—
161D172—24no—
162D172—42no—
163C4×D43—84no—
164Dic86—24no—
165Dic86—42no—
166C8×C43—24no—
167C43⋊C8—24no—
168C4×#488—431nomaximal, Sylow
169C22×C43C2×C4×D411yescharacteristic
170C22×C43C2×#12411yescharacteristic
171C22×C43#53211yescharacteristic
172C22×C43C2×#13512yes—
173C22×C43C2×#13512yes—
174C2×D43—44no—
175C2×D43—42no—
176C2×D43—81no—
177C2×D43—81no—
178C2×D43—82no—
179C4×C43—24no—
180C4×C43—44no—
181C4×C43—81no—
182C4×C43—81no—
183C4×C43C4×#4112yes—
184C4×C43#52912yes—
185Dic43—22no—
186Dic43—24no—
187Dic43—42no—
188Dic43—82no—
189Dic43#48814yescomplemented
190C2×#488—431no—
191C4×#125—431no—
192C4×#124—431no—
193#1991D4311yescharacteristic, complemented
194#1958—431no—
195#1934—432no—
196#1933—432no—
197#1835—431no—
198C4×#103—432no—
199C4×#102—432no—
200C42×C8—431no—
201C2×C43C4×#12411yescharacteristic
202C2×C43C4×#13512yes—
203C2×C43C2×#48811yescharacteristic
204C2×C43#313111yescharacteristic
205C2×C43#316812yes—
206D43—82no—
207C2×#125C2×D4311yescharacteristic
208C2×#124—431no—
209C2×C4×Q8—431no—
210C2×C4×D4—431no—
211#488—438no—
212C2×#103—432no—
213C2×#103—432no—
214C2×#102—432no—
215C2×#102—432no—
216C2×C4×C8—431no—
217C2×C4×C8—432no—
218C2×C4×C8—432no—
219C2×C4×C8C2×D4311yescharacteristic
220#391—431no—
221#390—431no—
222#389—432no—
223#388—862no—
224#387—862no—
225#382—431no—
226#382C2×D4311yescharacteristic
227C4×C4⋊C4—432no—
228C4×C4⋊C4—862no—
229C4×C22⋊C4—862no—
230C43—431no—
231#340—432no—
232#340—432no—
233#340C2×D4312yes—
234#340C2×D4312yes—
235C43C4×#48811yescharacteristic, complemented, Sylow
236C22×Q8—431no—
237C22×D4—431no—
238C23×C4—861no—
239C22×C8—432no—
240C22×C8C22×D4312yes—
241#125—22no—
242#125C4×D4314yescomplemented
243#124—434no—
244#124—862no—
245C4×Q8—864no—
246C4×D4—864no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—432no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—862no—
251C2×C4⋊C4C22×D4311yescharacteristic
252C2×C4⋊C4C22×D4311yescharacteristic
253C2×C4⋊C4C22×D4312yes—
254C2×C22⋊C4—862no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—862no—
257C2×C42—431no—
258C2×C42—432no—
259C2×C42—432no—
260C2×C42—431no—
261C2×C42—861no—
262C2×C42—862no—
263C2×C42C22×D4311yescharacteristic
264#103—438no—
265#103—864no—
266#102—438no—
267#102—864no—
268C4×C8—22no—
269C4×C8—434no—
270C4×C8—864no—
271C4×C8—864no—
272#95—22no—
273#95—862no—
274#95—862no—
275#95—862no—
276#95—862no—
277C24—861no—
278C2×Q8—432no—
279C2×Q8—861no—
280C2×Q8—862no—
281C2×Q8—862no—
282C2×D4—432no—
283C2×D4—862no—
284C2×D4—861no—
285C2×D4—862no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—431no—
290C22×C4—431no—
291C22×C4—432no—
292C22×C4—861no—
293C22×C4—862no—
294C22×C4—1722no—
295C22×C4—1724no—
296C22×C4D4×D4312yes—
297C22×C4C23×D4311yescharacteristic
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—434no—
301C2×C8—862no—
302C2×C8—862no—
303C2×C8#1062190214yes—
304C4⋊C4—28no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—862no—
309C4⋊C4—862no—
310C4⋊C4—1722no—
311C4⋊C4—1724no—
312C4⋊C4C2×C4×D4314yes—
313C22⋊C4—868no—
314C22⋊C4—1722no—
315C22⋊C4—1724no—
316C42—434no—
317C42—864no—
318C42—864no—
319C42—862no—
320C42—1722no—
321C42—1724no—
322C42C2×C4×D4312yes—
323C42#1062190012yes—
324C23—862no—
325C23—1721no—
326C23—1722no—
327C23—1722no—
328C23—1721no—
329C23C2×D4×D4311yescharacteristic
330Q8—864no—
331Q8—1722no—
332D4—864no—
333D4—1722no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—432no—
344C2×C4—434no—
345C2×C4—432no—
346C2×C4—434no—
347C2×C4—862no—
348C2×C4—862no—
349C2×C4—862no—
350C2×C4—862no—
351C2×C4—3444no—
352C2×C4—1722no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4(C22⋊D43)⋊C414yes—
358C2×C4C22×C4×D4311yescharacteristic
359C2×C4#41×D4312yes—
360C2×C4C2×#1062190011yescharacteristic
361C2×C4C2×#1062190212yes—
362C8—24no—
363C8—864no—
364C22—3441no—
365C22—3442no—
366C22—3441no—
367C22—1722no—
368C22—1724no—
369C22C2×(C22⋊D43)⋊C411yescharacteristic
370C22#124×D4311yescharacteristic
371C22#1458345011yescharacteristic
372C22#135×D4312yes—
373C22#135×D4312yes—
374C4—24no—
375C4—44no—
376C4—81no—
377C4—81no—
378C4—434no—
379C4—864no—
380C4—862no—
381C4—3442no—
382C4—1722no—
383C4C4×#1062190212yes—
384C4#1458343512yes—
385C2—3442no—
386C2#1913713811yescharacteristic
387C2#1914336312yes—
388C2#488×D4311yescharacteristic
389C2#1914491611yescharacteristic
390C2#1914516712yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1991C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1991D43
hypocenterC43C4×#488
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1991

Complements

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

NH ≅ G/Ntype
2. #125×Dic43C2semidirect
6. #19135272C2semidirect
7. #19134725C2semidirect
8. #19134414C2semidirect
10. C4×C8×Dic43C2semidirect
11. C43×#1991C2semidirect
15. #14583256C4semidirect
61. #13063248C2×C4semidirect
64. C4×C43⋊C8C2×C4semidirect
73. #125×C43C2×C4semidirect
189. Dic43#488semidirect
193. #1991D43semidirect
235. C43C4×#488semidirect
242. #125C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832562
#125×Dic432
#191371342
#191354062
#191352792
#191352722
#191347252
#191344142
#191344092
C4×C8×Dic432
C43×#19912
C4×#48843