Finite Group Databasebeta

← #25302698

Subgroups — #25302698

Order 11008.

4086 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×#14583446C216yesmaximal, complemented
2#19142992C211yesmaximal, characteristic, complemented
3#19142989C211yesmaximal, characteristic, complemented
4#19142949C216yesmaximal, complemented
5#19142941C211yesmaximal, characteristic, complemented
6#19142939C216yesmaximal, complemented
7#19142937C211yesmaximal, characteristic, complemented
8C4×#13063322C211yesmaximal, characteristic, complemented
9C4×#13063321C216yesmaximal, complemented
10C43×D43C211yesmaximal, characteristic, complemented
11C4×#127×C43C211yesmaximal, characteristic, complemented
12C22×#10621898C2214yes—
13#14583446—248no—
14C2×#13063324C2216yes—
15C2×#13063322C2211yescharacteristic
16C2×#13063321C2216yes—
17C2×#13063321C2216yes—
18C2×#13063311C22112yes—
19C2×#13063300C2216yes—
20C2×#13063298C22112yes—
21C2×#13063296C2216yes—
22C2×C4×D172C2216yes—
23C2×C4×C22⋊D43C22112yes—
24C2×C42×D43C2211yescharacteristic
25C2×C42×D43C2213yes—
26C2×C42×D43C2213yes—
27#14582802C2216yes—
28#14582801C2216yes—
29#14582800C2216yes—
30#14582799C22124yes—
31#14582769C2211yescharacteristic
32#14582768C2216yes—
33C42×Dic43C2213yes—
34C42×Dic43C2211yescharacteristic
35C42×Dic43C2213yes—
36C2×#127×C43C2211yescharacteristic
37C2×C4×D4×C43C2216yes—
38C43×#390C2216yes—
39C43×#384C2211yescharacteristic
40C43×C43C2211yescharacteristic
41C2×#10621898—248no—
42C22×Dic86C2314yes—
43C22×D172C2316yes—
44C22×D172C2314yes—
45C22×C22⋊D43C23112yes—
46C22×C22⋊D43C2314yes—
47C22×C22⋊D43C2314yes—
48C22×C4×D43C2314yes—
49C22×C4×D43C2313yes—
50C22×C4×D43C2313yes—
51C22×C4×D43C2311yescharacteristic
52#13063324—224no—
53#13063322—24no—
54#13063321—224no—
55#13063321—224no—
56#13063311—248no—
57#13063300—224no—
58#13063298—248no—
59#13063296—224no—
60C4×D172—224no—
61C4×C22⋊D43—248no—
62C2×C4⋊Dic43C2316yes—
63C2×Dic43⋊C4C23112yes—
64C2×C22⋊Dic43C23112yes—
65C2×(C2×D43)⋊C4C23112yes—
66C2×(C2×D43)⋊C4C23112yes—
67C2×C4×Dic43C2316yes—
68C2×C4×Dic43C2313yes—
69C2×C4×Dic43C2313yes—
70C2×C4×Dic43C2313yes—
71C2×C4×Dic43C2313yes—
72C2×C4×Dic43C2313yes—
73C42×D43—24no—
74C42×D43—212no—
75C42×D43D4124yescomplemented
76C22×D4×C43C2316yes—
77C23×C4×C43C2314yes—
78#127×C43—24no—
79C4×D4×C43—224no—
80C2×C4⋊C4×C43C2316yes—
81C2×C22⋊C4×C43C23112yes—
82C2×C42×C43C2313yes—
83C2×C42×C43C2313yes—
84C2×C42×C43C2311yescharacteristic
85C24×C43C2414yes—
86C23×D43C2414yes—
87C23×D43C2411yescharacteristic
88C2×D4×C43—212no—
89C2×D4×C43—212no—
90C2×D4×C43—212no—
91C22×C4×C43—224no—
92C22×C4×C43C2414yes—
93C22×C4×C43C2413yes—
94C22×C4×C43C2413yes—
95C22×C4×C43C2411yescharacteristic
96C2×C22⋊D43—224no—
97C2×C22⋊D43—224no—
98C2×C22⋊D43—248no—
99C2×C22⋊D43—224no—
100C22×Dic43C2414yes—
101C22×Dic43C2413yes—
102C22×Dic43C2411yescharacteristic
103C22×Dic43C2413yes—
104#10621898—464no—
105C2×D172—212no—
106C2×D172—212no—
107C2×D172—212no—
108C2×D172—224no—
109C2×C4×D43—26no—
110C2×C4×D43—26no—
111C2×C4×D43—212no—
112C2×C4×D43—224no—
113C2×C4×D43C2×D4112yes—
114C2×C4×D43C2×D4112yes—
115C2×C4×D43C2×D4112yes—
116C2×Dic86—224no—
117C4⋊C4×C43—212no—
118C22⋊C4×C43—224no—
119C42×C43—26no—
120C42×C43C2×D4112yes—
121C42×C43#4114yescomplemented
122C22⋊Dic43—224no—
123(C2×D43)⋊C4—224no—
124(C2×D43)⋊C4—224no—
125C4⋊Dic43—212no—
126Dic43⋊C4—224no—
127C4×Dic43—26no—
128C4×Dic43—212no—
129C4×Dic43C2×D4112yes—
130C4×Dic43C2×D4112yes—
131C4×Dic43C2×D4112yes—
132C4×Dic43#41112yescomplemented
133C23×C43—212no—
134C23×C43—212no—
135C23×C43—24no—
136C23×C43C2511yescharacteristic
137C22×D43—23no—
138C22×D43—21no—
139C22×D43—212no—
140C22×D43—24no—
141C22×D43—212no—
142C22×D43C22×D416yes—
143D4×C43—424no—
144C2×C4×C43—26no—
145C2×C4×C43—212no—
146C2×C4×C43—416no—
147C2×C4×C43C22×D416yes—
148C2×C4×C43C22×D416yes—
149C2×C4×C43C22×D416yes—
150C2×C4×C43C2×#4116yes—
151C2×C4×C43C2×#4116yes—
152C22⋊D43—416no—
153C22⋊D43—416no—
154C22⋊D43—448no—
155C2×Dic43—23no—
156C2×Dic43—23no—
157C2×Dic43—212no—
158C2×Dic43C22×D416yes—
159C2×Dic43C22×D416yes—
160C2×Dic43C22×D416yes—
161C2×Dic43C2×#41112yes—
162D172—416no—
163D172—424no—
164C4×D43—224no—
165C4×D43—224no—
166C4×D43—416no—
167C4×D43#127116yescomplemented
168Dic86—416no—
169#36644—431nomaximal, Sylow
170C22×C43—44no—
171C22×C43—412no—
172C22×C43—412no—
173C22×C43C23×D413yes—
174C22×C43C22×#4113yes—
175C22×C43C22×#4111yescharacteristic
176C2×D43—26no—
177C2×D43—26no—
178C2×D43—44no—
179C2×D43—412no—
180C2×D43—412no—
181C2×D43C2×#12714yes—
182C4×C43—26no—
183C4×C43—44no—
184C4×C43C2×#12714yes—
185C4×C43#532112yescomplemented
186Dic43—26no—
187Dic43—44no—
188Dic43C2×#12714yes—
189Dic43#532112yescomplemented
190C2×#532—436no—
191#2868—431no—
192#2867—431no—
193#2858—436no—
194#2856—436no—
195#2856—431no—
196#2856—431no—
197C4×#127—431no—
198C4×#127—436no—
199C4×#127D4311yescharacteristic, complemented
200C2×C43—431no—
201C2×C43—84no—
202C2×C43C22×#12711yescharacteristic
203C2×C43C2×#53213yes—
204C2×C43C2×#53213yes—
205D43—24no—
206D43—84no—
207C22×#41—434no—
208#532—8648no—
209C2×C4⋊Q8—436no—
210C2×#127—436no—
211C2×#127—436no—
212C2×#127—431no—
213C2×#127C2×D4311yescharacteristic
214C2×#124—4312no—
215C2×#121—436no—
216C2×#121—436no—
217C2×#121—4312no—
218C2×C4×D4—4312no—
219C2×C4×D4—436no—
220C2×C4×D4C2×D4316yes—
221C22×C42—433no—
222C22×C42—433no—
223C22×C42—431no—
224#390—436no—
225#390—436no—
226#390—4324no—
227#390—436no—
228#390C2×D4316yes—
229#384—436no—
230#384—431no—
231#384C2×D4311yescharacteristic
232C43—433no—
233C43—433no—
234C43—431no—
235C43C2×D4311yescharacteristic
236C43#3664411yescharacteristic, complemented, Sylow
237C2×#41—8648no—
238C22×Q8—434no—
239C22×D4—4312no—
240C22×D4—434no—
241C22×D4—434no—
242C22×D4—436no—
243C22×D4—434no—
244C22×D4C22×D4316yes—
245C23×C4—431no—
246C23×C4—433no—
247C23×C4—433no—
248C23×C4—434no—
249C23×C4C22×D4314yes—
250C4⋊Q8—8624no—
251#127—24no—
252#127—8624no—
253#127—8624no—
254#127—864no—
255#124—8648no—
256#121—8648no—
257#121—8624no—
258#121—8624no—
259C4×D4—224no—
260C4×D4—8648no—
261C4×D4—8624no—
262C2×C4⋊C4—4312no—
263C2×C4⋊C4—436no—
264C2×C4⋊C4C22×D4316yes—
265C2×C22⋊C4—4312no—
266C2×C22⋊C4—4312no—
267C2×C22⋊C4—4312no—
268C2×C22⋊C4C22×D43112yes—
269C2×C42—433no—
270C2×C42—433no—
271C2×C42—433no—
272C2×C42—433no—
273C2×C42—4324no—
274C2×C42—436no—
275C2×C42—433no—
276C2×C42—8612no—
277C2×C42—864no—
278C2×C42C22×D4313yes—
279C2×C42C22×D4311yescharacteristic
280C2×C42C22×D4313yes—
281C24—431no—
282C24—434no—
283C24C23×D4314yes—
284#41—17264no—
285C2×Q8—8624no—
286C2×D4—212no—
287C2×D4—212no—
288C2×D4—212no—
289C2×D4—8624no—
290C2×D4—8624no—
291C2×D4—8624no—
292C2×D4—8648no—
293C2×D4—8624no—
294C2×D4—8612no—
295C2×D4—8612no—
296C2×D4—8612no—
297C22×C4—224no—
298C22×C4—433no—
299C22×C4—431no—
300C22×C4—4312no—
301C22×C4—433no—
302C22×C4—4312no—
303C22×C4—4312no—
304C22×C4—434no—
305C22×C4—8612no—
306C22×C4—866no—
307C22×C4—866no—
308C22×C4—8624no—
309C22×C4C23×D4314yes—
310C22×C4C23×D4313yes—
311C22×C4C23×D4313yes—
312C22×C4C23×D4311yescharacteristic
313C4⋊C4—212no—
314C4⋊C4—8624no—
315C4⋊C4—8612no—
316C22⋊C4—224no—
317C22⋊C4—8624no—
318C22⋊C4—8624no—
319C22⋊C4—8624no—
320C42—26no—
321C42—4312no—
322C42—4312no—
323C42—4312no—
324C42—4312no—
325C42—8612no—
326C42—866no—
327C42#1062189814yescomplemented
328C42D4×D43112yes—
329C23—212no—
330C23—212no—
331C23—24no—
332C23—436no—
333C23—863no—
334C23—861no—
335C23—8612no—
336C23—8612no—
337C23—864no—
338C23C24×D4311yescharacteristic
339Q8—17216no—
340D4—424no—
341D4—17216no—
342D4—17216no—
343D4—17248no—
344D4—17216no—
345D4—17224no—
346C2×C4—26no—
347C2×C4—212no—
348C2×C4—416no—
349C2×C4—436no—
350C2×C4—436no—
351C2×C4—4312no—
352C2×C4—4316no—
353C2×C4—436no—
354C2×C4—8624no—
355C2×C4—863no—
356C2×C4—863no—
357C2×C4—8624no—
358C2×C4—8612no—
359C2×C4—17216no—
360C2×C4C2×D4×D4316yes—
361C2×C4C2×D4×D4316yes—
362C2×C4C2×D4×D4316yes—
363C2×C4#41×D4316yes—
364C2×C4C2×#1062189816yes—
365C22—44no—
366C22—412no—
367C22—412no—
368C22—434no—
369C22—866no—
370C22—866no—
371C22—1724no—
372C22—17212no—
373C22—17212no—
374C22C22×D4×D4313yes—
375C22C2×#41×D4313yes—
376C22C22×#1062189811yescharacteristic
377C4—26no—
378C4—44no—
379C4—434no—
380C4—4312no—
381C4—866no—
382C4—1724no—
383C4#127×D4314yes—
384C4#14583446112yescomplemented
385C2—84no—
386C2—864no—
387C2—3444no—
388C2C2×#127×D4311yescharacteristic
389C2#532×D4313yes—
390C2C2×#1458344613yes—
subgroupG/H
centerC22×C4C23×D43
commutator, socle, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC4×#127×C43C2
hypercenterC4×#127D43
hypocenterC43#36644
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
1. C2×#14583446C2semidirect
2. #19142992C2semidirect
3. #19142989C2semidirect
4. #19142949C2semidirect
5. #19142941C2semidirect
6. #19142939C2semidirect
7. #19142937C2semidirect
8. C4×#13063322C2semidirect
9. C4×#13063321C2semidirect
10. C43×D43C2semidirect
11. C4×#127×C43C2semidirect
75. C42×D43D4semidirect
121. C42×C43#41semidirect
132. C4×Dic43#41semidirect
167. C4×D43#127semidirect
185. C4×C43#532semidirect
189. Dic43#532semidirect
199. C4×#127D43semidirect
236. C43#36644semidirect
327. C42#10621898semidirect
384. C4#14583446semidirect

Maximal subgroups

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

subgroupindex
C2×#145834462
#191429922
#191429892
#191429492
#191429412
#191429392
#191429372
C4×#130633222
C4×#130633212
C43×D432
C4×#127×C432
#3664443