Finite Group Databasebeta

← #25966291

Subgroups — #25966291

Order 11008.

1834 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148408C212yesmaximal
2#19145139C216yesmaximal, complemented
3#19145135C213yesmaximal, complemented
4#19145133C216yesmaximal, complemented
5#19145131C213yesmaximal, complemented
6#19145107C213yesmaximal, complemented
7C2×#14583303C213yesmaximal, complemented
8#19143195C211yesmaximal, characteristic
9#19143193C212yesmaximal
10#131×Dic43C211yesmaximal, characteristic
11C43×#2913C211yesmaximal, characteristic
12C2×#13063332C2211yescharacteristic
13Q8×Dic86—22no—
14#14583625—22no—
15#14583608—26no—
16D4×Dic86—26no—
17#14583530C2216yes—
18#14583527C2216yes—
19#14583452C2216yes—
20C2×#13063324C2216yes—
21#14583382C2212yes—
22#41×Dic43C2211yescharacteristic
23#14583307C22112yes—
24#14583306C22112yes—
25#14583303C2213yes—
26#14583303C2216yes—
27#14583303C2216yes—
28#14583303C2216yes—
29#14583303C2211yescharacteristic
30#14583300C2213yes—
31#14583300C2213yes—
32#14583299C2216yes—
33#14583296C2216yes—
34#14582942C2216yes—
35#14582941C2216yes—
36#14582939C2216yes—
37#14582937C2213yes—
38#14582935C2216yes—
39C2×#13063259C2213yes—
40C2×#13063258C2216yes—
41#14582857C2213yes—
42#14582854C2213yes—
43M16×Dic43C2213yes—
44C2×C8×Dic43C2213yes—
45C2×#131×C43C2211yescharacteristic
46C43×#520C2212yes—
47C43×#428C2216yes—
48C43×#427C2213yes—
49C2×#107×C43C2213yes—
50C22×Dic86—26no—
51#13063332Q818yescomplemented
52C2×#10621877C2313yes—
53C22×C43⋊C8C2313yes—
54#13063325—26no—
55#13063324—26no—
56#13063324—26no—
57#13063324—26no—
58#13063324C2312yes—
59#13063324C2316yes—
60#13063324C23112yes—
61#13063317—26no—
62#13063316—26no—
63#13063316C2316yes—
64#13063316C2316yes—
65#13063304—212no—
66#13063302—26no—
67#13063302—26no—
68#13063302—212no—
69Q8×Dic43—22no—
70Q8×Dic43D411yescharacteristic
71Q8×Dic43D411yescharacteristic
72C4×Dic86—26no—
73C4×Dic86—26no—
74D4×Dic43—26no—
75D4×Dic43D413yes—
76D4×Dic43D413yes—
77#13063284C2316yes—
78#13063284C2313yes—
79C2×C4⋊Dic43C2316yes—
80C2×Dic43⋊C4—26no—
81C2×C4×Dic43C2313yes—
82#13063259C2311yescharacteristic
83#13063259C2313yes—
84#13063259C2316yes—
85#13063258C2312yes—
86#13063258C2316yes—
87#13063258C23112yes—
88#13063257C2316yes—
89#13063256C2316yes—
90#13063256C2316yes—
91#13063235C2316yes—
92C8×Dic43C2313yes—
93C8×Dic43C2313yes—
94C8×Dic43C2313yes—
95C8×Dic43C2311yescharacteristic
96C2×#41×C43C2311yescharacteristic
97#131×C43Q818yescomplemented
98C2×M16×C43C2313yes—
99C22×C8×C43C2313yes—
100C4×Q8×C43—22no—
101C4×D4×C43—26no—
102#117×C43C2316yes—
103C2×C4⋊C4×C43C2316yes—
104#107×C43C2311yescharacteristic
105#107×C43C2313yes—
106#107×C43C2316yes—
107#106×C43C2316yes—
108#41×C43C2×Q814yes—
109#41×C43C2×Q814yes—
110C2×Q8×C43C2×D411yescharacteristic
111C2×D4×C43C2×D413yes—
112C22×C4×C43—26no—
113C22×C4×C43C2413yes—
114C22×Dic43—26no—
115C22×Dic43C2×D413yes—
116C22×Dic43C2×D413yes—
117C2×Dic86—22no—
118C2×Dic86—26no—
119C2×Dic86—212no—
120C2×Dic86—812no—
121M16×C43C2×Q8112yescomplemented
122C2×C8×C43C2×Q8112yescomplemented
123C2×C8×C43C2413yes—
124C2×C8×C43C2411yescharacteristic
125C4⋊C4×C43—26no—
126C4⋊C4×C43C2412yes—
127C4⋊C4×C43C2416yes—
128C22⋊C4×C43—26no—
129C42×C43—26no—
130C22⋊Dic43—26no—
131C22⋊Dic43C2×D416yes—
132C4⋊Dic43—26no—
133C4⋊Dic43—26no—
134C4⋊Dic43—26no—
135C4⋊Dic43C2×D413yes—
136C4⋊Dic43C2×D413yes—
137C4⋊Dic43C2412yes—
138C4⋊Dic43C2416yes—
139Dic43⋊C4—26no—
140Dic43⋊C4—212no—
141Dic43⋊C4—22no—
142Dic43⋊C4—26no—
143Dic43⋊C4—26no—
144C4×Dic43—26no—
145C4×Dic43C2×D413yes—
146C4×Dic43C2×D413yes—
147C4×Dic43C2411yescharacteristic
148C4×Dic43C2413yes—
149#10621877C2×Q8112yescomplemented
150C2×C43⋊C8C2×Q8112yescomplemented
151C2×C43⋊C8C2411yescharacteristic
152C2×C43⋊C8C2413yes—
153C23×C43C22×D413yes—
154Q8×C43C4⋊Q814yes—
155D4×C43C4⋊Q8112yes—
156C2×C4×C43—22no—
157C2×C4×C43—26no—
158C2×C4×C43—86no—
159C2×C4×C43C22×D413yes—
160C2×C4×C43C22×Q816yes—
161C2×C4×C43C22×Q816yes—
162C2×C4×C43C2511yescharacteristic
163C2×Dic43—26no—
164C2×Dic43—26no—
165C2×Dic43—22no—
166C2×Dic43—26no—
167C2×Dic43—86no—
168C2×Dic43C22×D413yes—
169C2×Dic43C22×D413yes—
170C2×Dic43C22×D411yescharacteristic
171C2×Dic43C22×D411yescharacteristic
172Dic86—412no—
173Dic86—44no—
174Dic86—812no—
175C8×C43C22×Q812yes—
176C8×C43C22×Q816yes—
177C43⋊C8C22×Q812yes—
178C43⋊C8C22×Q816yes—
179#60667—431nomaximal, Sylow
180C22×C43—23no—
181C22×C43—23no—
182C22×C43C2×C4⋊Q816yes—
183C22×C43C23×D411yescharacteristic
184C4×C43—46no—
185C4×C43—42no—
186C4×C43C2×C4⋊Q816yes—
187C4×C43C23×Q811yescharacteristic
188C4×C43C23×Q811yescharacteristic
189Dic43—23no—
190Dic43—23no—
191Dic43—46no—
192Dic43—42no—
193Dic43#57612yes—
194Dic43#57812yes—
195#3503—432no—
196#3165—436no—
197#3164—436no—
198#3164—433no—
199#3164—433no—
200#3160—433no—
201C2×#500—433no—
202#2913—431no—
203#2913—432no—
204#2913D4311yescharacteristic
205C4×#131—431no—
206C2×C43—26no—
207C2×C43C22×C4⋊Q811yescharacteristic
208C2×C43C2×#57611yescharacteristic
209C2×C43C2×#57811yescharacteristic
210C2×#131—431no—
211C2×#131C2×D4311yescharacteristic
212Q82—862no—
213#557—862no—
214#554—866no—
215D4×Q8—866no—
216#544—436no—
217#544—436no—
218#533—436no—
219C2×C4⋊Q8—436no—
220#520—432no—
221#520C2×D4312yes—
222C4×#41—431no—
223#501—4312no—
224#501—4312no—
225#500—433no—
226#500—436no—
227#500—436no—
228#500—436no—
229#500—431no—
230#499—433no—
231#499—433no—
232#499—436no—
233#498—436no—
234#428—436no—
235#428—436no—
236#428—436no—
237#428C2×D4316yes—
238#427—433no—
239#427—436no—
240#427C2×D4313yes—
241C2×#107—433no—
242C2×#107—436no—
243C2×#107C2×D4313yes—
244#405—433no—
245#405—433no—
246C4×M16—433no—
247C2×C4×C8—433no—
248C43#6066711yescharacteristic, complemented, Sylow
249C2×#41C22×D4311yescharacteristic
250C22×Q8—866no—
251#131—438no—
252#131Dic8618yescomplemented
253C2×M16—433no—
254C2×M16C22×D4313yes—
255C22×C8—433no—
256C22×C8C22×D4313yes—
257C4⋊Q8—436no—
258C4⋊Q8—4312no—
259C4⋊Q8—432no—
260C4⋊Q8—866no—
261C4⋊Q8—866no—
262C4⋊Q8—866no—
263C4⋊Q8—866no—
264#125—436no—
265#125—436no—
266#125—866no—
267#125—866no—
268C22⋊Q8—8612no—
269C22⋊Q8—866no—
270C22⋊Q8—866no—
271C22⋊Q8—8612no—
272C4×Q8—22no—
273C4×Q8—431no—
274C4×Q8—431no—
275C4×Q8—866no—
276C4×Q8—866no—
277C4×Q8—862no—
278C4×D4—26no—
279C4×D4—433no—
280C4×D4—433no—
281C4×D4—866no—
282#117—433no—
283#117—436no—
284#117C22×D4316yes—
285C2×C4⋊C4—436no—
286C2×C4⋊C4—866no—
287C2×C4⋊C4C22×D4316yes—
288C2×C42—433no—
289#107—433no—
290#107—436no—
291#107—431no—
292#107—436no—
293#107—4312no—
294#107—432no—
295#107C22×D4313yes—
296#107C22×D4316yes—
297#107C22×D4311yescharacteristic
298#106—436no—
299#106—436no—
300#106—436no—
301#106C22×D4316yes—
302#97—436no—
303C4×C8—431no—
304C4×C8—433no—
305C4×C8—433no—
306C4×C8—433no—
307#41C2×Dic8614yes—
308#41Q8×D4314yes—
309C2×Q8—8612no—
310C2×Q8—862no—
311C2×Q8—866no—
312C2×Q8—34412no—
313C2×Q8D4×D4311yescharacteristic
314C2×D4D4×D4313yes—
315C22×C4—26no—
316C22×C4—433no—
317C22×C4—433no—
318C22×C4—866no—
319C22×C4C23×D4313yes—
320M16—4312no—
321M16C2×Dic86112yescomplemented
322C2×C8—4312no—
323C2×C8—431no—
324C2×C8—433no—
325C2×C8C2×Dic86112yescomplemented
326C2×C8C23×D4311yescharacteristic
327C2×C8C23×D4313yes—
328C4⋊C4—26no—
329C4⋊C4—433no—
330C4⋊C4—433no—
331C4⋊C4—432no—
332C4⋊C4—436no—
333C4⋊C4—866no—
334C4⋊C4—8612no—
335C4⋊C4—862no—
336C4⋊C4—866no—
337C4⋊C4—866no—
338C4⋊C4—866no—
339C4⋊C4—866no—
340C4⋊C4—866no—
341C4⋊C4C23×D4312yes—
342C4⋊C4C23×D4316yes—
343C22⋊C4—26no—
344C22⋊C4—436no—
345C22⋊C4—866no—
346C42—26no—
347C42—433no—
348C42—433no—
349C42—431no—
350C42—433no—
351C42—866no—
352C23C2×D4×D4313yes—
353Q8—34412no—
354Q8—17212no—
355Q8—1724no—
356Q8#1306332414yes—
357D4#13063324112yes—
358C2×C4—22no—
359C2×C4—26no—
360C2×C4—86no—
361C2×C4—431no—
362C2×C4—431no—
363C2×C4—433no—
364C2×C4—433no—
365C2×C4—866no—
366C2×C4—866no—
367C2×C4—862no—
368C2×C4—866no—
369C2×C4—3446no—
370C2×C4C2×D4×D4313yes—
371C2×C4C2×Q8×D4316yes—
372C2×C4C22×Dic8616yes—
373C2×C4C24×D4311yescharacteristic
374C8—432no—
375C8—436no—
376C8C22×Dic8612yes—
377C8C22×Dic8616yes—
378C22—23no—
379C22—23no—
380C22C2×#1306332416yes—
381C22C22×D4×D4311yescharacteristic
382C4—46no—
383C4—42no—
384C4—432no—
385C4—432no—
386C4—863no—
387C4—863no—
388C4—1726no—
389C4—1722no—
390C4C2×#1306332416yes—
391C4C22×Q8×D4311yescharacteristic
392C4C23×Dic8611yescharacteristic
393C2—26no—
394C2C22×#1306332411yescharacteristic
395C2#576×D4311yescharacteristic
396C2#578×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2913C2
socleC22×C43C23×D4
prime radicalC2×#41×C43C23
hypercenter#2913D43
hypocenterC43#60667
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2913

Complements

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

NH ≅ G/Ntype
2. #19145139C2semidirect
3. #19145135C2semidirect
4. #19145133C2semidirect
5. #19145131C2semidirect
6. #19145107C2semidirect
7. C2×#14583303C2semidirect
51. #13063332Q8semidirect
97. #131×C43Q8semidirect
121. M16×C43C2×Q8semidirect
122. C2×C8×C43C2×Q8semidirect
149. #10621877C2×Q8semidirect
150. C2×C43⋊C8C2×Q8semidirect
248. C43#60667semidirect
252. #131Dic86semidirect
321. M16C2×Dic86semidirect
325. C2×C8C2×Dic86semidirect

Maximal subgroups

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

subgroupindex
#191484082
#191451392
#191451352
#191451332
#191451312
#191451072
C2×#145833032
#191431952
#191431932
#131×Dic432
C43×#29132
#6066743