Finite Group Databasebeta

← #25013988

Subgroups — #25013988

Order 11008.

510 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D43C211yesmaximal, characteristic, complemented
2#19144177C211yesmaximal, characteristic
3C2×#14582710C211yesmaximal, characteristic, complemented
4C2×#14582708C211yesmaximal, characteristic, complemented
5#19134617C211yesmaximal, characteristic, complemented
6#19132700C211yesmaximal, characteristic, complemented
7C43×#1386C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9C22×C8×D43C2211yescharacteristic
10#14583411—21no—
11C2×#13063265C2211yescharacteristic
12C2×#13063264—21no—
13M32×D43—22no—
14M32×D43—22no—
15C2×C16×D43—21no—
16#14583141C411yescharacteristic, complemented
17#14583141C411yescharacteristic, complemented
18#14583136C411yescharacteristic, complemented
19#14583136C411yescharacteristic, complemented
20#14583129—21no—
21#14583129—21no—
22C2×#13063257C2211yescharacteristic
23#14582893—21no—
24#14582756—21no—
25#14582710—22no—
26#14582708—22no—
27#14582661—21no—
28C2×M32×C43C2211yescharacteristic
29C43×#427C2211yescharacteristic
30C2×#106×C43C2211yescharacteristic
31C2×#10621898—21no—
32C22×C4×D43D411yescharacteristic
33#13063347—21no—
34#13063347—21no—
35#13063347—21no—
36#13063347—21no—
37C2×Dic172C2×C411yescharacteristic
38C2×#10621873—21no—
39C2×D344C2×C411yescharacteristic
40C22×C43⋊C8D411yescharacteristic
41C2×C8×D43—21no—
42C2×C8×D43—21no—
43C2×C8×D43—21no—
44C2×C8×D43—21no—
45C2×C8×D43C2×C411yescharacteristic
46C2×C8×D43C2×C411yescharacteristic
47C2×C8×D43D411yescharacteristic
48C2×C8×D43D411yescharacteristic
49#13063309—41no—
50#13063305—21no—
51#13063305—21no—
52#13063300—21no—
53#13063300—21no—
54#13063295—41no—
55C4×D172—41no—
56C4×D172—41no—
57C2×C4⋊Dic43—21no—
58C2×(C2×D43)⋊C4—41no—
59#13063265—21no—
60#13063265D412yescomplemented
61#13063264—24no—
62C2×C43⋊C16—21no—
63C16×D43—24no—
64#13063257—21no—
65#13063257—21no—
66#13063248—21no—
67#13063248—21no—
68#13063245—21no—
69#13063245—21no—
70C43⋊#95—41no—
71C22×C8×C43C2311yescharacteristic
72#117×C43—21no—
73C2×C4⋊C4×C43—21no—
74M32×C43—21no—
75M32×C43D412yescomplemented
76C2×C16×C43—21no—
77#107×C43C2×C411yescharacteristic
78#107×C43C2×C411yescharacteristic
79#106×C43—21no—
80#106×C43—21no—
81#106×C43—21no—
82C23×D43D811yescharacteristic
83C22×C4×C43—41no—
84C22×C4×C43C2×D411yescharacteristic
85C2×C22⋊D43—41no—
86C22×Dic43—41no—
87C22×Dic43D811yescharacteristic
88#10621898—41no—
89#10621898—41no—
90#10621898—41no—
91#10621898—41no—
92C2×D172—21no—
93C2×D172—41no—
94C2×D172—41no—
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97C2×C4×D43—21no—
98C2×C4×D43—21no—
99C2×C4×D43—41no—
100C2×C4×D43C22⋊C411yescharacteristic
101C2×C4×D43C22⋊C411yescharacteristic
102C2×C4×D43SD1611yescharacteristic
103C2×C4×D43SD1611yescharacteristic
104C2×Dic86—21no—
105C2×C8×C43C22×C411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43#4111yescharacteristic
110C2×C8×C43#4111yescharacteristic
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C42×C43—41no—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—41no—
119(C2×D43)⋊C4—41no—
120(C2×D43)⋊C4—41no—
121(C2×D43)⋊C4—82no—
122C4⋊Dic43—41no—
123C4⋊Dic43—41no—
124C4⋊Dic43—41no—
125C4⋊Dic43—41no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8C22⋊C411yescharacteristic
129C2×C43⋊C8C22⋊C411yescharacteristic
130Dic172—21no—
131Dic172—21no—
132D344—21no—
133D344—21no—
134#10621873—41no—
135#10621873—41no—
136C8×D43—21no—
137C8×D43—21no—
138C8×D43—21no—
139C8×D43—21no—
140C8×D43—21no—
141C8×D43—21no—
142C8×D43—21no—
143C8×D43—21no—
144C16×C43—22no—
145C43⋊C16—22no—
146C23×C43C2×D811yescharacteristic
147C22×D43—21no—
148C22×D43—21no—
149C22×D43—22no—
150C22×D43—41no—
151C22×D43—41no—
152C22×D43#10211yescharacteristic
153C22×D43#10211yescharacteristic
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—81no—
157C2×C4×C43—81no—
158C2×C4×C43—81no—
159C2×C4×C43C2×C22⋊C411yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43C2×SD1611yescharacteristic
163C2×C4×C43#13511yescharacteristic
164C2×C4×C43#13511yescharacteristic
165C22⋊D43—81no—
166C22⋊D43—81no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—41no—
170C2×Dic43—81no—
171C2×Dic43—81no—
172C2×Dic43—81no—
173C2×Dic43#10211yescharacteristic
174C2×Dic43#10211yescharacteristic
175D172—41no—
176D172—41no—
177D172—82no—
178D172—82no—
179C4×D43—21no—
180C4×D43—21no—
181C4×D43—21no—
182C4×D43—21no—
183C4×D43—21no—
184C4×D43—21no—
185C4×D43—21no—
186C4×D43—21no—
187C4×D43—81no—
188C4×D43—81no—
189Dic86—41no—
190Dic86—41no—
191C8×C43C4×D411yescharacteristic
192C8×C43C4×D411yescharacteristic
193C8×C43#12011yescharacteristic
194C8×C43#12311yescharacteristic
195C43⋊C8—21no—
196C43⋊C8—21no—
197#13065—431nomaximal, Sylow
198C22×C43—21no—
199C22×C43—21no—
200C22×C43C2×#10211yescharacteristic
201C22×C43#46611yescharacteristic
202C22×C43#46611yescharacteristic
203C2×D43—21no—
204C2×D43—21no—
205C2×D43—21no—
206C2×D43—21no—
207C2×D43—21no—
208C2×D43—42no—
209C2×D43—42no—
210C2×D43—81no—
211C2×D43—81no—
212C2×D43—81no—
213C2×D43#36012yescomplemented
214C4×C43—81no—
215C4×C43—81no—
216C4×C43—161no—
217C4×C43#38611yescharacteristic
218C4×C43#41611yescharacteristic
219C4×C43#46511yescharacteristic
220C4×C43#46511yescharacteristic
221Dic43—21no—
222Dic43—21no—
223Dic43—81no—
224Dic43—161no—
225C22×M32—431no—
226#3050—431no—
227C2×#360—431no—
228C2×#360—431no—
229#1807—431no—
230#1386—431no—
231#1386D4311yescharacteristic, complemented
232C2×C43—21no—
233C2×C43—21no—
234C2×C43#189311yescharacteristic
235C2×C43C2×#36011yescharacteristic
236C2×C43#214511yescharacteristic
237D43—22no—
238D43—41no—
239D43—161no—
240C2×#135—431no—
241C23×C8—431no—
242#525—861no—
243C2×M32—431no—
244C2×M32—861no—
245C2×M32—862no—
246C2×M32—862no—
247C2×M32C2×D4311yescharacteristic
248C22×C16—861no—
249#467—431no—
250#467—431no—
251#466—431no—
252#466—431no—
253#465—861no—
254#465—861no—
255#427C2×D4311yescharacteristic
256C2×#106—431no—
257C2×#106C2×D4311yescharacteristic
258#416—861no—
259#380—861no—
260#360—862no—
261#360—862no—
262#340—861no—
263C43#1306511yescharacteristic, complemented, Sylow
264C2×#41—861no—
265C23×C4—431no—
266#135—861no—
267#135—861no—
268#135—861no—
269#135—861no—
270C2×Q16—431no—
271C2×SD16—861no—
272C2×D8—431no—
273C22×C8—431no—
274C22×C8—431no—
275C22×C8—431no—
276C22×C8—431no—
277C22×C8—431no—
278C22×C8—861no—
279C22×C8—861no—
280C22×C8—861no—
281C22×C8—861no—
282C22×C8C22×D4311yescharacteristic
283#123—1721no—
284C22⋊Q8—861no—
285C22⋊Q8—861no—
286#121—861no—
287#121—861no—
288#120—1721no—
289C4×D4—1721no—
290C4×D4—1721no—
291#117—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—861no—
294C2×C22⋊C4—1721no—
295M32—21no—
296M32—432no—
297M32—864no—
298M32—861no—
299M32D17212yescomplemented
300C2×C16—21no—
301C2×C16—864no—
302C2×C16—861no—
303#107C4×D4311yescharacteristic
304#107C4×D4311yescharacteristic
305#106—21no—
306#106—21no—
307#106—21no—
308#106—861no—
309#106—861no—
310#103—861no—
311#103—861no—
312#102—861no—
313#102—861no—
314#95—1721no—
315C24—431no—
316#41—1721no—
317#41—1721no—
318#41—1721no—
319#41—1721no—
320C2×Q8—861no—
321C2×D4—861no—
322C2×D4—1721no—
323C2×D4—1721no—
324C2×D4—1721no—
325C22×C4—41no—
326C22×C4—431no—
327C22×C4—431no—
328C22×C4—431no—
329C22×C4—431no—
330C22×C4—431no—
331C22×C4—861no—
332C22×C4—861no—
333C22×C4—861no—
334C22×C4—861no—
335C22×C4—1721no—
336C22×C4—1721no—
337C22×C4D4×D4311yescharacteristic
338Q16—861no—
339Q16—861no—
340SD16—1721no—
341SD16—1721no—
342D8—861no—
343D8—861no—
344C2×C8—431no—
345C2×C8—431no—
346C2×C8—861no—
347C2×C8—861no—
348C2×C8—861no—
349C2×C8—861no—
350C2×C8—861no—
351C2×C8—861no—
352C2×C8—861no—
353C2×C8—861no—
354C2×C8—861no—
355C2×C8—861no—
356C2×C8C2×C4×D4311yescharacteristic
357C2×C8C2×D17211yescharacteristic
358C2×C8#1062189811yescharacteristic
359C2×C8D4×D4311yescharacteristic
360C2×C8D4×D4311yescharacteristic
361C2×C8#1062190211yescharacteristic
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—1721no—
367C4⋊C4—1721no—
368C4⋊C4—1721no—
369C4⋊C4—1721no—
370C22⋊C4—41no—
371C22⋊C4—3442no—
372C22⋊C4—1721no—
373C22⋊C4—1721no—
374C22⋊C4—1721no—
375C22⋊C4—1721no—
376C42—41no—
377C16—22no—
378C16—862no—
379C23—431no—
380C23—431no—
381C23—862no—
382C23—861no—
383C23—861no—
384C23—1721no—
385C23—1721no—
386C23D8×D4311yescharacteristic
387Q8—1721no—
388Q8—1721no—
389D4—3442no—
390D4—3442no—
391D4—3441no—
392D4—3441no—
393D4—1721no—
394D4—1721no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—431no—
401C2×C4—431no—
402C2×C4—861no—
403C2×C4—861no—
404C2×C4—861no—
405C2×C4—861no—
406C2×C4—861no—
407C2×C4—861no—
408C2×C4—861no—
409C2×C4—861no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—3441no—
413C2×C4—3441no—
414C2×C4—3441no—
415C2×C4—3441no—
416C2×C4—3441no—
417C2×C4—1721no—
418C2×C4C22⋊C4×D4311yescharacteristic
419C2×C4#1306329811yescharacteristic
420C2×C4#1306330011yescharacteristic
421C2×C4SD16×D4311yescharacteristic
422C2×C4#1306334611yescharacteristic
423C2×C4#1306334811yescharacteristic
424C8—861no—
425C8—861no—
426C8#1306328711yescharacteristic
427C8C4×D17211yescharacteristic
428C8#1306329511yescharacteristic
429C8#1306331011yescharacteristic
430C22—21no—
431C22—21no—
432C22—432no—
433C22—861no—
434C22—861no—
435C22—861no—
436C22—861no—
437C22—861no—
438C22—3441no—
439C22—3441no—
440C22—3441no—
441C22—1722no—
442C22—1722no—
443C22#102×D4311yescharacteristic
444C22#1458313411yescharacteristic
445C22#1458313611yescharacteristic
446C4—81no—
447C4—81no—
448C4—161no—
449C4—861no—
450C4—861no—
451C4—3441no—
452C4—6881no—
453C4#1458277711yescharacteristic
454C4#1458289411yescharacteristic
455C4#1458312911yescharacteristic
456C4#1458313111yescharacteristic
457C2—21no—
458C2—21no—
459C2—862no—
460C2—1721no—
461C2—6881no—
462C2#1913502211yescharacteristic
463C2#360×D4311yescharacteristic
464C2#1913632911yescharacteristic
subgroupG/H
centerC22#102×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1386C2
socleC22×C43C2×#102
prime radical#19144177C2
cosocleC22×C8×C43C23
hypercenter#1386D43
hypocenterC43#13065
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
1. C2×M32×D43C2semidirect
3. C2×#14582710C2semidirect
4. C2×#14582708C2semidirect
5. #19134617C2semidirect
6. #19132700C2semidirect
7. C43×#1386C2semidirect
16. #14583141C4semidirect
17. #14583141C4semidirect
18. #14583136C4semidirect
19. #14583136C4semidirect
60. #13063265D4semidirect
75. M32×C43D4semidirect
213. C2×D43#360semidirect
231. #1386D43semidirect
263. C43#13065semidirect
299. M32D172semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D432
#191441772
C2×#145827102
C2×#145827082
#191346172
#191327002
C43×#13862
#1306543