Finite Group Databasebeta

← #25253598

Subgroups — #25253598

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146943C211yesmaximal, characteristic, complemented
2#19136831C211yesmaximal, characteristic, complemented
3#19136795C211yesmaximal, characteristic, complemented
4#19136773C211yesmaximal, characteristic, complemented
5#19136747C211yesmaximal, characteristic, complemented
6#19136710C211yesmaximal, characteristic, complemented
7#19136679C211yesmaximal, characteristic, complemented
8#19136647C211yesmaximal, characteristic, complemented
9#19136518C211yesmaximal, characteristic, complemented
10#19136512C211yesmaximal, characteristic, complemented
11#19136457C211yesmaximal, characteristic, complemented
12#19136421C211yesmaximal, characteristic, complemented
13#19136307C211yesmaximal, characteristic, complemented
14C2×#14582703C211yesmaximal, characteristic, complemented
15C43×#3285C211yesmaximal, characteristic, complemented
16#14583553—21no—
17C2×#13063268C2211yescharacteristic
18C2×#13063268C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20C2×#13063265C2211yescharacteristic
21C22×C43⋊C16C2211yescharacteristic
22#14583304C2211yescharacteristic
23#14583213—21no—
24#14583213—21no—
25#14583180—21no—
26#14583135C2211yescharacteristic
27#14583135C2211yescharacteristic
28C4×D344C2211yescharacteristic
29C2×#13063259C2211yescharacteristic
30C2×#13063259C2211yescharacteristic
31#14582724C2211yescharacteristic
32#14582724C2211yescharacteristic
33#14582724C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35#14582703C2211yescharacteristic
36#14582703C2211yescharacteristic
37#14582703C2211yescharacteristic
38#14582703C2211yescharacteristic
39#14582703C2211yescharacteristic
40#14582703C2211yescharacteristic
41#14582700C2211yescharacteristic
42#14582700C2211yescharacteristic
43#14582700C2211yescharacteristic
44#14582699C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46C22⋊(C43⋊C16)C2211yescharacteristic
47#14582675C2211yescharacteristic
48C2×#135×C43C2211yescharacteristic
49C22×Q16×C43C2211yescharacteristic
50C43×#548—21no—
51C43×#495C2211yescharacteristic
52C43×#467C2211yescharacteristic
53C43×#466C2211yescharacteristic
54C43×#464—21no—
55C43×#452—21no—
56C43×#448—21no—
57C4×Q16×C43C2211yescharacteristic
58C8×D4×C43C2211yescharacteristic
59C2×#10621900—41no—
60C2×D344C2311yescharacteristic
61#13063325—21no—
62#13063309—41no—
63#13063309—41no—
64#13063305—41no—
65#13063299—21no—
66#13063299—21no—
67C4×D172—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70#13063268—22no—
71#13063268—41no—
72#13063266—41no—
73#13063265—41no—
74C2×C43⋊C16—41no—
75C2×C43⋊C16C2311yescharacteristic
76C2×C43⋊C16C2311yescharacteristic
77C2×C43⋊C16C2311yescharacteristic
78C2×C43⋊C16C2311yescharacteristic
79#13063259—21no—
80#13063259—21no—
81#13063259—21no—
82#13063259C2311yescharacteristic
83#13063259C2311yescharacteristic
84#13063259C2311yescharacteristic
85#13063247—21no—
86#13063247—21no—
87#13063247—21no—
88C2×#41×C43—21no—
89C22×Q8×C43—21no—
90#135×C43—22no—
91#135×C43—41no—
92C2×Q16×C43—22no—
93C2×Q16×C43—21no—
94C2×Q16×C43—41no—
95C2×Q16×C43C2311yescharacteristic
96C2×Q16×C43C2311yescharacteristic
97C2×SD16×C43—21no—
98C2×SD16×C43—21no—
99C2×D8×C43C2311yescharacteristic
100C22×C8×C43C2311yescharacteristic
101C22×C8×C43C2311yescharacteristic
102#124×C43—21no—
103#124×C43—41no—
104C22⋊Q8×C43—21no—
105C22⋊Q8×C43—41no—
106#121×C43—21no—
107#121×C43—41no—
108C4×Q8×C43—21no—
109C4×D4×C43—41no—
110C4×D4×C43D411yescharacteristic
111#107×C43C2311yescharacteristic
112C4⋊C8×C43D411yescharacteristic
113#103×C43—21no—
114#103×C43—21no—
115#102×C43—21no—
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119#41×C43—42no—
120#41×C43—81no—
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—42no—
124C2×Q8×C43—41no—
125C2×Q8×C43—81no—
126C2×D4×C43—21no—
127C2×D4×C43—41no—
128C2×D4×C43—41no—
129C2×D4×C43D811yescharacteristic
130C22×C4×C43—41no—
131C22×C4×C43—41no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C2×C22⋊D43—41no—
135C2×C22⋊D43—41no—
136C22×Dic43—41no—
137C22×Dic43—41no—
138#10621900—84no—
139C2×D172—21no—
140C2×C4×D43—41no—
141C2×Dic86—41no—
142Q16×C43—21no—
143Q16×C43—21no—
144Q16×C43—21no—
145Q16×C43—42no—
146Q16×C43#4112yescomplemented
147SD16×C43—42no—
148SD16×C43—81no—
149D8×C43—21no—
150D8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43C2×D411yescharacteristic
156C2×C8×C43C2×D411yescharacteristic
157C2×C8×C43C2×D411yescharacteristic
158C2×C8×C43C2411yescharacteristic
159C4⋊C4×C43—21no—
160C4⋊C4×C43—41no—
161C4⋊C4×C43—41no—
162C4⋊C4×C43D811yescharacteristic
163C22⋊C4×C43—41no—
164C22⋊C4×C43—41no—
165C22⋊C4×C43—41no—
166C22⋊C4×C43—41no—
167C22⋊C4×C43D811yescharacteristic
168C22⋊C4×C43D811yescharacteristic
169C42×C43—41no—
170C42×C43C2×D411yescharacteristic
171(C2×D43)⋊C4—41no—
172(C2×D43)⋊C4—41no—
173(C2×D43)⋊C4—41no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—41no—
178C4⋊Dic43—41no—
179C4⋊Dic43—41no—
180D344—21no—
181D344—21no—
182C43⋊C16—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C43⋊C16—21no—
186C23×C43—41no—
187C23×C43C2×D811yescharacteristic
188C23×C43C2×D811yescharacteristic
189C22×D43—41no—
190Q8×C43—22no—
191Q8×C43—41no—
192Q8×C43—41no—
193Q8×C43—41no—
194Q8×C43—82no—
195D4×C43—22no—
196D4×C43—41no—
197D4×C43—41no—
198D4×C43—82no—
199D4×C43—82no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—82no—
208C2×C4×C43—82no—
209C2×C4×C43C2×D811yescharacteristic
210C2×C4×C43C2×D811yescharacteristic
211C2×C4×C43C2×D811yescharacteristic
212C2×C4×C43C2×D811yescharacteristic
213C2×C4×C43C22×D411yescharacteristic
214C22⋊D43—82no—
215C22⋊D43—82no—
216C2×Dic43—41no—
217C2×Dic43—41no—
218C2×Dic43—41no—
219C2×Dic43—82no—
220C2×Dic43—82no—
221D172—41no—
222D172—41no—
223C4×D43—82no—
224Dic86—82no—
225C8×C43—21no—
226C8×C43—21no—
227C8×C43—21no—
228C8×C43C2×#4111yescharacteristic
229C8×C43H(5,𝔽2)11yescharacteristic
230#33875—431nomaximal, Sylow
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—81no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43#50912yes—
240C22×C43C22×D811yescharacteristic
241C2×D43—81no—
242C2×D43—81no—
243C2×D43—81no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—42no—
249C4×C43—81no—
250C4×C43—81no—
251C4×C43#54611yescharacteristic
252C4×C43#57711yescharacteristic
253Dic43—81no—
254Dic43—81no—
255Dic43—81no—
256#3334—431no—
257#3285D4311yescharacteristic, complemented
258#2243—431no—
259#2236—431no—
260#2232—431no—
261#2227—431no—
262#2220—431no—
263#2215—431no—
264#2210—431no—
265#2186—431no—
266#2185—431no—
267#2175—431no—
268#2168—431no—
269#2139—431no—
270C2×#358—431no—
271C2×C43—22no—
272C2×C43—41no—
273C2×C43—161no—
274C2×C43#329411yescharacteristic
275C2×C43C2×#50911yescharacteristic
276C2×C43#341711yescharacteristic
277D43—161no—
278C2×#135C2×D4311yescharacteristic
279C22×Q16C2×D4311yescharacteristic
280#548—21no—
281#547—861no—
282C2×SD32—431no—
283C2×SD32—431no—
284C2×D16—431no—
285C2×M32—431no—
286C22×C16—431no—
287#500—431no—
288#495C2×D4311yescharacteristic
289#480—861no—
290#480—861no—
291#474—861no—
292#467C2×D4311yescharacteristic
293#466—431no—
294#466—431no—
295#466C2×D4311yescharacteristic
296#464—21no—
297#452—21no—
298#448—21no—
299C4×Q16C2×D4311yescharacteristic
300C4×D8—431no—
301C8×D4C2×D4311yescharacteristic
302C2×#107—431no—
303C2×#107—431no—
304#366—431no—
305#366—431no—
306#366—431no—
307C4⋊C16—431no—
308#358—431no—
309#358—431no—
310#358—431no—
311#358—431no—
312#358—431no—
313#358—431no—
314#357—431no—
315#357—431no—
316#357—431no—
317#357—431no—
318C22⋊C16—431no—
319C22⋊C16—431no—
320#346—431no—
321C43#3387511yescharacteristic, complemented, Sylow
322C2×#41—21no—
323C2×#41—1721no—
324C22×Q8—21no—
325#135—22no—
326#135—41no—
327C2×Q16—22no—
328C2×Q16—21no—
329C2×Q16—41no—
330C2×Q16C22×D4311yescharacteristic
331C2×Q16C22×D4311yescharacteristic
332C2×SD16—21no—
333C2×SD16—21no—
334C2×D8—431no—
335C2×D8C22×D4311yescharacteristic
336C22×C8C22×D4311yescharacteristic
337C22×C8C22×D4311yescharacteristic
338C4⋊Q8—861no—
339#124—21no—
340#124—41no—
341#123—1721no—
342#123—1721no—
343C22⋊Q8—21no—
344C22⋊Q8—41no—
345C22⋊Q8—1721no—
346#121—21no—
347#121—41no—
348#121—861no—
349#121—861no—
350C4×Q8—21no—
351C4×D4—41no—
352C4×D4—861no—
353C4×D4C22⋊D4311yescharacteristic
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356SD32—862no—
357SD32—1721no—
358D16—1721no—
359M32—1721no—
360C2×C16—431no—
361C2×C16—431no—
362C2×C16—431no—
363C2×C16—431no—
364C2×C16—1721no—
365#107—431no—
366#107—431no—
367#107—431no—
368#107—861no—
369#107—861no—
370#107—861no—
371#107C22×D4311yescharacteristic
372C4⋊C8C22⋊D4311yescharacteristic
373#103—21no—
374#103—21no—
375#102—21no—
376#102—861no—
377#102—861no—
378#102—861no—
379C22⋊C8C22⋊D4311yescharacteristic
380C22⋊C8C22⋊D4311yescharacteristic
381C4×C8C22×D4311yescharacteristic
382#41—42no—
383#41—81no—
384#41—3444no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—42no—
388C2×Q8—41no—
389C2×Q8—81no—
390C2×Q8—1721no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—861no—
395C2×D4—1721no—
396C2×D4—1721no—
397C2×D4#1062188211yescharacteristic
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—1721no—
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4C2×C22⋊D4311yescharacteristic
404C22×C4C2×C22⋊D4311yescharacteristic
405Q16—21no—
406Q16—21no—
407Q16—21no—
408Q16—42no—
409Q16#1062190012yescomplemented
410SD16—42no—
411SD16—81no—
412D8—21no—
413D8—21no—
414D8—861no—
415D8—861no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8C2×C22⋊D4311yescharacteristic
421C2×C8C2×C22⋊D4311yescharacteristic
422C2×C8C2×C22⋊D4311yescharacteristic
423C2×C8C23×D4311yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—861no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—1721no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C4⋊C4#1062188211yescharacteristic
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—1721no—
439C22⋊C4—1721no—
440C22⋊C4—1721no—
441C22⋊C4#1062188211yescharacteristic
442C22⋊C4#1062188211yescharacteristic
443C42—41no—
444C42C2×C22⋊D4311yescharacteristic
445C16—861no—
446C16—861no—
447C16—861no—
448C16—861no—
449C23—41no—
450C23—1721no—
451C23C2×#1062188211yescharacteristic
452C23C2×#1062188211yescharacteristic
453Q8—22no—
454Q8—41no—
455Q8—41no—
456Q8—41no—
457Q8—82no—
458Q8—3442no—
459D4—22no—
460D4—41no—
461D4—41no—
462D4—82no—
463D4—82no—
464D4—3442no—
465D4—3442no—
466D4—1721no—
467D4—1721no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—3442no—
478C2×C4—3442no—
479C2×C4—3442no—
480C2×C4—1721no—
481C2×C4—1721no—
482C2×C4—1721no—
483C2×C4C2×#1062188211yescharacteristic
484C2×C4C2×#1062188211yescharacteristic
485C2×C4C2×#1062188211yescharacteristic
486C2×C4C2×#1062188211yescharacteristic
487C2×C4C22×C22⋊D4311yescharacteristic
488C8—21no—
489C8—21no—
490C8—21no—
491C8C2×#1062190011yescharacteristic
492C8#1306337011yescharacteristic
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—3441no—
502C22—3441no—
503C22—3441no—
504C22#1458333412yes—
505C22C22×#1062188211yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—42no—
511C4—81no—
512C4—81no—
513C4—3441no—
514C4—3441no—
515C4—3441no—
516C4#1458354311yescharacteristic
517C4#1458371011yescharacteristic
518C2—22no—
519C2—41no—
520C2—161no—
521C2—6881no—
522C2#1914640811yescharacteristic
523C2C2×#1458333411yescharacteristic
524C2#1914774611yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3285C2
socleC22×C43C22×D8
hypercenter#3285D43
hypocenterC43#33875
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3285

Complements

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

NH ≅ G/Ntype
1. #19146943C2semidirect
2. #19136831C2semidirect
3. #19136795C2semidirect
4. #19136773C2semidirect
5. #19136747C2semidirect
6. #19136710C2semidirect
7. #19136679C2semidirect
8. #19136647C2semidirect
9. #19136518C2semidirect
10. #19136512C2semidirect
11. #19136457C2semidirect
12. #19136421C2semidirect
13. #19136307C2semidirect
14. C2×#14582703C2semidirect
15. C43×#3285C2semidirect
146. Q16×C43#41semidirect
257. #3285D43semidirect
321. C43#33875semidirect
409. Q16#10621900semidirect

Maximal subgroups

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

subgroupindex
#191469432
#191368312
#191367952
#191367732
#191367472
#191367102
#191366792
#191366472
#191365182
#191365122
#191364572
#191364212
#191363072
C2×#145827032
C43×#32852
#3387543