Finite Group Databasebeta

← #25251714

Subgroups — #25251714

Order 11008.

558 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143472C211yesmaximal, characteristic, complemented
2#19136778C211yesmaximal, characteristic, complemented
3#19136773C211yesmaximal, characteristic, complemented
4#19136756C211yesmaximal, characteristic, complemented
5#19136749C211yesmaximal, characteristic, complemented
6#19136632C211yesmaximal, characteristic, complemented
7#19136627C211yesmaximal, characteristic, complemented
8#19136516C211yesmaximal, characteristic, complemented
9#19136516C211yesmaximal, characteristic, complemented
10#19136469C211yesmaximal, characteristic, complemented
11#19136459C211yesmaximal, characteristic, complemented
12C4×#13063269C211yesmaximal, characteristic, complemented
13C4×#13063266C211yesmaximal, characteristic, complemented
14#19136402C211yesmaximal, characteristic, complemented
15C43×#3176C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17#14583379—21no—
18C2×#13063269C2211yescharacteristic
19C2×#13063269C2211yescharacteristic
20C2×#13063266C2211yescharacteristic
21C2×#13063266C2211yescharacteristic
22#14583001—21no—
23#14583001—21no—
24C4×Dic172C2211yescharacteristic
25C4×Dic172C2211yescharacteristic
26C4×D344C2211yescharacteristic
27C4×D344C2211yescharacteristic
28C2×#13063259C2211yescharacteristic
29#14582901—21no—
30#14582726C2211yescharacteristic
31#14582726C2211yescharacteristic
32#14582724C2211yescharacteristic
33#14582724C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35C4⋊(C43⋊C16)C2211yescharacteristic
36#14582702C2211yescharacteristic
37#14582702C2211yescharacteristic
38#14582700C2211yescharacteristic
39#14582700C2211yescharacteristic
40#14582700C2211yescharacteristic
41#14582700C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44C22⋊(C43⋊C16)C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46#14582675C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C43×#540—21no—
49C43×#499C2211yescharacteristic
50C43×#493C2211yescharacteristic
51C43×#490—21no—
52C43×#469—21no—
53C43×#466C2211yescharacteristic
54C43×#466C2211yescharacteristic
55C43×#442—21no—
56C4×D8×C43C2211yescharacteristic
57C4×D8×C43C2211yescharacteristic
58C43×#405C2211yescharacteristic
59C2×#10621898—21no—
60#13063347—22no—
61#13063347—22no—
62C2×Dic172C2311yescharacteristic
63C2×#10621873—21no—
64C2×D344C2311yescharacteristic
65C4×Dic86—21no—
66C4×Dic86—21no—
67C4×D172—21no—
68C4×D172—21no—
69(C22⋊D43)⋊C4—41no—
70(C22⋊D43)⋊C4—41no—
71#13063283—41no—
72C2×C4⋊Dic43—21no—
73C4⋊C4×D43—41no—
74#13063269—22no—
75#13063269—22no—
76#13063266—22no—
77#13063266—22no—
78C2×C43⋊C16C2311yescharacteristic
79C2×C43⋊C16C2311yescharacteristic
80C2×C43⋊C16C2311yescharacteristic
81C2×C43⋊C16C2311yescharacteristic
82#13063259—21no—
83#13063259C2311yescharacteristic
84#13063259C2311yescharacteristic
85#13063250—21no—
86#13063250—21no—
87#13063247—21no—
88#13063247—21no—
89C2×D8×C43—21no—
90C2×D8×C43C2311yescharacteristic
91C2×D8×C43C2311yescharacteristic
92C2×M16×C43D411yescharacteristic
93C22×C8×C43C2311yescharacteristic
94#127×C43—21no—
95#125×C43—21no—
96#123×C43—41no—
97#123×C43—41no—
98#121×C43—21no—
99#121×C43—21no—
100#121×C43—41no—
101#121×C43—41no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104#117×C43D411yescharacteristic
105#107×C43C2311yescharacteristic
106#107×C43C2311yescharacteristic
107#106×C43—21no—
108#102×C43—21no—
109#102×C43—21no—
110#102×C43—21no—
111#102×C43—21no—
112#97×C43D411yescharacteristic
113#97×C43D411yescharacteristic
114C4×C8×C43C2311yescharacteristic
115C4×C8×C43C2311yescharacteristic
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—41no—
119C2×D4×C43—41no—
120C2×D4×C43—41no—
121C2×D4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C2×C22⋊D43—41no—
126C22×Dic43—41no—
127#10621898—24no—
128#10621898—42no—
129C2×D172—21no—
130C2×C4×D43—41no—
131C2×C4×D43—41no—
132C2×C4×D43—41no—
133C2×Dic86—21no—
134D8×C43—21no—
135D8×C43—21no—
136D8×C43—21no—
137D8×C43—21no—
138D8×C43—42no—
139M16×C43—41no—
140C2×C8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43C2×D411yescharacteristic
143C2×C8×C43C2×D411yescharacteristic
144C2×C8×C43C2×D411yescharacteristic
145C2×C8×C43C2411yescharacteristic
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—41no—
149C4⋊C4×C43—41no—
150C4⋊C4×C43D811yescharacteristic
151C4⋊C4×C43D811yescharacteristic
152C22⋊C4×C43—41no—
153C22⋊C4×C43—41no—
154C22⋊C4×C43—41no—
155C22⋊C4×C43—41no—
156C22⋊C4×C43D811yescharacteristic
157C22⋊C4×C43D811yescharacteristic
158C42×C43C2×D411yescharacteristic
159C42×C43C2×D411yescharacteristic
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—41no—
165Dic43⋊C4—41no—
166Dic43⋊C4—41no—
167C4×Dic43—41no—
168C4×Dic43—41no—
169Dic172—21no—
170Dic172#4112yes—
171D344—21no—
172D344#4112yes—
173#10621873—24no—
174C43⋊C16—21no—
175C43⋊C16—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43C2×D811yescharacteristic
181C22×D43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—41no—
186D4×C43—161no—
187D4×C43—161no—
188D4×C43—161no—
189D4×C43—161no—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—161no—
195C2×C4×C43—161no—
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C2×D811yescharacteristic
198C2×C4×C43C2×D811yescharacteristic
199C2×C4×C43C2×D811yescharacteristic
200C2×C4×C43C2×D811yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C22⋊D43—44no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—161no—
207D172—22no—
208D172—41no—
209C4×D43—44no—
210C4×D43—161no—
211C4×D43—161no—
212Dic86—22no—
213Dic86—41no—
214C8×C43—21no—
215C8×C43—21no—
216C8×C43—21no—
217C8×C43C2×#4111yescharacteristic
218C8×C43C2×#4111yescharacteristic
219#33679—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—81no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43—81no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43C22×D811yescharacteristic
230C2×D43—42no—
231C2×D43—81no—
232C2×D43—81no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—81no—
239C4×C43—81no—
240C4×C43#52511yescharacteristic
241C4×C43#57511yescharacteristic
242Dic43—42no—
243Dic43—81no—
244Dic43—81no—
245#3176D4311yescharacteristic, complemented
246#2951—431no—
247#2233—431no—
248#2232—431no—
249#2229—431no—
250#2228—431no—
251#2207—431no—
252#2206—431no—
253#2186—431no—
254#2186—431no—
255#2177—431no—
256#2175—431no—
257C4×SD32—431no—
258C4×D16—431no—
259#2164—431no—
260C2×C43—41no—
261C2×C43—161no—
262C2×C43—161no—
263C2×C43#310011yescharacteristic
264C2×C43#341511yescharacteristic
265C2×C43#341611yescharacteristic
266D43—82no—
267C2×#135—431no—
268#540—21no—
269#520—861no—
270C2×SD32—431no—
271C2×SD32—431no—
272C2×D16—431no—
273C2×D16—431no—
274#499C2×D4311yescharacteristic
275#493C2×D4311yescharacteristic
276#490—21no—
277#469—21no—
278#466C2×D4311yescharacteristic
279#466C2×D4311yescharacteristic
280#442—21no—
281#440—861no—
282#440—861no—
283C4×Q16—431no—
284C4×Q16—431no—
285C4×D8—431no—
286C4×D8—431no—
287C4×D8C2×D4311yescharacteristic
288C4×D8C2×D4311yescharacteristic
289C2×#107—431no—
290#417—861no—
291#405C2×D4311yescharacteristic
292#367—431no—
293#367—431no—
294#366—431no—
295#366—431no—
296C4⋊C16—431no—
297C4⋊C16—431no—
298#358—431no—
299#358—431no—
300#357—431no—
301#357—431no—
302#357—431no—
303#357—431no—
304#357—431no—
305#357—431no—
306C22⋊C16—431no—
307C22⋊C16—431no—
308#346—431no—
309C4×C16—431no—
310C43#3367911yescharacteristic, complemented, Sylow
311C2×#41—861no—
312#135—862no—
313#135—862no—
314C2×Q16—431no—
315C2×SD16—861no—
316C2×D8—21no—
317C2×D8—431no—
318C2×D8C22×D4311yescharacteristic
319C2×D8C22×D4311yescharacteristic
320C2×M16C22⋊D4311yescharacteristic
321C22×C8C22×D4311yescharacteristic
322#127—21no—
323#125—21no—
324#123—41no—
325#123—41no—
326#121—21no—
327#121—21no—
328#121—41no—
329#121—41no—
330C4×Q8—861no—
331C4×Q8—861no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—861no—
335C4×D4—861no—
336C4×D4—1721no—
337C4×D4—1721no—
338#117—1721no—
339#117C22⋊D4311yescharacteristic
340C2×C4⋊C4—861no—
341C2×C4⋊C4—1721no—
342SD32—862no—
343SD32—862no—
344D16—862no—
345D16—862no—
346C2×C16—431no—
347C2×C16—431no—
348C2×C16—431no—
349C2×C16—431no—
350#107—431no—
351#107—431no—
352#107—861no—
353#107C22×D4311yescharacteristic
354#107C22×D4311yescharacteristic
355#106—21no—
356#103—861no—
357#103—861no—
358#102—21no—
359#102—21no—
360#102—21no—
361#102—21no—
362#102—861no—
363#102—861no—
364#97C22⋊D4311yescharacteristic
365#97C22⋊D4311yescharacteristic
366C4×C8C22×D4311yescharacteristic
367C4×C8C22×D4311yescharacteristic
368#41—864no—
369#41—1722no—
370C2×Q8—861no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—861no—
378C2×D4—1721no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—1721no—
382C22×C4—1721no—
383C22×C4—1721no—
384C22×C4—1721no—
385C22×C4C2×C22⋊D4311yescharacteristic
386Q16—432no—
387Q16—861no—
388SD16—864no—
389D8—21no—
390D8—21no—
391D8—21no—
392D8—21no—
393D8—42no—
394D8—432no—
395D8—861no—
396M16—41no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8C2×C22⋊D4311yescharacteristic
400C2×C8C2×C22⋊D4311yescharacteristic
401C2×C8C2×C22⋊D4311yescharacteristic
402C2×C8C23×D4311yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C4⋊C4—1721no—
410C4⋊C4—1721no—
411C4⋊C4—1721no—
412C4⋊C4#1062188211yescharacteristic
413C4⋊C4#1062188211yescharacteristic
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C22⋊C4#1062188211yescharacteristic
421C22⋊C4#1062188211yescharacteristic
422C42—1721no—
423C42—1721no—
424C42C2×C22⋊D4311yescharacteristic
425C42C2×C22⋊D4311yescharacteristic
426C16—861no—
427C16—861no—
428C16—861no—
429C16—861no—
430C23—41no—
431C23—41no—
432C23—1721no—
433C23C2×#1062188211yescharacteristic
434Q8—862no—
435Q8—1721no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—41no—
440D4—161no—
441D4—161no—
442D4—161no—
443D4—161no—
444D4—862no—
445D4—1724no—
446D4—1721no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—161no—
452C2×C4—161no—
453C2×C4—1724no—
454C2×C4—1721no—
455C2×C4—1721no—
456C2×C4—1721no—
457C2×C4—6881no—
458C2×C4—6881no—
459C2×C4—6881no—
460C2×C4C2×#1062188211yescharacteristic
461C2×C4C2×#1062188211yescharacteristic
462C2×C4C2×#1062188211yescharacteristic
463C2×C4C2×#1062188211yescharacteristic
464C2×C4C2×#1062188211yescharacteristic
465C2×C4C22×C22⋊D4311yescharacteristic
466C8—21no—
467C8—21no—
468C8—21no—
469C8#41×D4311yescharacteristic
470C8#41×D4311yescharacteristic
471C22—21no—
472C22—21no—
473C22—21no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—3441no—
481C22—3441no—
482C22—1722no—
483C22C22×#1062188211yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—81no—
490C4—81no—
491C4—3441no—
492C4—3441no—
493C4—1722no—
494C4#1458340611yescharacteristic
495C4#1458369711yescharacteristic
496C2—41no—
497C2—161no—
498C2—161no—
499C2—3442no—
500C2#1914459111yescharacteristic
501C2#1914773411yescharacteristic
502C2#1914774211yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3176C2
socleC22×C43C22×D8
hypercenter#3176D43
hypocenterC43#33679
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3176

Complements

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

NH ≅ G/Ntype
1. #19143472C2semidirect
2. #19136778C2semidirect
3. #19136773C2semidirect
4. #19136756C2semidirect
5. #19136749C2semidirect
6. #19136632C2semidirect
7. #19136627C2semidirect
8. #19136516C2semidirect
9. #19136516C2semidirect
10. #19136469C2semidirect
11. #19136459C2semidirect
12. C4×#13063269C2semidirect
13. C4×#13063266C2semidirect
14. #19136402C2semidirect
15. C43×#3176C2semidirect
245. #3176D43semidirect
310. C43#33679semidirect

Maximal subgroups

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

subgroupindex
#191434722
#191367782
#191367732
#191367562
#191367492
#191366322
#191366272
#191365162
#191364692
#191364592
C4×#130632692
C4×#130632662
#191364022
C43×#31762
#3367943