Finite Group Databasebeta

← #25249985

Subgroups — #25249985

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583330C211yesmaximal, characteristic
2#19143470C211yesmaximal, characteristic, complemented
3#19143465C211yesmaximal, characteristic, complemented
4#19136469C211yesmaximal, characteristic, complemented
5#19136468C211yesmaximal, characteristic, complemented
6#19136464C211yesmaximal, characteristic, complemented
7#19136463C211yesmaximal, characteristic, complemented
8C4×#13063270C211yesmaximal, characteristic, complemented
9SD32×Dic43C211yesmaximal, characteristic, complemented
10#19136446C211yesmaximal, characteristic, complemented
11#367×D43C211yesmaximal, characteristic, complemented
12#19136306C211yesmaximal, characteristic, complemented
13#19136304C211yesmaximal, characteristic, complemented
14#19136190C211yesmaximal, characteristic, complemented
15C4×SD32×C43C211yesmaximal, characteristic, complemented
16C2×#13063348C2211yescharacteristic
17C2×#13063344C2211yescharacteristic
18#14583381—21no—
19#14583378—21no—
20#14583330C418yescomplemented
21C2×#13063271C2211yescharacteristic
22C2×#13063270C2211yescharacteristic
23C2×#13063266C2211yescharacteristic
24C2×#13063264C2211yescharacteristic
25C2×C16×D43C2211yescharacteristic
26#14583002—21no—
27#14582999—21no—
28#14582997—21no—
29#14582996—21no—
30C4×Dic172C2211yescharacteristic
31Q16×Dic43C2211yescharacteristic
32#14582993C2211yescharacteristic
33C4×D344C2211yescharacteristic
34D8×Dic43C2211yescharacteristic
35#14582981C2211yescharacteristic
36#107×D43C2211yescharacteristic
37#107×D43C2211yescharacteristic
38#14582899—21no—
39#14582897—21no—
40#14582853C2211yescharacteristic
41#14582727C2211yescharacteristic
42#14582726C2211yescharacteristic
43#14582726C2211yescharacteristic
44#14582704C2211yescharacteristic
45#14582703C2211yescharacteristic
46#14582702C2211yescharacteristic
47#14582701C2211yescharacteristic
48#14582700C2211yescharacteristic
49#14582699C2211yescharacteristic
50#14582675C2211yescharacteristic
51#14582674C2211yescharacteristic
52C16×Dic43C2211yescharacteristic
53C2×SD32×C43C2211yescharacteristic
54C4×Q16×C43C2211yescharacteristic
55C4×D8×C43C2211yescharacteristic
56C43×#367C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C4×C16×C43C2211yescharacteristic
60C2×#10621902—21no—
61C2×#10621900—21no—
62#13063348—22no—
63#13063348C2×C414yescomplemented
64#13063344—22no—
65#13063344C2×C414yescomplemented
66C2×Dic172C2311yescharacteristic
67C2×#10621883—21no—
68C2×#10621884—21no—
69C2×D344C2311yescharacteristic
70C2×#10621872D411yescharacteristic
71C2×C8×D43C2311yescharacteristic
72Q8×Dic43—21no—
73C4×Dic86—21no—
74#13063290—21no—
75C4×D172—21no—
76C4×D172—41no—
77D4×Dic43—21no—
78#13063287—21no—
79#13063287—41no—
80C4×C22⋊D43—41no—
81(C22⋊D43)⋊C4—41no—
82#13063282—41no—
83#13063282D411yescharacteristic
84#13063281—41no—
85C2×Dic43⋊C4—41no—
86C4⋊C4×D43—21no—
87C4⋊C4×D43—21no—
88C4⋊C4×D43—41no—
89#13063271C2×C414yescomplemented
90#13063270C2×C414yescomplemented
91#13063266C2×C414yescomplemented
92#13063264—22no—
93C2×C43⋊C16C2311yescharacteristic
94C2×C43⋊C16C2311yescharacteristic
95C16×D43C2×C414yescomplemented
96#13063259C2311yescharacteristic
97#13063259C2311yescharacteristic
98#13063258—21no—
99#13063258—21no—
100#13063250—21no—
101#13063249—21no—
102#13063248—21no—
103#13063247—21no—
104#13063246—21no—
105#13063245—21no—
106#13063236D411yescharacteristic
107#13063235D411yescharacteristic
108C8×Dic43C2311yescharacteristic
109C2×Q16×C43C2311yescharacteristic
110C2×D8×C43C2311yescharacteristic
111C4×Q8×C43—21no—
112C4×D4×C43—21no—
113SD32×C43C2×C414yescomplemented
114C2×C16×C43C2311yescharacteristic
115C2×C16×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#107×C43C2311yescharacteristic
118#103×C43—21no—
119#102×C43—21no—
120C4×C8×C43C2311yescharacteristic
121C2×Q8×C43—21no—
122C2×D4×C43—21no—
123C22×C4×C43—41no—
124C2×C22⋊D43—41no—
125C22×Dic43—41no—
126C22×Dic43—41no—
127#10621902—24no—
128#10621902—42no—
129#10621900—24no—
130#10621900—42no—
131C2×D172—21no—
132C2×D172—41no—
133C2×C4×D43—41no—
134C2×C4×D43—41no—
135C2×C4×D43—41no—
136C2×C4×D43—41no—
137C2×C4×D43—41no—
138C2×C4×D43C2×D411yescharacteristic
139C2×Dic86—21no—
140Q16×C43—21no—
141Q16×C43C22×C412yes—
142D8×C43—21no—
143D8×C43C22×C412yes—
144C2×C8×C43C2×D411yescharacteristic
145C2×C8×C43C2411yescharacteristic
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C42×C43—41no—
151C42×C43C2×D411yescharacteristic
152C22⋊Dic43—41no—
153#10621884—24no—
154#10621883—24no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4D811yescharacteristic
158(C2×D43)⋊C4D811yescharacteristic
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161C4⋊Dic43—41no—
162Dic43⋊C4—41no—
163Dic43⋊C4—41no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166Dic43⋊C4D811yescharacteristic
167Dic43⋊C4D811yescharacteristic
168C4×Dic43—41no—
169C4×Dic43—41no—
170C4×Dic43—41no—
171C4×Dic43C2×D411yescharacteristic
172C2×C43⋊C8C2×D411yescharacteristic
173C2×C43⋊C8C2×D411yescharacteristic
174Dic172—21no—
175Dic172C22×C412yes—
176D344—21no—
177D344C22×C412yes—
178#10621872—22no—
179C8×D43C22×C412yes—
180C8×D43#4112yes—
181C16×C43—21no—
182C16×C43C22×C412yes—
183C43⋊C16—21no—
184C43⋊C16C22×C412yes—
185C23×C43—41no—
186C22×D43—41no—
187C22×D43C2×D811yescharacteristic
188Q8×C43—22no—
189Q8×C43—41no—
190D4×C43—22no—
191D4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—161no—
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C2×D811yescharacteristic
198C2×C4×C43C22×D411yescharacteristic
199C22⋊D43—44no—
200C2×Dic43—41no—
201C2×Dic43—44no—
202C2×Dic43—41no—
203C2×Dic43—41no—
204C2×Dic43—161no—
205C2×Dic43C2×D811yescharacteristic
206C2×Dic43C2×D811yescharacteristic
207C2×Dic43C2×D811yescharacteristic
208D172—22no—
209D172—44no—
210D172—41no—
211C4×D43—44no—
212C4×D43—161no—
213C4×D43—161no—
214C4×D43—161no—
215C4×D43—161no—
216C4×D43C4×D412yes—
217C4×D43#13512yes—
218Dic86—22no—
219Dic86—41no—
220C8×C43—21no—
221C8×C43C23×C411yescharacteristic
222C8×C43C2×#4111yescharacteristic
223C43⋊C8—21no—
224C43⋊C8C4×D412yes—
225#33460—431nomaximal, Sylow
226C22×C43—42no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43C22×D811yescharacteristic
230C2×D43—21no—
231C2×D43—21no—
232C2×D43—42no—
233C2×D43—81no—
234C2×D43—81no—
235C2×D43C4×D812yes—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—42no—
239C4×C43—81no—
240C4×C43—81no—
241C4×C43C2×C4×D411yescharacteristic
242C4×C43C2×#13511yescharacteristic
243Dic43—21no—
244Dic43—21no—
245Dic43—42no—
246Dic43—81no—
247Dic43—81no—
248Dic43C4×D812yes—
249C2×#508—431no—
250#2951—431no—
251#2951—431no—
252#2177—431no—
253#2177—431no—
254#2176—431no—
255#2176—431no—
256C4×SD32—431no—
257C4×SD32—431no—
258C4×SD32—431no—
259C4×SD32D4311yescharacteristic, complemented
260C2×#367—431no—
261#2139—431no—
262#2139—431no—
263#2108—431no—
264C2×C43—82no—
265C2×C43C2×C4×D811yescharacteristic
266C2×C43#341611yescharacteristic
267C2×C43#341611yescharacteristic
268D43—22no—
269D43—82no—
270C2×#135—431no—
271C2×#135—431no—
272#520—861no—
273#520—861no—
274#508—438no—
275C2×Q32—431no—
276C2×SD32—431no—
277C2×SD32C2×D4311yescharacteristic
278C2×D16—431no—
279C2×M32—431no—
280C22×C16—431no—
281#440—861no—
282#440—861no—
283#440—861no—
284#440—861no—
285C4×Q16—431no—
286C4×Q16—431no—
287C4×Q16—431no—
288C4×Q16C2×D4311yescharacteristic
289C4×D8—431no—
290C4×D8—431no—
291C4×D8—431no—
292C4×D8C2×D4311yescharacteristic
293C2×#107—431no—
294C2×#107—431no—
295#417—861no—
296#417—861no—
297#405—431no—
298#367—431no—
299#367—431no—
300#367—431no—
301#367C2×D4311yescharacteristic
302#358—431no—
303#358—431no—
304#358—431no—
305#358C2×D4311yescharacteristic
306#357—431no—
307#357—431no—
308#357—431no—
309#357C2×D4311yescharacteristic
310#346—431no—
311#346—431no—
312C4×C16—431no—
313C4×C16C2×D4311yescharacteristic
314C43#3346011yescharacteristic, complemented, Sylow
315C2×#41—861no—
316C2×#41—861no—
317#135—434no—
318#135—434no—
319#135—862no—
320#135—862no—
321C2×Q16—431no—
322C2×Q16C22×D4311yescharacteristic
323C2×SD16—861no—
324C2×SD16—861no—
325C2×D8—431no—
326C2×D8C22×D4311yescharacteristic
327C2×M16—431no—
328C22×C8—431no—
329C4×Q8—21no—
330C4×Q8—861no—
331C4×Q8—861no—
332C4×Q8—861no—
333C4×D4—21no—
334C4×D4—861no—
335C4×D4—861no—
336C4×D4—861no—
337C4×D4—1721no—
338C4×D4—1721no—
339C4×D4—1721no—
340C4×D4—1721no—
341#117—431no—
342#117—1721no—
343#117—1721no—
344C2×C4⋊C4—861no—
345C2×C4⋊C4—861no—
346C2×C4⋊C4—1721no—
347C2×C4⋊C4—1721no—
348Q32—434no—
349SD32—434no—
350SD32C4×D4314yescomplemented
351D16—434no—
352M32—862no—
353C2×C16—431no—
354C2×C16—434no—
355C2×C16—431no—
356C2×C16C22×D4311yescharacteristic
357C2×C16C22×D4311yescharacteristic
358#107—431no—
359#107—431no—
360#107—861no—
361#107—861no—
362#107C22×D4311yescharacteristic
363#107C22×D4311yescharacteristic
364#103—21no—
365#103—861no—
366#103—861no—
367#103—861no—
368#102—21no—
369#102—861no—
370#102—861no—
371#102—861no—
372#97—431no—
373#97—431no—
374C4×C8—431no—
375C4×C8C22×D4311yescharacteristic
376#41—864no—
377#41—864no—
378#41—1722no—
379#41—1722no—
380C2×Q8—21no—
381C2×Q8—861no—
382C2×D4—21no—
383C2×D4—861no—
384C2×D4—1721no—
385C2×D4—1721no—
386C22×C4—41no—
387C22×C4—431no—
388C22×C4—1721no—
389C22×C4—1721no—
390C22×C4—1721no—
391C22×C4—1721no—
392C22×C4—1721no—
393C22×C4—1721no—
394C22×C4—1721no—
395Q16—21no—
396Q16—432no—
397Q16—861no—
398Q16C2×C4×D4312yes—
399SD16—864no—
400SD16—864no—
401D8—21no—
402D8—432no—
403D8—861no—
404D8C2×C4×D4312yes—
405M16—862no—
406C2×C8—431no—
407C2×C8—432no—
408C2×C8—432no—
409C2×C8—431no—
410C2×C8D4×D4311yescharacteristic
411C2×C8C23×D4311yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—41no—
415C4⋊C4—431no—
416C4⋊C4—431no—
417C4⋊C4—861no—
418C4⋊C4—861no—
419C4⋊C4—1721no—
420C4⋊C4—1721no—
421C4⋊C4—1721no—
422C4⋊C4—1721no—
423C4⋊C4—1721no—
424C22⋊C4—41no—
425C22⋊C4—431no—
426C22⋊C4—431no—
427C22⋊C4—1721no—
428C22⋊C4—1721no—
429C22⋊C4—1721no—
430C42—41no—
431C42—431no—
432C42—1721no—
433C42—1721no—
434C42—1721no—
435C42D4×D4311yescharacteristic
436C16—21no—
437C16—432no—
438C16—861no—
439C16C2×C4×D4312yes—
440C23—41no—
441C23—431no—
442C23—1721no—
443Q8—22no—
444Q8—41no—
445Q8—862no—
446Q8—1721no—
447D4—22no—
448D4—41no—
449D4—862no—
450D4—1724no—
451D4—1724no—
452D4—1721no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—161no—
457C2×C4—431no—
458C2×C4—432no—
459C2×C4—432no—
460C2×C4—431no—
461C2×C4—431no—
462C2×C4—1724no—
463C2×C4—1724no—
464C2×C4—1721no—
465C2×C4—1721no—
466C2×C4—1721no—
467C2×C4—6881no—
468C2×C4—6881no—
469C2×C4—6881no—
470C2×C4—6881no—
471C2×C4—6881no—
472C2×C4D8×D4311yescharacteristic
473C2×C4D8×D4311yescharacteristic
474C2×C4C2×D4×D4311yescharacteristic
475C8—21no—
476C8—432no—
477C8—861no—
478C8C22×C4×D4311yescharacteristic
479C8#41×D4311yescharacteristic
480C22—42no—
481C22—81no—
482C22—81no—
483C22—432no—
484C22—861no—
485C22—861no—
486C22—3441no—
487C22—3441no—
488C22—1722no—
489C22C2×D8×D4311yescharacteristic
490C4—21no—
491C4—21no—
492C4—42no—
493C4—81no—
494C4—81no—
495C4—432no—
496C4—861no—
497C4—861no—
498C4—3441no—
499C4—3441no—
500C4—1722no—
501C4C4×D4×D4311yescharacteristic
502C4#135×D4311yescharacteristic
503C2—82no—
504C2—862no—
505C2—3442no—
506C2C4×D8×D4311yescharacteristic
507C2#1914773711yescharacteristic
508C2#1914773811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC4×SD32×C43C2
socleC22×C43C22×D8
prime radicalC2×#14583330C2
cosocleC2×C8×C43C24
hypercenterC4×SD32D43
hypocenterC43#33460
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. #19143470C2semidirect
3. #19143465C2semidirect
4. #19136469C2semidirect
5. #19136468C2semidirect
6. #19136464C2semidirect
7. #19136463C2semidirect
8. C4×#13063270C2semidirect
9. SD32×Dic43C2semidirect
10. #19136446C2semidirect
11. #367×D43C2semidirect
12. #19136306C2semidirect
13. #19136304C2semidirect
14. #19136190C2semidirect
15. C4×SD32×C43C2semidirect
20. #14583330C4semidirect
63. #13063348C2×C4semidirect
65. #13063344C2×C4semidirect
89. #13063271C2×C4semidirect
90. #13063270C2×C4semidirect
91. #13063266C2×C4semidirect
95. C16×D43C2×C4semidirect
113. SD32×C43C2×C4semidirect
259. C4×SD32D43semidirect
314. C43#33460semidirect
350. SD32C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833302
#191434702
#191434652
#191364692
#191364682
#191364642
#191364632
C4×#130632702
SD32×Dic432
#191364462
#367×D432
#191363062
#191363042
#191361902
C4×SD32×C432
#3346043