Finite Group Databasebeta

← #16019920

Subgroups — #16019920

Order 3328.

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#13127184C211yesmaximal, characteristic, complemented
2#13117072C211yesmaximal, characteristic, complemented
3#13117036C211yesmaximal, characteristic, complemented
4#13117014C211yesmaximal, characteristic, complemented
5#13116988C211yesmaximal, characteristic, complemented
6#13116951C211yesmaximal, characteristic, complemented
7#13116920C211yesmaximal, characteristic, complemented
8#13116888C211yesmaximal, characteristic, complemented
9#13116759C211yesmaximal, characteristic, complemented
10#13116753C211yesmaximal, characteristic, complemented
11#13116698C211yesmaximal, characteristic, complemented
12#13116662C211yesmaximal, characteristic, complemented
13#13116548C211yesmaximal, characteristic, complemented
14C2×#11718156C211yesmaximal, characteristic, complemented
15C13×#3285C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C22×C13×Q16C2211yescharacteristic
18C13×#548—21no—
19#11719260—21no—
20C13×#495C2211yescharacteristic
21C13×#467C2211yescharacteristic
22C13×#466C2211yescharacteristic
23C13×#464—21no—
24C13×#452—21no—
25C13×#448—21no—
26C4×C13×Q16C2211yescharacteristic
27C8×D4×C13C2211yescharacteristic
28C2×#88068C2211yescharacteristic
29C2×#88068C2211yescharacteristic
30C2×#88066C2211yescharacteristic
31#11718776C2211yescharacteristic
32#11718776C2211yescharacteristic
33C2×#88058C2211yescharacteristic
34C2×#88058C2211yescharacteristic
35C2×#88052C2211yescharacteristic
36C22×#6090C2211yescharacteristic
37#11718507—21no—
38#11718397—21no—
39#11718397—21no—
40C4×D104C2211yescharacteristic
41#11718343C2211yescharacteristic
42#11718156C2211yescharacteristic
43#11718156C2211yescharacteristic
44#11718156C2211yescharacteristic
45#11718156C2211yescharacteristic
46#11718156C2211yescharacteristic
47#11718156C2211yescharacteristic
48#11718154C2211yescharacteristic
49#11718154C2211yescharacteristic
50#11718154C2211yescharacteristic
51C22⋊#6090C2211yescharacteristic
52C22⋊#6090C2211yescharacteristic
53#11718083C2211yescharacteristic
54#11718081C2211yescharacteristic
55#11718081C2211yescharacteristic
56#11718081C2211yescharacteristic
57C4⋊#6090C2211yescharacteristic
58#11718053C2211yescharacteristic
59C2×C13×#41—21no—
60C22×Q8×C13—21no—
61C2×#6129—41no—
62C13×#135—22no—
63C13×#135—41no—
64C2×C13×Q16—22no—
65C2×C13×Q16—21no—
66C2×C13×Q16—41no—
67C2×C13×Q16C2311yescharacteristic
68C2×C13×Q16C2311yescharacteristic
69C2×C13×SD16—21no—
70C2×C13×SD16—21no—
71C2×C13×D8C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C13×#124—21no—
75C13×#124—41no—
76C13×C22⋊Q8—21no—
77C13×C22⋊Q8—41no—
78C13×#121—21no—
79C13×#121—41no—
80C4×Q8×C13—21no—
81C4×D4×C13—41no—
82C4×D4×C13D411yescharacteristic
83#88184—21no—
84#88184—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×D104C2311yescharacteristic
88#88151—41no—
89#88140—41no—
90#88140—41no—
91C4×D52—21no—
92#88123—21no—
93C13×#107C2311yescharacteristic
94C13×C4⋊C8D411yescharacteristic
95C13×#103—21no—
96C13×#103—21no—
97C13×#102—21no—
98C13×C22⋊C8D411yescharacteristic
99C13×C22⋊C8D411yescharacteristic
100C4×C8×C13C2311yescharacteristic
101#88068—22no—
102#88068—41no—
103#88066—41no—
104#88061—21no—
105#88061—21no—
106#88061—21no—
107#88058—21no—
108#88058—21no—
109#88058—21no—
110#88058C2311yescharacteristic
111#88058C2311yescharacteristic
112#88058C2311yescharacteristic
113#88052—41no—
114C2×#6090—41no—
115C2×#6090C2311yescharacteristic
116C2×#6090C2311yescharacteristic
117C2×#6090C2311yescharacteristic
118C2×#6090C2311yescharacteristic
119#33875—131nomaximal, Sylow
120C13×#41—42no—
121C13×#41—81no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—42no—
125C2×Q8×C13—41no—
126C2×Q8×C13—81no—
127C2×D4×C13—21no—
128C2×D4×C13—41no—
129C2×D4×C13—41no—
130C2×D4×C13D811yescharacteristic
131C22×C4×C13—41no—
132C22×C4×C13—41no—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C2×C22⋊D13—41no—
136C2×C22⋊D13—41no—
137C22×Dic13—41no—
138C22×Dic13—41no—
139#6129—84no—
140C2×D52—21no—
141C2×C4×D13—41no—
142C2×Dic26—41no—
143C13×Q16—21no—
144C13×Q16—21no—
145C13×Q16—21no—
146C13×Q16—42no—
147C13×Q16#4112yescomplemented
148C13×SD16—42no—
149C13×SD16—81no—
150C13×D8—21no—
151C13×D8—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13C2×D411yescharacteristic
157C2×C8×C13C2×D411yescharacteristic
158C2×C8×C13C2×D411yescharacteristic
159C2×C8×C13C2411yescharacteristic
160C13×C4⋊C4—21no—
161C13×C4⋊C4—41no—
162C13×C4⋊C4—41no—
163C13×C4⋊C4D811yescharacteristic
164C13×C22⋊C4—41no—
165C13×C22⋊C4—41no—
166C13×C22⋊C4—41no—
167C13×C22⋊C4—41no—
168C13×C22⋊C4D811yescharacteristic
169C13×C22⋊C4D811yescharacteristic
170C42×C13—41no—
171C42×C13C2×D411yescharacteristic
172#6103—41no—
173#6103—41no—
174#6103—41no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—41no—
179C4⋊Dic13—41no—
180C4⋊Dic13—41no—
181D104—21no—
182D104—21no—
183#6090—21no—
184#6090—21no—
185#6090—21no—
186#6090—21no—
187#3334—131no—
188#3285D1311yescharacteristic, complemented
189#2243—131no—
190#2236—131no—
191#2232—131no—
192#2227—131no—
193#2220—131no—
194#2215—131no—
195#2210—131no—
196#2186—131no—
197#2185—131no—
198#2175—131no—
199#2168—131no—
200#2139—131no—
201C2×#358—131no—
202C23×C13—41no—
203C23×C13C2×D811yescharacteristic
204C23×C13C2×D811yescharacteristic
205C22×D13—41no—
206Q8×C13—22no—
207Q8×C13—41no—
208Q8×C13—41no—
209Q8×C13—41no—
210Q8×C13—82no—
211D4×C13—22no—
212D4×C13—41no—
213D4×C13—41no—
214D4×C13—82no—
215D4×C13—82no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—82no—
224C2×C4×C13—82no—
225C2×C4×C13C2×D811yescharacteristic
226C2×C4×C13C2×D811yescharacteristic
227C2×C4×C13C2×D811yescharacteristic
228C2×C4×C13C2×D811yescharacteristic
229C2×C4×C13C22×D411yescharacteristic
230C22⋊D13—82no—
231C22⋊D13—82no—
232C2×Dic13—41no—
233C2×Dic13—41no—
234C2×Dic13—41no—
235C2×Dic13—82no—
236C2×Dic13—82no—
237D52—41no—
238D52—41no—
239C4×D13—82no—
240Dic26—82no—
241C8×C13—21no—
242C8×C13—21no—
243C8×C13—21no—
244C8×C13C2×#4111yescharacteristic
245C8×C13H(5,𝔽2)11yescharacteristic
246C2×#135C2×D1311yescharacteristic
247C22×Q16C2×D1311yescharacteristic
248#548—21no—
249#547—261no—
250C2×SD32—131no—
251C2×SD32—131no—
252C2×D16—131no—
253C2×M32—131no—
254C22×C16—131no—
255#500—131no—
256#495C2×D1311yescharacteristic
257#480—261no—
258#480—261no—
259#474—261no—
260#467C2×D1311yescharacteristic
261#466—131no—
262#466—131no—
263#466C2×D1311yescharacteristic
264#464—21no—
265#452—21no—
266#448—21no—
267C4×Q16C2×D1311yescharacteristic
268C4×D8—131no—
269C8×D4C2×D1311yescharacteristic
270C2×#107—131no—
271C2×#107—131no—
272#366—131no—
273#366—131no—
274#366—131no—
275C4⋊C16—131no—
276#358—131no—
277#358—131no—
278#358—131no—
279#358—131no—
280#358—131no—
281#358—131no—
282#357—131no—
283#357—131no—
284#357—131no—
285#357—131no—
286C22⋊C16—131no—
287C22⋊C16—131no—
288#346—131no—
289C22×C13—21no—
290C22×C13—21no—
291C22×C13—21no—
292C22×C13—21no—
293C22×C13—21no—
294C22×C13—81no—
295C22×C13—81no—
296C22×C13—81no—
297C22×C13#50912yes—
298C22×C13C22×D811yescharacteristic
299C2×D13—81no—
300C2×D13—81no—
301C2×D13—81no—
302C4×C13—21no—
303C4×C13—21no—
304C4×C13—21no—
305C4×C13—21no—
306C4×C13—42no—
307C4×C13—81no—
308C4×C13—81no—
309C4×C13#54611yescharacteristic
310C4×C13#57711yescharacteristic
311Dic13—81no—
312Dic13—81no—
313Dic13—81no—
314C2×#41—21no—
315C2×#41—521no—
316C22×Q8—21no—
317#135—22no—
318#135—41no—
319C2×Q16—22no—
320C2×Q16—21no—
321C2×Q16—41no—
322C2×Q16C22×D1311yescharacteristic
323C2×Q16C22×D1311yescharacteristic
324C2×SD16—21no—
325C2×SD16—21no—
326C2×D8—131no—
327C2×D8C22×D1311yescharacteristic
328C22×C8C22×D1311yescharacteristic
329C22×C8C22×D1311yescharacteristic
330C4⋊Q8—261no—
331#124—21no—
332#124—41no—
333#123—521no—
334#123—521no—
335C22⋊Q8—21no—
336C22⋊Q8—41no—
337C22⋊Q8—521no—
338#121—21no—
339#121—41no—
340#121—261no—
341#121—261no—
342C4×Q8—21no—
343C4×D4—41no—
344C4×D4—261no—
345C4×D4C22⋊D1311yescharacteristic
346C2×C4⋊C4—261no—
347C2×C4⋊C4—261no—
348SD32—262no—
349SD32—521no—
350D16—521no—
351M32—521no—
352C2×C16—131no—
353C2×C16—131no—
354C2×C16—131no—
355C2×C16—131no—
356C2×C16—521no—
357#107—131no—
358#107—131no—
359#107—131no—
360#107—261no—
361#107—261no—
362#107—261no—
363#107C22×D1311yescharacteristic
364C4⋊C8C22⋊D1311yescharacteristic
365#103—21no—
366#103—21no—
367#102—21no—
368#102—261no—
369#102—261no—
370#102—261no—
371C22⋊C8C22⋊D1311yescharacteristic
372C22⋊C8C22⋊D1311yescharacteristic
373C4×C8C22×D1311yescharacteristic
374C2×C13—22no—
375C2×C13—41no—
376C2×C13—161no—
377C2×C13#329411yescharacteristic
378C2×C13C2×#50911yescharacteristic
379C2×C13#341711yescharacteristic
380D13—161no—
381#41—42no—
382#41—81no—
383#41—1044no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—42no—
387C2×Q8—41no—
388C2×Q8—81no—
389C2×Q8—521no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—261no—
394C2×D4—521no—
395C2×D4—521no—
396C2×D4#610411yescharacteristic
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—521no—
400C22×C4—521no—
401C22×C4—521no—
402C22×C4C2×C22⋊D1311yescharacteristic
403C22×C4C2×C22⋊D1311yescharacteristic
404Q16—21no—
405Q16—21no—
406Q16—21no—
407Q16—42no—
408Q16#612912yescomplemented
409SD16—42no—
410SD16—81no—
411D8—21no—
412D8—21no—
413D8—261no—
414D8—261no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8C2×C22⋊D1311yescharacteristic
420C2×C8C2×C22⋊D1311yescharacteristic
421C2×C8C2×C22⋊D1311yescharacteristic
422C2×C8C23×D1311yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—261no—
427C4⋊C4—261no—
428C4⋊C4—261no—
429C4⋊C4—521no—
430C4⋊C4—521no—
431C4⋊C4—521no—
432C4⋊C4#610411yescharacteristic
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—521no—
438C22⋊C4—521no—
439C22⋊C4—521no—
440C22⋊C4#610411yescharacteristic
441C22⋊C4#610411yescharacteristic
442C42—41no—
443C42C2×C22⋊D1311yescharacteristic
444C16—261no—
445C16—261no—
446C16—261no—
447C16—261no—
448C13#3387511yescharacteristic, complemented, Sylow
449C23—41no—
450C23—521no—
451C23C2×#610411yescharacteristic
452C23C2×#610411yescharacteristic
453Q8—22no—
454Q8—41no—
455Q8—41no—
456Q8—41no—
457Q8—82no—
458Q8—1042no—
459D4—22no—
460D4—41no—
461D4—41no—
462D4—82no—
463D4—82no—
464D4—521no—
465D4—521no—
466D4—1042no—
467D4—1042no—
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—521no—
478C2×C4—521no—
479C2×C4—521no—
480C2×C4—1042no—
481C2×C4—1042no—
482C2×C4—1042no—
483C2×C4C2×#610411yescharacteristic
484C2×C4C2×#610411yescharacteristic
485C2×C4C2×#610411yescharacteristic
486C2×C4C2×#610411yescharacteristic
487C2×C4C22×C22⋊D1311yescharacteristic
488C8—21no—
489C8—21no—
490C8—21no—
491C8C2×#612911yescharacteristic
492C8#8825111yescharacteristic
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—1041no—
502C22—1041no—
503C22—1041no—
504C22#1171885412yes—
505C22C22×#610411yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—42no—
511C4—81no—
512C4—81no—
513C4—1041no—
514C4—1041no—
515C4—1041no—
516C4#1171951111yescharacteristic
517C4#1171954111yescharacteristic
518C2—22no—
519C2—41no—
520C2—161no—
521C2—2081no—
522C2#1312664911yescharacteristic
523C2C2×#1171885411yescharacteristic
524C2#1312798711yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3285C2
socleC22×C13C22×D8
hypercenter#3285D13
hypocenterC13#33875
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3285

Complements

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

NH ≅ G/Ntype
1. #13127184C2semidirect
2. #13117072C2semidirect
3. #13117036C2semidirect
4. #13117014C2semidirect
5. #13116988C2semidirect
6. #13116951C2semidirect
7. #13116920C2semidirect
8. #13116888C2semidirect
9. #13116759C2semidirect
10. #13116753C2semidirect
11. #13116698C2semidirect
12. #13116662C2semidirect
13. #13116548C2semidirect
14. C2×#11718156C2semidirect
15. C13×#3285C2semidirect
147. C13×Q16#41semidirect
188. #3285D13semidirect
408. Q16#6129semidirect
448. C13#33875semidirect

Maximal subgroups

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

subgroupindex
#131271842
#131170722
#131170362
#131170142
#131169882
#131169512
#131169202
#131168882
#131167592
#131167532
#131166982
#131166622
#131165482
C2×#117181562
C13×#32852
#3387513