Finite Group Databasebeta

← #16019914

Subgroups — #16019914

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#13126579C211yesmaximal, characteristic, complemented
2#13117075C211yesmaximal, characteristic, complemented
3#13117038C211yesmaximal, characteristic, complemented
4#13117016C211yesmaximal, characteristic, complemented
5#13116985C211yesmaximal, characteristic, complemented
6#13116947C211yesmaximal, characteristic, complemented
7#13116920C211yesmaximal, characteristic, complemented
8#13116891C211yesmaximal, characteristic, complemented
9#13116757C211yesmaximal, characteristic, complemented
10#13116752C211yesmaximal, characteristic, complemented
11#13116700C211yesmaximal, characteristic, complemented
12#13116662C211yesmaximal, characteristic, complemented
13#13116546C211yesmaximal, characteristic, complemented
14C2×#11718084C211yesmaximal, characteristic, complemented
15C13×#3334C211yesmaximal, characteristic, complemented
16C13×#547—21no—
17C22×Dic52C2211yescharacteristic
18C2×#88158C2211yescharacteristic
19#11719257—21no—
20C13×#500C2211yescharacteristic
21C13×#480—21no—
22C13×#480—21no—
23C13×#474—21no—
24C13×#466C2211yescharacteristic
25C13×#466C2211yescharacteristic
26C4×C13×D8C2211yescharacteristic
27C8×D4×C13C2211yescharacteristic
28C2×C13×#107C2211yescharacteristic
29C2×C13×#107C2211yescharacteristic
30C2×#88067C2211yescharacteristic
31C2×#88067C2211yescharacteristic
32C2×#88066C2211yescharacteristic
33#11718777C2211yescharacteristic
34#11718776C2211yescharacteristic
35C2×#88052C2211yescharacteristic
36C22×#6090C2211yescharacteristic
37#11718506—21no—
38#11718399—21no—
39#11718394—21no—
40C4×Dic52C2211yescharacteristic
41#11718357C2211yescharacteristic
42#11718154C2211yescharacteristic
43C22⋊#6090C2211yescharacteristic
44C22⋊#6090C2211yescharacteristic
45#11718084C2211yescharacteristic
46#11718084C2211yescharacteristic
47#11718084C2211yescharacteristic
48#11718084C2211yescharacteristic
49#11718084C2211yescharacteristic
50#11718084C2211yescharacteristic
51#11718083C2211yescharacteristic
52#11718083C2211yescharacteristic
53#11718083C2211yescharacteristic
54#11718081C2211yescharacteristic
55#11718081C2211yescharacteristic
56#11718081C2211yescharacteristic
57C4⋊#6090C2211yescharacteristic
58#11718053C2211yescharacteristic
59C2×C13×#41—41no—
60C2×#6127—21no—
61C22×Dic26—21no—
62C2×C13×D8C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C13×C4⋊Q8—21no—
66C13×#123—41no—
67C13×#123—41no—
68C13×C22⋊Q8—41no—
69C13×#121—21no—
70C13×#121—21no—
71C4×D4×C13—21no—
72C4×D4×C13D411yescharacteristic
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75#88193—41no—
76#88184—21no—
77#88178—21no—
78C2×Dic52—22no—
79C2×Dic52—21no—
80C2×Dic52—41no—
81C2×Dic52C2311yescharacteristic
82C2×Dic52C2311yescharacteristic
83#88158—22no—
84#88158—41no—
85C2×D104C2311yescharacteristic
86C2×#6095—21no—
87C2×#6095—21no—
88#88150—41no—
89#88139—41no—
90#88135—41no—
91#88129—21no—
92C4×Dic26—21no—
93C13×#107—21no—
94C13×#107—21no—
95C13×#107—21no—
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#107C2311yescharacteristic
99C13×C4⋊C8D411yescharacteristic
100C13×#102—21no—
101C13×#102—21no—
102C13×#102—21no—
103C13×C22⋊C8D411yescharacteristic
104C13×C22⋊C8D411yescharacteristic
105C4×C8×C13C2311yescharacteristic
106#88067—22no—
107#88067—41no—
108#88066—41no—
109#88061—21no—
110#88058C2311yescharacteristic
111#88056—21no—
112#88056—21no—
113#88052—41no—
114C2×#6090—41no—
115C2×#6090C2311yescharacteristic
116C2×#6090C2311yescharacteristic
117C2×#6090C2311yescharacteristic
118C2×#6090C2311yescharacteristic
119#33875—131nomaximal, Sylow
120C13×#41—84no—
121C2×Q8×C13—41no—
122C2×D4×C13—21no—
123C2×D4×C13—41no—
124C2×D4×C13—41no—
125C2×D4×C13D811yescharacteristic
126C22×C4×C13—41no—
127C22×C4×C13—41no—
128C22×C4×C13—41no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C2×C22⋊D13—41no—
132C2×C22⋊D13—41no—
133C22×Dic13—41no—
134#6127—42no—
135#6127—81no—
136C2×D52—21no—
137C2×C4×D13—41no—
138C2×Dic26—21no—
139C2×Dic26—21no—
140C2×Dic26—42no—
141C2×Dic26—41no—
142C2×Dic26—81no—
143C13×D8—21no—
144C13×D8—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13C2×D411yescharacteristic
150C2×C8×C13C2×D411yescharacteristic
151C2×C8×C13C2×D411yescharacteristic
152C2×C8×C13C2411yescharacteristic
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4—41no—
158C13×C4⋊C4—41no—
159C13×C4⋊C4D811yescharacteristic
160C13×C22⋊C4—41no—
161C13×C22⋊C4—41no—
162C13×C22⋊C4—41no—
163C13×C22⋊C4D811yescharacteristic
164C13×C22⋊C4D811yescharacteristic
165C42×C13C2×D411yescharacteristic
166C22⋊Dic13—41no—
167#6103—41no—
168#6103—41no—
169#6103—41no—
170C4⋊Dic13—21no—
171#6101—41no—
172#6101—41no—
173C4×Dic13—41no—
174Dic52—21no—
175Dic52—21no—
176Dic52—21no—
177Dic52—42no—
178Dic52#4112yescomplemented
179D104—21no—
180D104—21no—
181#6095—42no—
182#6095—81no—
183#6090—21no—
184#6090—21no—
185#6090—21no—
186#6090—21no—
187#3334D1311yescharacteristic, complemented
188#3285—131no—
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—82no—
207D4×C13—22no—
208D4×C13—41no—
209D4×C13—41no—
210D4×C13—82no—
211D4×C13—82no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—82no—
220C2×C4×C13—82no—
221C2×C4×C13—82no—
222C2×C4×C13C2×D811yescharacteristic
223C2×C4×C13C2×D811yescharacteristic
224C2×C4×C13C2×D811yescharacteristic
225C2×C4×C13C2×D811yescharacteristic
226C2×C4×C13C22×D411yescharacteristic
227C22⋊D13—82no—
228C22⋊D13—82no—
229C2×Dic13—41no—
230C2×Dic13—41no—
231C2×Dic13—41no—
232C2×Dic13—82no—
233D52—41no—
234D52—41no—
235C4×D13—82no—
236Dic26—22no—
237Dic26—41no—
238Dic26—41no—
239Dic26—41no—
240Dic26—82no—
241C8×C13—21no—
242C8×C13—21no—
243C8×C13—21no—
244C8×C13C2×#4111yescharacteristic
245C8×C13H(5,𝔽2)11yescharacteristic
246C2×#135—131no—
247C22×Q16—131no—
248#548—261no—
249#547—21no—
250C2×SD32—131no—
251C2×SD32—131no—
252C2×D16—131no—
253C2×M32—131no—
254C22×C16—131no—
255#500C2×D1311yescharacteristic
256#495—131no—
257#480—21no—
258#480—21no—
259#474—21no—
260#467—131no—
261#466—131no—
262#466C2×D1311yescharacteristic
263#466C2×D1311yescharacteristic
264#464—261no—
265#452—261no—
266#448—261no—
267C4×Q16—131no—
268C4×D8C2×D1311yescharacteristic
269C8×D4C2×D1311yescharacteristic
270C2×#107C2×D1311yescharacteristic
271C2×#107C2×D1311yescharacteristic
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—81no—
307C4×C13—81no—
308C4×C13—81no—
309C4×C13#54611yescharacteristic
310C4×C13#57711yescharacteristic
311Dic13—42no—
312Dic13—81no—
313Dic13—81no—
314C2×#41—41no—
315C2×#41—261no—
316C22×Q8—261no—
317#135—262no—
318#135—521no—
319C2×Q16—131no—
320C2×Q16—131no—
321C2×Q16—262no—
322C2×Q16—261no—
323C2×Q16—521no—
324C2×SD16—261no—
325C2×SD16—261no—
326C2×D8—131no—
327C2×D8C22×D1311yescharacteristic
328C22×C8C22×D1311yescharacteristic
329C22×C8C22×D1311yescharacteristic
330C4⋊Q8—21no—
331#124—261no—
332#124—521no—
333#123—41no—
334#123—41no—
335C22⋊Q8—41no—
336C22⋊Q8—261no—
337C22⋊Q8—521no—
338#121—21no—
339#121—21no—
340#121—261no—
341#121—521no—
342C4×Q8—261no—
343C4×D4—21no—
344C4×D4—521no—
345C4×D4C22⋊D1311yescharacteristic
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
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—21no—
358#107—21no—
359#107—21no—
360#107—131no—
361#107C22×D1311yescharacteristic
362#107C22×D1311yescharacteristic
363#107C22×D1311yescharacteristic
364C4⋊C8C22⋊D1311yescharacteristic
365#103—261no—
366#103—261no—
367#102—21no—
368#102—21no—
369#102—21no—
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—84no—
382#41—522no—
383#41—1041no—
384C2×Q8—41no—
385C2×Q8—261no—
386C2×Q8—261no—
387C2×Q8—522no—
388C2×Q8—521no—
389C2×Q8—1041no—
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—41no—
400C22×C4—521no—
401C22×C4—521no—
402C22×C4C2×C22⋊D1311yescharacteristic
403C22×C4C2×C22⋊D1311yescharacteristic
404Q16—132no—
405Q16—261no—
406Q16—261no—
407Q16—261no—
408Q16—522no—
409SD16—522no—
410SD16—1041no—
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—21no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—261no—
430C4⋊C4—521no—
431C4⋊C4—521no—
432C4⋊C4#610411yescharacteristic
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—521no—
437C22⋊C4—521no—
438C22⋊C4—521no—
439C22⋊C4—521no—
440C22⋊C4#610411yescharacteristic
441C22⋊C4#610411yescharacteristic
442C42—521no—
443C42C2×C22⋊D1311yescharacteristic
444C16—261no—
445C16—261no—
446C16—261no—
447C16—261no—
448C13#3387511yescharacteristic, complemented, Sylow
449C23—41no—
450C23—521no—
451C23C2×#610411yescharacteristic
452C23C2×#610411yescharacteristic
453Q8—82no—
454Q8—262no—
455Q8—521no—
456Q8—521no—
457Q8—521no—
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—82no—
478C2×C4—521no—
479C2×C4—521no—
480C2×C4—521no—
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—
491C8#41×D1311yescharacteristic
492C8#8825611yescharacteristic
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—1041no—
502C22—1041no—
503C22—1041no—
504C22#1171880812yes—
505C22C22×#610411yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—81no—
511C4—81no—
512C4—81no—
513C4—522no—
514C4—1041no—
515C4—1041no—
516C4#1171953411yescharacteristic
517C4#1171954211yescharacteristic
518C2—22no—
519C2—41no—
520C2—161no—
521C2—2081no—
522C2#1312664311yescharacteristic
523C2C2×#1171880811yescharacteristic
524C2#1312798711yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3334C2
socleC22×C13C22×D8
hypercenter#3334D13
hypocenterC13#33875
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #13126579C2semidirect
2. #13117075C2semidirect
3. #13117038C2semidirect
4. #13117016C2semidirect
5. #13116985C2semidirect
6. #13116947C2semidirect
7. #13116920C2semidirect
8. #13116891C2semidirect
9. #13116757C2semidirect
10. #13116752C2semidirect
11. #13116700C2semidirect
12. #13116662C2semidirect
13. #13116546C2semidirect
14. C2×#11718084C2semidirect
15. C13×#3334C2semidirect
178. Dic52#41semidirect
187. #3334D13semidirect
448. C13#33875semidirect

Maximal subgroups

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

subgroupindex
#131265792
#131170752
#131170382
#131170162
#131169852
#131169472
#131169202
#131168912
#131167572
#131167522
#131167002
#131166622
#131165462
C2×#117180842
C13×#33342
#3387513