Finite Group Databasebeta

← #15833024

Subgroups — #15833024

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124907C211yesmaximal, characteristic
2#13123930C211yesmaximal, characteristic, complemented
3#13113707C211yesmaximal, characteristic, complemented
4#13113693C211yesmaximal, characteristic, complemented
5#13113686C211yesmaximal, characteristic, complemented
6#13113672C211yesmaximal, characteristic, complemented
7#13113653C211yesmaximal, characteristic, complemented
8#13113648C211yesmaximal, characteristic, complemented
9C8×#6107C211yesmaximal, characteristic, complemented
10C8×#6105C211yesmaximal, characteristic, complemented
11#13113619C211yesmaximal, characteristic, complemented
12#13113270C211yesmaximal, characteristic
13#13113238C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#2988C211yesmaximal, characteristic
16C4×C13×#41C2211yescharacteristic
17#11719175C2211yescharacteristic
18C8×Q8×C13C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C8×D4×C13—21no—
21C8×D4×C13—21no—
22C8×D4×C13C2211yescharacteristic
23C8×D4×C13C2211yescharacteristic
24C13×#431—21no—
25C13×#431C2211yescharacteristic
26C2×C13×C4⋊C8—21no—
27C2×C13×C4⋊C8C2211yescharacteristic
28#11718900C411yescharacteristic
29#11718900C411yescharacteristic
30#11718692C411yescharacteristic
31C4×#6107C2211yescharacteristic
32C4×#6107C2211yescharacteristic
33#11718681C411yescharacteristic
34#11718680C411yescharacteristic
35C4×#6105C2211yescharacteristic
36C4×#6105C2211yescharacteristic
37#11718668C411yescharacteristic
38#11718657C411yescharacteristic
39#11718657C411yescharacteristic
40#11718587C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718489—21no—
44#11718489—21no—
45#11718381—21no—
46#11718381—21no—
47#11718340C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41C2×C411yescharacteristic
68C22×C8×C13—21no—
69C22×C8×C13—21no—
70C22×C8×C13—21no—
71C4×Q8×C13C2×C411yescharacteristic
72C4×Q8×C13C2311yescharacteristic
73C4×D4×C13—21no—
74C4×D4×C13—21no—
75C4×D4×C13C2×C411yescharacteristic
76C4×D4×C13C2311yescharacteristic
77C13×#117—21no—
78C13×#117C2×C411yescharacteristic
79C2×C42×C13—21no—
80C2×C42×C13C2311yescharacteristic
81C2×#6107C2×C411yescharacteristic
82C2×#6107C2×C411yescharacteristic
83C2×#6105C2×C411yescharacteristic
84C2×#6105C2×C411yescharacteristic
85#88180—21no—
86#88178—21no—
87#88178C2×C411yescharacteristic
88#88178C2×C411yescharacteristic
89#88124—21no—
90#88123C2×C411yescharacteristic
91#88123C2×C411yescharacteristic
92C4×Dic26—21no—
93C4×Dic26C2311yescharacteristic
94C4×Dic26C2311yescharacteristic
95C13×C4⋊C8—21no—
96C13×C4⋊C8—21no—
97C13×C4⋊C8—21no—
98C13×C4⋊C8D411yescharacteristic
99C13×C4⋊C8D411yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C22⋊C8—21no—
103C13×C22⋊C8—21no—
104C13×C22⋊C8D411yescharacteristic
105C13×C22⋊C8D411yescharacteristic
106C4×C8×C13—21no—
107C4×C8×C13—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#88075C2×C411yescharacteristic
111#88075C2×C411yescharacteristic
112#88072C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114C22⋊#1055—21no—
115C22⋊#1055—21no—
116C22⋊#1055C2×C411yescharacteristic
117C22⋊#1055C2×C411yescharacteristic
118#88055—21no—
119#88055—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124C8×Dic13—21no—
125C8×Dic13—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88050C2×C411yescharacteristic
129#88050C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055C2×C411yescharacteristic
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139#88043—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17921—131nomaximal, Sylow
145C13×#41—22no—
146C13×#41—22no—
147C2×Q8×C13C22×C411yescharacteristic
148C2×D4×C13—21no—
149C2×D4×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13#4111yescharacteristic
156C2×Dic26—21no—
157C2×Dic26C22×C411yescharacteristic
158C2×Dic26C22×C411yescharacteristic
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—81no—
162C2×C8×C13—81no—
163C2×C8×C13—81no—
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C4⋊C4C22×C411yescharacteristic
172C13×C22⋊C4—21no—
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13C22×C411yescharacteristic
179C42×C13C2×D411yescharacteristic
180C42×C13#4111yescharacteristic
181C42×C13C2411yescharacteristic
182C22⋊Dic13—21no—
183C22⋊Dic13—21no—
184#6107—22no—
185#6107—22no—
186#6105—22no—
187#6105—22no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13C22×C411yescharacteristic
192C4⋊Dic13C22×C411yescharacteristic
193#6101—21no—
194#6101—21no—
195#6101—21no—
196#6101—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207#3107—131no—
208#2988D1311yescharacteristic
209#2985—131no—
210#1587—131no—
211#1585—131no—
212#1584—131no—
213#1582—131no—
214#1579—131no—
215SD16⋊C8—131no—
216C8×Q16—131no—
217C8×SD16—131no—
218#1573—131no—
219#1488—131no—
220#1481—131no—
221#1454—131no—
222C23×C13—21no—
223C23×C13C4×D411yescharacteristic
224Q8×C13—21no—
225Q8×C13#13112yes—
226D4×C13—24no—
227D4×C13—21no—
228D4×C13#13112yes—
229C2×C4×C13—24no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—81no—
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C23×C411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—81no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—41no—
261C8×C13—41no—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—41no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#533—131no—
271C4×#41C2×D1311yescharacteristic
272#485—131no—
273#485—131no—
274#475—131no—
275#474—131no—
276#462—131no—
277#461—131no—
278#452—131no—
279#452—131no—
280#446—131no—
281#446—131no—
282#446—261no—
283#446—261no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8C2×D1311yescharacteristic
287C8×Q8C2×D1311yescharacteristic
288C4×Q16—131no—
289C4×Q16—131no—
290C4×SD16—131no—
291C4×SD16—131no—
292C8×D4—21no—
293C8×D4—21no—
294C8×D4C2×D1311yescharacteristic
295C8×D4C2×D1311yescharacteristic
296#433—261no—
297#433—261no—
298#432—131no—
299#431—21no—
300#431—131no—
301#431—131no—
302#431C2×D1311yescharacteristic
303C2×C4⋊C8—21no—
304C2×C4⋊C8C2×D1311yescharacteristic
305#335—131no—
306#335—131no—
307#334—131no—
308#334—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315D4⋊C8—131no—
316D4⋊C8—131no—
317#322—131no—
318#322—131no—
319#322—131no—
320C82—131no—
321C22×C13—21no—
322C22×C13—22no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—41no—
326C22×C13—41no—
327C22×C13C2×C4×D411yescharacteristic
328C4×C13—21no—
329C4×C13—22no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13C2×#13111yescharacteristic
336C4×C13C2×#13111yescharacteristic
337C4×C13#57711yescharacteristic
338C4×C13#57811yescharacteristic
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343C2×#41C4×D1311yescharacteristic
344C2×Q16—131no—
345C2×Q16—131no—
346C2×SD16—131no—
347C2×SD16—131no—
348C22×C8—21no—
349C22×C8—21no—
350C22×C8—21no—
351C4⋊Q8—131no—
352C4⋊Q8—131no—
353#125—261no—
354C22⋊Q8—131no—
355C22⋊Q8—131no—
356C22⋊Q8—261no—
357C4×Q8—131no—
358C4×Q8—131no—
359C4×Q8—261no—
360C4×Q8C4×D1311yescharacteristic
361C4×Q8C22×D1311yescharacteristic
362C4×D4—21no—
363C4×D4—21no—
364C4×D4C4×D1311yescharacteristic
365C4×D4C22×D1311yescharacteristic
366#117—21no—
367#117—261no—
368#117C4×D1311yescharacteristic
369C2×C42—21no—
370C2×C42C22×D1311yescharacteristic
371#107—131no—
372#107—131no—
373#106—131no—
374#106—131no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8C22⋊D1311yescharacteristic
388C4⋊C8C22⋊D1311yescharacteristic
389C4⋊C8C22×D1311yescharacteristic
390C4⋊C8C22×D1311yescharacteristic
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#102—131no—
398#102—131no—
399C22⋊C8—21no—
400C22⋊C8—21no—
401C22⋊C8—131no—
402C22⋊C8—131no—
403C22⋊C8—261no—
404C22⋊C8—261no—
405C22⋊C8C22⋊D1311yescharacteristic
406C22⋊C8C22⋊D1311yescharacteristic
407#97—261no—
408#97—261no—
409#97—261no—
410C4×C8—21no—
411C4×C8—21no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8C22×D1311yescharacteristic
419C4×C8C22×D1311yescharacteristic
420C2×C13—41no—
421C2×C13—42no—
422C2×C13#292911yescharacteristic
423C2×C13#294711yescharacteristic
424C2×C13#295711yescharacteristic
425#41—22no—
426#41—22no—
427C2×Q8—131no—
428C2×Q8—131no—
429C2×Q8—261no—
430C2×Q8C2×C4×D1311yescharacteristic
431C2×D4—21no—
432C2×D4C2×C4×D1311yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4C2×C4×D1311yescharacteristic
437C22×C4#612711yescharacteristic
438C22×C4C2×C22⋊D1311yescharacteristic
439Q16—262no—
440Q16—262no—
441SD16—262no—
442SD16—262no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—81no—
447C2×C8—81no—
448C2×C8—131no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8C2×C22⋊D1311yescharacteristic
457C2×C8C2×C22⋊D1311yescharacteristic
458C2×C8C2×C22⋊D1311yescharacteristic
459C2×C8C2×C22⋊D1311yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—131no—
463C4⋊C4—131no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4C2×C4×D1311yescharacteristic
472C4⋊C4C2×C4×D1311yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—261no—
482C42—261no—
483C42C2×C4×D1311yescharacteristic
484C42#612711yescharacteristic
485C42C2×C22⋊D1311yescharacteristic
486C42C23×D1311yescharacteristic
487C13#1792111yescharacteristic, complemented, Sylow
488C23—21no—
489C23C4×C22⋊D1311yescharacteristic
490Q8—21no—
491Q8—261no—
492Q8—261no—
493Q8—261no—
494Q8—261no—
495Q8—1041no—
496Q8#8815512yes—
497D4—24no—
498D4—21no—
499D4#8815512yes—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—81no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4C4×C22⋊D1311yescharacteristic
517C2×C4C4×C22⋊D1311yescharacteristic
518C2×C4C4×C22⋊D1311yescharacteristic
519C2×C4C22×C4×D1311yescharacteristic
520C2×C4C2×#612711yescharacteristic
521C2×C4C22×C22⋊D1311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—261no—
529C8—261no—
530C8—261no—
531C8—261no—
532C8—521no—
533C8—521no—
534C8—521no—
535C8—521no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—22no—
540C22—41no—
541C22—41no—
542C22C2×C4×C22⋊D1311yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—22no—
548C4—41no—
549C4—41no—
550C4—521no—
551C4—521no—
552C4—521no—
553C4—521no—
554C4C2×#8815511yescharacteristic
555C4C2×#8815511yescharacteristic
556C4#1171954111yescharacteristic
557C4#1171954311yescharacteristic
558C2—41no—
559C2—42no—
560C2#1312353011yescharacteristic
561C2#1312367511yescharacteristic
562C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2988C2
socleC22×C13C2×C4×D4
prime radicalC2×C13×#41C2×C4
cosocleC42×C13C24
hypercenter#2988D13
hypocenterC13#17921
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2988

Complements

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

NH ≅ G/Ntype
2. #13123930C2semidirect
3. #13113707C2semidirect
4. #13113693C2semidirect
5. #13113686C2semidirect
6. #13113672C2semidirect
7. #13113653C2semidirect
8. #13113648C2semidirect
9. C8×#6107C2semidirect
10. C8×#6105C2semidirect
11. #13113619C2semidirect
13. #13113238C2semidirect
14. #13113136C2semidirect
487. C13#17921semidirect

Maximal subgroups

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

subgroupindex
#131249072
#131239302
#131137072
#131136932
#131136862
#131136722
#131136532
#131136482
C8×#61072
C8×#61052
#131136192
#131132702
#131132382
#131131362
C13×#29882
#1792113