Finite Group Databasebeta

← #15833638

Subgroups — #15833638

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125419C211yesmaximal, characteristic
2#13123767C211yesmaximal, characteristic
3#13123765C211yesmaximal, characteristic
4#13113689C211yesmaximal, characteristic, complemented
5#13113688C211yesmaximal, characteristic, complemented
6#13113687C211yesmaximal, characteristic, complemented
7#13113686C211yesmaximal, characteristic, complemented
8#13113685C211yesmaximal, characteristic, complemented
9#13113684C211yesmaximal, characteristic, complemented
10#13113683C211yesmaximal, characteristic, complemented
11#13113593C211yesmaximal, characteristic
12#13113289C211yesmaximal, characteristic
13#13113289C211yesmaximal, characteristic
14D13×#322C211yesmaximal, characteristic
15C13×#1584C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17#11719283C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×Q16C2211yescharacteristic
21#11718849C411yescharacteristic
22#11718842C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6107C2211yescharacteristic
25#11718685C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718548C411yescharacteristic
28#11718535C411yescharacteristic
29#11718500—21no—
30#11718500—21no—
31#11718498C2211yescharacteristic
32#11718498C2211yescharacteristic
33#11718492C2211yescharacteristic
34#11718491—21no—
35#11718491C2211yescharacteristic
36#11718489—21no—
37#11718474C411yescharacteristic
38#11718474C411yescharacteristic
39#11718453C411yescharacteristic
40#11718453C411yescharacteristic
41#11718369—21no—
42#11718362—21no—
43C4×Dic52C2211yescharacteristic
44#11718350—21no—
45C4×C8×D13C2211yescharacteristic
46C4×C8×D13C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26—21no—
50C8×Dic26C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65#11718046C2211yescharacteristic
66#11718046C2211yescharacteristic
67C2×C13×Q16C2×C411yescharacteristic
68C4×Q8×C13C2311yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70#88200C2×C411yescharacteristic
71#88200C2×C411yescharacteristic
72#88198C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6107C2×C411yescharacteristic
76C2×Dic52C2×C411yescharacteristic
77C2×#6094—21no—
78C2×#6094—21no—
79C2×C8×D13—21no—
80C2×C8×D13C2×C411yescharacteristic
81C2×C8×D13C2×C411yescharacteristic
82C2×C8×D13D411yescharacteristic
83C2×C8×D13D411yescharacteristic
84#88151C2×C411yescharacteristic
85#88151C2×C411yescharacteristic
86#88150—21no—
87#88150—21no—
88#88143—21no—
89#88143—21no—
90#88142C2×C411yescharacteristic
91#88142C2×C411yescharacteristic
92#88126—21no—
93#88126—21no—
94C42×D13C2311yescharacteristic
95C4×Dic26—21no—
96C4×Dic26—21no—
97C4×Dic26C2311yescharacteristic
98C4×Dic26C2311yescharacteristic
99C13×#107C2×C411yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8—21no—
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×#103C2×C411yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×#97—21no—
107C4×C8×C13—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111#88075C2×C411yescharacteristic
112#88075C2×C411yescharacteristic
113#88058C2×C411yescharacteristic
114#88056C2×C411yescharacteristic
115#88056C2×C411yescharacteristic
116#88055—21no—
117#88055—21no—
118#88054—21no—
119#88054—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124C8×Dic13—21no—
125C8×Dic13—21no—
126C8×Dic13—21no—
127C8×Dic13C2×C411yescharacteristic
128C8×Dic13C2×C411yescharacteristic
129C8×Dic13D411yescharacteristic
130C8×Dic13D411yescharacteristic
131#88050C2×C411yescharacteristic
132#88050C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135C4⋊#1055—21no—
136C4⋊#1055—21no—
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139#88043—21no—
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17977—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×Q8×C13C22×C411yescharacteristic
147C2×C4×D13C22×C411yescharacteristic
148C2×C4×D13C2×D411yescharacteristic
149C2×C4×D13#4111yescharacteristic
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26C22×C411yescharacteristic
153C2×Dic26C22×C411yescharacteristic
154C13×Q16—41no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13C22×C411yescharacteristic
159C2×C8×C13C22×C411yescharacteristic
160C2×C8×C13C2×D411yescharacteristic
161C2×C8×C13C2×D411yescharacteristic
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4C22×C411yescharacteristic
165C13×C4⋊C4C22×C411yescharacteristic
166C42×C13—21no—
167C42×C13—21no—
168C42×C13C2411yescharacteristic
169#6107—41no—
170#6107—41no—
171#6103—21no—
172#6103—21no—
173#6103—21no—
174#6103—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13C22×C411yescharacteristic
178C4⋊Dic13C22×C411yescharacteristic
179#6101—21no—
180#6101—21no—
181#6101—21no—
182#6101—21no—
183#6101—21no—
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189C4×Dic13—21no—
190C4×Dic13—21no—
191C4×Dic13C22×C411yescharacteristic
192C4×Dic13C2×D411yescharacteristic
193C4×Dic13#4111yescharacteristic
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055C22×C411yescharacteristic
198C2×#1055C22×C411yescharacteristic
199C2×#1055C2×D411yescharacteristic
200C2×#1055C2×D411yescharacteristic
201Dic52—41no—
202#6094—42no—
203#6094—42no—
204C8×D13—22no—
205C8×D13—41no—
206C8×D13—41no—
207C8×D13—42no—
208C8×D13Q1614yescomplemented
209#3170—131no—
210#2960—131no—
211#2960—131no—
212#1584—131no—
213#1584—131no—
214#1584—131no—
215#1584—131no—
216#1584—131no—
217#1584—131no—
218#1584—131no—
219#1584D1311yescharacteristic, complemented
220#1567—131no—
221#1493—131no—
222#1493—131no—
223C2×#322—131no—
224C22×D13C4×D411yescharacteristic
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13C23×C411yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13C4×D411yescharacteristic
241C2×Dic13C4×D411yescharacteristic
242C2×Dic13C4×D411yescharacteristic
243C4×D13—21no—
244C4×D13—21no—
245C4×D13—22no—
246C4×D13C2×Q1612yes—
247C4×D13#13512yes—
248Dic26—21no—
249Dic26—21no—
250Dic26—21no—
251Dic26—21no—
252Dic26—42no—
253Dic26—42no—
254C8×C13—21no—
255C8×C13—21no—
256C8×C13—21no—
257C8×C13—41no—
258C8×C13—41no—
259C8×C13—41no—
260C8×C13C2×Q1612yes—
261#1055—21no—
262#1055—21no—
263#1055—21no—
264#1055—41no—
265#1055—41no—
266#1055—41no—
267#1055C2×Q1612yes—
268#533—131no—
269#533—131no—
270#500—131no—
271#494—131no—
272#487—131no—
273#487—131no—
274#467—131no—
275#467—131no—
276#467—131no—
277#467—131no—
278#446—131no—
279#446—131no—
280#446—131no—
281#446—261no—
282#446—261no—
283#446C2×D1311yescharacteristic
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C8×Q8—261no—
288C8×Q8—261no—
289C8×Q8C2×D1311yescharacteristic
290C4×Q16—131no—
291C4×Q16—131no—
292C4×Q16—131no—
293C4×Q16C2×D1311yescharacteristic
294#424—261no—
295#424—261no—
296#423—131no—
297#423—131no—
298#405—261no—
299#405—261no—
300C2×C4×C8—131no—
301C2×C4×C8—131no—
302C2×C4×C8—131no—
303#335—131no—
304#335—131no—
305#335—131no—
306#335C2×D1311yescharacteristic
307Q8⋊C8—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8C2×D1311yescharacteristic
314Q8⋊C8C2×D1311yescharacteristic
315#322—131no—
316#322—131no—
317#322—131no—
318#322C2×D1311yescharacteristic
319C22×C13C2×C4×D411yescharacteristic
320C2×D13—21no—
321C2×D13—21no—
322C2×D13C4×Q1612yes—
323C4×C13—21no—
324C4×C13—41no—
325C4×C13—41no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13#56811yescharacteristic
329C4×C13#56811yescharacteristic
330C4×C13C22×Q1611yescharacteristic
331C4×C13C2×#13511yescharacteristic
332Dic13—21no—
333Dic13—41no—
334Dic13—41no—
335Dic13—41no—
336Dic13—41no—
337Dic13C4×Q1612yes—
338Dic13#44412yes—
339C2×Q16—131no—
340C2×Q16—131no—
341C2×Q16—131no—
342C2×Q16C4×D1311yescharacteristic
343C2×M16—261no—
344C2×M16—261no—
345C22×C8—131no—
346C22×C8—131no—
347C22×C8—131no—
348C22×C8—131no—
349C22×C8—261no—
350C4⋊Q8—131no—
351C4⋊Q8—131no—
352C4⋊Q8—131no—
353C4⋊Q8—131no—
354#125—261no—
355#125—261no—
356C22⋊Q8—131no—
357C22⋊Q8—131no—
358C22⋊Q8—131no—
359C22⋊Q8—131no—
360C22⋊Q8—261no—
361C22⋊Q8—261no—
362C4×Q8—131no—
363C4×Q8—131no—
364C4×Q8—261no—
365C4×Q8—261no—
366C4×Q8C22×D1311yescharacteristic
367C4×Q8C22×D1311yescharacteristic
368#117—261no—
369#117—261no—
370C2×C42—131no—
371#107—131no—
372#107—131no—
373#107—131no—
374#107C4×D1311yescharacteristic
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—261no—
380C4⋊C8—261no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8C22×D1311yescharacteristic
388C4⋊C8C22×D1311yescharacteristic
389#103—131no—
390#103—131no—
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103C4×D1311yescharacteristic
396#103C4×D1311yescharacteristic
397#97—21no—
398#97—261no—
399#97—261no—
400#97—261no—
401C4×C8—21no—
402C4×C8—131no—
403C4×C8—131no—
404C4×C8—131no—
405C4×C8—131no—
406C4×C8—131no—
407C4×C8—131no—
408C4×C8—131no—
409C4×C8—261no—
410C4×C8—261no—
411C4×C8—261no—
412C4×C8—261no—
413C4×C8C22×D1311yescharacteristic
414C4×C8C22×D1311yescharacteristic
415C4×C8C22×D1311yescharacteristic
416C2×C13#293211yescharacteristic
417C2×C13C2×C4×Q1611yescharacteristic
418C2×C13C2×#44411yescharacteristic
419D13—22no—
420C2×Q8—131no—
421C2×Q8—131no—
422C2×Q8—261no—
423C2×Q8—261no—
424C2×Q8C2×C4×D1311yescharacteristic
425C2×Q8C2×C4×D1311yescharacteristic
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—131no—
429Q16—41no—
430Q16—521no—
431Q16—521no—
432Q16—521no—
433M16—522no—
434M16—522no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—131no—
439C2×C8—134no—
440C2×C8—131no—
441C2×C8—131no—
442C2×C8—131no—
443C2×C8—262no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—521no—
448C2×C8—521no—
449C2×C8—522no—
450C2×C8C2×C4×D1311yescharacteristic
451C2×C8C2×C4×D1311yescharacteristic
452C2×C8D4×D1311yescharacteristic
453C2×C8D4×D1311yescharacteristic
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—131no—
457C4⋊C4—131no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4C2×C4×D1311yescharacteristic
471C4⋊C4C2×C4×D1311yescharacteristic
472C22⋊C4—261no—
473C22⋊C4—261no—
474C22⋊C4—261no—
475C22⋊C4—261no—
476C42—21no—
477C42—21no—
478C42—131no—
479C42—131no—
480C42—131no—
481C42—261no—
482C42—261no—
483C42C23×D1311yescharacteristic
484C13#1797711yescharacteristic, complemented, Sylow
485C23—131no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—261no—
491Q8—261no—
492Q8—261no—
493Q8—261no—
494Q8—522no—
495Q8—522no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—131no—
501C2×C4—131no—
502C2×C4—132no—
503C2×C4—132no—
504C2×C4—131no—
505C2×C4—262no—
506C2×C4—261no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4C22×C4×D1311yescharacteristic
513C2×C4C2×D4×D1311yescharacteristic
514C2×C4#41×D1311yescharacteristic
515C8—21no—
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—132no—
522C8—261no—
523C8—261no—
524C8—261no—
525C8—521no—
526C8—521no—
527C8—521no—
528C8Q16×D1312yes—
529C22—132no—
530C22—261no—
531C22—261no—
532C22C4×D4×D1311yescharacteristic
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—132no—
539C4—132no—
540C4—261no—
541C4—521no—
542C4—521no—
543C4—521no—
544C4—521no—
545C4#1171945011yescharacteristic
546C4#1171945511yescharacteristic
547C4C2×Q16×D1311yescharacteristic
548C4D13×#13511yescharacteristic
549C2—262no—
550C2#1312355011yescharacteristic
551C2C4×Q16×D1311yescharacteristic
552C2D13×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1584C2
socleC22×C13C2×C4×D4
prime radicalC22×D13C4×D4
cosocleC42×C13C24
hypercenter#1584D13
hypocenterC13#17977
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #13113689C2semidirect
5. #13113688C2semidirect
6. #13113687C2semidirect
7. #13113686C2semidirect
8. #13113685C2semidirect
9. #13113684C2semidirect
10. #13113683C2semidirect
15. C13×#1584C2semidirect
208. C8×D13Q16semidirect
219. #1584D13semidirect
484. C13#17977semidirect

Maximal subgroups

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

subgroupindex
#131254192
#131237672
#131237652
#131136892
#131136882
#131136872
#131136862
#131136852
#131136842
#131136832
#131135932
#131132892
D13×#3222
C13×#15842
#1797713