Finite Group Databasebeta

← #15880596

Subgroups — #15880596

Order 3328.

838 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×#106C211yesmaximal, characteristic
2#13117709C211yesmaximal, characteristic
3#13117704C211yesmaximal, characteristic
4#13115578C211yesmaximal, characteristic, complemented
5#13115576C211yesmaximal, characteristic, complemented
6#13115423C211yesmaximal, characteristic, complemented
7#13115415C211yesmaximal, characteristic, complemented
8#13115413C211yesmaximal, characteristic, complemented
9#13114925C211yesmaximal, characteristic
10#13114921C211yesmaximal, characteristic
11#13114864C211yesmaximal, characteristic
12#13114734C211yesmaximal, characteristic, complemented
13#13114732C211yesmaximal, characteristic, complemented
14#13114611C211yesmaximal, characteristic
15C13×#1920C211yesmaximal, characteristic, complemented
16C22×C8×D13C2211yescharacteristic
17C2×#88146—21no—
18C2×C4⋊C4×D13C2211yescharacteristic
19C2×C4⋊C4×D13C2211yescharacteristic
20C2×C13×#106C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C4×C13×C4⋊C4C2211yescharacteristic
23C2×#88060C2211yescharacteristic
24C2×#88057C2211yescharacteristic
25C2×#88055C2211yescharacteristic
26#11718648C2211yescharacteristic
27#11718648C2211yescharacteristic
28#11718646C2211yescharacteristic
29#11718639—21no—
30C4⋊C4×Dic13C2211yescharacteristic
31C4⋊C4×Dic13C2211yescharacteristic
32#11718634C2211yescharacteristic
33C2×#88048C2211yescharacteristic
34C2×#88048C2211yescharacteristic
35C2×#88047C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37C4×#6103—21no—
38C4×#6103C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40#11718594—21no—
41#11718589C2211yescharacteristic
42C2×#88043C2211yescharacteristic
43D13×#106C418yescomplemented
44#11718328—21no—
45#11718325—21no—
46#11718316—21no—
47#11718313—21no—
48C13×#340C2211yescharacteristic
49C13×#340C2211yescharacteristic
50C13×#340C2211yescharacteristic
51C13×#336C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×C4×D13—21no—
61C22×C4×D13—21no—
62C22×C4×D13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C42×C13—21no—
71C2×C42×C13C2311yescharacteristic
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103D411yescharacteristic
75C2×#6103D411yescharacteristic
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C2×C8×D13—22no—
92C2×C8×D13—22no—
93C2×C8×D13C2×C414yes—
94#88146—44no—
95C4⋊C4×D13—22no—
96C4⋊C4×D13—22no—
97C4⋊C4×D13C2×C414yes—
98C4⋊C4×D13C2×C414yes—
99C13×#106C2×C414yes—
100C13×#95—21no—
101C13×#95—21no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071D411yescharacteristic
111#88071D411yescharacteristic
112#88060—22no—
113#88057C2×C414yes—
114#88055—22no—
115#88048C2×C414yes—
116#88048C2×C414yes—
117#88047—22no—
118#88047—22no—
119#88043—22no—
120#22615—131nomaximal, Sylow
121C23×D13C2×D411yescharacteristic
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2411yescharacteristic
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13C2×D411yescharacteristic
134C22×Dic13C2×D411yescharacteristic
135C22×Dic13C2×D411yescharacteristic
136C2×C4×D13—21no—
137C2×C4×D13—21no—
138C2×C4×D13—21no—
139C2×C4×D13—21no—
140C2×C4×D13—24no—
141C2×C4×D13—24no—
142C2×C4×D13—42no—
143C2×C4×D13—42no—
144C2×C4×D13—81no—
145C2×C4×D13—81no—
146C2×C4×D13C22×C412yes—
147C2×C4×D13#4112yes—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13C22×C412yes—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4C22×C412yes—
162C13×C4⋊C4C22×C412yes—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—81no—
166#6103—22no—
167#6103—22no—
168#6103—42no—
169#6103—42no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—42no—
177C4⋊Dic13C22×C412yes—
178C4⋊Dic13C22×C412yes—
179#6101—24no—
180#6101—24no—
181#6101—81no—
182#6101—81no—
183C4×Dic13—21no—
184C4×Dic13—21no—
185C4×Dic13—42no—
186C4×Dic13—42no—
187C4×Dic13—81no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055C22×C412yes—
192C2×#1055#4112yes—
193C2×#1055#4112yes—
194C8×D13—28no—
195C22×#106—131no—
196#2345—131no—
197#2344—131no—
198#1944—131no—
199#1944—131no—
200#1920—131no—
201#1920D1311yescharacteristic, complemented
202#1919—131no—
203#1919—131no—
204#1824—131no—
205#1823—131no—
206#1808—131no—
207#1776—131no—
208#1776—131no—
209#1752—131no—
210C23×C13C22×D411yescharacteristic
211C22×D13—21no—
212C22×D13—21no—
213C22×D13—21no—
214C22×D13—21no—
215C22×D13C4×D412yes—
216C22×D13AGL(1,ℤ/8)12yes—
217C22×D13#13712yes—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13C23×C411yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×C4×C132−1+411yescharacteristic
241C2×C4×C132−1+411yescharacteristic
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13C4×D412yes—
263C4×D13—22no—
264C4×D13—22no—
265C4×D13—22no—
266C4×D13—22no—
267C4×D13—48no—
268C4×D13—84no—
269C8×C13—22no—
270C8×C13—41no—
271#1055—41no—
272#1055#11714yescomplemented
273C23×C8—131no—
274C2×#117—261no—
275C22×C4⋊C4—131no—
276C22×C4⋊C4—131no—
277C2×#107—131no—
278C2×#107—131no—
279C2×#106—131no—
280C2×#106—131no—
281C2×#106—131no—
282C2×#106—138no—
283C2×#106C2×D1311yescharacteristic
284C2×C22⋊C8—131no—
285C2×#97—131no—
286C2×#97—131no—
287#389—131no—
288#389—131no—
289#389—131no—
290#389C2×D1311yescharacteristic
291#387—261no—
292#387—261no—
293#387—261no—
294#387—261no—
295#381—261no—
296#380—131no—
297#380—131no—
298#380—261no—
299C4×C4⋊C4—131no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4C2×D1311yescharacteristic
303C4×C22⋊C4—131no—
304C4×C22⋊C4—261no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340C2×D1311yescharacteristic
313#340C2×D1311yescharacteristic
314#340C2×D1311yescharacteristic
315#336—131no—
316#336C2×D1311yescharacteristic
317C22×C13C2×C4×D411yescharacteristic
318C22×C13#54711yescharacteristic
319C22×C13#54711yescharacteristic
320C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C13C2×#13711yescharacteristic
322C22×C13#57711yescharacteristic
323C22×C13#57711yescharacteristic
324C2×D13—22no—
325C2×D13—22no—
326C2×D13—22no—
327C2×D13—22no—
328C2×D13—22no—
329C2×D13—22no—
330C2×D13#44014yes—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—42no—
334C4×C13—42no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13C2×#11711yescharacteristic
338C4×C13#51911yescharacteristic
339C4×C13#55211yescharacteristic
340C4×C13#55211yescharacteristic
341Dic13—22no—
342Dic13—41no—
343Dic13—41no—
344Dic13—42no—
345Dic13—42no—
346Dic13—81no—
347Dic13—81no—
348C23×C4—131no—
349C23×C4—261no—
350C23×C4—261no—
351C22×C8—131no—
352C22×C8—134no—
353C22×C8—131no—
354C22×C8—262no—
355C22×C8—262no—
356C22×C8C22×D1311yescharacteristic
357C22×C8C22×D1311yescharacteristic
358#117—524no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—134no—
363C2×C4⋊C4—134no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—262no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C22⋊C4—131no—
378C2×C22⋊C4—131no—
379C2×C22⋊C4—261no—
380C2×C22⋊C4—261no—
381C2×C42—21no—
382C2×C42—131no—
383C2×C42—261no—
384C2×C42—261no—
385C2×C42—261no—
386C2×C42C22×D1311yescharacteristic
387#107—262no—
388#107—262no—
389#106—134no—
390#106—134no—
391#106—134no—
392#106C4×D1314yes—
393C22⋊C8—262no—
394#97—262no—
395#97—262no—
396#95—21no—
397#95—21no—
398#95—131no—
399#95—131no—
400#95—261no—
401#95—261no—
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408C2×C13#234411yescharacteristic
409C2×C13C2×#44011yescharacteristic
410C2×C13#294911yescharacteristic
411C2×C13#334411yescharacteristic
412C2×C13#334411yescharacteristic
413C2×C13#334511yescharacteristic
414C2×C13#334511yescharacteristic
415D13—24no—
416C24—131no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—131no—
422C22×C4—132no—
423C22×C4—132no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—264no—
427C22×C4—264no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—522no—
437C22×C4—522no—
438C22×C4—1041no—
439C22×C4—1041no—
440C22×C4D4×D1311yescharacteristic
441C22×C4D4×D1311yescharacteristic
442C22×C4C23×D1311yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—132no—
449C2×C8—132no—
450C2×C8—132no—
451C2×C8—268no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8C2×C4×D1312yes—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—42no—
463C4⋊C4—132no—
464C4⋊C4—132no—
465C4⋊C4—264no—
466C4⋊C4—264no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—522no—
474C4⋊C4—1041no—
475C4⋊C4—1041no—
476C4⋊C4C2×C4×D1312yes—
477C4⋊C4C2×C4×D1312yes—
478C22⋊C4—262no—
479C22⋊C4—262no—
480C22⋊C4—522no—
481C22⋊C4—522no—
482C42—21no—
483C42—21no—
484C42—81no—
485C42—261no—
486C42—261no—
487C42—522no—
488C42—522no—
489C42—1041no—
490C13#2261511yescharacteristic, complemented, Sylow
491C23—132no—
492C23—132no—
493C23—132no—
494C23—261no—
495C23—261no—
496C23—261no—
497C23—261no—
498C23C2×D4×D1311yescharacteristic
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—132no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—262no—
521C2×C4—262no—
522C2×C4—262no—
523C2×C4—262no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—262no—
529C2×C4—262no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—528no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—1044no—
544C2×C4C22×C4×D1311yescharacteristic
545C2×C4#8825411yescharacteristic
546C2×C4#41×D1311yescharacteristic
547C2×C4#41×D1311yescharacteristic
548C2×C4#41×D1311yescharacteristic
549C2×C4#8825711yescharacteristic
550C8—22no—
551C8—41no—
552C8—134no—
553C8—521no—
554C22—134no—
555C22—262no—
556C22—262no—
557C22—262no—
558C22—262no—
559C22—262no—
560C22—262no—
561C22C4×D4×D1311yescharacteristic
562C22#1171933611yescharacteristic
563C22#1171936011yescharacteristic
564C22#1171946711yescharacteristic
565C22#1171947511yescharacteristic
566C22D13×AGL(1,ℤ/8)11yescharacteristic
567C22D13×#13711yescharacteristic
568C4—42no—
569C4—42no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—262no—
575C4—522no—
576C4—522no—
577C4—521no—
578C4—521no—
579C4—1041no—
580C4—1041no—
581C4D13×#11711yescharacteristic
582C4#1171927711yescharacteristic
583C4#1171939811yescharacteristic
584C4#1171941311yescharacteristic
585C2—264no—
586C2#1311770211yescharacteristic
587C2D13×#44011yescharacteristic
588C2#1312369011yescharacteristic
589C2#1312729411yescharacteristic
590C2#1312729811yescharacteristic
591C2#1312730911yescharacteristic
592C2#1312731311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1920C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1920D13
hypocenterC13#22615
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
4. #13115578C2semidirect
5. #13115576C2semidirect
6. #13115423C2semidirect
7. #13115415C2semidirect
8. #13115413C2semidirect
12. #13114734C2semidirect
13. #13114732C2semidirect
15. C13×#1920C2semidirect
43. D13×#106C4semidirect
201. #1920D13semidirect
272. #1055#117semidirect
490. C13#22615semidirect

Maximal subgroups

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

subgroupindex
C2×D13×#1062
#131177092
#131177042
#131155782
#131155762
#131154232
#131154152
#131154132
#131149252
#131149212
#131148642
#131147342
#131147322
#131146112
C13×#19202
#2261513