Finite Group Databasebeta

← #15920515

Subgroups — #15920515

Order 3328.

802 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118534C211yesmaximal, characteristic
2#13117704C211yesmaximal, characteristic
3#13116397C211yesmaximal, characteristic, complemented
4#13116327C211yesmaximal, characteristic, complemented
5#13116326C211yesmaximal, characteristic, complemented
6#13115789C211yesmaximal, characteristic, complemented
7#13115591C211yesmaximal, characteristic, complemented
8#13115409C211yesmaximal, characteristic, complemented
9#13115408C211yesmaximal, characteristic, complemented
10#13115022C211yesmaximal, characteristic
11#13115015C211yesmaximal, characteristic
12#13114921C211yesmaximal, characteristic
13#13114862C211yesmaximal, characteristic
14D13×#340C211yesmaximal, characteristic
15C13×#2057C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×#88200—21no—
18C22×C8×D13C2211yescharacteristic
19C2×#88146—21no—
20C2×C4⋊C4×D13C2211yescharacteristic
21C2×C4⋊C4×D13C2211yescharacteristic
22C2×C13×#107C2211yescharacteristic
23C2×C13×#107C2211yescharacteristic
24C13×#389C2211yescharacteristic
25#11718890—21no—
26C2×#88060C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29#11718650—21no—
30#11718648C2211yescharacteristic
31#11718648C2211yescharacteristic
32#11718646C2211yescharacteristic
33#11718646C2211yescharacteristic
34#11718645—21no—
35#11718639—21no—
36#11718637C2211yescharacteristic
37C4⋊C4×Dic13C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C4×#6103C2211yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41#11718589C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43#11718325—21no—
44#11718316—21no—
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47C13×#336C2211yescharacteristic
48#11718143C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C22×Q8×C13—21no—
60C22×C4×D13—21no—
61C22×C4×D13—21no—
62C22×C4×D13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8—41no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74#88200—44no—
75C2×#6103—21no—
76C2×#6103—21no—
77C2×#6103D411yescharacteristic
78C2×#6103D411yescharacteristic
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C2×C8×D13—22no—
96C2×C8×D13—22no—
97C2×C8×D13—41no—
98#88146—44no—
99C4⋊C4×D13—22no—
100C4⋊C4×D13—22no—
101C4⋊C4×D13—41no—
102C4⋊C4×D13Q814yescomplemented
103C13×#107—22no—
104C13×#107—41no—
105C13×#95—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071D411yescharacteristic
114#88071D411yescharacteristic
115#88060—22no—
116#88058—22no—
117#88054—22no—
118#88047—41no—
119C4⋊#1055—41no—
120#25988—131nomaximal, Sylow
121C23×D13C2×D411yescharacteristic
122C2×Q8×C13—42no—
123C2×Q8×C13—42no—
124C2×Q8×C13—81no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2411yescharacteristic
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13C2×D411yescharacteristic
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13—21no—
142C2×C4×D13—21no—
143C2×C4×D13—24no—
144C2×C4×D13—42no—
145C2×C4×D13—42no—
146C2×C4×D13—42no—
147C2×C4×D13—42no—
148C2×C4×D13—81no—
149C2×C4×D13C2×Q812yes—
150C2×C4×D13#4112yes—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13#4112yes—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4—42no—
165C13×C4⋊C4C2×Q812yes—
166C13×C4⋊C4#4112yes—
167C42×C13—21no—
168C42×C13—21no—
169#6103—22no—
170#6103—42no—
171#6103—42no—
172#6103D814yes—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—42no—
181C4⋊Dic13—42no—
182C4⋊Dic13C2×Q812yes—
183#6101—24no—
184#6101—42no—
185#6101—42no—
186#6101—42no—
187#6101—81no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C4×Dic13—42no—
191C4×Dic13—42no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C8×D13—44no—
199#2440—131no—
200#2344—131no—
201#2099—131no—
202#2086—131no—
203#2086—131no—
204#2057D1311yescharacteristic, complemented
205#1988—131no—
206#1947—131no—
207#1918—131no—
208#1918—131no—
209#1852—131no—
210#1850—131no—
211#1823—131no—
212#1808—131no—
213C2×#340—131no—
214C23×C13C22×D411yescharacteristic
215C22×D13—21no—
216C22×D13—21no—
217C22×D13—21no—
218C22×D13—21no—
219C22×D13C22⋊Q812yes—
220C22×D13C2×D812yes—
221C22×D13#13712yes—
222Q8×C13—84no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
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×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13C2×D812yes—
241C2×C4×C13C22×Q811yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13H(5,𝔽2)11yescharacteristic
246C2×C4×C132−1+411yescharacteristic
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—22no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13C22⋊Q812yes—
267C2×Dic13C2×D812yes—
268C4×D13—22no—
269C4×D13—22no—
270C4×D13—22no—
271C4×D13—22no—
272C4×D13—48no—
273C4×D13—84no—
274C8×C13—22no—
275C8×C13—41no—
276#1055—41no—
277#1055—41no—
278C23×C8—131no—
279C2×C4⋊Q8C2×D1311yescharacteristic
280C2×C22⋊Q8—261no—
281C2×#117—261no—
282C22×C4⋊C4—131no—
283C22×C4⋊C4—131no—
284C2×#107—131no—
285C2×#107—131no—
286C2×#107C2×D1311yescharacteristic
287C2×#107C2×D1311yescharacteristic
288C2×C4⋊C8—131no—
289C2×C4⋊C8—131no—
290C2×C22⋊C8—131no—
291#398—261no—
292#395—261no—
293#389—131no—
294#389—131no—
295#389—131no—
296#389C2×D1311yescharacteristic
297#387—261no—
298#387—261no—
299#385—261no—
300#384—131no—
301#381—261no—
302#380—131no—
303#380—131no—
304C4×C4⋊C4—131no—
305C4×C4⋊C4—131no—
306C4×C22⋊C4—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340C2×D1311yescharacteristic
318#340C2×D1311yescharacteristic
319#336—131no—
320#336C2×D1311yescharacteristic
321C22×C13C2×C22⋊Q811yescharacteristic
322C22×C13#54611yescharacteristic
323C22×C13#54711yescharacteristic
324C22×C13C22×D811yescharacteristic
325C22×C13C2×#13711yescharacteristic
326C22×C13#57711yescharacteristic
327C22×C13#57811yescharacteristic
328C2×D13—22no—
329C2×D13—22no—
330C2×D13—22no—
331C2×D13—22no—
332C2×D13—22no—
333C2×D13—22no—
334C2×D13#47414yes—
335C4×C13—22no—
336C4×C13—42no—
337C4×C13—41no—
338C4×C13—42no—
339C4×C13—81no—
340C4×C13—81no—
341C4×C13#53311yescharacteristic
342C4×C13#54411yescharacteristic
343C4×C13#55111yescharacteristic
344C4×C13#55211yescharacteristic
345Dic13—22no—
346Dic13—22no—
347Dic13—41no—
348Dic13—42no—
349Dic13—81no—
350Dic13—81no—
351Dic13—81no—
352C22×Q8—21no—
353C23×C4—131no—
354C23×C4—261no—
355C23×C4—261no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—262no—
359C22×C8—262no—
360C22×C8—521no—
361C22×C8C22×D1311yescharacteristic
362C22×C8C22×D1311yescharacteristic
363C4⋊Q8—22no—
364C4⋊Q8—41no—
365C22⋊Q8—524no—
366#117—524no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—134no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—262no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—521no—
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C22⋊C4—131no—
389C2×C22⋊C4—131no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C42—131no—
393C2×C42—261no—
394C2×C42—261no—
395C2×C42C22×D1311yescharacteristic
396#107—22no—
397#107—41no—
398#107—262no—
399#107—521no—
400C4⋊C8—262no—
401C4⋊C8—521no—
402C22⋊C8—262no—
403#95—21no—
404#95—131no—
405#95—131no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413C2×C13#243811yescharacteristic
414C2×C13C2×#47411yescharacteristic
415C2×C13#308211yescharacteristic
416C2×C13#329411yescharacteristic
417C2×C13#331211yescharacteristic
418C2×C13#333411yescharacteristic
419C2×C13#334411yescharacteristic
420D13—24no—
421C24—131no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—81no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—132no—
432C22×C4—132no—
433C22×C4—131no—
434C22×C4—264no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—522no—
444C22×C4—522no—
445C22×C4—522no—
446C22×C4—522no—
447C22×C4—1041no—
448C22×C4D4×D1311yescharacteristic
449C22×C4D4×D1311yescharacteristic
450C22×C4C23×D1311yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—524no—
463C2×C8#613112yes—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—132no—
473C4⋊C4—264no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—522no—
482C4⋊C4—522no—
483C4⋊C4—522no—
484C4⋊C4—522no—
485C4⋊C4—522no—
486C4⋊C4—1041no—
487C4⋊C4#612912yes—
488C4⋊C4Q8×D1312yes—
489C22⋊C4—134no—
490C22⋊C4—262no—
491C22⋊C4—522no—
492C22⋊C4—522no—
493C42—21no—
494C42—21no—
495C42—261no—
496C42—261no—
497C42—522no—
498C42—522no—
499C13#2598811yescharacteristic, complemented, Sylow
500C23—132no—
501C23—132no—
502C23—132no—
503C23—261no—
504C23—261no—
505C23—261no—
506C23—261no—
507C23C2×D4×D1311yescharacteristic
508Q8—84no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—132no—
527C2×C4—132no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—262no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—262no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—262no—
540C2×C4—528no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—1044no—
553C2×C4D8×D1312yes—
554C2×C4C2×#612911yescharacteristic
555C2×C4#8825111yescharacteristic
556C2×C4C2×Q8×D1311yescharacteristic
557C2×C4C2×#613111yescharacteristic
558C2×C4#8825411yescharacteristic
559C2×C4#41×D1311yescharacteristic
560C8—22no—
561C8—41no—
562C8—521no—
563C8—521no—
564C22—134no—
565C22—262no—
566C22—262no—
567C22—262no—
568C22—262no—
569C22—262no—
570C22—262no—
571C22#1171929611yescharacteristic
572C22D13×C22⋊Q811yescharacteristic
573C22#1171943111yescharacteristic
574C22C2×D8×D1311yescharacteristic
575C22#1171947111yescharacteristic
576C22#1171948011yescharacteristic
577C22D13×#13711yescharacteristic
578C4—22no—
579C4—41no—
580C4—42no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—262no—
585C4—262no—
586C4—521no—
587C4—522no—
588C4—1041no—
589C4—1041no—
590C4—1041no—
591C4#1171934211yescharacteristic
592C4#1171934411yescharacteristic
593C4#1171943311yescharacteristic
594C4#1171943411yescharacteristic
595C2—264no—
596C2#1311850511yescharacteristic
597C2D13×#47411yescharacteristic
598C2#1312467311yescharacteristic
599C2#1312664211yescharacteristic
600C2#1312688011yescharacteristic
601C2#1312718311yescharacteristic
602C2#1312729011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2057C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenter#2057D13
hypocenterC13#25988
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
3. #13116397C2semidirect
4. #13116327C2semidirect
5. #13116326C2semidirect
6. #13115789C2semidirect
7. #13115591C2semidirect
8. #13115409C2semidirect
9. #13115408C2semidirect
15. C13×#2057C2semidirect
102. C4⋊C4×D13Q8semidirect
204. #2057D13semidirect
499. C13#25988semidirect

Maximal subgroups

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

subgroupindex
#131185342
#131177042
#131163972
#131163272
#131163262
#131157892
#131155912
#131154092
#131154082
#131150222
#131150152
#131149212
#131148622
D13×#3402
C13×#20572
#2598813