Finite Group Databasebeta

← #15867813

Subgroups — #15867813

Order 3328.

850 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718380C211yesmaximal, characteristic
2#13117231C211yesmaximal, characteristic
3#117×Dic13C211yesmaximal, characteristic
4#13115607C211yesmaximal, characteristic, complemented
5#13115605C211yesmaximal, characteristic, complemented
6#13115603C211yesmaximal, characteristic, complemented
7#13115601C211yesmaximal, characteristic, complemented
8#13115037C211yesmaximal, characteristic
9#13115035C211yesmaximal, characteristic
10#13115033C211yesmaximal, characteristic
11#13114736C211yesmaximal, characteristic, complemented
12#13114735C211yesmaximal, characteristic, complemented
13#13114732C211yesmaximal, characteristic, complemented
14#13114732C211yesmaximal, characteristic, complemented
15C13×#1854C211yesmaximal, characteristic
16C2×C13×#117C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19C2×C13×#107C2211yescharacteristic
20C2×C13×#106C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C13×#380C2211yescharacteristic
23#11718873C2211yescharacteristic
24C2×C22⋊#1055C2211yescharacteristic
25C2×#88058C2211yescharacteristic
26C2×#88057C2211yescharacteristic
27C2×#88055C2211yescharacteristic
28C2×#88055C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31#11718638C2211yescharacteristic
32#11718638C2211yescharacteristic
33C4⋊C4×Dic13C2211yescharacteristic
34C4⋊C4×Dic13C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37C4⋊C4×Dic13C2211yescharacteristic
38C4⋊C4×Dic13C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718604—21no—
44C22⋊C4×Dic13—21no—
45C22⋊C4×Dic13—21no—
46C22⋊C4×Dic13—21no—
47#11718593—21no—
48C42×Dic13—21no—
49#11718380C418yescomplemented
50#11718312—21no—
51#11718309—21no—
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13D411yescharacteristic
62C23×Dic13D411yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C13×#117—22no—
66C13×#117—22no—
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C42×C13—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76#88180—22no—
77#88180—22no—
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4×Dic13—21no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13C2×C414yes—
90C2×C4×Dic13D411yescharacteristic
91C2×C4×Dic13D411yescharacteristic
92C2×C4×Dic13Q814yes—
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C13×#107—22no—
98C13×#106—22no—
99C13×C22⋊C8C2×C414yes—
100C13×#95—21no—
101#88071—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#88071—21no—
111#88071—21no—
112C22⋊#1055C2×C414yes—
113#88058—22no—
114#88057—22no—
115#88055C2×C414yes—
116#88055C2×C414yes—
117#88054C2×C414yes—
118#88054C2×C414yes—
119#88048—22no—
120#88048—22no—
121#88047—22no—
122#88047—22no—
123#21366—131nomaximal, Sylow
124C24×C13C2×D411yescharacteristic
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13C22×C412yes—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×Q812yes—
136C22×C4×C13C2411yescharacteristic
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—41no—
142C22×Dic13—41no—
143C22×Dic13—41no—
144C22×Dic13—41no—
145C22×Dic13C4⋊C414yes—
146C22×Dic13C4⋊C414yes—
147C22×Dic13C2×D411yescharacteristic
148C22×Dic13C2×D411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×D411yescharacteristic
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13C22×C412yes—
156C2×C8×C13C22×C412yes—
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#4112yes—
164C13×C4⋊C4#4112yes—
165C13×C22⋊C4—24no—
166C13×C22⋊C4—42no—
167C42×C13—24no—
168C22⋊Dic13—24no—
169C22⋊Dic13—42no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13#4112yes—
177C4⋊Dic13#4112yes—
178C4×Dic13—24no—
179C4×Dic13—42no—
180C4×Dic13—42no—
181C4×Dic13—42no—
182C4×Dic13—42no—
183C4×Dic13—42no—
184C4×Dic13—42no—
185C4×Dic13C4⋊C414yes—
186C4×Dic13C4⋊C414yes—
187C4×Dic13C22×C412yes—
188C4×Dic13C22×C412yes—
189C4×Dic13C2×Q812yes—
190C4×Dic13C2×Q812yes—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055C22×C412yes—
196C2×#1055C22×C412yes—
197C2×#432—131no—
198#2283—131no—
199C4×#117—131no—
200#1949—131no—
201#1949—131no—
202#1949—131no—
203#1949—131no—
204#1854—131no—
205#1854—131no—
206#1854—131no—
207#1854D1311yescharacteristic
208#1776—131no—
209#1776—131no—
210#1776—131no—
211#1776—131no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13C2×C4⋊C412yes—
219C23×C13C22×D411yescharacteristic
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
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×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13C2×C4⋊C412yes—
239C2×C4×C13C23×C411yescharacteristic
240C2×C4×C13C22×Q811yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—44no—
256C2×Dic13—44no—
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×Dic13—41no—
267C2×Dic13C2×C4⋊C412yes—
268C2×Dic13C2×C4⋊C412yes—
269C2×Dic13C2×C4⋊C412yes—
270C2×Dic13C2×C4⋊C412yes—
271C8×C13—22no—
272C8×C13—22no—
273#1055—22no—
274#1055—22no—
275C2×#117—131no—
276C2×#117C2×D1311yescharacteristic
277C22×C42—131no—
278#432—138no—
279C2×#107—131no—
280C2×#107—131no—
281C2×#107—131no—
282C2×#107C2×D1311yescharacteristic
283C2×#106—131no—
284C2×#106—131no—
285C2×#106—131no—
286C2×#106C2×D1311yescharacteristic
287C2×C4⋊C8—131no—
288C2×C4⋊C8—131no—
289C2×C22⋊C8—131no—
290C2×C22⋊C8C2×D1311yescharacteristic
291C2×#97—131no—
292C2×#97—131no—
293#383—261no—
294#382—131no—
295#382—131no—
296#381—261no—
297#380—131no—
298#380C2×D1311yescharacteristic
299C4×C4⋊C4—131no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4—131no—
303C4×C4⋊C4—131no—
304C4×C4⋊C4—131no—
305C4×C22⋊C4—261no—
306C4×C22⋊C4—261no—
307C4×C22⋊C4—261no—
308#376—261no—
309#376—261no—
310C43—261no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340C2×D1311yescharacteristic
318#340C2×D1311yescharacteristic
319C22×C13—22no—
320C22×C13—22no—
321C22×C13—22no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13C22×C4⋊C411yescharacteristic
327C22×C13#52511yescharacteristic
328C22×C13#52511yescharacteristic
329C22×C13#57511yescharacteristic
330C22×C13#57511yescharacteristic
331C22×C13#57511yescharacteristic
332C22×C13#57511yescharacteristic
333C4×C13—22no—
334C4×C13—42no—
335C4×C13—42no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13C4×#4111yescharacteristic
339C4×C13C4×#4111yescharacteristic
340C4×C13#53311yescharacteristic
341C4×C13#53311yescharacteristic
342Dic13—22no—
343Dic13—22no—
344Dic13—22no—
345Dic13—22no—
346Dic13—42no—
347Dic13—42no—
348Dic13—81no—
349Dic13—81no—
350C23×C4—131no—
351C23×C4—131no—
352C23×C4C22×D1311yescharacteristic
353C22×C8—131no—
354C22×C8—131no—
355C22×C8C22×D1311yescharacteristic
356C22×C8C22×D1311yescharacteristic
357#117—22no—
358#117—22no—
359#117—262no—
360#117—262no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4C22×D1311yescharacteristic
366C2×C4⋊C4C22×D1311yescharacteristic
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C42—21no—
374C2×C42—134no—
375C2×C42—131no—
376C2×C42—131no—
377C2×C42—134no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—261no—
381C2×C42—261no—
382C2×C42—261no—
383C2×C42—261no—
384C2×C42—261no—
385C2×C42—261no—
386C2×C42—261no—
387#107—22no—
388#107—262no—
389#107—262no—
390#107—262no—
391#106—22no—
392#106—262no—
393#106—262no—
394#106—262no—
395C4⋊C8—134no—
396C4⋊C8—134no—
397C22⋊C8—134no—
398C22⋊C8C4×D1314yes—
399#97—134no—
400#97—134no—
401#95—21no—
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413C2×C13—42no—
414C2×C13#229611yescharacteristic
415C2×C13#291111yescharacteristic
416C2×C13#291111yescharacteristic
417C2×C13#311111yescharacteristic
418C2×C13#311111yescharacteristic
419C2×C13#311111yescharacteristic
420C2×C13#311111yescharacteristic
421C24D4×D1311yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—131no—
434C22×C4—134no—
435C22×C4—134no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—521no—
441C22×C4—521no—
442C22×C4—521no—
443C22×C4—521no—
444C22×C4C2×C4×D1312yes—
445C22×C4D4×D1311yescharacteristic
446C22×C4Q8×D1312yes—
447C22×C4C23×D1311yescharacteristic
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—132no—
453C2×C8—132no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8C2×C4×D1312yes—
459C2×C8C2×C4×D1312yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—132no—
467C4⋊C4—132no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4#612912yes—
475C4⋊C4#612912yes—
476C22⋊C4—24no—
477C22⋊C4—42no—
478C22⋊C4—264no—
479C22⋊C4—522no—
480C42—24no—
481C42—134no—
482C42—134no—
483C42—132no—
484C42—132no—
485C42—132no—
486C42—132no—
487C42—264no—
488C42—522no—
489C42—522no—
490C42—522no—
491C42—522no—
492C42—522no—
493C42—522no—
494C13#2136611yescharacteristic, complemented, Sylow
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23C4⋊C4×D1312yes—
502C23C2×D4×D1311yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—132no—
522C2×C4—132no—
523C2×C4—132no—
524C2×C4—132no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—524no—
536C2×C4—524no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4C4⋊C4×D1312yes—
548C2×C4C22×C4×D1311yescharacteristic
549C2×C4C2×#612911yescharacteristic
550C2×C4C2×#612911yescharacteristic
551C2×C4C2×Q8×D1311yescharacteristic
552C2×C4#41×D1311yescharacteristic
553C2×C4#41×D1311yescharacteristic
554C8—22no—
555C8—22no—
556C8—262no—
557C8—262no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22C2×C4⋊C4×D1311yescharacteristic
566C22#1171929111yescharacteristic
567C22#1171936111yescharacteristic
568C22#1171947311yescharacteristic
569C22#1171947311yescharacteristic
570C22#1171947811yescharacteristic
571C22#1171948211yescharacteristic
572C4—22no—
573C4—42no—
574C4—42no—
575C4—81no—
576C4—81no—
577C4—262no—
578C4—262no—
579C4—262no—
580C4—262no—
581C4—522no—
582C4—522no—
583C4—1041no—
584C4—1041no—
585C4C4×#612911yescharacteristic
586C4C4×#612911yescharacteristic
587C4#1171932711yescharacteristic
588C4#1171932711yescharacteristic
589C2—42no—
590C2#1311731511yescharacteristic
591C2#1312342311yescharacteristic
592C2#1312342411yescharacteristic
593C2#1312493811yescharacteristic
594C2#1312494011yescharacteristic
595C2#1312494611yescharacteristic
596C2#1312494811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1854C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#1854D13
hypocenterC13#21366
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #13115607C2semidirect
5. #13115605C2semidirect
6. #13115603C2semidirect
7. #13115601C2semidirect
11. #13114736C2semidirect
12. #13114735C2semidirect
13. #13114732C2semidirect
14. #13114732C2semidirect
49. #11718380C4semidirect
494. C13#21366semidirect

Maximal subgroups

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

subgroupindex
C2×#117183802
#131172312
#117×Dic132
#131156072
#131156052
#131156032
#131156012
#131150372
#131150352
#131150332
#131147362
#131147352
#131147322
C13×#18542
#2136613