Finite Group Databasebeta

← #15870634

Subgroups — #15870634

Order 3328.

868 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718424C211yesmaximal, characteristic
2#13117576C211yesmaximal, characteristic, complemented
3#13117197C211yesmaximal, characteristic
4#13115792C211yesmaximal, characteristic, complemented
5#13115596C211yesmaximal, characteristic, complemented
6#13115415C211yesmaximal, characteristic, complemented
7#13115404C211yesmaximal, characteristic, complemented
8#13115097C211yesmaximal, characteristic
9#13114834C211yesmaximal, characteristic
10#13114732C211yesmaximal, characteristic, complemented
11#106×Dic13C211yesmaximal, characteristic, complemented
12#13114692C211yesmaximal, characteristic, complemented
13#13114663C211yesmaximal, characteristic
14#102×Dic13C211yesmaximal, characteristic
15C13×#1864C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×D4×Dic13C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C2×#88144C2211yescharacteristic
20C2×C13×#106C2211yescharacteristic
21C2×C13×#102C2211yescharacteristic
22C2×C13×#102C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C2×#88072C2211yescharacteristic
25C2×#88072C2211yescharacteristic
26C4×C22⋊Dic13—21no—
27C2×#88071—21no—
28C2×#88057C2211yescharacteristic
29C2×#88055C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33#11718637C2211yescharacteristic
34C4⋊C4×Dic13C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37C4⋊C4×Dic13C2211yescharacteristic
38#11718634—21no—
39#11718633—21no—
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C22⋊C4×Dic13—21no—
43C22⋊C4×Dic13—21no—
44C4×C4⋊Dic13C2211yescharacteristic
45#11718593C2211yescharacteristic
46#11718589C2211yescharacteristic
47#11718424C418yescomplemented
48#11718314—21no—
49#11718313—21no—
50C13×#340C2211yescharacteristic
51C13×#336C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C23×Dic13—21no—
63C23×Dic13—21no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C22⋊C4—21no—
73C2×C42×C13C2311yescharacteristic
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76D4×Dic13—22no—
77D4×Dic13—22no—
78D4×Dic13C2×C414yes—
79D4×Dic13Q814yes—
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×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13C2311yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98#88144—22no—
99#88144C2×C414yescomplemented
100C13×#106—22no—
101C13×#102—22no—
102C13×#102C2×C414yes—
103C13×#95—21no—
104#88072—22no—
105#88072C2×C414yes—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071D411yescharacteristic
113#88071D411yescharacteristic
114#88071D411yescharacteristic
115#88071D411yescharacteristic
116#88057C2×C414yescomplemented
117#88055—22no—
118#88054—22no—
119#88054C2×C414yescomplemented
120C8×Dic13—22no—
121#88048—22no—
122#88047C2×C414yescomplemented
123#21619—131nomaximal, Sylow
124C24×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13C22×C412yes—
129C2×D4×C13C2×Q812yes—
130C2×D4×C13#4112yes—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—24no—
134C22×C4×C13—21no—
135C22×C4×C13—81no—
136C22×C4×C13—81no—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2411yescharacteristic
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—24no—
144C22×Dic13—24no—
145C22×Dic13—21no—
146C22×Dic13—81no—
147C22×Dic13—81no—
148C22×Dic13—81no—
149C22×Dic13—81no—
150C22×Dic13C2×D411yescharacteristic
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13C22×C412yes—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—81no—
165C13×C4⋊C4C22×C412yes—
166C13×C4⋊C4#4112yes—
167C13×C22⋊C4—24no—
168C42×C13—21no—
169C42×C13—21no—
170C22⋊Dic13—24no—
171C22⋊Dic13—24no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—24no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13C22×C412yes—
179C4⋊Dic13C22×C412yes—
180C4⋊Dic13C2×Q812yes—
181#6101—24no—
182#6101—81no—
183#6101—81no—
184#6101—81no—
185C4×Dic13—81no—
186C4×Dic13—81no—
187C4×Dic13—81no—
188C4×Dic13—81no—
189C4×Dic13—81no—
190C4×Dic13C22×C412yes—
191C4×Dic13C2×Q812yes—
192C4×Dic13#4112yes—
193C4×Dic13#4112yes—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C22×C412yes—
200C2×#478—131no—
201#2330—131no—
202#2275—131no—
203#1989—131no—
204#1948—131no—
205#1919—131no—
206#1918—131no—
207#1864—131no—
208#1864D1311yescharacteristic
209#1802—131no—
210#1776—131no—
211C4×#106—131no—
212#1768—131no—
213#1762—131no—
214C4×#102—131no—
215C23×C13—22no—
216C23×C13—22no—
217C23×C13—22no—
218C23×C13—41no—
219C23×C13—41no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13C22×D411yescharacteristic
223D4×C13—22no—
224D4×C13—22no—
225D4×C13—22no—
226D4×C13C4×Q814yes—
227C2×C4×C13—22no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—22no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—84no—
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×Q811yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—84no—
270C2×Dic13—84no—
271C2×Dic13C4×D412yes—
272C2×Dic13C4×D412yes—
273C2×Dic13C22⋊Q812yes—
274C2×Dic13C22⋊Q812yes—
275C8×C13—22no—
276C8×C13—41no—
277#1055—22no—
278#1055—41no—
279C2×#125—131no—
280C2×C4×D4—131no—
281C2×C4×D4—131no—
282C2×C4×D4C2×D1311yescharacteristic
283#478—138no—
284C2×#107—131no—
285C2×#106—131no—
286C2×#106—131no—
287C2×#106C2×D1311yescharacteristic
288C2×C4⋊C8—131no—
289C2×C4⋊C8—131no—
290C2×#102—131no—
291C2×#102—131no—
292C2×#102C2×D1311yescharacteristic
293C2×#102C2×D1311yescharacteristic
294C2×#97—131no—
295C2×C4×C8—131no—
296#389—131no—
297#389—261no—
298#389—261no—
299#389C2×D1311yescharacteristic
300#387—261no—
301#387—261no—
302#384—131no—
303C4×C4⋊C4—131no—
304C4×C4⋊C4—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—131no—
307C4×C4⋊C4—131no—
308C4×C22⋊C4—261no—
309C4×C22⋊C4—261no—
310C4×C22⋊C4—261no—
311#376—131no—
312C2×#95—261no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340C2×D1311yescharacteristic
321#336—131no—
322#336C2×D1311yescharacteristic
323C22×C13—24no—
324C22×C13—42no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—42no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13C2×C4×D411yescharacteristic
331C22×C13C2×C22⋊Q811yescharacteristic
332C22×C13#52511yescharacteristic
333C22×C13#57611yescharacteristic
334C22×C13#57711yescharacteristic
335C22×C13#57711yescharacteristic
336C22×C13#57711yescharacteristic
337C4×C13—41no—
338C4×C13—41no—
339C4×C13—42no—
340C4×C13—42no—
341C4×C13—81no—
342C4×C13C2×C4×Q811yescharacteristic
343C4×C13C4×#4111yescharacteristic
344C4×C13#52911yescharacteristic
345C4×C13#53311yescharacteristic
346Dic13—22no—
347Dic13—22no—
348Dic13—22no—
349Dic13—22no—
350Dic13—42no—
351Dic13—42no—
352Dic13—42no—
353Dic13—81no—
354C22×D4C22×D1311yescharacteristic
355C23×C4—21no—
356C23×C4—261no—
357C23×C4—261no—
358C22×C8—131no—
359C22×C8—131no—
360C22×C8C22×D1311yescharacteristic
361C22×C8C22×D1311yescharacteristic
362#125—134no—
363#125—262no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—134no—
367C4×D4—134no—
368C4×D4—262no—
369C4×D4—262no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C42—131no—
387C2×C42—131no—
388C2×C42—261no—
389C2×C42—261no—
390C2×C42—261no—
391C2×C42—261no—
392C2×C42—261no—
393C2×C42C22×D1311yescharacteristic
394#107—134no—
395#106—22no—
396#106—134no—
397#106—262no—
398C4⋊C8—134no—
399C4⋊C8—262no—
400#102—22no—
401#102—134no—
402#102—262no—
403#102C4×D1314yes—
404#97—262no—
405C4×C8—262no—
406#95—21no—
407#95—131no—
408#95—131no—
409#95—131no—
410#95—131no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417C2×C13—44no—
418C2×C13C4×C22⋊Q811yescharacteristic
419C2×C13#294611yescharacteristic
420C2×C13#295211yescharacteristic
421C2×C13#308111yescharacteristic
422C2×C13#308411yescharacteristic
423C2×C13#311911yescharacteristic
424C2×C13#312311yescharacteristic
425C24—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4C2×C4×D1312yes—
430C2×D4#612912yes—
431C2×D4Q8×D1312yes—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—24no—
435C22×C4—21no—
436C22×C4—81no—
437C22×C4—81no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—264no—
443C22×C4—264no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—1041no—
449C22×C4—1041no—
450C22×C4—1041no—
451C22×C4—1041no—
452C22×C4D4×D1311yescharacteristic
453C22×C4D4×D1311yescharacteristic
454C22×C4C23×D1311yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—132no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8C2×C4×D1312yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—81no—
472C4⋊C4—132no—
473C4⋊C4—132no—
474C4⋊C4—132no—
475C4⋊C4—264no—
476C4⋊C4—264no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—1041no—
483C4⋊C4—1041no—
484C4⋊C4—1041no—
485C4⋊C4C2×C4×D1312yes—
486C4⋊C4#612912yes—
487C22⋊C4—24no—
488C22⋊C4—264no—
489C22⋊C4—264no—
490C42—21no—
491C42—21no—
492C42—132no—
493C42—132no—
494C42—132no—
495C42—132no—
496C42—1041no—
497C42—1041no—
498C42—1041no—
499C42—1041no—
500C42—1041no—
501C13#2161911yescharacteristic, complemented, Sylow
502C23—22no—
503C23—22no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23C2×D4×D1311yescharacteristic
510D4—22no—
511D4—22no—
512D4—22no—
513D4#8814114yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—84no—
530C2×C4—132no—
531C2×C4—132no—
532C2×C4—132no—
533C2×C4—132no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—1044no—
555C2×C4—1044no—
556C2×C4C22×C4×D1311yescharacteristic
557C2×C4C2×#612911yescharacteristic
558C2×C4C2×#612911yescharacteristic
559C2×C4C2×Q8×D1311yescharacteristic
560C2×C4#41×D1311yescharacteristic
561C2×C4#41×D1311yescharacteristic
562C8—22no—
563C8—41no—
564C8—262no—
565C8—521no—
566C22—24no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22C4×D4×D1311yescharacteristic
574C22#1171929111yescharacteristic
575C22D13×C22⋊Q811yescharacteristic
576C22#1171946711yescharacteristic
577C22#1171947511yescharacteristic
578C22#1171947911yescharacteristic
579C22#1171948011yescharacteristic
580C4—42no—
581C4—41no—
582C4—41no—
583C4—42no—
584C4—81no—
585C4—262no—
586C4—262no—
587C4—262no—
588C4—262no—
589C4—522no—
590C4—522no—
591C4—522no—
592C4—1041no—
593C4C2×#8814111yescharacteristic
594C4C4×#612911yescharacteristic
595C4#1171932711yescharacteristic
596C4#1171935411yescharacteristic
597C2—44no—
598C2#1311736811yescharacteristic
599C2#1312366511yescharacteristic
600C2#1312371411yescharacteristic
601C2#1312466211yescharacteristic
602C2#1312469911yescharacteristic
603C2#1312503611yescharacteristic
604C2#1312508211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1864C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#1864D13
hypocenterC13#21619
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. #13117576C2semidirect
4. #13115792C2semidirect
5. #13115596C2semidirect
6. #13115415C2semidirect
7. #13115404C2semidirect
10. #13114732C2semidirect
11. #106×Dic13C2semidirect
12. #13114692C2semidirect
47. #11718424C4semidirect
99. #88144C2×C4semidirect
116. #88057C2×C4semidirect
119. #88054C2×C4semidirect
122. #88047C2×C4semidirect
501. C13#21619semidirect

Maximal subgroups

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

subgroupindex
C2×#117184242
#131175762
#131171972
#131157922
#131155962
#131154152
#131154042
#131150972
#131148342
#131147322
#106×Dic132
#131146922
#131146632
#102×Dic132
C13×#18642
#2161913