Finite Group Databasebeta

← #15870691

Subgroups — #15870691

Order 3328.

876 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718503C211yesmaximal, characteristic
2#13117584C211yesmaximal, characteristic, complemented
3#13117198C211yesmaximal, characteristic
4#13115787C211yesmaximal, characteristic, complemented
5#13115606C211yesmaximal, characteristic, complemented
6#13115422C211yesmaximal, characteristic, complemented
7#13115415C211yesmaximal, characteristic, complemented
8#13115100C211yesmaximal, characteristic
9#13115086C211yesmaximal, characteristic
10#13114847C211yesmaximal, characteristic
11#13114733C211yesmaximal, characteristic, complemented
12C4×#88057C211yesmaximal, characteristic, complemented
13#13114662C211yesmaximal, characteristic
14C4×#88061C211yesmaximal, characteristic
15C13×#1768C211yesmaximal, characteristic, complemented
16C2×C4×D52C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C2×#88123C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×#97C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24C13×#376C2211yescharacteristic
25C2×#88061C2211yescharacteristic
26C2×#88061C2211yescharacteristic
27C2×#88061C2211yescharacteristic
28C2×#88061C2211yescharacteristic
29C2×#88058C2211yescharacteristic
30C2×#88057C2211yescharacteristic
31C2×#88057C2211yescharacteristic
32C2×#88057C2211yescharacteristic
33#11718597C2211yescharacteristic
34C4×C4⋊Dic13C2211yescharacteristic
35C4×C4⋊Dic13C2211yescharacteristic
36C4×C4⋊Dic13C2211yescharacteristic
37C4×C4⋊Dic13C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718503C418yescomplemented
42#11718327—21no—
43#11718327—21no—
44#11718327—21no—
45D13×#95—21no—
46#11718315—21no—
47#11718315—21no—
48#11718307—21no—
49#11718307—21no—
50C13×#336C2211yescharacteristic
51C13×#336C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×C4×D13—21no—
63C22×C4×D13—21no—
64C22×Dic26—21no—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C2×C42×C13C2311yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×#6101—21no—
84C2×#6101—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C4×D52—22no—
91C4×D52—22no—
92C4×D52—22no—
93C4×D52—22no—
94C4×D52C2×C414yes—
95C4×D52Q814yescomplemented
96#88123—22no—
97#88123C2×C414yescomplemented
98C13×C4⋊C8—22no—
99C13×C4⋊C8C2×C414yescomplemented
100C13×#97—22no—
101C4×C8×C13—22no—
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
104C13×#95D411yescharacteristic
105C13×#95D411yescharacteristic
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88061—22no—
116#88061—22no—
117#88061C2×C414yes—
118#88061C2×C414yes—
119#88058—22no—
120#88057—22no—
121#88057C2×C414yescomplemented
122#88057C2×C414yescomplemented
123#21623—131nomaximal, Sylow
124C23×D13—21no—
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2411yescharacteristic
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52C22×C412yes—
143C2×D52C2×Q812yes—
144C2×D52#4112yes—
145C2×C4×D13—24no—
146C2×C4×D13—24no—
147C2×C4×D13—24no—
148C2×C4×D13—81no—
149C2×C4×D13—81no—
150C2×C4×D13—81no—
151C2×C4×D13—81no—
152C2×C4×D13—81no—
153C2×C4×D13—81no—
154C2×Dic26—24no—
155C2×Dic26—81no—
156C2×Dic26—81no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13C22×C412yes—
168C2×C8×C13C22×C412yes—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13C22×C412yes—
172C42×C13C2×Q812yes—
173C42×C13#4112yes—
174C42×C13#4112yes—
175#6103—24no—
176#6103—24no—
177#6103—24no—
178C4⋊Dic13—24no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13C22×C412yes—
189C4⋊Dic13C22×C412yes—
190C4⋊Dic13C22×C412yes—
191C4⋊Dic13C2×Q812yes—
192C4⋊Dic13#4112yes—
193#6101—81no—
194#6101—81no—
195C4×Dic13—81no—
196C4×Dic13—81no—
197C4×Dic13—81no—
198C4×Dic13—81no—
199C4×Dic13—81no—
200C2×#476—131no—
201#2331—131no—
202#2275—131no—
203#1988—131no—
204#1949—131no—
205#1920—131no—
206#1919—131no—
207#1864—131no—
208#1862—131no—
209#1804—131no—
210#1776—131no—
211C4×#106—131no—
212#1768D1311yescharacteristic, complemented
213#1762—131no—
214C4×#102—131no—
215C23×C13C22×D411yescharacteristic
216C22×D13—22no—
217C22×D13—22no—
218C22×D13—22no—
219C22×D13—41no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—41no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13C4×D412yes—
238C2×C4×C13C4×D412yes—
239C2×C4×C13C22⋊Q812yes—
240C2×C4×C13C22⋊Q812yes—
241C2×C4×C13C23×C411yescharacteristic
242C2×C4×C13C22×Q811yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—22no—
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×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268D52—22no—
269D52—22no—
270D52—22no—
271D52C4×Q814yes—
272C4×D13—84no—
273C4×D13—84no—
274C4×D13—84no—
275Dic26—84no—
276C8×C13—22no—
277C8×C13—22no—
278C8×C13—41no—
279C8×C13—41no—
280C2×C4⋊Q8—131no—
281C2×C4×D4—131no—
282C2×C4×D4—131no—
283C2×C4×D4—131no—
284#476—138no—
285C2×#107—131no—
286C2×#106—131no—
287C2×#106—131no—
288C2×#106—131no—
289C2×C4⋊C8C2×D1311yescharacteristic
290C2×C4⋊C8C2×D1311yescharacteristic
291C2×#102—131no—
292C2×#102—131no—
293C2×#102—131no—
294C2×#102—131no—
295C2×#97C2×D1311yescharacteristic
296C2×C4×C8C2×D1311yescharacteristic
297#391—261no—
298#391—261no—
299#389—131no—
300#389—131no—
301#387—261no—
302#387—261no—
303#382—131no—
304C4×C4⋊C4—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—131no—
307C4×C4⋊C4—131no—
308C4×C4⋊C4—131no—
309C4×C22⋊C4—261no—
310C4×C22⋊C4—261no—
311C4×C22⋊C4—261no—
312#376C2×D1311yescharacteristic
313C2×#95—261no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#336C2×D1311yescharacteristic
323#336C2×D1311yescharacteristic
324C22×C13C2×C4×D411yescharacteristic
325C22×C13C2×C22⋊Q811yescharacteristic
326C22×C13#52511yescharacteristic
327C22×C13#57611yescharacteristic
328C22×C13#57711yescharacteristic
329C22×C13#57711yescharacteristic
330C22×C13#57711yescharacteristic
331C2×D13—24no—
332C2×D13—42no—
333C2×D13—42no—
334C2×D13—42no—
335C2×D13—42no—
336C2×D13—42no—
337C2×D13—42no—
338C4×C13—22no—
339C4×C13—22no—
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13C2×C4×Q811yescharacteristic
345C4×C13C4×#4111yescharacteristic
346C4×C13#52911yescharacteristic
347C4×C13#53311yescharacteristic
348Dic13—42no—
349Dic13—42no—
350Dic13—42no—
351Dic13—42no—
352Dic13—42no—
353Dic13—81no—
354Dic13—81no—
355C22×Q8—261no—
356C22×D4—131no—
357C23×C4—261no—
358C23×C4—261no—
359C23×C4—261no—
360C22×C8C22×D1311yescharacteristic
361C22×C8C22×D1311yescharacteristic
362C22×C8C22×D1311yescharacteristic
363C22×C8C22×D1311yescharacteristic
364C4⋊Q8—134no—
365C4⋊Q8—262no—
366C4×D4—134no—
367C4×D4—134no—
368C4×D4—262no—
369C4×D4—262no—
370C4×D4—262no—
371C4×D4—262no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C22⋊C4—261no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C42—261no—
386C2×C42—261no—
387C2×C42—261no—
388C2×C42—261no—
389C2×C42—261no—
390C2×C42C22×D1311yescharacteristic
391C2×C42C22×D1311yescharacteristic
392C2×C42C22×D1311yescharacteristic
393#107—262no—
394#106—134no—
395#106—134no—
396#106—262no—
397C4⋊C8—22no—
398C4⋊C8C4×D1314yescomplemented
399#102—134no—
400#102—134no—
401#102—262no—
402#102—262no—
403#97—22no—
404C4×C8—22no—
405#95—261no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95D5211yescharacteristic
415#95D5211yescharacteristic
416#95D5211yescharacteristic
417#95D5211yescharacteristic
418C2×C13C4×C22⋊Q811yescharacteristic
419C2×C13#294611yescharacteristic
420C2×C13#294911yescharacteristic
421C2×C13#308111yescharacteristic
422C2×C13#308411yescharacteristic
423C2×C13#311811yescharacteristic
424C2×C13#312511yescharacteristic
425D13—44no—
426C24—261no—
427C2×Q8—264no—
428C2×Q8—1041no—
429C2×Q8—1041no—
430C2×D4—132no—
431C2×D4—132no—
432C2×D4—132no—
433C2×D4—261no—
434C2×D4—261no—
435C2×D4—261no—
436C22×C4—264no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—264no—
443C22×C4—264no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—1041no—
447C22×C4—1041no—
448C22×C4—1041no—
449C22×C4—1041no—
450C22×C4—1041no—
451C22×C4—1041no—
452C22×C4C2×D5211yescharacteristic
453C22×C4C2×D5211yescharacteristic
454C22×C4C2×D5211yescharacteristic
455C22×C4C2×D5211yescharacteristic
456C22×C4C2×D5211yescharacteristic
457C22×C4C2×D5211yescharacteristic
458C22×C4C23×D1311yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8C2×C4×D1312yes—
470C2×C8C2×C4×D1312yes—
471C4⋊C4—132no—
472C4⋊C4—132no—
473C4⋊C4—132no—
474C4⋊C4—132no—
475C4⋊C4—132no—
476C4⋊C4—264no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—1041no—
487C4⋊C4—1041no—
488C22⋊C4—264no—
489C22⋊C4—264no—
490C22⋊C4—264no—
491C42—21no—
492C42—21no—
493C42—1041no—
494C42—1041no—
495C42—1041no—
496C42—1041no—
497C42—1041no—
498C42C2×C4×D1312yes—
499C42#612712yes—
500C42#612912yes—
501C42Q8×D1312yes—
502C13#2162311yescharacteristic, complemented, Sylow
503C23—262no—
504C23—262no—
505C23—262no—
506C23—521no—
507C23—521no—
508C23—521no—
509C23—521no—
510C23C22×D5211yescharacteristic
511Q8—1044no—
512D4—134no—
513D4—262no—
514D4—262no—
515D4—262no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—262no—
531C2×C4—262no—
532C2×C4—262no—
533C2×C4—262no—
534C2×C4—262no—
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—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—1044no—
552C2×C4—1044no—
553C2×C4—1044no—
554C2×C4C4×D5212yes—
555C2×C4C4×D5212yes—
556C2×C4#8815112yes—
557C2×C4#8815112yes—
558C2×C4C22×C4×D1311yescharacteristic
559C2×C4C2×#612711yescharacteristic
560C2×C4C2×#612911yescharacteristic
561C2×C4C2×Q8×D1311yescharacteristic
562C2×C4#41×D1311yescharacteristic
563C2×C4#41×D1311yescharacteristic
564C8—22no—
565C8—22no—
566C8—41no—
567C8—41no—
568C22—264no—
569C22—522no—
570C22—522no—
571C22—522no—
572C22—522no—
573C22—522no—
574C22—522no—
575C22C2×C4×D5211yescharacteristic
576C22C2×#8815111yescharacteristic
577C22#1171922911yescharacteristic
578C22#1171945611yescharacteristic
579C22#1171945611yescharacteristic
580C22#1171945611yescharacteristic
581C22#1171945711yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—522no—
589C4—522no—
590C4—522no—
591C4—522no—
592C4—522no—
593C4—1041no—
594C4—1041no—
595C4C4×#612911yescharacteristic
596C4#1171926211yescharacteristic
597C4C4×Q8×D1311yescharacteristic
598C4#1171928311yescharacteristic
599C2—524no—
600C2C4×#8815111yescharacteristic
601C2#1312367011yescharacteristic
602C2#1312369711yescharacteristic
603C2#1312466811yescharacteristic
604C2#1312470011yescharacteristic
605C2#1312502211yescharacteristic
606C2#1312511511yescharacteristic
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1768C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1768D13
hypocenterC13#21623
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
2. #13117584C2semidirect
4. #13115787C2semidirect
5. #13115606C2semidirect
6. #13115422C2semidirect
7. #13115415C2semidirect
11. #13114733C2semidirect
12. C4×#88057C2semidirect
15. C13×#1768C2semidirect
41. #11718503C4semidirect
95. C4×D52Q8semidirect
97. #88123C2×C4semidirect
99. C13×C4⋊C8C2×C4semidirect
121. #88057C2×C4semidirect
122. #88057C2×C4semidirect
212. #1768D13semidirect
398. C4⋊C8C4×D13semidirect
502. C13#21623semidirect

Maximal subgroups

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

subgroupindex
C2×#117185032
#131175842
#131171982
#131157872
#131156062
#131154222
#131154152
#131151002
#131150862
#131148472
#131147332
C4×#880572
#131146622
C4×#880612
C13×#17682
#2162313