Finite Group Databasebeta

← #15870690

Subgroups — #15870690

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
1#13117585C211yesmaximal, characteristic, complemented
2#13117197C211yesmaximal, characteristic
3#13115789C211yesmaximal, characteristic, complemented
4#13115606C211yesmaximal, characteristic, complemented
5#13115423C211yesmaximal, characteristic, complemented
6#13115416C211yesmaximal, characteristic, complemented
7#13115099C211yesmaximal, characteristic
8#13115085C211yesmaximal, characteristic
9#13114846C211yesmaximal, characteristic
10#13114736C211yesmaximal, characteristic, complemented
11#106×Dic13C211yesmaximal, characteristic, complemented
12#13114695C211yesmaximal, characteristic, complemented
13#13114663C211yesmaximal, characteristic
14#102×Dic13C211yesmaximal, characteristic
15C2×C13×#476C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C2×D4×Dic13C2211yescharacteristic
20C13×#476C418yescomplemented
21C2×C13×#106C2211yescharacteristic
22C2×C13×#106C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×#102C2211yescharacteristic
25C2×C13×#102C2211yescharacteristic
26#11718891—21no—
27#11718891—21no—
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C4×C22⋊Dic13—21no—
31C2×#88071—21no—
32C2×#88058C2211yescharacteristic
33C2×#88057C2211yescharacteristic
34C2×#88055C2211yescharacteristic
35C2×C8×Dic13C2211yescharacteristic
36#11718646C2211yescharacteristic
37#11718646C2211yescharacteristic
38#11718642—21no—
39#11718642—21no—
40C4⋊C4×Dic13C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42C4⋊C4×Dic13C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44C22⋊C4×Dic13—21no—
45C22⋊C4×Dic13—21no—
46#11718597C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48#11718593C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×Q8×C13—21no—
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×Dic13—21no—
64C23×Dic13—21no—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8C2×C414yescomplemented
69C4×D4×C13—22no—
70C4×D4×C13C2×C414yes—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79D4×Dic13—22no—
80D4×Dic13—22no—
81D4×Dic13—22no—
82D4×Dic13Q814yescomplemented
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
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
98C13×#106C2×C414yescomplemented
99C13×#106C2×C414yescomplemented
100C13×C4⋊C8C2×C414yescomplemented
101C13×#102C2×C414yes—
102C13×#102C2×C414yes—
103#88072—22no—
104#88072—22no—
105#88071—21no—
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#88071D411yescharacteristic
115#88071D411yescharacteristic
116#88071D411yescharacteristic
117#88071D411yescharacteristic
118#88058—22no—
119#88057—22no—
120#88055—22no—
121C8×Dic13—22no—
122C4⋊#1055—22no—
123#21623—131nomaximal, Sylow
124C24×C13—21no—
125C2×Q8×C13—24no—
126C2×Q8×C13—81no—
127C2×Q8×C13—81no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13C22×C412yes—
132C2×D4×C13C2×Q812yes—
133C2×D4×C13#4112yes—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—24no—
138C22×C4×C13—81no—
139C22×C4×C13—81no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2411yescharacteristic
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—24no—
146C22×Dic13—24no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—81no—
150C22×Dic13—81no—
151C22×Dic13—81no—
152C22×Dic13—81no—
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C22×Dic13C2×D411yescharacteristic
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13C22×C412yes—
162C2×C8×C13C22×C412yes—
163C13×C4⋊C4—24no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4C22×C412yes—
168C13×C4⋊C4C22×C412yes—
169C13×C4⋊C4C22×C412yes—
170C13×C22⋊C4—24no—
171C42×C13C22×C412yes—
172C42×C13#4112yes—
173C22⋊Dic13—24no—
174C22⋊Dic13—24no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—81no—
182C4⋊Dic13—81no—
183C4⋊Dic13C2×Q812yes—
184C4⋊Dic13#4112yes—
185C4×Dic13—21no—
186C4×Dic13—21no—
187C4×Dic13—81no—
188C4×Dic13—81no—
189C4×Dic13—81no—
190C4×Dic13—81no—
191C4×Dic13—81no—
192C4×Dic13C2×Q812yes—
193C4×Dic13#4112yes—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#476D1311yescharacteristic
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#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
223Q8×C13—84no—
224D4×C13—22no—
225D4×C13—22no—
226D4×C13—22no—
227D4×C13C4×Q814yes—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
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—84no—
242C2×C4×C13C4×D412yes—
243C2×C4×C13C4×D412yes—
244C2×C4×C13C23×C411yescharacteristic
245C2×C4×C13C22×Q811yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—22no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—22no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—84no—
273C2×Dic13—84no—
274C2×Dic13C22⋊Q812yes—
275C2×Dic13C22⋊Q812yes—
276C8×C13—22no—
277C8×C13—22no—
278#1055—41no—
279#1055—41no—
280C2×C4⋊Q8C2×D1311yescharacteristic
281C2×C4×D4—131no—
282C2×C4×D4—131no—
283C2×C4×D4C2×D1311yescharacteristic
284#476Dic1318yescomplemented
285C2×#107—131no—
286C2×#106—131no—
287C2×#106C2×D1311yescharacteristic
288C2×#106C2×D1311yescharacteristic
289C2×C4⋊C8—131no—
290C2×C4⋊C8C2×D1311yescharacteristic
291C2×#102—131no—
292C2×#102—131no—
293C2×#102C2×D1311yescharacteristic
294C2×#102C2×D1311yescharacteristic
295C2×#97—131no—
296C2×C4×C8—131no—
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#376—131no—
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#336—131no—
323#336—131no—
324C22×C13—24no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—42no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13C2×C4×D411yescharacteristic
332C22×C13C2×C22⋊Q811yescharacteristic
333C22×C13#52511yescharacteristic
334C22×C13#57611yescharacteristic
335C22×C13#57711yescharacteristic
336C22×C13#57711yescharacteristic
337C22×C13#57711yescharacteristic
338C4×C13—22no—
339C4×C13—22no—
340C4×C13—42no—
341C4×C13—42no—
342C4×C13—42no—
343C4×C13C2×C4×Q811yescharacteristic
344C4×C13C4×#4111yescharacteristic
345C4×C13#52911yescharacteristic
346C4×C13#53311yescharacteristic
347Dic13—22no—
348Dic13—22no—
349Dic13—42no—
350Dic13—41no—
351Dic13—42no—
352Dic13—41no—
353Dic13—81no—
354Dic13—81no—
355C22×Q8—21no—
356C22×D4C22×D1311yescharacteristic
357C23×C4—21no—
358C23×C4—261no—
359C23×C4—261no—
360C22×C8—131no—
361C22×C8—131no—
362C22×C8C22×D1311yescharacteristic
363C22×C8C22×D1311yescharacteristic
364C4⋊Q8—22no—
365C4⋊Q8C2×Dic1314yescomplemented
366C4×D4—22no—
367C4×D4—134no—
368C4×D4—262no—
369C4×D4—262no—
370C4×D4—262no—
371C4×D4C2×Dic1314yes—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C42—131no—
386C2×C42—131no—
387C2×C42—261no—
388C2×C42—261no—
389C2×C42—261no—
390C2×C42—261no—
391C2×C42—261no—
392C2×C42C22×D1311yescharacteristic
393#107—262no—
394#106—262no—
395#106C2×Dic1314yescomplemented
396#106C2×Dic1314yescomplemented
397C4⋊C8—262no—
398C4⋊C8C2×Dic1314yescomplemented
399#102—262no—
400#102—262no—
401#102C2×Dic1314yes—
402#102C2×Dic1314yes—
403#97—262no—
404C4×C8—262no—
405#95—131no—
406#95—131no—
407#95—131no—
408#95—131no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418C2×C13—44no—
419C2×C13C4×C22⋊Q811yescharacteristic
420C2×C13#294611yescharacteristic
421C2×C13#294911yescharacteristic
422C2×C13#308111yescharacteristic
423C2×C13#308411yescharacteristic
424C2×C13#311811yescharacteristic
425C2×C13#312511yescharacteristic
426C24—21no—
427C2×Q8—24no—
428C2×Q8—81no—
429C2×Q8—81no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4Q8×D1312yes—
434C2×D4#613112yes—
435C2×D4C22×Dic1312yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—81no—
441C22×C4—81no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—264no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—264no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—1041no—
453C22×C4—1041no—
454C22×C4—1041no—
455C22×C4—1041no—
456C22×C4D4×D1311yescharacteristic
457C22×C4D4×D1311yescharacteristic
458C22×C4C23×D1311yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8C22×Dic1312yes—
470C2×C8C22×Dic1312yes—
471C4⋊C4—24no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—132no—
476C4⋊C4—132no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—1041no—
484C4⋊C4—1041no—
485C4⋊C4C22×Dic1312yes—
486C4⋊C4C22×Dic1312yes—
487C4⋊C4C22×Dic1312yes—
488C22⋊C4—24no—
489C22⋊C4—264no—
490C22⋊C4—264no—
491C42—132no—
492C42—132no—
493C42—261no—
494C42—261no—
495C42—1041no—
496C42—1041no—
497C42—1041no—
498C42—1041no—
499C42—1041no—
500C42#612912yes—
501C42C22×Dic1312yes—
502C13#2162311yescharacteristic, complemented, Sylow
503C23—22no—
504C23—22no—
505C23—22no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23C2×D4×D1311yescharacteristic
511Q8—84no—
512D4—22no—
513D4—22no—
514D4—22no—
515D4Q8×Dic1314yes—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
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—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—262no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—262no—
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—521no—
553C2×C4—521no—
554C2×C4—1044no—
555C2×C4—1044no—
556C2×C4D4×Dic1312yes—
557C2×C4D4×Dic1312yes—
558C2×C4C2×#612911yescharacteristic
559C2×C4C2×Q8×D1311yescharacteristic
560C2×C4C2×#613111yescharacteristic
561C2×C4#41×D1311yescharacteristic
562C2×C4#41×D1311yescharacteristic
563C2×C4C23×Dic1311yescharacteristic
564C8—22no—
565C8—22no—
566C8—521no—
567C8—521no—
568C22—24no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22D13×C22⋊Q811yescharacteristic
576C22#1171933211yescharacteristic
577C22#1171946711yescharacteristic
578C22#1171946711yescharacteristic
579C22#1171947911yescharacteristic
580C22#1171948011yescharacteristic
581C22C2×D4×Dic1311yescharacteristic
582C4—22no—
583C4—22no—
584C4—42no—
585C4—42no—
586C4—42no—
587C4—262no—
588C4—262no—
589C4—522no—
590C4—521no—
591C4—522no—
592C4—521no—
593C4—1041no—
594C4—1041no—
595C4#1171932711yescharacteristic
596C4#1171932911yescharacteristic
597C4C2×Q8×Dic1311yescharacteristic
598C4#41×Dic1311yescharacteristic
599C2—44no—
600C2C22⋊Q8×Dic1311yescharacteristic
601C2#1312366911yescharacteristic
602C2#1312369611yescharacteristic
603C2#1312466211yescharacteristic
604C2#1312469311yescharacteristic
605C2#1312502511yescharacteristic
606C2#1312511811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#476C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenterC2×#476D13
hypocenterC13#21623
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #13117585C2semidirect
3. #13115789C2semidirect
4. #13115606C2semidirect
5. #13115423C2semidirect
6. #13115416C2semidirect
10. #13114736C2semidirect
11. #106×Dic13C2semidirect
12. #13114695C2semidirect
20. C13×#476C4semidirect
68. C13×C4⋊Q8C2×C4semidirect
82. D4×Dic13Q8semidirect
98. C13×#106C2×C4semidirect
99. C13×#106C2×C4semidirect
100. C13×C4⋊C8C2×C4semidirect
284. #476Dic13semidirect
365. C4⋊Q8C2×Dic13semidirect
395. #106C2×Dic13semidirect
396. #106C2×Dic13semidirect
398. C4⋊C8C2×Dic13semidirect
502. C13#21623semidirect

Maximal subgroups

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

subgroupindex
#131175852
#131171972
#131157892
#131156062
#131154232
#131154162
#131150992
#131150852
#131148462
#131147362
#106×Dic132
#131146952
#131146632
#102×Dic132
C2×C13×#4762
#2162313