Finite Group Databasebeta

← #15870915

Subgroups — #15870915

Order 3328.

818 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718717C211yesmaximal, characteristic
2#13117577C211yesmaximal, characteristic, complemented
3#13115804C211yesmaximal, characteristic, complemented
4#13115653C211yesmaximal, characteristic
5#13115536C211yesmaximal, characteristic
6#13115529C211yesmaximal, characteristic, complemented
7#13115522C211yesmaximal, characteristic
8#13115515C211yesmaximal, characteristic, complemented
9#13114963C211yesmaximal, characteristic, complemented
10#13114666C211yesmaximal, characteristic, complemented
11#13114661C211yesmaximal, characteristic
12C4×#88075C211yesmaximal, characteristic, complemented
13C4×#88072C211yesmaximal, characteristic
14#13114523C211yesmaximal, characteristic, complemented
15C13×#2326C211yesmaximal, characteristic
16C2×C13×#124C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×#88124C2211yescharacteristic
20C13×#391C2211yescharacteristic
21C13×#390C2211yescharacteristic
22C13×#388—21no—
23C13×#388—21no—
24C13×#385—21no—
25C13×#385—21no—
26C13×#384C2211yescharacteristic
27C13×#376C2211yescharacteristic
28C2×#88075C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36#11718717C418yescomplemented
37#11718596C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718589C2211yescharacteristic
42C2×#88043C2211yescharacteristic
43C2×#88043C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45C2×C4×#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47C2×C4×#1055C2211yescharacteristic
48#11718316—21no—
49#11718316—21no—
50#11718308—21no—
51#11718308—21no—
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×Q8×C13C2311yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C13×#124—22no—
64C13×#124C2×C414yes—
65C4×Q8×C13—22no—
66C4×Q8×C13—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C42×C13—21no—
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88124—22no—
100#88124C2×C414yescomplemented
101C13×#95—21no—
102C13×#95—21no—
103C13×#95D411yescharacteristic
104C13×#95D411yescharacteristic
105C13×#95D411yescharacteristic
106C13×#95D411yescharacteristic
107#88075—22no—
108#88075—22no—
109#88075C2×C414yescomplemented
110#88075C2×C414yescomplemented
111#88072—22no—
112#88072—22no—
113#88072C2×C414yes—
114#88072C2×C414yes—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88043—22no—
120#88043—22no—
121#88043—22no—
122C4×#1055—22no—
123C4×#1055—22no—
124C4×#1055C2×C414yescomplemented
125#21643—131nomaximal, Sylow
126C24×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13C22×C412yes—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13C22×C412yes—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—42no—
143C22×C4×C13—81no—
144C22×C4×C13—81no—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2411yescharacteristic
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4—81no—
162C13×C4⋊C4—81no—
163C13×C22⋊C4—24no—
164C13×C22⋊C4—24no—
165C13×C22⋊C4—42no—
166C13×C22⋊C4—81no—
167C13×C22⋊C4—81no—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—42no—
171C42×C13C22×C412yes—
172C42×C13#4112yes—
173C42×C13#4112yes—
174C42×C13#4112yes—
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⋊Dic13C22×C412yes—
184C4⋊Dic13C22×C412yes—
185#6101—24no—
186#6101—24no—
187#6101—81no—
188#6101—81no—
189C4×Dic13—81no—
190C4×Dic13—81no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C22×C412yes—
200C2×#1055C22×C412yes—
201C2×#1055#4112yes—
202C2×#1055#4112yes—
203C2×#488—131no—
204#2330—131no—
205#2326D1311yescharacteristic
206#1992—131no—
207#1959—131no—
208#1936—131no—
209#1935—131no—
210#1934—131no—
211#1933—131no—
212#1834—131no—
213#1763—131no—
214#1762—131no—
215C4×#103—131no—
216C4×#102—131no—
217#1726—131no—
218C23×C13—22no—
219C23×C13—41no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13C22×D411yescharacteristic
226Q8×C13—22no—
227Q8×C13—22no—
228Q8×C13—41no—
229Q8×C13—41no—
230D4×C13—22no—
231D4×C13—22no—
232D4×C13—41no—
233D4×C13—41no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—22no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—84no—
258C2×C4×C13C4×D412yes—
259C2×C4×C13C4×D412yes—
260C2×C4×C13#12412yes—
261C2×C4×C13#12412yes—
262C2×C4×C13C23×C411yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280#1055—22no—
281#1055—22no—
282#1055—22no—
283#1055—22no—
284C2×#125—131no—
285C2×#124C2×D1311yescharacteristic
286C2×C4×Q8C2×D1311yescharacteristic
287C2×C4×D4C2×D1311yescharacteristic
288#488—138no—
289C2×#103—131no—
290C2×#103—131no—
291C2×#103—131no—
292C2×#103—131no—
293C2×#102—131no—
294C2×#102—131no—
295C2×#102—131no—
296C2×#102—131no—
297C2×#97—131no—
298C2×#97—131no—
299C2×#97—131no—
300C2×C4×C8—131no—
301C2×C4×C8—131no—
302C2×C4×C8—131no—
303#391C2×D1311yescharacteristic
304#390C2×D1311yescharacteristic
305#389—131no—
306#389—131no—
307#389—261no—
308#389—261no—
309#388—21no—
310#388—21no—
311#387—261no—
312#387—261no—
313#385—21no—
314#385—21no—
315#384—131no—
316#384C2×D1311yescharacteristic
317C4×C4⋊C4—131no—
318C4×C4⋊C4—131no—
319#376C2×D1311yescharacteristic
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—81no—
332C22×C13—81no—
333C22×C13—81no—
334C22×C13—81no—
335C22×C13C2×C4×D411yescharacteristic
336C22×C13C2×#12411yescharacteristic
337C22×C13#53211yescharacteristic
338C22×C13#57611yescharacteristic
339C22×C13#57711yescharacteristic
340C22×C13#57711yescharacteristic
341C22×C13#57811yescharacteristic
342C4×C13—22no—
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13—42no—
349C4×C13—81no—
350C4×C13—81no—
351C4×C13C4×#4111yescharacteristic
352C4×C13C4×#4111yescharacteristic
353C4×C13#52911yescharacteristic
354C4×C13#52911yescharacteristic
355Dic13—42no—
356Dic13—42no—
357Dic13—81no—
358Dic13—81no—
359C22×Q8C22×D1311yescharacteristic
360C22×D4C22×D1311yescharacteristic
361C23×C4—21no—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8—131no—
365C22×C8—131no—
366#125—134no—
367#125—262no—
368#124—22no—
369#124C4×D1314yes—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×D4—22no—
373C4×D4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395C2×C42—261no—
396C2×C42—261no—
397C2×C42C22×D1311yescharacteristic
398C2×C42C22×D1311yescharacteristic
399C2×C42C22×D1311yescharacteristic
400#103—134no—
401#103—134no—
402#103—262no—
403#103—262no—
404#102—134no—
405#102—134no—
406#102—262no—
407#102—262no—
408#97—262no—
409#97—262no—
410#97—262no—
411C4×C8—134no—
412C4×C8—262no—
413C4×C8—262no—
414#95—21no—
415#95—21no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95C22⋊D1311yescharacteristic
421#95C22⋊D1311yescharacteristic
422#95C22⋊D1311yescharacteristic
423#95C22⋊D1311yescharacteristic
424C2×C13—82no—
425C2×C13C4×#12411yescharacteristic
426C2×C13#295111yescharacteristic
427C2×C13#295211yescharacteristic
428C2×C13#313611yescharacteristic
429C2×C13#313711yescharacteristic
430C2×C13#317811yescharacteristic
431C2×C13#317911yescharacteristic
432C24—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×C4×D1312yes—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4C2×C4×D1312yes—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—42no—
449C22×C4—81no—
450C22×C4—81no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4C2×C22⋊D1311yescharacteristic
456C22×C4C2×C22⋊D1311yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C23×D1311yescharacteristic
462C2×C8—132no—
463C2×C8—132no—
464C2×C8—132no—
465C2×C8—132no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—42no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—132no—
482C4⋊C4—132no—
483C4⋊C4—264no—
484C4⋊C4—264no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—1041no—
492C4⋊C4—1041no—
493C4⋊C4—1041no—
494C4⋊C4—1041no—
495C22⋊C4—24no—
496C22⋊C4—24no—
497C22⋊C4—42no—
498C22⋊C4—81no—
499C22⋊C4—81no—
500C42—21no—
501C42—21no—
502C42—42no—
503C42—1041no—
504C42—1041no—
505C42C2×C4×D1312yes—
506C42#612712yes—
507C42#612912yes—
508C42#612912yes—
509C13#2164311yescharacteristic, complemented, Sylow
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23C22×C22⋊D1311yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—84no—
550C2×C4—262no—
551C2×C4—262no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4C4×C22⋊D1312yes—
563C2×C4C4×C22⋊D1312yes—
564C2×C4#8819012yes—
565C2×C4#8819012yes—
566C2×C4C22×C4×D1311yescharacteristic
567C2×C4C2×#612711yescharacteristic
568C2×C4C2×#612911yescharacteristic
569C2×C4C2×#612911yescharacteristic
570C2×C4#41×D1311yescharacteristic
571C2×C4#41×D1311yescharacteristic
572C8—262no—
573C8—262no—
574C8—262no—
575C8—262no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22C2×C4×C22⋊D1311yescharacteristic
584C22C2×#8819011yescharacteristic
585C22#1171953711yescharacteristic
586C22#1171954011yescharacteristic
587C22#1171954111yescharacteristic
588C22#1171954211yescharacteristic
589C22#1171954311yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—522no—
600C4—522no—
601C4—1041no—
602C4—1041no—
603C4C4×#612911yescharacteristic
604C4C4×#612911yescharacteristic
605C4#1171926211yescharacteristic
606C4#1171926211yescharacteristic
607C2—82no—
608C2C4×#8819011yescharacteristic
609C2#1312370911yescharacteristic
610C2#1312371711yescharacteristic
611C2#1312519011yescharacteristic
612C2#1312520111yescharacteristic
613C2#1312549811yescharacteristic
614C2#1312551311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2326C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#2326D13
hypocenterC13#21643
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #2326

Complements

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

NH ≅ G/Ntype
2. #13117577C2semidirect
3. #13115804C2semidirect
6. #13115529C2semidirect
8. #13115515C2semidirect
9. #13114963C2semidirect
10. #13114666C2semidirect
12. C4×#88075C2semidirect
14. #13114523C2semidirect
36. #11718717C4semidirect
100. #88124C2×C4semidirect
109. #88075C2×C4semidirect
110. #88075C2×C4semidirect
124. C4×#1055C2×C4semidirect
509. C13#21643semidirect

Maximal subgroups

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

subgroupindex
C2×#117187172
#131175772
#131158042
#131156532
#131155362
#131155292
#131155222
#131155152
#131149632
#131146662
#131146612
C4×#880752
C4×#880722
#131145232
C13×#23262
#2164313