Finite Group Databasebeta

← #15865110

Subgroups — #15865110

Order 3328.

898 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718542C211yesmaximal, characteristic
2#13117458C211yesmaximal, characteristic
3#13117190C211yesmaximal, characteristic
4#13115431C211yesmaximal, characteristic, complemented
5#13115421C211yesmaximal, characteristic, complemented
6#13115420C211yesmaximal, characteristic, complemented
7#13115415C211yesmaximal, characteristic, complemented
8#13115412C211yesmaximal, characteristic, complemented
9#13115409C211yesmaximal, characteristic, complemented
10#13115404C211yesmaximal, characteristic, complemented
11#13114554C211yesmaximal, characteristic
12#13114551C211yesmaximal, characteristic
13D13×#340C211yesmaximal, characteristic
14#13114531C211yesmaximal, characteristic
15C13×#1921C211yesmaximal, characteristic, complemented
16C22×#6094C2211yescharacteristic
17C22×C8×D13C2211yescharacteristic
18C2×#88146C2211yescharacteristic
19C2×#88146C2211yescharacteristic
20C2×C4⋊C4×D13C2211yescharacteristic
21C2×C4⋊C4×D13C2211yescharacteristic
22C2×#88126C2211yescharacteristic
23C2×C13×#107C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C4×C13×C4⋊C4C2211yescharacteristic
26C2×#88057C2211yescharacteristic
27#11718650—21no—
28#11718646C2211yescharacteristic
29#11718637—21no—
30C4⋊C4×Dic13C2211yescharacteristic
31C4⋊C4×Dic13C2211yescharacteristic
32#11718634C2211yescharacteristic
33C2×#88048C2211yescharacteristic
34C2×#88047C2211yescharacteristic
35C4×#6103—21no—
36C4×C4⋊Dic13C2211yescharacteristic
37C4×#6101—21no—
38#11718589C2211yescharacteristic
39#11718542C418yescomplemented
40#11718329—21no—
41#11718327—21no—
42#11718311—21no—
43#11718310—21no—
44C13×#340C2211yescharacteristic
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47C13×#336C2211yescharacteristic
48#11718143C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×C4×D13—21no—
61C22×C4×D13—21no—
62C22×C4×D13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C42×C13—21no—
71C2×C42×C13C2311yescharacteristic
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103D411yescharacteristic
75C2×#6103D411yescharacteristic
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101D411yescharacteristic
86C2×#6101D411yescharacteristic
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C2×#6094—22no—
96C2×#6094—22no—
97C2×#6094C2×C414yes—
98C2×C8×D13—22no—
99C2×C8×D13—22no—
100C2×C8×D13—22no—
101#88146—22no—
102#88146—22no—
103#88146C2×C414yes—
104#88146Q814yes—
105C4⋊C4×D13—22no—
106C4⋊C4×D13—22no—
107C4⋊C4×D13—22no—
108C4⋊C4×D13C2×C414yes—
109#88126—22no—
110#88126—22no—
111C13×#107C2×C414yescomplemented
112C13×#95—21no—
113C13×#95—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88057C2×C414yescomplemented
121#88048C2×C414yescomplemented
122#88047C2×C414yescomplemented
123#21035—131nomaximal, Sylow
124C23×D13C2×D411yescharacteristic
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2411yescharacteristic
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13C2×D411yescharacteristic
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C2×C4×D13—24no—
140C2×C4×D13—42no—
141C2×C4×D13—81no—
142C2×C4×D13—81no—
143C2×C4×D13—81no—
144C2×C4×D13—81no—
145C2×C4×D13C22×C412yes—
146C2×C4×D13C2×Q812yes—
147C2×C4×D13#4112yes—
148C2×C4×D13#4112yes—
149C2×C4×D13#4112yes—
150C2×C4×D13#4112yes—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
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—81no—
163C13×C4⋊C4C22×C412yes—
164C13×C4⋊C4C22×C412yes—
165C13×C4⋊C4C2×Q812yes—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—81no—
169#6103—24no—
170#6103—24no—
171#6103—22no—
172#6103—22no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—81no—
179C4⋊Dic13C22×C412yes—
180C4⋊Dic13C22×C412yes—
181C4⋊Dic13C2×Q812yes—
182#6101—24no—
183#6101—22no—
184#6101—22no—
185#6101—42no—
186#6101—81no—
187#6101—81no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C4×Dic13—24no—
191C4×Dic13—24no—
192C4×Dic13—81no—
193C4×Dic13—81no—
194C4×Dic13—81no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055C22×C412yes—
201#6094—28no—
202C8×D13—44no—
203C2×#428—131no—
204#2317—131no—
205#2274—131no—
206#1921—131no—
207#1921D1311yescharacteristic, complemented
208#1920—131no—
209#1920—131no—
210#1919—131no—
211#1919—131no—
212#1918—131no—
213#1918—131no—
214#1736—131no—
215#1735—131no—
216C2×#340—131no—
217#1729—131no—
218C23×C13C22×D411yescharacteristic
219C22×D13—21no—
220C22×D13—21no—
221C22×D13—21no—
222C22×D13—21no—
223C22×D13C4×D412yes—
224C22×D13C22⋊Q812yes—
225C22×D13#12312yes—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
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—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—41no—
243C2×C4×C13—41no—
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—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
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—
268C2×Dic13C4×D412yes—
269C2×Dic13C22⋊Q812yes—
270C2×Dic13#12312yes—
271C4×D13—84no—
272C4×D13—84no—
273C4×D13#11714yes—
274C4×D13C4×Q814yes—
275C4×D13#12514yes—
276C4×D13#12614yes—
277C8×C13—22no—
278C8×C13—41no—
279#1055—22no—
280#1055—41no—
281C22×M16—131no—
282C23×C8—131no—
283C2×#117—131no—
284C2×#117—131no—
285C2×#117—131no—
286C22×C4⋊C4—131no—
287C22×C4⋊C4—131no—
288#428—138no—
289C2×#107—131no—
290C2×#107C2×D1311yescharacteristic
291C2×#106—131no—
292C2×#106—131no—
293#389—131no—
294#389—131no—
295#389—131no—
296#389C2×D1311yescharacteristic
297#385—261no—
298#385—261no—
299#384—261no—
300#382—261no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4—131no—
303C4×C4⋊C4—131no—
304C4×C4⋊C4—261no—
305C4×C4⋊C4—261no—
306C4×C4⋊C4C2×D1311yescharacteristic
307C4×C22⋊C4—261no—
308C4×C22⋊C4—261no—
309#340—131no—
310#340—131no—
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340C2×D1311yescharacteristic
319#340C2×D1311yescharacteristic
320#340C2×D1311yescharacteristic
321#336—131no—
322#336—131no—
323#336—131no—
324#336C2×D1311yescharacteristic
325C22×C13C2×C4×D411yescharacteristic
326C22×C13C2×C22⋊Q811yescharacteristic
327C22×C13C2×#12311yescharacteristic
328C22×C13#57611yescharacteristic
329C22×C13#57711yescharacteristic
330C22×C13#57711yescharacteristic
331C22×C13#57811yescharacteristic
332C2×D13—22no—
333C2×D13—22no—
334C2×D13—22no—
335C2×D13—22no—
336C2×D13—22no—
337C2×D13—22no—
338C2×D13#38714yes—
339C4×C13—42no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13—42no—
343C4×C13—42no—
344C4×C13—81no—
345C4×C13C2×#11711yescharacteristic
346C4×C13C2×C4×Q811yescharacteristic
347C4×C13C2×#12511yescharacteristic
348C4×C13C2×#12611yescharacteristic
349Dic13—42no—
350Dic13—41no—
351Dic13—41no—
352Dic13—42no—
353Dic13—42no—
354Dic13—81no—
355Dic13#38714yes—
356C23×C4—131no—
357C23×C4—261no—
358C23×C4—261no—
359C2×M16—134no—
360C2×M16—262no—
361C2×M16—262no—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8—262no—
365C22×C8—262no—
366C22×C8—262no—
367C22×C8C22×D1311yescharacteristic
368C22×C8C22×D1311yescharacteristic
369#117—134no—
370#117—134no—
371#117—262no—
372#117—262no—
373#117—262no—
374#117—262no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—134no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—262no—
384C2×C4⋊C4—262no—
385C2×C4⋊C4—262no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4C22×D1311yescharacteristic
392C2×C4⋊C4C22×D1311yescharacteristic
393C2×C4⋊C4C22×D1311yescharacteristic
394C2×C4⋊C4C22×D1311yescharacteristic
395C2×C22⋊C4—131no—
396C2×C22⋊C4—131no—
397C2×C22⋊C4—261no—
398C2×C22⋊C4—261no—
399C2×C42—21no—
400C2×C42—131no—
401C2×C42—261no—
402C2×C42—261no—
403C2×C42—261no—
404C2×C42—261no—
405C2×C42—261no—
406C2×C42C22×D1311yescharacteristic
407#107—134no—
408#107C4×D1314yescomplemented
409#106—134no—
410#106—134no—
411#95—21no—
412#95—21no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419C2×C13C2×#38711yescharacteristic
420C2×C13#294611yescharacteristic
421C2×C13#294711yescharacteristic
422C2×C13#308311yescharacteristic
423C2×C13#308411yescharacteristic
424C2×C13#309611yescharacteristic
425C2×C13#309711yescharacteristic
426D13—24no—
427C24—131no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—131no—
433C22×C4—132no—
434C22×C4—132no—
435C22×C4—132no—
436C22×C4—132no—
437C22×C4—132no—
438C22×C4—132no—
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—264no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—522no—
447C22×C4—1041no—
448C22×C4—1041no—
449C22×C4—1041no—
450C22×C4—1041no—
451C22×C4D4×D1311yescharacteristic
452C22×C4D4×D1311yescharacteristic
453C22×C4C23×D1311yescharacteristic
454M16—268no—
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×C8—524no—
467C2×C8C2×C4×D1312yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—81no—
474C4⋊C4—132no—
475C4⋊C4—132no—
476C4⋊C4—132no—
477C4⋊C4—264no—
478C4⋊C4—262no—
479C4⋊C4—262no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—522no—
486C4⋊C4—1041no—
487C4⋊C4—1041no—
488C4⋊C4—1041no—
489C4⋊C4C2×C4×D1312yes—
490C4⋊C4C2×C4×D1312yes—
491C4⋊C4Q8×D1312yes—
492C22⋊C4—262no—
493C22⋊C4—262no—
494C22⋊C4—264no—
495C22⋊C4—264no—
496C42—21no—
497C42—21no—
498C42—81no—
499C42—264no—
500C42—264no—
501C42—261no—
502C42—261no—
503C42—1041no—
504C42—1041no—
505C42—1041no—
506C13#2103511yescharacteristic, complemented, Sylow
507C23—132no—
508C23—132no—
509C23—132no—
510C23—261no—
511C23—261no—
512C23—261no—
513C23—261no—
514C23C2×D4×D1311yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—132no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—134no—
537C2×C4—134no—
538C2×C4—134no—
539C2×C4—134no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—1044no—
559C2×C4—1044no—
560C2×C4C22×C4×D1311yescharacteristic
561C2×C4C2×Q8×D1311yescharacteristic
562C2×C4#41×D1311yescharacteristic
563C2×C4#41×D1311yescharacteristic
564C2×C4#41×D1311yescharacteristic
565C2×C4#41×D1311yescharacteristic
566C8—22no—
567C8—41no—
568C8—262no—
569C8—521no—
570C22—134no—
571C22—262no—
572C22—262no—
573C22—262no—
574C22—262no—
575C22—262no—
576C22—262no—
577C22C4×D4×D1311yescharacteristic
578C22D13×C22⋊Q811yescharacteristic
579C22D13×#12311yescharacteristic
580C22#1171947111yescharacteristic
581C22#1171947511yescharacteristic
582C22#1171947911yescharacteristic
583C22#1171948011yescharacteristic
584C4—42no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—134no—
591C4—522no—
592C4—522no—
593C4—522no—
594C4—521no—
595C4—521no—
596C4—1041no—
597C4D13×#11711yescharacteristic
598C4C4×Q8×D1311yescharacteristic
599C4D13×#12511yescharacteristic
600C4D13×#12611yescharacteristic
601C2—264no—
602C2D13×#38711yescharacteristic
603C2#1312366511yescharacteristic
604C2#1312367411yescharacteristic
605C2#1312468411yescharacteristic
606C2#1312469911yescharacteristic
607C2#1312478911yescharacteristic
608C2#1312480411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1921C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1921D13
hypocenterC13#21035
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
4. #13115431C2semidirect
5. #13115421C2semidirect
6. #13115420C2semidirect
7. #13115415C2semidirect
8. #13115412C2semidirect
9. #13115409C2semidirect
10. #13115404C2semidirect
15. C13×#1921C2semidirect
39. #11718542C4semidirect
111. C13×#107C2×C4semidirect
120. #88057C2×C4semidirect
121. #88048C2×C4semidirect
122. #88047C2×C4semidirect
207. #1921D13semidirect
408. #107C4×D13semidirect
506. C13#21035semidirect

Maximal subgroups

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

subgroupindex
C2×#117185422
#131174582
#131171902
#131154312
#131154212
#131154202
#131154152
#131154122
#131154092
#131154042
#131145542
#131145512
D13×#3402
#131145312
C13×#19212
#2103513