Finite Group Databasebeta

← #15907253

Subgroups — #15907253

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119144C211yesmaximal, characteristic
2#13116393C211yesmaximal, characteristic, complemented
3#13116308C211yesmaximal, characteristic, complemented
4#13116262C211yesmaximal, characteristic, complemented
5#13116262C211yesmaximal, characteristic, complemented
6#13115407C211yesmaximal, characteristic, complemented
7#13115407C211yesmaximal, characteristic, complemented
8#13115129C211yesmaximal, characteristic
9#13115024C211yesmaximal, characteristic, complemented
10#13115024C211yesmaximal, characteristic, complemented
11#13114922C211yesmaximal, characteristic, complemented
12#13114920C211yesmaximal, characteristic, complemented
13#13114863C211yesmaximal, characteristic, complemented
14C2×#11718121C211yesmaximal, characteristic, complemented
15D4×C13×C4⋊C4C211yesmaximal, characteristic
16C2×C4×D4×C13—21no—
17C2×C4×D4×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C2×#88189—21no—
21C22×C4⋊Dic13C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C13×#389—21no—
24C13×#385—21no—
25C13×#385—21no—
26C13×#384C2211yescharacteristic
27C13×#380C2211yescharacteristic
28C13×#380C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30#11718873C2211yescharacteristic
31#11718873C2211yescharacteristic
32#11718873C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36#11718644—21no—
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718614—21no—
42#11718604—21no—
43#11718589C2211yescharacteristic
44#11718589C2211yescharacteristic
45#11718121C2211yescharacteristic
46#11718121C2211yescharacteristic
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D4×C13D411yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13—21no—
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13—21no—
65C4×D4×C13—22no—
66C4×D4×C13—22no—
67C4×D4×C13—44no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4—41no—
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89C2×C22⋊Dic13—21no—
90#88189—44no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×#6101—21no—
99C2×#6101—21no—
100C22×#1055—22no—
101C22×#1055—22no—
102C22×#1055—41no—
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115C22⋊#1055—22no—
116C22⋊#1055—22no—
117C22⋊#1055—41no—
118#88047—22no—
119#88047—22no—
120#88047—41no—
121#88047—41no—
122#24933—131nomaximal, Sylow
123C24×C13C2×D411yescharacteristic
124C24×C13C2×D411yescharacteristic
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C2×D4×C13D814yes—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—81no—
147C22×C4×C13—81no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×C4×C13C2411yescharacteristic
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—42no—
160C22×Dic13—42no—
161C22×Dic13—42no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—42no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4—42no—
173C13×C4⋊C4—81no—
174C13×C4⋊C4#4112yes—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—42no—
178C13×C22⋊C4—42no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—42no—
182C22⋊Dic13—42no—
183C22⋊Dic13—42no—
184C22⋊Dic13—42no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—42no—
194#6101—42no—
195#6101—42no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—44no—
208C2×#1055#4112yes—
209#2486—131no—
210D4×C4⋊C4D1311yescharacteristic
211#2099—131no—
212#2083—131no—
213#2075—131no—
214#2075—131no—
215#1918—131no—
216#1918—131no—
217#1869—131no—
218#1852—131no—
219#1852—131no—
220#1823—131no—
221#1823—131no—
222#1808—131no—
223C2×#340—131no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13#12312yes—
235C23×C13C2×D812yes—
236C23×C13C2×D812yes—
237C23×C13#13712yes—
238C23×C13C22×D411yescharacteristic
239D4×C13—28no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—22no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—84no—
271C2×C4×C13—84no—
272C2×C4×C13#12312yes—
273C2×C4×C13C2×D812yes—
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13H(5,𝔽2)11yescharacteristic
279C2×C4×C132−1+411yescharacteristic
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—84no—
293#1055—22no—
294#1055—41no—
295#1055—41no—
296#1055—41no—
297C23×C8—131no—
298C2×#123—261no—
299C2×C4×D4—21no—
300C2×C4×D4C2×D1311yescharacteristic
301C22×C4⋊C4—131no—
302C22×C4⋊C4C2×D1311yescharacteristic
303C22×C4⋊C4C2×D1311yescharacteristic
304C2×#107—131no—
305C2×#107—131no—
306C2×#107—131no—
307C2×#107—131no—
308C2×C22⋊C8—131no—
309C2×C22⋊C8—131no—
310C2×C22⋊C8—131no—
311#398—261no—
312#397—261no—
313#389—21no—
314#389—131no—
315#389—131no—
316#385—21no—
317#385—21no—
318#384C2×D1311yescharacteristic
319#381—261no—
320#380—131no—
321#380—131no—
322#380—131no—
323#380C2×D1311yescharacteristic
324#380C2×D1311yescharacteristic
325C4×C4⋊C4C2×D1311yescharacteristic
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#336—131no—
339#336—131no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—22no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13#48014yes—
354C22×C13C2×#12311yescharacteristic
355C22×C13#54611yescharacteristic
356C22×C13#54711yescharacteristic
357C22×C13C22×D811yescharacteristic
358C22×C13C2×#13711yescharacteristic
359C22×C13#57711yescharacteristic
360C22×C13#57811yescharacteristic
361C4×C13—22no—
362C4×C13—22no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13—42no—
366C4×C13—81no—
367C4×C13—81no—
368C4×C13—81no—
369C4×C13#52911yescharacteristic
370C4×C13#53911yescharacteristic
371C4×C13#55111yescharacteristic
372C4×C13#55211yescharacteristic
373Dic13—81no—
374Dic13—81no—
375Dic13—81no—
376Dic13—81no—
377C22×D4C22⋊D1311yescharacteristic
378C23×C4—21no—
379C23×C4—21no—
380C23×C4—261no—
381C23×C4C22×D1311yescharacteristic
382C23×C4C22×D1311yescharacteristic
383C22×C8—131no—
384C22×C8—131no—
385C22×C8—131no—
386C22×C8—131no—
387C22×C8—262no—
388C22×C8—262no—
389C22×C8—521no—
390#123—524no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—44no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—41no—
402C2×C4⋊C4—131no—
403C2×C4⋊C4—131no—
404C2×C4⋊C4—131no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—262no—
407C2×C4⋊C4—262no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4C22⋊D1311yescharacteristic
412C2×C4⋊C4C22×D1311yescharacteristic
413C2×C4⋊C4C22×D1311yescharacteristic
414C2×C4⋊C4C22×D1311yescharacteristic
415C2×C4⋊C4C22×D1311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—261no—
419C2×C22⋊C4—261no—
420C2×C22⋊C4—261no—
421C2×C22⋊C4C22⋊D1311yescharacteristic
422C2×C22⋊C4C22⋊D1311yescharacteristic
423C2×C42—21no—
424C2×C42C22×D1311yescharacteristic
425#107—262no—
426#107—262no—
427#107—521no—
428#107—521no—
429C22⋊C8—262no—
430C22⋊C8—262no—
431C22⋊C8—521no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—261no—
436#95—261no—
437#95—261no—
438#95—261no—
439#95—261no—
440C2×C13—24no—
441C2×C13—42no—
442C2×C13#241911yescharacteristic
443C2×C13C2×#48011yescharacteristic
444C2×C13#309711yescharacteristic
445C2×C13#329411yescharacteristic
446C2×C13#331211yescharacteristic
447C2×C13#333411yescharacteristic
448C2×C13#334411yescharacteristic
449C24C2×C22⋊D1311yescharacteristic
450C24C2×C22⋊D1311yescharacteristic
451C2×D4—22no—
452C2×D4—22no—
453C2×D4#610414yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—522no—
479C22×C4—522no—
480C22×C4—522no—
481C22×C4#612712yes—
482C22×C4#612712yes—
483C22×C4C2×C22⋊D1311yescharacteristic
484C22×C4C2×C22⋊D1311yescharacteristic
485C22×C4C2×C22⋊D1311yescharacteristic
486C22×C4C2×C22⋊D1311yescharacteristic
487C22×C4C23×D1311yescharacteristic
488C2×C8—132no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—524no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—81no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—261no—
518C4⋊C4—261no—
519C4⋊C4—261no—
520C4⋊C4—261no—
521C4⋊C4—522no—
522C4⋊C4—522no—
523C4⋊C4—522no—
524C4⋊C4#612912yes—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—522no—
530C22⋊C4—522no—
531C22⋊C4—522no—
532C42—21no—
533C42—21no—
534C42—42no—
535C13#2493311yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23#8818312yes—
547C23C2×#610412yes—
548C23C2×#610412yes—
549C23#8819612yes—
550C23C22×C22⋊D1311yescharacteristic
551D4—28no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—84no—
583C2×C4—84no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—1044no—
597C2×C4#8818312yes—
598C2×C4C2×#610412yes—
599C2×C4C2×#612711yescharacteristic
600C2×C4C2×#612711yescharacteristic
601C2×C4C2×#612911yescharacteristic
602C2×C4#8825111yescharacteristic
603C2×C4#41×D1311yescharacteristic
604C2×C4#8825711yescharacteristic
605C8—262no—
606C8—521no—
607C8—521no—
608C8—521no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22#1171862814yes—
623C22C2×#8818311yescharacteristic
624C22C22×#610411yescharacteristic
625C22#1171951111yescharacteristic
626C22C2×#8819611yescharacteristic
627C22#1171952911yescharacteristic
628C22#1171954111yescharacteristic
629C22#1171954311yescharacteristic
630C4—22no—
631C4—22no—
632C4—41no—
633C4—41no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4—81no—
638C4—1041no—
639C4—1041no—
640C4—1041no—
641C4—1041no—
642C4#1171924311yescharacteristic
643C4#1171924611yescharacteristic
644C4#1171926111yescharacteristic
645C4#1171926911yescharacteristic
646C2—24no—
647C2—42no—
648C2#1311830711yescharacteristic
649C2C2×#1171862811yescharacteristic
650C2#1312480511yescharacteristic
651C2#1312664911yescharacteristic
652C2#1312688711yescharacteristic
653C2#1312717911yescharacteristic
654C2#1312728511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterD4×C4⋊C4D13
hypocenterC13#24933
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13116393C2semidirect
3. #13116308C2semidirect
4. #13116262C2semidirect
5. #13116262C2semidirect
6. #13115407C2semidirect
7. #13115407C2semidirect
9. #13115024C2semidirect
10. #13115024C2semidirect
11. #13114922C2semidirect
12. #13114920C2semidirect
13. #13114863C2semidirect
14. C2×#11718121C2semidirect
535. C13#24933semidirect

Maximal subgroups

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

subgroupindex
#131191442
#131163932
#131163082
#131162622
#131154072
#131151292
#131150242
#131149222
#131149202
#131148632
C2×#117181212
D4×C13×C4⋊C42
#2493313