Finite Group Databasebeta

← #15920576

Subgroups — #15920576

Order 3328.

774 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118538C211yesmaximal, characteristic
2#13116394C211yesmaximal, characteristic, complemented
3#13116338C211yesmaximal, characteristic, complemented
4#13116338C211yesmaximal, characteristic, complemented
5#13116169C211yesmaximal, characteristic, complemented
6#13115788C211yesmaximal, characteristic, complemented
7#13115599C211yesmaximal, characteristic, complemented
8#13115414C211yesmaximal, characteristic, complemented
9#13115414C211yesmaximal, characteristic, complemented
10#13115028C211yesmaximal, characteristic
11#13115016C211yesmaximal, characteristic
12#13114926C211yesmaximal, characteristic
13#13114859C211yesmaximal, characteristic
14C2×#11718121C211yesmaximal, characteristic
15C13×#2345C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C23×#1055C2211yescharacteristic
19C2×#88132—21no—
20C2×#88123C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#387—21no—
24C13×#387—21no—
25C13×#380—21no—
26C13×#380C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4—21no—
30C4×C13×C22⋊C4C2211yescharacteristic
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×#88048C2211yescharacteristic
34C2×#88048C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37#11718611—21no—
38#11718596C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43#11718322—21no—
44#11718317—21no—
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
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C22×Dic26—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4Q814yescomplemented
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4D411yescharacteristic
74C2×C13×C22⋊C4D411yescharacteristic
75C2×C42×C13—21no—
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C22⋊Dic13—21no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—41no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×#6101—21no—
91C2×#6101—21no—
92C22×#1055—22no—
93C22×#1055—22no—
94C22×#1055—41no—
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88132—44no—
100#88123—22no—
101#88123—41no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95D411yescharacteristic
108C13×#95D411yescharacteristic
109#88071—21no—
110#88071—21no—
111#88071—21no—
112C22⋊#1055—22no—
113#88048—22no—
114#88048—22no—
115#88048—41no—
116#88048—41no—
117C4⋊#1055—22no—
118C4⋊#1055—41no—
119#25992—131nomaximal, Sylow
120C24×C13C2×D411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—24no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—81no—
131C22×C4×C13—81no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×Q812yes—
138C22×C4×C13#4112yes—
139C22×C4×C13C2411yescharacteristic
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—42no—
145C22×Dic13—42no—
146C22×Dic13—81no—
147C2×Dic26—42no—
148C2×Dic26—42no—
149C2×Dic26—81no—
150C13×C4⋊C4—24no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—81no—
158C13×C4⋊C4—81no—
159C13×C4⋊C4C2×Q812yes—
160C13×C4⋊C4C2×Q812yes—
161C13×C22⋊C4—22no—
162C13×C22⋊C4—42no—
163C13×C22⋊C4SD1614yes—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—81no—
169C42×C13—81no—
170C22⋊Dic13—42no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—42no—
179C4⋊Dic13—42no—
180C4⋊Dic13—42no—
181C4⋊Dic13—81no—
182C4⋊Dic13#4112yes—
183#6101—42no—
184#6101—42no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—44no—
197C2×#1055#4112yes—
198#2440—131no—
199#2345D1311yescharacteristic
200#2099—131no—
201#2088—131no—
202#2088—131no—
203#2058—131no—
204#1988—131no—
205#1948—131no—
206#1919—131no—
207#1919—131no—
208#1853—131no—
209#1850—131no—
210#1824—131no—
211#1807—131no—
212C2×#340—131no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13C22⋊Q812yes—
218C23×C13C2×SD1612yes—
219C23×C13#13712yes—
220C23×C13C22×D411yescharacteristic
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—84no—
250C2×C4×C13C22⋊Q812yes—
251C2×C4×C13C2×SD1612yes—
252C2×C4×C13C2×SD1612yes—
253C2×C4×C13C22×Q811yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13H(5,𝔽2)11yescharacteristic
258C2×C4×C132−1+411yescharacteristic
259C2×Dic13—22no—
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×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—84no—
272Dic26—84no—
273#1055—22no—
274#1055—41no—
275#1055—41no—
276#1055—41no—
277C23×C8—131no—
278C2×C4⋊Q8—131no—
279C2×C22⋊Q8—261no—
280C22×C4⋊C4—131no—
281C22×C4⋊C4C2×D1311yescharacteristic
282C2×#106—131no—
283C2×#106—131no—
284C2×#106—131no—
285C2×#106—131no—
286C2×C4⋊C8—131no—
287C2×C4⋊C8—131no—
288C2×C22⋊C8—131no—
289#398—261no—
290#395—261no—
291#389—131no—
292#389—131no—
293#389C2×D1311yescharacteristic
294#389C2×D1311yescharacteristic
295#387—21no—
296#387—21no—
297#385—261no—
298#384—131no—
299#380—21no—
300#380—131no—
301#380C2×D1311yescharacteristic
302C4×C4⋊C4C2×D1311yescharacteristic
303C4×C4⋊C4C2×D1311yescharacteristic
304C4×C22⋊C4—21no—
305C4×C22⋊C4C2×D1311yescharacteristic
306#340—131no—
307#340—131no—
308#340—131no—
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#336—131no—
319#336—131no—
320C22×C13—22no—
321C22×C13—22no—
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—22no—
326C22×C13#47514yes—
327C22×C13C2×C22⋊Q811yescharacteristic
328C22×C13#54611yescharacteristic
329C22×C13#54711yescharacteristic
330C22×C13C22×SD1611yescharacteristic
331C22×C13C2×#13711yescharacteristic
332C22×C13#57611yescharacteristic
333C22×C13#57711yescharacteristic
334C4×C13—22no—
335C4×C13—22no—
336C4×C13—22no—
337C4×C13—42no—
338C4×C13—42no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13—81no—
342C4×C13—81no—
343C4×C13#53311yescharacteristic
344C4×C13#54411yescharacteristic
345C4×C13#55111yescharacteristic
346C4×C13#55211yescharacteristic
347Dic13—42no—
348Dic13—81no—
349Dic13—81no—
350Dic13—81no—
351C22×Q8—261no—
352C23×C4—21no—
353C23×C4—261no—
354C23×C4C22×D1311yescharacteristic
355C22×C8—131no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8—262no—
360C22×C8—262no—
361C22×C8—521no—
362C4⋊Q8—262no—
363C4⋊Q8—521no—
364C22⋊Q8—524no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—262no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—521no—
381C2×C4⋊C4Dic2614yescomplemented
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—261no—
388C2×C22⋊C4C22⋊D1311yescharacteristic
389C2×C22⋊C4C22⋊D1311yescharacteristic
390C2×C42—21no—
391C2×C42—21no—
392C2×C42C22×D1311yescharacteristic
393C2×C42C22×D1311yescharacteristic
394#106—262no—
395#106—262no—
396#106—521no—
397#106—521no—
398C4⋊C8—262no—
399C4⋊C8—521no—
400C22⋊C8—262no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—261no—
407#95—261no—
408#95—261no—
409#95C22⋊D1311yescharacteristic
410#95C22⋊D1311yescharacteristic
411C2×C13—24no—
412C2×C13#243811yescharacteristic
413C2×C13C2×#47511yescharacteristic
414C2×C13#308111yescharacteristic
415C2×C13#329511yescharacteristic
416C2×C13#332011yescharacteristic
417C2×C13#333511yescharacteristic
418C2×C13#334611yescharacteristic
419C24C2×C22⋊D1311yescharacteristic
420C2×Q8—522no—
421C2×Q8—522no—
422C2×Q8—1041no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—81no—
433C22×C4—81no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—522no—
439C22×C4—522no—
440C22×C4—1041no—
441C22×C4C2×Dic2612yes—
442C22×C4#612712yes—
443C22×C4C2×C22⋊D1311yescharacteristic
444C22×C4C2×C22⋊D1311yescharacteristic
445C22×C4C2×C22⋊D1311yescharacteristic
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C2×C22⋊D1311yescharacteristic
448C22×C4C23×D1311yescharacteristic
449C2×C8—132no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—524no—
462C4⋊C4—24no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—132no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—522no—
480C4⋊C4—522no—
481C4⋊C4—522no—
482C4⋊C4—522no—
483C4⋊C4—522no—
484C4⋊C4—1041no—
485C4⋊C4C2×Dic2612yes—
486C4⋊C4C2×Dic2612yes—
487C22⋊C4—22no—
488C22⋊C4—42no—
489C22⋊C4—522no—
490C22⋊C4#610614yes—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—81no—
496C42—81no—
497C13#2599211yescharacteristic, complemented, Sylow
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23#8817812yes—
503C23C2×#610612yes—
504C23#8820512yes—
505C23C22×C22⋊D1311yescharacteristic
506Q8—1044no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
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—41no—
534C2×C4—41no—
535C2×C4—84no—
536C2×C4—262no—
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—1044no—
549C2×C4#8817812yes—
550C2×C4C2×#610612yes—
551C2×C4C2×#610612yes—
552C2×C4C22×Dic2611yescharacteristic
553C2×C4C2×#612711yescharacteristic
554C2×C4#41×D1311yescharacteristic
555C2×C4#41×D1311yescharacteristic
556C2×C4#8825611yescharacteristic
557C2×C4#8825711yescharacteristic
558C8—262no—
559C8—521no—
560C8—521no—
561C8—521no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22#1171868114yes—
569C22C2×#8817811yescharacteristic
570C22C22×#610611yescharacteristic
571C22C2×#8820511yescharacteristic
572C22#1171952911yescharacteristic
573C22#1171953411yescharacteristic
574C22#1171954011yescharacteristic
575C22#1171954111yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—42no—
580C4—42no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—522no—
586C4—1041no—
587C4—1041no—
588C4—1041no—
589C4#1171922211yescharacteristic
590C4#1171922411yescharacteristic
591C4#1171923211yescharacteristic
592C4#1171923611yescharacteristic
593C2—24no—
594C2#1311850611yescharacteristic
595C2C2×#1171868111yescharacteristic
596C2#1312466711yescharacteristic
597C2#1312665411yescharacteristic
598C2#1312700111yescharacteristic
599C2#1312718711yescharacteristic
600C2#1312732111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2345C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2345D13
hypocenterC13#25992
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #13116394C2semidirect
3. #13116338C2semidirect
4. #13116338C2semidirect
5. #13116169C2semidirect
6. #13115788C2semidirect
7. #13115599C2semidirect
8. #13115414C2semidirect
9. #13115414C2semidirect
67. C2×C13×C4⋊C4Q8semidirect
381. C2×C4⋊C4Dic26semidirect
497. C13#25992semidirect

Maximal subgroups

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

subgroupindex
#131185382
#131163942
#131163382
#131161692
#131157882
#131155992
#131154142
#131150282
#131150162
#131149262
#131148592
C2×#117181212
C13×#23452
#2599213