Finite Group Databasebeta

← #15925264

Subgroups — #15925264

Order 3328.

718 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120324C211yesmaximal, characteristic
2#13116380C211yesmaximal, characteristic, complemented
3#13116370C211yesmaximal, characteristic
4#13116245C211yesmaximal, characteristic, complemented
5#13116240C211yesmaximal, characteristic
6#13115777C211yesmaximal, characteristic, complemented
7#13115768C211yesmaximal, characteristic
8#13115650C211yesmaximal, characteristic
9#13115597C211yesmaximal, characteristic, complemented
10#13115477C211yesmaximal, characteristic, complemented
11#13115470C211yesmaximal, characteristic, complemented
12#13115463C211yesmaximal, characteristic
13#13115456C211yesmaximal, characteristic
14#13114734C211yesmaximal, characteristic, complemented
15Q8×C13×C4⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13—21no—
17C2×C4×Q8×C13C2211yescharacteristic
18C2×#88129C2211yescharacteristic
19C13×#389—21no—
20C13×#389—21no—
21C13×#389—21no—
22C13×#384C2211yescharacteristic
23C13×#384C2211yescharacteristic
24C13×#384C2211yescharacteristic
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28#11718892—21no—
29#11718654—21no—
30#11718651—21no—
31#11718651—21no—
32C2×#88050C2211yescharacteristic
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718600C2211yescharacteristic
45#11718600C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47#11718590C2211yescharacteristic
48#11718590C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13D411yescharacteristic
60C22×D52C2311yescharacteristic
61C22×Dic26C2311yescharacteristic
62C4×Q8×C13—22no—
63C4×Q8×C13—22no—
64C4×Q8×C13—44no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4D411yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C42×C13—21no—
79C2×C42×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×#6103—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4×Dic13—21no—
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97#88129—22no—
98#88129—22no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88050—22no—
108#88050—22no—
109#88050—41no—
110#88050—41no—
111#88049—22no—
112#88049—22no—
113#88049—41no—
114#88049—41no—
115#88048—22no—
116#88048—41no—
117#88048—41no—
118#88047—22no—
119C4⋊#1055—22no—
120#88043—22no—
121#26328—131nomaximal, Sylow
122C23×D13—21no—
123C2×Q8×C13—22no—
124C2×Q8×C13—22no—
125C2×Q8×C13—22no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2411yescharacteristic
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×Dic26—21no—
147C2×Dic26—21no—
148C2×Dic26—21no—
149C2×Dic26—21no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4—42no—
165C13×C4⋊C4—81no—
166C13×C4⋊C4—81no—
167C13×C4⋊C4—81no—
168C13×C4⋊C4#4112yes—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—42no—
174C42×C13—42no—
175C42×C13—42no—
176C42×C13#4112yes—
177C42×C13#4112yes—
178#6103—42no—
179#6103—42no—
180#6103—42no—
181#6103—42no—
182#6103—81no—
183#6103—81no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4×Dic13—81no—
189C2×#1055—21no—
190C2×#1055—21no—
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×#1055—21no—
200C2×#1055#4112yes—
201#2592—131no—
202Q8×C4⋊C4D1311yescharacteristic, complemented
203#2096—131no—
204#2094—131no—
205#2072—131no—
206#2071—131no—
207#1985—131no—
208#1983—131no—
209#1959—131no—
210#1948—131no—
211#1928—131no—
212#1927—131no—
213#1926—131no—
214#1925—131no—
215#1776—131no—
216C23×C13C22×D411yescharacteristic
217C22×D13—41no—
218C22×D13—41no—
219C22×D13—41no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—41no—
223C22×D13—41no—
224Q8×C13—28no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
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—22no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
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—41no—
250C2×C4×C13—41no—
251C2×C4×C13#12312yes—
252C2×C4×C13#12312yes—
253C2×C4×C13AGL(1,ℤ/8)12yes—
254C2×C4×C13#13712yes—
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13H(5,𝔽2)11yescharacteristic
260C2×C4×C132−1+411yescharacteristic
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—
270D52—41no—
271D52—41no—
272D52—41no—
273D52—41no—
274Dic26—41no—
275Dic26—41no—
276Dic26—41no—
277Dic26—41no—
278#1055—22no—
279#1055—41no—
280#1055—41no—
281#1055—41no—
282C2×#124—131no—
283C2×C4×Q8—21no—
284C2×C4×Q8C2×D1311yescharacteristic
285C2×#107—131no—
286C2×#106—131no—
287C2×#106—131no—
288C2×#106—131no—
289C2×C4⋊C8—131no—
290C2×#103—131no—
291C2×#103—131no—
292C2×#103—131no—
293C2×#103—131no—
294C2×#102—131no—
295C2×#102—131no—
296C2×#102—131no—
297C2×#102—131no—
298C2×#97—131no—
299#397—261no—
300#393—261no—
301#391—131no—
302#391—131no—
303#390—131no—
304#390—131no—
305#389—21no—
306#389—21no—
307#389—21no—
308#388—261no—
309#388—261no—
310#384C2×D1311yescharacteristic
311#384C2×D1311yescharacteristic
312#384C2×D1311yescharacteristic
313C4×C4⋊C4—131no—
314C4×C4⋊C4C2×D1311yescharacteristic
315C4×C4⋊C4C2×D1311yescharacteristic
316C4×C4⋊C4C2×D1311yescharacteristic
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#336—131no—
322#336—131no—
323#336—131no—
324#336—131no—
325C22×C13C2×#12311yescharacteristic
326C22×C13#54811yescharacteristic
327C22×C13#55011yescharacteristic
328C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C13C2×#13711yescharacteristic
330C22×C13#57711yescharacteristic
331C22×C13#57711yescharacteristic
332C2×D13—81no—
333C2×D13—81no—
334C2×D13—81no—
335C2×D13—81no—
336C2×D13—81no—
337C2×D13—81no—
338C2×D13—81no—
339C4×C13—22no—
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—22no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13—42no—
346C4×C13—81no—
347C4×C13—81no—
348C4×C13—81no—
349C4×C13#52911yescharacteristic
350C4×C13#54211yescharacteristic
351C4×C13#55611yescharacteristic
352C4×C13#55911yescharacteristic
353Dic13—81no—
354Dic13—81no—
355Dic13—81no—
356C22×Q8—131no—
357C22×Q8C22⋊D1311yescharacteristic
358C22×D4—131no—
359C22×C8—131no—
360C22×C8—131no—
361C22×C8—131no—
362C22×C8—131no—
363#124—262no—
364#124—262no—
365C4×Q8—22no—
366C4×Q8—22no—
367C4×Q8—44no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4C22⋊D1311yescharacteristic
377C2×C4⋊C4C22⋊D1311yescharacteristic
378C2×C4⋊C4C22⋊D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C22⋊C4—261no—
388C2×C22⋊C4—261no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—261no—
393C2×C42C22×D1311yescharacteristic
394C2×C42C22×D1311yescharacteristic
395C2×C42C22×D1311yescharacteristic
396#107—262no—
397#106—262no—
398#106—521no—
399#106—521no—
400C4⋊C8—262no—
401#103—262no—
402#103—262no—
403#103—521no—
404#103—521no—
405#102—262no—
406#102—262no—
407#102—521no—
408#102—521no—
409#97—262no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418C2×C13#244811yescharacteristic
419C2×C13#309211yescharacteristic
420C2×C13#309911yescharacteristic
421C2×C13#336911yescharacteristic
422C2×C13#337311yescharacteristic
423C2×C13#339711yescharacteristic
424C2×C13#340011yescharacteristic
425D13—161no—
426C24—261no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—261no—
431C2×Q8—261no—
432C2×Q8—261no—
433C2×Q8—261no—
434C2×Q8—261no—
435C2×Q8—261no—
436C2×D4—261no—
437C2×D4—261no—
438C2×D4—261no—
439C2×D4—261no—
440C2×D4—261no—
441C2×D4—261no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4C2×C22⋊D1311yescharacteristic
450C22×C4C2×C22⋊D1311yescharacteristic
451C22×C4C2×C22⋊D1311yescharacteristic
452C22×C4C2×C22⋊D1311yescharacteristic
453C22×C4C2×C22⋊D1311yescharacteristic
454C22×C4C2×C22⋊D1311yescharacteristic
455C22×C4C23×D1311yescharacteristic
456C2×C8—132no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4#613112yes—
489C22⋊C4—522no—
490C22⋊C4—522no—
491C22⋊C4—522no—
492C22⋊C4—522no—
493C22⋊C4—1041no—
494C22⋊C4—1041no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—42no—
500C42—42no—
501C42—42no—
502C42—1041no—
503C42#612712yes—
504C42#612712yes—
505C13#2632811yescharacteristic, complemented, Sylow
506C23—521no—
507C23—521no—
508C23—521no—
509C23—521no—
510C23—521no—
511C23—521no—
512C23—521no—
513C23C22×C22⋊D1311yescharacteristic
514Q8—28no—
515Q8—521no—
516Q8—521no—
517Q8—521no—
518Q8—521no—
519D4—521no—
520D4—521no—
521D4—521no—
522D4—521no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
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—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#8818312yes—
559C2×C4#8818312yes—
560C2×C4#8818612yes—
561C2×C4#8819612yes—
562C2×C4C2×#612711yescharacteristic
563C2×C4C2×#612711yescharacteristic
564C2×C4C2×#613111yescharacteristic
565C2×C4#8825411yescharacteristic
566C2×C4#41×D1311yescharacteristic
567C2×C4#8825611yescharacteristic
568C8—262no—
569C8—521no—
570C8—521no—
571C8—521no—
572C22—1041no—
573C22—1041no—
574C22—1041no—
575C22—1041no—
576C22—1041no—
577C22—1041no—
578C22—1041no—
579C22C2×#8818311yescharacteristic
580C22C2×#8818611yescharacteristic
581C22C2×#8819611yescharacteristic
582C22#1171952211yescharacteristic
583C22#1171953911yescharacteristic
584C22#1171954111yescharacteristic
585C22#1171954211yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—42no—
591C4—41no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—1041no—
597C4—1041no—
598C4—1041no—
599C4#1171927311yescharacteristic
600C4#1171928511yescharacteristic
601C4#1171928711yescharacteristic
602C4#1171929011yescharacteristic
603C2—2081no—
604C2#1311862811yescharacteristic
605C2#1312475911yescharacteristic
606C2#1312482511yescharacteristic
607C2#1312757611yescharacteristic
608C2#1312762811yescharacteristic
609C2#1312785211yescharacteristic
610C2#1312788511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingQ8×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenterQ8×C4⋊C4D13
hypocenterC13#26328
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13116380C2semidirect
4. #13116245C2semidirect
6. #13115777C2semidirect
9. #13115597C2semidirect
10. #13115477C2semidirect
11. #13115470C2semidirect
14. #13114734C2semidirect
15. Q8×C13×C4⋊C4C2semidirect
202. Q8×C4⋊C4D13semidirect
505. C13#26328semidirect

Maximal subgroups

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

subgroupindex
#131203242
#131163802
#131163702
#131162452
#131162402
#131157772
#131157682
#131156502
#131155972
#131154772
#131154702
#131154632
#131154562
#131147342
Q8×C13×C4⋊C42
#2632813