Finite Group Databasebeta

← #15926573

Subgroups — #15926573

Order 3328.

746 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118527C211yesmaximal, characteristic
2#13117861C211yesmaximal, characteristic
3#13116405C211yesmaximal, characteristic, complemented
4#13116334C211yesmaximal, characteristic, complemented
5#13116216C211yesmaximal, characteristic, complemented
6#13115978C211yesmaximal, characteristic, complemented
7#13115783C211yesmaximal, characteristic, complemented
8#13115408C211yesmaximal, characteristic, complemented
9#13115259C211yesmaximal, characteristic
10#13115146C211yesmaximal, characteristic
11#13115093C211yesmaximal, characteristic, complemented
12#13115037C211yesmaximal, characteristic
13#13114852C211yesmaximal, characteristic, complemented
14#13114553C211yesmaximal, characteristic
15C13×#1850C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19C2×#88178C2211yescharacteristic
20C2×#88123C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×C22⋊C8C2211yescharacteristic
25C4×C13×C22⋊C4C2211yescharacteristic
26#11718873C2211yescharacteristic
27C2×#88058C2211yescharacteristic
28C2×#88057C2211yescharacteristic
29C2×#88056C2211yescharacteristic
30C2×#88056C2211yescharacteristic
31C2×#88056C2211yescharacteristic
32C2×#88056C2211yescharacteristic
33#11718609—21no—
34#11718608—21no—
35#11718606—21no—
36#11718605—21no—
37#11718597C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39#11718590C2211yescharacteristic
40#11718589C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718316—21no—
44#11718313—21no—
45#11718310—21no—
46#11718307—21no—
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×Dic26—21no—
61C22×Dic26C2311yescharacteristic
62C22×C8×C13—22no—
63C22×C8×C13—41no—
64C22×C8×C13—41no—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C2×C13×C22⋊C4D411yescharacteristic
70C2×C13×C22⋊C4D411yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—21no—
77#88180—22no—
78#88180—22no—
79#88180—41no—
80#88180—41no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89#88178—22no—
90#88178Q814yescomplemented
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100#88123—22no—
101#88123—41no—
102C4×Dic26—22no—
103C4×Dic26—41no—
104C13×C4⋊C8—41no—
105C13×C4⋊C8—41no—
106C13×C22⋊C8—22no—
107C13×#95D411yescharacteristic
108C13×#95D411yescharacteristic
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88058—22no—
119#88057—41no—
120#88056—22no—
121#88056—41no—
122#88056—41no—
123#88056—41no—
124#26415—131nomaximal, Sylow
125C24×C13C2×D411yescharacteristic
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×Q812yes—
136C22×C4×C13#4112yes—
137C22×C4×C13C2411yescharacteristic
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C2×Dic26—21no—
147C2×Dic26—21no—
148C2×Dic26—21no—
149C2×Dic26—21no—
150C2×Dic26—21no—
151C2×Dic26—42no—
152C2×Dic26—42no—
153C2×Dic26—81no—
154C2×Dic26C2×Q812yes—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—44no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—41no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C22⋊Dic13—24no—
175C22⋊Dic13—42no—
176C22⋊Dic13—42no—
177C22⋊Dic13—81no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—42no—
190C4⋊Dic13C2×Q812yes—
191C4⋊Dic13#4112yes—
192C4⋊Dic13#4112yes—
193#6101—24no—
194#6101—42no—
195#6101—42no—
196#6101—42no—
197#6101—81no—
198C4×Dic13—42no—
199C4×Dic13—42no—
200C4×Dic13—42no—
201C4×Dic13—42no—
202#2439—131no—
203#2362—131no—
204#2101—131no—
205#2088—131no—
206#2066—131no—
207#2024—131no—
208#1987—131no—
209#1918—131no—
210#1892—131no—
211#1873—131no—
212#1863—131no—
213#1854—131no—
214#1850D1311yescharacteristic
215#1805—131no—
216#1735—131no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13C22⋊Q812yes—
224C23×C13C22×D411yescharacteristic
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
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—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13C22⋊Q812yes—
243C2×C4×C13#13512yes—
244C2×C4×C13C22×Q811yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13H(5,𝔽2)11yescharacteristic
249C2×C4×C13H(5,𝔽2)11yescharacteristic
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
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×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274Dic26—22no—
275Dic26—22no—
276Dic26—41no—
277Dic26—41no—
278Dic26—84no—
279C8×C13—41no—
280C8×C13—41no—
281C8×C13—41no—
282C8×C13—41no—
283C23×C8C2×D1311yescharacteristic
284C2×C4⋊Q8—131no—
285C2×C22⋊Q8—131no—
286C2×C4×Q8—131no—
287C2×#117—131no—
288C2×#117—131no—
289C2×#107—131no—
290C2×#106—131no—
291C2×C4⋊C8C2×D1311yescharacteristic
292C2×C4⋊C8C2×D1311yescharacteristic
293C2×#103—131no—
294C2×#103—131no—
295C2×#103—131no—
296C2×#103—131no—
297C2×C22⋊C8C2×D1311yescharacteristic
298#396—261no—
299#393—261no—
300#391—131no—
301#391—261no—
302#389—131no—
303#389—131no—
304#389—131no—
305#388—261no—
306#388—261no—
307#387—261no—
308#387—261no—
309#382—131no—
310#380—131no—
311C4×C4⋊C4—131no—
312C4×C4⋊C4—261no—
313C4×C22⋊C4C2×D1311yescharacteristic
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#336C2×D1311yescharacteristic
325#336C2×D1311yescharacteristic
326C22×C13—22no—
327C22×C13—22no—
328C22×C13—22no—
329C22×C13—41no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13C2×C22⋊Q811yescharacteristic
334C22×C13#54611yescharacteristic
335C22×C13#54611yescharacteristic
336C22×C13C2×#13511yescharacteristic
337C22×C13#57511yescharacteristic
338C22×C13#57711yescharacteristic
339C22×C13#57811yescharacteristic
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13#52911yescharacteristic
346C4×C13#53811yescharacteristic
347C4×C13#55411yescharacteristic
348C4×C13#55411yescharacteristic
349Dic13—42no—
350Dic13—42no—
351Dic13—42no—
352Dic13—42no—
353Dic13—81no—
354Dic13—81no—
355Dic13—81no—
356Dic13—81no—
357C22×Q8—131no—
358C22×Q8—261no—
359C23×C4C22×D1311yescharacteristic
360C22×C8—22no—
361C22×C8—41no—
362C22×C8—41no—
363C22×C8C22×D1311yescharacteristic
364C22×C8C22×D1311yescharacteristic
365C22×C8C22×D1311yescharacteristic
366C22×C8C22×D1311yescharacteristic
367C4⋊Q8—262no—
368C4⋊Q8—521no—
369C22⋊Q8—134no—
370C22⋊Q8—262no—
371C4×Q8—262no—
372C4×Q8—521no—
373#117—262no—
374#117—262no—
375#117—521no—
376#117—521no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4D5211yescharacteristic
395C2×C22⋊C4D5211yescharacteristic
396C2×C42—261no—
397C2×C42—261no—
398C2×C42—261no—
399C2×C42—261no—
400C2×C42C22×D1311yescharacteristic
401C2×C42C22×D1311yescharacteristic
402#107—262no—
403#106—521no—
404C4⋊C8—41no—
405C4⋊C8—41no—
406#103—262no—
407#103—521no—
408#103—521no—
409#103—521no—
410C22⋊C8—22no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95D5211yescharacteristic
421#95D5211yescharacteristic
422C2×C13—42no—
423C2×C13#245011yescharacteristic
424C2×C13#307611yescharacteristic
425C2×C13#308211yescharacteristic
426C2×C13#330011yescharacteristic
427C2×C13#330311yescharacteristic
428C2×C13#331111yescharacteristic
429C2×C13#331311yescharacteristic
430C24C2×D5211yescharacteristic
431C2×Q8—132no—
432C2×Q8—261no—
433C2×Q8—261no—
434C2×Q8—261no—
435C2×Q8—261no—
436C2×Q8—261no—
437C2×Q8—522no—
438C2×Q8—522no—
439C2×Q8—1041no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4C2×D5211yescharacteristic
453C22×C4C2×D5211yescharacteristic
454C22×C4C2×D5211yescharacteristic
455C22×C4C2×D5211yescharacteristic
456C22×C4C2×D5211yescharacteristic
457C22×C4#612912yes—
458C22×C4Q8×D1312yes—
459C22×C4C23×D1311yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—44no—
473C4⋊C4—132no—
474C4⋊C4—132no—
475C4⋊C4—132no—
476C4⋊C4—264no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—522no—
489C4⋊C4—522no—
490C4⋊C4—522no—
491C4⋊C4—522no—
492C4⋊C4—1041no—
493C22⋊C4—22no—
494C22⋊C4—41no—
495C22⋊C4—264no—
496C22⋊C4—522no—
497C22⋊C4—522no—
498C22⋊C4—1041no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—522no—
504C42—522no—
505C42—522no—
506C42—522no—
507C13#2641511yescharacteristic, complemented, Sylow
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23#8815112yes—
515C23C22×D5211yescharacteristic
516Q8—262no—
517Q8—262no—
518Q8—521no—
519Q8—521no—
520Q8—1044no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—262no—
539C2×C4—262no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
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—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4#8815112yes—
563C2×C4#8815812yes—
564C2×C4C2×#612911yescharacteristic
565C2×C4#8825111yescharacteristic
566C2×C4#8825111yescharacteristic
567C2×C4C2×Q8×D1311yescharacteristic
568C2×C4#41×D1311yescharacteristic
569C2×C4#41×D1311yescharacteristic
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22C2×#8815111yescharacteristic
582C22#1171925911yescharacteristic
583C22#1171925911yescharacteristic
584C22C2×#8815811yescharacteristic
585C22#1171945311yescharacteristic
586C22#1171945611yescharacteristic
587C22#1171945811yescharacteristic
588C4—22no—
589C4—22no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—522no—
594C4—522no—
595C4—522no—
596C4—522no—
597C4—1041no—
598C4—1041no—
599C4—1041no—
600C4—1041no—
601C4#1171929811yescharacteristic
602C4#1171934111yescharacteristic
603C4#1171934111yescharacteristic
604C4#1171935411yescharacteristic
605C2—42no—
606C2#1311865811yescharacteristic
607C2#1312462611yescharacteristic
608C2#1312467911yescharacteristic
609C2#1312672511yescharacteristic
610C2#1312676511yescharacteristic
611C2#1312687411yescharacteristic
612C2#1312690411yescharacteristic
subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1850C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1850D13
hypocenterC13#26415
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
3. #13116405C2semidirect
4. #13116334C2semidirect
5. #13116216C2semidirect
6. #13115978C2semidirect
7. #13115783C2semidirect
8. #13115408C2semidirect
11. #13115093C2semidirect
13. #13114852C2semidirect
90. #88178Q8semidirect
507. C13#26415semidirect

Maximal subgroups

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

subgroupindex
#131185272
#131178612
#131164052
#131163342
#131162162
#131159782
#131157832
#131154082
#131152592
#131151462
#131150932
#131150372
#131148522
#131145532
C13×#18502
#2641513