Finite Group Databasebeta

← #15926631

Subgroups — #15926631

Order 3328.

738 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#13117861C211yesmaximal, characteristic
2#13116393C211yesmaximal, characteristic, complemented
3#13116338C211yesmaximal, characteristic, complemented
4#13116214C211yesmaximal, characteristic, complemented
5#13115984C211yesmaximal, characteristic, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115425C211yesmaximal, characteristic, complemented
8#13115257C211yesmaximal, characteristic
9#13115148C211yesmaximal, characteristic
10#13115089C211yesmaximal, characteristic, complemented
11#13115033C211yesmaximal, characteristic
12#13115016C211yesmaximal, characteristic
13#13114838C211yesmaximal, characteristic, complemented
14#13114552C211yesmaximal, characteristic
15C13×#2441C211yesmaximal, characteristic
16C2×C13×#125C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19C2×#88178C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C13×#399—21no—
23C13×#396—21no—
24C13×#389—21no—
25C13×#389C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#387—21no—
28C13×#384C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88050C2211yescharacteristic
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38#11718606—21no—
39#11718605—21no—
40C4×C4⋊Dic13C2211yescharacteristic
41#11718590C2211yescharacteristic
42#11718589C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45#11718313—21no—
46#11718310—21no—
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×C13C2311yescharacteristic
60C22×Dic26C2311yescharacteristic
61C13×#125—22no—
62C13×#125—41no—
63C13×#117—22no—
64C13×#117—41no—
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⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4D411yescharacteristic
78C2×C13×C22⋊C4D411yescharacteristic
79C2×C42×C13—21no—
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13—21no—
84#88180—22no—
85#88180—41no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89#88178—22no—
90#88178Q814yes—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C22×#1055—22no—
98C22×#1055—41no—
99C22×#1055—41no—
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C4×Dic26—22no—
105C4×Dic26—41no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95D411yescharacteristic
110C13×#95D411yescharacteristic
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115C22⋊#1055—22no—
116#88050—22no—
117#88050—41no—
118#88050—41no—
119#88050—41no—
120#88048—41no—
121#88047—22no—
122C4⋊#1055—41no—
123C4⋊#1055—41no—
124#26419—131nomaximal, Sylow
125C24×C13C2×D411yescharacteristic
126C22×C4×C13—21no—
127C22×C4×C13—21no—
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×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×Q812yes—
140C22×C4×C13#4112yes—
141C22×C4×C13C2411yescharacteristic
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×Dic26C2×Q812yes—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—42no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4—42no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4—81no—
164C13×C4⋊C4—81no—
165C13×C4⋊C4#4112yes—
166C13×C22⋊C4—22no—
167C13×C22⋊C4—41no—
168C13×C22⋊C4—42no—
169C13×C22⋊C4—81no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—42no—
175C22⋊Dic13—24no—
176C22⋊Dic13—42no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13C2×Q812yes—
182C4⋊Dic13#4112yes—
183#6101—24no—
184#6101—42no—
185#6101—42no—
186C4×Dic13—42no—
187C4×Dic13—42no—
188C4×Dic13—42no—
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—21no—
201C2×#1055—44no—
202#2441D1311yescharacteristic
203#2362—131no—
204#2099—131no—
205#2088—131no—
206#2066—131no—
207#2026—131no—
208#1989—131no—
209#1921—131no—
210#1892—131no—
211#1873—131no—
212#1863—131no—
213#1854—131no—
214#1850—131no—
215#1803—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—22no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
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—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13C22⋊Q812yes—
255C2×C4×C13#13512yes—
256C2×C4×C13C22×Q811yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13H(5,𝔽2)11yescharacteristic
261C2×C4×C13H(5,𝔽2)11yescharacteristic
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—22no—
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—
278#1055—41no—
279#1055—41no—
280#1055—41no—
281#1055—41no—
282C23×C8—131no—
283C2×#125C2×D1311yescharacteristic
284C2×C22⋊Q8—131no—
285C2×C4×Q8—131no—
286C2×#117—131no—
287C2×#117C2×D1311yescharacteristic
288C2×#107—131no—
289C2×#106—131no—
290C2×C4⋊C8—131no—
291C2×C4⋊C8—131no—
292C2×#103—131no—
293C2×#103—131no—
294C2×#103—131no—
295C2×#103—131no—
296C2×C22⋊C8—131no—
297#399—21no—
298#396—21no—
299#391—131no—
300#389—21no—
301#389—131no—
302#389C2×D1311yescharacteristic
303#389C2×D1311yescharacteristic
304#388—261no—
305#388—261no—
306#387—21no—
307#387—261no—
308#384C2×D1311yescharacteristic
309#380C2×D1311yescharacteristic
310C4×C4⋊C4—131no—
311C4×C4⋊C4—261no—
312C4×C22⋊C4C2×D1311yescharacteristic
313#340—131no—
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#336—131no—
324#336—131no—
325C22×C13—22no—
326C22×C13—22no—
327C22×C13—22no—
328C22×C13—41no—
329C22×C13—41no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13C2×C22⋊Q811yescharacteristic
333C22×C13#54611yescharacteristic
334C22×C13#54611yescharacteristic
335C22×C13C2×#13511yescharacteristic
336C22×C13#57511yescharacteristic
337C22×C13#57711yescharacteristic
338C22×C13#57811yescharacteristic
339C4×C13—22no—
340C4×C13—22no—
341C4×C13—41no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13—42no—
345C4×C13—81no—
346C4×C13—81no—
347C4×C13—81no—
348C4×C13#52911yescharacteristic
349C4×C13#53811yescharacteristic
350C4×C13#55411yescharacteristic
351C4×C13#55411yescharacteristic
352Dic13—42no—
353Dic13—42no—
354Dic13—42no—
355Dic13—81no—
356C22×Q8—131no—
357C23×C4C22×D1311yescharacteristic
358C22×C8—131no—
359C22×C8—131no—
360C22×C8—131no—
361C22×C8—131no—
362C22×C8—262no—
363C22×C8—521no—
364C22×C8—521no—
365#125—22no—
366#125—41no—
367C22⋊Q8—134no—
368C22⋊Q8—262no—
369C4×Q8—262no—
370C4×Q8—521no—
371#117—22no—
372#117—41no—
373#117—262no—
374#117—521no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
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⋊C4C22×D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C4⋊C4C22×D1311yescharacteristic
390C2×C4⋊C4C22×D1311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4—261no—
395C2×C22⋊C4C22⋊D1311yescharacteristic
396C2×C22⋊C4C22⋊D1311yescharacteristic
397C2×C42—21no—
398C2×C42—261no—
399C2×C42—261no—
400C2×C42—261no—
401C2×C42C22×D1311yescharacteristic
402C2×C42C22×D1311yescharacteristic
403#107—262no—
404#106—521no—
405C4⋊C8—521no—
406C4⋊C8—521no—
407#103—262no—
408#103—521no—
409#103—521no—
410#103—521no—
411C22⋊C8—262no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95C22⋊D1311yescharacteristic
420#95C22⋊D1311yescharacteristic
421C2×C13—42no—
422C2×C13#245011yescharacteristic
423C2×C13#307611yescharacteristic
424C2×C13#308211yescharacteristic
425C2×C13#330011yescharacteristic
426C2×C13#330411yescharacteristic
427C2×C13#330711yescharacteristic
428C2×C13#331511yescharacteristic
429C24C2×C22⋊D1311yescharacteristic
430C2×Q8—132no—
431C2×Q8—261no—
432C2×Q8—261no—
433C2×Q8—261no—
434C2×Q8—261no—
435C2×Q8—261no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
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×C4Q8×D1312yes—
449C22×C4#613112yes—
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—261no—
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—
468C2×C8—524no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—132no—
483C4⋊C4—132no—
484C4⋊C4—264no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—522no—
490C4⋊C4—522no—
491C4⋊C4#612912yes—
492C22⋊C4—22no—
493C22⋊C4—41no—
494C22⋊C4—42no—
495C22⋊C4—81no—
496C22⋊C4—264no—
497C22⋊C4—522no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—42no—
503C42—522no—
504C42—522no—
505C42—522no—
506C13#2641911yescharacteristic, complemented, Sylow
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23#8820012yes—
514C23C22×C22⋊D1311yescharacteristic
515Q8—262no—
516Q8—262no—
517Q8—521no—
518Q8—521no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
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—262no—
549C2×C4—262no—
550C2×C4—262no—
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#8820012yes—
561C2×C4#8820412yes—
562C2×C4C2×#612911yescharacteristic
563C2×C4#8825111yescharacteristic
564C2×C4C2×Q8×D1311yescharacteristic
565C2×C4C2×#613111yescharacteristic
566C2×C4#41×D1311yescharacteristic
567C2×C4#8825611yescharacteristic
568C8—521no—
569C8—521no—
570C8—521no—
571C8—521no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22#1171951111yescharacteristic
580C22C2×#8820011yescharacteristic
581C22C2×#8820411yescharacteristic
582C22#1171952711yescharacteristic
583C22#1171953411yescharacteristic
584C22#1171954111yescharacteristic
585C22#1171954311yescharacteristic
586C4—22no—
587C4—22no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4—522no—
596C4—522no—
597C4—522no—
598C4—1041no—
599C4#1171932911yescharacteristic
600C4#1171934011yescharacteristic
601C4#1171934111yescharacteristic
602C4#1171934911yescharacteristic
603C2—42no—
604C2#1311865611yescharacteristic
605C2#1312461811yescharacteristic
606C2#1312467211yescharacteristic
607C2#1312671711yescharacteristic
608C2#1312677511yescharacteristic
609C2#1312680611yescharacteristic
610C2#1312693211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2441C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2441D13
hypocenterC13#26419
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2441

Complements

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

NH ≅ G/Ntype
2. #13116393C2semidirect
3. #13116338C2semidirect
4. #13116214C2semidirect
5. #13115984C2semidirect
6. #13115794C2semidirect
7. #13115425C2semidirect
10. #13115089C2semidirect
13. #13114838C2semidirect
506. C13#26419semidirect

Maximal subgroups

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

subgroupindex
#131178612
#131163932
#131163382
#131162142
#131159842
#131157942
#131154252
#131152572
#131151482
#131150892
#131150332
#131150162
#131148382
#131145522
C13×#24412
#2641913