Finite Group Databasebeta

← #15794053

Subgroups — #15794053

Order 3328.

1486 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
1C2×#11718604C211yesmaximal, characteristic
2C2×#11718603C212yesmaximal
3#13113100C212yesmaximal, complemented
4#13113099C212yesmaximal, complemented
5#13113094C212yesmaximal, complemented
6#13113091C212yesmaximal, complemented
7#13113081C211yesmaximal, characteristic
8#13113079C212yesmaximal
9C13×#1439C211yesmaximal, characteristic
10C24×Dic13C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C22⋊C4C2212yes—
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic13C2212yes—
15C22×C22⋊Dic13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×#6101C2212yes—
18C22×#6101C2212yes—
19C22×#6101C2212yes—
20C2×C13×#95C2212yes—
21C2×C13×#95C2211yescharacteristic
22C2×#88071C2212yes—
23C2×#88071C2212yes—
24C2×#88071C2211yescharacteristic
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31#11718604C418yescomplemented
32#11718603—28no—
33C25×C13C2311yescharacteristic
34C23×C4×C13C2312yes—
35C23×C4×C13C2312yes—
36C23×C4×C13C2311yescharacteristic
37C23×C4×C13C2311yescharacteristic
38C23×Dic13—41no—
39C23×Dic13—41no—
40C23×Dic13—41no—
41C23×Dic13—41no—
42C23×Dic13C2×C414yes—
43C23×Dic13D414yes—
44C23×Dic13Q814yes—
45C23×Dic13C2312yes—
46C23×Dic13C2312yes—
47C23×Dic13C2312yes—
48C23×Dic13C2312yes—
49C2×C13×C4⋊C4—42no—
50C2×C13×C4⋊C4—41no—
51C2×C13×C22⋊C4—24no—
52C2×C13×C22⋊C4—41no—
53C2×C13×C22⋊C4—41no—
54C2×C13×C22⋊C4—42no—
55C2×C13×C22⋊C4—42no—
56C2×C13×C22⋊C4C2×C414yes—
57C2×C22⋊Dic13—24no—
58C2×C22⋊Dic13—41no—
59C2×C22⋊Dic13—41no—
60C2×C22⋊Dic13—42no—
61C2×C22⋊Dic13—42no—
62C2×C22⋊Dic13C2×C414yes—
63C2×C4⋊Dic13—41no—
64C2×C4⋊Dic13—42no—
65C2×#6101—24no—
66C2×#6101—24no—
67C2×#6101—42no—
68C2×#6101—42no—
69C2×#6101—42no—
70C2×#6101—42no—
71C2×#6101—42no—
72C2×#6101—42no—
73C2×#6101—42no—
74C13×#95—42no—
75C13×#95—41no—
76#88071—24no—
77#88071—24no—
78#88071—42no—
79#88071—42no—
80#88071—42no—
81#88071—42no—
82#88071—41no—
83#88071C2×C418yes—
84#88071C2×C418yes—
85#14674—131nomaximal, Sylow
86C24×C13—22no—
87C24×C13—22no—
88C24×C13—21no—
89C24×C13—21no—
90C24×C13—21no—
91C24×C13—21no—
92C24×C13—22no—
93C24×C13—22no—
94C24×C13C22×C412yes—
95C24×C13C2×D412yes—
96C24×C13C2×Q812yes—
97C24×C13C2411yescharacteristic
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13C22×C412yes—
121C22×C4×C13C22×C412yes—
122C22×Dic13—22no—
123C22×Dic13—22no—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—44no—
147C22×Dic13—44no—
148C22×Dic13—44no—
149C22×Dic13—44no—
150C22×Dic13—44no—
151C22×Dic13—44no—
152C22×Dic13C4⋊C4116yescomplemented
153C22×Dic13C22×C414yes—
154C22×Dic13C22×C414yes—
155C22×Dic13C2×D414yes—
156C22×Dic13C2×Q814yes—
157C13×C4⋊C4—44no—
158C13×C22⋊C4—44no—
159C13×C22⋊C4—48no—
160C22⋊Dic13—44no—
161C22⋊Dic13—48no—
162C4⋊Dic13—44no—
163#6101—48no—
164#6101—48no—
165#6101—48no—
166C2×#381—131no—
167C2×#380—132no—
168#1444—132no—
169#1444—132no—
170#1442—132no—
171#1442—132no—
172#1439—132no—
173#1439—131no—
174#1439D1311yescharacteristic
175C23×C13—22no—
176C23×C13—22no—
177C23×C13—24no—
178C23×C13—24no—
179C23×C13—22no—
180C23×C13—22no—
181C23×C13—24no—
182C23×C13—24no—
183C23×C13—22no—
184C23×C13—22no—
185C23×C13—24no—
186C23×C13—24no—
187C23×C13—41no—
188C23×C13—41no—
189C23×C13—42no—
190C23×C13—42no—
191C23×C13—42no—
192C23×C13—42no—
193C23×C13—42no—
194C23×C13—41no—
195C23×C13—41no—
196C23×C13—42no—
197C23×C13C2×C4⋊C414yes—
198C23×C13C23×C411yescharacteristic
199C23×C13C22×D411yescharacteristic
200C23×C13C22×Q811yescharacteristic
201C23×C13H(5,𝔽2)11yescharacteristic
202C23×C13H(5,𝔽2)11yescharacteristic
203C23×C13H(5,𝔽2)11yescharacteristic
204C23×C13H(5,𝔽2)11yescharacteristic
205C23×C13H(5,𝔽2)12yes—
206C23×C13H(5,𝔽2)12yes—
207C23×C132−1+412yes—
208C23×C132−1+412yes—
209C2×C4×C13—22no—
210C2×C4×C13—22no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×Dic13—24no—
234C2×Dic13—24no—
235C2×Dic13—24no—
236C2×Dic13—24no—
237C2×Dic13—24no—
238C2×Dic13—24no—
239C2×Dic13—24no—
240C2×Dic13—24no—
241C2×Dic13—24no—
242C2×Dic13—416no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13C2×C4⋊C418yes—
262C24×C4—131no—
263C22×C4⋊C4—132no—
264C22×C4⋊C4—132no—
265C22×C4⋊C4—132no—
266C22×C4⋊C4—131no—
267C22×C4⋊C4C2×D1311yescharacteristic
268C22×C22⋊C4—131no—
269C22×C22⋊C4—132no—
270C22×C22⋊C4C2×D1312yes—
271C22×C22⋊C4C2×D1311yescharacteristic
272#381—138no—
273#380—268no—
274C2×#95—132no—
275C2×#95—132no—
276C2×#95—132no—
277C2×#95—132no—
278C2×#95—132no—
279C2×#95—131no—
280C2×#95—132no—
281C2×#95—132no—
282C2×#95—132no—
283C2×#95C2×D1311yescharacteristic
284C2×#95C2×D1312yes—
285C22×C13—24no—
286C22×C13—28no—
287C22×C13—44no—
288C22×C13—42no—
289C22×C13—42no—
290C22×C13—44no—
291C22×C13—42no—
292C22×C13—42no—
293C22×C13—44no—
294C22×C13—42no—
295C22×C13—42no—
296C22×C13C22×C4⋊C411yescharacteristic
297C22×C13#51811yescharacteristic
298C22×C13#51811yescharacteristic
299C22×C13#52012yes—
300C22×C13#52012yes—
301C22×C13#53411yescharacteristic
302C22×C13#53411yescharacteristic
303C22×C13#53512yes—
304C22×C13#53612yes—
305C22×C13#54311yescharacteristic
306C22×C13#54311yescharacteristic
307C22×C13#54412yes—
308C22×C13#54412yes—
309C22×C13#56011yescharacteristic
310C22×C13#56011yescharacteristic
311C22×C13#56012yes—
312C22×C13#56212yes—
313C22×C13#56212yes—
314C22×C13#56212yes—
315C22×C13#56212yes—
316C22×C13#56311yescharacteristic
317C22×C13#56311yescharacteristic
318C22×C13#56312yes—
319C4×C13—42no—
320C4×C13—42no—
321C4×C13—82no—
322C4×C13—82no—
323Dic13—28no—
324Dic13—44no—
325Dic13—82no—
326Dic13—82no—
327C25C22×D1311yescharacteristic
328C23×C4—132no—
329C23×C4—134no—
330C23×C4—134no—
331C23×C4—134no—
332C23×C4—132no—
333C23×C4—132no—
334C23×C4—132no—
335C23×C4—521no—
336C23×C4—521no—
337C23×C4—521no—
338C23×C4—521no—
339C23×C4C22×D1312yes—
340C23×C4C22×D1312yes—
341C23×C4C22×D1311yescharacteristic
342C23×C4C22×D1311yescharacteristic
343C2×C4⋊C4—42no—
344C2×C4⋊C4—41no—
345C2×C4⋊C4—264no—
346C2×C4⋊C4—264no—
347C2×C4⋊C4—522no—
348C2×C4⋊C4—522no—
349C2×C4⋊C4—522no—
350C2×C4⋊C4—522no—
351C2×C4⋊C4—522no—
352C2×C4⋊C4—522no—
353C2×C4⋊C4—522no—
354C2×C4⋊C4—522no—
355C2×C4⋊C4—521no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—134no—
362C2×C22⋊C4—264no—
363C2×C22⋊C4—521no—
364C2×C22⋊C4—521no—
365C2×C22⋊C4—522no—
366C2×C22⋊C4—522no—
367C2×C22⋊C4C4×D1314yes—
368#95—41no—
369#95—42no—
370#95—138no—
371#95—138no—
372#95—264no—
373#95—264no—
374#95—521no—
375#95—522no—
376#95—522no—
377#95—522no—
378#95—522no—
379C2×C13—44no—
380C2×C13#231511yescharacteristic
381C2×C13#231712yes—
382C2×C13#237611yescharacteristic
383C2×C13#237612yes—
384C2×C13#237611yescharacteristic
385C2×C13#281511yescharacteristic
386C2×C13#281612yes—
387C2×C13#281711yescharacteristic
388C2×C13#284111yescharacteristic
389C2×C13#284112yes—
390C2×C13#284111yescharacteristic
391C24—22no—
392C24—22no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—22no—
398C24—22no—
399C24C2×C4×D1312yes—
400C24D4×D1312yes—
401C24Q8×D1312yes—
402C24C23×D1311yescharacteristic
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—134no—
426C22×C4—134no—
427C22×C4—134no—
428C22×C4—1316no—
429C22×C4—134no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—524no—
455C22×C4—524no—
456C22×C4—524no—
457C22×C4—524no—
458C22×C4—524no—
459C22×C4—524no—
460C22×C4C2×C4×D1312yes—
461C22×C4C2×C4×D1312yes—
462C4⋊C4—44no—
463C4⋊C4—528no—
464C4⋊C4—528no—
465C4⋊C4—528no—
466C4⋊C4—524no—
467C22⋊C4—44no—
468C22⋊C4—48no—
469C22⋊C4—524no—
470C22⋊C4—528no—
471C13#1467411yescharacteristic, complemented, Sylow
472C23—22no—
473C23—22no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—22no—
478C23—22no—
479C23—24no—
480C23—24no—
481C23—22no—
482C23—22no—
483C23—24no—
484C23—41no—
485C23—41no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—41no—
490C23—42no—
491C23—41no—
492C23—42no—
493C23—42no—
494C23C4⋊C4×D1314yes—
495C23C22×C4×D1311yescharacteristic
496C23C2×D4×D1311yescharacteristic
497C23#8825111yescharacteristic
498C23#8825112yes—
499C23#8825111yescharacteristic
500C23#8825112yes—
501C23C2×Q8×D1311yescharacteristic
502C23#8825611yescharacteristic
503C23#8825611yescharacteristic
504C23#8825712yes—
505C23#8825712yes—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—138no—
531C2×C4—264no—
532C2×C4—264no—
533C2×C4—264no—
534C2×C4—264no—
535C2×C4—264no—
536C2×C4—264no—
537C2×C4—264no—
538C2×C4—264no—
539C2×C4—264no—
540C2×C4—5216no—
541C2×C4—522no—
542C2×C4—522no—
543C2×C4—522no—
544C2×C4—522no—
545C2×C4—522no—
546C2×C4—522no—
547C2×C4—522no—
548C2×C4—522no—
549C2×C4—522no—
550C2×C4—522no—
551C2×C4—522no—
552C2×C4—522no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—522no—
559C22—24no—
560C22—28no—
561C22—42no—
562C22—44no—
563C22—42no—
564C22—42no—
565C22—44no—
566C22—42no—
567C22—42no—
568C22—44no—
569C22—42no—
570C22#1171919111yescharacteristic
571C22C2×C4⋊C4×D1311yescharacteristic
572C22#1171922611yescharacteristic
573C22#1171925112yes—
574C22#1171925112yes—
575C22#1171929712yes—
576C22#1171930011yescharacteristic
577C22#1171931011yescharacteristic
578C22#1171931011yescharacteristic
579C22#1171932512yes—
580C22#1171932612yes—
581C22#1171932612yes—
582C22#1171932812yes—
583C22#1171932812yes—
584C22#1171933911yescharacteristic
585C22#1171933911yescharacteristic
586C22#1171935312yes—
587C22#1171935611yescharacteristic
588C22#1171937212yes—
589C22#1171937711yescharacteristic
590C22#1171938912yes—
591C22#1171941712yes—
592C22#1171942511yescharacteristic
593C4—42no—
594C4—42no—
595C4—82no—
596C4—82no—
597C4—268no—
598C4—524no—
599C4—1042no—
600C4—1042no—
601C2—44no—
602C2#1311744911yescharacteristic
603C2#1311745512yes—
604C2#1311797911yescharacteristic
605C2#1311798212yes—
606C2#1311798611yescharacteristic
607C2#1312286111yescharacteristic
608C2#1312286812yes—
609C2#1312287411yescharacteristic
610C2#1312309611yescharacteristic
611C2#1312309712yes—
612C2#1312309811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#14674
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. #13113100C2semidirect
4. #13113099C2semidirect
5. #13113094C2semidirect
6. #13113091C2semidirect
31. #11718604C4semidirect
152. C22×Dic13C4⋊C4semidirect
471. C13#14674semidirect

Maximal subgroups

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

subgroupindex
C2×#117186042
C2×#117186032
#131131002
#131130992
#131130942
#131130912
#131130812
#131130792
C13×#14392
#1467413