Finite Group Databasebeta

← #15799706

Subgroups — #15799706

Order 3328.

1334 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718320C211yesmaximal, characteristic
2C2×#11718647C211yesmaximal, characteristic
3C2×#11718643C211yesmaximal, characteristic
4C2×#11718633C211yesmaximal, characteristic
5C2×#11718637C211yesmaximal, characteristic
6#13113102C212yesmaximal
7#13113102C212yesmaximal
8#13113064C212yesmaximal
9#13113064C212yesmaximal
10#95×Dic13C211yesmaximal, characteristic
11C2×C13×#400C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic13C2211yescharacteristic
15C22×#6101C2212yes—
16C22×#6101C2212yes—
17C22×#6101C2211yescharacteristic
18C22×#6101C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×C4×Dic13C2212yes—
21C22×C4×Dic13C2211yescharacteristic
22C13×#400—24no—
23C2×C13×#95C2212yes—
24C2×C13×#95C2212yes—
25C2×C13×#95C2211yescharacteristic
26C2×#88071C2211yescharacteristic
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36#11718647—24no—
37#11718643—24no—
38#11718637—24no—
39#11718633—24no—
40#11718320—24no—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—22no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—22no—
60C2×C4⋊Dic13—22no—
61C2×#6101—22no—
62C2×#6101—22no—
63C2×#6101—22no—
64C2×#6101—22no—
65C2×#6101—22no—
66C2×#6101—22no—
67C2×#6101—24no—
68C2×#6101—24no—
69C2×#6101—24no—
70C2×#6101—28no—
71C2×#6101—28no—
72C2×#6101Q814yes—
73C2×C4×Dic13—24no—
74C2×C4×Dic13—24no—
75C2×C4×Dic13—24no—
76C2×C4×Dic13—24no—
77C2×C4×Dic13D414yes—
78C13×#95—24no—
79C13×#95—24no—
80C13×#95D414yes—
81#88071—24no—
82#88071—24no—
83#88071—22no—
84#88071—22no—
85#88071—24no—
86#88071—24no—
87#88071—24no—
88#88071—24no—
89#88071—24no—
90#88071D414yes—
91#15153—131nomaximal, Sylow
92C24×C13C2411yescharacteristic
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—22no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—24no—
115C22×C4×C13—24no—
116C22×C4×C13—22no—
117C22×C4×C13C2×D412yes—
118C22×C4×C13C2×D412yes—
119C22×C4×C13C2×D414yes—
120C22×C4×C13C2×D412yes—
121C22×C4×C13C2×Q812yes—
122C22×Dic13—22no—
123C22×Dic13—21no—
124C22×Dic13—21no—
125C22×Dic13—21no—
126C22×Dic13—21no—
127C22×Dic13—21no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—21no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—21no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—24no—
145C22×Dic13—24no—
146C22×Dic13—22no—
147C22×Dic13C2×D414yes—
148C22×Dic13C2×D412yes—
149C22×Dic13C2×D412yes—
150C22×Dic13C2×Q812yes—
151C22×Dic13C2×Q812yes—
152C22×Dic13#4114yes—
153C22×Dic13#4112yes—
154C22×Dic13#4114yes—
155C22×Dic13#4114yes—
156C13×C4⋊C4—44no—
157C13×C4⋊C4—44no—
158C4⋊Dic13—44no—
159#6101—28no—
160#6101—44no—
161#6101—44no—
162#6101—48no—
163#6101—48no—
164C4×Dic13—28no—
165C4×Dic13—48no—
166C2×#400—131no—
167C2×#400—131no—
168C2×#400—131no—
169C2×#400D1311yescharacteristic
170C2×#389—131no—
171C2×#384—131no—
172#1445—132no—
173#1445—132no—
174C4⋊#95—132no—
175C4⋊#95—132no—
176C4×#95—131no—
177C23×C13C22×D411yescharacteristic
178C23×C13C22×D411yescharacteristic
179C23×C13C22×D411yescharacteristic
180C23×C13C22×Q811yescharacteristic
181C23×C13C2×#4111yescharacteristic
182C23×C13C2×#4112yes—
183C23×C13C2×#4112yes—
184C23×C13C2×#4112yes—
185C23×C132−1+412yes—
186C23×C132−1+411yescharacteristic
187C23×C132−1+411yescharacteristic
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—24no—
191C2×C4×C13—24no—
192C2×C4×C13—22no—
193C2×C4×C13—24no—
194C2×C4×C13—24no—
195C2×C4×C13—24no—
196C2×C4×C13—22no—
197C2×C4×C13—22no—
198C2×C4×C13—42no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—42no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—41no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—41no—
211C2×C4×C13—44no—
212C2×C4×C13—44no—
213C2×C4×C13—41no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13#12714yes—
217C2×Dic13—22no—
218C2×Dic13—22no—
219C2×Dic13—24no—
220C2×Dic13—24no—
221C2×Dic13—22no—
222C2×Dic13—24no—
223C2×Dic13—24no—
224C2×Dic13—24no—
225C2×Dic13—22no—
226C2×Dic13—22no—
227C2×Dic13—42no—
228C2×Dic13—41no—
229C2×Dic13—41no—
230C2×Dic13—42no—
231C2×Dic13—41no—
232C2×Dic13—41no—
233C2×Dic13—42no—
234C2×Dic13—42no—
235C2×Dic13—41no—
236C2×Dic13—42no—
237C2×Dic13—42no—
238C2×Dic13—41no—
239C2×Dic13—42no—
240C2×Dic13—44no—
241C2×Dic13—44no—
242C2×Dic13—41no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13C22⋊Q814yes—
246C2×Dic13#12314yes—
247C2×Dic13#12414yes—
248C2×Dic13#12414yes—
249C2×Dic13#12518yes—
250C2×Dic13#12618yes—
251C22×C4⋊C4—131no—
252C22×C4⋊C4—131no—
253C22×C4⋊C4—132no—
254C22×C4⋊C4—131no—
255C22×C4⋊C4—132no—
256C22×C4⋊C4—131no—
257C22×C4⋊C4C2×D1311yescharacteristic
258C22×C4⋊C4C2×D1311yescharacteristic
259C22×C42—131no—
260C22×C42—132no—
261#400—24no—
262#400—264no—
263#400—264no—
264#400—264no—
265#389—264no—
266#384—264no—
267C2×#95—131no—
268C2×#95—132no—
269C2×#95—132no—
270C2×#95—132no—
271C2×#95—132no—
272C2×#95—132no—
273C2×#95—132no—
274C2×#95—132no—
275C2×#95—131no—
276C2×#95—131no—
277C2×#95C2×D1312yes—
278C2×#95C2×D1312yes—
279C2×#95C2×D1311yescharacteristic
280C22×C13C2×C22⋊Q811yescharacteristic
281C22×C13C2×#12311yescharacteristic
282C22×C13C2×#12411yescharacteristic
283C22×C13C2×#12411yescharacteristic
284C22×C13C2×#12512yes—
285C22×C13C2×#12612yes—
286C22×C13C2×#12711yescharacteristic
287C22×C13#53212yes—
288C22×C13#53212yes—
289C22×C13#53611yescharacteristic
290C22×C13#53611yescharacteristic
291C22×C13#54112yes—
292C22×C13#54112yes—
293C22×C13#54711yescharacteristic
294C22×C13#54712yes—
295C22×C13#54711yescharacteristic
296C22×C13#54712yes—
297C22×C13D4×Q811yescharacteristic
298C22×C13D4×Q811yescharacteristic
299C22×C13#55212yes—
300C22×C13#55212yes—
301C22×C13#55612yes—
302C22×C13#55712yes—
303C4×C13—24no—
304C4×C13—44no—
305C4×C13—42no—
306C4×C13—82no—
307C4×C13—81no—
308Dic13—24no—
309Dic13—44no—
310Dic13—42no—
311Dic13—82no—
312Dic13—81no—
313Dic13#40018yescomplemented
314C23×C4—131no—
315C23×C4—131no—
316C23×C4—131no—
317C23×C4—132no—
318C23×C4—132no—
319C23×C4—131no—
320C23×C4C22×D1312yes—
321C23×C4C22×D1311yescharacteristic
322C23×C4C22×D1311yescharacteristic
323C23×C4C22×D1312yes—
324C23×C4C22×D1311yescharacteristic
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—134no—
332C2×C4⋊C4—262no—
333C2×C4⋊C4—262no—
334C2×C4⋊C4—264no—
335C2×C4⋊C4—268no—
336C2×C4⋊C4—268no—
337C2×C4⋊C4—264no—
338C2×C4⋊C4—264no—
339C2×C4⋊C4—262no—
340C2×C4⋊C4—262no—
341C2×C4⋊C4—262no—
342C2×C4⋊C4—262no—
343C2×C4⋊C4—262no—
344C2×C4⋊C4—262no—
345C2×C4⋊C4—262no—
346C2×C42—134no—
347C2×C42—264no—
348C2×C42—264no—
349C2×C42—264no—
350C2×C42—264no—
351#95—24no—
352#95—24no—
353#95—134no—
354#95—264no—
355#95—262no—
356#95—262no—
357#95—264no—
358#95—264no—
359#95—264no—
360#95—264no—
361#95—264no—
362#95—264no—
363#95C22⋊D1314yes—
364C2×C13C2×#40011yescharacteristic
365C2×C13#249612yes—
366C2×C13#249612yes—
367C2×C13#250111yescharacteristic
368C2×C13#250311yescharacteristic
369C2×C13#250612yes—
370C2×C13#250612yes—
371C2×C13#254211yescharacteristic
372C2×C13#256811yescharacteristic
373C2×C13#264211yescharacteristic
374C2×C13#285811yescharacteristic
375C24C23×D1311yescharacteristic
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—132no—
401C22×C4—132no—
402C22×C4—132no—
403C22×C4—134no—
404C22×C4—134no—
405C22×C4—132no—
406C22×C4—134no—
407C22×C4—134no—
408C22×C4—132no—
409C22×C4—261no—
410C22×C4—262no—
411C22×C4—261no—
412C22×C4—261no—
413C22×C4—261no—
414C22×C4—261no—
415C22×C4—262no—
416C22×C4—262no—
417C22×C4—262no—
418C22×C4—262no—
419C22×C4—262no—
420C22×C4—261no—
421C22×C4—261no—
422C22×C4—262no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—262no—
426C22×C4—261no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—264no—
430C22×C4—264no—
431C22×C4—262no—
432C22×C4—261no—
433C22×C4—262no—
434C22×C4D4×D1312yes—
435C22×C4D4×D1312yes—
436C22×C4Q8×D1312yes—
437C22×C4C2×C22⋊D1314yes—
438C22×C4C2×C22⋊D1312yes—
439C4⋊C4—44no—
440C4⋊C4—44no—
441C4⋊C4—268no—
442C4⋊C4—524no—
443C4⋊C4—528no—
444C4⋊C4—528no—
445C4⋊C4—524no—
446C4⋊C4—524no—
447C42—268no—
448C42—528no—
449C13#1515311yescharacteristic, complemented, Sylow
450C23C2×D4×D1311yescharacteristic
451C23C2×D4×D1311yescharacteristic
452C23C2×Q8×D1311yescharacteristic
453C23#8825411yescharacteristic
454C23#41×D1311yescharacteristic
455C23#41×D1312yes—
456C23#41×D1312yes—
457C23#41×D1312yes—
458C23#8825711yescharacteristic
459C23#8825712yes—
460C23C22×C22⋊D1311yescharacteristic
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—44no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—134no—
490C2×C4—134no—
491C2×C4—134no—
492C2×C4—138no—
493C2×C4—138no—
494C2×C4—134no—
495C2×C4—262no—
496C2×C4—262no—
497C2×C4—264no—
498C2×C4—264no—
499C2×C4—262no—
500C2×C4—262no—
501C2×C4—264no—
502C2×C4—262no—
503C2×C4—264no—
504C2×C4—264no—
505C2×C4—521no—
506C2×C4—521no—
507C2×C4—521no—
508C2×C4—521no—
509C2×C4—522no—
510C2×C4—522no—
511C2×C4—522no—
512C2×C4—522no—
513C2×C4—521no—
514C2×C4—522no—
515C2×C4—522no—
516C2×C4—524no—
517C2×C4—521no—
518C2×C4—521no—
519C2×C4—522no—
520C2×C4—524no—
521C2×C4—522no—
522C2×C4—522no—
523C2×C4#8819414yes—
524C22D13×C22⋊Q811yescharacteristic
525C22#1171933311yescharacteristic
526C22#1171933611yescharacteristic
527C22#1171933711yescharacteristic
528C22#1171935311yescharacteristic
529C22D13×#12311yescharacteristic
530C22#1171936012yes—
531C22#1171937312yes—
532C22D13×#12411yescharacteristic
533C22D13×#12411yescharacteristic
534C22#1171939012yes—
535C22D13×#12512yes—
536C22#1171939812yes—
537C22#1171940112yes—
538C22#1171940612yes—
539C22#1171940712yes—
540C22D13×#12612yes—
541C22#1171941312yes—
542C22C2×#8819411yescharacteristic
543C22Q8×C22⋊D1311yescharacteristic
544C22#1171952911yescharacteristic
545C22#1171952912yes—
546C22#1171953712yes—
547C4—24no—
548C4—44no—
549C4—42no—
550C4—81no—
551C4—82no—
552C4—138no—
553C4—264no—
554C4—524no—
555C4—522no—
556C4—1041no—
557C4—1042no—
558C2D13×#40011yescharacteristic
559C2#1311925312yes—
560C2#1311925512yes—
561C2#1311930511yescharacteristic
562C2#1311931611yescharacteristic
563C2#1311934712yes—
564C2#1311935112yes—
565C2#1311978611yescharacteristic
566C2#1312004711yescharacteristic
567C2#1312078311yescharacteristic
568C2#1312319111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, prime radical, cosocleC24×C13C24
FittingC2×C13×#400C2
hypercenterC2×#400D13
hypocenterC13#15153
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
313. Dic13#400semidirect
449. C13#15153semidirect

Maximal subgroups

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

subgroupindex
C2×#117183202
C2×#117186472
C2×#117186432
C2×#117186332
C2×#117186372
#131131022
#131130642
#95×Dic132
C2×C13×#4002
#1515313