Finite Group Databasebeta

← #16023239

Subgroups — #16023239

Order 3328.

3038 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88200C211yesmaximal, characteristic
2C2×D13×#117C211yesmaximal, characteristic
3#13117859C214yesmaximal, complemented
4#13117837C214yesmaximal, complemented
5#13117706C214yesmaximal, complemented
6#13117686C214yesmaximal
7#13117512C214yesmaximal, complemented
8#13117452C211yesmaximal, characteristic, complemented
9#13117422C211yesmaximal, characteristic, complemented
10C4×#88200C214yesmaximal, complemented
11#13117215C211yesmaximal, characteristic
12#13117192C211yesmaximal, characteristic, complemented
13C2×C13×#519C211yesmaximal, characteristic, complemented
14C23×Q8×C13C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C13×#519—28no—
17C2×C4×Q8×C13C2214yescomplemented
18C2×C4×Q8×C13C2214yescomplemented
19C2×C13×#117C2214yes—
20C2×C13×#117C2211yescharacteristic
21C2×C13×#117C2211yescharacteristic
22C2×#88200C4116yescomplemented
23C2×#88200C2212yes—
24C2×#88200C2212yes—
25C2×#88200C2212yes—
26C2×#88200C2212yes—
27C22×#6103C2212yes—
28C2×#88180C2211yescharacteristic
29C2×#88180C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×#6101C2212yes—
32D13×#117—28no—
33C2×#88146C2212yes—
34C2×C4⋊C4×D13C2212yes—
35C2×C22⋊C4×D13C2212yes—
36C2×#88131C2212yes—
37C2×#88126C2212yes—
38C2×C42×D13C2212yes—
39#11718891C2214yescomplemented
40#11718891C2214yescomplemented
41#11718872C2214yes—
42#11718651C2218yes—
43#11718650C2218yes—
44#11718648C2212yes—
45#11718648C2212yes—
46#11718639C2218yescomplemented
47C4⋊C4×Dic13C2214yescomplemented
48#11718634C2214yescomplemented
49#11718633C2218yescomplemented
50#11718616C2212yes—
51#11718604C2212yes—
52#11718603C2214yes—
53C22⋊C4×Dic13C2214yes—
54#11718601C2218yes—
55C4×#6103C2212yes—
56C4×#6103C2212yes—
57C4×#6103C2218yes—
58C4×C4⋊Dic13C2214yescomplemented
59#11718594C2218yescomplemented
60C4×#6101C2218yescomplemented
61#11718589C2214yescomplemented
62C24×D13C2311yescharacteristic
63C22×Q8×C13—24no—
64C22×Q8×C13—24no—
65C22×Q8×C13C2×C418yescomplemented
66C22×Q8×C13C2312yes—
67C22×Q8×C13C2312yes—
68C23×C4×C13C2312yes—
69C23×C4×C13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2312yes—
72C22×C4×D13—24no—
73C22×C4×D13—24no—
74C22×C4×D13C2×C418yes—
75C22×C4×D13C2314yes—
76C22×C4×D13C2311yescharacteristic
77C22×C4×D13C2311yescharacteristic
78C22×C4×D13C2311yescharacteristic
79C22×C4×D13C2311yescharacteristic
80C4×Q8×C13—216no—
81C4×Q8×C13—216no—
82C13×#117—24no—
83C13×#117—216no—
84C13×#117D418yes—
85C2×C13×C4⋊C4C2318yes—
86C2×C13×C4⋊C4C2312yes—
87C2×C13×C4⋊C4C2312yes—
88C2×C13×C22⋊C4C2312yes—
89C2×C13×C22⋊C4C2312yes—
90C2×C42×C13C2312yes—
91C2×C42×C13C2318yes—
92C2×C42×C13C2312yes—
93C2×C22⋊Dic13C2312yes—
94C2×C22⋊Dic13C2312yes—
95#88200C2×C4116yes—
96#88200C2×C4116yes—
97#88200C2×C4116yescomplemented
98#88200C2×C4116yescomplemented
99C2×#6103C2×C4116yes—
100C2×#6103C2314yes—
101C2×#6103C2314yes—
102C2×#6103C2314yes—
103C2×#6103C2314yes—
104C2×#6103C2314yes—
105#88180—24no—
106#88180—24no—
107C2×C4⋊Dic13C2×C418yescomplemented
108C2×C4⋊Dic13C2312yes—
109C2×C4⋊Dic13C2312yes—
110C2×C4⋊Dic13C2312yes—
111C2×C4⋊Dic13C2312yes—
112C2×#6101C2×C4116yescomplemented
113C2×#6101C2314yes—
114C2×#6101C2318yes—
115C2×#6101C2314yes—
116C2×#6101C2314yes—
117C2×C4×Dic13C2312yes—
118C2×C4×Dic13C2314yes—
119C2×C4×Dic13C2312yes—
120C2×C4×Dic13C2318yes—
121#88146—28no—
122C4⋊C4×D13—28no—
123C22⋊C4×D13—28no—
124#88131—28no—
125#88126—28no—
126C42×D13—28no—
127#88071C2318yes—
128#88071C2314yes—
129#88071C2318yes—
130#88071C2314yes—
131#88071C2318yes—
132#88071C2318yes—
133#34203—131nomaximal, Sylow
134C24×C13C2411yescharacteristic
135C23×D13—22no—
136C23×D13—22no—
137C23×D13—24no—
138C23×D13—42no—
139C23×D13C22×C414yes—
140C23×D13C2411yescharacteristic
141C23×D13C2411yescharacteristic
142C2×Q8×C13—232no—
143C2×Q8×C13—24no—
144C2×Q8×C13—24no—
145C2×Q8×C13—24no—
146C2×Q8×C13—24no—
147C2×Q8×C13C22×C418yes—
148C2×Q8×C13C22×C418yes—
149C22×C4×C13—24no—
150C22×C4×C13—24no—
151C22×C4×C13C22×C418yes—
152C22×C4×C13C22×C414yes—
153C22×C4×C13C2×D414yes—
154C22×C4×C13#4114yes—
155C22×C4×C13C2414yes—
156C22×C4×C13C2414yes—
157C22×C4×C13C2414yes—
158C22×C4×C13C2411yescharacteristic
159C22×C4×C13C2411yescharacteristic
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—44no—
163C22×Dic13C22×C414yes—
164C22×Dic13C22×C418yes—
165C22×Dic13C2414yes—
166C22×Dic13C2414yes—
167C22×Dic13C2411yescharacteristic
168C22×Dic13C2414yes—
169C22×Dic13C2411yescharacteristic
170C2×C4×D13—232no—
171C2×C4×D13—22no—
172C2×C4×D13—22no—
173C2×C4×D13—22no—
174C2×C4×D13—22no—
175C2×C4×D13—22no—
176C2×C4×D13—22no—
177C2×C4×D13—22no—
178C2×C4×D13—22no—
179C2×C4×D13—28no—
180C2×C4×D13—28no—
181C2×C4×D13—44no—
182C2×C4×D13C22×C414yes—
183C2×C4×D13C22×C414yes—
184C2×C4×D13C22×C414yes—
185C2×C4×D13C22×C414yes—
186C13×C4⋊C4—216no—
187C13×C4⋊C4—24no—
188C13×C4⋊C4C2×D418yes—
189C13×C22⋊C4—24no—
190C13×C22⋊C4C2×D418yes—
191C42×C13—216no—
192C42×C13—24no—
193C42×C13C2×D418yes—
194C22⋊Dic13—24no—
195C22⋊Dic13—24no—
196#6103—28no—
197#6103—28no—
198#6103—44no—
199#6103C22×C4116yes—
200#6103C22×C4116yes—
201C4⋊Dic13—24no—
202C4⋊Dic13—24no—
203C4⋊Dic13C22×C418yes—
204C4⋊Dic13C22×C418yes—
205#6101—28no—
206#6101—48no—
207#6101C22×C4116yes—
208#6101C22×C4116yes—
209C4×Dic13—24no—
210C4×Dic13—28no—
211C4×Dic13—24no—
212C4×Dic13—48no—
213C22×C22⋊Q8—131no—
214C2×#519D1311yescharacteristic, complemented
215C22×#117—131no—
216#2362—134no—
217#2360—134no—
218#2344—134no—
219#2342—134no—
220#2323—134no—
221#2316—131no—
222#2310—131no—
223C4×C22⋊Q8—134no—
224#2280—131no—
225#2274—131no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13C23×C412yes—
229C23×C13C22×D412yes—
230C23×C13C2×#4112yes—
231C23×C13C2511yescharacteristic
232C22×D13—21no—
233C22×D13—21no—
234C22×D13—22no—
235C22×D13—28no—
236C22×D13—21no—
237C22×D13—21no—
238C22×D13—22no—
239C22×D13—22no—
240C22×D13—28no—
241C22×D13—44no—
242C22×D13—48no—
243C22×D13—48no—
244C22×D13C23×C412yes—
245C22×D13C23×C412yes—
246C22×D132−1+414yes—
247Q8×C13—216no—
248Q8×C13—216no—
249C2×C4×C13—216no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—24no—
255C2×C4×C13—24no—
256C2×C4×C13—24no—
257C2×C4×C13C4×D4116yes—
258C2×C4×C13C23×C418yes—
259C2×C4×C13C23×C412yes—
260C2×C4×C13C23×C412yes—
261C2×C4×C13C22×D418yes—
262C2×C4×C13C22×D412yes—
263C2×C4×C13C22×D412yes—
264C2×C4×C13C2×#4112yes—
265C2×C4×C13C2×#4112yes—
266C2×Dic13—28no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—28no—
272C2×Dic13—24no—
273C2×Dic13—24no—
274C2×Dic13—24no—
275C2×Dic13—24no—
276C2×Dic13—24no—
277C2×Dic13—24no—
278C2×Dic13—48no—
279C2×Dic13C23×C412yes—
280C2×Dic13C23×C412yes—
281C2×Dic13C23×C418yes—
282C4×D13—28no—
283C4×D13—28no—
284C4×D13—28no—
285C4×D13—28no—
286C4×D13—416no—
287C23×Q8C2×D1311yescharacteristic
288C24×C4—131no—
289C2×C22⋊Q8—1316no—
290C2×C22⋊Q8—132no—
291C2×C22⋊Q8—132no—
292C2×C22⋊Q8—132no—
293C2×C22⋊Q8—132no—
294#519—28no—
295C2×C4×Q8C2×D1314yescomplemented
296C2×C4×Q8C2×D1314yescomplemented
297C2×#117—131no—
298C2×#117—131no—
299C2×#117—132no—
300C2×#117—132no—
301C2×#117—132no—
302C2×#117—268no—
303C2×#117C2×D1311yescharacteristic
304C2×#117C2×D1314yes—
305C2×#117C2×D1311yescharacteristic
306C22×C4⋊C4—131no—
307C22×C4⋊C4—132no—
308C22×C4⋊C4—132no—
309C22×C22⋊C4—132no—
310C22×C22⋊C4—132no—
311C22×C42—132no—
312#391—134no—
313#391—134no—
314#389—134no—
315#389—138no—
316#389—134no—
317#388—138no—
318#388—138no—
319#387—138no—
320#387—138no—
321#385—138no—
322#381—134no—
323#381—132no—
324#380—132no—
325#380—132no—
326#380—134no—
327#379—132no—
328C4×C4⋊C4—134no—
329C4×C4⋊C4—134no—
330C4×C4⋊C4—138no—
331C4×C22⋊C4—134no—
332C4×C22⋊C4—138no—
333C4×C22⋊C4—132no—
334C4×C22⋊C4—132no—
335C22×C13—22no—
336C22×C13—22no—
337C22×C13—24no—
338C22×C13—24no—
339C22×C13C2×C4×D414yes—
340C22×C13C24×C411yescharacteristic
341C22×C13C23×D411yescharacteristic
342C22×C13C22×#4111yescharacteristic
343C22×C13C2×2−1+412yes—
344C22×C13#58512yes—
345C2×D13—22no—
346C2×D13—22no—
347C2×D13—24no—
348C2×D13—24no—
349C2×D13—22no—
350C2×D13—22no—
351C2×D13—22no—
352C2×D13—416no—
353C2×D13—42no—
354C2×D13—42no—
355C2×D13#51914yescomplemented
356C4×C13—28no—
357C4×C13—28no—
358C4×C13—44no—
359C4×C13C2×C4×D414yes—
360C4×C13C2×C4×D414yes—
361Dic13—22no—
362Dic13—22no—
363Dic13—28no—
364Dic13—44no—
365Dic13—44no—
366C25—131no—
367C22×Q8—24no—
368C22×Q8—24no—
369C22×Q8C4×D1318yescomplemented
370C22×Q8C22×D1312yes—
371C22×Q8C22×D1312yes—
372C23×C4—131no—
373C23×C4—132no—
374C23×C4—138no—
375C23×C4—131no—
376C23×C4—131no—
377C23×C4—131no—
378C23×C4—131no—
379C23×C4—134no—
380C23×C4—264no—
381C23×C4—264no—
382C23×C4C22×D1312yes—
383C23×C4C22×D1311yescharacteristic
384C22⋊Q8—1316no—
385C22⋊Q8—1316no—
386C22⋊Q8—1316no—
387C22⋊Q8—1316no—
388C4×Q8—216no—
389C4×Q8—216no—
390#117—24no—
391#117—216no—
392#117—264no—
393#117—264no—
394#117—268no—
395#117—268no—
396#117—268no—
397#117C22⋊D1318yes—
398C2×C4⋊C4—1316no—
399C2×C4⋊C4—138no—
400C2×C4⋊C4—134no—
401C2×C4⋊C4—134no—
402C2×C4⋊C4—132no—
403C2×C4⋊C4—132no—
404C2×C4⋊C4—134no—
405C2×C4⋊C4—132no—
406C2×C4⋊C4—132no—
407C2×C4⋊C4—138no—
408C2×C4⋊C4—268no—
409C2×C4⋊C4C22×D1312yes—
410C2×C4⋊C4C22×D1318yes—
411C2×C4⋊C4C22×D1312yes—
412C2×C22⋊C4—1316no—
413C2×C22⋊C4—134no—
414C2×C22⋊C4—134no—
415C2×C22⋊C4—132no—
416C2×C22⋊C4—132no—
417C2×C22⋊C4—134no—
418C2×C22⋊C4—134no—
419C2×C22⋊C4—134no—
420C2×C22⋊C4—268no—
421C2×C22⋊C4C22×D1312yes—
422C2×C22⋊C4C22×D1312yes—
423C2×C42—134no—
424C2×C42—132no—
425C2×C42—132no—
426C2×C42—138no—
427C2×C42—268no—
428C2×C42C22×D1312yes—
429C2×C42C22×D1318yes—
430C2×C42C22×D1312yes—
431#95—134no—
432#95—138no—
433#95—134no—
434#95—138no—
435#95—138no—
436#95—138no—
437C2×C13—24no—
438C2×C13C22×C4×D411yescharacteristic
439C2×C13C2×#51911yescharacteristic
440C2×C13#342811yescharacteristic
441C2×C13#348912yes—
442C2×C13#349512yes—
443D13—24no—
444D13—42no—
445C24—131no—
446C24—131no—
447C24—134no—
448C24—264no—
449C24—262no—
450C24—262no—
451C24—522no—
452C24C23×D1311yescharacteristic
453C2×Q8—232no—
454C2×Q8—24no—
455C2×Q8—24no—
456C2×Q8—24no—
457C2×Q8—24no—
458C2×Q8C2×C4×D1318yes—
459C2×Q8C2×C4×D1318yes—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—134no—
463C22×C4—131no—
464C22×C4—134no—
465C22×C4—131no—
466C22×C4—138no—
467C22×C4—134no—
468C22×C4—134no—
469C22×C4—134no—
470C22×C4—134no—
471C22×C4—134no—
472C22×C4—134no—
473C22×C4—268no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—2632no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—268no—
486C22×C4—524no—
487C22×C4—524no—
488C22×C4C2×C4×D1318yes—
489C22×C4C2×C4×D1314yes—
490C22×C4#612714yes—
491C22×C4C2×C22⋊D1314yes—
492C22×C4C23×D1314yes—
493C22×C4C23×D1314yes—
494C22×C4C23×D1314yes—
495C22×C4C23×D1311yescharacteristic
496C22×C4C23×D1311yescharacteristic
497C4⋊C4—216no—
498C4⋊C4—24no—
499C4⋊C4—1316no—
500C4⋊C4—1316no—
501C4⋊C4—138no—
502C4⋊C4—138no—
503C4⋊C4—264no—
504C4⋊C4—268no—
505C4⋊C4—264no—
506C4⋊C4—528no—
507C4⋊C4C2×C22⋊D1318yes—
508C22⋊C4—24no—
509C22⋊C4—1316no—
510C22⋊C4—1316no—
511C22⋊C4—268no—
512C22⋊C4—264no—
513C22⋊C4—264no—
514C22⋊C4—268no—
515C22⋊C4—524no—
516C22⋊C4C2×C22⋊D1318yes—
517C42—216no—
518C42—24no—
519C42—264no—
520C42—268no—
521C42—264no—
522C42—528no—
523C42C2×C22⋊D1318yes—
524C13#3420311yescharacteristic, complemented, Sylow
525C23—22no—
526C23—22no—
527C23—132no—
528C23—134no—
529C23—132no—
530C23—268no—
531C23—261no—
532C23—262no—
533C23—261no—
534C23—268no—
535C23—261no—
536C23—262no—
537C23—262no—
538C23—261no—
539C23—524no—
540C23—528no—
541C23—528no—
542C23C22×C4×D1312yes—
543C23C2×#612712yes—
544C23C22×C22⋊D1312yes—
545C23C24×D1311yescharacteristic
546Q8—216no—
547Q8—216no—
548C2×C4—216no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—138no—
557C2×C4—132no—
558C2×C4—132no—
559C2×C4—268no—
560C2×C4—261no—
561C2×C4—261no—
562C2×C4—268no—
563C2×C4—261no—
564C2×C4—261no—
565C2×C4—268no—
566C2×C4—268no—
567C2×C4—268no—
568C2×C4—268no—
569C2×C4—264no—
570C2×C4—264no—
571C2×C4—264no—
572C2×C4—264no—
573C2×C4—264no—
574C2×C4—264no—
575C2×C4—5216no—
576C2×C4—528no—
577C2×C4C4×C22⋊D13116yes—
578C2×C4C22×C4×D1318yes—
579C2×C4C22×C4×D1312yes—
580C2×C4C22×C4×D1312yes—
581C2×C4C2×#612712yes—
582C2×C4C2×#612712yes—
583C2×C4C22×C22⋊D1318yes—
584C2×C4C22×C22⋊D1312yes—
585C2×C4C22×C22⋊D1312yes—
586C22—24no—
587C22—22no—
588C22—22no—
589C22—24no—
590C22—134no—
591C22—264no—
592C22—262no—
593C22—262no—
594C22—264no—
595C22—262no—
596C22—262no—
597C22—262no—
598C22—5216no—
599C22—522no—
600C22—522no—
601C22C2×C4×C22⋊D1314yes—
602C22C23×C4×D1311yescharacteristic
603C22C22×#612711yescharacteristic
604C22D13×2−1+412yes—
605C22#1171965212yes—
606C22C23×C22⋊D1311yescharacteristic
607C4—28no—
608C4—28no—
609C4—44no—
610C4—262no—
611C4—262no—
612C4—268no—
613C4—524no—
614C4—524no—
615C4C2×C4×C22⋊D1314yes—
616C4C2×C4×C22⋊D1314yes—
617C2—24no—
618C2—264no—
619C2—522no—
620C2C22×C4×C22⋊D1311yescharacteristic
621C2D13×#51911yescharacteristic
622C2#1312803811yescharacteristic
623C2#1312850912yes—
624C2#1312857812yes—
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC2×C13×#519C2
socle, cosocleC23×C13C25
prime radicalC24×D13C23
hypercenterC2×#519D13
hypocenterC13#34203
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
3. #13117859C2semidirect
4. #13117837C2semidirect
5. #13117706C2semidirect
7. #13117512C2semidirect
8. #13117452C2semidirect
9. #13117422C2semidirect
10. C4×#88200C2semidirect
12. #13117192C2semidirect
13. C2×C13×#519C2semidirect
17. C2×C4×Q8×C13C22semidirect
18. C2×C4×Q8×C13C22semidirect
22. C2×#88200C4semidirect
39. #11718891C22semidirect
40. #11718891C22semidirect
46. #11718639C22semidirect
47. C4⋊C4×Dic13C22semidirect
48. #11718634C22semidirect
49. #11718633C22semidirect
58. C4×C4⋊Dic13C22semidirect
59. #11718594C22semidirect
60. C4×#6101C22semidirect
61. #11718589C22semidirect
65. C22×Q8×C13C2×C4semidirect
97. #88200C2×C4semidirect
98. #88200C2×C4semidirect
107. C2×C4⋊Dic13C2×C4semidirect
112. C2×#6101C2×C4semidirect
214. C2×#519D13semidirect
295. C2×C4×Q8C2×D13semidirect
296. C2×C4×Q8C2×D13semidirect
355. C2×D13#519semidirect
369. C22×Q8C4×D13semidirect
524. C13#34203semidirect

Maximal subgroups

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

subgroupindex
C22×#882002
C2×D13×#1172
#131178592
#131178372
#131177062
#131176862
#131175122
#131174522
#131174222
C4×#882002
#131172152
#131171922
C2×C13×#5192
#3420313