Finite Group Databasebeta

← #15784681

Subgroups — #15784681

Order 3328.

2118 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88131C211yesmaximal, characteristic
2C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
3C2×#11718310C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic13C212yesmaximal
5#13113090C211yesmaximal, characteristic, complemented
6#13113087C212yesmaximal, complemented
7#13113086C211yesmaximal, characteristic, complemented
8#13113081C211yesmaximal, characteristic
9#13113079C212yesmaximal
10#95×Dic13C212yesmaximal, complemented
11C13×#1439C211yesmaximal, characteristic
12C24×Dic13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2212yes—
15C22×C13×C22⋊C4C2211yescharacteristic
16C22×C22⋊Dic13C2212yes—
17C22×C22⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×#6101C2212yes—
20C22×#6101C2211yescharacteristic
21C22×#6101C2211yescharacteristic
22C22×C4×Dic13C2212yes—
23C22×C4×Dic13C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C2×#88131—24no—
27C2×#88131—24no—
28C2×#88131C418yescomplemented
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37C2×#88071C2212yes—
38C4⋊C4×Dic13—24no—
39C22⋊C4×Dic13—28no—
40#11718310—24no—
41C25×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×Dic13—22no—
47C23×Dic13—22no—
48C23×Dic13—22no—
49C23×Dic13—22no—
50C23×Dic13C2×C414yes—
51C23×Dic13D414yes—
52C23×Dic13Q814yes—
53C23×Dic13C2311yescharacteristic
54C23×Dic13C2312yes—
55C23×Dic13C2312yes—
56C23×Dic13C2311yescharacteristic
57C23×Dic13C2311yescharacteristic
58C23×Dic13C2311yescharacteristic
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—24no—
61C2×C13×C22⋊C4—24no—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4—24no—
65C2×C13×C22⋊C4—24no—
66C2×C13×C22⋊C4C2×C414yes—
67C2×C22⋊Dic13—24no—
68C2×C22⋊Dic13—22no—
69C2×C22⋊Dic13—22no—
70C2×C22⋊Dic13—24no—
71C2×C22⋊Dic13—24no—
72C2×C22⋊Dic13C2×C414yes—
73C2×C4⋊Dic13—22no—
74C2×C4⋊Dic13—24no—
75C2×#6101—22no—
76C2×#6101—22no—
77C2×#6101—24no—
78C2×#6101—22no—
79C2×#6101—22no—
80C2×#6101—24no—
81C2×#6101—24no—
82C2×#6101C2×C414yes—
83C2×#6101C2×C414yes—
84C2×C4×Dic13—22no—
85C2×C4×Dic13—22no—
86C2×C4×Dic13—24no—
87C2×C4×Dic13—24no—
88C2×C4×Dic13—24no—
89C2×C4×Dic13—24no—
90C2×C4×Dic13—24no—
91C2×C4×Dic13—24no—
92C2×C4×Dic13C2×C414yes—
93C2×C4×Dic13C2×C414yes—
94C2×C4×Dic13D414yes—
95C2×C4×Dic13D414yes—
96#88131—232no—
97C13×#95—22no—
98C13×#95—24no—
99#88071—22no—
100#88071—24no—
101#88071—24no—
102#88071—24no—
103#88071—24no—
104#88071—24no—
105#88071—24no—
106#13852—131nomaximal, Sylow
107C24×C13—21no—
108C24×C13—21no—
109C24×C13—22no—
110C24×C13—22no—
111C24×C13—22no—
112C24×C13—22no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13C22×C412yes—
116C24×C13C2×D412yes—
117C24×C13C2×Q812yes—
118C24×C13C2411yescharacteristic
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13C22×C412yes—
138C22×C4×C13C22×C412yes—
139C22×C4×C13C2×D412yes—
140C22×C4×C13C2×D412yes—
141C22×C4×C13#4114yes—
142C22×C4×C13#4114yes—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—28no—
150C22×Dic13—28no—
151C22×Dic13—28no—
152C22×Dic13—28no—
153C22×Dic13—28no—
154C22×Dic13—28no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13C4⋊C4116yescomplemented
172C22×Dic13C22×C412yes—
173C22×Dic13C22×C412yes—
174C22×Dic13C22×C412yes—
175C22×Dic13C22×C412yes—
176C22×Dic13C2×D412yes—
177C22×Dic13C2×D412yes—
178C22×Dic13C2×D412yes—
179C22×Dic13C2×D412yes—
180C22×Dic13C2×D412yes—
181C22×Dic13C2×D412yes—
182C22×Dic13C2×Q812yes—
183C22×Dic13C2×Q812yes—
184C22×Dic13#4114yes—
185C22×Dic13#4114yes—
186C22×Dic13#4112yes—
187C22×Dic13#4112yes—
188C13×C4⋊C4—28no—
189C13×C22⋊C4—216no—
190C13×C22⋊C4—28no—
191C22⋊Dic13—216no—
192C22⋊Dic13—28no—
193C4⋊Dic13—28no—
194#6101—216no—
195#6101—28no—
196#6101—28no—
197C4×Dic13—28no—
198C4×Dic13—48no—
199C4×Dic13—48no—
200C4×Dic13C22⋊C4116yescomplemented
201C22×#117—131no—
202C2×C4×C4⋊C4—131no—
203C2×C4×C4⋊C4—131no—
204C2×C4×C22⋊C4—132no—
205#1441—131no—
206#1441—132no—
207#1441—131no—
208#1439—132no—
209#1439—131no—
210#1439D1311yescharacteristic
211C4×#95—132no—
212C23×C13—22no—
213C23×C13—22no—
214C23×C13—24no—
215C23×C13—24no—
216C23×C13—22no—
217C23×C13—22no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—24no—
221C23×C13—24no—
222C23×C13—24no—
223C23×C13—24no—
224C23×C13—41no—
225C23×C13—42no—
226C23×C13—41no—
227C23×C13—42no—
228C23×C13—42no—
229C23×C13—42no—
230C23×C13—42no—
231C23×C13—42no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13C2×C4⋊C414yes—
235C23×C13C23×C411yescharacteristic
236C23×C13C22×D411yescharacteristic
237C23×C13C22×D411yescharacteristic
238C23×C13C22×D411yescharacteristic
239C23×C13C22×Q811yescharacteristic
240C23×C13C2×#4111yescharacteristic
241C23×C13C2×#4111yescharacteristic
242C23×C13C2×#4112yes—
243C23×C13C2×#4112yes—
244C23×C13C2×#4112yes—
245C23×C13C2×#4112yes—
246C2×C4×C13—24no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—24no—
250C2×C4×C13—22no—
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×C13—24no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13C2×C22⋊C414yes—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—24no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—24no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—232no—
281C2×Dic13—22no—
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—24no—
286C2×Dic13—24no—
287C2×Dic13—24no—
288C2×Dic13—24no—
289C2×Dic13—42no—
290C2×Dic13—42no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—42no—
296C2×Dic13—42no—
297C2×Dic13—42no—
298C2×Dic13—42no—
299C2×Dic13—42no—
300C2×Dic13C2×C22⋊C414yes—
301C2×Dic13C2×C22⋊C414yes—
302C2×Dic13C2×C4⋊C414yes—
303C2×Dic13C2×C4⋊C414yes—
304C2×Dic13#11714yes—
305C2×Dic13#12114yes—
306C2×Dic13#12114yes—
307C2×Dic13C22⋊Q814yes—
308C2×Dic13C22⋊Q814yes—
309C24×C4—131no—
310C2×#117—138no—
311C2×#117—264no—
312C2×#117—264no—
313C22×C4⋊C4—131no—
314C22×C4⋊C4—131no—
315C22×C4⋊C4—132no—
316C22×C4⋊C4—131no—
317C22×C4⋊C4C2×D1311yescharacteristic
318C22×C22⋊C4—131no—
319C22×C22⋊C4—132no—
320C22×C22⋊C4C2×D1312yes—
321C22×C22⋊C4C2×D1311yescharacteristic
322C22×C42—131no—
323C22×C42—131no—
324C22×C42—132no—
325C22×C42—132no—
326C4×C4⋊C4—264no—
327C4×C4⋊C4—264no—
328C4×C22⋊C4—268no—
329C2×#95—132no—
330C2×#95—132no—
331C2×#95—132no—
332C2×#95—132no—
333C2×#95—131no—
334C2×#95—132no—
335C2×#95—132no—
336C2×#95C2×D1312yes—
337C2×#95C2×D1311yescharacteristic
338C22×C13—24no—
339C22×C13—28no—
340C22×C13—42no—
341C22×C13—42no—
342C22×C13—44no—
343C22×C13—42no—
344C22×C13—42no—
345C22×C13—44no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13—44no—
349C22×C13C22×C22⋊C411yescharacteristic
350C22×C13C22×C4⋊C411yescharacteristic
351C22×C13C2×#11711yescharacteristic
352C22×C13C4×#4112yes—
353C22×C13C4×#4112yes—
354C22×C13C2×#12111yescharacteristic
355C22×C13C2×#12111yescharacteristic
356C22×C13C2×C22⋊Q811yescharacteristic
357C22×C13C2×C22⋊Q811yescharacteristic
358C22×C13#52512yes—
359C22×C13#52511yescharacteristic
360C22×C13#52512yes—
361C22×C13#52512yes—
362C22×C13#52511yescharacteristic
363C22×C13#52912yes—
364C22×C13#52912yes—
365C22×C13#52912yes—
366C22×C13#52912yes—
367C22×C13#53212yes—
368C22×C13#53211yescharacteristic
369C22×C13#53211yescharacteristic
370C22×C13#53312yes—
371C22×C13#53312yes—
372C4×C13—24no—
373C4×C13—44no—
374C4×C13—44no—
375C4×C13—42no—
376Dic13—24no—
377Dic13—24no—
378Dic13—44no—
379Dic13—44no—
380Dic13—42no—
381Dic13#38018yes—
382C25C22×D1311yescharacteristic
383C23×C4—131no—
384C23×C4—134no—
385C23×C4—134no—
386C23×C4—134no—
387C23×C4—131no—
388C23×C4—131no—
389C23×C4—131no—
390C23×C4—132no—
391C23×C4—132no—
392C23×C4—262no—
393C23×C4—262no—
394C23×C4—262no—
395C23×C4—262no—
396C23×C4C22×D1311yescharacteristic
397C23×C4C22×D1312yes—
398C23×C4C22×D1312yes—
399C23×C4C22×D1311yescharacteristic
400#117—2632no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—134no—
404C2×C4⋊C4—134no—
405C2×C4⋊C4—262no—
406C2×C4⋊C4—262no—
407C2×C4⋊C4—264no—
408C2×C4⋊C4—264no—
409C2×C4⋊C4—264no—
410C2×C4⋊C4—262no—
411C2×C4⋊C4—262no—
412C2×C4⋊C4—262no—
413C2×C4⋊C4—264no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—134no—
420C2×C22⋊C4—262no—
421C2×C22⋊C4—262no—
422C2×C22⋊C4—264no—
423C2×C22⋊C4—264no—
424C2×C22⋊C4—264no—
425C2×C22⋊C4C4×D1314yes—
426C2×C42—134no—
427C2×C42—134no—
428C2×C42—134no—
429C2×C42—134no—
430C2×C42—262no—
431C2×C42—262no—
432C2×C42—264no—
433C2×C42—264no—
434C2×C42—264no—
435C2×C42—264no—
436C2×C42—264no—
437C2×C42—264no—
438#95—22no—
439#95—24no—
440#95—264no—
441#95—264no—
442#95—264no—
443#95—264no—
444#95—264no—
445#95—262no—
446#95—264no—
447C2×C13—44no—
448C2×C13C2×#38011yescharacteristic
449C2×C13#229612yes—
450C2×C13#229711yescharacteristic
451C2×C13#229711yescharacteristic
452C2×C13#229812yes—
453C2×C13#239211yescharacteristic
454C2×C13#239211yescharacteristic
455C2×C13#239212yes—
456C2×C13#239611yescharacteristic
457C2×C13#239611yescharacteristic
458C2×C13#239612yes—
459C24—21no—
460C24—21no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—21no—
466C24—21no—
467C24C2×C4×D1312yes—
468C24D4×D1312yes—
469C24Q8×D1312yes—
470C24C23×D1311yescharacteristic
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—132no—
490C22×C4—132no—
491C22×C4—132no—
492C22×C4—132no—
493C22×C4—132no—
494C22×C4—132no—
495C22×C4—132no—
496C22×C4—1316no—
497C22×C4—132no—
498C22×C4—132no—
499C22×C4—132no—
500C22×C4—132no—
501C22×C4—132no—
502C22×C4—132no—
503C22×C4—132no—
504C22×C4—134no—
505C22×C4—134no—
506C22×C4—268no—
507C22×C4—268no—
508C22×C4—268no—
509C22×C4—268no—
510C22×C4—268no—
511C22×C4—268no—
512C22×C4—261no—
513C22×C4—261no—
514C22×C4—262no—
515C22×C4—262no—
516C22×C4—261no—
517C22×C4—261no—
518C22×C4—262no—
519C22×C4—262no—
520C22×C4—262no—
521C22×C4—262no—
522C22×C4—261no—
523C22×C4—261no—
524C22×C4—262no—
525C22×C4—262no—
526C22×C4—262no—
527C22×C4—262no—
528C22×C4—262no—
529C22×C4—262no—
530C22×C4—262no—
531C22×C4—262no—
532C22×C4—262no—
533C22×C4—262no—
534C22×C4C2×C4×D1312yes—
535C22×C4C2×C4×D1312yes—
536C22×C4D4×D1312yes—
537C22×C4D4×D1312yes—
538C22×C4#612914yes—
539C22×C4#612914yes—
540C4⋊C4—28no—
541C4⋊C4—268no—
542C4⋊C4—2616no—
543C4⋊C4—268no—
544C4⋊C4—268no—
545C22⋊C4—216no—
546C22⋊C4—28no—
547C22⋊C4—268no—
548C22⋊C4—2616no—
549C42—1316no—
550C42—268no—
551C42—528no—
552C42—528no—
553C13#1385211yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—22no—
560C23—22no—
561C23—24no—
562C23—24no—
563C23—22no—
564C23—22no—
565C23—24no—
566C23—41no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—41no—
572C23—41no—
573C23—42no—
574C23—42no—
575C23—41no—
576C23C4⋊C4×D1314yes—
577C23C22×C4×D1311yescharacteristic
578C23C2×D4×D1311yescharacteristic
579C23C2×D4×D1311yescharacteristic
580C23C2×D4×D1311yescharacteristic
581C23C2×#612912yes—
582C23C2×#612912yes—
583C23C2×Q8×D1311yescharacteristic
584C23#41×D1311yescharacteristic
585C23#41×D1311yescharacteristic
586C23#41×D1312yes—
587C23#41×D1312yes—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—134no—
612C2×C4—134no—
613C2×C4—134no—
614C2×C4—134no—
615C2×C4—134no—
616C2×C4—134no—
617C2×C4—134no—
618C2×C4—134no—
619C2×C4—134no—
620C2×C4—2632no—
621C2×C4—262no—
622C2×C4—262no—
623C2×C4—264no—
624C2×C4—262no—
625C2×C4—262no—
626C2×C4—264no—
627C2×C4—262no—
628C2×C4—262no—
629C2×C4—262no—
630C2×C4—262no—
631C2×C4—262no—
632C2×C4—264no—
633C2×C4—264no—
634C2×C4—264no—
635C2×C4—264no—
636C2×C4—264no—
637C2×C4—264no—
638C2×C4—264no—
639C2×C4—522no—
640C2×C4—521no—
641C2×C4—522no—
642C2×C4—522no—
643C2×C4—522no—
644C2×C4—522no—
645C2×C4—522no—
646C2×C4—522no—
647C2×C4—521no—
648C2×C4—522no—
649C2×C4—522no—
650C2×C4C22⋊C4×D1314yes—
651C22—24no—
652C22—28no—
653C22—42no—
654C22—42no—
655C22—44no—
656C22—42no—
657C22—42no—
658C22—44no—
659C22—42no—
660C22—42no—
661C22—44no—
662C22C2×C22⋊C4×D1311yescharacteristic
663C22C2×C4⋊C4×D1311yescharacteristic
664C22D13×#11711yescharacteristic
665C22C4×#612912yes—
666C22C4×#612912yes—
667C22#1171929112yes—
668C22#1171929111yescharacteristic
669C22#1171930112yes—
670C22#1171930512yes—
671C22D13×#12111yescharacteristic
672C22D13×#12111yescharacteristic
673C22#1171931112yes—
674C22#1171932712yes—
675C22#1171932712yes—
676C22D13×C22⋊Q811yescharacteristic
677C22D13×C22⋊Q811yescharacteristic
678C22#1171935412yes—
679C22#1171936112yes—
680C22#1171936111yescharacteristic
681C22#1171937311yescharacteristic
682C22#1171938512yes—
683C22#1171941112yes—
684C22#1171942111yescharacteristic
685C4—24no—
686C4—44no—
687C4—44no—
688C4—42no—
689C4—138no—
690C4—264no—
691C4—264no—
692C4—524no—
693C4—524no—
694C4—522no—
695C2—44no—
696C2D13×#38011yescharacteristic
697C2#1311731512yes—
698C2#1311732111yescharacteristic
699C2#1311732311yescharacteristic
700C2#1311733012yes—
701C2#1311807111yescharacteristic
702C2#1311807311yescharacteristic
703C2#1311807912yes—
704C2#1311810311yescharacteristic
705C2#1311810511yescharacteristic
706C2#1311811112yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#13852
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic13C2semidirect
3. C2×#11718310C2semidirect
5. #13113090C2semidirect
6. #13113087C2semidirect
7. #13113086C2semidirect
10. #95×Dic13C2semidirect
28. C2×#88131C4semidirect
171. C22×Dic13C4⋊C4semidirect
200. C4×Dic13C22⋊C4semidirect
553. C13#13852semidirect

Maximal subgroups

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

subgroupindex
C22×#881312
C2×C4⋊C4×Dic132
C2×#117183102
C2×C22⋊C4×Dic132
#131130902
#131130872
#131130862
#131130812
#131130792
#95×Dic132
C13×#14392
#1385213