Finite Group Databasebeta

← #15880452

Subgroups — #15880452

Order 3328.

932 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718366C211yesmaximal, characteristic
2C2×#11718346C211yesmaximal, characteristic
3C4×C4⋊C4×D13C211yesmaximal, characteristic
4#13115559C211yesmaximal, characteristic, complemented
5#13115557C211yesmaximal, characteristic, complemented
6#13115400C211yesmaximal, characteristic, complemented
7#13115398C211yesmaximal, characteristic, complemented
8#13115393C211yesmaximal, characteristic, complemented
9#13115391C211yesmaximal, characteristic, complemented
10#13114903C211yesmaximal, characteristic
11#13114903C211yesmaximal, characteristic
12#13114813C211yesmaximal, characteristic
13#13114711C211yesmaximal, characteristic, complemented
14#13114599C211yesmaximal, characteristic
15C13×#1771C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D13C411yescharacteristic
17C2×C4⋊C4×D13C411yescharacteristic
18C2×C42×D13C2211yescharacteristic
19C2×C42×D13C2211yescharacteristic
20C2×C42×D13C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×#97C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24C2×C4×C8×C13C2211yescharacteristic
25C4×C13×C4⋊C4C2211yescharacteristic
26C2×#88060C2211yescharacteristic
27C2×#88060C2211yescharacteristic
28C2×#88060C2211yescharacteristic
29C2×#88060C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×#88054C2211yescharacteristic
34C4⋊C4×Dic13C411yescharacteristic
35C4⋊C4×Dic13C411yescharacteristic
36C4×C4⋊Dic13C2211yescharacteristic
37C4×#6101C2211yescharacteristic
38C4×#6101C2211yescharacteristic
39C2×C4⋊#1055C2211yescharacteristic
40C2×#88043C2211yescharacteristic
41C2×#88043C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718366—24no—
44#11718346—24no—
45D13×#95C411yescharacteristic
46D13×#95C411yescharacteristic
47#11718310C411yescharacteristic
48#11718310C411yescharacteristic
49C13×#336C2211yescharacteristic
50C13×#336C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×C4×D13C2×C411yescharacteristic
62C22×C4×D13C2×C411yescharacteristic
63C22×C4×D13C2×C411yescharacteristic
64C22×C4×D13C2×C411yescharacteristic
65C22×C4×D13C2×C411yescharacteristic
66C22×C4×D13C2×C411yescharacteristic
67C22×C4×D13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C2×C13×C4⋊C4C2×C411yescharacteristic
73C2×C13×C4⋊C4C2×C411yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C2×C42×C13C2311yescharacteristic
77C2×C4⋊Dic13C2×C411yescharacteristic
78C2×C4⋊Dic13C2×C411yescharacteristic
79C2×#6101C2×C411yescharacteristic
80C2×#6101C2×C411yescharacteristic
81C2×#6101C2×C411yescharacteristic
82C2×#6101C2×C411yescharacteristic
83C2×C4×Dic13C2×C411yescharacteristic
84C2×C4×Dic13C2×C411yescharacteristic
85C2×C4×Dic13C2×C411yescharacteristic
86C2×C4×Dic13C2×C411yescharacteristic
87C2×C4×Dic13C2×C411yescharacteristic
88C2×C4×Dic13C2×C411yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C4⋊C4×D13—24no—
97C4⋊C4×D13—24no—
98C42×D13—22no—
99C42×D13—22no—
100C42×D13—22no—
101C42×D13—22no—
102C42×D13—22no—
103C42×D13—22no—
104C13×C4⋊C8—22no—
105C13×#97—22no—
106C13×#97—22no—
107C4×C8×C13—22no—
108C13×#95C2×C411yescharacteristic
109C13×#95C2×C411yescharacteristic
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116#88060—22no—
117#88060—22no—
118#88060—22no—
119#88060D414yes—
120#88054—22no—
121#88054—22no—
122#88054—22no—
123#88054—22no—
124C4⋊#1055—22no—
125#88043—22no—
126#88043—22no—
127C4×#1055—22no—
128#22601—131nomaximal, Sylow
129C23×D13C22×C411yescharacteristic
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C22×C411yescharacteristic
132C22×C4×C13C22×C411yescharacteristic
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C2411yescharacteristic
137C22×Dic13C22×C411yescharacteristic
138C22×Dic13C22×C411yescharacteristic
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C2×C4×D13—22no—
145C2×C4×D13—22no—
146C2×C4×D13—22no—
147C2×C4×D13—22no—
148C2×C4×D13—21no—
149C2×C4×D13—21no—
150C2×C4×D13—21no—
151C2×C4×D13—21no—
152C2×C4×D13—22no—
153C2×C4×D13—22no—
154C2×C4×D13—22no—
155C2×C4×D13—22no—
156C2×C4×D13—22no—
157C2×C4×D13—22no—
158C2×C4×D13—22no—
159C2×C4×D13—22no—
160C2×C4×D13—22no—
161C2×C4×D13—22no—
162C2×C4×D13—41no—
163C2×C4×D13—41no—
164C2×C4×D13—41no—
165C2×C4×D13M1614yes—
166C2×C4×D13C2×D412yes—
167C2×C4×D13#4112yes—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13C2×D412yes—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13#4112yes—
187C42×C13#4112yes—
188C4⋊Dic13—22no—
189C4⋊Dic13—22no—
190#6101—22no—
191#6101—22no—
192#6101—22no—
193#6101M1614yes—
194C4×Dic13—22no—
195C4×Dic13—22no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—22no—
203C4×Dic13—22no—
204C4×Dic13—22no—
205C4×Dic13—22no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055C2×D412yes—
218C2×#432—131no—
219C2×#431—131no—
220C2×C4×C4⋊C4—131no—
221#1940—131no—
222#1940—131no—
223#1917—131no—
224#1917—131no—
225#1916—131no—
226#1916—131no—
227#1817—131no—
228#1817—131no—
229#1797—131no—
230#1771—131no—
231#1771D1311yescharacteristic, complemented
232#1749—131no—
233C23×C13C23×C411yescharacteristic
234C22×D13—21no—
235C22×D13—21no—
236C22×D13—21no—
237C22×D13—21no—
238C22×D13C4×D412yes—
239C22×D13C2×M1612yes—
240C22×D13#13112yes—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13#11712yes—
256C2×C4×C13#11712yes—
257C2×C4×C13C2×M1612yes—
258C2×C4×C13C2×M1612yes—
259C2×C4×C13C22×D411yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C132−1+411yescharacteristic
264C2×C4×C132−1+411yescharacteristic
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13C4×D412yes—
283C2×Dic13C2×M1612yes—
284C2×Dic13C2×M1612yes—
285C2×Dic13C2×M1612yes—
286C4×D13—28no—
287C4×D13—28no—
288C4×D13—22no—
289C4×D13—22no—
290C4×D13—22no—
291C4×D13—22no—
292C4×D13—44no—
293C4×D13—44no—
294C4×D13—44no—
295C4×D13—44no—
296C8×C13—22no—
297C8×C13—41no—
298C8×C13—41no—
299C8×C13—41no—
300#1055—22no—
301#1055—41no—
302#1055—41no—
303#1055—41no—
304C22×C4⋊C4—131no—
305C22×C4⋊C4—131no—
306C22×C42—131no—
307C22×C42—131no—
308C22×C42—131no—
309#432—264no—
310#431—264no—
311C2×C4⋊C8—131no—
312C2×C4⋊C8—131no—
313C2×C4⋊C8—131no—
314C2×C4⋊C8—131no—
315C2×C4⋊C8—131no—
316C2×C4⋊C8C2×D1311yescharacteristic
317C2×C22⋊C8—131no—
318C2×C22⋊C8—131no—
319C2×C22⋊C8—131no—
320C2×C22⋊C8—131no—
321C2×#97—131no—
322C2×#97—131no—
323C2×#97C2×D1311yescharacteristic
324C2×#97C2×D1311yescharacteristic
325C2×C4×C8—131no—
326C2×C4×C8C2×D1311yescharacteristic
327C4×C4⋊C4—131no—
328C4×C4⋊C4—131no—
329C4×C4⋊C4—131no—
330C4×C4⋊C4—131no—
331C4×C4⋊C4—131no—
332C4×C4⋊C4—131no—
333C4×C4⋊C4—131no—
334C4×C4⋊C4C2×D1311yescharacteristic
335C2×#95—131no—
336C2×#95—131no—
337#336—131no—
338#336—131no—
339#336—131no—
340#336—131no—
341#336—131no—
342#336—131no—
343#336—131no—
344#336—131no—
345#336—131no—
346#336—131no—
347#336C2×D1311yescharacteristic
348#336C2×D1311yescharacteristic
349C22×C13C2×#11711yescharacteristic
350C22×C13C2×C4×D411yescharacteristic
351C22×C13#51911yescharacteristic
352C22×C13C22×M1611yescharacteristic
353C22×C13C22×M1611yescharacteristic
354C22×C13C2×#13111yescharacteristic
355C22×C13#56811yescharacteristic
356C2×D13—22no—
357C2×D13—22no—
358C2×D13—22no—
359C2×D13—22no—
360C2×D13—22no—
361C2×D13—22no—
362C2×D13#43514yes—
363C4×C13—22no—
364C4×C13—22no—
365C4×C13—22no—
366C4×C13—22no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13#54711yescharacteristic
370C4×C13#54711yescharacteristic
371C4×C13#55211yescharacteristic
372C4×C13#55211yescharacteristic
373Dic13—22no—
374Dic13—22no—
375Dic13—22no—
376Dic13—22no—
377Dic13—41no—
378Dic13—41no—
379Dic13—41no—
380C23×C4—131no—
381C23×C4—131no—
382C23×C4—131no—
383C23×C4—131no—
384C23×C4—131no—
385C23×C4—131no—
386C23×C4—131no—
387C22×C8—131no—
388C22×C8—131no—
389C22×C8—131no—
390C22×C8—131no—
391C22×C8C22×D1311yescharacteristic
392C22×C8C22×D1311yescharacteristic
393C22×C8C22×D1311yescharacteristic
394C22×C8C22×D1311yescharacteristic
395C2×C4⋊C4—131no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—131no—
398C2×C4⋊C4—131no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—264no—
402C2×C4⋊C4—264no—
403C2×C4⋊C4C4×D1311yescharacteristic
404C2×C4⋊C4C4×D1311yescharacteristic
405C2×C42—131no—
406C2×C42—131no—
407C2×C42—131no—
408C2×C42—131no—
409C2×C42—131no—
410C2×C42—131no—
411C2×C42—131no—
412C2×C42—131no—
413C2×C42—131no—
414C2×C42—262no—
415C2×C42—262no—
416C2×C42—262no—
417C2×C42—262no—
418C2×C42—262no—
419C2×C42—262no—
420C2×C42C22×D1311yescharacteristic
421C2×C42C22×D1311yescharacteristic
422C2×C42C22×D1311yescharacteristic
423C4⋊C8—22no—
424C4⋊C8—262no—
425C4⋊C8—262no—
426C4⋊C8—262no—
427C4⋊C8—262no—
428C4⋊C8—262no—
429C22⋊C8—134no—
430C22⋊C8—262no—
431C22⋊C8—262no—
432C22⋊C8—262no—
433#97—22no—
434#97—22no—
435#97—262no—
436#97—262no—
437C4×C8—22no—
438C4×C8—262no—
439#95—131no—
440#95—131no—
441#95—131no—
442#95—131no—
443#95—131no—
444#95—131no—
445#95C4×D1311yescharacteristic
446#95C4×D1311yescharacteristic
447C2×C13#234411yescharacteristic
448C2×C13#292011yescharacteristic
449C2×C13#292411yescharacteristic
450C2×C13C2×#43511yescharacteristic
451C2×C13D4×M1611yescharacteristic
452C2×C13#298311yescharacteristic
453C2×C13#298411yescharacteristic
454D13—24no—
455C24—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—131no—
460C22×C4—134no—
461C22×C4—132no—
462C22×C4—132no—
463C22×C4—131no—
464C22×C4—131no—
465C22×C4—131no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—521no—
485C22×C4—521no—
486C22×C4—521no—
487C22×C4C2×C4×D1311yescharacteristic
488C22×C4C2×C4×D1311yescharacteristic
489C22×C4C2×C4×D1311yescharacteristic
490C22×C4C2×C4×D1311yescharacteristic
491C22×C4C2×C4×D1311yescharacteristic
492C22×C4C2×C4×D1311yescharacteristic
493C22×C4C23×D1311yescharacteristic
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—132no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8D4×D1312yes—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—134no—
521C4⋊C4—262no—
522C4⋊C4—262no—
523C4⋊C4—262no—
524C4⋊C4—262no—
525C4⋊C4—262no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—262no—
531C42—262no—
532C42—262no—
533C42—262no—
534C42—262no—
535C42—262no—
536C42—261no—
537C42—261no—
538C42—261no—
539C42—261no—
540C42—261no—
541C42—261no—
542C42#612712yes—
543C42#612712yes—
544C13#2260111yescharacteristic, complemented, Sylow
545C23—132no—
546C23—132no—
547C23—132no—
548C23—261no—
549C23—261no—
550C23—261no—
551C23—261no—
552C23C22×C4×D1311yescharacteristic
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—132no—
568C2×C4—132no—
569C2×C4—132no—
570C2×C4—132no—
571C2×C4—268no—
572C2×C4—268no—
573C2×C4—261no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—262no—
584C2×C4—262no—
585C2×C4—261no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—261no—
590C2×C4—261no—
591C2×C4—261no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—524no—
595C2×C4—524no—
596C2×C4—524no—
597C2×C4—524no—
598C2×C4#8812612yes—
599C2×C4#8812612yes—
600C2×C4M16×D1312yes—
601C2×C4M16×D1312yes—
602C2×C4C2×#612711yescharacteristic
603C2×C4C2×#612711yescharacteristic
604C2×C4C2×D4×D1311yescharacteristic
605C2×C4#8825411yescharacteristic
606C2×C4#41×D1311yescharacteristic
607C2×C4#8825711yescharacteristic
608C8—22no—
609C8—41no—
610C8—41no—
611C8—41no—
612C8—262no—
613C8—521no—
614C8—521no—
615C8—521no—
616C22—134no—
617C22—262no—
618C22—262no—
619C22—262no—
620C22—262no—
621C22—262no—
622C22—262no—
623C22C2×#8812611yescharacteristic
624C22C4×D4×D1311yescharacteristic
625C22#1171927711yescharacteristic
626C22C2×M16×D1311yescharacteristic
627C22C2×M16×D1311yescharacteristic
628C22D13×#13111yescharacteristic
629C22#1171945511yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—22no—
634C4—41no—
635C4—41no—
636C4—262no—
637C4—262no—
638C4—262no—
639C4—262no—
640C4—521no—
641C4—521no—
642C4—521no—
643C4#1171921211yescharacteristic
644C4#1171923411yescharacteristic
645C4#1171925611yescharacteristic
646C4#1171928611yescharacteristic
647C2—264no—
648C2#1311770111yescharacteristic
649C2#1312346711yescharacteristic
650C2#1312349111yescharacteristic
651C2D13×#43511yescharacteristic
652C2#1312356911yescharacteristic
653C2#1312391811yescharacteristic
654C2#1312392211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1771C2
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1771D13
hypocenterC13#22601
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
4. #13115559C2semidirect
5. #13115557C2semidirect
6. #13115400C2semidirect
7. #13115398C2semidirect
8. #13115393C2semidirect
9. #13115391C2semidirect
13. #13114711C2semidirect
15. C13×#1771C2semidirect
231. #1771D13semidirect
544. C13#22601semidirect

Maximal subgroups

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

subgroupindex
C2×#117183662
C2×#117183462
C4×C4⋊C4×D132
#131155592
#131155572
#131154002
#131153982
#131153932
#131153912
#131149032
#131148132
#131147112
#131145992
C13×#17712
#2260113