Finite Group Databasebeta

← #15867113

Subgroups — #15867113

Order 3328.

860 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718370C211yesmaximal, characteristic, complemented
2C2×#11718366C211yesmaximal, characteristic, complemented
3#13117280C211yesmaximal, characteristic
4#13115634C211yesmaximal, characteristic
5#13115630C211yesmaximal, characteristic
6#13115559C211yesmaximal, characteristic, complemented
7#13115554C211yesmaximal, characteristic, complemented
8#13115449C211yesmaximal, characteristic, complemented
9#13115449C211yesmaximal, characteristic, complemented
10#13115442C211yesmaximal, characteristic, complemented
11#13115442C211yesmaximal, characteristic, complemented
12#13114693C211yesmaximal, characteristic, complemented
13#13114603C211yesmaximal, characteristic, complemented
14C4×#88060C211yesmaximal, characteristic, complemented
15C13×#1726C211yesmaximal, characteristic, complemented
16C2×C4×D52C2211yescharacteristic
17C2×#88126C2211yescharacteristic
18C2×C42×D13C2211yescharacteristic
19C2×C13×#97C2211yescharacteristic
20C2×C13×#97C2211yescharacteristic
21C2×C13×#97C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24C2×C4×C8×C13C2211yescharacteristic
25C13×#376C2211yescharacteristic
26C2×#88060C2211yescharacteristic
27C2×#88060C2211yescharacteristic
28C2×#88060C2211yescharacteristic
29C2×#88060C2211yescharacteristic
30C2×#88060C2211yescharacteristic
31C2×#88060C2211yescharacteristic
32C2×#88060C2211yescharacteristic
33C2×#88060C2211yescharacteristic
34C2×#88054C2211yescharacteristic
35C2×#88054C2211yescharacteristic
36C2×#88054C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C4×#6103C2211yescharacteristic
39C4×#6103C2211yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×#88043C2211yescharacteristic
44C2×C4×#1055C2211yescharacteristic
45#11718370—24no—
46#11718366—24no—
47#11718331C411yescharacteristic
48#11718331C411yescharacteristic
49#11718329C411yescharacteristic
50#11718329C411yescharacteristic
51#11718326C411yescharacteristic
52#11718326C411yescharacteristic
53#11718314C411yescharacteristic
54#11718314C411yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D52C2×C411yescharacteristic
62C22×C4×D13C2×C411yescharacteristic
63C22×C4×D13C2×C411yescharacteristic
64C22×C4×D13C2311yescharacteristic
65C22×C4×D13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×#6103C2×C411yescharacteristic
74C2×#6103C2×C411yescharacteristic
75C2×#6103C2×C411yescharacteristic
76C2×#6103C2×C411yescharacteristic
77C2×#6103C2×C411yescharacteristic
78C2×#6103C2×C411yescharacteristic
79C2×#6103C2×C411yescharacteristic
80C2×#6103C2×C411yescharacteristic
81C2×C4⋊Dic13C2×C411yescharacteristic
82C2×C4⋊Dic13C2×C411yescharacteristic
83C2×C4⋊Dic13C2×C411yescharacteristic
84C2×#6101C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×C4×Dic13C2×C411yescharacteristic
87C2×C4×Dic13C2×C411yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C4×D52—22no—
95C4×D52—22no—
96#88126—22no—
97#88126—22no—
98C42×D13—22no—
99C42×D13—22no—
100C13×#97—22no—
101C13×#97—22no—
102C13×#97D414yescomplemented
103C4×C8×C13—22no—
104C4×C8×C13—22no—
105C4×C8×C13—22no—
106C13×#95C2×C411yescharacteristic
107C13×#95C2×C411yescharacteristic
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#88060—22no—
120#88060—22no—
121#88060—22no—
122#88060—22no—
123#88060—22no—
124#88054—22no—
125#88054—22no—
126#88054—22no—
127#88054—22no—
128C4⋊#1055—22no—
129C4⋊#1055—22no—
130#88043—22no—
131C4×#1055—22no—
132#21273—131nomaximal, Sylow
133C23×D13C22×C411yescharacteristic
134C23×D13C22×C411yescharacteristic
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C2411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C2×D52—22no—
149C2×D52—22no—
150C2×D52—41no—
151C2×C4×D13—22no—
152C2×C4×D13—22no—
153C2×C4×D13—22no—
154C2×C4×D13—21no—
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—22no—
167C2×C4×D13—41no—
168C2×C4×D13—41no—
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×C13C2×D412yes—
178C2×C8×C13C2×D412yes—
179C2×C8×C13#4112yes—
180C2×C8×C13#4112yes—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13C2×D412yes—
184C42×C13#4112yes—
185C42×C13#4112yes—
186C42×C13#4112yes—
187#6103—22no—
188#6103—22no—
189#6103—22no—
190#6103—22no—
191#6103—22no—
192#6103—22no—
193#6103—41no—
194#6103—41no—
195C4⋊Dic13—22no—
196C4⋊Dic13—22no—
197C4⋊Dic13—41no—
198#6101—22no—
199#6101—22no—
200C4×Dic13—22no—
201C4×Dic13—22no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
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×#1055—21no—
218C2×#433—131no—
219C2×#432—131no—
220#2290—131no—
221#1955—131no—
222#1954—131no—
223#1940—131no—
224#1939—131no—
225#1924—131no—
226#1924—131no—
227#1923—131no—
228#1923—131no—
229#1768—131no—
230#1750—131no—
231C4×C22⋊C8—131no—
232#1726D1311yescharacteristic, complemented
233C23×C13C23×C411yescharacteristic
234C22×D13—21no—
235C22×D13—21no—
236C22×D13—21no—
237C22×D13—21no—
238C22×D13—21no—
239C22×D13—21no—
240C22×D13—21no—
241C22×D13—21no—
242C22×D13—21no—
243C22×D13—21no—
244C22×D13—21no—
245C22×D13—21no—
246C22×D13—21no—
247C22×D13#13112yes—
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—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13#11712yes—
263C2×C4×C13#11712yes—
264C2×C4×C13C4×D412yes—
265C2×C4×C13C4×D412yes—
266C2×C4×C13C22×D411yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
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×Dic13—21no—
283C2×Dic13—21no—
284C2×Dic13—21no—
285C2×Dic13—21no—
286C2×Dic13—21no—
287C2×Dic13—21no—
288C2×Dic13—21no—
289C2×Dic13#13112yes—
290D52—44no—
291C4×D13—44no—
292C4×D13—44no—
293C4×D13—41no—
294C4×D13—41no—
295C4×D13—41no—
296C4×D13—41no—
297C4×D13—41no—
298C4×D13—41no—
299C4×D13—41no—
300C4×D13—41no—
301C8×C13—22no—
302C8×C13—22no—
303C8×C13—22no—
304C8×C13—22no—
305#1055—41no—
306#1055—41no—
307#1055—41no—
308#1055—41no—
309C2×C4×D4—131no—
310C2×#117—131no—
311C22×C42—131no—
312#433—264no—
313#432—264no—
314C2×C4⋊C8—131no—
315C2×C4⋊C8—131no—
316C2×C4⋊C8—131no—
317C2×C4⋊C8—131no—
318C2×C4⋊C8—131no—
319C2×C4⋊C8—131no—
320C2×C22⋊C8—131no—
321C2×C22⋊C8—131no—
322C2×C22⋊C8—131no—
323C2×C22⋊C8—131no—
324C2×C22⋊C8—131no—
325C2×C22⋊C8—131no—
326C2×C22⋊C8—131no—
327C2×C22⋊C8—131no—
328C2×#97—131no—
329C2×#97C2×D1311yescharacteristic
330C2×#97C2×D1311yescharacteristic
331C2×#97C2×D1311yescharacteristic
332C2×C4×C8—131no—
333C2×C4×C8C2×D1311yescharacteristic
334C2×C4×C8C2×D1311yescharacteristic
335C2×C4×C8C2×D1311yescharacteristic
336#388—131no—
337#388—131no—
338#387—131no—
339#387—131no—
340#386—131no—
341#386—131no—
342#385—131no—
343#385—131no—
344C4×C4⋊C4—131no—
345C4×C22⋊C4—131no—
346C4×C22⋊C4—131no—
347#376C2×D1311yescharacteristic
348#336—131no—
349#336—131no—
350#336—131no—
351#336—131no—
352#336—131no—
353#336—131no—
354C22×C13C2×#11711yescharacteristic
355C22×C13C2×C4×D411yescharacteristic
356C22×C13C4×#4111yescharacteristic
357C22×C13C2×#13111yescharacteristic
358C22×C13C2×#13111yescharacteristic
359C22×C13#56811yescharacteristic
360C22×C13#56811yescharacteristic
361C2×D13—22no—
362C2×D13—22no—
363C2×D13—22no—
364C2×D13—41no—
365C2×D13—41no—
366C2×D13—41no—
367C2×D13—41no—
368C2×D13—41no—
369C2×D13—41no—
370C2×D13—41no—
371C2×D13—41no—
372C2×D13—41no—
373C2×D13—41no—
374C2×D13—41no—
375C4×C13—22no—
376C4×C13—22no—
377C4×C13—22no—
378C4×C13—22no—
379C4×C13—41no—
380C4×C13—41no—
381C4×C13#52911yescharacteristic
382C4×C13#52911yescharacteristic
383C4×C13#53211yescharacteristic
384C4×C13#53211yescharacteristic
385Dic13—22no—
386Dic13—41no—
387Dic13—41no—
388Dic13—41no—
389Dic13—41no—
390Dic13—41no—
391C22×D4—131no—
392C23×C4—131no—
393C23×C4—131no—
394C23×C4—131no—
395C23×C4—131no—
396C22×C8—131no—
397C22×C8—131no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8C22×D1311yescharacteristic
401C22×C8C22×D1311yescharacteristic
402C22×C8C22×D1311yescharacteristic
403C22×C8C22×D1311yescharacteristic
404C4×D4—262no—
405C4×D4—262no—
406#117—262no—
407#117—262no—
408C2×C4⋊C4—131no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C22⋊C4—131no—
414C2×C22⋊C4—131no—
415C2×C22⋊C4—131no—
416C2×C22⋊C4—131no—
417C2×C22⋊C4—131no—
418C2×C22⋊C4—131no—
419C2×C22⋊C4—131no—
420C2×C22⋊C4—131no—
421C2×C42—131no—
422C2×C42—131no—
423C2×C42—131no—
424C2×C42—131no—
425C2×C42—262no—
426C2×C42—262no—
427C2×C42C22×D1311yescharacteristic
428C2×C42C22×D1311yescharacteristic
429C2×C42C22×D1311yescharacteristic
430C4⋊C8—262no—
431C4⋊C8—262no—
432C4⋊C8—262no—
433C4⋊C8—262no—
434C4⋊C8—262no—
435C4⋊C8—262no—
436C22⋊C8—262no—
437C22⋊C8—262no—
438C22⋊C8—262no—
439C22⋊C8—262no—
440C22⋊C8—262no—
441C22⋊C8—262no—
442C22⋊C8—262no—
443C22⋊C8—262no—
444#97—22no—
445#97—22no—
446#97—262no—
447#97D5214yescomplemented
448C4×C8—22no—
449C4×C8—22no—
450C4×C8—22no—
451C4×C8—262no—
452#95—131no—
453#95—131no—
454#95—131no—
455#95—131no—
456#95—131no—
457#95—131no—
458#95C4×D1311yescharacteristic
459#95C4×D1311yescharacteristic
460#95C4×D1311yescharacteristic
461#95C4×D1311yescharacteristic
462C2×C13#229311yescharacteristic
463C2×C13#292411yescharacteristic
464C2×C13#292511yescharacteristic
465C2×C13#293311yescharacteristic
466C2×C13#293311yescharacteristic
467C2×C13#296611yescharacteristic
468C2×C13#296711yescharacteristic
469D13—42no—
470D13—81no—
471C24—131no—
472C24—131no—
473C2×D4—262no—
474C2×D4—262no—
475C2×D4—521no—
476C22×C4—131no—
477C22×C4—131no—
478C22×C4—131no—
479C22×C4—131no—
480C22×C4—131no—
481C22×C4—131no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—261no—
497C22×C4—261no—
498C22×C4—521no—
499C22×C4—521no—
500C22×C4C2×C4×D1311yescharacteristic
501C22×C4C2×C4×D1311yescharacteristic
502C22×C4C2×C4×D1311yescharacteristic
503C22×C4C2×C4×D1311yescharacteristic
504C22×C4C2×C4×D1311yescharacteristic
505C22×C4C2×C4×D1311yescharacteristic
506C22×C4C23×D1311yescharacteristic
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8C2×D5212yes—
528C2×C8C2×D5212yes—
529C2×C8#612712yes—
530C2×C8#612712yes—
531C4⋊C4—262no—
532C4⋊C4—262no—
533C4⋊C4—262no—
534C4⋊C4—262no—
535C4⋊C4—521no—
536C22⋊C4—262no—
537C22⋊C4—262no—
538C22⋊C4—262no—
539C22⋊C4—262no—
540C22⋊C4—262no—
541C22⋊C4—262no—
542C22⋊C4—521no—
543C22⋊C4—521no—
544C42—21no—
545C42—21no—
546C42—262no—
547C42—262no—
548C42—261no—
549C42—261no—
550C42—261no—
551C42—261no—
552C42C2×D5212yes—
553C42#612712yes—
554C42#612712yes—
555C42#612712yes—
556C13#2127311yescharacteristic, complemented, Sylow
557C23—132no—
558C23—261no—
559C23—261no—
560C23—261no—
561C23—261no—
562C23—261no—
563C23—261no—
564C23—261no—
565C23—261no—
566C23—261no—
567C23—261no—
568C23—261no—
569C23—261no—
570C23—261no—
571C23C22×C4×D1311yescharacteristic
572D4—524no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—132no—
588C2×C4—261no—
589C2×C4—261no—
590C2×C4—261no—
591C2×C4—261no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—261no—
595C2×C4—261no—
596C2×C4—261no—
597C2×C4—261no—
598C2×C4—261no—
599C2×C4—261no—
600C2×C4—261no—
601C2×C4—261no—
602C2×C4—261no—
603C2×C4—261no—
604C2×C4—261no—
605C2×C4—524no—
606C2×C4—524no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4#8812612yes—
616C2×C4#8812612yes—
617C2×C4C4×D5212yes—
618C2×C4C4×D5212yes—
619C2×C4C22×D5211yescharacteristic
620C2×C4C2×#612711yescharacteristic
621C2×C4C2×#612711yescharacteristic
622C2×C4C2×#612711yescharacteristic
623C2×C4C2×#612711yescharacteristic
624C2×C4C2×#612711yescharacteristic
625C8—22no—
626C8—22no—
627C8—22no—
628C8—22no—
629C8—521no—
630C8—521no—
631C8—521no—
632C8—521no—
633C22—262no—
634C22—262no—
635C22—262no—
636C22—521no—
637C22—521no—
638C22—521no—
639C22—521no—
640C22—521no—
641C22—521no—
642C22—521no—
643C22—521no—
644C22—521no—
645C22—521no—
646C22—521no—
647C22C2×#8812611yescharacteristic
648C22C2×C4×D5211yescharacteristic
649C22C4×#612711yescharacteristic
650C22D13×#13111yescharacteristic
651C22D13×#13111yescharacteristic
652C22#1171945511yescharacteristic
653C22#1171945511yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—22no—
658C4—41no—
659C4—41no—
660C4—262no—
661C4—521no—
662C4—521no—
663C4—521no—
664C4—521no—
665C4—521no—
666C4#1171918211yescharacteristic
667C4#1171918211yescharacteristic
668C4#1171918411yescharacteristic
669C4#1171918411yescharacteristic
670C2—522no—
671C2—1041no—
672C2#1311730011yescharacteristic
673C2#1312349111yescharacteristic
674C2#1312350011yescharacteristic
675C2#1312356411yescharacteristic
676C2#1312356411yescharacteristic
677C2#1312380711yescharacteristic
678C2#1312381711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1726C2
prime radicalC22×D52C2×C4
cosocleC22×C4×C13C24
hypercenter#1726D13
hypocenterC13#21273
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1726

Complements

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

NH ≅ G/Ntype
1. C2×#11718370C2semidirect
2. C2×#11718366C2semidirect
6. #13115559C2semidirect
7. #13115554C2semidirect
8. #13115449C2semidirect
9. #13115449C2semidirect
10. #13115442C2semidirect
11. #13115442C2semidirect
12. #13114693C2semidirect
13. #13114603C2semidirect
14. C4×#88060C2semidirect
15. C13×#1726C2semidirect
102. C13×#97D4semidirect
232. #1726D13semidirect
447. #97D52semidirect
556. C13#21273semidirect

Maximal subgroups

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

subgroupindex
C2×#117183702
C2×#117183662
#131172802
#131156342
#131156302
#131155592
#131155542
#131154492
#131154422
#131146932
#131146032
C4×#880602
C13×#17262
#2127313