Finite Group Databasebeta

← #15880502

Subgroups — #15880502

Order 3328.

780 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718380C211yesmaximal, characteristic
2#13117318C211yesmaximal, characteristic
3#13115556C211yesmaximal, characteristic, complemented
4#13115551C211yesmaximal, characteristic, complemented
5#13115400C211yesmaximal, characteristic, complemented
6#13115397C211yesmaximal, characteristic, complemented
7#13115397C211yesmaximal, characteristic, complemented
8#13115393C211yesmaximal, characteristic, complemented
9#13114907C211yesmaximal, characteristic
10#13114902C211yesmaximal, characteristic
11#13114818C211yesmaximal, characteristic
12#13114710C211yesmaximal, characteristic, complemented
13#13114704C211yesmaximal, characteristic, complemented
14#13114604C211yesmaximal, characteristic
15C2×C13×#433C211yesmaximal, characteristic
16C2×C13×#117C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19C13×#433—24no—
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C2×C13×#97C2211yescharacteristic
25C2×C4×C8×C13C2211yescharacteristic
26C2×C22⋊#1055C2211yescharacteristic
27C2×C22⋊#1055C2211yescharacteristic
28C2×#88055C2211yescharacteristic
29C2×#88055C2211yescharacteristic
30C2×#88055C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×#88054C2211yescharacteristic
34C2×#88054C2211yescharacteristic
35C2×C8×Dic13C2211yescharacteristic
36#11718634C411yescharacteristic
37#11718634C411yescharacteristic
38#11718634C411yescharacteristic
39#11718634C411yescharacteristic
40#11718607C411yescharacteristic
41#11718607C411yescharacteristic
42#11718607C411yescharacteristic
43#11718607C411yescharacteristic
44C4×#6101C2211yescharacteristic
45C4×#6101C2211yescharacteristic
46C4×#6101C2211yescharacteristic
47C4×#6101C2211yescharacteristic
48#11718380—24no—
49#11718142C2211yescharacteristic
50#11718142C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13C2×C411yescharacteristic
63C23×Dic13C2×C411yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C13×#117—22no—
69C13×#117—22no—
70C2×C13×C4⋊C4C2×C411yescharacteristic
71C2×C13×C4⋊C4C2×C411yescharacteristic
72C2×C13×C22⋊C4C2×C411yescharacteristic
73C2×C13×C22⋊C4C2×C411yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C2×C22⋊Dic13C2×C411yescharacteristic
77C2×C22⋊Dic13C2×C411yescharacteristic
78#88180—22no—
79#88180—22no—
80C2×C4⋊Dic13C2×C411yescharacteristic
81C2×C4⋊Dic13C2×C411yescharacteristic
82C2×#6101C2×C411yescharacteristic
83C2×#6101C2×C411yescharacteristic
84C2×#6101C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×#6101C2×C411yescharacteristic
90C2×C4×Dic13—22no—
91C2×C4×Dic13—22no—
92C2×C4×Dic13C2×C411yescharacteristic
93C2×C4×Dic13C2×C411yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C13×C4⋊C8—22no—
103C13×C4⋊C8—22no—
104C13×C22⋊C8—22no—
105C13×C22⋊C8D414yes—
106C13×#97—22no—
107C4×C8×C13—22no—
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116C22⋊#1055—22no—
117C22⋊#1055—22no—
118#88055—22no—
119#88055—22no—
120#88055—22no—
121#88054—22no—
122#88054—22no—
123#88054—22no—
124#88054—22no—
125C8×Dic13—22no—
126#22605—131nomaximal, Sylow
127C24×C13C22×C411yescharacteristic
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13C22×C411yescharacteristic
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C2×D412yes—
138C22×C4×C13#4112yes—
139C22×C4×C13C2411yescharacteristic
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—41no—
144C22×Dic13—41no—
145C22×Dic13—41no—
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C411yescharacteristic
153C22×Dic13C22×C411yescharacteristic
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13C2×D412yes—
165C2×C8×C13C2×D412yes—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—22no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C22⋊Dic13—22no—
175C22⋊Dic13—22no—
176C4⋊Dic13—22no—
177C4⋊Dic13—22no—
178#6101—22no—
179#6101—22no—
180#6101—41no—
181#6101—41no—
182#6101—41no—
183#6101—41no—
184#6101—41no—
185#6101—41no—
186C4×Dic13—22no—
187C4×Dic13—22no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13#4112yes—
195C4×Dic13#4112yes—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#433D1311yescharacteristic
209C2×#432—131no—
210#2296—131no—
211#1940—131no—
212#1939—131no—
213#1917—131no—
214#1917—131no—
215#1917—131no—
216#1916—131no—
217#1818—131no—
218#1817—131no—
219#1798—131no—
220#1771—131no—
221#1770—131no—
222#1750—131no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13C4×D412yes—
230C23×C13C23×C411yescharacteristic
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
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×C13C4×D412yes—
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C132−1+411yescharacteristic
255C2×C4×C132−1+411yescharacteristic
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
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—44no—
278C2×Dic13—44no—
279C2×Dic13#11712yes—
280C2×Dic13#11712yes—
281C2×Dic13#13112yes—
282C8×C13—22no—
283C8×C13—22no—
284C8×C13—41no—
285C8×C13—41no—
286#1055—41no—
287#1055—41no—
288#1055—41no—
289#1055—41no—
290C2×#117—131no—
291C2×#117C2×D1311yescharacteristic
292C22×C42—131no—
293#433—24no—
294#432—264no—
295C2×C4⋊C8—131no—
296C2×C4⋊C8—131no—
297C2×C4⋊C8—131no—
298C2×C4⋊C8—131no—
299C2×C4⋊C8C2×D1311yescharacteristic
300C2×C4⋊C8C2×D1311yescharacteristic
301C2×C22⋊C8—131no—
302C2×C22⋊C8—131no—
303C2×C22⋊C8C2×D1311yescharacteristic
304C2×C22⋊C8C2×D1311yescharacteristic
305C2×#97—131no—
306C2×#97—131no—
307C2×#97—131no—
308C2×#97C2×D1311yescharacteristic
309C2×C4×C8—131no—
310C2×C4×C8C2×D1311yescharacteristic
311#389—131no—
312#389—131no—
313#389—131no—
314#389—131no—
315#385—131no—
316#385—131no—
317#385—131no—
318#385—131no—
319C4×C4⋊C4—131no—
320C4×C4⋊C4—131no—
321C4×C4⋊C4—131no—
322C4×C4⋊C4—131no—
323#336—131no—
324#336—131no—
325#336—131no—
326#336—131no—
327#336—131no—
328#336—131no—
329#336—131no—
330#336—131no—
331#336—131no—
332#336—131no—
333#336—131no—
334#336—131no—
335C22×C13—22no—
336C22×C13—22no—
337C22×C13—22no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13C2×#11711yescharacteristic
343C22×C13C2×C4×D411yescharacteristic
344C22×C13#51911yescharacteristic
345C22×C13C2×#13111yescharacteristic
346C22×C13#56811yescharacteristic
347C22×C13#56811yescharacteristic
348C22×C13#56811yescharacteristic
349C4×C13—22no—
350C4×C13—41no—
351C4×C13—41no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13#54711yescharacteristic
355C4×C13#54711yescharacteristic
356C4×C13#55211yescharacteristic
357C4×C13#55211yescharacteristic
358Dic13—22no—
359Dic13—22no—
360Dic13—22no—
361Dic13—41no—
362Dic13—41no—
363Dic13—41no—
364Dic13—41no—
365Dic13—41no—
366C23×C4—131no—
367C23×C4—131no—
368C23×C4C22×D1311yescharacteristic
369C22×C8—131no—
370C22×C8—131no—
371C22×C8—131no—
372C22×C8—131no—
373C22×C8C22×D1311yescharacteristic
374C22×C8C22×D1311yescharacteristic
375C22×C8C22×D1311yescharacteristic
376C22×C8C22×D1311yescharacteristic
377#117—22no—
378#117—22no—
379#117—262no—
380#117—262no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4C4×D1311yescharacteristic
392C2×C4⋊C4C4×D1311yescharacteristic
393C2×C22⋊C4—131no—
394C2×C22⋊C4—131no—
395C2×C22⋊C4C4×D1311yescharacteristic
396C2×C22⋊C4C4×D1311yescharacteristic
397C2×C42—131no—
398C2×C42—131no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—262no—
404C2×C42—262no—
405C2×C42C22×D1311yescharacteristic
406C2×C42C22×D1311yescharacteristic
407C4⋊C8—22no—
408C4⋊C8—22no—
409C4⋊C8—262no—
410C4⋊C8—262no—
411C4⋊C8—262no—
412C4⋊C8—262no—
413C22⋊C8—22no—
414C22⋊C8—262no—
415C22⋊C8—262no—
416C22⋊C8C22⋊D1314yes—
417#97—22no—
418#97—262no—
419#97—262no—
420#97—262no—
421C4×C8—22no—
422C4×C8—262no—
423#95—131no—
424#95—131no—
425#95—131no—
426#95—131no—
427#95—131no—
428#95—131no—
429#95—131no—
430#95—131no—
431C2×C13—42no—
432C2×C13#234411yescharacteristic
433C2×C13#292311yescharacteristic
434C2×C13#292511yescharacteristic
435C2×C13#293011yescharacteristic
436C2×C13#293311yescharacteristic
437C2×C13#298511yescharacteristic
438C2×C13#298711yescharacteristic
439C24C2×C4×D1311yescharacteristic
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—521no—
456C22×C4—521no—
457C22×C4—521no—
458C22×C4C2×C4×D1311yescharacteristic
459C22×C4C2×C4×D1311yescharacteristic
460C22×C4C2×C4×D1311yescharacteristic
461C22×C4C2×C4×D1311yescharacteristic
462C22×C4C2×C4×D1311yescharacteristic
463C22×C4#612712yes—
464C22×C4C2×C22⋊D1312yes—
465C22×C4C23×D1311yescharacteristic
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8C2×C22⋊D1312yes—
489C2×C8C2×C22⋊D1312yes—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—262no—
493C4⋊C4—262no—
494C4⋊C4—262no—
495C4⋊C4—262no—
496C4⋊C4—521no—
497C4⋊C4—521no—
498C4⋊C4—521no—
499C4⋊C4—521no—
500C4⋊C4—521no—
501C4⋊C4—521no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—262no—
505C22⋊C4—262no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—132no—
511C42—132no—
512C42—262no—
513C42—262no—
514C42—261no—
515C42—261no—
516C42—261no—
517C42—261no—
518C42—261no—
519C42—261no—
520C13#2260511yescharacteristic, complemented, Sylow
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23C4×C22⋊D1312yes—
528C23C22×C4×D1311yescharacteristic
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—132no—
548C2×C4—132no—
549C2×C4—132no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—261no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—261no—
565C2×C4—261no—
566C2×C4—261no—
567C2×C4—261no—
568C2×C4—261no—
569C2×C4—261no—
570C2×C4—261no—
571C2×C4—524no—
572C2×C4—524no—
573C2×C4C4×C22⋊D1312yes—
574C2×C4C2×#612711yescharacteristic
575C2×C4#41×D1311yescharacteristic
576C2×C4#41×D1311yescharacteristic
577C2×C4#8825711yescharacteristic
578C2×C4#8825711yescharacteristic
579C2×C4C22×C22⋊D1311yescharacteristic
580C8—22no—
581C8—22no—
582C8—41no—
583C8—41no—
584C8—521no—
585C8—521no—
586C8—521no—
587C8—521no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22#1171922111yescharacteristic
596C22D13×#11711yescharacteristic
597C22D13×#13111yescharacteristic
598C22#1171945511yescharacteristic
599C22#1171945511yescharacteristic
600C22#1171945511yescharacteristic
601C22C2×C4×C22⋊D1311yescharacteristic
602C4—22no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—262no—
608C4—262no—
609C4—262no—
610C4—521no—
611C4—521no—
612C4—521no—
613C4—521no—
614C4—521no—
615C4#1171923611yescharacteristic
616C4#1171923611yescharacteristic
617C4#1171952911yescharacteristic
618C4#1171952911yescharacteristic
619C2—42no—
620C2#1311770611yescharacteristic
621C2#1312348411yescharacteristic
622C2#1312349911yescharacteristic
623C2#1312353711yescharacteristic
624C2#1312355811yescharacteristic
625C2#1312392811yescharacteristic
626C2#1312394011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#433C2
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenterC2×#433D13
hypocenterC13#22605
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
3. #13115556C2semidirect
4. #13115551C2semidirect
5. #13115400C2semidirect
6. #13115397C2semidirect
7. #13115397C2semidirect
8. #13115393C2semidirect
12. #13114710C2semidirect
13. #13114704C2semidirect
520. C13#22605semidirect

Maximal subgroups

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

subgroupindex
C2×#117183802
#131173182
#131155562
#131155512
#131154002
#131153972
#131153932
#131149072
#131149022
#131148182
#131147102
#131147042
#131146042
C2×C13×#4332
#2260513