Finite Group Databasebeta

← #15867753

Subgroups — #15867753

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718381C211yesmaximal, characteristic
2C2×#11718783C211yesmaximal, characteristic
3#13117332C211yesmaximal, characteristic
4#13115558C211yesmaximal, characteristic, complemented
5#13115556C211yesmaximal, characteristic, complemented
6#13115553C211yesmaximal, characteristic, complemented
7#13115551C211yesmaximal, characteristic, complemented
8#13115019C211yesmaximal, characteristic
9#13115016C211yesmaximal, characteristic
10#13115013C211yesmaximal, characteristic
11#13114695C211yesmaximal, characteristic, complemented
12#13114692C211yesmaximal, characteristic, complemented
13#13114688C211yesmaximal, characteristic, complemented
14C4⋊C8×Dic13C211yesmaximal, characteristic, complemented
15C13×#1851C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C23×#1055C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C4×C13×C22⋊C4C2211yescharacteristic
23C4×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊#1055C2211yescharacteristic
25#11718783—24no—
26C2×#88055C2211yescharacteristic
27C2×#88055C2211yescharacteristic
28C2×#88055C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×#88054C2211yescharacteristic
34C2×#88054C2211yescharacteristic
35C2×C8×Dic13C2211yescharacteristic
36C2×C8×Dic13C2211yescharacteristic
37C2×C8×Dic13C2211yescharacteristic
38#11718606C411yescharacteristic
39#11718606C411yescharacteristic
40#11718605C411yescharacteristic
41#11718605C411yescharacteristic
42#11718593C2211yescharacteristic
43C4×#6101C2211yescharacteristic
44C4×#6101C2211yescharacteristic
45C42×Dic13C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48#11718381—24no—
49#11718315C411yescharacteristic
50#11718315C411yescharacteristic
51#11718314C411yescharacteristic
52#11718314C411yescharacteristic
53C13×#336C2211yescharacteristic
54C13×#336C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C2×C13×M16—22no—
63C2×C13×M16—22no—
64C2×C13×M16—22no—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C2×C13×C22⋊C4C2×C411yescharacteristic
70C2×C13×C22⋊C4C2×C411yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C22⋊Dic13C2×C411yescharacteristic
74C2×C22⋊Dic13C2×C411yescharacteristic
75C2×C22⋊Dic13C2×C411yescharacteristic
76C2×C22⋊Dic13C2×C411yescharacteristic
77#88180D414yes—
78#88180Q814yes—
79C2×C4⋊Dic13C2×C411yescharacteristic
80C2×C4⋊Dic13C2×C411yescharacteristic
81C2×#6101C2×C411yescharacteristic
82C2×#6101C2×C411yescharacteristic
83C2×#6101C2×C411yescharacteristic
84C2×#6101C2×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
92C2×C4×Dic13C2311yescharacteristic
93C22×#1055—22no—
94C22×#1055—22no—
95C22×#1055—22no—
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C13×C4⋊C8—22no—
101C13×C4⋊C8—22no—
102C13×C22⋊C8—22no—
103C13×#95C2×C411yescharacteristic
104C13×#95C2×C411yescharacteristic
105#88071C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115C22⋊#1055—22no—
116#88055—22no—
117#88055—22no—
118#88055—22no—
119#88054—22no—
120#88054—22no—
121#88054—22no—
122#88054—22no—
123#88054—22no—
124#88054—22no—
125C8×Dic13—22no—
126C8×Dic13—22no—
127C8×Dic13—22no—
128C4⋊#1055—22no—
129C4⋊#1055—22no—
130#21357—131nomaximal, Sylow
131C24×C13C22×C411yescharacteristic
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C2×D412yes—
142C22×C4×C13C2×Q812yes—
143C22×C4×C13C2411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C13×M16—28no—
153C2×C8×C13—21no—
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#4112yes—
164C2×C8×C13#4112yes—
165C13×C22⋊C4—22no—
166C13×C22⋊C4—41no—
167C42×C13—21no—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C22⋊Dic13—22no—
172C22⋊Dic13—41no—
173C22⋊Dic13C4⋊C414yes—
174C22⋊Dic13C4⋊C414yes—
175C4⋊Dic13C4⋊C414yes—
176C4⋊Dic13C4⋊C414yes—
177#6101—22no—
178#6101—22no—
179#6101—41no—
180#6101—41no—
181C4×Dic13—22no—
182C4×Dic13—21no—
183C4×Dic13—21no—
184C4×Dic13—21no—
185C4×Dic13—21no—
186C4×Dic13—22no—
187C4×Dic13—41no—
188C4×Dic13—41no—
189C4×Dic13C2×D412yes—
190C4×Dic13C2×D412yes—
191C4×Dic13C2×Q812yes—
192C4×Dic13C2×Q812yes—
193C2×#1055—28no—
194C2×#1055—21no—
195C2×#1055—21no—
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#4112yes—
205C2×#1055#4112yes—
206C2×#433—131no—
207C2×#405—131no—
208#2298—131no—
209#1940—131no—
210#1940—131no—
211#1939—131no—
212#1939—131no—
213#1851—131no—
214#1851D1311yescharacteristic
215#1850—131no—
216#1850—131no—
217#1768—131no—
218#1768—131no—
219#1767—131no—
220C4×C4⋊C8—131no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13C2×C4⋊C412yes—
228C23×C13C23×C411yescharacteristic
229C2×C4×C13—21no—
230C2×C4×C13—21no—
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×C13C2×C4⋊C412yes—
247C2×C4×C13#13112yes—
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C22×Q811yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×Dic13—21no—
255C2×Dic13—21no—
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×Dic13C2×C4⋊C412yes—
274C2×Dic13C2×C4⋊C412yes—
275C2×Dic13C2×C4⋊C412yes—
276C2×Dic13C2×C4⋊C412yes—
277C2×Dic13#13112yes—
278C8×C13—22no—
279C8×C13—22no—
280C8×C13—41no—
281C8×C13—41no—
282#1055—22no—
283#1055—22no—
284#1055—41no—
285#1055—41no—
286C22×M16C2×D1311yescharacteristic
287C23×C8—131no—
288C2×#117—131no—
289#433—264no—
290C2×C4⋊C8—131no—
291C2×C4⋊C8—131no—
292C2×C4⋊C8—131no—
293C2×C4⋊C8—131no—
294C2×C4⋊C8—131no—
295C2×C4⋊C8—131no—
296C2×C4⋊C8—131no—
297C2×C4⋊C8—131no—
298C2×C4⋊C8C2×D1311yescharacteristic
299C2×C4⋊C8C2×D1311yescharacteristic
300C2×C22⋊C8—131no—
301C2×C22⋊C8C2×D1311yescharacteristic
302#405—264no—
303C2×#97—131no—
304C2×#97—131no—
305C2×#97—131no—
306C2×C4×C8—131no—
307C2×C4×C8—131no—
308C2×C4×C8—131no—
309#388—131no—
310#388—131no—
311#388—131no—
312#388—131no—
313#387—131no—
314#387—131no—
315#387—131no—
316#387—131no—
317C4×C4⋊C4—131no—
318C4×C4⋊C4—131no—
319C4×C22⋊C4—131no—
320C4×C22⋊C4C2×D1311yescharacteristic
321#376—131no—
322C43—131no—
323#336—131no—
324#336—131no—
325#336—131no—
326#336—131no—
327#336—131no—
328#336—131no—
329#336C2×D1311yescharacteristic
330#336C2×D1311yescharacteristic
331C22×C13—22no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13C22×C4⋊C411yescharacteristic
339C22×C13C4×#4111yescharacteristic
340C22×C13C4×#4111yescharacteristic
341C22×C13C2×#13111yescharacteristic
342C22×C13C2×#13111yescharacteristic
343C22×C13#56811yescharacteristic
344C22×C13#56811yescharacteristic
345C4×C13—22no—
346C4×C13—22no—
347C4×C13—41no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13#52511yescharacteristic
351C4×C13#52511yescharacteristic
352C4×C13#53311yescharacteristic
353C4×C13#53311yescharacteristic
354Dic13—22no—
355Dic13—22no—
356Dic13—22no—
357Dic13—22no—
358Dic13—22no—
359Dic13—41no—
360Dic13—41no—
361Dic13—41no—
362C23×C4C22×D1311yescharacteristic
363C2×M16—22no—
364C2×M16—22no—
365C2×M16—22no—
366C22×C8—131no—
367C22×C8—131no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8—262no—
371C22×C8—262no—
372C22×C8—262no—
373C22×C8C22×D1311yescharacteristic
374C22×C8C22×D1311yescharacteristic
375C22×C8C22×D1311yescharacteristic
376C22×C8C22×D1311yescharacteristic
377#117—134no—
378#117—134no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C22⋊C4—131no—
386C2×C22⋊C4—131no—
387C2×C22⋊C4—131no—
388C2×C22⋊C4—131no—
389C2×C22⋊C4C4×D1311yescharacteristic
390C2×C22⋊C4C4×D1311yescharacteristic
391C2×C42—131no—
392C2×C42—131no—
393C2×C42—131no—
394C2×C42—131no—
395C2×C42—131no—
396C2×C42—131no—
397C2×C42—131no—
398C2×C42—131no—
399C2×C42C22×D1311yescharacteristic
400C2×C42C22×D1311yescharacteristic
401C4⋊C8—22no—
402C4⋊C8—22no—
403C4⋊C8—262no—
404C4⋊C8—262no—
405C4⋊C8—262no—
406C4⋊C8—262no—
407C4⋊C8—262no—
408C4⋊C8—262no—
409C4⋊C8—262no—
410C4⋊C8—262no—
411C22⋊C8—22no—
412C22⋊C8—262no—
413#97—262no—
414#97—262no—
415#97—262no—
416C4×C8—262no—
417C4×C8—262no—
418C4×C8—262no—
419#95—131no—
420#95—131no—
421#95—131no—
422#95—131no—
423#95—131no—
424#95—131no—
425#95—131no—
426#95—131no—
427#95—131no—
428#95—131no—
429#95C4×D1311yescharacteristic
430#95C4×D1311yescharacteristic
431C2×C13—42no—
432C2×C13#229611yescharacteristic
433C2×C13#290611yescharacteristic
434C2×C13#290611yescharacteristic
435C2×C13#296611yescharacteristic
436C2×C13#296711yescharacteristic
437C2×C13#296811yescharacteristic
438C2×C13#296911yescharacteristic
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×C4C2×C4×D1311yescharacteristic
453C22×C4C2×C4×D1311yescharacteristic
454C22×C4C2×C4×D1311yescharacteristic
455C22×C4C2×C4×D1311yescharacteristic
456C22×C4C2×C4×D1311yescharacteristic
457C22×C4D4×D1312yes—
458C22×C4Q8×D1312yes—
459C22×C4C23×D1311yescharacteristic
460M16—28no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—132no—
472C2×C8—132no—
473C2×C8—268no—
474C2×C8—261no—
475C2×C8—261no—
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#612912yes—
485C2×C8#612912yes—
486C4⋊C4—134no—
487C4⋊C4—134no—
488C4⋊C4—262no—
489C4⋊C4—262no—
490C4⋊C4—521no—
491C4⋊C4—521no—
492C22⋊C4—22no—
493C22⋊C4—41no—
494C22⋊C4—134no—
495C22⋊C4—134no—
496C22⋊C4—262no—
497C22⋊C4—521no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—132no—
503C42—132no—
504C42—132no—
505C42—132no—
506C42—262no—
507C42—262no—
508C42—261no—
509C42—261no—
510C42—261no—
511C42—261no—
512C42—521no—
513C42—521no—
514C13#2135711yescharacteristic, complemented, Sylow
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23C4⋊C4×D1312yes—
522C23C22×C4×D1311yescharacteristic
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—132no—
541C2×C4—132no—
542C2×C4—132no—
543C2×C4—132no—
544C2×C4—132no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
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×C4C4⋊C4×D1312yes—
565C2×C4#8816112yes—
566C2×C4C2×D4×D1311yescharacteristic
567C2×C4C2×#612911yescharacteristic
568C2×C4C2×#612911yescharacteristic
569C2×C4C2×Q8×D1311yescharacteristic
570C2×C4#41×D1311yescharacteristic
571C2×C4#41×D1311yescharacteristic
572C8—22no—
573C8—22no—
574C8—41no—
575C8—41no—
576C8—262no—
577C8—262no—
578C8—521no—
579C8—521no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C2×C4⋊C4×D1311yescharacteristic
588C22C4×#612911yescharacteristic
589C22C4×#612911yescharacteristic
590C22C2×#8816111yescharacteristic
591C22#1171945011yescharacteristic
592C22D13×#13111yescharacteristic
593C22#1171945511yescharacteristic
594C4—22no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—262no—
600C4—262no—
601C4—262no—
602C4—262no—
603C4—262no—
604C4—521no—
605C4—521no—
606C4—521no—
607C4#1171929111yescharacteristic
608C4#1171932711yescharacteristic
609C4#1171932711yescharacteristic
610C4#1171936111yescharacteristic
611C2—42no—
612C2#1311731511yescharacteristic
613C2#1312340311yescharacteristic
614C2#1312340511yescharacteristic
615C2#1312380611yescharacteristic
616C2#1312382211yescharacteristic
617C2#1312382711yescharacteristic
618C2#1312384311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1851C2
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenter#1851D13
hypocenterC13#21357
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
4. #13115558C2semidirect
5. #13115556C2semidirect
6. #13115553C2semidirect
7. #13115551C2semidirect
11. #13114695C2semidirect
12. #13114692C2semidirect
13. #13114688C2semidirect
14. C4⋊C8×Dic13C2semidirect
514. C13#21357semidirect

Maximal subgroups

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

subgroupindex
C2×#117183812
C2×#117187832
#131173322
#131155582
#131155562
#131155532
#131155512
#131150192
#131150162
#131150132
#131146952
#131146922
#131146882
C4⋊C8×Dic132
C13×#18512
#2135713