Finite Group Databasebeta

← #15869006

Subgroups — #15869006

Order 3328.

1096 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718789C211yesmaximal, characteristic, complemented
2C2×#11718367C211yesmaximal, characteristic, complemented
3C2×#11718788C211yesmaximal, characteristic, complemented
4C4×#88184C211yesmaximal, characteristic
5#13115634C211yesmaximal, characteristic, complemented
6#13115559C211yesmaximal, characteristic, complemented
7#13115442C211yesmaximal, characteristic, complemented
8#13115442C211yesmaximal, characteristic, complemented
9#13115133C211yesmaximal, characteristic, complemented
10#13115133C211yesmaximal, characteristic, complemented
11#13114816C211yesmaximal, characteristic, complemented
12#13114708C211yesmaximal, characteristic, complemented
13#13114619C211yesmaximal, characteristic, complemented
14C8×#6103C211yesmaximal, characteristic, complemented
15C2×C4×C13×M16C211yesmaximal, characteristic, complemented
16C22×C13×M16C2211yescharacteristic
17C22×C13×M16C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C2×#88184C411yescharacteristic
20C2×C4×C22⋊D13C2211yescharacteristic
21C2×C4×C22⋊D13C2211yescharacteristic
22C22×#6094C2211yescharacteristic
23C22×C8×D13C2211yescharacteristic
24C2×C4×D52C2211yescharacteristic
25C4×C13×M16—24no—
26C2×C13×#97C2211yescharacteristic
27C2×C13×#97C2211yescharacteristic
28C2×C4×C8×C13C2211yescharacteristic
29C2×C4×C8×C13C2211yescharacteristic
30#11718874C411yescharacteristic
31#11718874C411yescharacteristic
32#11718873C411yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35#11718789—24no—
36#11718788—24no—
37C2×#88060C2211yescharacteristic
38C2×#88060C2211yescharacteristic
39C2×#88060C2211yescharacteristic
40C2×#88060C2211yescharacteristic
41C2×#88060C2211yescharacteristic
42C2×#88060C2211yescharacteristic
43C2×#88055C2211yescharacteristic
44C2×#88054C2211yescharacteristic
45C2×#88054C2211yescharacteristic
46C2×C8×Dic13C2211yescharacteristic
47#11718601C411yescharacteristic
48#11718601C411yescharacteristic
49#11718600C411yescharacteristic
50C4×#6103C2211yescharacteristic
51C4×#6103C2211yescharacteristic
52C4×C4⋊Dic13C2211yescharacteristic
53#11718589C411yescharacteristic
54C2×C4⋊#1055C2211yescharacteristic
55C2×C4⋊#1055C2211yescharacteristic
56#11718367—24no—
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63C23×C4×C13C2×C411yescharacteristic
64C23×C4×C13C2×C411yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C22×C22⋊D13C2×C411yescharacteristic
67C22×C22⋊D13C2×C411yescharacteristic
68C22×D52C2×C411yescharacteristic
69C22×C4×D13C2311yescharacteristic
70C22×C4×D13C2311yescharacteristic
71C2×C13×M16—22no—
72C2×C13×M16—22no—
73C2×C13×M16—22no—
74C2×C13×M16—22no—
75C2×C13×M16—22no—
76C2×C13×M16D414yescomplemented
77C22×C8×C13C2311yescharacteristic
78C22×C8×C13C2311yescharacteristic
79C22×C8×C13C2311yescharacteristic
80C22×C8×C13C2311yescharacteristic
81C2×C42×C13—22no—
82C2×C42×C13—22no—
83C2×C42×C13C2×C411yescharacteristic
84C2×C42×C13C2×C411yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13C2×C411yescharacteristic
88C2×C22⋊Dic13C2×C411yescharacteristic
89#88184—24no—
90C4×C22⋊D13—22no—
91C4×C22⋊D13—22no—
92C4×C22⋊D13—22no—
93C4×C22⋊D13—22no—
94C2×#6103C2×C411yescharacteristic
95C2×#6103C2×C411yescharacteristic
96C2×#6103C2×C411yescharacteristic
97C2×#6103C2×C411yescharacteristic
98C2×#6103C2×C411yescharacteristic
99C2×#6103C2×C411yescharacteristic
100C2×#6103C2×C411yescharacteristic
101C2×#6103C2×C411yescharacteristic
102C2×C4⋊Dic13C2×C411yescharacteristic
103C2×C4⋊Dic13C2×C411yescharacteristic
104C2×C4⋊Dic13C2×C411yescharacteristic
105C2×#6101C2×C411yescharacteristic
106C2×#6101C2×C411yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C2×C4×Dic13C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C22×#1055C2311yescharacteristic
113C2×#6094—22no—
114C2×#6094—22no—
115C2×#6094—22no—
116C2×C8×D13—22no—
117C2×C8×D13—22no—
118C2×C8×D13—22no—
119C4×D52—22no—
120C4×D52—22no—
121C13×#97—22no—
122C13×#97D414yescomplemented
123C4×C8×C13—22no—
124C4×C8×C13—22no—
125#88071C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129#88071C2×C411yescharacteristic
130#88071C2×C411yescharacteristic
131C22⋊#1055—22no—
132C22⋊#1055—22no—
133#88060—22no—
134#88060—22no—
135#88060—22no—
136#88060—22no—
137#88060—22no—
138#88060—22no—
139#88055—22no—
140#88054—22no—
141#88054—22no—
142C8×Dic13—22no—
143C4⋊#1055—22no—
144C4⋊#1055—22no—
145#21490—131nomaximal, Sylow
146C24×C13C22×C411yescharacteristic
147C23×D13C22×C411yescharacteristic
148C23×D13C22×C411yescharacteristic
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—41no—
158C22×C4×C13—41no—
159C22×C4×C13C22×C411yescharacteristic
160C22×C4×C13C22×C411yescharacteristic
161C22×C4×C13C22×C411yescharacteristic
162C22×C4×C13C22×C411yescharacteristic
163C22×C4×C13C22×C411yescharacteristic
164C22×C4×C13C2×D412yes—
165C22×C4×C13#4112yes—
166C22×C4×C13C2411yescharacteristic
167C2×C22⋊D13—22no—
168C2×C22⋊D13—22no—
169C2×C22⋊D13—22no—
170C2×C22⋊D13—22no—
171C2×C22⋊D13—41no—
172C2×C22⋊D13—41no—
173C22×Dic13C22×C411yescharacteristic
174C22×Dic13C22×C411yescharacteristic
175C22×Dic13C22×C411yescharacteristic
176C22×Dic13C22×C411yescharacteristic
177C22×Dic13C22×C411yescharacteristic
178C22×Dic13C22×C411yescharacteristic
179C2×D52—22no—
180C2×D52—22no—
181C2×D52—41no—
182C2×C4×D13—21no—
183C2×C4×D13—21no—
184C2×C4×D13—21no—
185C2×C4×D13—21no—
186C2×C4×D13—21no—
187C2×C4×D13—21no—
188C2×C4×D13—21no—
189C2×C4×D13—21no—
190C2×C4×D13—21no—
191C2×C4×D13—21no—
192C2×C4×D13—21no—
193C2×C4×D13—21no—
194C13×M16—28no—
195C13×M16—28no—
196C2×C8×C13—21no—
197C2×C8×C13—21no—
198C2×C8×C13—21no—
199C2×C8×C13—21no—
200C2×C8×C13—21no—
201C2×C8×C13—21no—
202C2×C8×C13C2×D412yes—
203C2×C8×C13C2×D412yes—
204C2×C8×C13C2×D412yes—
205C2×C8×C13C2×D412yes—
206C2×C8×C13#4112yes—
207C2×C8×C13#4112yes—
208C42×C13—22no—
209C42×C13—22no—
210C42×C13—21no—
211C42×C13—21no—
212C42×C13C2×D412yes—
213C42×C13#4112yes—
214C22⋊Dic13—22no—
215C22⋊Dic13—22no—
216#6103—22no—
217#6103—22no—
218#6103—22no—
219#6103—22no—
220#6103—22no—
221#6103—22no—
222#6103—22no—
223#6103M1614yescomplemented
224C4⋊Dic13—22no—
225C4⋊Dic13—22no—
226C4⋊Dic13—41no—
227#6101—22no—
228#6101—22no—
229C4×Dic13—21no—
230C4×Dic13—21no—
231C4×Dic13—21no—
232C4×Dic13—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055—21no—
244C2×#1055—21no—
245#6094—44no—
246C8×D13—44no—
247C2×#436—131no—
248C2×#435—131no—
249C2×#435—131no—
250C2×C4×M16D1311yescharacteristic, complemented
251C4×#121—131no—
252#1955—131no—
253#1940—131no—
254#1923—131no—
255#1923—131no—
256#1870—131no—
257#1870—131no—
258#1797—131no—
259#1771—131no—
260#1753—131no—
261C8×C22⋊C4—131no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13C4×D412yes—
269C23×C13C23×C411yescharacteristic
270C22×D13—21no—
271C22×D13—21no—
272C22×D13—21no—
273C22×D13—21no—
274C22×D13—21no—
275C22×D13—21no—
276C22×D13—21no—
277C22×D13—21no—
278C22×D13—21no—
279C22×D13—21no—
280C22×D13—21no—
281C22×D13—21no—
282C22×D13—21no—
283C22×D13C2×M1612yes—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—44no—
299C2×C4×C13—44no—
300C2×C4×C13C4×D412yes—
301C2×C4×C13C4×D412yes—
302C2×C4×C13C4×D412yes—
303C2×C4×C13C2×M1612yes—
304C2×C4×C13#13112yes—
305C2×C4×C13C22×D411yescharacteristic
306C2×C4×C13C22×D411yescharacteristic
307C2×C4×C13C2×#4111yescharacteristic
308C2×C4×C13C2×#4111yescharacteristic
309C2×C4×C13C2×#4111yescharacteristic
310C2×C4×C13C2×#4111yescharacteristic
311C22⋊D13—44no—
312C22⋊D13—44no—
313C2×Dic13—21no—
314C2×Dic13—21no—
315C2×Dic13—21no—
316C2×Dic13—21no—
317C2×Dic13—21no—
318C2×Dic13—21no—
319C2×Dic13—21no—
320C2×Dic13—21no—
321C2×Dic13—21no—
322C2×Dic13—21no—
323C2×Dic13—21no—
324C2×Dic13—21no—
325C2×Dic13—21no—
326C2×Dic13—21no—
327C2×Dic13—21no—
328C2×Dic13—21no—
329C2×Dic13—21no—
330C2×Dic13C2×M1612yes—
331D52—44no—
332C4×D13—41no—
333C4×D13—41no—
334C4×D13—41no—
335C4×D13—41no—
336C4×D13—41no—
337C4×D13—41no—
338C4×D13—41no—
339C4×D13—41no—
340C8×C13—22no—
341C8×C13—22no—
342C8×C13—22no—
343C8×C13#12114yescomplemented
344#1055—41no—
345#1055—41no—
346#1055—41no—
347#1055—41no—
348C22×M16—131no—
349C22×M16C2×D1311yescharacteristic
350C22×M16C2×D1311yescharacteristic
351C23×C8—131no—
352C2×#121—131no—
353C2×C4×D4—131no—
354C2×C4×D4—131no—
355C2×C4×D4—131no—
356C22×C42C2×D1311yescharacteristic
357#436—264no—
358#435—264no—
359#435—264no—
360C2×C4⋊C8—131no—
361C2×C4⋊C8—131no—
362C2×C4⋊C8—131no—
363C2×C4⋊C8—131no—
364C2×C22⋊C8—131no—
365C2×C22⋊C8—131no—
366C2×C22⋊C8—131no—
367C2×C22⋊C8—131no—
368C2×C22⋊C8—131no—
369C2×C22⋊C8—131no—
370C2×C22⋊C8—131no—
371C2×C22⋊C8—131no—
372C4×M16—24no—
373C2×#97—131no—
374C2×#97C2×D1311yescharacteristic
375C2×#97C2×D1311yescharacteristic
376C2×C4×C8—131no—
377C2×C4×C8C2×D1311yescharacteristic
378C2×C4×C8C2×D1311yescharacteristic
379#390—131no—
380#389—131no—
381#388—131no—
382#388—131no—
383#386—131no—
384#386—131no—
385#380—131no—
386C4×C4⋊C4—131no—
387C4×C22⋊C4—131no—
388C4×C22⋊C4—131no—
389#336—131no—
390#336—131no—
391#336—131no—
392#336—131no—
393#336—131no—
394#336—131no—
395C22×C13—22no—
396C22×C13—22no—
397C22×C13—22no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—41no—
401C22×C13—41no—
402C22×C13C2×C4×D411yescharacteristic
403C22×C13C2×C4×D411yescharacteristic
404C22×C13C4×#4111yescharacteristic
405C22×C13C22×M1611yescharacteristic
406C22×C13C2×#13111yescharacteristic
407C22×C13#56811yescharacteristic
408C22×C13#56811yescharacteristic
409C2×D13—22no—
410C2×D13—22no—
411C2×D13—22no—
412C2×D13—41no—
413C2×D13—41no—
414C2×D13—41no—
415C2×D13—41no—
416C2×D13—41no—
417C2×D13—41no—
418C2×D13—41no—
419C2×D13—41no—
420C2×D13—41no—
421C2×D13—41no—
422C2×D13—41no—
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—22no—
426C4×C13—22no—
427C4×C13—22no—
428C4×C13C2×#12111yescharacteristic
429C4×C13#52511yescharacteristic
430C4×C13#52911yescharacteristic
431C4×C13#53211yescharacteristic
432Dic13—22no—
433Dic13—41no—
434Dic13—41no—
435Dic13—41no—
436Dic13—41no—
437Dic13—41no—
438C22×D4—131no—
439C22×D4—131no—
440C22×D4—131no—
441C23×C4—131no—
442C23×C4—131no—
443C23×C4C4×D1311yescharacteristic
444C23×C4C4×D1311yescharacteristic
445C23×C4C22×D1311yescharacteristic
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—262no—
452C2×M16—262no—
453C2×M16—262no—
454C2×M16D5214yescomplemented
455C22×C8—131no—
456C22×C8—131no—
457C22×C8—131no—
458C22×C8—131no—
459C22×C8—262no—
460C22×C8—262no—
461C22×C8—262no—
462C22×C8C22×D1311yescharacteristic
463C22×C8C22×D1311yescharacteristic
464C22×C8C22×D1311yescharacteristic
465C22×C8C22×D1311yescharacteristic
466#121—264no—
467C4×D4—262no—
468C4×D4—262no—
469C4×D4—262no—
470C4×D4—262no—
471C4×D4—262no—
472C4×D4—262no—
473C2×C4⋊C4—131no—
474C2×C4⋊C4—131no—
475C2×C4⋊C4—131no—
476C2×C4⋊C4—131no—
477C2×C4⋊C4—131no—
478C2×C22⋊C4—131no—
479C2×C22⋊C4—131no—
480C2×C22⋊C4—131no—
481C2×C22⋊C4—131no—
482C2×C22⋊C4—131no—
483C2×C22⋊C4—131no—
484C2×C22⋊C4—131no—
485C2×C22⋊C4—131no—
486C2×C22⋊C4—131no—
487C2×C22⋊C4—131no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—131no—
491C2×C42—131no—
492C2×C42C4×D1311yescharacteristic
493C2×C42C4×D1311yescharacteristic
494C2×C42C22×D1311yescharacteristic
495C2×C42C22×D1311yescharacteristic
496C4⋊C8—262no—
497C4⋊C8—262no—
498C4⋊C8—262no—
499C4⋊C8—262no—
500C22⋊C8—262no—
501C22⋊C8—262no—
502C22⋊C8—262no—
503C22⋊C8—262no—
504C22⋊C8—262no—
505C22⋊C8—262no—
506C22⋊C8—262no—
507C22⋊C8—262no—
508#97—22no—
509#97—262no—
510#97C22⋊D1314yescomplemented
511C4×C8—22no—
512C4×C8—22no—
513C4×C8—262no—
514#95—131no—
515#95—131no—
516#95—131no—
517#95—131no—
518#95—131no—
519#95—131no—
520C2×C13—42no—
521C2×C13C4×#12111yescharacteristic
522C2×C13#293311yescharacteristic
523C2×C13D4×M1611yescharacteristic
524C2×C13D4×M1611yescharacteristic
525C2×C13#293511yescharacteristic
526C2×C13#296511yescharacteristic
527C2×C13#296711yescharacteristic
528D13—42no—
529D13—81no—
530C24—131no—
531C24—131no—
532C24C2×C4×D1311yescharacteristic
533C2×D4—262no—
534C2×D4—262no—
535C2×D4—262no—
536C2×D4—262no—
537C2×D4—262no—
538C2×D4—262no—
539C2×D4—521no—
540C2×D4—521no—
541C2×D4—521no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—131no—
553C22×C4—131no—
554C22×C4—131no—
555C22×C4—131no—
556C22×C4—131no—
557C22×C4—131no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4C2×C4×D1311yescharacteristic
571C22×C4C2×C4×D1311yescharacteristic
572C22×C4C2×C4×D1311yescharacteristic
573C22×C4C2×C4×D1311yescharacteristic
574C22×C4C2×C4×D1311yescharacteristic
575C22×C4C2×D5212yes—
576C22×C4#612712yes—
577C22×C4C23×D1311yescharacteristic
578M16—28no—
579M16—28no—
580M16—524no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—261no—
590C2×C8—261no—
591C2×C8—261no—
592C2×C8—261no—
593C2×C8—261no—
594C2×C8—261no—
595C2×C8—261no—
596C2×C8—261no—
597C2×C8—261no—
598C2×C8—261no—
599C2×C8—524no—
600C2×C8C2×D5212yes—
601C2×C8C2×D5212yes—
602C2×C8#612712yes—
603C2×C8#612712yes—
604C2×C8C2×C22⋊D1312yes—
605C2×C8C2×C22⋊D1312yes—
606C4⋊C4—262no—
607C4⋊C4—262no—
608C4⋊C4—262no—
609C4⋊C4—262no—
610C4⋊C4—521no—
611C22⋊C4—134no—
612C22⋊C4—262no—
613C22⋊C4—262no—
614C22⋊C4—262no—
615C22⋊C4—262no—
616C22⋊C4—262no—
617C22⋊C4—262no—
618C22⋊C4—262no—
619C22⋊C4—262no—
620C22⋊C4—262no—
621C42—22no—
622C42—22no—
623C42—21no—
624C42—21no—
625C42—261no—
626C42—261no—
627C42—261no—
628C42—261no—
629C42#612712yes—
630C42C2×C22⋊D1312yes—
631C13#2149011yescharacteristic, complemented, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—132no—
639C23—261no—
640C23—261no—
641C23—261no—
642C23—261no—
643C23—261no—
644C23—261no—
645C23—261no—
646C23—261no—
647C23—261no—
648C23—261no—
649C23—261no—
650C23—261no—
651C23—261no—
652C23C4×D5212yes—
653C23C22×C4×D1311yescharacteristic
654D4—524no—
655D4—524no—
656D4—524no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—132no—
674C2×C4—261no—
675C2×C4—261no—
676C2×C4—261no—
677C2×C4—261no—
678C2×C4—261no—
679C2×C4—261no—
680C2×C4—261no—
681C2×C4—261no—
682C2×C4—261no—
683C2×C4—261no—
684C2×C4—261no—
685C2×C4—261no—
686C2×C4—261no—
687C2×C4—261no—
688C2×C4—261no—
689C2×C4—261no—
690C2×C4—261no—
691C2×C4—521no—
692C2×C4—521no—
693C2×C4—521no—
694C2×C4—521no—
695C2×C4—521no—
696C2×C4—521no—
697C2×C4—521no—
698C2×C4—521no—
699C2×C4C4×D5212yes—
700C2×C4M16×D1312yes—
701C2×C4#8816112yes—
702C2×C4C4×C22⋊D1312yes—
703C2×C4C4×C22⋊D1312yes—
704C2×C4C22×D5211yescharacteristic
705C2×C4C2×#612711yescharacteristic
706C2×C4C2×#612711yescharacteristic
707C2×C4C2×#612711yescharacteristic
708C2×C4C2×#612711yescharacteristic
709C2×C4C22×C22⋊D1311yescharacteristic
710C8—22no—
711C8—22no—
712C8—22no—
713C8—521no—
714C8—521no—
715C8—521no—
716C8—521no—
717C8#8818414yescomplemented
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—262no—
726C22—262no—
727C22—262no—
728C22—521no—
729C22—521no—
730C22—521no—
731C22—521no—
732C22—521no—
733C22—521no—
734C22—521no—
735C22—521no—
736C22—521no—
737C22—521no—
738C22—521no—
739C22C2×C4×D5211yescharacteristic
740C22C4×#612711yescharacteristic
741C22C2×M16×D1311yescharacteristic
742C22C2×#8816111yescharacteristic
743C22#1171945011yescharacteristic
744C22#1171945011yescharacteristic
745C22C2×C4×C22⋊D1311yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—262no—
752C4—521no—
753C4—521no—
754C4—521no—
755C4—521no—
756C4—521no—
757C4#1171918211yescharacteristic
758C4#1171918411yescharacteristic
759C4C2×#8818411yescharacteristic
760C4#1171949611yescharacteristic
761C2—42no—
762C2—522no—
763C2—1041no—
764C2C4×#8818411yescharacteristic
765C2#1312356111yescharacteristic
766C2M16×C22⋊D1311yescharacteristic
767C2M16×D5211yescharacteristic
768C2#1312358211yescharacteristic
769C2#1312379811yescharacteristic
770C2#1312382111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C4×C13×M16C2
prime radicalC2×#88184C4
cosocleC22×C4×C13C24
hypercenterC2×C4×M16D13
hypocenterC13#21490
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#11718789C2semidirect
2. C2×#11718367C2semidirect
3. C2×#11718788C2semidirect
5. #13115634C2semidirect
6. #13115559C2semidirect
7. #13115442C2semidirect
8. #13115442C2semidirect
9. #13115133C2semidirect
10. #13115133C2semidirect
11. #13114816C2semidirect
12. #13114708C2semidirect
13. #13114619C2semidirect
14. C8×#6103C2semidirect
15. C2×C4×C13×M16C2semidirect
76. C2×C13×M16D4semidirect
122. C13×#97D4semidirect
223. #6103M16semidirect
250. C2×C4×M16D13semidirect
343. C8×C13#121semidirect
454. C2×M16D52semidirect
510. #97C22⋊D13semidirect
631. C13#21490semidirect
717. C8#88184semidirect

Maximal subgroups

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

subgroupindex
C2×#117187892
C2×#117183672
C2×#117187882
C4×#881842
#131156342
#131155592
#131154422
#131151332
#131148162
#131147082
#131146192
C8×#61032
C2×C4×C13×M162
#2149013