Finite Group Databasebeta

← #15786379

Subgroups — #15786379

Order 3328.

2054 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88142C211yesmaximal, characteristic
2C22×#88141C211yesmaximal, characteristic
3C2×#11718307C211yesmaximal, characteristic
4C2×#11718307C211yesmaximal, characteristic
5C2×#11718307C211yesmaximal, characteristic
6#13113088C211yesmaximal, characteristic
7#13113087C211yesmaximal, characteristic
8#13113086C211yesmaximal, characteristic
9#13113071C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic
11#13113068C211yesmaximal, characteristic
12#13113067C211yesmaximal, characteristic
13#13113064C211yesmaximal, characteristic
14#95×Dic13C211yesmaximal, characteristic
15C13×#1441C211yesmaximal, characteristic
16C23×Dic26C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101C2211yescharacteristic
22C22×#6101C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×#88142—24no—
32C2×#88142—24no—
33C2×#88142C418yescomplemented
34C2×#88141—24no—
35C2×#88141—24no—
36C2×#88141—24no—
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718307—24no—
58#11718307—24no—
59#11718307—24no—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C22×Dic26—22no—
76C22×Dic26—22no—
77C22×Dic26—22no—
78C22×Dic26—22no—
79C22×Dic26—22no—
80C22×Dic26—22no—
81C22×Dic26—22no—
82C22×Dic26—22no—
83C22×Dic26—22no—
84C22×Dic26—22no—
85C22×Dic26C2×C414yes—
86C22×Dic26C2×C414yes—
87C22×Dic26D414yes—
88C22×Dic26D414yes—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4C2×C414yes—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13C2×C414yes—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101—22no—
110C2×#6101C2×C414yes—
111C2×#6101C2×C414yes—
112C2×#6101D414yes—
113C2×C4×Dic13—22no—
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—22no—
124C2×C4×Dic13—22no—
125C2×C4×Dic13—22no—
126C2×C4×Dic13C2×C414yes—
127C2×C4×Dic13D414yes—
128#88142—232no—
129#88141—232no—
130C13×#95—22no—
131C13×#95—22no—
132C13×#95—22no—
133C13×#95—22no—
134C13×#95—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—22no—
143#88071—22no—
144#88071—22no—
145#88071—22no—
146#88071—22no—
147#88071—22no—
148#88071Q814yescomplemented
149#88071Q814yescomplemented
150#14024—131nomaximal, Sylow
151C24×C13C2411yescharacteristic
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13C22×C412yes—
192C22×C4×C13C22×C412yes—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C2×D412yes—
195C22×C4×C13C2×D412yes—
196C22×C4×C13C2×D412yes—
197C22×C4×C13C2×D412yes—
198C22×C4×C13C2×Q812yes—
199C22×C4×C13C2×Q812yes—
200C22×C4×C13#4112yes—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13C22×C412yes—
239C22×Dic13C22×C412yes—
240C22×Dic13C22×C412yes—
241C22×Dic13C22×C412yes—
242C22×Dic13C2×D412yes—
243C22×Dic13C2×D412yes—
244C22×Dic13C2×D412yes—
245C22×Dic13C2×D412yes—
246C22×Dic13C2×D412yes—
247C22×Dic13C2×D412yes—
248C22×Dic13C2×D412yes—
249C22×Dic13C2×D412yes—
250C22×Dic13C2×Q812yes—
251C22×Dic13C2×Q812yes—
252C22×Dic13C2×Q812yes—
253C22×Dic13C2×Q812yes—
254C22×Dic13#4112yes—
255C22×Dic13#4112yes—
256C22×Dic13#4112yes—
257C2×Dic26—28no—
258C2×Dic26—28no—
259C2×Dic26—28no—
260C2×Dic26—28no—
261C2×Dic26—28no—
262C2×Dic26—28no—
263C2×Dic26—28no—
264C2×Dic26—28no—
265C2×Dic26—28no—
266C2×Dic26—44no—
267C2×Dic26—44no—
268C2×Dic26—44no—
269C2×Dic26—44no—
270C2×Dic26C22⋊C4116yes—
271C13×C4⋊C4—28no—
272C13×C4⋊C4—28no—
273C4⋊Dic13—28no—
274#6101—28no—
275#6101—28no—
276#6101—28no—
277#6101—28no—
278#6101—44no—
279C4×Dic13—28no—
280C4×Dic13—28no—
281C4×Dic13—28no—
282C4×Dic13—28no—
283C4×Dic13—44no—
284C22×C4⋊Q8—131no—
285C22×C4×Q8—131no—
286C2×#391—131no—
287C2×#391—131no—
288C2×#391—131no—
289#1441—131no—
290#1441—131no—
291#1441—131no—
292#1441D1311yescharacteristic
293#1436—131no—
294#1436—131no—
295#1436—131no—
296#1436—131no—
297C4⋊#95—131no—
298C4×#95—131no—
299C23×C13C23×C411yescharacteristic
300C23×C13C22×D411yescharacteristic
301C23×C13C22×D411yescharacteristic
302C23×C13C22×D411yescharacteristic
303C23×C13C22×D411yescharacteristic
304C23×C13C22×Q811yescharacteristic
305C23×C13C22×Q811yescharacteristic
306C23×C13C2×#4111yescharacteristic
307C23×C13C2×#4111yescharacteristic
308C23×C13C2×#4111yescharacteristic
309C23×C13C2×#4111yescharacteristic
310C23×C132−1+411yescharacteristic
311C23×C132−1+411yescharacteristic
312C23×C132−1+411yescharacteristic
313C23×C132−1+411yescharacteristic
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13—41no—
349C2×C4×C13—41no—
350C2×C4×C13—41no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13C2×C22⋊C414yes—
362C2×C4×C13C4×Q814yescomplemented
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—41no—
391C2×Dic13—41no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—41no—
400C2×Dic13—41no—
401C2×Dic13—41no—
402C2×Dic13—41no—
403C2×Dic13—41no—
404C2×Dic13—41no—
405C2×Dic13—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
408C2×Dic13—41no—
409C2×Dic13C2×C22⋊C414yes—
410C2×Dic13C2×C22⋊C414yes—
411C2×Dic13C4×D414yes—
412C2×Dic13C4×D414yes—
413C2×Dic13C4×Q814yescomplemented
414C2×Dic13#12014yes—
415C2×Dic13#12114yes—
416C2×Dic13#12114yes—
417C2×Dic13#12314yes—
418C2×Dic13C4⋊Q814yescomplemented
419Dic26—232no—
420Dic26—416no—
421C23×Q8—131no—
422C23×Q8—131no—
423C2×C4⋊Q8—138no—
424C2×C4⋊Q8—264no—
425C2×C4⋊Q8—264no—
426C2×C4×Q8—264no—
427C2×C4×Q8—264no—
428C2×C4×Q8—264no—
429C22×C4⋊C4—131no—
430C22×C4⋊C4—131no—
431C22×C4⋊C4—131no—
432C22×C4⋊C4—131no—
433C22×C4⋊C4—131no—
434C22×C4⋊C4—131no—
435C22×C4⋊C4C2×D1311yescharacteristic
436C22×C4⋊C4C2×D1311yescharacteristic
437C22×C42—131no—
438C22×C42—131no—
439C22×C42—131no—
440C22×C42—131no—
441C22×C42—131no—
442#391—264no—
443#391—264no—
444#391—264no—
445C2×#95—131no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95C2×D1311yescharacteristic
461C2×#95C2×D1311yescharacteristic
462C2×#95C2×D1311yescharacteristic
463C2×#95C2×D1311yescharacteristic
464C2×#95C2×D1311yescharacteristic
465C22×C13C22×C22⋊C411yescharacteristic
466C22×C13C2×C4×D411yescharacteristic
467C22×C13C2×C4×D411yescharacteristic
468C22×C13C2×C4×Q811yescharacteristic
469C22×C13C2×C4×Q811yescharacteristic
470C22×C13#51911yescharacteristic
471C22×C13#51911yescharacteristic
472C22×C13C2×#12011yescharacteristic
473C22×C13C2×#12111yescharacteristic
474C22×C13C2×#12111yescharacteristic
475C22×C13C2×#12311yescharacteristic
476C22×C13C2×C4⋊Q811yescharacteristic
477C22×C13#53211yescharacteristic
478C22×C13#53311yescharacteristic
479C22×C13#53311yescharacteristic
480C22×C13#53611yescharacteristic
481C22×C13#53611yescharacteristic
482C22×C13#54111yescharacteristic
483C22×C13#54111yescharacteristic
484C22×C13#54711yescharacteristic
485C22×C13#54711yescharacteristic
486C22×C13#54811yescharacteristic
487C22×C13#54811yescharacteristic
488C22×C13#54811yescharacteristic
489C22×C13#54811yescharacteristic
490C22×C13D4×Q811yescharacteristic
491C22×C13D4×Q811yescharacteristic
492C22×C13D4×Q811yescharacteristic
493C22×C13D4×Q811yescharacteristic
494C22×C13D4×Q811yescharacteristic
495C22×C13D4×Q811yescharacteristic
496C22×C13#55611yescharacteristic
497C22×C13#55611yescharacteristic
498C22×C13#55711yescharacteristic
499C22×C13#55711yescharacteristic
500C4×C13—24no—
501C4×C13—24no—
502C4×C13—42no—
503C4×C13—42no—
504C4×C13—42no—
505C4×C13—42no—
506C4×C13—81no—
507Dic13—24no—
508Dic13—24no—
509Dic13—24no—
510Dic13—42no—
511Dic13—42no—
512Dic13—42no—
513Dic13—81no—
514Dic13#38618yes—
515C22×Q8—134no—
516C22×Q8—134no—
517C22×Q8—134no—
518C22×Q8—134no—
519C22×Q8—262no—
520C22×Q8—262no—
521C22×Q8—262no—
522C22×Q8—262no—
523C22×Q8—262no—
524C22×Q8—262no—
525C22×Q8—262no—
526C22×Q8—262no—
527C22×Q8—262no—
528C22×Q8—262no—
529C23×C4—131no—
530C23×C4—131no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4C22×D1311yescharacteristic
538C23×C4C22×D1311yescharacteristic
539C23×C4C22×D1311yescharacteristic
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C4⋊Q8—2632no—
545C4×Q8—2632no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—134no—
552C2×C4⋊C4—134no—
553C2×C4⋊C4—134no—
554C2×C4⋊C4—134no—
555C2×C4⋊C4—262no—
556C2×C4⋊C4—262no—
557C2×C4⋊C4—262no—
558C2×C4⋊C4—262no—
559C2×C4⋊C4—262no—
560C2×C4⋊C4—262no—
561C2×C4⋊C4—262no—
562C2×C4⋊C4—262no—
563C2×C4⋊C4—262no—
564C2×C4⋊C4—262no—
565C2×C4⋊C4—262no—
566C2×C4⋊C4—262no—
567C2×C4⋊C4—262no—
568C2×C4⋊C4—262no—
569C2×C4⋊C4C4×D1314yes—
570C2×C42—134no—
571C2×C42—134no—
572C2×C42—262no—
573C2×C42—262no—
574C2×C42—262no—
575C2×C42—262no—
576C2×C42—262no—
577C2×C42—262no—
578C2×C42—262no—
579C2×C42—262no—
580C2×C42—262no—
581C2×C42—262no—
582C2×C42—262no—
583C2×C42—262no—
584C2×C42—262no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—134no—
591#95—134no—
592#95—262no—
593#95—262no—
594#95—262no—
595#95—262no—
596#95—262no—
597#95—262no—
598#95—262no—
599#95—262no—
600#95—262no—
601#95—262no—
602#95—262no—
603#95—262no—
604#95—262no—
605C2×C13C2×#38611yescharacteristic
606C2×C13C4×C4⋊Q811yescharacteristic
607C2×C13#232711yescharacteristic
608C2×C13Q8×C22⋊C411yescharacteristic
609C2×C13Q8×C22⋊C411yescharacteristic
610C2×C13#236511yescharacteristic
611C2×C13#236511yescharacteristic
612C2×C13#242911yescharacteristic
613C2×C13#242911yescharacteristic
614C2×C13#243211yescharacteristic
615C2×C13#243411yescharacteristic
616C2×C13#244611yescharacteristic
617C2×C13#244611yescharacteristic
618C2×C13#254511yescharacteristic
619C2×C13#254611yescharacteristic
620C24C23×D1311yescharacteristic
621C2×Q8—1316no—
622C2×Q8—268no—
623C2×Q8—268no—
624C2×Q8—268no—
625C2×Q8—268no—
626C2×Q8—268no—
627C2×Q8—268no—
628C2×Q8—268no—
629C2×Q8—268no—
630C2×Q8—268no—
631C2×Q8—524no—
632C2×Q8—524no—
633C2×Q8—524no—
634C2×Q8—524no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—132no—
686C22×C4—132no—
687C22×C4—132no—
688C22×C4—132no—
689C22×C4—132no—
690C22×C4—132no—
691C22×C4—132no—
692C22×C4—132no—
693C22×C4—261no—
694C22×C4—261no—
695C22×C4—261no—
696C22×C4—261no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4C2×C4×D1312yes—
731C22×C4C2×C4×D1312yes—
732C22×C4C2×C4×D1312yes—
733C22×C4D4×D1312yes—
734C22×C4D4×D1312yes—
735C22×C4D4×D1312yes—
736C22×C4D4×D1312yes—
737C22×C4#612912yes—
738C22×C4Q8×D1312yes—
739C22×C4Q8×D1312yes—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—268no—
743C4⋊C4—268no—
744C4⋊C4—268no—
745C4⋊C4—268no—
746C4⋊C4—268no—
747C4⋊C4—524no—
748C42—268no—
749C42—268no—
750C42—268no—
751C42—268no—
752C42—524no—
753C13#1402411yescharacteristic, complemented, Sylow
754C23C22×C4×D1311yescharacteristic
755C23C2×D4×D1311yescharacteristic
756C23C2×D4×D1311yescharacteristic
757C23C2×D4×D1311yescharacteristic
758C23C2×D4×D1311yescharacteristic
759C23C2×#612911yescharacteristic
760C23C2×Q8×D1311yescharacteristic
761C23C2×Q8×D1311yescharacteristic
762C23#8825411yescharacteristic
763C23#41×D1311yescharacteristic
764C23#41×D1311yescharacteristic
765C23#41×D1311yescharacteristic
766C23#8825711yescharacteristic
767C23#8825711yescharacteristic
768C23#8825711yescharacteristic
769Q8—2632no—
770Q8—5216no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—134no—
819C2×C4—134no—
820C2×C4—134no—
821C2×C4—134no—
822C2×C4—134no—
823C2×C4—134no—
824C2×C4—134no—
825C2×C4—134no—
826C2×C4—134no—
827C2×C4—134no—
828C2×C4—262no—
829C2×C4—262no—
830C2×C4—262no—
831C2×C4—262no—
832C2×C4—262no—
833C2×C4—262no—
834C2×C4—262no—
835C2×C4—262no—
836C2×C4—262no—
837C2×C4—262no—
838C2×C4—262no—
839C2×C4—262no—
840C2×C4—262no—
841C2×C4—262no—
842C2×C4—262no—
843C2×C4—262no—
844C2×C4—262no—
845C2×C4—262no—
846C2×C4—262no—
847C2×C4—262no—
848C2×C4—262no—
849C2×C4—262no—
850C2×C4—262no—
851C2×C4—262no—
852C2×C4—262no—
853C2×C4—262no—
854C2×C4—262no—
855C2×C4—521no—
856C2×C4—521no—
857C2×C4—521no—
858C2×C4—521no—
859C2×C4—521no—
860C2×C4—521no—
861C2×C4—521no—
862C2×C4—521no—
863C2×C4—521no—
864C2×C4—521no—
865C2×C4—521no—
866C2×C4—521no—
867C2×C4—521no—
868C2×C4—521no—
869C2×C4—521no—
870C2×C4—521no—
871C2×C4—521no—
872C2×C4—521no—
873C2×C4—521no—
874C2×C4C22⋊C4×D1314yes—
875C2×C4#8814114yescomplemented
876C22C2×C22⋊C4×D1311yescharacteristic
877C22C2×#8814111yescharacteristic
878C22#1171922111yescharacteristic
879C22C4×D4×D1311yescharacteristic
880C22C4×D4×D1311yescharacteristic
881C22C4×Q8×D1311yescharacteristic
882C22#1171927711yescharacteristic
883C22D13×#12011yescharacteristic
884C22#1171930111yescharacteristic
885C22#1171930311yescharacteristic
886C22#1171930311yescharacteristic
887C22D13×#12111yescharacteristic
888C22D13×#12111yescharacteristic
889C22#1171931611yescharacteristic
890C22#1171932711yescharacteristic
891C22#1171933311yescharacteristic
892C22#1171933711yescharacteristic
893C22#1171933711yescharacteristic
894C22#1171933711yescharacteristic
895C22#1171933711yescharacteristic
896C22#1171933811yescharacteristic
897C22#1171934611yescharacteristic
898C22#1171935311yescharacteristic
899C22D13×#12311yescharacteristic
900C22#1171936011yescharacteristic
901C22#1171938211yescharacteristic
902C22#1171939011yescharacteristic
903C22#1171939011yescharacteristic
904C22#1171939311yescharacteristic
905C22#1171940111yescharacteristic
906C22#1171940611yescharacteristic
907C22#1171940711yescharacteristic
908C22D13×C4⋊Q811yescharacteristic
909C22#1171943211yescharacteristic
910C22#1171943211yescharacteristic
911C4—24no—
912C4—24no—
913C4—42no—
914C4—42no—
915C4—42no—
916C4—42no—
917C4—81no—
918C4—138no—
919C4—264no—
920C4—264no—
921C4—264no—
922C4—522no—
923C4—522no—
924C4—522no—
925C4—1041no—
926C2D13×#38611yescharacteristic
927C2#1311740711yescharacteristic
928C2#1311755111yescharacteristic
929C2#1311766811yescharacteristic
930C2#1311767011yescharacteristic
931C2#1311788911yescharacteristic
932C2#1311789111yescharacteristic
933C2#1311842811yescharacteristic
934C2#1311843011yescharacteristic
935C2#1311845911yescharacteristic
936C2#1311847511yescharacteristic
937C2#1311860511yescharacteristic
938C2#1311860711yescharacteristic
939C2#1311981111yescharacteristic
940C2#1311982011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1441D13
hypocenterC13#14024
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
33. C2×#88142C4semidirect
148. #88071Q8semidirect
149. #88071Q8semidirect
362. C2×C4×C13C4×Q8semidirect
413. C2×Dic13C4×Q8semidirect
418. C2×Dic13C4⋊Q8semidirect
753. C13#14024semidirect
875. C2×C4#88141semidirect

Maximal subgroups

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

subgroupindex
C22×#881422
C22×#881412
C2×#117183072
#131130882
#131130872
#131130862
#131130712
#131130702
#131130682
#131130672
#131130642
#95×Dic132
C13×#14412
#1402413