Finite Group Databasebeta

← #15793008

Subgroups — #15793008

Order 3328.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718334C211yesmaximal, characteristic
2C2×#11718635C211yesmaximal, characteristic, complemented
3C2×#11718307C211yesmaximal, characteristic, complemented
4C2×#11718650C211yesmaximal, characteristic
5C2×#11718650C211yesmaximal, characteristic
6#13113099C211yesmaximal, characteristic, complemented
7#13113095C211yesmaximal, characteristic, complemented
8#13113094C211yesmaximal, characteristic, complemented
9#13113078C211yesmaximal, characteristic
10#13113072C211yesmaximal, characteristic
11#13113072C211yesmaximal, characteristic
12#13113062C211yesmaximal, characteristic, complemented
13#13113061C211yesmaximal, characteristic, complemented
14#13113057C211yesmaximal, characteristic
15C13×#1444C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51#11718650—24no—
52#11718650—24no—
53#11718635—24no—
54#11718334C418yescomplemented
55#11718307—24no—
56C24×D13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C22×C4×D13—22no—
72C22×C4×D13—22no—
73C22×C4×D13—22no—
74C22×C4×D13—41no—
75C22×C4×D13—41no—
76C22×C4×D13—41no—
77C22×C4×D13—41no—
78C22×Dic26—22no—
79C22×Dic26—22no—
80C22×Dic26—22no—
81C22×Dic26—22no—
82C22×Dic26—41no—
83C22×Dic26—41no—
84C22×Dic26C2×C414yescomplemented
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—41no—
89C2×C13×C4⋊C4—41no—
90C2×C13×C4⋊C4—41no—
91C2×C13×C4⋊C4—41no—
92C2×C13×C4⋊C4—41no—
93C2×C13×C4⋊C4—41no—
94C2×#6103—22no—
95C2×#6103—22no—
96C2×#6103—22no—
97C2×#6103—22no—
98C2×#6103—22no—
99C2×#6103—22no—
100C2×#6103—22no—
101C2×#6103—22no—
102C2×#6103—41no—
103C2×#6103—41no—
104C2×#6103—41no—
105C2×#6103—41no—
106C2×#6103—41no—
107C2×#6103—41no—
108C2×#6103C2×C414yes—
109C2×#6103C2×C414yes—
110C2×#6103C2×C414yes—
111C2×#6103Q814yescomplemented
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101—41no—
116C2×#6101—41no—
117C2×#6101—41no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—41no—
123C2×C4×Dic13—41no—
124C13×#95—22no—
125C13×#95—41no—
126C13×#95—41no—
127C13×#95C2×C414yescomplemented
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—41no—
136#88071—41no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#88071C2×C414yescomplemented
141#88071C2×C414yescomplemented
142#88071D414yes—
143#88071D414yes—
144#14575—131nomaximal, Sylow
145C24×C13C2411yescharacteristic
146C23×D13—21no—
147C23×D13—21no—
148C23×D13—21no—
149C23×D13—21no—
150C23×D13—21no—
151C23×D13—21no—
152C23×D13—21no—
153C23×D13—21no—
154C23×D13—21no—
155C23×D13—21no—
156C23×D13—21no—
157C23×D13—21no—
158C23×D13C22×C412yes—
159C23×D13C2×Q812yes—
160C23×D13#4112yes—
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×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13C22×C412yes—
204C22×C4×C13C22×C412yes—
205C22×C4×C13C22×C412yes—
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×D412yes—
208C22×C4×C13C2×Q812yes—
209C22×C4×C13#4112yes—
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×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13C22×C412yes—
251C22×Dic13C22×C412yes—
252C22×Dic13C22×C412yes—
253C22×Dic13C2×D412yes—
254C22×Dic13C2×D412yes—
255C22×Dic13C2×D412yes—
256C22×Dic13C2×D412yes—
257C22×Dic13C2×Q812yes—
258C22×Dic13#4112yes—
259C2×C4×D13—44no—
260C2×C4×D13—44no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—44no—
266C2×Dic26—28no—
267C2×Dic26—28no—
268C2×Dic26—44no—
269C2×Dic26—44no—
270C2×Dic26—44no—
271C2×Dic26—44no—
272C2×Dic26—44no—
273C13×C4⋊C4—44no—
274C13×C4⋊C4—44no—
275C13×C4⋊C4—44no—
276#6103—28no—
277#6103—28no—
278#6103—44no—
279#6103—44no—
280#6103—44no—
281#6103—44no—
282#6101—44no—
283#6101—44no—
284C4×Dic13—44no—
285C4×Dic13—44no—
286C2×#393—131no—
287C2×#391—131no—
288C2×#391—131no—
289C2×#385—131no—
290C2×#385—131no—
291#1444—131no—
292#1444D1311yescharacteristic, complemented
293#1442—131no—
294#1442—131no—
295#1439—131no—
296#1437—131no—
297#1437—131no—
298#1434—131no—
299#1434—131no—
300C22⋊#95—131no—
301C23×C13C23×C411yescharacteristic
302C23×C13C22×D411yescharacteristic
303C23×C13C22×D411yescharacteristic
304C23×C13C22×Q811yescharacteristic
305C23×C13C2×#4111yescharacteristic
306C23×C13C2×#4111yescharacteristic
307C23×C13C2×#4111yescharacteristic
308C23×C13H(5,𝔽2)11yescharacteristic
309C23×C13H(5,𝔽2)11yescharacteristic
310C23×C13H(5,𝔽2)11yescharacteristic
311C23×C13H(5,𝔽2)11yescharacteristic
312C23×C13H(5,𝔽2)11yescharacteristic
313C23×C132−1+411yescharacteristic
314C23×C132−1+411yescharacteristic
315C23×C132−1+411yescharacteristic
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—41no—
335C22×D13—41no—
336C22×D13—41no—
337C22×D13—41no—
338C22×D13—41no—
339C22×D13—41no—
340C22×D13—41no—
341C22×D13—41no—
342C22×D13—41no—
343C22×D13—41no—
344C22×D13—41no—
345C22×D13—41no—
346C22×D13—41no—
347C22×D13—41no—
348C22×D13—41no—
349C22×D13—41no—
350C22×D13C4×Q814yes—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13C4×D414yes—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
423C2×Dic13—22no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13—41no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13—41no—
445C2×Dic13—41no—
446C2×Dic13—41no—
447C2×Dic13—41no—
448C2×Dic13C4×D414yes—
449C4×D13—416no—
450Dic26—416no—
451C23×Q8—131no—
452C24×C4—131no—
453C22×C4⋊C4—131no—
454C22×C4⋊C4—131no—
455C22×C4⋊C4C2×D1311yescharacteristic
456C22×C4⋊C4C2×D1311yescharacteristic
457C22×C4⋊C4C2×D1311yescharacteristic
458C22×C22⋊C4—131no—
459C22×C22⋊C4—131no—
460C22×C22⋊C4—131no—
461C22×C22⋊C4—131no—
462C22×C22⋊C4—131no—
463C22×C22⋊C4—131no—
464C22×C42—131no—
465C22×C42—131no—
466#393—138no—
467#391—264no—
468#391—264no—
469#385—264no—
470#385—264no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95C2×D1311yescharacteristic
488C2×#95C2×D1311yescharacteristic
489C2×#95C2×D1311yescharacteristic
490C2×#95C2×D1311yescharacteristic
491C22×C13C2×C4×D411yescharacteristic
492C22×C13C2×C4×D411yescharacteristic
493C22×C13C2×C4×Q811yescharacteristic
494C22×C13#51811yescharacteristic
495C22×C13#52011yescharacteristic
496C22×C13#52011yescharacteristic
497C22×C13#52011yescharacteristic
498C22×C13#53511yescharacteristic
499C22×C13#53511yescharacteristic
500C22×C13#53611yescharacteristic
501C22×C13#53611yescharacteristic
502C22×C13#53811yescharacteristic
503C22×C13#53911yescharacteristic
504C22×C13#54211yescharacteristic
505C22×C13#54211yescharacteristic
506C22×C13#54211yescharacteristic
507C22×C13#54211yescharacteristic
508C22×C13#54311yescharacteristic
509C22×C13#54411yescharacteristic
510C22×C13D4211yescharacteristic
511C22×C13#54611yescharacteristic
512C22×C13#54611yescharacteristic
513C22×C13#54611yescharacteristic
514C22×C13#54611yescharacteristic
515C22×C13D4×Q811yescharacteristic
516C22×C13D4×Q811yescharacteristic
517C22×C13#55111yescharacteristic
518C22×C13#55211yescharacteristic
519C22×C13#55211yescharacteristic
520C22×C13#55411yescharacteristic
521C22×C13#55411yescharacteristic
522C22×C13H(3,𝔽4)11yescharacteristic
523C22×C13#56211yescharacteristic
524C22×C13#56211yescharacteristic
525C22×C13#56311yescharacteristic
526C2×D13—24no—
527C2×D13—24no—
528C2×D13—24no—
529C2×D13—42no—
530C2×D13—42no—
531C2×D13—42no—
532C2×D13—42no—
533C2×D13—42no—
534C2×D13—42no—
535C2×D13—42no—
536C2×D13—42no—
537C2×D13—42no—
538C2×D13—42no—
539C2×D13—42no—
540C2×D13—42no—
541C4×C13—24no—
542C4×C13—42no—
543C4×C13—42no—
544C4×C13—42no—
545C4×C13—42no—
546C4×C13—81no—
547C4×C13—81no—
548Dic13—24no—
549Dic13—42no—
550Dic13—42no—
551Dic13—42no—
552Dic13—42no—
553Dic13—42no—
554Dic13—42no—
555C25—131no—
556C22×Q8—134no—
557C22×Q8—262no—
558C22×Q8—262no—
559C22×Q8—262no—
560C22×Q8—262no—
561C22×Q8—521no—
562C22×Q8—521no—
563C23×C4—131no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4—131no—
567C23×C4—131no—
568C23×C4—131no—
569C23×C4—131no—
570C23×C4—262no—
571C23×C4—262no—
572C23×C4—262no—
573C23×C4—521no—
574C23×C4—521no—
575C23×C4—521no—
576C23×C4—521no—
577C23×C4C22×D1311yescharacteristic
578C23×C4C22×D1311yescharacteristic
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582C23×C4C22×D1311yescharacteristic
583C23×C4C22×D1311yescharacteristic
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C4⋊C4—521no—
597C2×C4⋊C4—521no—
598C2×C4⋊C4—521no—
599C2×C22⋊C4—134no—
600C2×C22⋊C4—134no—
601C2×C22⋊C4—134no—
602C2×C22⋊C4—134no—
603C2×C22⋊C4—262no—
604C2×C22⋊C4—262no—
605C2×C22⋊C4—262no—
606C2×C22⋊C4—262no—
607C2×C22⋊C4—262no—
608C2×C22⋊C4—262no—
609C2×C22⋊C4—262no—
610C2×C22⋊C4—262no—
611C2×C22⋊C4—521no—
612C2×C22⋊C4—521no—
613C2×C22⋊C4—521no—
614C2×C22⋊C4—521no—
615C2×C22⋊C4—521no—
616C2×C22⋊C4—521no—
617C2×C42—262no—
618C2×C42—262no—
619C2×C42—262no—
620C2×C42—262no—
621C2×C42—521no—
622C2×C42—521no—
623#95—22no—
624#95—41no—
625#95—41no—
626#95—134no—
627#95—134no—
628#95—134no—
629#95—134no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—262no—
635#95—262no—
636#95—262no—
637#95—521no—
638#95—521no—
639#95—521no—
640#95—521no—
641#95—521no—
642#95C4×D1314yescomplemented
643C2×C13#232611yescharacteristic
644C2×C13#232611yescharacteristic
645C2×C13#232911yescharacteristic
646C2×C13#235811yescharacteristic
647C2×C13#236011yescharacteristic
648C2×C13#236011yescharacteristic
649C2×C13#237911yescharacteristic
650C2×C13#267011yescharacteristic
651C2×C13#267711yescharacteristic
652C2×C13#268711yescharacteristic
653C2×C13#268711yescharacteristic
654C2×C13#269211yescharacteristic
655C2×C13#269211yescharacteristic
656C2×C13#276311yescharacteristic
657C2×C13#276411yescharacteristic
658D13—44no—
659C24—132no—
660C24—132no—
661C24—132no—
662C24—261no—
663C24—261no—
664C24—261no—
665C24—261no—
666C24—261no—
667C24—261no—
668C24—261no—
669C24—261no—
670C24—261no—
671C24—261no—
672C24—261no—
673C24—261no—
674C24C23×D1311yescharacteristic
675C2×Q8—268no—
676C2×Q8—268no—
677C2×Q8—524no—
678C2×Q8—524no—
679C2×Q8—524no—
680C2×Q8—524no—
681C2×Q8—524no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—132no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—132no—
728C22×C4—132no—
729C22×C4—132no—
730C22×C4—132no—
731C22×C4—132no—
732C22×C4—132no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—261no—
763C22×C4—261no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—261no—
769C22×C4—261no—
770C22×C4—261no—
771C22×C4—261no—
772C22×C4—261no—
773C22×C4—524no—
774C22×C4—524no—
775C22×C4—524no—
776C22×C4—524no—
777C22×C4—524no—
778C22×C4—524no—
779C22×C4—524no—
780C22×C4C2×C4×D1312yes—
781C22×C4C2×C4×D1312yes—
782C22×C4C2×C4×D1312yes—
783C22×C4D4×D1312yes—
784C22×C4D4×D1312yes—
785C22×C4Q8×D1312yes—
786C22×C4#613112yes—
787C4⋊C4—44no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—524no—
791C4⋊C4—524no—
792C22⋊C4—268no—
793C22⋊C4—268no—
794C22⋊C4—524no—
795C22⋊C4—524no—
796C22⋊C4—524no—
797C22⋊C4—524no—
798C42—524no—
799C42—524no—
800C13#1457511yescharacteristic, complemented, Sylow
801C23—134no—
802C23—262no—
803C23—262no—
804C23—262no—
805C23—262no—
806C23—262no—
807C23—262no—
808C23—262no—
809C23—262no—
810C23—262no—
811C23—262no—
812C23—262no—
813C23—262no—
814C23—262no—
815C23—262no—
816C23—262no—
817C23—262no—
818C23—262no—
819C23—262no—
820C23—521no—
821C23—521no—
822C23—521no—
823C23—521no—
824C23—521no—
825C23—521no—
826C23—521no—
827C23—521no—
828C23—521no—
829C23—521no—
830C23—521no—
831C23—521no—
832C23—521no—
833C23—521no—
834C23—521no—
835C23—521no—
836C23C22×C4×D1311yescharacteristic
837C23C2×D4×D1311yescharacteristic
838C23C2×D4×D1311yescharacteristic
839C23#8825111yescharacteristic
840C23#8825111yescharacteristic
841C23#8825111yescharacteristic
842C23#8825111yescharacteristic
843C23C2×Q8×D1311yescharacteristic
844C23C2×#613111yescharacteristic
845C23#8825411yescharacteristic
846C23#8825411yescharacteristic
847C23#41×D1311yescharacteristic
848C23#41×D1311yescharacteristic
849C23#8825611yescharacteristic
850C23#8825711yescharacteristic
851Q8—5216no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—134no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—262no—
905C2×C4—262no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—262no—
909C2×C4—262no—
910C2×C4—262no—
911C2×C4—262no—
912C2×C4—262no—
913C2×C4—262no—
914C2×C4—262no—
915C2×C4—262no—
916C2×C4—262no—
917C2×C4—262no—
918C2×C4—262no—
919C2×C4—262no—
920C2×C4—262no—
921C2×C4—262no—
922C2×C4—262no—
923C2×C4—262no—
924C2×C4—262no—
925C2×C4—5216no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4—521no—
939C2×C4—521no—
940C2×C4—521no—
941C2×C4—521no—
942C2×C4—521no—
943C2×C4—521no—
944C2×C4—521no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
949C2×C4—521no—
950C2×C4#8814714yes—
951C22—264no—
952C22—264no—
953C22—264no—
954C22—522no—
955C22—522no—
956C22—522no—
957C22—522no—
958C22—522no—
959C22—522no—
960C22—522no—
961C22—522no—
962C22—522no—
963C22—522no—
964C22—522no—
965C22—522no—
966C22C2×#8814711yescharacteristic
967C22#1171920911yescharacteristic
968C22#1171920911yescharacteristic
969C22C4×D4×D1311yescharacteristic
970C22#1171925011yescharacteristic
971C22#1171925111yescharacteristic
972C22C4×Q8×D1311yescharacteristic
973C22#1171929511yescharacteristic
974C22#1171929711yescharacteristic
975C22#1171929911yescharacteristic
976C22#1171931511yescharacteristic
977C22#1171931711yescharacteristic
978C22#1171931811yescharacteristic
979C22#1171933311yescharacteristic
980C22#1171933511yescharacteristic
981C22#1171933711yescharacteristic
982C22#1171933911yescharacteristic
983C22#1171934111yescharacteristic
984C22#1171934211yescharacteristic
985C22#1171934511yescharacteristic
986C22#1171935111yescharacteristic
987C22#1171935211yescharacteristic
988C22#1171935911yescharacteristic
989C22#1171936711yescharacteristic
990C22#1171937211yescharacteristic
991C22#1171939711yescharacteristic
992C22#1171939811yescharacteristic
993C22#1171939911yescharacteristic
994C22#1171942011yescharacteristic
995C22#1171942911yescharacteristic
996C22#1171943211yescharacteristic
997C22#1171943411yescharacteristic
998C22#1171943511yescharacteristic
999C22#1171943811yescharacteristic
1000C22#1171943811yescharacteristic
1001C4—24no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—81no—
1007C4—81no—
1008C4—264no—
1009C4—522no—
1010C4—522no—
1011C4—522no—
1012C4—522no—
1013C4—522no—
1014C4—522no—
1015C2—524no—
1016C2#1311754211yescharacteristic
1017C2#1311754411yescharacteristic
1018C2#1311757011yescharacteristic
1019C2#1311781211yescharacteristic
1020C2#1311783811yescharacteristic
1021C2#1311784011yescharacteristic
1022C2#1311800911yescharacteristic
1023C2#1312106111yescharacteristic
1024C2#1312115011yescharacteristic
1025C2#1312125011yescharacteristic
1026C2#1312126411yescharacteristic
1027C2#1312132511yescharacteristic
1028C2#1312133911yescharacteristic
1029C2#1312224611yescharacteristic
1030C2#1312225511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1444C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1444D13
hypocenterC13#14575
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
2. C2×#11718635C2semidirect
3. C2×#11718307C2semidirect
6. #13113099C2semidirect
7. #13113095C2semidirect
8. #13113094C2semidirect
12. #13113062C2semidirect
13. #13113061C2semidirect
15. C13×#1444C2semidirect
54. #11718334C4semidirect
84. C22×Dic26C2×C4semidirect
111. C2×#6103Q8semidirect
127. C13×#95C2×C4semidirect
140. #88071C2×C4semidirect
141. #88071C2×C4semidirect
292. #1444D13semidirect
642. #95C4×D13semidirect
800. C13#14575semidirect

Maximal subgroups

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

subgroupindex
C2×#117183342
C2×#117186352
C2×#117183072
C2×#117186502
#131130992
#131130952
#131130942
#131130782
#131130722
#131130622
#131130612
#131130572
C13×#14442
#1457513