Finite Group Databasebeta

← #15791411

Subgroups — #15791411

Order 3328.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic
2C2×#11718642C211yesmaximal, characteristic, complemented
3#13113106C211yesmaximal, characteristic, complemented
4#13113106C211yesmaximal, characteristic, complemented
5#13113105C211yesmaximal, characteristic, complemented
6#13113103C211yesmaximal, characteristic, complemented
7#13113082C211yesmaximal, characteristic
8#13113078C211yesmaximal, characteristic
9#13113074C211yesmaximal, characteristic
10#13113072C211yesmaximal, characteristic
11#13113066C211yesmaximal, characteristic, complemented
12#13113065C211yesmaximal, characteristic, complemented
13#13113057C211yesmaximal, characteristic
14#13113057C211yesmaximal, characteristic
15C2×C13×#387C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×#88151—24no—
32C2×#88151—24no—
33C2×#88151C418yescomplemented
34C13×#387—24no—
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
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
55#11718642—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—41no—
74C22×C4×D13—41no—
75C22×C4×D13—41no—
76C22×C4×D13—41no—
77C22×C4×D13C2×C414yes—
78C22×Dic26—22no—
79C22×Dic26—22no—
80C22×Dic26—41no—
81C22×Dic26—41no—
82C22×Dic26—41no—
83C22×Dic26—41no—
84C22×Dic26C2×C414yes—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—41no—
88C2×C13×C4⋊C4C2×C414yes—
89C2×C13×C4⋊C4D414yes—
90C2×C13×C4⋊C4D414yes—
91C2×C42×C13—22no—
92C2×C42×C13—22no—
93C2×C42×C13—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—22no—
103C2×#6103—41no—
104C2×#6103—41no—
105C2×#6103—41no—
106C2×#6103—41no—
107C2×#6103—41no—
108C2×#6103—41no—
109C2×#6103C2×C414yes—
110C2×#6103C2×C414yes—
111C2×#6103Q814yescomplemented
112C2×C4⋊Dic13—22no—
113C2×C4⋊Dic13—22no—
114C2×C4⋊Dic13—22no—
115C2×C4⋊Dic13—22no—
116C2×C4⋊Dic13—22no—
117C2×C4⋊Dic13—22no—
118C2×C4⋊Dic13—41no—
119C2×C4⋊Dic13C2×C414yes—
120C2×C4⋊Dic13C2×C414yes—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—41no—
124#88151—232no—
125C13×#95—22no—
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—41no—
134#88071—41no—
135#88071—41no—
136#88071—41no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#88071—41no—
141#88071—41no—
142#88071—41no—
143#88071—41no—
144#88071—41no—
145#14448—131nomaximal, Sylow
146C24×C13C2411yescharacteristic
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×D13—21no—
159C23×D13C22×C412yes—
160C23×D13C2×Q812yes—
161C23×D13#4112yes—
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×C13C22×C412yes—
201C22×C4×C13C22×C412yes—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13C2×D412yes—
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×D412yes—
208C22×C4×C13C2×D412yes—
209C22×C4×C13C2×Q812yes—
210C22×C4×C13#4112yes—
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×Dic13—21no—
251C22×Dic13—21no—
252C22×Dic13—21no—
253C22×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13C22×C412yes—
256C22×Dic13C22×C412yes—
257C22×Dic13C22×C412yes—
258C22×Dic13C2×Q812yes—
259C22×Dic13#4112yes—
260C2×C4×D13—28no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—44no—
266C2×C4×D13—44no—
267C2×Dic26—28no—
268C2×Dic26—44no—
269C2×Dic26—44no—
270C2×Dic26—44no—
271C2×Dic26—44no—
272C2×Dic26—44no—
273C2×Dic26—44no—
274C13×C4⋊C4—44no—
275C13×C4⋊C4C22⋊C4116yescomplemented
276C42×C13—44no—
277#6103—28no—
278#6103—28no—
279#6103—44no—
280#6103—44no—
281#6103—44no—
282#6103—44no—
283C4⋊Dic13—28no—
284C4⋊Dic13—28no—
285C4⋊Dic13—44no—
286C4×Dic13—44no—
287C22×C22⋊Q8—131no—
288C2×#387—131no—
289C2×#387D1311yescharacteristic, complemented
290#1446—131no—
291#1446—131no—
292#1445—131no—
293#1445—131no—
294#1439—131no—
295#1439—131no—
296#1437—131no—
297#1437—131no—
298C4⋊#95—131no—
299C4⋊#95—131no—
300C22⋊#95—131no—
301C22⋊#95—131no—
302C23×C13C23×C411yescharacteristic
303C23×C13C22×D411yescharacteristic
304C23×C13C22×D411yescharacteristic
305C23×C13C22×Q811yescharacteristic
306C23×C13C2×#4111yescharacteristic
307C23×C13C2×#4111yescharacteristic
308C23×C13C2×#4111yescharacteristic
309C23×C13H(5,𝔽2)11yescharacteristic
310C23×C13H(5,𝔽2)11yescharacteristic
311C23×C13H(5,𝔽2)11yescharacteristic
312C23×C13H(5,𝔽2)11yescharacteristic
313C23×C13H(5,𝔽2)11yescharacteristic
314C23×C132−1+411yescharacteristic
315C23×C132−1+411yescharacteristic
316C23×C132−1+411yescharacteristic
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—22no—
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×D13—41no—
351C22×D13C4×Q814yes—
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—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
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×C13C2×C22⋊C414yes—
399C2×C4×C13C2×C22⋊C414yes—
400C2×C4×C13C2×C22⋊C414yes—
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—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
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×Dic13—41no—
449C2×Dic13—41no—
450C4×D13—416no—
451Dic26—416no—
452C23×Q8—131no—
453C24×C4—131no—
454C2×C22⋊Q8—138no—
455C2×C22⋊Q8—264no—
456C2×C22⋊Q8—264no—
457C22×C4⋊C4—131no—
458C22×C4⋊C4—131no—
459C22×C4⋊C4—131no—
460C22×C4⋊C4C2×D1311yescharacteristic
461C22×C4⋊C4C2×D1311yescharacteristic
462C22×C22⋊C4—131no—
463C22×C22⋊C4—131no—
464C22×C22⋊C4—131no—
465C22×C22⋊C4—131no—
466C22×C22⋊C4—131no—
467C22×C22⋊C4—131no—
468C22×C42—131no—
469C22×C42C2×D1311yescharacteristic
470#387—24no—
471#387—264no—
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×#95—131no—
488C2×#95C2×D1311yescharacteristic
489C2×#95C2×D1311yescharacteristic
490C2×#95C2×D1311yescharacteristic
491C2×#95C2×D1311yescharacteristic
492C22×C13C22×C22⋊C411yescharacteristic
493C22×C13C2×C4×Q811yescharacteristic
494C22×C13C4×#4111yescharacteristic
495C22×C13#51811yescharacteristic
496C22×C13#51811yescharacteristic
497C22×C13#51911yescharacteristic
498C22×C13#52011yescharacteristic
499C22×C13#53511yescharacteristic
500C22×C13#53511yescharacteristic
501C22×C13#53511yescharacteristic
502C22×C13#53511yescharacteristic
503C22×C13#53811yescharacteristic
504C22×C13#53911yescharacteristic
505C22×C13#53911yescharacteristic
506C22×C13#53911yescharacteristic
507C22×C13#54211yescharacteristic
508C22×C13#54211yescharacteristic
509C22×C13#54311yescharacteristic
510C22×C13#54411yescharacteristic
511C22×C13#54611yescharacteristic
512C22×C13#54611yescharacteristic
513C22×C13#54711yescharacteristic
514C22×C13#54711yescharacteristic
515C22×C13#54811yescharacteristic
516C22×C13#54811yescharacteristic
517C22×C13D4×Q811yescharacteristic
518C22×C13D4×Q811yescharacteristic
519C22×C13#55111yescharacteristic
520C22×C13#55111yescharacteristic
521C22×C13#55411yescharacteristic
522C22×C13#55411yescharacteristic
523C22×C13#56211yescharacteristic
524C22×C13#56211yescharacteristic
525C22×C13#56311yescharacteristic
526C22×C13#56311yescharacteristic
527C2×D13—24no—
528C2×D13—24no—
529C2×D13—24no—
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—
541C2×D13—42no—
542C4×C13—24no—
543C4×C13—24no—
544C4×C13—24no—
545C4×C13—42no—
546C4×C13—42no—
547C4×C13—81no—
548C4×C13—81no—
549Dic13—42no—
550Dic13—42no—
551Dic13—42no—
552Dic13—42no—
553Dic13—42no—
554Dic13—81no—
555Dic13—81no—
556C25—131no—
557C22×Q8—134no—
558C22×Q8—262no—
559C22×Q8—262no—
560C22×Q8—521no—
561C22×Q8—521no—
562C22×Q8—521no—
563C22×Q8—521no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4—131no—
567C23×C4—131no—
568C23×C4—131no—
569C23×C4—134no—
570C23×C4—131no—
571C23×C4—131no—
572C23×C4—262no—
573C23×C4—262no—
574C23×C4—521no—
575C23×C4—521no—
576C23×C4—521no—
577C23×C4—521no—
578C23×C4C22×D1311yescharacteristic
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582C23×C4C22×D1311yescharacteristic
583C23×C4C22×D1311yescharacteristic
584C23×C4C22×D1311yescharacteristic
585C22⋊Q8—2632no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—134no—
590C2×C4⋊C4—134no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C4⋊C4—262no—
597C2×C4⋊C4—521no—
598C2×C4⋊C4C4×D1314yes—
599C2×C4⋊C4D5214yes—
600C2×C4⋊C4C22⋊D1314yes—
601C2×C22⋊C4—134no—
602C2×C22⋊C4—134no—
603C2×C22⋊C4—134no—
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—262no—
612C2×C22⋊C4—262no—
613C2×C22⋊C4—521no—
614C2×C22⋊C4—521no—
615C2×C22⋊C4—521no—
616C2×C22⋊C4—521no—
617C2×C22⋊C4—521no—
618C2×C22⋊C4—521no—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—41no—
622C2×C42—262no—
623C2×C42—262no—
624C2×C42—521no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—521no—
634#95—521no—
635#95—521no—
636#95—521no—
637#95—521no—
638#95—521no—
639#95—521no—
640#95—521no—
641#95—521no—
642#95—521no—
643#95—521no—
644#95—521no—
645C2×C13#230911yescharacteristic
646C2×C13#232911yescharacteristic
647C2×C13#233211yescharacteristic
648C2×C13#233911yescharacteristic
649C2×C13Q8×C22⋊C411yescharacteristic
650C2×C13#236811yescharacteristic
651C2×C13#237811yescharacteristic
652C2×C13#269211yescharacteristic
653C2×C13#269211yescharacteristic
654C2×C13#269611yescharacteristic
655C2×C13#269611yescharacteristic
656C2×C13#272011yescharacteristic
657C2×C13#272011yescharacteristic
658C2×C13#272311yescharacteristic
659C2×C13#272311yescharacteristic
660D13—44no—
661C24—132no—
662C24—132no—
663C24—132no—
664C24—261no—
665C24—261no—
666C24—261no—
667C24—261no—
668C24—261no—
669C24—261no—
670C24—261no—
671C24—261no—
672C24—261no—
673C24—261no—
674C24—261no—
675C24—261no—
676C24C23×D1311yescharacteristic
677C2×Q8—268no—
678C2×Q8—524no—
679C2×Q8—524no—
680C2×Q8—524no—
681C2×Q8—524no—
682C2×Q8—524no—
683C2×Q8—524no—
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—132no—
723C22×C4—132no—
724C22×C4—132no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
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—268no—
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—524no—
773C22×C4—524no—
774C22×C4—524no—
775C22×C4—524no—
776C22×C4—524no—
777C22×C4—524no—
778C22×C4C2×C4×D1312yes—
779C22×C4C2×C4×D1312yes—
780C22×C4C2×C4×D1312yes—
781C22×C4C2×D5212yes—
782C22×C4C2×D5212yes—
783C22×C4C2×D5212yes—
784C22×C4#612912yes—
785C22×C4Q8×D1312yes—
786C22×C4C2×C22⋊D1312yes—
787C22×C4C2×C22⋊D1312yes—
788C22×C4C2×C22⋊D1312yes—
789C4⋊C4—44no—
790C4⋊C4—268no—
791C4⋊C4—268no—
792C4⋊C4—524no—
793C4⋊C4#6103116yescomplemented
794C22⋊C4—268no—
795C22⋊C4—268no—
796C22⋊C4—524no—
797C22⋊C4—524no—
798C22⋊C4—524no—
799C22⋊C4—524no—
800C42—44no—
801C42—524no—
802C13#1444811yescharacteristic, complemented, Sylow
803C23—134no—
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—262no—
821C23—262no—
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—
836C23—521no—
837C23—521no—
838C23C22×C4×D1311yescharacteristic
839C23C22×D5211yescharacteristic
840C23C2×#612911yescharacteristic
841C23#8825111yescharacteristic
842C23C2×Q8×D1311yescharacteristic
843C23#8825411yescharacteristic
844C23#41×D1311yescharacteristic
845C23#41×D1311yescharacteristic
846C23#8825611yescharacteristic
847C23#8825611yescharacteristic
848C23#8825611yescharacteristic
849C23#8825611yescharacteristic
850C23#8825711yescharacteristic
851C23#8825711yescharacteristic
852C23C22×C22⋊D1311yescharacteristic
853Q8—5216no—
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—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
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—262no—
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—5216no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
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×C4C2×#610314yes—
951C2×C4C2×#610314yes—
952C2×C4C2×#610314yes—
953C22—264no—
954C22—264no—
955C22—264no—
956C22—522no—
957C22—522no—
958C22—522no—
959C22—522no—
960C22—522no—
961C22—522no—
962C22—522no—
963C22—522no—
964C22—522no—
965C22—522no—
966C22—522no—
967C22—522no—
968C22#1171922611yescharacteristic
969C22#1171922611yescharacteristic
970C22#1171923011yescharacteristic
971C22#1171923011yescharacteristic
972C22C4×#612911yescharacteristic
973C22#1171925111yescharacteristic
974C22#1171925911yescharacteristic
975C22#1171926011yescharacteristic
976C22C4×Q8×D1311yescharacteristic
977C22#1171927711yescharacteristic
978C22Q8×D5211yescharacteristic
979C22#1171928111yescharacteristic
980C22#1171933911yescharacteristic
981C22#1171934011yescharacteristic
982C22#1171934811yescharacteristic
983C22#1171935211yescharacteristic
984C22#1171936211yescharacteristic
985C22#1171936311yescharacteristic
986C22#1171937011yescharacteristic
987C22#1171937211yescharacteristic
988C22#1171939411yescharacteristic
989C22#1171939511yescharacteristic
990C22#1171939711yescharacteristic
991C22#1171940411yescharacteristic
992C22#1171941011yescharacteristic
993C22#1171941211yescharacteristic
994C22#1171941511yescharacteristic
995C22#1171941711yescharacteristic
996C22C22×#610311yescharacteristic
997C22#1171951111yescharacteristic
998C22Q8×C22⋊D1311yescharacteristic
999C22#1171952911yescharacteristic
1000C22#1171953511yescharacteristic
1001C22#1171953511yescharacteristic
1002C22#1171953611yescharacteristic
1003C4—24no—
1004C4—24no—
1005C4—24no—
1006C4—42no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4—522no—
1011C4—522no—
1012C4—522no—
1013C4—522no—
1014C4—522no—
1015C4—1041no—
1016C4—1041no—
1017C2—524no—
1018C2#1311741611yescharacteristic
1019C2#1311756511yescharacteristic
1020C2#1311758811yescharacteristic
1021C2#1311766111yescharacteristic
1022C2Q8×#610311yescharacteristic
1023C2#1311791811yescharacteristic
1024C2#1311800011yescharacteristic
1025C2#1312132811yescharacteristic
1026C2#1312133011yescharacteristic
1027C2#1312138211yescharacteristic
1028C2#1312138411yescharacteristic
1029C2#1312171211yescharacteristic
1030C2#1312171411yescharacteristic
1031C2#1312175111yescharacteristic
1032C2#1312175311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#387C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#387D13
hypocenterC13#14448
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C2×#11718642C2semidirect
3. #13113106C2semidirect
4. #13113106C2semidirect
5. #13113105C2semidirect
6. #13113103C2semidirect
11. #13113066C2semidirect
12. #13113065C2semidirect
15. C2×C13×#387C2semidirect
33. C2×#88151C4semidirect
111. C2×#6103Q8semidirect
275. C13×C4⋊C4C22⋊C4semidirect
289. C2×#387D13semidirect
793. C4⋊C4#6103semidirect
802. C13#14448semidirect

Maximal subgroups

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

subgroupindex
C22×#881512
C2×#117186422
#131131062
#131131052
#131131032
#131130822
#131130782
#131130742
#131130722
#131130662
#131130652
#131130572
C2×C13×#3872
#1444813