Finite Group Databasebeta

← #15787414

Subgroups — #15787414

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88200C211yesmaximal, characteristic
2C2×#11718639C211yesmaximal, characteristic, complemented
3C2×C4×#6101C211yesmaximal, characteristic, complemented
4C2×#11718327C211yesmaximal, characteristic
5#13113107C211yesmaximal, characteristic, complemented
6#13113088C211yesmaximal, characteristic, complemented
7#13113080C211yesmaximal, characteristic
8#13113078C211yesmaximal, characteristic
9#13113074C211yesmaximal, characteristic
10#13113072C211yesmaximal, characteristic
11#13113070C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13#13113067C211yesmaximal, characteristic, complemented
14#13113057C211yesmaximal, characteristic
15C2×C13×#391C211yesmaximal, characteristic, complemented
16C23×Q8×C13C2211yescharacteristic
17C23×C4×D13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C2×#88200—24no—
21C2×#88200—24no—
22C2×#88200C418yescomplemented
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C13×#391—24no—
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
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#11718639—24no—
56C4×#6101—24no—
57#11718327—24no—
58C24×D13C2311yescharacteristic
59C22×Q8×C13—22no—
60C22×Q8×C13—22no—
61C22×Q8×C13—22no—
62C22×Q8×C13—22no—
63C22×Q8×C13—41no—
64C22×Q8×C13—41no—
65C22×Q8×C13C2×C414yes—
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C22×C4×D13—22no—
81C22×C4×D13—22no—
82C22×C4×D13—22no—
83C22×C4×D13—22no—
84C22×C4×D13—41no—
85C22×C4×D13—41no—
86C22×C4×D13C2×C414yes—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—41no—
90C2×C42×C13—22no—
91C2×C42×C13—22no—
92C2×C42×C13—41no—
93#88200—232no—
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—22no—
104C2×#6103—22no—
105C2×#6103—22no—
106C2×#6103—22no—
107C2×#6103—41no—
108C2×#6103—41no—
109C2×#6103C2×C414yes—
110C2×#6103C2×C414yes—
111C2×#6103Q814yescomplemented
112C2×C4⋊Dic13—22no—
113C2×C4⋊Dic13—22no—
114C2×C4⋊Dic13C2×C414yes—
115C2×#6101—22no—
116C2×#6101—22no—
117C2×#6101—22no—
118C2×#6101—22no—
119C2×#6101—22no—
120C2×#6101C2×C414yes—
121C2×#6101C2×C414yes—
122C2×#6101D414yes—
123C2×#6101D414yes—
124C2×C4×Dic13—22no—
125C2×C4×Dic13—22no—
126C2×C4×Dic13—22no—
127C2×C4×Dic13—22no—
128C2×C4×Dic13—22no—
129C2×C4×Dic13—22no—
130C2×C4×Dic13—22no—
131C2×C4×Dic13—41no—
132C2×C4×Dic13—41no—
133C13×#95—22no—
134C13×#95—22no—
135C13×#95—22no—
136C13×#95D414yes—
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#88071—22no—
149#88071—41no—
150#88071—41no—
151#14099—131nomaximal, Sylow
152C24×C13C2411yescharacteristic
153C23×D13—21no—
154C23×D13—21no—
155C23×D13—21no—
156C23×D13—21no—
157C23×D13—21no—
158C23×D13—21no—
159C23×D13—21no—
160C23×D13—21no—
161C23×D13—21no—
162C23×D13—21no—
163C23×D13—21no—
164C23×D13—21no—
165C23×D13C22×C412yes—
166C23×D13C2×Q812yes—
167C23×D13#4112yes—
168C2×Q8×C13—28no—
169C2×Q8×C13—28no—
170C2×Q8×C13—44no—
171C2×Q8×C13—44no—
172C2×Q8×C13—44no—
173C2×Q8×C13—44no—
174C2×Q8×C13—44no—
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×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13C22×C412yes—
213C22×C4×C13C22×C412yes—
214C22×C4×C13C22×C412yes—
215C22×C4×C13C2×D412yes—
216C22×C4×C13C2×D412yes—
217C22×C4×C13C2×D412yes—
218C22×C4×C13C2×D412yes—
219C22×C4×C13C2×D412yes—
220C22×C4×C13C2×Q812yes—
221C22×C4×C13#4112yes—
222C22×C4×C13#4112yes—
223C22×C4×C13#4112yes—
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×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13—21no—
261C22×Dic13—21no—
262C22×Dic13—21no—
263C22×Dic13C22×C412yes—
264C22×Dic13C22×C412yes—
265C22×Dic13C22×C412yes—
266C22×Dic13C2×D412yes—
267C22×Dic13C2×D412yes—
268C22×Dic13C2×D412yes—
269C22×Dic13C2×D412yes—
270C22×Dic13C2×Q812yes—
271C22×Dic13#4112yes—
272C22×Dic13#4112yes—
273C2×C4×D13—28no—
274C2×C4×D13—28no—
275C2×C4×D13—44no—
276C2×C4×D13—44no—
277C2×C4×D13—44no—
278C2×C4×D13—44no—
279C2×C4×D13—44no—
280C13×C4⋊C4—44no—
281C42×C13—44no—
282#6103—28no—
283#6103—28no—
284#6103—28no—
285#6103—28no—
286#6103—44no—
287#6103—44no—
288C4⋊Dic13—28no—
289#6101—28no—
290#6101—28no—
291#6101C22⋊C4116yescomplemented
292C4×Dic13—28no—
293C4×Dic13—44no—
294C4×Dic13—44no—
295C22×C22⋊Q8—131no—
296C2×#391D1311yescharacteristic, complemented
297C2×#387—131no—
298C2×C4×C4⋊C4—131no—
299C2×C4×C22⋊C4—131no—
300#1446—131no—
301#1441—131no—
302#1439—131no—
303#1439—131no—
304#1437—131no—
305#1437—131no—
306#1436—131no—
307#1436—131no—
308#1436—131no—
309C22⋊#95—131no—
310C23×C13C23×C411yescharacteristic
311C23×C13C22×D411yescharacteristic
312C23×C13C22×D411yescharacteristic
313C23×C13C22×D411yescharacteristic
314C23×C13C22×Q811yescharacteristic
315C23×C13C2×#4111yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13C2×#4111yescharacteristic
318C23×C13C2×#4111yescharacteristic
319C23×C13C2×#4111yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13H(5,𝔽2)11yescharacteristic
322C23×C13H(5,𝔽2)11yescharacteristic
323C23×C132−1+411yescharacteristic
324C23×C132−1+411yescharacteristic
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—22no—
336C22×D13—22no—
337C22×D13—22no—
338C22×D13—22no—
339C22×D13—22no—
340C22×D13—22no—
341C22×D13—22no—
342C22×D13—22no—
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×D13—41no—
352C22×D13—41no—
353C22×D13—41no—
354C22×D13—41no—
355C22×D13—41no—
356C22×D13—41no—
357C22×D13—41no—
358C22×D13—41no—
359C22×D13C4×Q814yes—
360Q8×C13—416no—
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—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
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×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13C2×C22⋊C414yes—
408C2×C4×C13C4×D414yes—
409C2×C4×C13C22⋊Q814yescomplemented
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—22no—
425C2×Dic13—22no—
426C2×Dic13—22no—
427C2×Dic13—22no—
428C2×Dic13—22no—
429C2×Dic13—22no—
430C2×Dic13—22no—
431C2×Dic13—22no—
432C2×Dic13—22no—
433C2×Dic13—22no—
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—
450C2×Dic13—41no—
451C2×Dic13—41no—
452C2×Dic13—41no—
453C2×Dic13—41no—
454C2×Dic13—41no—
455C2×Dic13—41no—
456C2×Dic13—41no—
457C2×Dic13C2×C22⋊C414yes—
458C2×Dic13C2×C22⋊C414yes—
459C4×D13—416no—
460C23×Q8C2×D1311yescharacteristic
461C24×C4—131no—
462C2×C22⋊Q8—138no—
463C2×C22⋊Q8—264no—
464C2×C22⋊Q8—264no—
465C22×C4⋊C4—131no—
466C22×C4⋊C4—131no—
467C22×C4⋊C4—131no—
468C22×C4⋊C4—131no—
469C22×C4⋊C4C2×D1311yescharacteristic
470C22×C22⋊C4—131no—
471C22×C22⋊C4—131no—
472C22×C22⋊C4—131no—
473C22×C22⋊C4—131no—
474C22×C22⋊C4—131no—
475C22×C22⋊C4—131no—
476C22×C42—131no—
477C22×C42—131no—
478C22×C42—131no—
479C22×C42C2×D1311yescharacteristic
480#391—24no—
481#387—264no—
482C4×C4⋊C4—264no—
483C4×C22⋊C4—264no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95—131no—
490C2×#95—131no—
491C2×#95—131no—
492C2×#95—131no—
493C2×#95—131no—
494C2×#95—131no—
495C2×#95—131no—
496C2×#95—131no—
497C2×#95—131no—
498C2×#95C2×D1311yescharacteristic
499C2×#95C2×D1311yescharacteristic
500C2×#95C2×D1311yescharacteristic
501C2×#95C2×D1311yescharacteristic
502C22×C13C22×C22⋊C411yescharacteristic
503C22×C13C2×C4×D411yescharacteristic
504C22×C13C2×C4×Q811yescharacteristic
505C22×C13C4×#4111yescharacteristic
506C22×C13C4×#4111yescharacteristic
507C22×C13#51811yescharacteristic
508C22×C13#51911yescharacteristic
509C22×C13C2×C22⋊Q811yescharacteristic
510C22×C13#52511yescharacteristic
511C22×C13#52511yescharacteristic
512C22×C13#52511yescharacteristic
513C22×C13#52911yescharacteristic
514C22×C13#53211yescharacteristic
515C22×C13#53211yescharacteristic
516C22×C13#53311yescharacteristic
517C22×C13#53911yescharacteristic
518C22×C13#53911yescharacteristic
519C22×C13#54211yescharacteristic
520C22×C13#54211yescharacteristic
521C22×C13D4211yescharacteristic
522C22×C13D4211yescharacteristic
523C22×C13#54611yescharacteristic
524C22×C13#54611yescharacteristic
525C22×C13#54711yescharacteristic
526C22×C13#54811yescharacteristic
527C22×C13#54811yescharacteristic
528C22×C13#54811yescharacteristic
529C22×C13D4×Q811yescharacteristic
530C22×C13D4×Q811yescharacteristic
531C22×C13#55111yescharacteristic
532C22×C13#55111yescharacteristic
533C22×C13#55211yescharacteristic
534C22×C13#55411yescharacteristic
535C22×C13#55411yescharacteristic
536C22×C13#55611yescharacteristic
537C2×D13—24no—
538C2×D13—24no—
539C2×D13—24no—
540C2×D13—42no—
541C2×D13—42no—
542C2×D13—42no—
543C2×D13—42no—
544C2×D13—42no—
545C2×D13—42no—
546C2×D13—42no—
547C2×D13—42no—
548C2×D13—42no—
549C2×D13—42no—
550C2×D13—42no—
551C2×D13—42no—
552C4×C13—24no—
553C4×C13—24no—
554C4×C13—24no—
555C4×C13—42no—
556C4×C13—42no—
557C4×C13—42no—
558C4×C13—81no—
559Dic13—24no—
560Dic13—24no—
561Dic13—42no—
562Dic13—42no—
563Dic13—42no—
564Dic13—42no—
565Dic13—81no—
566C25—131no—
567C22×Q8—22no—
568C22×Q8—22no—
569C22×Q8—22no—
570C22×Q8—22no—
571C22×Q8—41no—
572C22×Q8—41no—
573C22×Q8C4×D1314yes—
574C23×C4—131no—
575C23×C4—131no—
576C23×C4—131no—
577C23×C4—131no—
578C23×C4—131no—
579C23×C4—131no—
580C23×C4—134no—
581C23×C4—131no—
582C23×C4—262no—
583C23×C4—262no—
584C23×C4—262no—
585C23×C4—262no—
586C23×C4—521no—
587C23×C4—521no—
588C23×C4C22×D1311yescharacteristic
589C23×C4C22×D1311yescharacteristic
590C23×C4C22×D1311yescharacteristic
591C23×C4C22×D1311yescharacteristic
592C23×C4C22×D1311yescharacteristic
593C23×C4C22×D1311yescharacteristic
594C23×C4C22×D1311yescharacteristic
595C22⋊Q8—2632no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—134no—
600C2×C4⋊C4—134no—
601C2×C4⋊C4—134no—
602C2×C4⋊C4—134no—
603C2×C4⋊C4—134no—
604C2×C4⋊C4—262no—
605C2×C4⋊C4—262no—
606C2×C4⋊C4—262no—
607C2×C4⋊C4—262no—
608C2×C4⋊C4—262no—
609C2×C4⋊C4—262no—
610C2×C4⋊C4—262no—
611C2×C22⋊C4—134no—
612C2×C22⋊C4—134no—
613C2×C22⋊C4—134no—
614C2×C22⋊C4—262no—
615C2×C22⋊C4—262no—
616C2×C22⋊C4—262no—
617C2×C22⋊C4—262no—
618C2×C22⋊C4—262no—
619C2×C22⋊C4—262no—
620C2×C22⋊C4—262no—
621C2×C22⋊C4—262no—
622C2×C22⋊C4—262no—
623C2×C22⋊C4—262no—
624C2×C22⋊C4—262no—
625C2×C22⋊C4—262no—
626C2×C22⋊C4—262no—
627C2×C22⋊C4—521no—
628C2×C22⋊C4—521no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—41no—
632C2×C42—262no—
633C2×C42—262no—
634C2×C42—262no—
635C2×C42—262no—
636C2×C42—262no—
637C2×C42—262no—
638C2×C42—262no—
639C2×C42—521no—
640C2×C42—521no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—262no—
645#95—262no—
646#95—262no—
647#95—262no—
648#95—262no—
649#95—262no—
650#95—262no—
651#95—262no—
652#95—262no—
653#95—262no—
654#95—262no—
655#95—262no—
656#95—521no—
657#95—521no—
658#95C22⋊D1314yes—
659C2×C13#229711yescharacteristic
660C2×C13C4×C22⋊Q811yescharacteristic
661C2×C13#233211yescharacteristic
662C2×C13D4×C22⋊C411yescharacteristic
663C2×C13Q8×C22⋊C411yescharacteristic
664C2×C13#236211yescharacteristic
665C2×C13#236811yescharacteristic
666C2×C13#244911yescharacteristic
667C2×C13#245211yescharacteristic
668C2×C13#246111yescharacteristic
669C2×C13#246311yescharacteristic
670C2×C13#246511yescharacteristic
671C2×C13#247711yescharacteristic
672C2×C13#255611yescharacteristic
673C2×C13#256011yescharacteristic
674D13—44no—
675C24—132no—
676C24—132no—
677C24—132no—
678C24—261no—
679C24—261no—
680C24—261no—
681C24—261no—
682C24—261no—
683C24—261no—
684C24—261no—
685C24—261no—
686C24—261no—
687C24—261no—
688C24—261no—
689C24—261no—
690C24C23×D1311yescharacteristic
691C2×Q8—28no—
692C2×Q8—28no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8—44no—
697C2×Q8—44no—
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—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—132no—
736C22×C4—132no—
737C22×C4—132no—
738C22×C4—132no—
739C22×C4—132no—
740C22×C4—132no—
741C22×C4—132no—
742C22×C4—132no—
743C22×C4—132no—
744C22×C4—132no—
745C22×C4—268no—
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—261no—
774C22×C4—261no—
775C22×C4—261no—
776C22×C4—261no—
777C22×C4—261no—
778C22×C4—268no—
779C22×C4—261no—
780C22×C4—261no—
781C22×C4—261no—
782C22×C4—261no—
783C22×C4—261no—
784C22×C4—261no—
785C22×C4—261no—
786C22×C4—524no—
787C22×C4—524no—
788C22×C4—524no—
789C22×C4—524no—
790C22×C4—524no—
791C22×C4C2×C4×D1312yes—
792C22×C4C2×C4×D1312yes—
793C22×C4C2×C4×D1312yes—
794C22×C4#612712yes—
795C22×C4D4×D1312yes—
796C22×C4D4×D1312yes—
797C22×C4Q8×D1312yes—
798C22×C4#613112yes—
799C22×C4#613112yes—
800C22×C4C2×C22⋊D1312yes—
801C22×C4C2×C22⋊D1312yes—
802C22×C4C2×C22⋊D1312yes—
803C4⋊C4—44no—
804C4⋊C4—1316no—
805C4⋊C4—268no—
806C4⋊C4—268no—
807C4⋊C4—268no—
808C22⋊C4—268no—
809C22⋊C4—268no—
810C22⋊C4—268no—
811C22⋊C4—268no—
812C22⋊C4—524no—
813C22⋊C4—524no—
814C42—44no—
815C42—268no—
816C42—524no—
817C42—524no—
818C13#1409911yescharacteristic, complemented, Sylow
819C23—134no—
820C23—262no—
821C23—262no—
822C23—262no—
823C23—262no—
824C23—262no—
825C23—262no—
826C23—262no—
827C23—262no—
828C23—262no—
829C23—262no—
830C23—262no—
831C23—262no—
832C23—262no—
833C23—262no—
834C23—262no—
835C23—262no—
836C23—262no—
837C23—262no—
838C23—521no—
839C23—521no—
840C23—521no—
841C23—521no—
842C23—521no—
843C23—521no—
844C23—521no—
845C23—521no—
846C23—521no—
847C23—521no—
848C23—521no—
849C23—521no—
850C23—521no—
851C23—521no—
852C23—521no—
853C23—521no—
854C23C22×C4×D1311yescharacteristic
855C23C2×#612711yescharacteristic
856C23C2×D4×D1311yescharacteristic
857C23C2×D4×D1311yescharacteristic
858C23#8825111yescharacteristic
859C23#8825111yescharacteristic
860C23C2×Q8×D1311yescharacteristic
861C23C2×#613111yescharacteristic
862C23C2×#613111yescharacteristic
863C23#8825411yescharacteristic
864C23#41×D1311yescharacteristic
865C23#41×D1311yescharacteristic
866C23#41×D1311yescharacteristic
867C23#8825711yescharacteristic
868C23C22×C22⋊D1311yescharacteristic
869Q8—416no—
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—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—134no—
917C2×C4—134no—
918C2×C4—262no—
919C2×C4—262no—
920C2×C4—262no—
921C2×C4—262no—
922C2×C4—262no—
923C2×C4—262no—
924C2×C4—262no—
925C2×C4—262no—
926C2×C4—262no—
927C2×C4—262no—
928C2×C4—262no—
929C2×C4—262no—
930C2×C4—262no—
931C2×C4—262no—
932C2×C4—262no—
933C2×C4—262no—
934C2×C4—262no—
935C2×C4—262no—
936C2×C4—262no—
937C2×C4—262no—
938C2×C4—262no—
939C2×C4—262no—
940C2×C4—262no—
941C2×C4—262no—
942C2×C4—5216no—
943C2×C4—521no—
944C2×C4—521no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
949C2×C4—521no—
950C2×C4—521no—
951C2×C4—521no—
952C2×C4—521no—
953C2×C4—521no—
954C2×C4—521no—
955C2×C4—521no—
956C2×C4—521no—
957C2×C4—521no—
958C2×C4—521no—
959C2×C4—521no—
960C2×C4—521no—
961C2×C4—521no—
962C2×C4—521no—
963C2×C4—521no—
964C2×C4—521no—
965C2×C4—521no—
966C2×C4C22⋊C4×D1314yes—
967C2×C4C4×C22⋊D1314yes—
968C2×C4#8820014yescomplemented
969C22—264no—
970C22—264no—
971C22—264no—
972C22—522no—
973C22—522no—
974C22—522no—
975C22—522no—
976C22—522no—
977C22—522no—
978C22—522no—
979C22—522no—
980C22—522no—
981C22—522no—
982C22—522no—
983C22—522no—
984C22C2×C22⋊C4×D1311yescharacteristic
985C22#1171919111yescharacteristic
986C22#1171919511yescharacteristic
987C22#1171919511yescharacteristic
988C22C4×Q8×D1311yescharacteristic
989C22#1171927711yescharacteristic
990C22C4×#613111yescharacteristic
991C22C4×#613111yescharacteristic
992C22#1171928311yescharacteristic
993C22#1171928511yescharacteristic
994C22#1171928611yescharacteristic
995C22#1171928911yescharacteristic
996C22#1171933211yescharacteristic
997C22#1171933211yescharacteristic
998C22#1171933711yescharacteristic
999C22#1171933811yescharacteristic
1000C22#1171934111yescharacteristic
1001C22#1171934211yescharacteristic
1002C22#1171934311yescharacteristic
1003C22#1171935011yescharacteristic
1004C22#1171937311yescharacteristic
1005C22#1171937411yescharacteristic
1006C22#1171938211yescharacteristic
1007C22#1171938411yescharacteristic
1008C22#1171943011yescharacteristic
1009C22#1171943211yescharacteristic
1010C22#1171943511yescharacteristic
1011C22#1171943811yescharacteristic
1012C22C2×C4×C22⋊D1311yescharacteristic
1013C22D4×C22⋊D1311yescharacteristic
1014C22D4×C22⋊D1311yescharacteristic
1015C22C2×#8820011yescharacteristic
1016C22#1171952211yescharacteristic
1017C22#1171952911yescharacteristic
1018C22#1171953311yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—24no—
1022C4—42no—
1023C4—42no—
1024C4—42no—
1025C4—81no—
1026C4—264no—
1027C4—264no—
1028C4—522no—
1029C4—522no—
1030C4—522no—
1031C4—522no—
1032C4—1041no—
1033C2—524no—
1034C2#1311732511yescharacteristic
1035C2C4×#8820011yescharacteristic
1036C2#1311759111yescharacteristic
1037C2C22⋊C4×C22⋊D1311yescharacteristic
1038C2#1311767011yescharacteristic
1039C2#1311785911yescharacteristic
1040C2#1311791511yescharacteristic
1041C2#1311864111yescharacteristic
1042C2#1311868211yescharacteristic
1043C2#1311879911yescharacteristic
1044C2#1311882911yescharacteristic
1045C2#1311886411yescharacteristic
1046C2#1311904411yescharacteristic
1047C2#1311992511yescharacteristic
1048C2#1311998711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#391C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#391D13
hypocenterC13#14099
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#11718639C2semidirect
3. C2×C4×#6101C2semidirect
5. #13113107C2semidirect
6. #13113088C2semidirect
11. #13113070C2semidirect
12. #13113067C2semidirect
13. #13113067C2semidirect
15. C2×C13×#391C2semidirect
22. C2×#88200C4semidirect
111. C2×#6103Q8semidirect
291. #6101C22⋊C4semidirect
296. C2×#391D13semidirect
409. C2×C4×C13C22⋊Q8semidirect
818. C13#14099semidirect
968. C2×C4#88200semidirect

Maximal subgroups

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

subgroupindex
C22×#882002
C2×#117186392
C2×C4×#61012
C2×#117183272
#131131072
#131130882
#131130802
#131130782
#131130742
#131130722
#131130702
#131130672
#131130572
C2×C13×#3912
#1409913