Finite Group Databasebeta

← #15786722

Subgroups — #15786722

Order 3328.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718891C211yesmaximal, characteristic, complemented
2C2×#11718611C211yesmaximal, characteristic
3C2×C22⋊C4×Dic13C211yesmaximal, characteristic
4C22×#88071C211yesmaximal, characteristic
5#13113107C211yesmaximal, characteristic, complemented
6#13113104C211yesmaximal, characteristic, complemented
7#13113089C211yesmaximal, characteristic, complemented
8#13113089C211yesmaximal, characteristic, complemented
9#13113068C211yesmaximal, characteristic, complemented
10#13113068C211yesmaximal, characteristic, complemented
11#13113065C211yesmaximal, characteristic, complemented
12#13113059C211yesmaximal, characteristic
13#13113058C211yesmaximal, characteristic
14#13113058C211yesmaximal, characteristic
15C22×C13×C22⋊Q8C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C2×C13×C22⋊Q8—24no—
21C2×C13×C22⋊Q8—24no—
22C2×C13×C22⋊Q8C418yescomplemented
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34#11718891—24no—
35C2×#88071—24no—
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
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56#11718611—24no—
57C22⋊C4×Dic13—24no—
58C25×C13C2311yescharacteristic
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×C414yescomplemented
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—41no—
71C23×C4×C13—41no—
72C23×C4×C13C2×C414yes—
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×Dic13—22no—
80C23×Dic13—22no—
81C23×Dic13—22no—
82C23×Dic13—22no—
83C23×Dic13—22no—
84C23×Dic13—22no—
85C23×Dic13—22no—
86C23×Dic13—22no—
87C23×Dic13—22no—
88C23×Dic13—41no—
89C23×Dic13—41no—
90C23×Dic13—41no—
91C23×Dic13—41no—
92C23×Dic13Q814yescomplemented
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C13×C22⋊Q8—232no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—22no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4C2×C414yescomplemented
109C2×C13×C4⋊C4C2×C414yescomplemented
110C2×C13×C4⋊C4C2×C414yescomplemented
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4C2×C414yes—
114C2×C13×C22⋊C4C2×C414yes—
115C2×C13×C22⋊C4D414yes—
116C2×C13×C22⋊C4D414yes—
117C2×C22⋊Dic13—22no—
118C2×C22⋊Dic13—22no—
119C2×C22⋊Dic13—22no—
120C2×C22⋊Dic13—22no—
121C2×C22⋊Dic13—22no—
122C2×C22⋊Dic13Q814yescomplemented
123C2×C4⋊Dic13—22no—
124C2×C4⋊Dic13—22no—
125C2×C4⋊Dic13—22no—
126C2×C4⋊Dic13—22no—
127C2×C4⋊Dic13—41no—
128C2×C4⋊Dic13—41no—
129C2×C4×Dic13—22no—
130C2×C4×Dic13—22no—
131C2×C4×Dic13—22no—
132C2×C4×Dic13—22no—
133C2×C4×Dic13—41no—
134C2×C4×Dic13—41no—
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#88071—41no—
149#88071—41no—
150#88071—41no—
151#88071—41no—
152#88071—41no—
153#88071—41no—
154#88071D414yes—
155#14052—131nomaximal, Sylow
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13C22×C412yes—
165C24×C13C2×D412yes—
166C24×C13C2×D412yes—
167C24×C13C2×Q812yes—
168C24×C13C2×Q812yes—
169C24×C13#4112yes—
170C24×C13#4112yes—
171C24×C13C2411yescharacteristic
172C2×Q8×C13—28no—
173C2×Q8×C13—28no—
174C2×Q8×C13—44no—
175C2×Q8×C13—44no—
176C2×Q8×C13—44no—
177C2×Q8×C13—44no—
178C2×Q8×C13—44no—
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—28no—
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—28no—
211C22×C4×C13—44no—
212C22×C4×C13—44no—
213C22×C4×C13—44no—
214C22×C4×C13—44no—
215C22×C4×C13—44no—
216C22×C4×C13C22×C412yes—
217C22×C4×C13C22×C412yes—
218C22×C4×C13C22×C412yes—
219C22×C4×C13C22×C412yes—
220C22×C4×C13C22×C412yes—
221C22×C4×C13C22×C412yes—
222C22×C4×C13C2×D412yes—
223C22×C4×C13C2×D412yes—
224C22×C4×C13C2×D412yes—
225C22×C4×C13C2×D412yes—
226C22×C4×C13C2×D412yes—
227C22×C4×C13#4112yes—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—28no—
233C22×Dic13—28no—
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×Dic13—21no—
264C22×Dic13—28no—
265C22×Dic13—21no—
266C22×Dic13—21no—
267C22×Dic13—21no—
268C22×Dic13—21no—
269C22×Dic13—21no—
270C22×Dic13—21no—
271C22×Dic13—21no—
272C22×Dic13—21no—
273C22×Dic13—21no—
274C22×Dic13—21no—
275C22×Dic13—21no—
276C22×Dic13—21no—
277C22×Dic13—21no—
278C22×Dic13—21no—
279C22×Dic13—44no—
280C22×Dic13—44no—
281C22×Dic13—44no—
282C22×Dic13—44no—
283C22×Dic13—44no—
284C22×Dic13—44no—
285C22×Dic13—44no—
286C22×Dic13—44no—
287C22×Dic13—44no—
288C22×Dic13—44no—
289C22×Dic13—44no—
290C22×Dic13C2×D412yes—
291C22×Dic13C2×D412yes—
292C22×Dic13C2×Q812yes—
293C22×Dic13C2×Q812yes—
294C22×Dic13C2×Q812yes—
295C22×Dic13C2×Q812yes—
296C22×Dic13#4112yes—
297C22×Dic13#4112yes—
298C13×C4⋊C4—28no—
299C13×C4⋊C4—28no—
300C13×C4⋊C4—28no—
301C13×C22⋊C4—28no—
302C13×C22⋊C4C22⋊C4116yes—
303C22⋊Dic13—28no—
304C22⋊Dic13—44no—
305C4⋊Dic13—44no—
306C4⋊Dic13—44no—
307C4×Dic13—44no—
308C4×Dic13—44no—
309C22×C22⋊Q8D1311yescharacteristic
310C2×#391—131no—
311C2×#385—131no—
312C2×C4×C22⋊C4—131no—
313C22×#95—131no—
314#1446—131no—
315#1445—131no—
316#1441—131no—
317#1441—131no—
318#1436—131no—
319#1436—131no—
320C4⋊#95—131no—
321C22⋊#95—131no—
322C22⋊#95—131no—
323C22⋊#95—131no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13—22no—
340C23×C13—22no—
341C23×C13—22no—
342C23×C13—22no—
343C23×C13—22no—
344C23×C13—22no—
345C23×C13—22no—
346C23×C13—22no—
347C23×C13—22no—
348C23×C13—22no—
349C23×C13—22no—
350C23×C13—22no—
351C23×C13—22no—
352C23×C13C2×C22⋊C414yes—
353C23×C13C4×Q814yes—
354C23×C13C4×Q814yes—
355C23×C13C22⋊Q814yes—
356C23×C13C22⋊Q814yes—
357C23×C13#12414yes—
358C23×C13C4⋊Q814yes—
359C23×C13C23×C411yescharacteristic
360C23×C13C22×D411yescharacteristic
361C23×C13C22×D411yescharacteristic
362C23×C13C22×D411yescharacteristic
363C23×C13C22×Q811yescharacteristic
364C23×C13C22×Q811yescharacteristic
365C23×C13C2×#4111yescharacteristic
366C23×C13C2×#4111yescharacteristic
367C23×C13C2×#4111yescharacteristic
368C23×C13C2×#4111yescharacteristic
369C23×C13C2×#4111yescharacteristic
370C23×C13H(5,𝔽2)11yescharacteristic
371C23×C13H(5,𝔽2)11yescharacteristic
372C23×C13H(5,𝔽2)11yescharacteristic
373C23×C132−1+411yescharacteristic
374Q8×C13—416no—
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—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—22no—
398C2×C4×C13—22no—
399C2×C4×C13—22no—
400C2×C4×C13—22no—
401C2×C4×C13—22no—
402C2×C4×C13—416no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13C2×C22⋊C414yes—
416C2×C4×C13C2×C22⋊C414yes—
417C2×C4×C13C4×D414yes—
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—22no—
435C2×Dic13—22no—
436C2×Dic13—22no—
437C2×Dic13—22no—
438C2×Dic13—22no—
439C2×Dic13—416no—
440C2×Dic13—416no—
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×Dic13—41no—
458C2×Dic13—41no—
459C2×Dic13—41no—
460C2×Dic13—41no—
461C2×Dic13—41no—
462C2×Dic13—41no—
463C2×Dic13—41no—
464C2×Dic13—41no—
465C2×Dic13—41no—
466C2×Dic13—41no—
467C2×Dic13—41no—
468C2×Dic13—41no—
469C2×Dic13—41no—
470C2×Dic13—41no—
471C2×Dic13—41no—
472C2×Dic13—41no—
473C2×Dic13—41no—
474C2×Dic13—41no—
475C2×Dic13C22⋊Q814yescomplemented
476C23×Q8C2×D1311yescharacteristic
477C24×C4—131no—
478C24×C4—131no—
479C24×C4C2×D1311yescharacteristic
480C2×C22⋊Q8—24no—
481C2×C22⋊Q8—24no—
482C2×C22⋊Q8Dic1318yescomplemented
483C22×C4⋊C4—131no—
484C22×C4⋊C4—131no—
485C22×C4⋊C4C2×D1311yescharacteristic
486C22×C4⋊C4C2×D1311yescharacteristic
487C22×C4⋊C4C2×D1311yescharacteristic
488C22×C22⋊C4—131no—
489C22×C22⋊C4—131no—
490C22×C22⋊C4C2×D1311yescharacteristic
491C22×C22⋊C4C2×D1311yescharacteristic
492C22×C42—131no—
493C22×C42—131no—
494#391—264no—
495#385—264no—
496C4×C22⋊C4—264no—
497C2×#95—131no—
498C2×#95—131no—
499C2×#95—131no—
500C2×#95—131no—
501C2×#95—131no—
502C2×#95—131no—
503C2×#95—131no—
504C2×#95—131no—
505C2×#95—131no—
506C2×#95—131no—
507C2×#95—131no—
508C2×#95—131no—
509C2×#95—131no—
510C2×#95—131no—
511C2×#95—131no—
512C2×#95—131no—
513C2×#95—131no—
514C2×#95—131no—
515C2×#95—131no—
516C2×#95—131no—
517C2×#95—264no—
518C22×C13—24no—
519C22×C13—24no—
520C22×C13—24no—
521C22×C13—24no—
522C22×C13—24no—
523C22×C13—24no—
524C22×C13—24no—
525C22×C13—24no—
526C22×C13—24no—
527C22×C13—24no—
528C22×C13—24no—
529C22×C13—24no—
530C22×C13—24no—
531C22×C13—24no—
532C22×C13#39118yescomplemented
533C22×C13C22×C22⋊C411yescharacteristic
534C22×C13C2×C4×D411yescharacteristic
535C22×C13C2×C4×Q811yescharacteristic
536C22×C13C2×C4×Q811yescharacteristic
537C22×C13C4×#4111yescharacteristic
538C22×C13#51811yescharacteristic
539C22×C13#52011yescharacteristic
540C22×C13C2×C22⋊Q811yescharacteristic
541C22×C13C2×C22⋊Q811yescharacteristic
542C22×C13C2×C22⋊Q811yescharacteristic
543C22×C13#52511yescharacteristic
544C22×C13C2×#12411yescharacteristic
545C22×C13#52911yescharacteristic
546C22×C13C2×C4⋊Q811yescharacteristic
547C22×C13#53311yescharacteristic
548C22×C13#53811yescharacteristic
549C22×C13#53911yescharacteristic
550C22×C13#54311yescharacteristic
551C22×C13#54411yescharacteristic
552C22×C13D4211yescharacteristic
553C22×C13D4211yescharacteristic
554C22×C13#54611yescharacteristic
555C22×C13#54611yescharacteristic
556C22×C13#54611yescharacteristic
557C22×C13#54611yescharacteristic
558C22×C13#54611yescharacteristic
559C22×C13#54711yescharacteristic
560C22×C13#54711yescharacteristic
561C22×C13D4×Q811yescharacteristic
562C22×C13#55111yescharacteristic
563C22×C13#55111yescharacteristic
564C22×C13#55211yescharacteristic
565C22×C13#55411yescharacteristic
566C22×C13#55411yescharacteristic
567C22×C13#55411yescharacteristic
568C4×C13—24no—
569C4×C13—24no—
570C4×C13—24no—
571C4×C13—42no—
572C4×C13—42no—
573C4×C13—42no—
574Dic13—24no—
575Dic13—42no—
576Dic13—42no—
577Dic13—42no—
578Dic13—42no—
579Dic13—42no—
580Dic13—81no—
581Dic13—81no—
582C25C22×D1311yescharacteristic
583C22×Q8—22no—
584C22×Q8—22no—
585C22×Q8—22no—
586C22×Q8—22no—
587C22×Q8—41no—
588C22×Q8—41no—
589C22×Q8C2×Dic1314yescomplemented
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—22no—
594C23×C4—41no—
595C23×C4—41no—
596C23×C4—131no—
597C23×C4—131no—
598C23×C4—131no—
599C23×C4—131no—
600C23×C4—131no—
601C23×C4—131no—
602C23×C4—134no—
603C23×C4—131no—
604C23×C4—131no—
605C23×C4—262no—
606C23×C4—262no—
607C23×C4—262no—
608C23×C4—262no—
609C23×C4—262no—
610C23×C4—262no—
611C23×C4—262no—
612C23×C4—262no—
613C23×C4—262no—
614C23×C4—521no—
615C23×C4—521no—
616C23×C4—521no—
617C23×C4—521no—
618C23×C4C2×Dic1314yes—
619C23×C4C22×D1311yescharacteristic
620C23×C4C22×D1311yescharacteristic
621C23×C4C22×D1311yescharacteristic
622C23×C4C22×D1311yescharacteristic
623C23×C4C22×D1311yescharacteristic
624C23×C4C22×D1311yescharacteristic
625C22⋊Q8—232no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—262no—
633C2×C4⋊C4—262no—
634C2×C4⋊C4—262no—
635C2×C4⋊C4—262no—
636C2×C4⋊C4—521no—
637C2×C4⋊C4—521no—
638C2×C4⋊C4C2×Dic1314yescomplemented
639C2×C4⋊C4C2×Dic1314yescomplemented
640C2×C4⋊C4C2×Dic1314yescomplemented
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—134no—
644C2×C22⋊C4—262no—
645C2×C22⋊C4—262no—
646C2×C22⋊C4—262no—
647C2×C22⋊C4—262no—
648C2×C22⋊C4—262no—
649C2×C22⋊C4C2×Dic1314yes—
650C2×C22⋊C4C2×Dic1314yes—
651C2×C22⋊C4C22⋊D1314yes—
652C2×C22⋊C4C22⋊D1314yes—
653C2×C42—262no—
654C2×C42—262no—
655C2×C42—262no—
656C2×C42—262no—
657C2×C42—521no—
658C2×C42—521no—
659#95—134no—
660#95—262no—
661#95—262no—
662#95—262no—
663#95—262no—
664#95—262no—
665#95—262no—
666#95—262no—
667#95—262no—
668#95—262no—
669#95—262no—
670#95—262no—
671#95—262no—
672#95—262no—
673#95—521no—
674#95—521no—
675#95—521no—
676#95—521no—
677#95—521no—
678#95—521no—
679C2×C13—28no—
680C2×C13C2×#39111yescharacteristic
681C2×C13C4×C22⋊Q811yescharacteristic
682C2×C13#232911yescharacteristic
683C2×C13D4×C22⋊C411yescharacteristic
684C2×C13#233911yescharacteristic
685C2×C13#236011yescharacteristic
686C2×C13#236811yescharacteristic
687C2×C13#243711yescharacteristic
688C2×C13#243811yescharacteristic
689C2×C13#244011yescharacteristic
690C2×C13#244911yescharacteristic
691C2×C13#245011yescharacteristic
692C2×C13#247211yescharacteristic
693C2×C13#248811yescharacteristic
694C2×C13#254911yescharacteristic
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24Q8×D1312yes—
704C24Q8×D1312yes—
705C24#613112yes—
706C24#613112yes—
707C24C22×Dic1312yes—
708C24C2×C22⋊D1312yes—
709C24C2×C22⋊D1312yes—
710C24C23×D1311yescharacteristic
711C2×Q8—28no—
712C2×Q8—28no—
713C2×Q8—44no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—44no—
717C2×Q8—44no—
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—28no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—28no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—132no—
756C22×C4—132no—
757C22×C4—132no—
758C22×C4—132no—
759C22×C4—132no—
760C22×C4—132no—
761C22×C4—132no—
762C22×C4—132no—
763C22×C4—268no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—268no—
769C22×C4—268no—
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—261no—
779C22×C4—261no—
780C22×C4—261no—
781C22×C4—261no—
782C22×C4—261no—
783C22×C4—261no—
784C22×C4—261no—
785C22×C4—261no—
786C22×C4—261no—
787C22×C4—261no—
788C22×C4—261no—
789C22×C4—261no—
790C22×C4—261no—
791C22×C4—261no—
792C22×C4—261no—
793C22×C4—261no—
794C22×C4—261no—
795C22×C4—261no—
796C22×C4—261no—
797C22×C4—261no—
798C22×C4—261no—
799C22×C4—261no—
800C22×C4—261no—
801C22×C4—261no—
802C22×C4—261no—
803C22×C4—261no—
804C22×C4—261no—
805C22×C4—261no—
806C22×C4—261no—
807C22×C4—261no—
808C22×C4—261no—
809C22×C4—261no—
810C22×C4—261no—
811C22×C4—261no—
812C22×C4—261no—
813C22×C4—261no—
814C22×C4—524no—
815C22×C4—524no—
816C22×C4—524no—
817C22×C4—524no—
818C22×C4—524no—
819C22×C4—524no—
820C22×C4—524no—
821C22×C4—524no—
822C22×C4—524no—
823C22×C4—524no—
824C22×C4—524no—
825C22×C4D4×D1312yes—
826C22×C4#612912yes—
827C22×C4C22×Dic1312yes—
828C22×C4C22×Dic1312yes—
829C22×C4C22×Dic1312yes—
830C22×C4C22×Dic1312yes—
831C22×C4C22×Dic1312yes—
832C22×C4C22×Dic1312yes—
833C22×C4C2×C22⋊D1312yes—
834C22×C4C2×C22⋊D1312yes—
835C22×C4C2×C22⋊D1312yes—
836C22×C4C2×C22⋊D1312yes—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—524no—
841C4⋊C4—524no—
842C22⋊C4—28no—
843C22⋊C4—268no—
844C22⋊C4—524no—
845C22⋊C4C22⋊Dic13116yes—
846C42—524no—
847C42—524no—
848C13#1405211yescharacteristic, complemented, Sylow
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23#8819814yes—
878C23Q8×Dic1314yes—
879C23Q8×Dic1314yes—
880C23#8820014yes—
881C23#8820014yes—
882C23#8820114yes—
883C23C2×C22⋊Dic1314yes—
884C23C2×D4×D1311yescharacteristic
885C23C2×#612911yescharacteristic
886C23#8825111yescharacteristic
887C23#8825111yescharacteristic
888C23C2×Q8×D1311yescharacteristic
889C23C2×Q8×D1311yescharacteristic
890C23C2×#613111yescharacteristic
891C23C2×#613111yescharacteristic
892C23#41×D1311yescharacteristic
893C23#41×D1311yescharacteristic
894C23#8825611yescharacteristic
895C23#8825711yescharacteristic
896C23C23×Dic1311yescharacteristic
897C23C22×C22⋊D1311yescharacteristic
898C23C22×C22⋊D1311yescharacteristic
899Q8—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—416no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—134no—
941C2×C4—262no—
942C2×C4—262no—
943C2×C4—262no—
944C2×C4—262no—
945C2×C4—262no—
946C2×C4—262no—
947C2×C4—262no—
948C2×C4—262no—
949C2×C4—262no—
950C2×C4—262no—
951C2×C4—262no—
952C2×C4—262no—
953C2×C4—262no—
954C2×C4—262no—
955C2×C4—262no—
956C2×C4—262no—
957C2×C4—262no—
958C2×C4—262no—
959C2×C4—262no—
960C2×C4—262no—
961C2×C4—262no—
962C2×C4—5216no—
963C2×C4—5216no—
964C2×C4—521no—
965C2×C4—521no—
966C2×C4—521no—
967C2×C4—521no—
968C2×C4—521no—
969C2×C4—521no—
970C2×C4—521no—
971C2×C4—521no—
972C2×C4—521no—
973C2×C4—521no—
974C2×C4—521no—
975C2×C4—521no—
976C2×C4—521no—
977C2×C4—521no—
978C2×C4—521no—
979C2×C4—521no—
980C2×C4—521no—
981C2×C4—521no—
982C2×C4—521no—
983C2×C4—521no—
984C2×C4—521no—
985C2×C4—521no—
986C2×C4—521no—
987C2×C4—521no—
988C2×C4—521no—
989C2×C4—521no—
990C2×C4—521no—
991C2×C4—521no—
992C2×C4—521no—
993C2×C4—521no—
994C2×C4—521no—
995C2×C4—521no—
996C2×C4—521no—
997C2×C4—521no—
998C2×C4D4×Dic1314yes—
999C2×C4C2×C22⋊Dic1314yes—
1000C2×C4C2×C22⋊Dic1314yes—
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22#1171889118yescomplemented
1016C22#1171932711yescharacteristic
1017C22#1171932811yescharacteristic
1018C22#1171932911yescharacteristic
1019C22D13×C22⋊Q811yescharacteristic
1020C22#1171933211yescharacteristic
1021C22#1171933511yescharacteristic
1022C22#1171933711yescharacteristic
1023C22#1171933911yescharacteristic
1024C22#1171934011yescharacteristic
1025C22#1171934111yescharacteristic
1026C22#1171934111yescharacteristic
1027C22#1171934211yescharacteristic
1028C22#1171934211yescharacteristic
1029C22#1171934711yescharacteristic
1030C22#1171934911yescharacteristic
1031C22#1171935011yescharacteristic
1032C22C2×D4×Dic1311yescharacteristic
1033C22#1171950311yescharacteristic
1034C22D4×C22⋊D1311yescharacteristic
1035C22D4×C22⋊D1311yescharacteristic
1036C22#1171951111yescharacteristic
1037C22#1171951111yescharacteristic
1038C22C2×#8819811yescharacteristic
1039C22C2×Q8×Dic1311yescharacteristic
1040C22C2×Q8×Dic1311yescharacteristic
1041C22C2×#8820011yescharacteristic
1042C22C2×#8820011yescharacteristic
1043C22C2×#8820111yescharacteristic
1044C22#1171952911yescharacteristic
1045C22#1171952911yescharacteristic
1046C22#41×Dic1311yescharacteristic
1047C22#1171953211yescharacteristic
1048C22#1171953411yescharacteristic
1049C22#1171953411yescharacteristic
1050C22C22×C22⋊Dic1311yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—24no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—264no—
1058C4—522no—
1059C4—522no—
1060C4—522no—
1061C4—522no—
1062C4—522no—
1063C4—1041no—
1064C4—1041no—
1065C2—28no—
1066C2C2×#1171889111yescharacteristic
1067C2C22⋊Q8×Dic1311yescharacteristic
1068C2#1311757111yescharacteristic
1069C2D4×C22⋊Dic1311yescharacteristic
1070C2#1311766611yescharacteristic
1071C2#1311784511yescharacteristic
1072C2#1311792111yescharacteristic
1073C2#1311849911yescharacteristic
1074C2#1311850811yescharacteristic
1075C2#1311853511yescharacteristic
1076C2#1311864111yescharacteristic
1077C2#1311865611yescharacteristic
1078C2#1311896911yescharacteristic
1079C2#1311916811yescharacteristic
1080C2#1311984411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C13×C22⋊Q8C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22×C22⋊Q8D13
hypocenterC13#14052
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11718891C2semidirect
5. #13113107C2semidirect
6. #13113104C2semidirect
7. #13113089C2semidirect
8. #13113089C2semidirect
9. #13113068C2semidirect
10. #13113068C2semidirect
11. #13113065C2semidirect
22. C2×C13×C22⋊Q8C4semidirect
65. C22×Q8×C13C2×C4semidirect
92. C23×Dic13Q8semidirect
108. C2×C13×C4⋊C4C2×C4semidirect
109. C2×C13×C4⋊C4C2×C4semidirect
110. C2×C13×C4⋊C4C2×C4semidirect
122. C2×C22⋊Dic13Q8semidirect
475. C2×Dic13C22⋊Q8semidirect
482. C2×C22⋊Q8Dic13semidirect
532. C22×C13#391semidirect
589. C22×Q8C2×Dic13semidirect
638. C2×C4⋊C4C2×Dic13semidirect
639. C2×C4⋊C4C2×Dic13semidirect
640. C2×C4⋊C4C2×Dic13semidirect
848. C13#14052semidirect
1015. C22#11718891semidirect

Maximal subgroups

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

subgroupindex
C2×#117188912
C2×#117186112
C2×C22⋊C4×Dic132
C22×#880712
#131131072
#131131042
#131130892
#131130682
#131130652
#131130592
#131130582
C22×C13×C22⋊Q82
#1405213