Finite Group Databasebeta

← #15784482

Subgroups — #15784482

Order 3328.

2666 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88135C211yesmaximal, characteristic
2C2×#11718618C211yesmaximal, characteristic
3C2×#11718618C211yesmaximal, characteristic
4C2×C4×#6101C211yesmaximal, characteristic, complemented
5C2×#11718310C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
7C2×C4×#6103C211yesmaximal, characteristic, complemented
8#13113073C211yesmaximal, characteristic, complemented
9#13113072C211yesmaximal, characteristic, complemented
10#13113072C211yesmaximal, characteristic, complemented
11#13113064C211yesmaximal, characteristic, complemented
12#13113058C211yesmaximal, characteristic, complemented
13#13113057C211yesmaximal, characteristic, complemented
14#95×Dic13C211yesmaximal, characteristic, complemented
15C13×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D13C2211yescharacteristic
17C24×Dic13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C2×#88135—24no—
40C2×#88135—24no—
41C2×#88135C418yescomplemented
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54#11718618C418yescomplemented
55#11718618C418yescomplemented
56C22⋊C4×Dic13—24no—
57C4×#6103—24no—
58C4×#6101—24no—
59#11718310—24no—
60C25×C13C2311yescharacteristic
61C24×D13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C22×C22⋊D13—22no—
69C22×C22⋊D13—22no—
70C22×C22⋊D13—22no—
71C22×C22⋊D13—22no—
72C22×C22⋊D13C2×C414yes—
73C22×C22⋊D13C2×C414yes—
74C22×C22⋊D13C2×C414yes—
75C23×Dic13—22no—
76C23×Dic13—22no—
77C23×Dic13—22no—
78C23×Dic13—22no—
79C23×Dic13—41no—
80C23×Dic13—41no—
81C23×Dic13C2×C414yes—
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C22×C4×D13—22no—
90C22×C4×D13—22no—
91C22×C4×D13—22no—
92C22×C4×D13—22no—
93C22×C4×D13—41no—
94C22×C4×D13—41no—
95C22×C4×D13C2×C414yes—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—41no—
101C2×C13×C22⋊C4—41no—
102C2×C13×C22⋊C4C2×C414yes—
103C2×C13×C22⋊C4C2×C414yescomplemented
104C2×C13×C22⋊C4C2×C414yescomplemented
105C2×C42×C13—22no—
106C2×C42×C13—22no—
107C2×C42×C13—41no—
108C2×C22⋊Dic13—22no—
109C2×C22⋊Dic13—22no—
110C2×C22⋊Dic13—41no—
111C2×C22⋊Dic13—41no—
112C2×C22⋊Dic13C2×C414yescomplemented
113C2×C22⋊Dic13C2×C414yescomplemented
114C2×#6103—22no—
115C2×#6103—22no—
116C2×#6103—22no—
117C2×#6103—22no—
118C2×#6103—22no—
119C2×#6103—22no—
120C2×#6103—41no—
121C2×#6103—41no—
122C2×#6103—41no—
123C2×#6103—41no—
124C2×#6103C2×C414yes—
125C2×#6103C2×C414yescomplemented
126C2×#6103C2×C414yescomplemented
127C2×#6103C2×C414yescomplemented
128C2×#6103C2×C414yescomplemented
129C2×#6101—22no—
130C2×#6101—22no—
131C2×#6101—22no—
132C2×#6101—22no—
133C2×#6101C2×C414yes—
134C2×#6101C2×C414yescomplemented
135C2×#6101C2×C414yescomplemented
136C2×#6101D414yes—
137C2×#6101D414yes—
138C2×C4×Dic13—22no—
139C2×C4×Dic13—22no—
140C2×C4×Dic13—22no—
141C2×C4×Dic13—22no—
142C2×C4×Dic13—22no—
143C2×C4×Dic13—22no—
144C2×C4×Dic13—22no—
145C2×C4×Dic13—22no—
146C2×C4×Dic13—22no—
147C2×C4×Dic13—22no—
148C2×C4×Dic13—22no—
149C2×C4×Dic13—22no—
150C2×C4×Dic13—41no—
151C2×C4×Dic13—41no—
152C2×C4×Dic13—41no—
153C2×C4×Dic13C2×C414yes—
154C2×C4×Dic13C2×C414yescomplemented
155C2×C4×Dic13C2×C414yescomplemented
156#88135—232no—
157C13×#95—22no—
158C13×#95—22no—
159C13×#95—41no—
160#88071—22no—
161#88071—22no—
162#88071—22no—
163#88071—22no—
164#88071—22no—
165#88071—22no—
166#88071—22no—
167#88071—41no—
168#88071D414yescomplemented
169#13820—131nomaximal, Sylow
170C24×C13—21no—
171C24×C13—21no—
172C24×C13—21no—
173C24×C13—21no—
174C24×C13—21no—
175C24×C13—21no—
176C24×C13—21no—
177C24×C13—21no—
178C24×C13—21no—
179C24×C13—21no—
180C24×C13—21no—
181C24×C13—21no—
182C24×C13C22×C412yes—
183C24×C13C22×C412yes—
184C24×C13C22×C412yes—
185C24×C13C2411yescharacteristic
186C23×D13—21no—
187C23×D13—21no—
188C23×D13—21no—
189C23×D13—21no—
190C23×D13—21no—
191C23×D13—21no—
192C23×D13—21no—
193C23×D13—21no—
194C23×D13—21no—
195C23×D13—21no—
196C23×D13—21no—
197C23×D13—21no—
198C23×D13C22×C412yes—
199C23×D13C22×C412yes—
200C23×D13C22×C412yes—
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×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13C22×C412yes—
234C22×C4×C13C22×C412yes—
235C22×C4×C13C22×C412yes—
236C22×C4×C13C22×C412yes—
237C22×C4×C13C22×C412yes—
238C22×C4×C13C22×C412yes—
239C22×C4×C13C2×D412yes—
240C22×C4×C13C2×D412yes—
241C22×C4×C13C2×D412yes—
242C22×C4×C13#4112yes—
243C2×C22⋊D13—28no—
244C2×C22⋊D13—28no—
245C2×C22⋊D13—28no—
246C2×C22⋊D13—28no—
247C2×C22⋊D13—28no—
248C2×C22⋊D13—28no—
249C2×C22⋊D13C42116yescomplemented
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—21no—
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—21no—
280C22×Dic13—28no—
281C22×Dic13—28no—
282C22×Dic13—44no—
283C22×Dic13—44no—
284C22×Dic13—44no—
285C22×Dic13—44no—
286C22×Dic13—44no—
287C22×Dic13C22×C412yes—
288C22×Dic13C22×C412yes—
289C22×Dic13C22×C412yes—
290C22×Dic13C22×C412yes—
291C22×Dic13C22×C412yes—
292C22×Dic13C22×C412yes—
293C22×Dic13C22×C412yes—
294C22×Dic13C22×C412yes—
295C22×Dic13C22×C412yes—
296C22×Dic13C2×D412yes—
297C22×Dic13C2×D412yes—
298C22×Dic13C2×D412yes—
299C22×Dic13C2×D412yes—
300C22×Dic13C2×D412yes—
301C22×Dic13C2×D412yes—
302C22×Dic13#4112yes—
303C22×Dic13#4112yes—
304C22×Dic13#4112yes—
305C22×Dic13#4112yes—
306C2×C4×D13—28no—
307C2×C4×D13—28no—
308C2×C4×D13—44no—
309C2×C4×D13—44no—
310C2×C4×D13—44no—
311C2×C4×D13—44no—
312C2×C4×D13—44no—
313C13×C22⋊C4—28no—
314C13×C22⋊C4—28no—
315C13×C22⋊C4—44no—
316C42×C13—44no—
317C22⋊Dic13—28no—
318C22⋊Dic13—44no—
319#6103—28no—
320#6103—28no—
321#6103—28no—
322#6103—44no—
323#6103—44no—
324#6101—28no—
325#6101—28no—
326#6101C22⋊C4116yescomplemented
327C4×Dic13—28no—
328C4×Dic13—28no—
329C4×Dic13—28no—
330C4×Dic13—44no—
331C4×Dic13—44no—
332C4×Dic13—44no—
333C22×C4×D4—131no—
334C2×#390—131no—
335C2×#390—131no—
336C2×C4×C4⋊C4—131no—
337C2×C4×C4⋊C4—131no—
338C2×C4×C22⋊C4—131no—
339C2×C4×C22⋊C4—131no—
340#1437—131no—
341#1437—131no—
342#1437—131no—
343#1437D1311yescharacteristic, complemented
344C4⋊#95—131no—
345C22⋊#95—131no—
346C22⋊#95—131no—
347C4×#95—131no—
348C23×C13—22no—
349C23×C13—22no—
350C23×C13—22no—
351C23×C13—22no—
352C23×C13—22no—
353C23×C13—22no—
354C23×C13—22no—
355C23×C13—22no—
356C23×C13—22no—
357C23×C13—22no—
358C23×C13—22no—
359C23×C13—22no—
360C23×C13—22no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13—22no—
364C23×C13—22no—
365C23×C13—22no—
366C23×C13—41no—
367C23×C13—41no—
368C23×C13—41no—
369C23×C13—41no—
370C23×C13—41no—
371C23×C13—41no—
372C23×C13—41no—
373C23×C13—41no—
374C23×C13—41no—
375C23×C13—41no—
376C23×C13—41no—
377C23×C13—41no—
378C23×C13—41no—
379C23×C13—41no—
380C23×C13—41no—
381C23×C13—41no—
382C23×C13C2×C4214yes—
383C23×C13C23×C411yescharacteristic
384C23×C13C23×C411yescharacteristic
385C23×C13C23×C411yescharacteristic
386C23×C13C22×D411yescharacteristic
387C23×C13C22×D411yescharacteristic
388C23×C13C22×D411yescharacteristic
389C23×C13C2×#4111yescharacteristic
390C23×C13C2×#4111yescharacteristic
391C23×C13C2×#4111yescharacteristic
392C23×C13C2×#4111yescharacteristic
393C23×C13C2×#4111yescharacteristic
394C23×C13H(5,𝔽2)11yescharacteristic
395C23×C13H(5,𝔽2)11yescharacteristic
396C23×C13H(5,𝔽2)11yescharacteristic
397C23×C132−1+411yescharacteristic
398C22×D13—22no—
399C22×D13—22no—
400C22×D13—22no—
401C22×D13—22no—
402C22×D13—22no—
403C22×D13—22no—
404C22×D13—22no—
405C22×D13—22no—
406C22×D13—22no—
407C22×D13—22no—
408C22×D13—22no—
409C22×D13—22no—
410C22×D13—22no—
411C22×D13—22no—
412C22×D13—22no—
413C22×D13—22no—
414C22×D13—22no—
415C22×D13—22no—
416C22×D13—41no—
417C22×D13—41no—
418C22×D13—41no—
419C22×D13—41no—
420C22×D13—41no—
421C22×D13—41no—
422C22×D13—41no—
423C22×D13—41no—
424C22×D13—41no—
425C22×D13—41no—
426C22×D13—41no—
427C22×D13—41no—
428C22×D13—41no—
429C22×D13—41no—
430C22×D13—41no—
431C22×D13—41no—
432C22×D13C2×C4214yes—
433C2×C4×C13—22no—
434C2×C4×C13—22no—
435C2×C4×C13—22no—
436C2×C4×C13—22no—
437C2×C4×C13—22no—
438C2×C4×C13—22no—
439C2×C4×C13—22no—
440C2×C4×C13—22no—
441C2×C4×C13—22no—
442C2×C4×C13—22no—
443C2×C4×C13—22no—
444C2×C4×C13—22no—
445C2×C4×C13—22no—
446C2×C4×C13—22no—
447C2×C4×C13—22no—
448C2×C4×C13—22no—
449C2×C4×C13—22no—
450C2×C4×C13—22no—
451C2×C4×C13—22no—
452C2×C4×C13—22no—
453C2×C4×C13—22no—
454C2×C4×C13—22no—
455C2×C4×C13—22no—
456C2×C4×C13—22no—
457C2×C4×C13—41no—
458C2×C4×C13—41no—
459C2×C4×C13—41no—
460C2×C4×C13—41no—
461C2×C4×C13—41no—
462C2×C4×C13—41no—
463C2×C4×C13—41no—
464C2×C4×C13—41no—
465C2×C4×C13—41no—
466C2×C4×C13—41no—
467C2×C4×C13—41no—
468C2×C4×C13—41no—
469C2×C4×C13—41no—
470C2×C4×C13—41no—
471C2×C4×C13—41no—
472C2×C4×C13—41no—
473C2×C4×C13C2×C22⋊C414yes—
474C2×C4×C13C4×D414yescomplemented
475C22⋊D13—232no—
476C2×Dic13—22no—
477C2×Dic13—22no—
478C2×Dic13—22no—
479C2×Dic13—22no—
480C2×Dic13—22no—
481C2×Dic13—22no—
482C2×Dic13—22no—
483C2×Dic13—22no—
484C2×Dic13—22no—
485C2×Dic13—22no—
486C2×Dic13—22no—
487C2×Dic13—22no—
488C2×Dic13—22no—
489C2×Dic13—22no—
490C2×Dic13—22no—
491C2×Dic13—22no—
492C2×Dic13—22no—
493C2×Dic13—22no—
494C2×Dic13—22no—
495C2×Dic13—22no—
496C2×Dic13—22no—
497C2×Dic13—22no—
498C2×Dic13—22no—
499C2×Dic13—22no—
500C2×Dic13—22no—
501C2×Dic13—22no—
502C2×Dic13—22no—
503C2×Dic13—416no—
504C2×Dic13—41no—
505C2×Dic13—41no—
506C2×Dic13—41no—
507C2×Dic13—41no—
508C2×Dic13—41no—
509C2×Dic13—41no—
510C2×Dic13—41no—
511C2×Dic13—41no—
512C2×Dic13—41no—
513C2×Dic13—41no—
514C2×Dic13—41no—
515C2×Dic13—41no—
516C2×Dic13C2×C4214yes—
517C2×Dic13C2×C22⋊C414yes—
518C2×Dic13C2×C22⋊C414yes—
519C2×Dic13#11714yes—
520C2×Dic13C4×D414yes—
521C2×Dic13C4×D414yes—
522C2×Dic13C4×D414yes—
523C2×Dic13C4×D414yes—
524C2×Dic13C4×D414yes—
525C2×Dic13C4×D414yescomplemented
526C4×D13—416no—
527C23×D4—131no—
528C24×C4—131no—
529C24×C4—131no—
530C2×C4×D4—138no—
531C2×C4×D4—264no—
532C2×C4×D4—264no—
533C22×C4⋊C4—131no—
534C22×C4⋊C4—131no—
535C22×C4⋊C4—131no—
536C22×C22⋊C4—131no—
537C22×C22⋊C4—131no—
538C22×C22⋊C4—131no—
539C22×C22⋊C4—131no—
540C22×C22⋊C4—131no—
541C22×C22⋊C4—131no—
542C22×C22⋊C4—131no—
543C22×C22⋊C4C2×D1311yescharacteristic
544C22×C22⋊C4C2×D1311yescharacteristic
545C22×C22⋊C4C2×D1311yescharacteristic
546C22×C42—131no—
547C22×C42—131no—
548C22×C42—131no—
549C22×C42—131no—
550C22×C42—131no—
551C22×C42—131no—
552C22×C42C2×D1311yescharacteristic
553#390—138no—
554#390—138no—
555C4×C4⋊C4—264no—
556C4×C4⋊C4—264no—
557C4×C22⋊C4—264no—
558C4×C22⋊C4—264no—
559C2×#95—131no—
560C2×#95—131no—
561C2×#95—131no—
562C2×#95—131no—
563C2×#95—131no—
564C2×#95—131no—
565C2×#95—131no—
566C2×#95—131no—
567C2×#95—131no—
568C2×#95C2×D1311yescharacteristic
569C2×#95C2×D1311yescharacteristic
570C2×#95C2×D1311yescharacteristic
571C22×C13—24no—
572C22×C13—24no—
573C22×C13—24no—
574C22×C13—42no—
575C22×C13—42no—
576C22×C13—42no—
577C22×C13—42no—
578C22×C13—42no—
579C22×C13—42no—
580C22×C13—42no—
581C22×C13—42no—
582C22×C13—42no—
583C22×C13—42no—
584C22×C13—42no—
585C22×C13—42no—
586C22×C13C22×C4211yescharacteristic
587C22×C13C22×C22⋊C411yescharacteristic
588C22×C13C2×#11711yescharacteristic
589C22×C13C2×C4×D411yescharacteristic
590C22×C13C2×C4×D411yescharacteristic
591C22×C13C2×C4×D411yescharacteristic
592C22×C13C2×C4×D411yescharacteristic
593C22×C13C2×C4×D411yescharacteristic
594C22×C13C2×C4×D411yescharacteristic
595C22×C13C2×C4×D411yescharacteristic
596C22×C13C4×#4111yescharacteristic
597C22×C13C4×#4111yescharacteristic
598C22×C13C4×#4111yescharacteristic
599C22×C13#51811yescharacteristic
600C22×C13#51811yescharacteristic
601C22×C13#51811yescharacteristic
602C22×C13#52011yescharacteristic
603C22×C13#52011yescharacteristic
604C22×C13#52011yescharacteristic
605C22×C13D4211yescharacteristic
606C22×C13D4211yescharacteristic
607C22×C13#54611yescharacteristic
608C22×C13#54611yescharacteristic
609C22×C13#54711yescharacteristic
610C22×C13#54811yescharacteristic
611C22×C13#54811yescharacteristic
612C22×C13#55011yescharacteristic
613C22×C13#55011yescharacteristic
614C22×C13#55011yescharacteristic
615C22×C13#55311yescharacteristic
616C22×C13#55311yescharacteristic
617C22×C13#55511yescharacteristic
618C22×C13#55611yescharacteristic
619C22×C13#55911yescharacteristic
620C22×C13#55911yescharacteristic
621C2×D13—24no—
622C2×D13—24no—
623C2×D13—24no—
624C2×D13—42no—
625C2×D13—42no—
626C2×D13—42no—
627C2×D13—42no—
628C2×D13—42no—
629C2×D13—42no—
630C2×D13—42no—
631C2×D13—42no—
632C2×D13—42no—
633C2×D13—42no—
634C2×D13—42no—
635C2×D13—42no—
636C4×C13—24no—
637C4×C13—24no—
638C4×C13—42no—
639C4×C13—42no—
640C4×C13—42no—
641C4×C13—42no—
642Dic13—24no—
643Dic13—24no—
644Dic13—24no—
645Dic13—42no—
646Dic13—42no—
647Dic13—42no—
648Dic13C4×C22⋊C418yescomplemented
649C25—131no—
650C25C22×D1311yescharacteristic
651C22×D4—134no—
652C22×D4—134no—
653C22×D4—134no—
654C22×D4—262no—
655C22×D4—262no—
656C22×D4—262no—
657C22×D4—262no—
658C23×C4—131no—
659C23×C4—131no—
660C23×C4—131no—
661C23×C4—131no—
662C23×C4—131no—
663C23×C4—131no—
664C23×C4—131no—
665C23×C4—134no—
666C23×C4—134no—
667C23×C4—262no—
668C23×C4—262no—
669C23×C4—262no—
670C23×C4—262no—
671C23×C4—262no—
672C23×C4—262no—
673C23×C4—262no—
674C23×C4—262no—
675C23×C4—521no—
676C23×C4—521no—
677C23×C4—521no—
678C23×C4—521no—
679C23×C4C22×D1311yescharacteristic
680C23×C4C22×D1311yescharacteristic
681C23×C4C22×D1311yescharacteristic
682C23×C4C22×D1311yescharacteristic
683C23×C4C22×D1311yescharacteristic
684C23×C4C22×D1311yescharacteristic
685C4×D4—2632no—
686C2×C4⋊C4—134no—
687C2×C4⋊C4—134no—
688C2×C4⋊C4—134no—
689C2×C4⋊C4—134no—
690C2×C4⋊C4—134no—
691C2×C4⋊C4—262no—
692C2×C4⋊C4—262no—
693C2×C4⋊C4—262no—
694C2×C4⋊C4—262no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—134no—
702C2×C22⋊C4—134no—
703C2×C22⋊C4—134no—
704C2×C22⋊C4—134no—
705C2×C22⋊C4—134no—
706C2×C22⋊C4—134no—
707C2×C22⋊C4—134no—
708C2×C22⋊C4—262no—
709C2×C22⋊C4—262no—
710C2×C22⋊C4—262no—
711C2×C22⋊C4—262no—
712C2×C22⋊C4—262no—
713C2×C22⋊C4—262no—
714C2×C22⋊C4—262no—
715C2×C22⋊C4—262no—
716C2×C22⋊C4—521no—
717C2×C22⋊C4—521no—
718C2×C22⋊C4—521no—
719C2×C22⋊C4—521no—
720C2×C22⋊C4—521no—
721C2×C22⋊C4—521no—
722C2×C22⋊C4C4×D1314yes—
723C2×C22⋊C4C4×D1314yescomplemented
724C2×C22⋊C4C4×D1314yescomplemented
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—41no—
728C2×C42—134no—
729C2×C42—134no—
730C2×C42—134no—
731C2×C42—262no—
732C2×C42—262no—
733C2×C42—262no—
734C2×C42—262no—
735C2×C42—262no—
736C2×C42—262no—
737C2×C42—262no—
738C2×C42—262no—
739C2×C42—262no—
740C2×C42—262no—
741C2×C42—262no—
742C2×C42—262no—
743C2×C42—521no—
744C2×C42—521no—
745C2×C42—521no—
746#95—22no—
747#95—22no—
748#95—41no—
749#95—134no—
750#95—262no—
751#95—262no—
752#95—262no—
753#95—262no—
754#95—262no—
755#95—262no—
756#95—262no—
757#95—521no—
758C2×C13—44no—
759C2×C13C2×C4×C22⋊C411yescharacteristic
760C2×C13C42×D411yescharacteristic
761C2×C13#227511yescharacteristic
762C2×C13D4×C22⋊C411yescharacteristic
763C2×C13#234111yescharacteristic
764C2×C13#235411yescharacteristic
765C2×C13#235711yescharacteristic
766C2×C13#236111yescharacteristic
767C2×C13#236111yescharacteristic
768C2×C13#236311yescharacteristic
769C2×C13#236311yescharacteristic
770C2×C13#236611yescharacteristic
771C2×C13#236611yescharacteristic
772C2×C13#236711yescharacteristic
773C2×C13#236711yescharacteristic
774D13—44no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—132no—
788C24—132no—
789C24—132no—
790C24—261no—
791C24—261no—
792C24—261no—
793C24—261no—
794C24—261no—
795C24—261no—
796C24—261no—
797C24—261no—
798C24—261no—
799C24—261no—
800C24—261no—
801C24—261no—
802C24C2×C4×D1312yes—
803C24C2×C4×D1312yes—
804C24C2×C4×D1312yes—
805C24C23×D1311yescharacteristic
806C2×D4—1316no—
807C2×D4—268no—
808C2×D4—268no—
809C2×D4—268no—
810C2×D4—268no—
811C2×D4—268no—
812C2×D4—268no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—132no—
846C22×C4—132no—
847C22×C4—132no—
848C22×C4—132no—
849C22×C4—132no—
850C22×C4—132no—
851C22×C4—132no—
852C22×C4—132no—
853C22×C4—132no—
854C22×C4—132no—
855C22×C4—132no—
856C22×C4—132no—
857C22×C4—132no—
858C22×C4—132no—
859C22×C4—132no—
860C22×C4—132no—
861C22×C4—132no—
862C22×C4—132no—
863C22×C4—132no—
864C22×C4—268no—
865C22×C4—268no—
866C22×C4—268no—
867C22×C4—261no—
868C22×C4—261no—
869C22×C4—261no—
870C22×C4—261no—
871C22×C4—261no—
872C22×C4—261no—
873C22×C4—261no—
874C22×C4—261no—
875C22×C4—261no—
876C22×C4—261no—
877C22×C4—261no—
878C22×C4—261no—
879C22×C4—261no—
880C22×C4—261no—
881C22×C4—261no—
882C22×C4—261no—
883C22×C4—261no—
884C22×C4—261no—
885C22×C4—261no—
886C22×C4—261no—
887C22×C4—261no—
888C22×C4—261no—
889C22×C4—261no—
890C22×C4—261no—
891C22×C4—261no—
892C22×C4—261no—
893C22×C4—261no—
894C22×C4—261no—
895C22×C4—261no—
896C22×C4—261no—
897C22×C4—268no—
898C22×C4—524no—
899C22×C4—524no—
900C22×C4—524no—
901C22×C4—524no—
902C22×C4—524no—
903C22×C4—524no—
904C22×C4—524no—
905C22×C4—524no—
906C22×C4—524no—
907C22×C4—524no—
908C22×C4C2×C4×D1312yes—
909C22×C4C2×C4×D1312yes—
910C22×C4C2×C4×D1312yes—
911C22×C4C2×C4×D1312yes—
912C22×C4C2×C4×D1312yes—
913C22×C4C2×C4×D1312yes—
914C22×C4D4×D1312yes—
915C22×C4D4×D1312yes—
916C22×C4D4×D1312yes—
917C22×C4#612912yes—
918C4⋊C4—1316no—
919C4⋊C4—268no—
920C4⋊C4—268no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—44no—
924C22⋊C4—268no—
925C22⋊C4—268no—
926C22⋊C4—268no—
927C22⋊C4—268no—
928C22⋊C4—524no—
929C22⋊C4—524no—
930C22⋊C4—524no—
931C42—44no—
932C42—268no—
933C42—268no—
934C42—268no—
935C42—524no—
936C42—524no—
937C42—524no—
938C13#1382011yescharacteristic, complemented, Sylow
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—134no—
974C23—262no—
975C23—262no—
976C23—262no—
977C23—262no—
978C23—262no—
979C23—262no—
980C23—262no—
981C23—262no—
982C23—262no—
983C23—262no—
984C23—262no—
985C23—262no—
986C23—262no—
987C23—262no—
988C23—262no—
989C23—262no—
990C23—262no—
991C23—262no—
992C23—521no—
993C23—521no—
994C23—521no—
995C23—521no—
996C23—521no—
997C23—521no—
998C23—521no—
999C23—521no—
1000C23—521no—
1001C23—521no—
1002C23—521no—
1003C23—521no—
1004C23—521no—
1005C23—521no—
1006C23—521no—
1007C23—521no—
1008C23C42×D1314yes—
1009C23C22×C4×D1311yescharacteristic
1010C23C22×C4×D1311yescharacteristic
1011C23C22×C4×D1311yescharacteristic
1012C23C2×D4×D1311yescharacteristic
1013C23C2×D4×D1311yescharacteristic
1014C23C2×D4×D1311yescharacteristic
1015C23C2×#612911yescharacteristic
1016C23#8825111yescharacteristic
1017C23#8825111yescharacteristic
1018C23#41×D1311yescharacteristic
1019C23#41×D1311yescharacteristic
1020C23#41×D1311yescharacteristic
1021C23#41×D1311yescharacteristic
1022C23#8825611yescharacteristic
1023C23#8825711yescharacteristic
1024D4—2632no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—134no—
1066C2×C4—134no—
1067C2×C4—134no—
1068C2×C4—134no—
1069C2×C4—134no—
1070C2×C4—134no—
1071C2×C4—134no—
1072C2×C4—134no—
1073C2×C4—134no—
1074C2×C4—134no—
1075C2×C4—262no—
1076C2×C4—262no—
1077C2×C4—262no—
1078C2×C4—262no—
1079C2×C4—262no—
1080C2×C4—262no—
1081C2×C4—262no—
1082C2×C4—262no—
1083C2×C4—262no—
1084C2×C4—262no—
1085C2×C4—262no—
1086C2×C4—262no—
1087C2×C4—262no—
1088C2×C4—262no—
1089C2×C4—262no—
1090C2×C4—262no—
1091C2×C4—262no—
1092C2×C4—262no—
1093C2×C4—262no—
1094C2×C4—262no—
1095C2×C4—262no—
1096C2×C4—262no—
1097C2×C4—262no—
1098C2×C4—262no—
1099C2×C4—262no—
1100C2×C4—262no—
1101C2×C4—262no—
1102C2×C4—5216no—
1103C2×C4—5216no—
1104C2×C4—521no—
1105C2×C4—521no—
1106C2×C4—521no—
1107C2×C4—521no—
1108C2×C4—521no—
1109C2×C4—521no—
1110C2×C4—521no—
1111C2×C4—521no—
1112C2×C4—521no—
1113C2×C4—521no—
1114C2×C4—521no—
1115C2×C4—521no—
1116C2×C4C22⋊C4×D1314yes—
1117C2×C4#8813514yescomplemented
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—264no—
1134C22—264no—
1135C22—264no—
1136C22—522no—
1137C22—522no—
1138C22—522no—
1139C22—522no—
1140C22—522no—
1141C22—522no—
1142C22—522no—
1143C22—522no—
1144C22—522no—
1145C22—522no—
1146C22—522no—
1147C22—522no—
1148C22C2×C42×D1311yescharacteristic
1149C22C2×C22⋊C4×D1311yescharacteristic
1150C22C2×#8813511yescharacteristic
1151C22#1171919111yescharacteristic
1152C22D13×#11711yescharacteristic
1153C22#1171922711yescharacteristic
1154C22#1171922811yescharacteristic
1155C22C4×#612911yescharacteristic
1156C22C4×#612911yescharacteristic
1157C22C4×D4×D1311yescharacteristic
1158C22C4×D4×D1311yescharacteristic
1159C22C4×D4×D1311yescharacteristic
1160C22C4×D4×D1311yescharacteristic
1161C22C4×D4×D1311yescharacteristic
1162C22C4×D4×D1311yescharacteristic
1163C22#1171925011yescharacteristic
1164C22#1171925011yescharacteristic
1165C22#1171925111yescharacteristic
1166C22#1171925111yescharacteristic
1167C22#1171929511yescharacteristic
1168C22#1171930311yescharacteristic
1169C22#1171930411yescharacteristic
1170C22#1171930411yescharacteristic
1171C22#1171930611yescharacteristic
1172C22#1171931411yescharacteristic
1173C22#1171931511yescharacteristic
1174C22#1171935911yescharacteristic
1175C22#1171936011yescharacteristic
1176C22#1171936911yescharacteristic
1177C22#1171937511yescharacteristic
1178C22#1171938211yescharacteristic
1179C22#1171938611yescharacteristic
1180C22#1171940711yescharacteristic
1181C22#1171941411yescharacteristic
1182C22#1171942311yescharacteristic
1183C4—24no—
1184C4—24no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—42no—
1189C4—138no—
1190C4—264no—
1191C4—264no—
1192C4—264no—
1193C4—522no—
1194C4—522no—
1195C4—522no—
1196C2—44no—
1197C2—524no—
1198C2C4×C22⋊C4×D1311yescharacteristic
1199C2C4×#8813511yescharacteristic
1200C2#1311719511yescharacteristic
1201C2#1311765411yescharacteristic
1202C2#1311767511yescharacteristic
1203C2#1311778211yescharacteristic
1204C2#1311780611yescharacteristic
1205C2#1311784711yescharacteristic
1206C2#1311784911yescharacteristic
1207C2#1311786911yescharacteristic
1208C2#1311787111yescharacteristic
1209C2#1311789711yescharacteristic
1210C2#1311789911yescharacteristic
1211C2#1311790211yescharacteristic
1212C2#1311791011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC13×#1437C2
socle, cosocleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenter#1437D13
hypocenterC13#13820
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×C4×#6101C2semidirect
5. C2×#11718310C2semidirect
6. C2×C22⋊C4×Dic13C2semidirect
7. C2×C4×#6103C2semidirect
8. #13113073C2semidirect
9. #13113072C2semidirect
10. #13113072C2semidirect
11. #13113064C2semidirect
12. #13113058C2semidirect
13. #13113057C2semidirect
14. #95×Dic13C2semidirect
15. C13×#1437C2semidirect
41. C2×#88135C4semidirect
54. #11718618C4semidirect
55. #11718618C4semidirect
103. C2×C13×C22⋊C4C2×C4semidirect
104. C2×C13×C22⋊C4C2×C4semidirect
112. C2×C22⋊Dic13C2×C4semidirect
113. C2×C22⋊Dic13C2×C4semidirect
125. C2×#6103C2×C4semidirect
126. C2×#6103C2×C4semidirect
127. C2×#6103C2×C4semidirect
128. C2×#6103C2×C4semidirect
134. C2×#6101C2×C4semidirect
135. C2×#6101C2×C4semidirect
154. C2×C4×Dic13C2×C4semidirect
155. C2×C4×Dic13C2×C4semidirect
168. #88071D4semidirect
249. C2×C22⋊D13C42semidirect
326. #6101C22⋊C4semidirect
343. #1437D13semidirect
474. C2×C4×C13C4×D4semidirect
525. C2×Dic13C4×D4semidirect
648. Dic13C4×C22⋊C4semidirect
723. C2×C22⋊C4C4×D13semidirect
724. C2×C22⋊C4C4×D13semidirect
938. C13#13820semidirect
1117. C2×C4#88135semidirect

Maximal subgroups

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

subgroupindex
C22×#881352
C2×#117186182
C2×C4×#61012
C2×#117183102
C2×C22⋊C4×Dic132
C2×C4×#61032
#131130732
#131130722
#131130642
#131130582
#131130572
#95×Dic132
C13×#14372
#1382013