Finite Group Databasebeta

← #15784285

Subgroups — #15784285

Order 3328.

2194 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718882C211yesmaximal, characteristic
2C2×#11718881C211yesmaximal, characteristic
3C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
5#13113073C211yesmaximal, characteristic, complemented
6#13113073C211yesmaximal, characteristic, complemented
7#13113073C211yesmaximal, characteristic, complemented
8#13113073C211yesmaximal, characteristic, complemented
9#13113070C211yesmaximal, characteristic, complemented
10#13113070C211yesmaximal, characteristic, complemented
11#13113061C211yesmaximal, characteristic, complemented
12#13113059C211yesmaximal, characteristic, complemented
13#13113058C211yesmaximal, characteristic, complemented
14#95×Dic13C211yesmaximal, characteristic, complemented
15C2×C13×#386C211yesmaximal, characteristic
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C13×#386C418yescomplemented
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38#11718882C418yescomplemented
39#11718881C418yescomplemented
40C4×C22⋊Dic13—24no—
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
55C22⋊C4×Dic13—24no—
56C25×C13C2311yescharacteristic
57C25×C13C2311yescharacteristic
58C22×D4×C13—41no—
59C22×D4×C13—41no—
60C22×D4×C13—41no—
61C22×D4×C13—41no—
62C22×D4×C13C2×C414yes—
63C22×D4×C13C2×C414yes—
64C22×D4×C13C2×C414yes—
65C23×C4×C13—22no—
66C23×C4×C13—22no—
67C23×C4×C13—41no—
68C23×C4×C13—41no—
69C23×C4×C13—41no—
70C23×C4×C13—41no—
71C23×C4×C13C2×C414yescomplemented
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×Dic13—22no—
78C23×Dic13—22no—
79C23×Dic13—41no—
80C23×Dic13—41no—
81C23×Dic13—41no—
82C23×Dic13—41no—
83C23×Dic13C2×C414yescomplemented
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C2×C13×C22⋊C4—22no—
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—41no—
95C2×C13×C22⋊C4—41no—
96C2×C13×C22⋊C4—41no—
97C2×C13×C22⋊C4—41no—
98C2×C13×C22⋊C4C2×C414yes—
99C2×C13×C22⋊C4C2×C414yes—
100C2×C13×C22⋊C4C2×C414yescomplemented
101C2×C22⋊Dic13—22no—
102C2×C22⋊Dic13—22no—
103C2×C22⋊Dic13—22no—
104C2×C22⋊Dic13—22no—
105C2×C22⋊Dic13—22no—
106C2×C22⋊Dic13—22no—
107C2×C22⋊Dic13—41no—
108C2×C22⋊Dic13—41no—
109C2×C22⋊Dic13—41no—
110C2×C22⋊Dic13—41no—
111C2×C22⋊Dic13—41no—
112C2×C22⋊Dic13—41no—
113C2×C22⋊Dic13—41no—
114C2×C22⋊Dic13—41no—
115C2×C22⋊Dic13C2×C414yes—
116C2×C22⋊Dic13C2×C414yes—
117C2×C22⋊Dic13C2×C414yescomplemented
118C2×C22⋊Dic13C2×C414yescomplemented
119C2×C22⋊Dic13C2×C414yescomplemented
120C2×C22⋊Dic13C2×C414yescomplemented
121C2×C22⋊Dic13C2×C414yescomplemented
122C2×C4⋊Dic13—41no—
123C2×C4⋊Dic13—41no—
124C2×C4⋊Dic13C2×C414yescomplemented
125C2×C4×Dic13—22no—
126C2×C4×Dic13—22no—
127C2×C4×Dic13—22no—
128C2×C4×Dic13—41no—
129C2×C4×Dic13—41no—
130C2×C4×Dic13—41no—
131C2×C4×Dic13—41no—
132C2×C4×Dic13—41no—
133C2×C4×Dic13—41no—
134C2×C4×Dic13—41no—
135C2×C4×Dic13—41no—
136C2×C4×Dic13—41no—
137C2×C4×Dic13—41no—
138C2×C4×Dic13C2×C414yescomplemented
139C2×C4×Dic13D414yescomplemented
140C13×#95C2×C414yescomplemented
141C13×#95C2×C414yescomplemented
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#88071C2×C414yescomplemented
155#88071C2×C414yescomplemented
156#13791—131nomaximal, Sylow
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13—21no—
165C24×C13—21no—
166C24×C13—21no—
167C24×C13—21no—
168C24×C13—21no—
169C24×C13—21no—
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×C13C22×C412yes—
182C24×C13C22×C412yes—
183C24×C13C22×C412yes—
184C24×C13C22×C412yes—
185C24×C13C22×C412yes—
186C24×C13C22×C412yes—
187C24×C13C2411yescharacteristic
188C2×D4×C13—44no—
189C2×D4×C13—44no—
190C2×D4×C13—44no—
191C2×D4×C13—44no—
192C2×D4×C13—44no—
193C2×D4×C13—44no—
194C2×D4×C13C42116yescomplemented
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×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—28no—
222C22×C4×C13—44no—
223C22×C4×C13—44no—
224C22×C4×C13—44no—
225C22×C4×C13—44no—
226C22×C4×C13—44no—
227C22×C4×C13—44no—
228C22×C4×C13C22×C412yes—
229C22×C4×C13C22×C412yes—
230C22×C4×C13C22×C412yes—
231C22×C4×C13C22×C412yes—
232C22×C4×C13C22×C412yes—
233C22×C4×C13C22×C412yes—
234C22×C4×C13C22×C412yes—
235C22×C4×C13C2×D412yes—
236C22×C4×C13#4112yes—
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—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—21no—
281C22×Dic13—28no—
282C22×Dic13—44no—
283C22×Dic13—44no—
284C22×Dic13—44no—
285C22×Dic13—44no—
286C22×Dic13—44no—
287C22×Dic13—44no—
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×Dic13#4112yes—
299C22×Dic13#4112yes—
300C13×C22⋊C4—28no—
301C13×C22⋊C4—44no—
302C13×C22⋊C4—44no—
303C22⋊Dic13—28no—
304C22⋊Dic13—28no—
305C22⋊Dic13—28no—
306C22⋊Dic13—44no—
307C22⋊Dic13—44no—
308C22⋊Dic13—44no—
309C22⋊Dic13—44no—
310C4⋊Dic13—44no—
311C4×Dic13—44no—
312C4×Dic13—44no—
313C4×Dic13—44no—
314C4×Dic13—44no—
315C4×Dic13—44no—
316C2×#390—131no—
317C2×#386—131no—
318C2×#386D1311yescharacteristic
319C2×C4×C22⋊C4—131no—
320C2×C4×C22⋊C4—131no—
321#1437—131no—
322#1437—131no—
323#1437—131no—
324#1437—131no—
325#1436—131no—
326#1436—131no—
327#1434—131no—
328C22⋊#95—131no—
329C22⋊#95—131no—
330C4×#95—131no—
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×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—22no—
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×C13—41no—
383C23×C13—41no—
384C23×C13—41no—
385C23×C13—41no—
386C23×C13—41no—
387C23×C13—41no—
388C23×C13—41no—
389C23×C13—41no—
390C23×C13—41no—
391C23×C13—41no—
392C23×C13—41no—
393C23×C13—41no—
394C23×C13—41no—
395C23×C13—41no—
396C23×C13—41no—
397C23×C13—41no—
398C23×C13—41no—
399C23×C13C2×C4214yes—
400C23×C13C2×C4214yes—
401C23×C13C23×C411yescharacteristic
402C23×C13C23×C411yescharacteristic
403C23×C13C23×C411yescharacteristic
404C23×C13C22×D411yescharacteristic
405C23×C13C2×#4111yescharacteristic
406C23×C13C2×#4111yescharacteristic
407C23×C13C2×#4111yescharacteristic
408C23×C13H(5,𝔽2)11yescharacteristic
409C23×C13H(5,𝔽2)11yescharacteristic
410C23×C13H(5,𝔽2)11yescharacteristic
411C23×C13H(5,𝔽2)11yescharacteristic
412C23×C13H(5,𝔽2)11yescharacteristic
413C23×C13H(5,𝔽2)11yescharacteristic
414C23×C13H(5,𝔽2)11yescharacteristic
415C23×C132−1+411yescharacteristic
416D4×C13—416no—
417C2×C4×C13—22no—
418C2×C4×C13—22no—
419C2×C4×C13—22no—
420C2×C4×C13—22no—
421C2×C4×C13—22no—
422C2×C4×C13—22no—
423C2×C4×C13—22no—
424C2×C4×C13—22no—
425C2×C4×C13—22no—
426C2×C4×C13—22no—
427C2×C4×C13—22no—
428C2×C4×C13—22no—
429C2×C4×C13—22no—
430C2×C4×C13—22no—
431C2×C4×C13—22no—
432C2×C4×C13—22no—
433C2×C4×C13—22no—
434C2×C4×C13—22no—
435C2×C4×C13—22no—
436C2×C4×C13—22no—
437C2×C4×C13—22no—
438C2×C4×C13—416no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13—41no—
450C2×C4×C13—41no—
451C2×C4×C13C2×C4214yes—
452C2×C4×C13C4×D414yes—
453C2×Dic13—22no—
454C2×Dic13—22no—
455C2×Dic13—22no—
456C2×Dic13—22no—
457C2×Dic13—22no—
458C2×Dic13—22no—
459C2×Dic13—22no—
460C2×Dic13—22no—
461C2×Dic13—22no—
462C2×Dic13—22no—
463C2×Dic13—22no—
464C2×Dic13—22no—
465C2×Dic13—22no—
466C2×Dic13—22no—
467C2×Dic13—22no—
468C2×Dic13—22no—
469C2×Dic13—22no—
470C2×Dic13—22no—
471C2×Dic13—22no—
472C2×Dic13—22no—
473C2×Dic13—22no—
474C2×Dic13—22no—
475C2×Dic13—22no—
476C2×Dic13—22no—
477C2×Dic13—22no—
478C2×Dic13—22no—
479C2×Dic13—22no—
480C2×Dic13—22no—
481C2×Dic13—22no—
482C2×Dic13—22no—
483C2×Dic13—416no—
484C2×Dic13—41no—
485C2×Dic13—41no—
486C2×Dic13—41no—
487C2×Dic13—41no—
488C2×Dic13—41no—
489C2×Dic13—41no—
490C2×Dic13—41no—
491C2×Dic13—41no—
492C2×Dic13—41no—
493C2×Dic13—41no—
494C2×Dic13—41no—
495C2×Dic13—41no—
496C2×Dic13—41no—
497C2×Dic13—41no—
498C2×Dic13—41no—
499C2×Dic13—41no—
500C2×Dic13—41no—
501C2×Dic13—41no—
502C2×Dic13—41no—
503C2×Dic13—41no—
504C2×Dic13—41no—
505C2×Dic13—41no—
506C2×Dic13—41no—
507C2×Dic13—41no—
508C2×Dic13C4×D414yes—
509C2×Dic13C4×D414yes—
510C23×D4C2×D1311yescharacteristic
511C24×C4—131no—
512C24×C4C2×D1311yescharacteristic
513C22×C4⋊C4—131no—
514C22×C22⋊C4—131no—
515C22×C22⋊C4—131no—
516C22×C22⋊C4—131no—
517C22×C22⋊C4—131no—
518C22×C22⋊C4—131no—
519C22×C22⋊C4—131no—
520C22×C22⋊C4—131no—
521C22×C22⋊C4C2×D1311yescharacteristic
522C22×C22⋊C4C2×D1311yescharacteristic
523C22×C22⋊C4C2×D1311yescharacteristic
524C22×C42—131no—
525C22×C42—131no—
526C22×C42—131no—
527C22×C42—131no—
528C22×C42—131no—
529#390—138no—
530#386—138no—
531#386Dic1318yescomplemented
532C4×C22⋊C4—264no—
533C4×C22⋊C4—264no—
534C2×#95—131no—
535C2×#95—131no—
536C2×#95—131no—
537C2×#95—131no—
538C2×#95—131no—
539C2×#95—131no—
540C2×#95—131no—
541C2×#95—131no—
542C2×#95—131no—
543C2×#95—131no—
544C2×#95—131no—
545C2×#95—131no—
546C2×#95—131no—
547C2×#95—131no—
548C2×#95C2×D1311yescharacteristic
549C2×#95C2×D1311yescharacteristic
550C22×C13—24no—
551C22×C13—24no—
552C22×C13—24no—
553C22×C13—24no—
554C22×C13—24no—
555C22×C13—24no—
556C22×C13—42no—
557C22×C13—42no—
558C22×C13—42no—
559C22×C13—42no—
560C22×C13—42no—
561C22×C13—42no—
562C22×C13—42no—
563C22×C13—42no—
564C22×C13—42no—
565C22×C13—42no—
566C22×C13—42no—
567C22×C13—42no—
568C22×C13—42no—
569C22×C13—42no—
570C22×C13—42no—
571C22×C13—42no—
572C22×C13—42no—
573C22×C13—42no—
574C22×C13—42no—
575C22×C13—42no—
576C22×C13—42no—
577C22×C13—42no—
578C22×C13—42no—
579C22×C13—42no—
580C22×C13C22×C4211yescharacteristic
581C22×C13C2×C4×D411yescharacteristic
582C22×C13C2×C4×D411yescharacteristic
583C22×C13C2×C4×D411yescharacteristic
584C22×C13C4×#4111yescharacteristic
585C22×C13C4×#4111yescharacteristic
586C22×C13C4×#4111yescharacteristic
587C22×C13#51811yescharacteristic
588C22×C13#51811yescharacteristic
589C22×C13#51811yescharacteristic
590C22×C13#51811yescharacteristic
591C22×C13#51811yescharacteristic
592C22×C13#51811yescharacteristic
593C22×C13#51811yescharacteristic
594C22×C13#51811yescharacteristic
595C22×C13#51811yescharacteristic
596C22×C13#52011yescharacteristic
597C22×C13#52011yescharacteristic
598C22×C13#52011yescharacteristic
599C22×C13#53411yescharacteristic
600C22×C13#53511yescharacteristic
601C22×C13#53511yescharacteristic
602C22×C13#53711yescharacteristic
603C22×C13#53811yescharacteristic
604C22×C13#53811yescharacteristic
605C22×C13#53811yescharacteristic
606C22×C13#53811yescharacteristic
607C22×C13#53811yescharacteristic
608C22×C13#53911yescharacteristic
609C22×C13#54011yescharacteristic
610C22×C13#54011yescharacteristic
611C22×C13#54011yescharacteristic
612C22×C13#54011yescharacteristic
613C22×C13#54211yescharacteristic
614C22×C13#54211yescharacteristic
615C4×C13—24no—
616C4×C13—24no—
617C4×C13—42no—
618C4×C13—42no—
619C4×C13—42no—
620Dic13—24no—
621Dic13—24no—
622Dic13—42no—
623Dic13—42no—
624Dic13—42no—
625Dic13—42no—
626Dic13—42no—
627Dic13—42no—
628C25C22×D1311yescharacteristic
629C25C22×D1311yescharacteristic
630C22×D4—41no—
631C22×D4—41no—
632C22×D4—41no—
633C22×D4—41no—
634C22×D4C4×D1314yes—
635C22×D4C4×D1314yes—
636C22×D4C2×Dic1314yes—
637C23×C4—22no—
638C23×C4—22no—
639C23×C4—41no—
640C23×C4—41no—
641C23×C4—41no—
642C23×C4—41no—
643C23×C4—131no—
644C23×C4—131no—
645C23×C4—131no—
646C23×C4—131no—
647C23×C4—131no—
648C23×C4—131no—
649C23×C4—131no—
650C23×C4—131no—
651C23×C4—134no—
652C23×C4—262no—
653C23×C4—262no—
654C23×C4—521no—
655C23×C4—521no—
656C23×C4—521no—
657C23×C4—521no—
658C23×C4C2×Dic1314yescomplemented
659C23×C4C22×D1311yescharacteristic
660C23×C4C22×D1311yescharacteristic
661C23×C4C22×D1311yescharacteristic
662C23×C4C22×D1311yescharacteristic
663C23×C4C22×D1311yescharacteristic
664C2×C4⋊C4—134no—
665C2×C4⋊C4—521no—
666C2×C4⋊C4—521no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—134no—
674C2×C22⋊C4—134no—
675C2×C22⋊C4—134no—
676C2×C22⋊C4—134no—
677C2×C22⋊C4—134no—
678C2×C22⋊C4—134no—
679C2×C22⋊C4—134no—
680C2×C22⋊C4—262no—
681C2×C22⋊C4—262no—
682C2×C22⋊C4—262no—
683C2×C22⋊C4—262no—
684C2×C22⋊C4—262no—
685C2×C22⋊C4—262no—
686C2×C22⋊C4—521no—
687C2×C22⋊C4—521no—
688C2×C22⋊C4—521no—
689C2×C22⋊C4—521no—
690C2×C22⋊C4—521no—
691C2×C22⋊C4—521no—
692C2×C22⋊C4—521no—
693C2×C22⋊C4—521no—
694C2×C22⋊C4C2×Dic1314yes—
695C2×C22⋊C4C2×Dic1314yes—
696C2×C22⋊C4C2×Dic1314yescomplemented
697C2×C42—134no—
698C2×C42—134no—
699C2×C42—262no—
700C2×C42—262no—
701C2×C42—262no—
702C2×C42—521no—
703C2×C42—521no—
704C2×C42—521no—
705C2×C42—521no—
706C2×C42—521no—
707C2×C42—521no—
708C2×C42—521no—
709C2×C42—521no—
710C2×C42—521no—
711C2×C42—521no—
712#95—134no—
713#95—134no—
714#95—262no—
715#95—262no—
716#95—262no—
717#95—262no—
718#95—262no—
719#95—262no—
720#95—521no—
721#95—521no—
722#95—521no—
723#95—521no—
724#95—521no—
725#95—521no—
726#95C2×Dic1314yescomplemented
727#95C2×Dic1314yescomplemented
728C2×C13—44no—
729C2×C13—44no—
730C2×C13C42×D411yescharacteristic
731C2×C13#227311yescharacteristic
732C2×C13#227511yescharacteristic
733C2×C13#232111yescharacteristic
734C2×C13#232111yescharacteristic
735C2×C13#232411yescharacteristic
736C2×C13#232411yescharacteristic
737C2×C13#232511yescharacteristic
738C2×C13#232811yescharacteristic
739C2×C13#233311yescharacteristic
740C2×C13#233311yescharacteristic
741C2×C13#233311yescharacteristic
742C2×C13#233511yescharacteristic
743C2×C13#233511yescharacteristic
744C2×C13#233711yescharacteristic
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24C2×C4×D1312yes—
770C24C2×C4×D1312yes—
771C24C2×C4×D1312yes—
772C24C2×C4×D1312yes—
773C24C22×Dic1312yes—
774C24C22×Dic1312yes—
775C24C23×D1311yescharacteristic
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4C4×Dic13116yescomplemented
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—28no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—132no—
817C22×C4—132no—
818C22×C4—132no—
819C22×C4—132no—
820C22×C4—132no—
821C22×C4—132no—
822C22×C4—132no—
823C22×C4—132no—
824C22×C4—132no—
825C22×C4—132no—
826C22×C4—132no—
827C22×C4—132no—
828C22×C4—268no—
829C22×C4—261no—
830C22×C4—261no—
831C22×C4—261no—
832C22×C4—261no—
833C22×C4—261no—
834C22×C4—261no—
835C22×C4—261no—
836C22×C4—261no—
837C22×C4—261no—
838C22×C4—261no—
839C22×C4—261no—
840C22×C4—261no—
841C22×C4—261no—
842C22×C4—261no—
843C22×C4—261no—
844C22×C4—261no—
845C22×C4—261no—
846C22×C4—261no—
847C22×C4—261no—
848C22×C4—261no—
849C22×C4—261no—
850C22×C4—261no—
851C22×C4—261no—
852C22×C4—261no—
853C22×C4—261no—
854C22×C4—261no—
855C22×C4—261no—
856C22×C4—261no—
857C22×C4—261no—
858C22×C4—261no—
859C22×C4—261no—
860C22×C4—261no—
861C22×C4—261no—
862C22×C4—261no—
863C22×C4—261no—
864C22×C4—261no—
865C22×C4—261no—
866C22×C4—261no—
867C22×C4—261no—
868C22×C4—261no—
869C22×C4—261no—
870C22×C4—261no—
871C22×C4—261no—
872C22×C4—261no—
873C22×C4—524no—
874C22×C4—524no—
875C22×C4—524no—
876C22×C4—524no—
877C22×C4—524no—
878C22×C4—524no—
879C22×C4C2×C4×D1312yes—
880C22×C4C2×C4×D1312yes—
881C22×C4D4×D1312yes—
882C22×C4#612912yes—
883C22×C4C22×Dic1312yes—
884C22×C4C22×Dic1312yes—
885C22×C4C22×Dic1312yes—
886C22×C4C22×Dic1312yes—
887C22×C4C22×Dic1312yes—
888C4⋊C4—524no—
889C22⋊C4—28no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—268no—
893C22⋊C4—268no—
894C22⋊C4—268no—
895C22⋊C4—524no—
896C22⋊C4—524no—
897C22⋊C4—524no—
898C22⋊C4—524no—
899C42—524no—
900C42—524no—
901C42—524no—
902C42—524no—
903C42—524no—
904C13#1379111yescharacteristic, complemented, Sylow
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
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—
973C23C2×C4×Dic1314yes—
974C23C2×C4×Dic1314yes—
975C23C22×C4×D1311yescharacteristic
976C23C22×C4×D1311yescharacteristic
977C23C2×D4×D1311yescharacteristic
978C23C2×#612911yescharacteristic
979C23#8825111yescharacteristic
980C23#8825111yescharacteristic
981C23#8825111yescharacteristic
982C23#8825111yescharacteristic
983C23#8825111yescharacteristic
984C23#8825111yescharacteristic
985C23#41×D1311yescharacteristic
986C23#41×D1311yescharacteristic
987C23#8825611yescharacteristic
988C23#8825711yescharacteristic
989C23C23×Dic1311yescharacteristic
990D4—416no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—134no—
1026C2×C4—134no—
1027C2×C4—262no—
1028C2×C4—262no—
1029C2×C4—262no—
1030C2×C4—262no—
1031C2×C4—262no—
1032C2×C4—262no—
1033C2×C4—262no—
1034C2×C4—262no—
1035C2×C4—262no—
1036C2×C4—262no—
1037C2×C4—262no—
1038C2×C4—262no—
1039C2×C4—262no—
1040C2×C4—262no—
1041C2×C4—262no—
1042C2×C4—262no—
1043C2×C4—262no—
1044C2×C4—262no—
1045C2×C4—262no—
1046C2×C4—262no—
1047C2×C4—262no—
1048C2×C4—262no—
1049C2×C4—262no—
1050C2×C4—262no—
1051C2×C4—262no—
1052C2×C4—262no—
1053C2×C4—262no—
1054C2×C4—262no—
1055C2×C4—262no—
1056C2×C4—262no—
1057C2×C4—5216no—
1058C2×C4—521no—
1059C2×C4—521no—
1060C2×C4—521no—
1061C2×C4—521no—
1062C2×C4—521no—
1063C2×C4—521no—
1064C2×C4—521no—
1065C2×C4—521no—
1066C2×C4—521no—
1067C2×C4—521no—
1068C2×C4—521no—
1069C2×C4—521no—
1070C2×C4—521no—
1071C2×C4—521no—
1072C2×C4—521no—
1073C2×C4—521no—
1074C2×C4—521no—
1075C2×C4—521no—
1076C2×C4—521no—
1077C2×C4—521no—
1078C2×C4—521no—
1079C2×C4—521no—
1080C2×C4—521no—
1081C2×C4—521no—
1082C2×C4C2×C4×Dic1314yes—
1083C2×C4D4×Dic1314yes—
1084C22—24no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22#1171919111yescharacteristic
1115C22#1171919111yescharacteristic
1116C22#1171919111yescharacteristic
1117C22#1171919111yescharacteristic
1118C22C4×#612911yescharacteristic
1119C22C4×#612911yescharacteristic
1120C22C4×D4×D1311yescharacteristic
1121C22C4×D4×D1311yescharacteristic
1122C22#1171925011yescharacteristic
1123C22#1171925011yescharacteristic
1124C22#1171925111yescharacteristic
1125C22#1171925111yescharacteristic
1126C22#1171929411yescharacteristic
1127C22#1171929711yescharacteristic
1128C22#1171929811yescharacteristic
1129C22#1171929811yescharacteristic
1130C22#1171930811yescharacteristic
1131C22#1171931211yescharacteristic
1132C22#1171931311yescharacteristic
1133C22#1171931811yescharacteristic
1134C22#1171931811yescharacteristic
1135C22#1171932011yescharacteristic
1136C22#1171932011yescharacteristic
1137C22#1171932411yescharacteristic
1138C22#1171936211yescharacteristic
1139C22#1171936511yescharacteristic
1140C22#1171936711yescharacteristic
1141C22#1171936811yescharacteristic
1142C22C22×C4×Dic1311yescharacteristic
1143C22C2×D4×Dic1311yescharacteristic
1144C22#1171950311yescharacteristic
1145C22#1171950311yescharacteristic
1146C22#1171950311yescharacteristic
1147C22#41×Dic1311yescharacteristic
1148C22#1171953211yescharacteristic
1149C4—24no—
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—264no—
1155C4—264no—
1156C4—522no—
1157C4—522no—
1158C4—522no—
1159C4—522no—
1160C4—522no—
1161C4—522no—
1162C2—44no—
1163C2—44no—
1164C2C4×D4×Dic1311yescharacteristic
1165C2#1311718911yescharacteristic
1166C2#1311719711yescharacteristic
1167C2#1311749211yescharacteristic
1168C2#1311749711yescharacteristic
1169C2#1311752611yescharacteristic
1170C2#1311753111yescharacteristic
1171C2#1311753811yescharacteristic
1172C2#1311755711yescharacteristic
1173C2#1311759711yescharacteristic
1174C2#1311760211yescharacteristic
1175C2#1311760311yescharacteristic
1176C2#1311762711yescharacteristic
1177C2#1311763011yescharacteristic
1178C2#1311764511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC2×C13×#386C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#386D13
hypocenterC13#13791
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic13C2semidirect
4. C2×C4×C22⋊Dic13C2semidirect
5. #13113073C2semidirect
6. #13113073C2semidirect
7. #13113073C2semidirect
8. #13113073C2semidirect
9. #13113070C2semidirect
10. #13113070C2semidirect
11. #13113061C2semidirect
12. #13113059C2semidirect
13. #13113058C2semidirect
14. #95×Dic13C2semidirect
35. C13×#386C4semidirect
38. #11718882C4semidirect
39. #11718881C4semidirect
71. C23×C4×C13C2×C4semidirect
83. C23×Dic13C2×C4semidirect
100. C2×C13×C22⋊C4C2×C4semidirect
117. C2×C22⋊Dic13C2×C4semidirect
118. C2×C22⋊Dic13C2×C4semidirect
119. C2×C22⋊Dic13C2×C4semidirect
120. C2×C22⋊Dic13C2×C4semidirect
121. C2×C22⋊Dic13C2×C4semidirect
124. C2×C4⋊Dic13C2×C4semidirect
138. C2×C4×Dic13C2×C4semidirect
139. C2×C4×Dic13D4semidirect
140. C13×#95C2×C4semidirect
141. C13×#95C2×C4semidirect
154. #88071C2×C4semidirect
155. #88071C2×C4semidirect
194. C2×D4×C13C42semidirect
531. #386Dic13semidirect
658. C23×C4C2×Dic13semidirect
696. C2×C22⋊C4C2×Dic13semidirect
726. #95C2×Dic13semidirect
727. #95C2×Dic13semidirect
782. C2×D4C4×Dic13semidirect
904. C13#13791semidirect

Maximal subgroups

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

subgroupindex
C2×#117188822
C2×#117188812
C2×C22⋊C4×Dic132
C2×C4×C22⋊Dic132
#131130732
#131130702
#131130612
#131130592
#131130582
#95×Dic132
C2×C13×#3862
#1379113