Finite Group Databasebeta

← #15787404

Subgroups — #15787404

Order 3328.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718891C211yesmaximal, characteristic, complemented
2C2×#11718612C211yesmaximal, characteristic, complemented
3C2×#11718881C211yesmaximal, characteristic
4C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
5#13113107C211yesmaximal, characteristic, complemented
6#13113085C211yesmaximal, characteristic, complemented
7#13113081C211yesmaximal, characteristic, complemented
8#13113077C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic, complemented
10#13113073C211yesmaximal, characteristic, complemented
11#13113073C211yesmaximal, characteristic, complemented
12#13113063C211yesmaximal, characteristic, complemented
13#13113058C211yesmaximal, characteristic, complemented
14C4×#88071C211yesmaximal, characteristic, complemented
15C22×C13×#124C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C2×C13×#124—24no—
20C2×C13×#124—24no—
21C2×C13×#124C418yescomplemented
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C42×C13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38#11718891—24no—
39#11718881—24no—
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#11718612—24no—
57C22⋊C4×Dic13—24no—
58C25×C13C2311yescharacteristic
59C25×C13C2311yescharacteristic
60C22×Q8×C13—22no—
61C22×Q8×C13—22no—
62C22×Q8×C13—22no—
63C22×Q8×C13—22no—
64C22×Q8×C13—41no—
65C22×Q8×C13—41no—
66C22×Q8×C13C2×C414yescomplemented
67C22×D4×C13—22no—
68C22×D4×C13—22no—
69C22×D4×C13—22no—
70C22×D4×C13—22no—
71C22×D4×C13—41no—
72C22×D4×C13—41no—
73C22×D4×C13C2×C414yes—
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—41no—
85C23×Dic13—41no—
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C13×#124—232no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4C2×C414yes—
102C2×C13×C22⋊C4C2×C414yes—
103C2×C13×C22⋊C4C2×C414yescomplemented
104C2×C13×C22⋊C4C2×C414yescomplemented
105C2×C13×C22⋊C4D414yes—
106C2×C13×C22⋊C4D414yes—
107C2×C42×C13—22no—
108C2×C42×C13—22no—
109C2×C42×C13C2×C414yescomplemented
110C2×C22⋊Dic13—22no—
111C2×C22⋊Dic13—22no—
112C2×C22⋊Dic13—22no—
113C2×C22⋊Dic13—22no—
114C2×C22⋊Dic13—22no—
115C2×C22⋊Dic13—22no—
116C2×C22⋊Dic13—22no—
117C2×C22⋊Dic13—22no—
118C2×C22⋊Dic13—22no—
119C2×C22⋊Dic13—22no—
120C2×C22⋊Dic13—22no—
121C2×C22⋊Dic13—22no—
122C2×C22⋊Dic13—22no—
123C2×C22⋊Dic13—22no—
124C2×C22⋊Dic13—22no—
125C2×C22⋊Dic13—41no—
126C2×C22⋊Dic13—41no—
127C2×C22⋊Dic13—41no—
128C2×C22⋊Dic13—41no—
129C2×C22⋊Dic13—41no—
130C2×C22⋊Dic13—41no—
131C2×C4⋊Dic13—22no—
132C2×C4⋊Dic13—22no—
133C2×C4⋊Dic13—41no—
134C2×C4×Dic13—22no—
135C2×C4×Dic13—22no—
136C2×C4×Dic13—22no—
137C2×C4×Dic13—22no—
138C2×C4×Dic13—22no—
139C2×C4×Dic13—22no—
140C2×C4×Dic13—41no—
141C2×C4×Dic13—41no—
142C2×C4×Dic13—41no—
143#88071—22no—
144#88071—22no—
145#88071—22no—
146#88071—22no—
147#88071—22no—
148#88071—22no—
149#88071—22no—
150#88071—22no—
151#88071—22no—
152#88071—22no—
153#88071—22no—
154#88071—22no—
155#88071—22no—
156#88071—41no—
157#88071—41no—
158#88071D414yes—
159#14098—131nomaximal, Sylow
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×C13—21no—
182C24×C13—21no—
183C24×C13—21no—
184C24×C13—21no—
185C24×C13—21no—
186C24×C13C22×C412yes—
187C24×C13C22×C412yes—
188C24×C13C2×D412yes—
189C24×C13C2×D412yes—
190C24×C13C2411yescharacteristic
191C2×Q8×C13—28no—
192C2×Q8×C13—28no—
193C2×Q8×C13—44no—
194C2×Q8×C13—44no—
195C2×Q8×C13—44no—
196C2×Q8×C13—44no—
197C2×Q8×C13—44no—
198C2×D4×C13—28no—
199C2×D4×C13—28no—
200C2×D4×C13—44no—
201C2×D4×C13—44no—
202C2×D4×C13—44no—
203C2×D4×C13—44no—
204C2×D4×C13—44no—
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×C13C22×C412yes—
230C22×C4×C13C22×C412yes—
231C22×C4×C13C22×C412yes—
232C22×C4×C13C22×C412yes—
233C22×C4×C13C22×C412yes—
234C22×C4×C13C2×D412yes—
235C22×C4×C13C2×D412yes—
236C22×C4×C13C2×D412yes—
237C22×C4×C13C2×D412yes—
238C22×C4×C13C2×D412yes—
239C22×C4×C13#4112yes—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—28no—
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—21no—
282C22×Dic13—21no—
283C22×Dic13—21no—
284C22×Dic13—21no—
285C22×Dic13—21no—
286C22×Dic13—21no—
287C22×Dic13—21no—
288C22×Dic13—21no—
289C22×Dic13—44no—
290C22×Dic13—44no—
291C22×Dic13—44no—
292C22×Dic13—44no—
293C22×Dic13—44no—
294C22×Dic13—44no—
295C22×Dic13C2×D412yes—
296C22×Dic13C2×D412yes—
297C22×Dic13#4112yes—
298C22×Dic13#4112yes—
299C22×Dic13#4112yes—
300C22×Dic13#4112yes—
301C22×Dic13#4112yes—
302C22×Dic13#4112yes—
303C13×C22⋊C4—28no—
304C13×C22⋊C4—28no—
305C13×C22⋊C4—28no—
306C13×C22⋊C4C22⋊C4116yescomplemented
307C42×C13—28no—
308C22⋊Dic13—28no—
309C22⋊Dic13—44no—
310C22⋊Dic13—44no—
311C22⋊Dic13—44no—
312C22⋊Dic13—44no—
313C22⋊Dic13—44no—
314C22⋊Dic13—44no—
315C4⋊Dic13—44no—
316C4×Dic13—44no—
317C4×Dic13—44no—
318C4×Dic13—44no—
319C22×#124D1311yescharacteristic
320C2×#391—131no—
321C2×#388—131no—
322C2×#386—131no—
323C2×C4×C22⋊C4—131no—
324#1446—131no—
325#1440—131no—
326#1439—131no—
327#1438—131no—
328#1437—131no—
329#1437—131no—
330#1437—131no—
331#1434—131no—
332C22⋊#95—131no—
333C4×#95—131no—
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—41no—
360C23×C13—41no—
361C23×C13—41no—
362C23×C13—41no—
363C23×C13—41no—
364C23×C13—41no—
365C23×C13—41no—
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×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×C13—41no—
400C23×C13—41no—
401C23×C13—41no—
402C23×C13—41no—
403C23×C13C2×C22⋊C414yes—
404C23×C13C23×C411yescharacteristic
405C23×C13C22×D411yescharacteristic
406C23×C13C22×D411yescharacteristic
407C23×C13C22×D411yescharacteristic
408C23×C13C2×#4111yescharacteristic
409C23×C13C2×#4111yescharacteristic
410C23×C13C2×#4111yescharacteristic
411C23×C13C2×#4111yescharacteristic
412C23×C13C2×#4111yescharacteristic
413C23×C13C2×#4111yescharacteristic
414C23×C13C2×#4111yescharacteristic
415C23×C13H(5,𝔽2)11yescharacteristic
416C23×C13H(5,𝔽2)11yescharacteristic
417C23×C13H(5,𝔽2)11yescharacteristic
418C23×C132−1+411yescharacteristic
419Q8×C13—416no—
420D4×C13—416no—
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—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—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13—41no—
450C2×C4×C13—41no—
451C2×C4×C13—41no—
452C2×C4×C13—41no—
453C2×C4×C13C2×C22⋊C414yes—
454C2×C4×C13C2×C22⋊C414yes—
455C2×C4×C13C4×D414yes—
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—416no—
478C2×Dic13—41no—
479C2×Dic13—41no—
480C2×Dic13—41no—
481C2×Dic13—41no—
482C2×Dic13—41no—
483C2×Dic13—41no—
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×Dic13—41no—
509C2×Dic13—41no—
510C2×Dic13—41no—
511C2×Dic13—41no—
512C2×Dic13#12414yescomplemented
513C23×Q8C2×D1311yescharacteristic
514C23×D4C2×D1311yescharacteristic
515C24×C4—131no—
516C2×#124—24no—
517C2×#124—24no—
518C2×#124Dic1318yescomplemented
519C22×C4⋊C4—131no—
520C22×C22⋊C4—131no—
521C22×C22⋊C4—131no—
522C22×C22⋊C4—131no—
523C22×C22⋊C4—131no—
524C22×C22⋊C4—131no—
525C22×C22⋊C4—131no—
526C22×C22⋊C4—131no—
527C22×C22⋊C4C2×D1311yescharacteristic
528C22×C22⋊C4C2×D1311yescharacteristic
529C22×C22⋊C4C2×D1311yescharacteristic
530C22×C22⋊C4C2×D1311yescharacteristic
531C22×C42—131no—
532C22×C42—131no—
533C22×C42—131no—
534C22×C42C2×D1311yescharacteristic
535#391—264no—
536#388—264no—
537#386—264no—
538C4×C22⋊C4—264no—
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×#95—131no—
549C2×#95—131no—
550C2×#95—131no—
551C2×#95—131no—
552C2×#95—131no—
553C2×#95—131no—
554C2×#95—131no—
555C22×C13—24no—
556C22×C13—24no—
557C22×C13—24no—
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—81no—
578C22×C13—81no—
579C22×C13—81no—
580C22×C13—81no—
581C22×C13—81no—
582C22×C13—81no—
583C22×C13—81no—
584C22×C13—81no—
585C22×C13C22×C22⋊C411yescharacteristic
586C22×C13C2×C4×D411yescharacteristic
587C22×C13C4×#4111yescharacteristic
588C22×C13C4×#4111yescharacteristic
589C22×C13C4×#4111yescharacteristic
590C22×C13#51811yescharacteristic
591C22×C13#52011yescharacteristic
592C22×C13#52511yescharacteristic
593C22×C13#52511yescharacteristic
594C22×C13C2×#12411yescharacteristic
595C22×C13#52911yescharacteristic
596C22×C13#52911yescharacteristic
597C22×C13#53211yescharacteristic
598C22×C13#53211yescharacteristic
599C22×C13#53211yescharacteristic
600C22×C13#53811yescharacteristic
601C22×C13#53811yescharacteristic
602C22×C13#54211yescharacteristic
603C22×C13#54211yescharacteristic
604C22×C13D4211yescharacteristic
605C22×C13D4211yescharacteristic
606C22×C13#54611yescharacteristic
607C22×C13#54611yescharacteristic
608C22×C13#54611yescharacteristic
609C22×C13#54611yescharacteristic
610C22×C13#54611yescharacteristic
611C22×C13#54711yescharacteristic
612C22×C13#54711yescharacteristic
613C22×C13#54811yescharacteristic
614C22×C13#55111yescharacteristic
615C22×C13#55111yescharacteristic
616C22×C13#55511yescharacteristic
617C22×C13#55511yescharacteristic
618C22×C13#55611yescharacteristic
619C22×C13#55911yescharacteristic
620C4×C13—24no—
621C4×C13—24no—
622C4×C13—24no—
623C4×C13—42no—
624C4×C13—42no—
625Dic13—24no—
626Dic13—42no—
627Dic13—42no—
628Dic13—42no—
629Dic13—42no—
630Dic13—42no—
631Dic13—81no—
632Dic13—81no—
633C25C22×D1311yescharacteristic
634C25C22×D1311yescharacteristic
635C22×Q8—22no—
636C22×Q8—22no—
637C22×Q8—22no—
638C22×Q8—22no—
639C22×Q8—41no—
640C22×Q8—41no—
641C22×Q8C2×Dic1314yescomplemented
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—22no—
645C22×D4—22no—
646C22×D4—41no—
647C22×D4—41no—
648C22×D4C2×Dic1314yes—
649C23×C4—131no—
650C23×C4—131no—
651C23×C4—131no—
652C23×C4—131no—
653C23×C4—131no—
654C23×C4—131no—
655C23×C4—131no—
656C23×C4—131no—
657C23×C4—262no—
658C23×C4—262no—
659C23×C4—262no—
660C23×C4—262no—
661C23×C4—262no—
662C23×C4—521no—
663C23×C4—521no—
664C23×C4C22×D1311yescharacteristic
665C23×C4C22×D1311yescharacteristic
666C23×C4C22×D1311yescharacteristic
667C23×C4C22×D1311yescharacteristic
668C23×C4C22×D1311yescharacteristic
669#124—232no—
670C2×C4⋊C4—262no—
671C2×C4⋊C4—262no—
672C2×C4⋊C4—521no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—262no—
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—262no—
687C2×C22⋊C4—262no—
688C2×C22⋊C4—262no—
689C2×C22⋊C4—262no—
690C2×C22⋊C4—262no—
691C2×C22⋊C4—262no—
692C2×C22⋊C4—262no—
693C2×C22⋊C4—262no—
694C2×C22⋊C4—521no—
695C2×C22⋊C4—521no—
696C2×C22⋊C4—521no—
697C2×C22⋊C4—521no—
698C2×C22⋊C4—521no—
699C2×C22⋊C4—521no—
700C2×C22⋊C4C2×Dic1314yes—
701C2×C22⋊C4C2×Dic1314yes—
702C2×C22⋊C4C2×Dic1314yescomplemented
703C2×C22⋊C4C2×Dic1314yescomplemented
704C2×C22⋊C4C22⋊D1314yes—
705C2×C22⋊C4C22⋊D1314yes—
706C2×C42—22no—
707C2×C42—22no—
708C2×C42—262no—
709C2×C42—262no—
710C2×C42—262no—
711C2×C42—262no—
712C2×C42—262no—
713C2×C42—262no—
714C2×C42—521no—
715C2×C42—521no—
716C2×C42—521no—
717C2×C42C2×Dic1314yescomplemented
718#95—134no—
719#95—262no—
720#95—262no—
721#95—262no—
722#95—262no—
723#95—262no—
724#95—262no—
725#95—262no—
726#95—262no—
727#95—262no—
728#95—262no—
729#95—262no—
730#95—262no—
731#95—262no—
732#95—521no—
733#95—521no—
734C2×C13—44no—
735C2×C13—82no—
736C2×C13#229711yescharacteristic
737C2×C13C4×#12411yescharacteristic
738C2×C13#233711yescharacteristic
739C2×C13D4×C22⋊C411yescharacteristic
740C2×C13#233911yescharacteristic
741C2×C13#236711yescharacteristic
742C2×C13#237211yescharacteristic
743C2×C13#245911yescharacteristic
744C2×C13#246111yescharacteristic
745C2×C13#247211yescharacteristic
746C2×C13#247411yescharacteristic
747C2×C13#249111yescharacteristic
748C2×C13#252111yescharacteristic
749C2×C13#255511yescharacteristic
750C2×C13#255711yescharacteristic
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—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24C22×Dic1312yes—
778C24C22×Dic1312yes—
779C24C2×C22⋊D1312yes—
780C24C2×C22⋊D1312yes—
781C24C23×D1311yescharacteristic
782C2×Q8—28no—
783C2×Q8—28no—
784C2×Q8—44no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
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—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
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—261no—
829C22×C4—261no—
830C22×C4—261no—
831C22×C4—261no—
832C22×C4—268no—
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—261no—
874C22×C4—261no—
875C22×C4—261no—
876C22×C4—261no—
877C22×C4—524no—
878C22×C4—524no—
879C22×C4—524no—
880C22×C4—524no—
881C22×C4—524no—
882C22×C4—524no—
883C22×C4D4×D1312yes—
884C22×C4#612912yes—
885C22×C4C22×Dic1312yes—
886C22×C4C22×Dic1312yes—
887C22×C4C22×Dic1312yes—
888C22×C4C22×Dic1312yes—
889C22×C4C22×Dic1312yes—
890C22×C4C2×C22⋊D1312yes—
891C22×C4C2×C22⋊D1312yes—
892C22×C4C2×C22⋊D1312yes—
893C22×C4C2×C22⋊D1312yes—
894C4⋊C4—524no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—268no—
899C22⋊C4—524no—
900C22⋊C4—524no—
901C22⋊C4—524no—
902C22⋊C4—524no—
903C22⋊C4—524no—
904C22⋊C4—524no—
905C22⋊C4C22⋊Dic13116yescomplemented
906C42—28no—
907C42—524no—
908C42—524no—
909C42—524no—
910C13#1409811yescharacteristic, complemented, Sylow
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—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
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—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C2×C22⋊Dic1314yes—
981C23C2×D4×D1311yescharacteristic
982C23C2×#612911yescharacteristic
983C23#8825111yescharacteristic
984C23#8825111yescharacteristic
985C23#41×D1311yescharacteristic
986C23#41×D1311yescharacteristic
987C23#41×D1311yescharacteristic
988C23#41×D1311yescharacteristic
989C23#41×D1311yescharacteristic
990C23#41×D1311yescharacteristic
991C23#8825611yescharacteristic
992C23#8825711yescharacteristic
993C23C23×Dic1311yescharacteristic
994C23C22×C22⋊D1311yescharacteristic
995C23C22×C22⋊D1311yescharacteristic
996Q8—416no—
997D4—416no—
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—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—134no—
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—5216no—
1053C2×C4—521no—
1054C2×C4—521no—
1055C2×C4—521no—
1056C2×C4—521no—
1057C2×C4—521no—
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×C4—521no—
1083C2×C4—521no—
1084C2×C4—521no—
1085C2×C4—521no—
1086C2×C4—521no—
1087C2×C4D4×Dic1314yes—
1088C2×C4C2×C22⋊Dic1314yes—
1089C2×C4C2×C22⋊Dic1314yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
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—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22#1171937311yescharacteristic
1121C22#1171937411yescharacteristic
1122C22#1171937411yescharacteristic
1123C22#1171937511yescharacteristic
1124C22#1171937511yescharacteristic
1125C22#1171937611yescharacteristic
1126C22D13×#12411yescharacteristic
1127C22#1171938111yescharacteristic
1128C22#1171938211yescharacteristic
1129C22#1171938311yescharacteristic
1130C22#1171938311yescharacteristic
1131C22#1171938411yescharacteristic
1132C22#1171938411yescharacteristic
1133C22#1171938511yescharacteristic
1134C22#1171938511yescharacteristic
1135C22#1171938611yescharacteristic
1136C22C2×D4×Dic1311yescharacteristic
1137C22#1171950311yescharacteristic
1138C22D4×C22⋊D1311yescharacteristic
1139C22D4×C22⋊D1311yescharacteristic
1140C22#1171951111yescharacteristic
1141C22#1171951111yescharacteristic
1142C22#1171952911yescharacteristic
1143C22#1171952911yescharacteristic
1144C22#41×Dic1311yescharacteristic
1145C22#41×Dic1311yescharacteristic
1146C22#41×Dic1311yescharacteristic
1147C22#1171953211yescharacteristic
1148C22#1171953311yescharacteristic
1149C22#1171953311yescharacteristic
1150C22#1171953411yescharacteristic
1151C22#1171953411yescharacteristic
1152C22#1171953711yescharacteristic
1153C22#1171953711yescharacteristic
1154C22C22×C22⋊Dic1311yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—264no—
1161C4—522no—
1162C4—522no—
1163C4—522no—
1164C4—522no—
1165C4—522no—
1166C4—1041no—
1167C4—1041no—
1168C2—44no—
1169C2—82no—
1170C2#1311732711yescharacteristic
1171C2#124×Dic1311yescharacteristic
1172C2#1311765111yescharacteristic
1173C2D4×C22⋊Dic1311yescharacteristic
1174C2#1311766611yescharacteristic
1175C2#1311791111yescharacteristic
1176C2#1311794811yescharacteristic
1177C2#1311876911yescharacteristic
1178C2#1311879911yescharacteristic
1179C2#1311895811yescharacteristic
1180C2#1311898811yescharacteristic
1181C2#1311919611yescharacteristic
1182C2#1311953611yescharacteristic
1183C2#1311990711yescharacteristic
1184C2#1311993311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C13×#124C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC22×#124D13
hypocenterC13#14098
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C2×#11718891C2semidirect
2. C2×#11718612C2semidirect
4. C2×C22⋊C4×Dic13C2semidirect
5. #13113107C2semidirect
6. #13113085C2semidirect
7. #13113081C2semidirect
9. #13113073C2semidirect
10. #13113073C2semidirect
11. #13113073C2semidirect
12. #13113063C2semidirect
13. #13113058C2semidirect
14. C4×#88071C2semidirect
21. C2×C13×#124C4semidirect
66. C22×Q8×C13C2×C4semidirect
103. C2×C13×C22⋊C4C2×C4semidirect
104. C2×C13×C22⋊C4C2×C4semidirect
109. C2×C42×C13C2×C4semidirect
306. C13×C22⋊C4C22⋊C4semidirect
512. C2×Dic13#124semidirect
518. C2×#124Dic13semidirect
641. C22×Q8C2×Dic13semidirect
702. C2×C22⋊C4C2×Dic13semidirect
703. C2×C22⋊C4C2×Dic13semidirect
717. C2×C42C2×Dic13semidirect
905. C22⋊C4C22⋊Dic13semidirect
910. C13#14098semidirect

Maximal subgroups

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

subgroupindex
C2×#117188912
C2×#117186122
C2×#117188812
C2×C22⋊C4×Dic132
#131131072
#131130852
#131130812
#131130772
#131130732
#131130632
#131130582
C4×#880712
C22×C13×#1242
#1409813