Finite Group Databasebeta

← #15787209

Subgroups — #15787209

Order 3328.

1478 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718612C211yesmaximal, characteristic
2C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
3#13113098C211yesmaximal, characteristic, complemented
4#13113093C211yesmaximal, characteristic, complemented
5#13113085C211yesmaximal, characteristic
6#13113081C211yesmaximal, characteristic
7#13113073C211yesmaximal, characteristic
8#13113073C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic, complemented
11#13113070C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13#13113063C211yesmaximal, characteristic, complemented
14C4×#88071C211yesmaximal, characteristic, complemented
15C2×C13×#388C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C13×#388C418yescomplemented
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
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
52C4⋊C4×Dic13—24no—
53#11718612—24no—
54C25×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4C2×C414yes—
72C2×C13×C22⋊C4—22no—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—41no—
77C2×C13×C22⋊C4—41no—
78C2×C13×C22⋊C4C2×C414yes—
79C2×C13×C22⋊C4C2×C414yes—
80C2×C13×C22⋊C4C2×C414yes—
81C2×C42×C13—41no—
82C2×C42×C13—41no—
83C2×C42×C13C2×C414yes—
84C2×C22⋊Dic13—22no—
85C2×C22⋊Dic13—22no—
86C2×C22⋊Dic13—22no—
87C2×C22⋊Dic13—22no—
88C2×C22⋊Dic13—22no—
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—41no—
93C2×C22⋊Dic13—41no—
94C2×C22⋊Dic13—41no—
95C2×C22⋊Dic13—41no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13—22no—
99C2×C4⋊Dic13—22no—
100C2×C4⋊Dic13—22no—
101C2×C4⋊Dic13—22no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—41no—
108C2×C4×Dic13—41no—
109C2×C4×Dic13—41no—
110C2×C4×Dic13—41no—
111C2×C4×Dic13—41no—
112C2×C4×Dic13—41no—
113C2×C4×Dic13D414yes—
114C13×#95C2×C414yes—
115C13×#95C2×C414yes—
116#88071—22no—
117#88071—22no—
118#88071—22no—
119#88071—22no—
120#88071—22no—
121#88071—22no—
122#88071—22no—
123#88071—22no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—41no—
131#88071—41no—
132#88071—41no—
133#88071—41no—
134#14085—131nomaximal, Sylow
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13C22×C412yes—
150C24×C13C2411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13C22×C412yes—
184C22×C4×C13C22×C412yes—
185C22×C4×C13C22×C412yes—
186C22×C4×C13C22×C412yes—
187C22×C4×C13C22×C412yes—
188C22×C4×C13C22×C412yes—
189C22×C4×C13C2×D412yes—
190C22×C4×C13#4112yes—
191C22×C4×C13#4112yes—
192C22×C4×C13#4112yes—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13C2×D412yes—
242C22×Dic13C2×D412yes—
243C22×Dic13#4112yes—
244C22×Dic13#4112yes—
245C22×Dic13#4112yes—
246C22×Dic13#4112yes—
247C22×Dic13#4112yes—
248C22×Dic13#4112yes—
249C13×C4⋊C4—28no—
250C13×C22⋊C4—28no—
251C13×C22⋊C4—28no—
252C13×C22⋊C4—44no—
253C42×C13—44no—
254C22⋊Dic13—44no—
255C22⋊Dic13—44no—
256C22⋊Dic13—44no—
257C22⋊Dic13—44no—
258C4⋊Dic13—28no—
259C4⋊Dic13—44no—
260C4×Dic13—28no—
261C4×Dic13—44no—
262C4×Dic13—44no—
263C4×Dic13—44no—
264C2×#388—131no—
265C2×#388D1311yescharacteristic
266C2×C4×C4⋊C4—131no—
267#1443—131no—
268#1442—131no—
269#1440—131no—
270#1439—131no—
271#1437—131no—
272#1437—131no—
273#1437—131no—
274#1436—131no—
275#1436—131no—
276#1436—131no—
277#1434—131no—
278C4×#95—131no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—41no—
287C23×C13—41no—
288C23×C13—41no—
289C23×C13—41no—
290C23×C13—41no—
291C23×C13—41no—
292C23×C13—41no—
293C23×C13—41no—
294C23×C13—41no—
295C23×C13—41no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
299C23×C13—41no—
300C23×C13—41no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13C23×C411yescharacteristic
315C23×C13C22×D411yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13C2×#4111yescharacteristic
318C23×C13C2×#4111yescharacteristic
319C23×C13C2×#4111yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C23×C13C2×#4111yescharacteristic
324C23×C13C2×#4111yescharacteristic
325C23×C13H(5,𝔽2)11yescharacteristic
326C23×C13H(5,𝔽2)11yescharacteristic
327C23×C13H(5,𝔽2)11yescharacteristic
328C23×C132−1+411yescharacteristic
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13#11714yes—
370C2×C4×C13C4×D414yes—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—41no—
400C2×Dic13—41no—
401C2×Dic13—41no—
402C2×Dic13—41no—
403C2×Dic13—41no—
404C2×Dic13—41no—
405C2×Dic13—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
408C2×Dic13—41no—
409C2×Dic13—41no—
410C2×Dic13—41no—
411C2×Dic13—41no—
412C2×Dic13—41no—
413C2×Dic13—41no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13#12414yes—
427C22×C4⋊C4—131no—
428C22×C4⋊C4—131no—
429C22×C4⋊C4C2×D1311yescharacteristic
430C22×C22⋊C4—131no—
431C22×C22⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4C2×D1311yescharacteristic
435C22×C22⋊C4C2×D1311yescharacteristic
436C22×C22⋊C4C2×D1311yescharacteristic
437C22×C42—131no—
438C22×C42—131no—
439C22×C42—131no—
440C22×C42—131no—
441C22×C42C2×D1311yescharacteristic
442#388—264no—
443#388Dic1318yescomplemented
444C4×C4⋊C4—264no—
445C2×#95—131no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95C2×D1311yescharacteristic
464C2×#95C2×D1311yescharacteristic
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—81no—
473C22×C13—81no—
474C22×C13—81no—
475C22×C13—81no—
476C22×C13—81no—
477C22×C13—81no—
478C22×C13—81no—
479C22×C13—81no—
480C22×C13C2×#11711yescharacteristic
481C22×C13C2×C4×D411yescharacteristic
482C22×C13C4×#4111yescharacteristic
483C22×C13C4×#4111yescharacteristic
484C22×C13C4×#4111yescharacteristic
485C22×C13#51811yescharacteristic
486C22×C13#52011yescharacteristic
487C22×C13#52511yescharacteristic
488C22×C13#52511yescharacteristic
489C22×C13C2×#12411yescharacteristic
490C22×C13#52911yescharacteristic
491C22×C13#52911yescharacteristic
492C22×C13#52911yescharacteristic
493C22×C13#52911yescharacteristic
494C22×C13#53211yescharacteristic
495C22×C13#53411yescharacteristic
496C22×C13#53711yescharacteristic
497C22×C13#53811yescharacteristic
498C22×C13#53911yescharacteristic
499C22×C13#55111yescharacteristic
500C22×C13#55111yescharacteristic
501C22×C13#55211yescharacteristic
502C22×C13#55311yescharacteristic
503C22×C13#55311yescharacteristic
504C22×C13#55311yescharacteristic
505C22×C13#55311yescharacteristic
506C22×C13#55311yescharacteristic
507C22×C13#55311yescharacteristic
508C22×C13#55311yescharacteristic
509C22×C13#55611yescharacteristic
510C22×C13#55611yescharacteristic
511C22×C13#55611yescharacteristic
512C22×C13#55911yescharacteristic
513C22×C13#55911yescharacteristic
514C22×C13#55911yescharacteristic
515C4×C13—24no—
516C4×C13—24no—
517C4×C13—42no—
518C4×C13—42no—
519C4×C13—42no—
520C4×C13—42no—
521Dic13—24no—
522Dic13—42no—
523Dic13—42no—
524Dic13—42no—
525Dic13—42no—
526Dic13—42no—
527Dic13—81no—
528Dic13—81no—
529C25C22×D1311yescharacteristic
530C23×C4—131no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4C22×D1311yescharacteristic
539C23×C4C22×D1311yescharacteristic
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—262no—
547C2×C4⋊C4—262no—
548C2×C4⋊C4—262no—
549C2×C4⋊C4—262no—
550C2×C4⋊C4—262no—
551C2×C4⋊C4—262no—
552C2×C4⋊C4C2×Dic1314yes—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—41no—
559C2×C22⋊C4—262no—
560C2×C22⋊C4—262no—
561C2×C22⋊C4—262no—
562C2×C22⋊C4—262no—
563C2×C22⋊C4—262no—
564C2×C22⋊C4—262no—
565C2×C22⋊C4—262no—
566C2×C22⋊C4—262no—
567C2×C22⋊C4—521no—
568C2×C22⋊C4—521no—
569C2×C22⋊C4—521no—
570C2×C22⋊C4—521no—
571C2×C22⋊C4C2×Dic1314yes—
572C2×C22⋊C4C2×Dic1314yes—
573C2×C22⋊C4C2×Dic1314yes—
574C2×C42—41no—
575C2×C42—41no—
576C2×C42—134no—
577C2×C42—262no—
578C2×C42—262no—
579C2×C42—262no—
580C2×C42—262no—
581C2×C42—262no—
582C2×C42—521no—
583C2×C42—521no—
584C2×C42—521no—
585C2×C42—521no—
586C2×C42—521no—
587C2×C42—521no—
588C2×C42C2×Dic1314yes—
589#95—262no—
590#95—262no—
591#95—262no—
592#95—262no—
593#95—262no—
594#95—262no—
595#95—262no—
596#95—262no—
597#95—262no—
598#95—262no—
599#95—262no—
600#95—262no—
601#95—262no—
602#95—262no—
603#95—521no—
604#95—521no—
605#95—521no—
606#95—521no—
607#95C2×Dic1314yes—
608#95C2×Dic1314yes—
609C2×C13—82no—
610C2×C13#229011yescharacteristic
611C2×C13C4×#12411yescharacteristic
612C2×C13#232511yescharacteristic
613C2×C13#234711yescharacteristic
614C2×C13#235711yescharacteristic
615C2×C13#237311yescharacteristic
616C2×C13#237411yescharacteristic
617C2×C13#259111yescharacteristic
618C2×C13#259211yescharacteristic
619C2×C13#259411yescharacteristic
620C2×C13#259511yescharacteristic
621C2×C13#259611yescharacteristic
622C2×C13#259711yescharacteristic
623C2×C13#260111yescharacteristic
624C2×C13#260211yescharacteristic
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24C22×Dic1312yes—
640C24C23×D1311yescharacteristic
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—132no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—261no—
682C22×C4—261no—
683C22×C4—261no—
684C22×C4—261no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
691C22×C4—261no—
692C22×C4—261no—
693C22×C4—261no—
694C22×C4—261no—
695C22×C4—261no—
696C22×C4—261no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4#612712yes—
730C22×C4#612712yes—
731C22×C4D4×D1312yes—
732C22×C4#612912yes—
733C22×C4C22×Dic1312yes—
734C22×C4C22×Dic1312yes—
735C22×C4C22×Dic1312yes—
736C22×C4C22×Dic1312yes—
737C22×C4C22×Dic1312yes—
738C22×C4C22×Dic1312yes—
739C4⋊C4—28no—
740C4⋊C4—268no—
741C4⋊C4—524no—
742C22⋊C4—28no—
743C22⋊C4—28no—
744C22⋊C4—44no—
745C22⋊C4—524no—
746C22⋊C4—524no—
747C22⋊C4—524no—
748C22⋊C4—524no—
749C42—44no—
750C42—268no—
751C42—524no—
752C42—524no—
753C42—524no—
754C13#1408511yescharacteristic, complemented, Sylow
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23C2×#612711yescharacteristic
791C23C2×#612711yescharacteristic
792C23C2×D4×D1311yescharacteristic
793C23C2×#612911yescharacteristic
794C23#8825111yescharacteristic
795C23#8825111yescharacteristic
796C23#41×D1311yescharacteristic
797C23#41×D1311yescharacteristic
798C23#41×D1311yescharacteristic
799C23#41×D1311yescharacteristic
800C23#41×D1311yescharacteristic
801C23#41×D1311yescharacteristic
802C23#8825611yescharacteristic
803C23#8825711yescharacteristic
804C23C23×Dic1311yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—134no—
846C2×C4—262no—
847C2×C4—262no—
848C2×C4—262no—
849C2×C4—262no—
850C2×C4—262no—
851C2×C4—262no—
852C2×C4—262no—
853C2×C4—262no—
854C2×C4—262no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—521no—
868C2×C4—521no—
869C2×C4—521no—
870C2×C4—521no—
871C2×C4—521no—
872C2×C4—521no—
873C2×C4—521no—
874C2×C4—521no—
875C2×C4—521no—
876C2×C4—521no—
877C2×C4—521no—
878C2×C4—521no—
879C2×C4—521no—
880C2×C4—521no—
881C2×C4—521no—
882C2×C4—521no—
883C2×C4—521no—
884C2×C4—521no—
885C2×C4—521no—
886C2×C4—521no—
887C2×C4—521no—
888C2×C4—521no—
889C2×C4—521no—
890C2×C4—521no—
891C2×C4—521no—
892C2×C4—521no—
893C2×C4—521no—
894C2×C4—521no—
895C2×C4—521no—
896C2×C4—521no—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—521no—
900C2×C4—521no—
901C2×C4#8818014yes—
902C2×C4D4×Dic1314yes—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22#1171923511yescharacteristic
919C22#1171923511yescharacteristic
920C22#1171923811yescharacteristic
921C22#1171923811yescharacteristic
922C22#1171924311yescharacteristic
923C22#1171924311yescharacteristic
924C22#1171925211yescharacteristic
925C22#1171925211yescharacteristic
926C22#1171926311yescharacteristic
927C22#1171926311yescharacteristic
928C22#1171926411yescharacteristic
929C22#1171926411yescharacteristic
930C22#1171930211yescharacteristic
931C22#1171930711yescharacteristic
932C22#1171931011yescharacteristic
933C22#1171932211yescharacteristic
934C22#1171936411yescharacteristic
935C22#1171936611yescharacteristic
936C22#1171936611yescharacteristic
937C22#1171936911yescharacteristic
938C22#1171937311yescharacteristic
939C22D13×#12411yescharacteristic
940C22#1171938511yescharacteristic
941C22#1171938511yescharacteristic
942C22#1171940711yescharacteristic
943C22#1171941011yescharacteristic
944C22#1171941311yescharacteristic
945C22#1171941411yescharacteristic
946C22C2×#8818011yescharacteristic
947C22C2×D4×Dic1311yescharacteristic
948C22#1171950311yescharacteristic
949C22#41×Dic1311yescharacteristic
950C22#41×Dic1311yescharacteristic
951C22#41×Dic1311yescharacteristic
952C22#1171953211yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—264no—
960C4—522no—
961C4—522no—
962C4—522no—
963C4—522no—
964C4—522no—
965C4—1041no—
966C4—1041no—
967C2—82no—
968C2#1311728111yescharacteristic
969C2#124×Dic1311yescharacteristic
970C2#1311754111yescharacteristic
971C2#1311772911yescharacteristic
972C2#1311780911yescharacteristic
973C2#1311796011yescharacteristic
974C2#1311797211yescharacteristic
975C2#1312031411yescharacteristic
976C2#1312032211yescharacteristic
977C2#1312034711yescharacteristic
978C2#1312036211yescharacteristic
979C2#1312037711yescharacteristic
980C2#1312039211yescharacteristic
981C2#1312044011yescharacteristic
982C2#1312045511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#388C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#388D13
hypocenterC13#14085
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic13C2semidirect
3. #13113098C2semidirect
4. #13113093C2semidirect
10. #13113070C2semidirect
11. #13113070C2semidirect
12. #13113068C2semidirect
13. #13113063C2semidirect
14. C4×#88071C2semidirect
31. C13×#388C4semidirect
443. #388Dic13semidirect
754. C13#14085semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
C2×C4⋊C4×Dic132
#131130982
#131130932
#131130852
#131130812
#131130732
#131130702
#131130682
#131130632
C4×#880712
C2×C13×#3882
#1408513