Finite Group Databasebeta

← #15785261

Subgroups — #15785261

Order 3328.

1586 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718311C211yesmaximal, characteristic, complemented
2C2×#11718604C211yesmaximal, characteristic
3C2×C22⋊C4×Dic13C211yesmaximal, characteristic
4#13113097C211yesmaximal, characteristic, complemented
5#13113096C211yesmaximal, characteristic, complemented
6#13113079C211yesmaximal, characteristic
7#13113079C211yesmaximal, characteristic
8#13113073C211yesmaximal, characteristic
9#13113069C211yesmaximal, characteristic, complemented
10#13113067C211yesmaximal, characteristic, complemented
11#13113061C211yesmaximal, characteristic, complemented
12#13113061C211yesmaximal, characteristic, complemented
13#13113058C211yesmaximal, characteristic
14C4×#88071C211yesmaximal, characteristic, complemented
15C13×#1437C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
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×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
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
51#11718604—24no—
52C22⋊C4×Dic13C418yescomplemented
53#11718311—24no—
54C25×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—22no—
62C23×Dic13—22no—
63C23×Dic13—22no—
64C23×Dic13—22no—
65C23×Dic13—41no—
66C23×Dic13—41no—
67C23×Dic13C2×C414yes—
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—41no—
83C2×C13×C22⋊C4—41no—
84C2×C13×C22⋊C4C2×C414yes—
85C2×C42×C13—22no—
86C2×C42×C13—41no—
87C2×C42×C13—41no—
88C2×C22⋊Dic13—22no—
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—41no—
95C2×C22⋊Dic13—41no—
96C2×C22⋊Dic13C2×C414yes—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—41no—
102C2×#6101—41no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13—41no—
107C2×C4×Dic13—41no—
108C2×C4×Dic13—41no—
109C2×C4×Dic13—41no—
110C2×C4×Dic13C2×C414yes—
111C2×C4×Dic13C2×C414yes—
112C13×#95—22no—
113C13×#95—22no—
114C13×#95—22no—
115#88071—22no—
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—41no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071C2×C414yes—
132#88071C2×C414yes—
133#88071D414yes—
134#13917—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×C13C22×C412yes—
148C24×C13#4112yes—
149C24×C13#4112yes—
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×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
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—28no—
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—28no—
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×Dic13—44no—
242C22×Dic13—44no—
243C22×Dic13—44no—
244C22×Dic13—44no—
245C22×Dic13—44no—
246C22×Dic13C22×C412yes—
247C22×Dic13C22×C412yes—
248C22×Dic13C22×C412yes—
249C22×Dic13C22×C412yes—
250C22×Dic13C2×D412yes—
251C22×Dic13C2×D412yes—
252C22×Dic13#4112yes—
253C22×Dic13#4112yes—
254C22×Dic13#4112yes—
255C22×Dic13#4112yes—
256C13×C22⋊C4—28no—
257C13×C22⋊C4—44no—
258C13×C22⋊C4—44no—
259C42×C13—44no—
260C22⋊Dic13—28no—
261C22⋊Dic13—44no—
262C22⋊Dic13—44no—
263#6101—44no—
264#6101—44no—
265C4×Dic13—28no—
266C4×Dic13—44no—
267C4×Dic13—44no—
268C2×#382—131no—
269C2×#381—131no—
270C2×C4×C22⋊C4—131no—
271#1443—131no—
272#1443—131no—
273#1439—131no—
274#1439—131no—
275#1437—131no—
276#1437D1311yescharacteristic
277#1436—131no—
278#1436—131no—
279#1434—131no—
280#1434—131no—
281C22⋊#95—131no—
282C4×#95—131no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
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×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13#11714yes—
318C23×C13C23×C411yescharacteristic
319C23×C13C22×D411yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C23×C13C2×#4111yescharacteristic
324C23×C13C2×#4111yescharacteristic
325C23×C13C2×#4111yescharacteristic
326C23×C13C2×#4111yescharacteristic
327C23×C13C2×#4111yescharacteristic
328C23×C13C2×#4111yescharacteristic
329C23×C13H(5,𝔽2)11yescharacteristic
330C23×C13H(5,𝔽2)11yescharacteristic
331C23×C13H(5,𝔽2)11yescharacteristic
332C23×C132−1+411yescharacteristic
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—41no—
349C2×C4×C13—41no—
350C2×C4×C13—41no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
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—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13#11714yes—
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—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—416no—
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—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13#11714yes—
431C2×Dic13C4×D414yes—
432C24×C4—131no—
433C22×C4⋊C4—131no—
434C22×C4⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C22⋊C4—131no—
438C22×C22⋊C4C2×D1311yescharacteristic
439C22×C22⋊C4C2×D1311yescharacteristic
440C22×C22⋊C4C2×D1311yescharacteristic
441C22×C42—131no—
442C22×C42—131no—
443C22×C42—131no—
444C22×C42C2×D1311yescharacteristic
445#382—264no—
446#381—264no—
447C4×C22⋊C4—138no—
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×#95—131no—
464C2×#95—131no—
465C2×#95—131no—
466C2×#95—131no—
467C2×#95C2×D1311yescharacteristic
468C2×#95C2×D1311yescharacteristic
469C2×#95C2×D1311yescharacteristic
470C22×C13—24no—
471C22×C13—24no—
472C22×C13—24no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13C2×#11711yescharacteristic
486C22×C13C2×#11711yescharacteristic
487C22×C13C2×#11711yescharacteristic
488C22×C13C2×C4×D411yescharacteristic
489C22×C13C4×#4111yescharacteristic
490C22×C13#51811yescharacteristic
491C22×C13#52011yescharacteristic
492C22×C13#52911yescharacteristic
493C22×C13#52911yescharacteristic
494C22×C13#52911yescharacteristic
495C22×C13#52911yescharacteristic
496C22×C13#52911yescharacteristic
497C22×C13#52911yescharacteristic
498C22×C13#53211yescharacteristic
499C22×C13#53211yescharacteristic
500C22×C13#53811yescharacteristic
501C22×C13#53811yescharacteristic
502C22×C13#53911yescharacteristic
503C22×C13#53911yescharacteristic
504C22×C13#54611yescharacteristic
505C22×C13#54611yescharacteristic
506C22×C13#54611yescharacteristic
507C22×C13#54811yescharacteristic
508C22×C13#55111yescharacteristic
509C22×C13#55111yescharacteristic
510C22×C13#55111yescharacteristic
511C22×C13#55111yescharacteristic
512C22×C13#55211yescharacteristic
513C22×C13#55211yescharacteristic
514C22×C13#55211yescharacteristic
515C22×C13#55311yescharacteristic
516C22×C13#55311yescharacteristic
517C22×C13#55311yescharacteristic
518C22×C13#55911yescharacteristic
519C22×C13#55911yescharacteristic
520C4×C13—24no—
521C4×C13—42no—
522C4×C13—42no—
523C4×C13—42no—
524C4×C13—81no—
525C4×C13—81no—
526Dic13—24no—
527Dic13—24no—
528Dic13—42no—
529Dic13—42no—
530Dic13—42no—
531Dic13—42no—
532Dic13—81no—
533Dic13—81no—
534C25C22×D1311yescharacteristic
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—131no—
541C23×C4—134no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—262no—
545C23×C4—262no—
546C23×C4—262no—
547C23×C4—262no—
548C23×C4—521no—
549C23×C4—521no—
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C23×C4C22×D1311yescharacteristic
555C23×C4C22×D1311yescharacteristic
556C2×C4⋊C4—262no—
557C2×C4⋊C4—262no—
558C2×C4⋊C4—262no—
559C2×C4⋊C4—262no—
560C2×C4⋊C4—521no—
561C2×C4⋊C4—521no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—134no—
571C2×C22⋊C4—262no—
572C2×C22⋊C4—262no—
573C2×C22⋊C4—262no—
574C2×C22⋊C4—262no—
575C2×C22⋊C4—262no—
576C2×C22⋊C4—262no—
577C2×C22⋊C4—521no—
578C2×C22⋊C4—521no—
579C2×C22⋊C4C4×D1314yes—
580C2×C42—22no—
581C2×C42—41no—
582C2×C42—41no—
583C2×C42—134no—
584C2×C42—134no—
585C2×C42—262no—
586C2×C42—262no—
587C2×C42—262no—
588C2×C42—521no—
589C2×C42—521no—
590C2×C42—521no—
591C2×C42—521no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—134no—
596#95—134no—
597#95—134no—
598#95—262no—
599#95—262no—
600#95—262no—
601#95—262no—
602#95—262no—
603#95—262no—
604#95—262no—
605#95—262no—
606#95—262no—
607#95—262no—
608#95—262no—
609#95—262no—
610#95—521no—
611#95—521no—
612#95—521no—
613#95—521no—
614C2×C13—44no—
615C2×C13#228311yescharacteristic
616C2×C13#229311yescharacteristic
617C2×C13#231811yescharacteristic
618C2×C13#234211yescharacteristic
619C2×C13#234311yescharacteristic
620C2×C13#235211yescharacteristic
621C2×C13#235711yescharacteristic
622C2×C13#255711yescharacteristic
623C2×C13#255711yescharacteristic
624C2×C13#255811yescharacteristic
625C2×C13#255811yescharacteristic
626C2×C13#257511yescharacteristic
627C2×C13#257511yescharacteristic
628C2×C13#257611yescharacteristic
629C2×C13#257611yescharacteristic
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24C2×C4×D1312yes—
643C24#612712yes—
644C24#612712yes—
645C24C23×D1311yescharacteristic
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—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—132no—
686C22×C4—132no—
687C22×C4—132no—
688C22×C4—132no—
689C22×C4—132no—
690C22×C4—132no—
691C22×C4—132no—
692C22×C4—268no—
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—268no—
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—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—524no—
741C22×C4—524no—
742C22×C4—524no—
743C22×C4—524no—
744C22×C4—524no—
745C22×C4C2×C4×D1312yes—
746C22×C4C2×C4×D1312yes—
747C22×C4D4×D1312yes—
748C22×C4#612912yes—
749C22×C4#612912yes—
750C22×C4#612912yes—
751C4⋊C4—524no—
752C4⋊C4—524no—
753C22⋊C4—28no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—268no—
757C22⋊C4—524no—
758C22⋊C4—524no—
759C42—44no—
760C42—268no—
761C42—524no—
762C42—524no—
763C13#1391711yescharacteristic, complemented, Sylow
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23#8812614yes—
799C23C22×C4×D1311yescharacteristic
800C23C2×#612711yescharacteristic
801C23C2×#612711yescharacteristic
802C23C2×D4×D1311yescharacteristic
803C23C2×#612911yescharacteristic
804C23C2×#612911yescharacteristic
805C23C2×#612911yescharacteristic
806C23#8825111yescharacteristic
807C23#8825111yescharacteristic
808C23#41×D1311yescharacteristic
809C23#41×D1311yescharacteristic
810C23#41×D1311yescharacteristic
811C23#41×D1311yescharacteristic
812C23#8825611yescharacteristic
813C23#8825711yescharacteristic
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—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—134no—
856C2×C4—134no—
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—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
874C2×C4—262no—
875C2×C4—262no—
876C2×C4—262no—
877C2×C4—262no—
878C2×C4—262no—
879C2×C4—262no—
880C2×C4—262no—
881C2×C4—5216no—
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—521no—
902C2×C4—521no—
903C2×C4—521no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4#8813114yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×#8812611yescharacteristic
929C22C2×#8813111yescharacteristic
930C22#1171919511yescharacteristic
931C22#1171920011yescharacteristic
932C22D13×#11711yescharacteristic
933C22#1171923211yescharacteristic
934C22#1171923611yescharacteristic
935C22C4×#612911yescharacteristic
936C22#1171924311yescharacteristic
937C22#1171924311yescharacteristic
938C22#1171924311yescharacteristic
939C22#1171924311yescharacteristic
940C22#1171924611yescharacteristic
941C22C4×D4×D1311yescharacteristic
942C22#1171925011yescharacteristic
943C22#1171925111yescharacteristic
944C22#1171925511yescharacteristic
945C22#1171926111yescharacteristic
946C22#1171926111yescharacteristic
947C22#1171929811yescharacteristic
948C22#1171930111yescharacteristic
949C22#1171930511yescharacteristic
950C22#1171930611yescharacteristic
951C22#1171930711yescharacteristic
952C22#1171931511yescharacteristic
953C22#1171932211yescharacteristic
954C22#1171936611yescharacteristic
955C22#1171936911yescharacteristic
956C22#1171937011yescharacteristic
957C22#1171938211yescharacteristic
958C22#1171938511yescharacteristic
959C22#1171938611yescharacteristic
960C22#1171941311yescharacteristic
961C22#1171941411yescharacteristic
962C22#1171942111yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—81no—
968C4—81no—
969C4—264no—
970C4—264no—
971C4—522no—
972C4—522no—
973C4—522no—
974C4—522no—
975C4—1041no—
976C4—1041no—
977C2—44no—
978C2#1311723011yescharacteristic
979C2#1311729811yescharacteristic
980C2#1311746211yescharacteristic
981C2#1311767911yescharacteristic
982C2#1311769011yescharacteristic
983C2#1311776411yescharacteristic
984C2#1311780611yescharacteristic
985C2#1311993211yescharacteristic
986C2#1311994011yescharacteristic
987C2#1311994711yescharacteristic
988C2#1311995511yescharacteristic
989C2#1312012211yescharacteristic
990C2#1312013011yescharacteristic
991C2#1312013711yescharacteristic
992C2#1312014511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1437C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1437D13
hypocenterC13#13917
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
1. C2×#11718311C2semidirect
4. #13113097C2semidirect
5. #13113096C2semidirect
9. #13113069C2semidirect
10. #13113067C2semidirect
11. #13113061C2semidirect
12. #13113061C2semidirect
14. C4×#88071C2semidirect
52. C22⋊C4×Dic13C4semidirect
763. C13#13917semidirect

Maximal subgroups

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

subgroupindex
C2×#117183112
C2×#117186042
C2×C22⋊C4×Dic132
#131130972
#131130962
#131130792
#131130732
#131130692
#131130672
#131130612
#131130582
C4×#880712
C13×#14372
#1391713