Finite Group Databasebeta

← #15793514

Subgroups — #15793514

Order 3328.

1290 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718654C211yesmaximal, characteristic
2#13113096C211yesmaximal, characteristic, complemented
3#13113084C211yesmaximal, characteristic
4#13113080C211yesmaximal, characteristic
5#13113078C211yesmaximal, characteristic
6#13113072C211yesmaximal, characteristic
7#13113072C211yesmaximal, characteristic
8#13113072C211yesmaximal, characteristic
9#13113071C211yesmaximal, characteristic, complemented
10#13113068C211yesmaximal, characteristic, complemented
11#13113068C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13#13113061C211yesmaximal, characteristic, complemented
14#13113060C211yesmaximal, characteristic, complemented
15C13×#1441C211yesmaximal, characteristic, complemented
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
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
51#11718654C418yescomplemented
52C24×D13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—41no—
69C2×C13×C4⋊C4—41no—
70C2×C13×C4⋊C4—41no—
71C2×C13×C4⋊C4—41no—
72C2×C13×C4⋊C4C2×C414yes—
73C2×#6103—22no—
74C2×#6103—22no—
75C2×#6103—22no—
76C2×#6103—22no—
77C2×#6103—22no—
78C2×#6103—22no—
79C2×#6103—41no—
80C2×#6103—41no—
81C2×#6103—41no—
82C2×#6103—41no—
83C2×#6103—41no—
84C2×#6103—41no—
85C2×#6103—41no—
86C2×#6103—41no—
87C2×#6103—41no—
88C2×#6103—41no—
89C2×#6103—41no—
90C2×#6103—41no—
91C2×#6103C2×C414yes—
92C2×#6103C2×C414yes—
93C2×#6103C2×C414yes—
94C2×#6101—22no—
95C2×#6101—22no—
96C2×#6101—41no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13—22no—
99C2×C4×Dic13—41no—
100C2×C4×Dic13—41no—
101C2×C4×Dic13—41no—
102C2×C4×Dic13—41no—
103C2×C4×Dic13—41no—
104C2×C4×Dic13—41no—
105C2×C4×Dic13—41no—
106C13×#95—22no—
107C13×#95—41no—
108C13×#95—41no—
109C13×#95—41no—
110C13×#95—41no—
111#88071—22no—
112#88071—22no—
113#88071—22no—
114#88071—22no—
115#88071—22no—
116#88071—22no—
117#88071—41no—
118#88071—41no—
119#88071—41no—
120#88071—41no—
121#88071—41no—
122#88071—41no—
123#88071—41no—
124#88071—41no—
125#88071C2×C414yes—
126#88071C2×C414yes—
127#88071C2×C414yes—
128#14616—131nomaximal, Sylow
129C24×C13C2411yescharacteristic
130C23×D13—21no—
131C23×D13—21no—
132C23×D13—21no—
133C23×D13—21no—
134C23×D13—21no—
135C23×D13—21no—
136C23×D13—21no—
137C23×D13—21no—
138C23×D13—21no—
139C23×D13—21no—
140C23×D13—21no—
141C23×D13—21no—
142C23×D13—21no—
143C23×D13—21no—
144C23×D13C22×C412yes—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
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×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13C22×C412yes—
190C22×C4×C13C22×C412yes—
191C22×C4×C13C22×C412yes—
192C22×C4×C13#4112yes—
193C22×C4×C13#4112yes—
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×Dic13C22×C412yes—
237C22×Dic13C22×C412yes—
238C22×Dic13C22×C412yes—
239C22×Dic13#4112yes—
240C22×Dic13#4112yes—
241C22×Dic13#4112yes—
242C22×Dic13#4112yes—
243C13×C4⋊C4—44no—
244C13×C4⋊C4—44no—
245#6103—44no—
246#6103—44no—
247#6103—44no—
248#6103—44no—
249#6103—44no—
250#6103—44no—
251#6103—44no—
252#6101—44no—
253C4×Dic13—44no—
254C4×Dic13—44no—
255C4×Dic13—44no—
256C2×#397—131no—
257#1443—131no—
258#1441D1311yescharacteristic, complemented
259#1440—131no—
260#1439—131no—
261#1439—131no—
262#1437—131no—
263#1437—131no—
264#1437—131no—
265#1436—131no—
266#1436—131no—
267#1436—131no—
268#1436—131no—
269#1434—131no—
270#1434—131no—
271C23×C13C23×C411yescharacteristic
272C23×C13C2×#4111yescharacteristic
273C23×C13C2×#4111yescharacteristic
274C23×C13C2×#4111yescharacteristic
275C23×C13C2×#4111yescharacteristic
276C23×C13C2×#4111yescharacteristic
277C23×C13C2×#4111yescharacteristic
278C23×C13H(5,𝔽2)11yescharacteristic
279C23×C13H(5,𝔽2)11yescharacteristic
280C23×C13H(5,𝔽2)11yescharacteristic
281C23×C13H(5,𝔽2)11yescharacteristic
282C23×C13H(5,𝔽2)11yescharacteristic
283C23×C13H(5,𝔽2)11yescharacteristic
284C23×C132−1+411yescharacteristic
285C23×C132−1+411yescharacteristic
286C22×D13—22no—
287C22×D13—22no—
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—22no—
291C22×D13—22no—
292C22×D13—22no—
293C22×D13—41no—
294C22×D13—41no—
295C22×D13—41no—
296C22×D13—41no—
297C22×D13—41no—
298C22×D13—41no—
299C22×D13—41no—
300C22×D13—41no—
301C22×D13—41no—
302C22×D13—41no—
303C22×D13—41no—
304C22×D13—41no—
305C22×D13—41no—
306C22×D13—41no—
307C22×D13—41no—
308C22×D13—41no—
309C22×D13—41no—
310C22×D13—41no—
311C22×D13—41no—
312C22×D13—41no—
313C22×D13—41no—
314C22×D13—41no—
315C22×D13—41no—
316C22×D13—41no—
317C22×D13—41no—
318C22×D13—41no—
319C22×D13—41no—
320C22×D13—41no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
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—41no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
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×Dic13—22no—
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—41no—
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—
419C22×C4⋊C4—131no—
420C22×C4⋊C4C2×D1311yescharacteristic
421C22×C4⋊C4C2×D1311yescharacteristic
422C22×C22⋊C4—131no—
423C22×C22⋊C4—131no—
424C22×C22⋊C4—131no—
425C22×C22⋊C4—131no—
426C22×C22⋊C4—131no—
427C22×C22⋊C4—131no—
428C22×C22⋊C4—131no—
429C22×C42—131no—
430C22×C42—131no—
431C22×C42—131no—
432#397—138no—
433C2×#95—131no—
434C2×#95—131no—
435C2×#95—131no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C2×#95—131no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95C2×D1311yescharacteristic
451C2×#95C2×D1311yescharacteristic
452C2×#95C2×D1311yescharacteristic
453C2×#95C2×D1311yescharacteristic
454C2×#95C2×D1311yescharacteristic
455C22×C13C4×#4111yescharacteristic
456C22×C13C4×#4111yescharacteristic
457C22×C13C4×#4111yescharacteristic
458C22×C13#51811yescharacteristic
459C22×C13#51811yescharacteristic
460C22×C13#52011yescharacteristic
461C22×C13#52011yescharacteristic
462C22×C13#53811yescharacteristic
463C22×C13#53811yescharacteristic
464C22×C13#53811yescharacteristic
465C22×C13#53811yescharacteristic
466C22×C13#53811yescharacteristic
467C22×C13#53911yescharacteristic
468C22×C13#54011yescharacteristic
469C22×C13#54011yescharacteristic
470C22×C13#54011yescharacteristic
471C22×C13#54211yescharacteristic
472C22×C13#54211yescharacteristic
473C22×C13#54211yescharacteristic
474C22×C13#55111yescharacteristic
475C22×C13#55111yescharacteristic
476C22×C13#55111yescharacteristic
477C22×C13#55211yescharacteristic
478C22×C13#55211yescharacteristic
479C22×C13#55311yescharacteristic
480C22×C13#55311yescharacteristic
481C22×C13#55311yescharacteristic
482C22×C13#55311yescharacteristic
483C22×C13#55611yescharacteristic
484C22×C13#55611yescharacteristic
485C22×C13#55911yescharacteristic
486C22×C13#56011yescharacteristic
487C22×C13#56211yescharacteristic
488C22×C13#56211yescharacteristic
489C22×C13#56311yescharacteristic
490C2×D13—42no—
491C2×D13—42no—
492C2×D13—42no—
493C2×D13—42no—
494C2×D13—42no—
495C2×D13—42no—
496C2×D13—42no—
497C2×D13—81no—
498C2×D13—81no—
499C2×D13—81no—
500C2×D13—81no—
501C2×D13—81no—
502C2×D13—81no—
503C2×D13—81no—
504C2×D13—81no—
505C4×C13—42no—
506C4×C13—42no—
507C4×C13—42no—
508C4×C13—42no—
509C4×C13—42no—
510C4×C13—81no—
511C4×C13—81no—
512Dic13—42no—
513Dic13—42no—
514Dic13—42no—
515Dic13—42no—
516Dic13—42no—
517Dic13—42no—
518Dic13—42no—
519C25—131no—
520C23×C4—131no—
521C23×C4—131no—
522C23×C4—131no—
523C23×C4—131no—
524C23×C4—131no—
525C23×C4—131no—
526C23×C4—131no—
527C23×C4C22×D1311yescharacteristic
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530C23×C4C22×D1311yescharacteristic
531C23×C4C22×D1311yescharacteristic
532C23×C4C22×D1311yescharacteristic
533C23×C4C22×D1311yescharacteristic
534C2×C4⋊C4—22no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4—262no—
540C2×C4⋊C4—262no—
541C2×C4⋊C4—521no—
542C2×C4⋊C4C4×D1314yes—
543C2×C22⋊C4—134no—
544C2×C22⋊C4—134no—
545C2×C22⋊C4—134no—
546C2×C22⋊C4—262no—
547C2×C22⋊C4—262no—
548C2×C22⋊C4—262no—
549C2×C22⋊C4—262no—
550C2×C22⋊C4—262no—
551C2×C22⋊C4—262no—
552C2×C22⋊C4—521no—
553C2×C22⋊C4—521no—
554C2×C22⋊C4—521no—
555C2×C22⋊C4—521no—
556C2×C22⋊C4—521no—
557C2×C22⋊C4—521no—
558C2×C22⋊C4—521no—
559C2×C22⋊C4—521no—
560C2×C22⋊C4—521no—
561C2×C22⋊C4—521no—
562C2×C22⋊C4—521no—
563C2×C22⋊C4—521no—
564C2×C42—262no—
565C2×C42—262no—
566C2×C42—521no—
567C2×C42—521no—
568C2×C42—521no—
569C2×C42—521no—
570C2×C42—521no—
571C2×C42—521no—
572C2×C42—521no—
573#95—22no—
574#95—41no—
575#95—41no—
576#95—41no—
577#95—41no—
578#95—134no—
579#95—134no—
580#95—134no—
581#95—262no—
582#95—262no—
583#95—262no—
584#95—262no—
585#95—262no—
586#95—262no—
587#95—521no—
588#95—521no—
589#95—521no—
590#95—521no—
591#95—521no—
592#95—521no—
593#95—521no—
594#95—521no—
595C2×C13#233311yescharacteristic
596C2×C13#233511yescharacteristic
597C2×C13#233711yescharacteristic
598C2×C13#237311yescharacteristic
599C2×C13#237311yescharacteristic
600C2×C13#237411yescharacteristic
601C2×C13#237611yescharacteristic
602C2×C13#274911yescharacteristic
603C2×C13#275911yescharacteristic
604C2×C13#276111yescharacteristic
605C2×C13#277311yescharacteristic
606C2×C13#277911yescharacteristic
607C2×C13#278611yescharacteristic
608C2×C13#279711yescharacteristic
609C2×C13#280011yescharacteristic
610D13—82no—
611C24—132no—
612C24—261no—
613C24—261no—
614C24—261no—
615C24—261no—
616C24—261no—
617C24—261no—
618C24—261no—
619C24—261no—
620C24—261no—
621C24—261no—
622C24—261no—
623C24—261no—
624C24—261no—
625C24—261no—
626C24C23×D1311yescharacteristic
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
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—132no—
672C22×C4—132no—
673C22×C4—132no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—261no—
679C22×C4—261no—
680C22×C4—261no—
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×C4C2×C4×D1312yes—
721C22×C4C2×C4×D1312yes—
722C22×C4C2×C4×D1312yes—
723C22×C4#612912yes—
724C22×C4#613112yes—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—524no—
728C22⋊C4—524no—
729C22⋊C4—524no—
730C22⋊C4—524no—
731C22⋊C4—524no—
732C22⋊C4—524no—
733C22⋊C4—524no—
734C22⋊C4—524no—
735C42—524no—
736C42—524no—
737C42—524no—
738C13#1461611yescharacteristic, complemented, Sylow
739C23—262no—
740C23—262no—
741C23—262no—
742C23—262no—
743C23—262no—
744C23—262no—
745C23—262no—
746C23—521no—
747C23—521no—
748C23—521no—
749C23—521no—
750C23—521no—
751C23—521no—
752C23—521no—
753C23—521no—
754C23—521no—
755C23—521no—
756C23—521no—
757C23—521no—
758C23—521no—
759C23—521no—
760C23—521no—
761C23—521no—
762C23—521no—
763C23—521no—
764C23—521no—
765C23—521no—
766C23—521no—
767C23—521no—
768C23—521no—
769C23—521no—
770C23—521no—
771C23—521no—
772C23—521no—
773C23—521no—
774C23C22×C4×D1311yescharacteristic
775C23C2×#612911yescharacteristic
776C23#8825111yescharacteristic
777C23#8825111yescharacteristic
778C23#8825111yescharacteristic
779C23#8825111yescharacteristic
780C23C2×#613111yescharacteristic
781C23#8825411yescharacteristic
782C23#8825411yescharacteristic
783C23#41×D1311yescharacteristic
784C23#41×D1311yescharacteristic
785C23#41×D1311yescharacteristic
786C23#41×D1311yescharacteristic
787C23#8825611yescharacteristic
788C23#8825611yescharacteristic
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
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—262no—
839C2×C4—262no—
840C2×C4—262no—
841C2×C4—262no—
842C2×C4—262no—
843C2×C4—262no—
844C2×C4—262no—
845C2×C4—262no—
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—521no—
860C2×C4—521no—
861C2×C4—521no—
862C2×C4—521no—
863C2×C4—521no—
864C2×C4—521no—
865C2×C4—521no—
866C2×C4—521no—
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—
887C22—522no—
888C22—522no—
889C22—522no—
890C22—522no—
891C22—522no—
892C22—522no—
893C22—522no—
894C22—1041no—
895C22—1041no—
896C22—1041no—
897C22—1041no—
898C22—1041no—
899C22—1041no—
900C22—1041no—
901C22—1041no—
902C22#1171919111yescharacteristic
903C22#1171920911yescharacteristic
904C22#1171922711yescharacteristic
905C22C4×#612911yescharacteristic
906C22#1171925011yescharacteristic
907C22C4×#613111yescharacteristic
908C22#1171927911yescharacteristic
909C22#1171929811yescharacteristic
910C22#1171930611yescharacteristic
911C22#1171931811yescharacteristic
912C22#1171932011yescharacteristic
913C22#1171932011yescharacteristic
914C22#1171932411yescharacteristic
915C22#1171932511yescharacteristic
916C22#1171934211yescharacteristic
917C22#1171934211yescharacteristic
918C22#1171934311yescharacteristic
919C22#1171934511yescharacteristic
920C22#1171934511yescharacteristic
921C22#1171934611yescharacteristic
922C22#1171934911yescharacteristic
923C22#1171935211yescharacteristic
924C22#1171936211yescharacteristic
925C22#1171936311yescharacteristic
926C22#1171936911yescharacteristic
927C22#1171938311yescharacteristic
928C22#1171939811yescharacteristic
929C22#1171939811yescharacteristic
930C22#1171940011yescharacteristic
931C22#1171940511yescharacteristic
932C22#1171941411yescharacteristic
933C22#1171941411yescharacteristic
934C22#1171943711yescharacteristic
935C22#1171943811yescharacteristic
936C22#1171944011yescharacteristic
937C4—42no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—81no—
943C4—81no—
944C4—522no—
945C4—522no—
946C4—522no—
947C4—522no—
948C4—522no—
949C4—522no—
950C4—522no—
951C2—1042no—
952C2#1311759711yescharacteristic
953C2#1311762211yescharacteristic
954C2#1311764811yescharacteristic
955C2#1311794911yescharacteristic
956C2#1311795911yescharacteristic
957C2#1311796811yescharacteristic
958C2#1311798111yescharacteristic
959C2#1312206511yescharacteristic
960C2#1312220911yescharacteristic
961C2#1312221611yescharacteristic
962C2#1312238611yescharacteristic
963C2#1312247611yescharacteristic
964C2#1312255811yescharacteristic
965C2#1312269911yescharacteristic
966C2#1312272511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1441D13
hypocenterC13#14616
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. #13113096C2semidirect
9. #13113071C2semidirect
10. #13113068C2semidirect
11. #13113068C2semidirect
12. #13113067C2semidirect
13. #13113061C2semidirect
14. #13113060C2semidirect
15. C13×#1441C2semidirect
51. #11718654C4semidirect
258. #1441D13semidirect
738. C13#14616semidirect

Maximal subgroups

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

subgroupindex
C2×#117186542
#131130962
#131130842
#131130802
#131130782
#131130722
#131130712
#131130682
#131130672
#131130612
#131130602
C13×#14412
#1461613