Finite Group Databasebeta

← #15787080

Subgroups — #15787080

Order 3328.

1578 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718308C211yesmaximal, characteristic, complemented
2C2×#11718606C211yesmaximal, characteristic
3C2×#11718612C211yesmaximal, characteristic
4C2×#11718605C211yesmaximal, characteristic
5C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
6#13113096C211yesmaximal, characteristic, complemented
7#13113086C211yesmaximal, characteristic, complemented
8#13113079C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113073C211yesmaximal, characteristic
11#13113067C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13#13113062C211yesmaximal, characteristic, complemented
14#95×Dic13C211yesmaximal, characteristic, complemented
15C13×#1439C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
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
51C4⋊C4×Dic13—24no—
52#11718612—24no—
53#11718606C418yescomplemented
54#11718605—24no—
55#11718308—24no—
56C25×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—41no—
80C2×C13×C22⋊C4—41no—
81C2×C13×C22⋊C4—41no—
82C2×C13×C22⋊C4C2×C414yes—
83C2×C22⋊Dic13—22no—
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⋊Dic13C2×C414yes—
94C2×C22⋊Dic13C2×C414yes—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13D414yes—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—41no—
106C2×#6101C2×C414yes—
107C2×C4×Dic13—22no—
108C2×C4×Dic13—22no—
109C2×C4×Dic13—22no—
110C2×C4×Dic13—22no—
111C2×C4×Dic13—22no—
112C2×C4×Dic13—22no—
113C2×C4×Dic13—22no—
114C2×C4×Dic13—41no—
115C2×C4×Dic13—41no—
116C2×C4×Dic13—41no—
117C2×C4×Dic13—41no—
118C2×C4×Dic13—41no—
119C2×C4×Dic13—41no—
120C2×C4×Dic13C2×C414yes—
121C2×C4×Dic13D414yes—
122C13×#95—22no—
123C13×#95—22no—
124C13×#95—41no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071C2×C414yes—
139#88071C2×C414yes—
140#14077—131nomaximal, Sylow
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×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13C22×C412yes—
156C24×C13C2411yescharacteristic
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×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13C22×C412yes—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C2×D412yes—
195C22×C4×C13C2×D412yes—
196C22×C4×C13#4112yes—
197C22×C4×C13#4112yes—
198C22×C4×C13#4112yes—
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×Dic13—21no—
242C22×Dic13C22×C412yes—
243C22×Dic13C22×C412yes—
244C22×Dic13C22×C412yes—
245C22×Dic13C22×C412yes—
246C22×Dic13C2×D412yes—
247C22×Dic13C2×D412yes—
248C22×Dic13C2×D412yes—
249C22×Dic13C2×D412yes—
250C22×Dic13#4112yes—
251C22×Dic13#4112yes—
252C22×Dic13#4112yes—
253C22×Dic13#4112yes—
254C22×Dic13#4112yes—
255C13×C4⋊C4—28no—
256C13×C22⋊C4—28no—
257C13×C22⋊C4—44no—
258C13×C22⋊C4—44no—
259C22⋊Dic13—28no—
260C22⋊Dic13—28no—
261C22⋊Dic13—44no—
262C22⋊Dic13—44no—
263C4⋊Dic13—28no—
264#6101—28no—
265#6101—44no—
266#6101—44no—
267C4×Dic13—28no—
268C4×Dic13—44no—
269C4×Dic13—44no—
270C4×Dic13—44no—
271C4×Dic13—44no—
272C2×#389—131no—
273C2×#388—131no—
274C2×#388—131no—
275C2×#388—131no—
276C2×C4×C4⋊C4—131no—
277#1443—131no—
278#1441—131no—
279#1439—131no—
280#1439D1311yescharacteristic
281#1437—131no—
282#1437—131no—
283#1436—131no—
284#1436—131no—
285#1434—131no—
286C4×#95—131no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
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×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13C23×C411yescharacteristic
323C23×C13C22×D411yescharacteristic
324C23×C13C22×D411yescharacteristic
325C23×C13C2×#4111yescharacteristic
326C23×C13C2×#4111yescharacteristic
327C23×C13C2×#4111yescharacteristic
328C23×C13C2×#4111yescharacteristic
329C23×C13C2×#4111yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13H(5,𝔽2)11yescharacteristic
334C23×C13H(5,𝔽2)11yescharacteristic
335C23×C132−1+411yescharacteristic
336C23×C132−1+411yescharacteristic
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—22no—
354C2×C4×C13—22no—
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—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13C4×D414yes—
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—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
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—41no—
431C2×Dic13—41no—
432C2×Dic13#11714yes—
433C2×Dic13C4×D414yes—
434C2×Dic13#12114yes—
435C22×C4⋊C4—131no—
436C22×C4⋊C4—131no—
437C22×C4⋊C4—131no—
438C22×C4⋊C4—131no—
439C22×C4⋊C4C2×D1311yescharacteristic
440C22×C22⋊C4—131no—
441C22×C22⋊C4—131no—
442C22×C22⋊C4—131no—
443C22×C22⋊C4—131no—
444C22×C22⋊C4C2×D1311yescharacteristic
445C22×C22⋊C4C2×D1311yescharacteristic
446C22×C22⋊C4C2×D1311yescharacteristic
447C22×C42—131no—
448C22×C42—131no—
449C22×C42—131no—
450C22×C42—131no—
451C22×C42—131no—
452#389—264no—
453#388—138no—
454#388—264no—
455#388—264no—
456C4×C4⋊C4—264no—
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×#95—131no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95C2×D1311yescharacteristic
473C2×#95C2×D1311yescharacteristic
474C2×#95C2×D1311yescharacteristic
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—81no—
483C22×C13—81no—
484C22×C13—81no—
485C22×C13—81no—
486C22×C13—81no—
487C22×C13—81no—
488C22×C13—81no—
489C22×C13—81no—
490C22×C13C2×#11711yescharacteristic
491C22×C13C2×C4×D411yescharacteristic
492C22×C13C2×C4×D411yescharacteristic
493C22×C13C4×#4111yescharacteristic
494C22×C13C4×#4111yescharacteristic
495C22×C13#52011yescharacteristic
496C22×C13#52011yescharacteristic
497C22×C13C2×#12111yescharacteristic
498C22×C13#52511yescharacteristic
499C22×C13#52911yescharacteristic
500C22×C13#52911yescharacteristic
501C22×C13#52911yescharacteristic
502C22×C13#53211yescharacteristic
503C22×C13#53211yescharacteristic
504C22×C13#53211yescharacteristic
505C22×C13#53411yescharacteristic
506C22×C13#53611yescharacteristic
507C22×C13#53911yescharacteristic
508C22×C13#53911yescharacteristic
509C22×C13#54611yescharacteristic
510C22×C13#54611yescharacteristic
511C22×C13#54811yescharacteristic
512C22×C13#54811yescharacteristic
513C22×C13#55111yescharacteristic
514C22×C13#55211yescharacteristic
515C22×C13#55211yescharacteristic
516C22×C13#55311yescharacteristic
517C22×C13#55311yescharacteristic
518C22×C13#55311yescharacteristic
519C22×C13#55311yescharacteristic
520C22×C13#55611yescharacteristic
521C22×C13#55611yescharacteristic
522C22×C13#55611yescharacteristic
523C22×C13#55611yescharacteristic
524C22×C13#55911yescharacteristic
525C4×C13—24no—
526C4×C13—42no—
527C4×C13—42no—
528C4×C13—42no—
529C4×C13—42no—
530C4×C13—81no—
531Dic13—24no—
532Dic13—24no—
533Dic13—24no—
534Dic13—42no—
535Dic13—42no—
536Dic13—42no—
537Dic13—42no—
538Dic13—81no—
539C25C22×D1311yescharacteristic
540C23×C4—131no—
541C23×C4—131no—
542C23×C4—131no—
543C23×C4—131no—
544C23×C4—131no—
545C23×C4—131no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4C22×D1311yescharacteristic
549C23×C4C22×D1311yescharacteristic
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1311yescharacteristic
553C23×C4C22×D1311yescharacteristic
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—134no—
558C2×C4⋊C4—134no—
559C2×C4⋊C4—262no—
560C2×C4⋊C4—262no—
561C2×C4⋊C4—262no—
562C2×C4⋊C4—262no—
563C2×C4⋊C4—262no—
564C2×C4⋊C4—262no—
565C2×C4⋊C4—262no—
566C2×C4⋊C4—262no—
567C2×C4⋊C4—262no—
568C2×C4⋊C4—521no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—134no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—262no—
580C2×C22⋊C4—262no—
581C2×C22⋊C4—262no—
582C2×C22⋊C4—262no—
583C2×C22⋊C4—262no—
584C2×C22⋊C4—262no—
585C2×C22⋊C4—262no—
586C2×C22⋊C4—262no—
587C2×C22⋊C4—262no—
588C2×C22⋊C4—521no—
589C2×C22⋊C4C4×D1314yes—
590C2×C42—134no—
591C2×C42—134no—
592C2×C42—262no—
593C2×C42—262no—
594C2×C42—262no—
595C2×C42—262no—
596C2×C42—262no—
597C2×C42—262no—
598C2×C42—262no—
599C2×C42—521no—
600C2×C42—521no—
601C2×C42—521no—
602C2×C42—521no—
603C2×C42—521no—
604C2×C42—521no—
605#95—22no—
606#95—22no—
607#95—41no—
608#95—134no—
609#95—134no—
610#95—262no—
611#95—262no—
612#95—262no—
613#95—262no—
614#95—262no—
615#95—262no—
616#95—262no—
617#95—262no—
618#95—262no—
619#95—262no—
620#95—262no—
621#95—262no—
622#95—262no—
623C2×C13—82no—
624C2×C13#229311yescharacteristic
625C2×C13C4×#12111yescharacteristic
626C2×C13#232211yescharacteristic
627C2×C13#234711yescharacteristic
628C2×C13#235211yescharacteristic
629C2×C13#236711yescharacteristic
630C2×C13#237311yescharacteristic
631C2×C13#254311yescharacteristic
632C2×C13#254511yescharacteristic
633C2×C13#255811yescharacteristic
634C2×C13#256011yescharacteristic
635C2×C13#259411yescharacteristic
636C2×C13#259611yescharacteristic
637C2×C13#260211yescharacteristic
638C2×C13#260411yescharacteristic
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×C4×D1312yes—
654C24C23×D1311yescharacteristic
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—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—132no—
691C22×C4—132no—
692C22×C4—132no—
693C22×C4—132no—
694C22×C4—132no—
695C22×C4—132no—
696C22×C4—132no—
697C22×C4—132no—
698C22×C4—132no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—132no—
702C22×C4—132no—
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—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4C2×C4×D1312yes—
747C22×C4C2×C4×D1312yes—
748C22×C4D4×D1312yes—
749C22×C4D4×D1312yes—
750C22×C4#612912yes—
751C22×C4#612912yes—
752C22×C4#612912yes—
753C4⋊C4—28no—
754C4⋊C4—268no—
755C4⋊C4—268no—
756C4⋊C4—524no—
757C4⋊C4—524no—
758C22⋊C4—28no—
759C22⋊C4—44no—
760C22⋊C4—44no—
761C22⋊C4—268no—
762C22⋊C4—268no—
763C22⋊C4—524no—
764C22⋊C4—524no—
765C42—268no—
766C42—524no—
767C42—524no—
768C42—524no—
769C42—524no—
770C13#1407711yescharacteristic, complemented, Sylow
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
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—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23C22×C4×D1311yescharacteristic
807C23C2×D4×D1311yescharacteristic
808C23C2×D4×D1311yescharacteristic
809C23C2×#612911yescharacteristic
810C23C2×#612911yescharacteristic
811C23C2×#612911yescharacteristic
812C23#8825111yescharacteristic
813C23#8825111yescharacteristic
814C23#8825411yescharacteristic
815C23#41×D1311yescharacteristic
816C23#41×D1311yescharacteristic
817C23#41×D1311yescharacteristic
818C23#41×D1311yescharacteristic
819C23#41×D1311yescharacteristic
820C23#8825711yescharacteristic
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—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
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—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—134no—
863C2×C4—134no—
864C2×C4—134no—
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—262no—
882C2×C4—262no—
883C2×C4—262no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—262no—
894C2×C4—262no—
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—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4#8813514yes—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22C2×#8813511yescharacteristic
935C22#1171920911yescharacteristic
936C22D13×#11711yescharacteristic
937C22C4×#612911yescharacteristic
938C22C4×#612911yescharacteristic
939C22C4×D4×D1311yescharacteristic
940C22#1171925111yescharacteristic
941C22#1171929111yescharacteristic
942C22#1171929211yescharacteristic
943C22#1171929411yescharacteristic
944C22#1171930111yescharacteristic
945C22#1171930111yescharacteristic
946C22#1171930311yescharacteristic
947C22#1171930611yescharacteristic
948C22D13×#12111yescharacteristic
949C22#1171931711yescharacteristic
950C22#1171931711yescharacteristic
951C22#1171931911yescharacteristic
952C22#1171933311yescharacteristic
953C22#1171933811yescharacteristic
954C22#1171934311yescharacteristic
955C22#1171934411yescharacteristic
956C22#1171934411yescharacteristic
957C22#1171934611yescharacteristic
958C22#1171935411yescharacteristic
959C22#1171935411yescharacteristic
960C22#1171936511yescharacteristic
961C22#1171936611yescharacteristic
962C22#1171936611yescharacteristic
963C22#1171937311yescharacteristic
964C22#1171937611yescharacteristic
965C22#1171937611yescharacteristic
966C22#1171940711yescharacteristic
967C22#1171941111yescharacteristic
968C22#1171941811yescharacteristic
969C4—24no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—81no—
975C4—264no—
976C4—264no—
977C4—264no—
978C4—522no—
979C4—522no—
980C4—522no—
981C4—522no—
982C4—1041no—
983C2—82no—
984C2#1311729611yescharacteristic
985C2#1311734611yescharacteristic
986C2#1311750311yescharacteristic
987C2#1311772611yescharacteristic
988C2#1311775811yescharacteristic
989C2#1311790611yescharacteristic
990C2#1311795111yescharacteristic
991C2#1311979911yescharacteristic
992C2#1311981111yescharacteristic
993C2#1311994511yescharacteristic
994C2#1311997311yescharacteristic
995C2#1312034511yescharacteristic
996C2#1312037311yescharacteristic
997C2#1312044111yescharacteristic
998C2#1312046911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#14077
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#11718308C2semidirect
5. C2×C4⋊C4×Dic13C2semidirect
6. #13113096C2semidirect
7. #13113086C2semidirect
11. #13113067C2semidirect
12. #13113067C2semidirect
13. #13113062C2semidirect
14. #95×Dic13C2semidirect
53. #11718606C4semidirect
770. C13#14077semidirect

Maximal subgroups

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

subgroupindex
C2×#117183082
C2×#117186062
C2×#117186122
C2×#117186052
C2×C4⋊C4×Dic132
#131130962
#131130862
#131130792
#131130732
#131130672
#131130622
#95×Dic132
C13×#14392
#1407713