Finite Group Databasebeta

← #15784504

Subgroups — #15784504

Order 3328.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718601C211yesmaximal, characteristic
2C2×#11718330C211yesmaximal, characteristic
3C2×C4×#6101C211yesmaximal, characteristic, complemented
4C2×C4×#6103C211yesmaximal, characteristic
5C2×#11718327C211yesmaximal, characteristic
6#13113074C211yesmaximal, characteristic
7#13113072C211yesmaximal, characteristic
8#13113069C211yesmaximal, characteristic, complemented
9#13113067C211yesmaximal, characteristic, complemented
10#13113062C211yesmaximal, characteristic, complemented
11#13113061C211yesmaximal, characteristic, complemented
12#13113057C211yesmaximal, characteristic
13C4×#88071C211yesmaximal, characteristic, complemented
14#95×Dic13C211yesmaximal, characteristic, complemented
15C4×C13×#95C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
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×C13×#95C2211yescharacteristic
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#11718601C418yescomplemented
52C4×#6103—24no—
53C4×#6101—24no—
54#11718330C418yescomplemented
55#11718327C418yescomplemented
56C24×D13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C22×C4×D13—22no—
72C22×C4×D13—22no—
73C22×C4×D13—22no—
74C22×C4×D13—22no—
75C22×C4×D13—41no—
76C22×C4×D13—41no—
77C22×C4×D13C2×C414yes—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×C42×C13—22no—
81C2×C42×C13—22no—
82C2×C42×C13—41no—
83C2×C42×C13—41no—
84C2×C42×C13—41no—
85C2×C42×C13—41no—
86C2×C42×C13C2×C414yescomplemented
87C2×#6103—22no—
88C2×#6103—22no—
89C2×#6103—22no—
90C2×#6103—22no—
91C2×#6103—22no—
92C2×#6103—22no—
93C2×#6103—41no—
94C2×#6103—41no—
95C2×#6103—41no—
96C2×#6103—41no—
97C2×#6103C2×C414yes—
98C2×#6103C2×C414yes—
99C2×#6103C2×C414yes—
100C2×#6103C2×C414yes—
101C2×#6103C2×C414yes—
102C2×#6103C2×C414yes—
103C2×#6103C2×C414yes—
104C2×#6103C2×C414yes—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101C2×C414yescomplemented
110C2×#6101C2×C414yescomplemented
111C2×C4×Dic13—22no—
112C2×C4×Dic13—22no—
113C2×C4×Dic13—22no—
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—41no—
118C2×C4×Dic13—41no—
119C2×C4×Dic13—41no—
120C2×C4×Dic13—41no—
121C2×C4×Dic13—41no—
122C2×C4×Dic13—41no—
123C2×C4×Dic13C2×C414yes—
124C2×C4×Dic13C2×C414yes—
125C2×C4×Dic13C2×C414yescomplemented
126C13×#95—22no—
127C13×#95—22no—
128C13×#95C2×C414yes—
129C13×#95C2×C414yescomplemented
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—41no—
138#88071—41no—
139#88071C2×C414yes—
140#88071C2×C414yescomplemented
141#88071C2×C414yescomplemented
142#88071C2×C414yescomplemented
143#88071D414yes—
144#13822—131nomaximal, Sylow
145C24×C13C2411yescharacteristic
146C23×D13—21no—
147C23×D13—21no—
148C23×D13—21no—
149C23×D13—21no—
150C23×D13—21no—
151C23×D13—21no—
152C23×D13—21no—
153C23×D13—21no—
154C23×D13—21no—
155C23×D13—21no—
156C23×D13—21no—
157C23×D13—21no—
158C23×D13C22×C412yes—
159C23×D13C22×C412yes—
160C23×D13C22×C412yes—
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×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C22×C412yes—
197C22×C4×C13C22×C412yes—
198C22×C4×C13C22×C412yes—
199C22×C4×C13C22×C412yes—
200C22×C4×C13C22×C412yes—
201C22×C4×C13C22×C412yes—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C22×C412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13#4112yes—
206C22×C4×C13#4112yes—
207C22×C4×C13#4112yes—
208C22×C4×C13#4112yes—
209C22×C4×C13#4112yes—
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×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13C22×C412yes—
247C22×Dic13C22×C412yes—
248C22×Dic13C22×C412yes—
249C22×Dic13C22×C412yes—
250C22×Dic13C22×C412yes—
251C22×Dic13C22×C412yes—
252C22×Dic13C22×C412yes—
253C22×Dic13C22×C412yes—
254C22×Dic13C22×C412yes—
255C22×Dic13C2×D412yes—
256C22×Dic13C2×D412yes—
257C22×Dic13#4112yes—
258C22×Dic13#4112yes—
259C2×C4×D13—28no—
260C2×C4×D13—28no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—44no—
266C42×C13—44no—
267C42×C13—44no—
268C42×C13—44no—
269#6103—28no—
270#6103—28no—
271#6103—28no—
272#6103—44no—
273#6103—44no—
274#6103C42116yescomplemented
275#6101—28no—
276#6101—28no—
277C4×Dic13—28no—
278C4×Dic13—44no—
279C4×Dic13—44no—
280C4×Dic13—44no—
281C4×Dic13—44no—
282C2×#388—131no—
283C2×#388—131no—
284C2×C4×C4⋊C4—131no—
285C2×C4×C22⋊C4—131no—
286C2×C4×C22⋊C4—131no—
287#1437—131no—
288#1437—131no—
289#1436—131no—
290#1436—131no—
291#1434—131no—
292#1434—131no—
293C22⋊#95—131no—
294C4×#95—131no—
295C4×#95—131no—
296C4×#95D1311yescharacteristic, complemented
297C23×C13C23×C411yescharacteristic
298C23×C13C23×C411yescharacteristic
299C23×C13C23×C411yescharacteristic
300C23×C13C22×D411yescharacteristic
301C23×C13C2×#4111yescharacteristic
302C23×C13C2×#4111yescharacteristic
303C23×C13C2×#4111yescharacteristic
304C23×C13C2×#4111yescharacteristic
305C23×C13C2×#4111yescharacteristic
306C23×C13C2×#4111yescharacteristic
307C23×C13C2×#4111yescharacteristic
308C23×C13H(5,𝔽2)11yescharacteristic
309C23×C13H(5,𝔽2)11yescharacteristic
310C23×C13H(5,𝔽2)11yescharacteristic
311C23×C132−1+411yescharacteristic
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—41no—
331C22×D13—41no—
332C22×D13—41no—
333C22×D13—41no—
334C22×D13—41no—
335C22×D13—41no—
336C22×D13—41no—
337C22×D13—41no—
338C22×D13—41no—
339C22×D13—41no—
340C22×D13—41no—
341C22×D13—41no—
342C22×D13—41no—
343C22×D13—41no—
344C22×D13—41no—
345C22×D13—41no—
346C22×D13C2×C4214yes—
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—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13C2×C4214yes—
393C2×C4×C13#11714yes—
394C2×C4×C13#11714yes—
395C2×C4×C13C4×D414yes—
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—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
423C2×Dic13—22no—
424C2×Dic13—22no—
425C2×Dic13—22no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13—41no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13C2×C4214yes—
443C2×Dic13C4×D414yes—
444C2×Dic13C4×D414yes—
445C4×D13—416no—
446C24×C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C22⋊C4—131no—
450C22×C22⋊C4—131no—
451C22×C22⋊C4—131no—
452C22×C22⋊C4—131no—
453C22×C22⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C42—131no—
456C22×C42—131no—
457C22×C42—131no—
458C22×C42—131no—
459C22×C42—131no—
460C22×C42C2×D1311yescharacteristic
461C22×C42C2×D1311yescharacteristic
462C22×C42C2×D1311yescharacteristic
463#388—138no—
464#388—138no—
465C4×C4⋊C4—264no—
466C4×C22⋊C4—138no—
467C4×C22⋊C4—264no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95C2×D1311yescharacteristic
483C2×#95C2×D1311yescharacteristic
484C2×#95C2×D1311yescharacteristic
485C2×#95C2×D1311yescharacteristic
486C22×C13C22×C4211yescharacteristic
487C22×C13C2×#11711yescharacteristic
488C22×C13C2×#11711yescharacteristic
489C22×C13C2×C4×D411yescharacteristic
490C22×C13C2×C4×D411yescharacteristic
491C22×C13C2×C4×D411yescharacteristic
492C22×C13C4×#4111yescharacteristic
493C22×C13C4×#4111yescharacteristic
494C22×C13C4×#4111yescharacteristic
495C22×C13C4×#4111yescharacteristic
496C22×C13C4×#4111yescharacteristic
497C22×C13C4×#4111yescharacteristic
498C22×C13C4×#4111yescharacteristic
499C22×C13#51811yescharacteristic
500C22×C13#51811yescharacteristic
501C22×C13#51811yescharacteristic
502C22×C13#52011yescharacteristic
503C22×C13#52011yescharacteristic
504C22×C13#52011yescharacteristic
505C22×C13#54611yescharacteristic
506C22×C13#54611yescharacteristic
507C22×C13#54611yescharacteristic
508C22×C13#54811yescharacteristic
509C22×C13#55111yescharacteristic
510C22×C13#55111yescharacteristic
511C22×C13#55211yescharacteristic
512C22×C13#55311yescharacteristic
513C22×C13#55311yescharacteristic
514C22×C13#55311yescharacteristic
515C22×C13#55311yescharacteristic
516C22×C13#55311yescharacteristic
517C22×C13#55611yescharacteristic
518C22×C13#55611yescharacteristic
519C22×C13#55911yescharacteristic
520C22×C13#55911yescharacteristic
521C2×D13—24no—
522C2×D13—24no—
523C2×D13—24no—
524C2×D13—42no—
525C2×D13—42no—
526C2×D13—42no—
527C2×D13—42no—
528C2×D13—42no—
529C2×D13—42no—
530C2×D13—42no—
531C2×D13—42no—
532C2×D13—42no—
533C2×D13—42no—
534C2×D13—42no—
535C2×D13—42no—
536C4×C13—24no—
537C4×C13—24no—
538C4×C13—24no—
539C4×C13—24no—
540C4×C13—42no—
541C4×C13—42no—
542C4×C13—42no—
543Dic13—24no—
544Dic13—24no—
545Dic13—24no—
546Dic13—42no—
547Dic13—42no—
548Dic13—42no—
549Dic13—42no—
550C25—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—131no—
557C23×C4—131no—
558C23×C4—134no—
559C23×C4—262no—
560C23×C4—262no—
561C23×C4—262no—
562C23×C4—262no—
563C23×C4—521no—
564C23×C4—521no—
565C23×C4C22×D1311yescharacteristic
566C23×C4C22×D1311yescharacteristic
567C23×C4C22×D1311yescharacteristic
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C2×C4⋊C4—134no—
573C2×C4⋊C4—134no—
574C2×C4⋊C4—262no—
575C2×C4⋊C4—262no—
576C2×C4⋊C4—262no—
577C2×C4⋊C4—262no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—134no—
581C2×C22⋊C4—134no—
582C2×C22⋊C4—134no—
583C2×C22⋊C4—134no—
584C2×C22⋊C4—134no—
585C2×C22⋊C4—134no—
586C2×C22⋊C4—262no—
587C2×C22⋊C4—262no—
588C2×C22⋊C4—262no—
589C2×C22⋊C4—262no—
590C2×C22⋊C4—262no—
591C2×C22⋊C4—262no—
592C2×C22⋊C4—521no—
593C2×C22⋊C4—521no—
594C2×C22⋊C4—521no—
595C2×C22⋊C4—521no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—41no—
601C2×C42—41no—
602C2×C42—41no—
603C2×C42—41no—
604C2×C42—134no—
605C2×C42—134no—
606C2×C42—134no—
607C2×C42—262no—
608C2×C42—262no—
609C2×C42—262no—
610C2×C42—262no—
611C2×C42—262no—
612C2×C42—262no—
613C2×C42—521no—
614C2×C42—521no—
615C2×C42—521no—
616C2×C42—521no—
617C2×C42—521no—
618C2×C42—521no—
619C2×C42C4×D1314yescomplemented
620#95—22no—
621#95—22no—
622#95—134no—
623#95—134no—
624#95—134no—
625#95—134no—
626#95—134no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—521no—
635#95—521no—
636#95C4×D1314yes—
637#95C4×D1314yescomplemented
638C2×C13C4×#11711yescharacteristic
639C2×C13C42×D411yescharacteristic
640C2×C13#227511yescharacteristic
641C2×C13#234211yescharacteristic
642C2×C13#234711yescharacteristic
643C2×C13#235211yescharacteristic
644C2×C13#235711yescharacteristic
645C2×C13#236411yescharacteristic
646C2×C13#236411yescharacteristic
647C2×C13#236711yescharacteristic
648C2×C13#236711yescharacteristic
649C2×C13#237311yescharacteristic
650C2×C13#237311yescharacteristic
651C2×C13#237411yescharacteristic
652C2×C13#237411yescharacteristic
653D13—44no—
654C24—132no—
655C24—132no—
656C24—132no—
657C24—261no—
658C24—261no—
659C24—261no—
660C24—261no—
661C24—261no—
662C24—261no—
663C24—261no—
664C24—261no—
665C24—261no—
666C24—261no—
667C24—261no—
668C24—261no—
669C24C23×D1311yescharacteristic
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—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—132no—
705C22×C4—132no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
711C22×C4—132no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
715C22×C4—132no—
716C22×C4—132no—
717C22×C4—268no—
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×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—268no—
755C22×C4—524no—
756C22×C4—524no—
757C22×C4—524no—
758C22×C4—524no—
759C22×C4—524no—
760C22×C4C2×C4×D1312yes—
761C22×C4C2×C4×D1312yes—
762C22×C4C2×C4×D1312yes—
763C22×C4C2×C4×D1312yes—
764C22×C4C2×C4×D1312yes—
765C22×C4C2×C4×D1312yes—
766C22×C4C2×C4×D1312yes—
767C22×C4C2×C4×D1312yes—
768C22×C4C2×C4×D1312yes—
769C22×C4#612712yes—
770C22×C4#612712yes—
771C22×C4#612712yes—
772C22×C4#612712yes—
773C22×C4D4×D1312yes—
774C22×C4#613112yes—
775C4⋊C4—268no—
776C4⋊C4—268no—
777C22⋊C4—1316no—
778C22⋊C4—268no—
779C22⋊C4—268no—
780C22⋊C4—268no—
781C22⋊C4—524no—
782C22⋊C4—524no—
783C42—44no—
784C42—44no—
785C42—44no—
786C42—268no—
787C42—524no—
788C42—524no—
789C42—524no—
790C42—524no—
791C13#1382211yescharacteristic, complemented, Sylow
792C23—134no—
793C23—262no—
794C23—262no—
795C23—262no—
796C23—262no—
797C23—262no—
798C23—262no—
799C23—262no—
800C23—262no—
801C23—262no—
802C23—262no—
803C23—262no—
804C23—262no—
805C23—262no—
806C23—262no—
807C23—262no—
808C23—262no—
809C23—262no—
810C23—262no—
811C23—521no—
812C23—521no—
813C23—521no—
814C23—521no—
815C23—521no—
816C23—521no—
817C23—521no—
818C23—521no—
819C23—521no—
820C23—521no—
821C23—521no—
822C23—521no—
823C23—521no—
824C23—521no—
825C23—521no—
826C23—521no—
827C23C22×C4×D1311yescharacteristic
828C23C22×C4×D1311yescharacteristic
829C23C22×C4×D1311yescharacteristic
830C23C2×#612711yescharacteristic
831C23C2×#612711yescharacteristic
832C23C2×#612711yescharacteristic
833C23C2×#612711yescharacteristic
834C23C2×D4×D1311yescharacteristic
835C23#8825111yescharacteristic
836C23#8825111yescharacteristic
837C23C2×#613111yescharacteristic
838C23#41×D1311yescharacteristic
839C23#41×D1311yescharacteristic
840C23#8825611yescharacteristic
841C23#8825711yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—134no—
888C2×C4—134no—
889C2×C4—134no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—262no—
894C2×C4—262no—
895C2×C4—262no—
896C2×C4—262no—
897C2×C4—262no—
898C2×C4—262no—
899C2×C4—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—262no—
905C2×C4—262no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—262no—
909C2×C4—262no—
910C2×C4—262no—
911C2×C4—262no—
912C2×C4—262no—
913C2×C4—262no—
914C2×C4—262no—
915C2×C4—262no—
916C2×C4—262no—
917C2×C4—262no—
918C2×C4—262no—
919C2×C4—262no—
920C2×C4—5216no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4C42×D1314yes—
938C2×C4#8812614yes—
939C2×C4#8812614yes—
940C2×C4#8814714yes—
941C22—264no—
942C22—264no—
943C22—264no—
944C22—522no—
945C22—522no—
946C22—522no—
947C22—522no—
948C22—522no—
949C22—522no—
950C22—522no—
951C22—522no—
952C22—522no—
953C22—522no—
954C22—522no—
955C22—522no—
956C22C2×C42×D1311yescharacteristic
957C22C2×#8812611yescharacteristic
958C22C2×#8812611yescharacteristic
959C22C4×#612711yescharacteristic
960C22C4×#612711yescharacteristic
961C22C4×#612711yescharacteristic
962C22C4×#612711yescharacteristic
963C22#1171919111yescharacteristic
964C22#1171919511yescharacteristic
965C22#1171919511yescharacteristic
966C22C2×#8814711yescharacteristic
967C22#1171921911yescharacteristic
968C22#1171921911yescharacteristic
969C22#1171922711yescharacteristic
970C22#1171922811yescharacteristic
971C22#1171923211yescharacteristic
972C22#1171923511yescharacteristic
973C22#1171923611yescharacteristic
974C22#1171923811yescharacteristic
975C22#1171924511yescharacteristic
976C22C4×D4×D1311yescharacteristic
977C22C4×D4×D1311yescharacteristic
978C22#1171925011yescharacteristic
979C22#1171925011yescharacteristic
980C22#1171925111yescharacteristic
981C22#1171925111yescharacteristic
982C22#1171925511yescharacteristic
983C22#1171925711yescharacteristic
984C22#1171926111yescharacteristic
985C22#1171926311yescharacteristic
986C22#1171926411yescharacteristic
987C22C4×#613111yescharacteristic
988C22C4×#613111yescharacteristic
989C22#1171928911yescharacteristic
990C22#1171929011yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—264no—
999C4—264no—
1000C4—264no—
1001C4—522no—
1002C4—522no—
1003C4—522no—
1004C4—522no—
1005C2—524no—
1006C2C4×#8812611yescharacteristic
1007C2C4×#8814711yescharacteristic
1008C2#1311719511yescharacteristic
1009C2#1311767911yescharacteristic
1010C2#1311772511yescharacteristic
1011C2#1311775911yescharacteristic
1012C2#1311780511yescharacteristic
1013C2#1311788311yescharacteristic
1014C2#1311788711yescharacteristic
1015C2#1311790511yescharacteristic
1016C2#1311790811yescharacteristic
1017C2#1311795011yescharacteristic
1018C2#1311795611yescharacteristic
1019C2#1311796511yescharacteristic
1020C2#1311796711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC4×C13×#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4×#95D13
hypocenterC13#13822
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
3. C2×C4×#6101C2semidirect
8. #13113069C2semidirect
9. #13113067C2semidirect
10. #13113062C2semidirect
11. #13113061C2semidirect
13. C4×#88071C2semidirect
14. #95×Dic13C2semidirect
15. C4×C13×#95C2semidirect
51. #11718601C4semidirect
54. #11718330C4semidirect
55. #11718327C4semidirect
86. C2×C42×C13C2×C4semidirect
109. C2×#6101C2×C4semidirect
110. C2×#6101C2×C4semidirect
125. C2×C4×Dic13C2×C4semidirect
129. C13×#95C2×C4semidirect
140. #88071C2×C4semidirect
141. #88071C2×C4semidirect
142. #88071C2×C4semidirect
274. #6103C42semidirect
296. C4×#95D13semidirect
619. C2×C42C4×D13semidirect
637. #95C4×D13semidirect
791. C13#13822semidirect

Maximal subgroups

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

subgroupindex
C2×#117186012
C2×#117183302
C2×C4×#61012
C2×C4×#61032
C2×#117183272
#131130742
#131130722
#131130692
#131130672
#131130622
#131130612
#131130572
C4×#880712
#95×Dic132
C4×C13×#952
#1382213