Finite Group Databasebeta

← #15789342

Subgroups — #15789342

Order 3328.

1926 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88131C211yesmaximal, characteristic
2C2×#11718308C211yesmaximal, characteristic, complemented
3C2×#11718633C211yesmaximal, characteristic, complemented
4C2×#11718603C211yesmaximal, characteristic
5C2×#11718603C211yesmaximal, characteristic
6#13113100C211yesmaximal, characteristic, complemented
7#13113099C211yesmaximal, characteristic, complemented
8#13113094C211yesmaximal, characteristic, complemented
9#13113091C211yesmaximal, characteristic, complemented
10#13113081C211yesmaximal, characteristic
11#13113079C211yesmaximal, characteristic
12#13113079C211yesmaximal, characteristic
13#13113064C211yesmaximal, characteristic, complemented
14#13113064C211yesmaximal, characteristic, complemented
15C13×#1439C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C2×#88131—24no—
36C2×#88131—24no—
37C2×#88131—24no—
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54#11718633—24no—
55#11718603—24no—
56#11718603C418yescomplemented
57#11718308—24no—
58C25×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×Dic13—22no—
66C23×Dic13—22no—
67C23×Dic13—22no—
68C23×Dic13—22no—
69C23×Dic13C2×C414yes—
70C23×Dic13D414yes—
71C23×Dic13Q814yes—
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—41no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—41no—
88C2×C13×C22⋊C4—41no—
89C2×C13×C22⋊C4—41no—
90C2×C13×C22⋊C4—41no—
91C2×C13×C22⋊C4C2×C414yes—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—22no—
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—41no—
97C2×C22⋊Dic13—41no—
98C2×C22⋊Dic13—41no—
99C2×C22⋊Dic13—41no—
100C2×C22⋊Dic13C2×C414yes—
101C2×C4⋊Dic13—22no—
102C2×C4⋊Dic13—41no—
103C2×C4⋊Dic13—41no—
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101—22no—
110C2×#6101—22no—
111C2×#6101—22no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101—22no—
116C2×#6101—22no—
117C2×#6101—22no—
118C2×#6101—22no—
119C2×#6101—22no—
120C2×#6101—22no—
121C2×#6101—22no—
122C2×#6101—41no—
123C2×#6101—41no—
124C2×#6101—41no—
125C2×#6101—41no—
126C2×#6101C2×C414yes—
127C2×#6101C2×C414yes—
128C2×C4×Dic13—22no—
129C2×C4×Dic13—22no—
130C2×C4×Dic13—22no—
131C2×C4×Dic13—22no—
132C2×C4×Dic13D414yes—
133C2×C4×Dic13D414yes—
134#88131—232no—
135C13×#95—22no—
136C13×#95—41no—
137C13×#95—41no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—22no—
143#88071—41no—
144#88071—41no—
145#88071—41no—
146#88071—41no—
147#88071—41no—
148#88071—41no—
149#88071C2×C414yes—
150#88071C2×C414yes—
151#14264—131nomaximal, Sylow
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13C22×C412yes—
165C24×C13C2×D412yes—
166C24×C13C2×Q812yes—
167C24×C13C2411yescharacteristic
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×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13C22×C412yes—
207C22×C4×C13C22×C412yes—
208C22×C4×C13C2×D412yes—
209C22×C4×C13C2×D412yes—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—28no—
215C22×Dic13—28no—
216C22×Dic13—28no—
217C22×Dic13—28no—
218C22×Dic13—28no—
219C22×Dic13—28no—
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×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13—21no—
252C22×Dic13—21no—
253C22×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13C4⋊C4116yescomplemented
259C22×Dic13C22×C412yes—
260C22×Dic13C22×C412yes—
261C22×Dic13C22×C412yes—
262C22×Dic13C22×C412yes—
263C22×Dic13C2×D412yes—
264C22×Dic13C2×D412yes—
265C22×Dic13C2×D412yes—
266C22×Dic13C2×D412yes—
267C22×Dic13C2×D412yes—
268C22×Dic13C2×D412yes—
269C22×Dic13C2×Q812yes—
270C22×Dic13C2×Q812yes—
271C22×Dic13#4112yes—
272C22×Dic13#4112yes—
273C13×C4⋊C4—44no—
274C13×C22⋊C4—28no—
275C13×C22⋊C4—44no—
276C13×C22⋊C4—44no—
277C22⋊Dic13—28no—
278C22⋊Dic13—44no—
279C22⋊Dic13—44no—
280C4⋊Dic13—44no—
281#6101—28no—
282#6101—28no—
283#6101—28no—
284#6101—28no—
285#6101—44no—
286#6101—44no—
287#6101—44no—
288#6101—44no—
289C4×Dic13—28no—
290C4×Dic13—28no—
291C22×#117—131no—
292C2×#389—131no—
293C2×#389—131no—
294C2×#380—131no—
295C2×#380—131no—
296#1444—131no—
297#1444—131no—
298#1442—131no—
299#1442—131no—
300#1439—131no—
301#1439—131no—
302#1439—131no—
303#1439D1311yescharacteristic
304C4⋊#95—131no—
305C4⋊#95—131no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—41no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13—41no—
339C23×C13—41no—
340C23×C13C2×C4⋊C414yes—
341C23×C13C23×C411yescharacteristic
342C23×C13C22×D411yescharacteristic
343C23×C13C22×D411yescharacteristic
344C23×C13C22×D411yescharacteristic
345C23×C13C22×Q811yescharacteristic
346C23×C13C2×#4111yescharacteristic
347C23×C13C2×#4111yescharacteristic
348C23×C13H(5,𝔽2)11yescharacteristic
349C23×C13H(5,𝔽2)11yescharacteristic
350C23×C13H(5,𝔽2)11yescharacteristic
351C23×C13H(5,𝔽2)11yescharacteristic
352C23×C132−1+411yescharacteristic
353C23×C132−1+411yescharacteristic
354C23×C132−1+411yescharacteristic
355C23×C132−1+411yescharacteristic
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—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×C13—41no—
379C2×C4×C13—41no—
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×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—232no—
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—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—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×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13—41no—
445C2×Dic13—41no—
446C2×Dic13—41no—
447C2×Dic13C2×C4⋊C414yes—
448C2×Dic13C2×C4⋊C414yes—
449C2×Dic13C4×D414yes—
450C2×Dic13C4×D414yes—
451C2×Dic13#12014yes—
452C2×Dic13C22⋊Q814yes—
453C2×Dic13C22⋊Q814yes—
454C2×Dic13#12314yes—
455C24×C4—131no—
456C2×#117—264no—
457C2×#117—264no—
458C2×#117—264no—
459C22×C4⋊C4—131no—
460C22×C4⋊C4—131no—
461C22×C4⋊C4—131no—
462C22×C4⋊C4—131no—
463C22×C4⋊C4—131no—
464C22×C4⋊C4—131no—
465C22×C4⋊C4—131no—
466C22×C4⋊C4—131no—
467C22×C4⋊C4—131no—
468C22×C4⋊C4C2×D1311yescharacteristic
469C22×C22⋊C4—131no—
470C22×C22⋊C4—131no—
471C22×C22⋊C4—131no—
472C22×C22⋊C4C2×D1311yescharacteristic
473C22×C22⋊C4C2×D1311yescharacteristic
474C22×C22⋊C4C2×D1311yescharacteristic
475C22×C42—131no—
476C22×C42—131no—
477#389—264no—
478#389—264no—
479#380—138no—
480#380—264no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95—131no—
490C2×#95—131no—
491C2×#95—131no—
492C2×#95—131no—
493C2×#95—131no—
494C2×#95C2×D1311yescharacteristic
495C2×#95C2×D1311yescharacteristic
496C2×#95C2×D1311yescharacteristic
497C22×C13—24no—
498C22×C13—24no—
499C22×C13—24no—
500C22×C13—42no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13—42no—
512C22×C13C22×C4⋊C411yescharacteristic
513C22×C13C2×C4×D411yescharacteristic
514C22×C13C2×C4×D411yescharacteristic
515C22×C13#51811yescharacteristic
516C22×C13#51911yescharacteristic
517C22×C13#52011yescharacteristic
518C22×C13#52011yescharacteristic
519C22×C13C2×#12011yescharacteristic
520C22×C13C2×C22⋊Q811yescharacteristic
521C22×C13C2×C22⋊Q811yescharacteristic
522C22×C13C2×#12311yescharacteristic
523C22×C13#53511yescharacteristic
524C22×C13#53511yescharacteristic
525C22×C13#53511yescharacteristic
526C22×C13#53611yescharacteristic
527C22×C13#53611yescharacteristic
528C22×C13#53611yescharacteristic
529C22×C13#53711yescharacteristic
530C22×C13#53711yescharacteristic
531C22×C13#53711yescharacteristic
532C22×C13#53711yescharacteristic
533C22×C13#53711yescharacteristic
534C22×C13#53711yescharacteristic
535C22×C13#54011yescharacteristic
536C22×C13#54011yescharacteristic
537C22×C13#54111yescharacteristic
538C22×C13#54111yescharacteristic
539C22×C13#54211yescharacteristic
540C22×C13#54211yescharacteristic
541C22×C13#54211yescharacteristic
542C22×C13#54211yescharacteristic
543C22×C13#54411yescharacteristic
544C22×C13#54411yescharacteristic
545C22×C13#54411yescharacteristic
546C22×C13#54411yescharacteristic
547C4×C13—42no—
548C4×C13—42no—
549C4×C13—42no—
550C4×C13—42no—
551C4×C13—81no—
552C4×C13—81no—
553Dic13—24no—
554Dic13—42no—
555Dic13—42no—
556Dic13—42no—
557Dic13—42no—
558Dic13—81no—
559Dic13—81no—
560Dic13#38518yes—
561C25C22×D1311yescharacteristic
562C23×C4—131no—
563C23×C4—134no—
564C23×C4—134no—
565C23×C4—134no—
566C23×C4—131no—
567C23×C4—131no—
568C23×C4—131no—
569C23×C4—131no—
570C23×C4—131no—
571C23×C4—131no—
572C23×C4—131no—
573C23×C4—262no—
574C23×C4—262no—
575C23×C4—262no—
576C23×C4—262no—
577C23×C4C22×D1311yescharacteristic
578C23×C4C22×D1311yescharacteristic
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582C23×C4C22×D1311yescharacteristic
583#117—2632no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—134no—
588C2×C4⋊C4—134no—
589C2×C4⋊C4—262no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C4⋊C4—262no—
597C2×C4⋊C4—262no—
598C2×C4⋊C4—262no—
599C2×C4⋊C4—262no—
600C2×C4⋊C4—262no—
601C2×C4⋊C4—262no—
602C2×C4⋊C4—262no—
603C2×C4⋊C4—262no—
604C2×C4⋊C4—262no—
605C2×C4⋊C4—262no—
606C2×C4⋊C4—262no—
607C2×C4⋊C4—262no—
608C2×C4⋊C4—521no—
609C2×C4⋊C4—521no—
610C2×C4⋊C4—521no—
611C2×C4⋊C4—521no—
612C2×C4⋊C4—521no—
613C2×C4⋊C4—521no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—134no—
623C2×C22⋊C4—262no—
624C2×C22⋊C4—262no—
625C2×C22⋊C4—262no—
626C2×C22⋊C4—262no—
627C2×C22⋊C4—521no—
628C2×C22⋊C4—521no—
629C2×C22⋊C4—521no—
630C2×C22⋊C4—521no—
631C2×C22⋊C4C4×D1314yes—
632C2×C42—134no—
633C2×C42—134no—
634C2×C42—262no—
635C2×C42—262no—
636C2×C42—262no—
637C2×C42—262no—
638#95—22no—
639#95—41no—
640#95—41no—
641#95—134no—
642#95—134no—
643#95—262no—
644#95—262no—
645#95—262no—
646#95—262no—
647#95—262no—
648#95—521no—
649#95—521no—
650#95—521no—
651#95—521no—
652#95—521no—
653#95—521no—
654C2×C13—44no—
655C2×C13C2×#38511yescharacteristic
656C2×C13#231611yescharacteristic
657C2×C13#231711yescharacteristic
658C2×C13#232311yescharacteristic
659C2×C13#232311yescharacteristic
660C2×C13#232411yescharacteristic
661C2×C13#232411yescharacteristic
662C2×C13#261511yescharacteristic
663C2×C13#261611yescharacteristic
664C2×C13#262411yescharacteristic
665C2×C13#262511yescharacteristic
666C2×C13#262811yescharacteristic
667C2×C13#262811yescharacteristic
668C2×C13#262911yescharacteristic
669C2×C13#262911yescharacteristic
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24C2×C4×D1312yes—
683C24D4×D1312yes—
684C24Q8×D1312yes—
685C24C23×D1311yescharacteristic
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—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—132no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—132no—
728C22×C4—132no—
729C22×C4—132no—
730C22×C4—132no—
731C22×C4—1316no—
732C22×C4—132no—
733C22×C4—132no—
734C22×C4—132no—
735C22×C4—132no—
736C22×C4—132no—
737C22×C4—132no—
738C22×C4—132no—
739C22×C4—268no—
740C22×C4—268no—
741C22×C4—268no—
742C22×C4—268no—
743C22×C4—268no—
744C22×C4—268no—
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—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—261no—
763C22×C4—261no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—261no—
769C22×C4—261no—
770C22×C4—261no—
771C22×C4—261no—
772C22×C4—261no—
773C22×C4—261no—
774C22×C4—261no—
775C22×C4—261no—
776C22×C4—261no—
777C22×C4—261no—
778C22×C4—261no—
779C22×C4—261no—
780C22×C4—261no—
781C22×C4—261no—
782C22×C4—261no—
783C22×C4—261no—
784C22×C4—261no—
785C22×C4—261no—
786C22×C4—261no—
787C22×C4C2×C4×D1312yes—
788C22×C4C2×C4×D1312yes—
789C22×C4D4×D1312yes—
790C22×C4D4×D1312yes—
791C4⋊C4—44no—
792C4⋊C4—268no—
793C4⋊C4—268no—
794C4⋊C4—268no—
795C4⋊C4—268no—
796C4⋊C4—524no—
797C4⋊C4—524no—
798C4⋊C4—524no—
799C4⋊C4—524no—
800C4⋊C4—524no—
801C22⋊C4—28no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—268no—
805C22⋊C4—524no—
806C22⋊C4—524no—
807C42—268no—
808C42—268no—
809C13#1426411yescharacteristic, complemented, Sylow
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23C4⋊C4×D1314yes—
845C23C22×C4×D1311yescharacteristic
846C23C2×D4×D1311yescharacteristic
847C23C2×D4×D1311yescharacteristic
848C23C2×D4×D1311yescharacteristic
849C23#8825111yescharacteristic
850C23#8825111yescharacteristic
851C23#8825111yescharacteristic
852C23#8825111yescharacteristic
853C23C2×Q8×D1311yescharacteristic
854C23#41×D1311yescharacteristic
855C23#41×D1311yescharacteristic
856C23#8825711yescharacteristic
857C23#8825711yescharacteristic
858C23#8825711yescharacteristic
859C23#8825711yescharacteristic
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—41no—
873C2×C4—41no—
874C2×C4—41no—
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—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—134no—
903C2×C4—134no—
904C2×C4—134no—
905C2×C4—134no—
906C2×C4—134no—
907C2×C4—134no—
908C2×C4—134no—
909C2×C4—134no—
910C2×C4—2632no—
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—262no—
921C2×C4—262no—
922C2×C4—262no—
923C2×C4—262no—
924C2×C4—262no—
925C2×C4—262no—
926C2×C4—262no—
927C2×C4—262no—
928C2×C4—262no—
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×C4—521no—
938C2×C4—521no—
939C2×C4—521no—
940C2×C4—521no—
941C2×C4—521no—
942C2×C4—521no—
943C2×C4—521no—
944C2×C4—521no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
949C2×C4—521no—
950C2×C4—521no—
951C2×C4—521no—
952C2×C4—521no—
953C2×C4—521no—
954C2×C4—521no—
955C2×C4—521no—
956C2×C4—521no—
957C2×C4—521no—
958C2×C4—521no—
959C22—24no—
960C22—24no—
961C22—24no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22#1171919111yescharacteristic
975C22C2×C4⋊C4×D1311yescharacteristic
976C22#1171922111yescharacteristic
977C22C4×D4×D1311yescharacteristic
978C22C4×D4×D1311yescharacteristic
979C22#1171925111yescharacteristic
980C22#1171925111yescharacteristic
981C22D13×#12011yescharacteristic
982C22#1171929711yescharacteristic
983C22#1171929711yescharacteristic
984C22#1171930211yescharacteristic
985C22#1171930211yescharacteristic
986C22#1171930211yescharacteristic
987C22#1171930211yescharacteristic
988C22#1171931311yescharacteristic
989C22#1171931311yescharacteristic
990C22#1171932011yescharacteristic
991C22#1171932011yescharacteristic
992C22#1171932811yescharacteristic
993C22#1171932811yescharacteristic
994C22#1171932811yescharacteristic
995C22#1171932811yescharacteristic
996C22D13×C22⋊Q811yescharacteristic
997C22D13×C22⋊Q811yescharacteristic
998C22#1171935311yescharacteristic
999C22#1171935311yescharacteristic
1000C22D13×#12311yescharacteristic
1001C22#1171936711yescharacteristic
1002C22#1171936711yescharacteristic
1003C22#1171937411yescharacteristic
1004C22#1171937411yescharacteristic
1005C22#1171938011yescharacteristic
1006C22#1171940611yescharacteristic
1007C22#1171940611yescharacteristic
1008C22#1171942011yescharacteristic
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—81no—
1014C4—81no—
1015C4—138no—
1016C4—264no—
1017C4—522no—
1018C4—522no—
1019C4—522no—
1020C4—522no—
1021C4—1041no—
1022C4—1041no—
1023C2—44no—
1024C2D13×#38511yescharacteristic
1025C2#1311745311yescharacteristic
1026C2#1311745511yescharacteristic
1027C2#1311751111yescharacteristic
1028C2#1311751511yescharacteristic
1029C2#1311752211yescharacteristic
1030C2#1311752611yescharacteristic
1031C2#1312055911yescharacteristic
1032C2#1312056411yescharacteristic
1033C2#1312062411yescharacteristic
1034C2#1312063211yescharacteristic
1035C2#1312065611yescharacteristic
1036C2#1312066211yescharacteristic
1037C2#1312066511yescharacteristic
1038C2#1312066511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#14264
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#11718308C2semidirect
3. C2×#11718633C2semidirect
6. #13113100C2semidirect
7. #13113099C2semidirect
8. #13113094C2semidirect
9. #13113091C2semidirect
13. #13113064C2semidirect
14. #13113064C2semidirect
56. #11718603C4semidirect
258. C22×Dic13C4⋊C4semidirect
809. C13#14264semidirect

Maximal subgroups

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

subgroupindex
C22×#881312
C2×#117183082
C2×#117186332
C2×#117186032
#131131002
#131130992
#131130942
#131130912
#131130812
#131130792
#131130642
C13×#14392
#1426413