Finite Group Databasebeta

← #15785568

Subgroups — #15785568

Order 3328.

2006 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×C22⋊C4×Dic13C211yesmaximal, characteristic
6#13113081C211yesmaximal, characteristic
7#13113079C211yesmaximal, characteristic
8#13113079C211yesmaximal, characteristic
9#13113065C211yesmaximal, characteristic, complemented
10#13113064C211yesmaximal, characteristic, complemented
11#13113064C211yesmaximal, characteristic, complemented
12#13113064C211yesmaximal, characteristic, complemented
13#13113061C211yesmaximal, characteristic, complemented
14#13113060C211yesmaximal, 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×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C2×#88131—24no—
36C2×#88131—24no—
37C2×#88131C418yescomplemented
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—
56C22⋊C4×Dic13—24no—
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—22no—
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—22no—
88C2×C13×C22⋊C4—22no—
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—22no—
97C2×C22⋊Dic13—22no—
98C2×C22⋊Dic13—41no—
99C2×C22⋊Dic13—41no—
100C2×C22⋊Dic13C2×C414yes—
101C2×C4⋊Dic13—22no—
102C2×C4⋊Dic13—22no—
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—41no—
117C2×#6101—41no—
118C2×#6101C2×C414yes—
119C2×#6101C2×C414yes—
120C2×#6101D414yes—
121C2×#6101D414yes—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—22no—
124C2×C4×Dic13—22no—
125C2×C4×Dic13—22no—
126C2×C4×Dic13—22no—
127C2×C4×Dic13—22no—
128C2×C4×Dic13—22no—
129C2×C4×Dic13—22no—
130C2×C4×Dic13—22no—
131C2×C4×Dic13—22no—
132C2×C4×Dic13C2×C414yes—
133C2×C4×Dic13C2×C414yes—
134#88131—232no—
135C13×#95—22no—
136C13×#95—22no—
137C13×#95—41no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—22no—
143#88071—22no—
144#88071—22no—
145#88071—22no—
146#88071—22no—
147#88071—22no—
148#88071—41no—
149#88071—41no—
150#88071—41no—
151#13951—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×C13C22×C412yes—
205C22×C4×C13C22×C412yes—
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×D412yes—
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—28no—
219C22×Dic13—28no—
220C22×Dic13—28no—
221C22×Dic13—28no—
222C22×Dic13—28no—
223C22×Dic13—28no—
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×Dic13C4⋊C4116yescomplemented
257C22×Dic13C22×C412yes—
258C22×Dic13C22×C412yes—
259C22×Dic13C22×C412yes—
260C22×Dic13C22×C412yes—
261C22×Dic13C2×D412yes—
262C22×Dic13C2×D412yes—
263C22×Dic13C2×D412yes—
264C22×Dic13C2×D412yes—
265C22×Dic13C2×D412yes—
266C22×Dic13C2×D412yes—
267C22×Dic13C2×Q812yes—
268C22×Dic13C2×Q812yes—
269C22×Dic13#4112yes—
270C22×Dic13#4112yes—
271C22×Dic13#4112yes—
272C22×Dic13#4112yes—
273C13×C4⋊C4—44no—
274C13×C22⋊C4—28no—
275C13×C22⋊C4—28no—
276C13×C22⋊C4—44no—
277C22⋊Dic13—28no—
278C22⋊Dic13—28no—
279C22⋊Dic13—44no—
280C4⋊Dic13—44no—
281#6101—28no—
282#6101—44no—
283#6101—44no—
284#6101—44no—
285#6101—44no—
286#6101C22⋊C4116yescomplemented
287C4×Dic13—28no—
288C4×Dic13—28no—
289C4×Dic13—44no—
290C4×Dic13—44no—
291C22×#117—131no—
292C2×#389—131no—
293C2×#389—131no—
294C2×#380—131no—
295C2×C4×C22⋊C4—131no—
296#1439—131no—
297#1439—131no—
298#1439—131no—
299#1439D1311yescharacteristic
300C4⋊#95—131no—
301C4⋊#95—131no—
302C4⋊#95—131no—
303C4⋊#95—131no—
304#1434—131no—
305#1434—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×C13C2×#4111yescharacteristic
349C23×C13C2×#4111yescharacteristic
350C23×C13C2×#4111yescharacteristic
351C23×C13C2×#4111yescharacteristic
352C23×C13H(5,𝔽2)11yescharacteristic
353C23×C13H(5,𝔽2)11yescharacteristic
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—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
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×C13C2×C22⋊C414yes—
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—232no—
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—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×Dic13C2×C22⋊C414yes—
447C2×Dic13C2×C22⋊C414yes—
448C2×Dic13C2×C4⋊C414yes—
449C2×Dic13C2×C4⋊C414yes—
450C2×Dic13#11714yes—
451C2×Dic13#12114yes—
452C2×Dic13#12114yes—
453C2×Dic13C22⋊Q814yes—
454C2×Dic13C22⋊Q814yes—
455C24×C4—131no—
456C2×#117—138no—
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⋊C4C2×D1311yescharacteristic
467C22×C22⋊C4—131no—
468C22×C22⋊C4—131no—
469C22×C22⋊C4—131no—
470C22×C22⋊C4C2×D1311yescharacteristic
471C22×C22⋊C4C2×D1311yescharacteristic
472C22×C22⋊C4C2×D1311yescharacteristic
473C22×C42—131no—
474C22×C42—131no—
475C22×C42—131no—
476C22×C42—131no—
477#389—264no—
478#389—264no—
479#380—264no—
480C4×C22⋊C4—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×C22⋊C411yescharacteristic
513C22×C13C22×C4⋊C411yescharacteristic
514C22×C13C2×#11711yescharacteristic
515C22×C13C4×#4111yescharacteristic
516C22×C13C4×#4111yescharacteristic
517C22×C13#52011yescharacteristic
518C22×C13#52011yescharacteristic
519C22×C13C2×#12111yescharacteristic
520C22×C13C2×#12111yescharacteristic
521C22×C13C2×C22⋊Q811yescharacteristic
522C22×C13C2×C22⋊Q811yescharacteristic
523C22×C13#52511yescharacteristic
524C22×C13#52511yescharacteristic
525C22×C13#53311yescharacteristic
526C22×C13#53311yescharacteristic
527C22×C13#53511yescharacteristic
528C22×C13#53611yescharacteristic
529C22×C13#54411yescharacteristic
530C22×C13#54411yescharacteristic
531C22×C13#54611yescharacteristic
532C22×C13#54611yescharacteristic
533C22×C13#54711yescharacteristic
534C22×C13#54711yescharacteristic
535C22×C13#54811yescharacteristic
536C22×C13#54811yescharacteristic
537C22×C13#55011yescharacteristic
538C22×C13#55011yescharacteristic
539C22×C13#55211yescharacteristic
540C22×C13#55211yescharacteristic
541C22×C13#55311yescharacteristic
542C22×C13#55311yescharacteristic
543C22×C13#55511yescharacteristic
544C22×C13#55511yescharacteristic
545C22×C13#55611yescharacteristic
546C22×C13#55611yescharacteristic
547C4×C13—24no—
548C4×C13—42no—
549C4×C13—42no—
550C4×C13—42no—
551C4×C13—81no—
552C4×C13—81no—
553Dic13—24no—
554Dic13—24no—
555Dic13—42no—
556Dic13—42no—
557Dic13—42no—
558Dic13—81no—
559Dic13—81no—
560Dic13#38018yes—
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—22no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—134no—
588C2×C4⋊C4—134no—
589C2×C4⋊C4—134no—
590C2×C4⋊C4—134no—
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—521no—
606C2×C4⋊C4—521no—
607C2×C4⋊C4—521no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—134no—
617C2×C22⋊C4—262no—
618C2×C22⋊C4—262no—
619C2×C22⋊C4—262no—
620C2×C22⋊C4—262no—
621C2×C22⋊C4—262no—
622C2×C22⋊C4—262no—
623C2×C22⋊C4—521no—
624C2×C22⋊C4—521no—
625C2×C22⋊C4C4×D1314yes—
626C2×C42—134no—
627C2×C42—134no—
628C2×C42—262no—
629C2×C42—262no—
630C2×C42—262no—
631C2×C42—262no—
632C2×C42—262no—
633C2×C42—262no—
634C2×C42—262no—
635C2×C42—262no—
636C2×C42—262no—
637C2×C42—262no—
638#95—22no—
639#95—22no—
640#95—41no—
641#95—262no—
642#95—262no—
643#95—262no—
644#95—262no—
645#95—262no—
646#95—262no—
647#95—262no—
648#95—262no—
649#95—262no—
650#95—262no—
651#95—521no—
652#95—521no—
653#95—521no—
654C2×C13—44no—
655C2×C13C2×#38011yescharacteristic
656C2×C13#229611yescharacteristic
657C2×C13#231711yescharacteristic
658C2×C13#233911yescharacteristic
659C2×C13#234111yescharacteristic
660C2×C13#234611yescharacteristic
661C2×C13#234711yescharacteristic
662C2×C13#241411yescharacteristic
663C2×C13#241411yescharacteristic
664C2×C13#241511yescharacteristic
665C2×C13#241511yescharacteristic
666C2×C13#243911yescharacteristic
667C2×C13#243911yescharacteristic
668C2×C13#244111yescharacteristic
669C2×C13#244111yescharacteristic
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—132no—
723C22×C4—132no—
724C22×C4—132no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—132no—
728C22×C4—132no—
729C22×C4—1316no—
730C22×C4—132no—
731C22×C4—132no—
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×C4C2×C4×D1312yes—
786C22×C4C2×C4×D1312yes—
787C22×C4D4×D1312yes—
788C22×C4D4×D1312yes—
789C22×C4#612912yes—
790C22×C4#612912yes—
791C4⋊C4—44no—
792C4⋊C4—1316no—
793C4⋊C4—268no—
794C4⋊C4—524no—
795C4⋊C4—524no—
796C4⋊C4—524no—
797C4⋊C4—524no—
798C4⋊C4—524no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—268no—
803C22⋊C4—268no—
804C22⋊C4—524no—
805C42—268no—
806C42—268no—
807C42—524no—
808C42—524no—
809C13#1395111yescharacteristic, 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
849C23C2×#612911yescharacteristic
850C23C2×#612911yescharacteristic
851C23#8825111yescharacteristic
852C23#8825111yescharacteristic
853C23C2×Q8×D1311yescharacteristic
854C23#41×D1311yescharacteristic
855C23#41×D1311yescharacteristic
856C23#41×D1311yescharacteristic
857C23#41×D1311yescharacteristic
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—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—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—134no—
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—262no—
930C2×C4—262no—
931C2×C4—262no—
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×C4C22⋊C4×D1314yes—
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—
974C22C2×C22⋊C4×D1311yescharacteristic
975C22C2×C4⋊C4×D1311yescharacteristic
976C22D13×#11711yescharacteristic
977C22C4×#612911yescharacteristic
978C22C4×#612911yescharacteristic
979C22#1171925111yescharacteristic
980C22#1171925111yescharacteristic
981C22#1171929111yescharacteristic
982C22#1171929611yescharacteristic
983C22#1171929711yescharacteristic
984C22#1171930311yescharacteristic
985C22#1171930411yescharacteristic
986C22#1171930611yescharacteristic
987C22D13×#12111yescharacteristic
988C22D13×#12111yescharacteristic
989C22#1171931511yescharacteristic
990C22#1171931611yescharacteristic
991C22#1171932111yescharacteristic
992C22#1171932711yescharacteristic
993C22#1171932711yescharacteristic
994C22#1171932811yescharacteristic
995C22#1171932811yescharacteristic
996C22D13×C22⋊Q811yescharacteristic
997C22D13×C22⋊Q811yescharacteristic
998C22#1171935311yescharacteristic
999C22#1171935511yescharacteristic
1000C22#1171936011yescharacteristic
1001C22#1171936111yescharacteristic
1002C22#1171936611yescharacteristic
1003C22#1171937511yescharacteristic
1004C22#1171937611yescharacteristic
1005C22#1171938211yescharacteristic
1006C22#1171940711yescharacteristic
1007C22#1171941311yescharacteristic
1008C22#1171942311yescharacteristic
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—81no—
1014C4—81no—
1015C4—138no—
1016C4—264no—
1017C4—264no—
1018C4—522no—
1019C4—522no—
1020C4—522no—
1021C4—1041no—
1022C4—1041no—
1023C2—44no—
1024C2D13×#38011yescharacteristic
1025C2#1311731511yescharacteristic
1026C2#1311745511yescharacteristic
1027C2#1311766211yescharacteristic
1028C2#1311767511yescharacteristic
1029C2#1311771811yescharacteristic
1030C2#1311772611yescharacteristic
1031C2#1311824711yescharacteristic
1032C2#1311824911yescharacteristic
1033C2#1311825811yescharacteristic
1034C2#1311826011yescharacteristic
1035C2#1311852011yescharacteristic
1036C2#1311852211yescharacteristic
1037C2#1311854211yescharacteristic
1038C2#1311854411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#13951
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
9. #13113065C2semidirect
10. #13113064C2semidirect
11. #13113064C2semidirect
12. #13113064C2semidirect
13. #13113061C2semidirect
14. #13113060C2semidirect
37. C2×#88131C4semidirect
256. C22×Dic13C4⋊C4semidirect
286. #6101C22⋊C4semidirect
809. C13#13951semidirect

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
C2×C22⋊C4×Dic132
#131130812
#131130792
#131130652
#131130642
#131130612
#131130602
C13×#14392
#1395113