Finite Group Databasebeta

← #15786046

Subgroups — #15786046

Order 3328.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88132C211yesmaximal, characteristic
2C2×#11718307C211yesmaximal, characteristic, complemented
3C2×#11718307C211yesmaximal, characteristic, complemented
4C2×#11718633C211yesmaximal, characteristic, complemented
5C2×#11718603C211yesmaximal, characteristic
6C2×#11718310C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×Dic13C211yesmaximal, characteristic
8#13113103C211yesmaximal, characteristic, complemented
9#13113102C211yesmaximal, characteristic, complemented
10#13113079C211yesmaximal, characteristic
11#13113073C211yesmaximal, characteristic
12#13113073C211yesmaximal, characteristic
13#13113065C211yesmaximal, characteristic, complemented
14#13113064C211yesmaximal, characteristic, complemented
15C13×#1439C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C2×#88132—24no—
36C2×#88132—24no—
37C2×#88132C418yescomplemented
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#11718310—24no—
58#11718307—24no—
59#11718307—24no—
60C25×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×Dic13—22no—
68C23×Dic13—22no—
69C23×Dic13—22no—
70C23×Dic13—22no—
71C23×Dic13—22no—
72C23×Dic13—22no—
73C23×Dic13C2×C414yes—
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C22×Dic26—22no—
83C22×Dic26—22no—
84C22×Dic26—22no—
85C22×Dic26—22no—
86C22×Dic26—22no—
87C22×Dic26—22no—
88C22×Dic26C2×C414yes—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—41no—
92C2×C13×C22⋊C4—22no—
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—41no—
100C2×C13×C22⋊C4C2×C414yes—
101C2×C22⋊Dic13—22no—
102C2×C22⋊Dic13—22no—
103C2×C22⋊Dic13—22no—
104C2×C22⋊Dic13—22no—
105C2×C22⋊Dic13—22no—
106C2×C22⋊Dic13—22no—
107C2×C22⋊Dic13—41no—
108C2×C22⋊Dic13C2×C414yes—
109C2×C22⋊Dic13Q814yescomplemented
110C2×C4⋊Dic13—22no—
111C2×C4⋊Dic13—22no—
112C2×C4⋊Dic13C2×C414yes—
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×#6101C2×C414yes—
124C2×#6101C2×C414yes—
125C2×#6101D414yes—
126C2×#6101D414yes—
127C2×#6101D414yes—
128C2×C4×Dic13—22no—
129C2×C4×Dic13—22no—
130C2×C4×Dic13—22no—
131C2×C4×Dic13—22no—
132C2×C4×Dic13—22no—
133C2×C4×Dic13—22no—
134C2×C4×Dic13—22no—
135C2×C4×Dic13—22no—
136C2×C4×Dic13—22no—
137C2×C4×Dic13—41no—
138C2×C4×Dic13—41no—
139C2×C4×Dic13D414yes—
140#88132—232no—
141C13×#95—22no—
142C13×#95—22no—
143C13×#95—22no—
144#88071—22no—
145#88071—22no—
146#88071—22no—
147#88071—22no—
148#88071—22no—
149#88071—22no—
150#88071—22no—
151#88071—22no—
152#88071—22no—
153#88071—22no—
154#88071—22no—
155#88071—22no—
156#88071—22no—
157#13997—131nomaximal, Sylow
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13—21no—
165C24×C13—21no—
166C24×C13—21no—
167C24×C13—21no—
168C24×C13—21no—
169C24×C13—21no—
170C24×C13C22×C412yes—
171C24×C13C2×Q812yes—
172C24×C13#4112yes—
173C24×C13C2411yescharacteristic
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×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13C22×C412yes—
210C22×C4×C13C22×C412yes—
211C22×C4×C13C2×D412yes—
212C22×C4×C13C2×D412yes—
213C22×C4×C13C2×D412yes—
214C22×C4×C13C2×D412yes—
215C22×C4×C13#4112yes—
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×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—28no—
249C22×Dic13—28no—
250C22×Dic13—28no—
251C22×Dic13—21no—
252C22×Dic13—21no—
253C22×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13—44no—
259C22×Dic13—44no—
260C22×Dic13—44no—
261C22×Dic13—44no—
262C22×Dic13C22×C412yes—
263C22×Dic13C22×C412yes—
264C22×Dic13C22×C412yes—
265C22×Dic13C22×C412yes—
266C22×Dic13C2×D412yes—
267C22×Dic13C2×D412yes—
268C22×Dic13C2×D412yes—
269C22×Dic13C2×D412yes—
270C22×Dic13C2×D412yes—
271C22×Dic13C2×D412yes—
272C22×Dic13C2×D412yes—
273C22×Dic13C2×D412yes—
274C22×Dic13C2×Q812yes—
275C22×Dic13C2×Q812yes—
276C22×Dic13#4112yes—
277C22×Dic13#4112yes—
278C22×Dic13#4112yes—
279C2×Dic26—28no—
280C2×Dic26—28no—
281C2×Dic26—28no—
282C2×Dic26—44no—
283C2×Dic26—44no—
284C2×Dic26—44no—
285C2×Dic26—44no—
286C13×C4⋊C4—44no—
287C13×C22⋊C4—28no—
288C13×C22⋊C4—28no—
289C13×C22⋊C4—44no—
290C22⋊Dic13—28no—
291C22⋊Dic13—28no—
292C22⋊Dic13—44no—
293C4⋊Dic13—28no—
294#6101—28no—
295#6101—28no—
296#6101—44no—
297#6101—44no—
298#6101C22⋊C4116yescomplemented
299C4×Dic13—28no—
300C4×Dic13—44no—
301C4×Dic13—44no—
302C4×Dic13—44no—
303C22×C22⋊Q8—131no—
304C2×#391—131no—
305C2×#391—131no—
306C2×#389—131no—
307C2×#380—131no—
308C2×C4×C4⋊C4—131no—
309C2×C4×C22⋊C4—131no—
310#1445—131no—
311#1445—131no—
312#1439—131no—
313#1439D1311yescharacteristic
314#1437—131no—
315#1437—131no—
316C4⋊#95—131no—
317C4⋊#95—131no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13—41no—
339C23×C13—41no—
340C23×C13—41no—
341C23×C13—41no—
342C23×C13—41no—
343C23×C13—41no—
344C23×C13—41no—
345C23×C13—41no—
346C23×C13—41no—
347C23×C13—41no—
348C23×C13—41no—
349C23×C13—41no—
350C23×C13—41no—
351C23×C13—41no—
352C23×C13C4×Q814yes—
353C23×C13C23×C411yescharacteristic
354C23×C13C22×D411yescharacteristic
355C23×C13C22×D411yescharacteristic
356C23×C13C22×D411yescharacteristic
357C23×C13C22×D411yescharacteristic
358C23×C13C22×Q811yescharacteristic
359C23×C13C2×#4111yescharacteristic
360C23×C13C2×#4111yescharacteristic
361C23×C13C2×#4111yescharacteristic
362C23×C13C2×#4111yescharacteristic
363C23×C13C2×#4111yescharacteristic
364C23×C13H(5,𝔽2)11yescharacteristic
365C23×C132−1+411yescharacteristic
366C23×C132−1+411yescharacteristic
367C23×C132−1+411yescharacteristic
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—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
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×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13C2×C22⋊C414yes—
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—22no—
427C2×Dic13—22no—
428C2×Dic13—22no—
429C2×Dic13—22no—
430C2×Dic13—22no—
431C2×Dic13—22no—
432C2×Dic13—22no—
433C2×Dic13—22no—
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×Dic13—41no—
448C2×Dic13—41no—
449C2×Dic13—41no—
450C2×Dic13—416no—
451C2×Dic13—41no—
452C2×Dic13—41no—
453C2×Dic13—41no—
454C2×Dic13—41no—
455C2×Dic13—41no—
456C2×Dic13—41no—
457C2×Dic13—41no—
458C2×Dic13C2×C22⋊C414yes—
459C2×Dic13C2×C22⋊C414yes—
460C2×Dic13C4×D414yes—
461C2×Dic13C4×D414yes—
462C2×Dic13#12114yes—
463C2×Dic13#12114yes—
464C2×Dic13C22⋊Q814yescomplemented
465C2×Dic13#12414yes—
466C2×Dic13#12714yes—
467Dic26—416no—
468C23×Q8—131no—
469C24×C4—131no—
470C2×C22⋊Q8—138no—
471C2×C22⋊Q8—264no—
472C2×C22⋊Q8—264no—
473C22×C4⋊C4—131no—
474C22×C4⋊C4—131no—
475C22×C4⋊C4—131no—
476C22×C4⋊C4—131no—
477C22×C4⋊C4—131no—
478C22×C4⋊C4—131no—
479C22×C4⋊C4C2×D1311yescharacteristic
480C22×C22⋊C4—131no—
481C22×C22⋊C4—131no—
482C22×C22⋊C4—131no—
483C22×C22⋊C4C2×D1311yescharacteristic
484C22×C22⋊C4C2×D1311yescharacteristic
485C22×C22⋊C4C2×D1311yescharacteristic
486C22×C42—131no—
487C22×C42—131no—
488C22×C42—131no—
489C22×C42—131no—
490#391—264no—
491#391—264no—
492#389—264no—
493#380—264no—
494C4×C4⋊C4—264no—
495C4×C22⋊C4—264no—
496C2×#95—131no—
497C2×#95—131no—
498C2×#95—131no—
499C2×#95—131no—
500C2×#95—131no—
501C2×#95—131no—
502C2×#95—131no—
503C2×#95—131no—
504C2×#95—131no—
505C2×#95—131no—
506C2×#95—131no—
507C2×#95—131no—
508C2×#95—131no—
509C2×#95C2×D1311yescharacteristic
510C2×#95C2×D1311yescharacteristic
511C2×#95C2×D1311yescharacteristic
512C22×C13—24no—
513C22×C13—24no—
514C22×C13—24no—
515C22×C13—42no—
516C22×C13—42no—
517C22×C13—42no—
518C22×C13—42no—
519C22×C13—42no—
520C22×C13—42no—
521C22×C13—42no—
522C22×C13—42no—
523C22×C13—42no—
524C22×C13—42no—
525C22×C13—42no—
526C22×C13—42no—
527C22×C13C22×C22⋊C411yescharacteristic
528C22×C13C2×C4×D411yescharacteristic
529C22×C13C2×C4×D411yescharacteristic
530C22×C13C2×C4×Q811yescharacteristic
531C22×C13C4×#4111yescharacteristic
532C22×C13#51911yescharacteristic
533C22×C13#52011yescharacteristic
534C22×C13C2×#12111yescharacteristic
535C22×C13C2×#12111yescharacteristic
536C22×C13C2×C22⋊Q811yescharacteristic
537C22×C13#52511yescharacteristic
538C22×C13C2×#12411yescharacteristic
539C22×C13#52911yescharacteristic
540C22×C13C2×#12711yescharacteristic
541C22×C13#53311yescharacteristic
542C22×C13#53611yescharacteristic
543C22×C13#53711yescharacteristic
544C22×C13#54111yescharacteristic
545C22×C13#54211yescharacteristic
546C22×C13#54611yescharacteristic
547C22×C13#54611yescharacteristic
548C22×C13#54611yescharacteristic
549C22×C13#54711yescharacteristic
550C22×C13#54711yescharacteristic
551C22×C13#54711yescharacteristic
552C22×C13#54811yescharacteristic
553C22×C13#54811yescharacteristic
554C22×C13#54811yescharacteristic
555C22×C13D4×Q811yescharacteristic
556C22×C13D4×Q811yescharacteristic
557C22×C13D4×Q811yescharacteristic
558C22×C13#55211yescharacteristic
559C22×C13#55211yescharacteristic
560C22×C13#55411yescharacteristic
561C22×C13#55611yescharacteristic
562C4×C13—24no—
563C4×C13—42no—
564C4×C13—42no—
565C4×C13—42no—
566C4×C13—42no—
567C4×C13—81no—
568Dic13—24no—
569Dic13—24no—
570Dic13—42no—
571Dic13—42no—
572Dic13—42no—
573Dic13—42no—
574Dic13—81no—
575Dic13#39018yes—
576C25C22×D1311yescharacteristic
577C22×Q8—134no—
578C22×Q8—262no—
579C22×Q8—262no—
580C22×Q8—262no—
581C22×Q8—262no—
582C22×Q8—262no—
583C22×Q8—262no—
584C23×C4—131no—
585C23×C4—131no—
586C23×C4—131no—
587C23×C4—134no—
588C23×C4—131no—
589C23×C4—131no—
590C23×C4—131no—
591C23×C4—131no—
592C23×C4—131no—
593C23×C4—262no—
594C23×C4—262no—
595C23×C4—262no—
596C23×C4—262no—
597C23×C4—262no—
598C23×C4—262no—
599C23×C4C22×D1311yescharacteristic
600C23×C4C22×D1311yescharacteristic
601C23×C4C22×D1311yescharacteristic
602C23×C4C22×D1311yescharacteristic
603C23×C4C22×D1311yescharacteristic
604C23×C4C22×D1311yescharacteristic
605C22⋊Q8—2632no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—134no—
610C2×C4⋊C4—134no—
611C2×C4⋊C4—134no—
612C2×C4⋊C4—134no—
613C2×C4⋊C4—134no—
614C2×C4⋊C4—134no—
615C2×C4⋊C4—262no—
616C2×C4⋊C4—262no—
617C2×C4⋊C4—262no—
618C2×C4⋊C4—262no—
619C2×C4⋊C4—262no—
620C2×C4⋊C4—262no—
621C2×C4⋊C4—262no—
622C2×C4⋊C4—262no—
623C2×C4⋊C4—262no—
624C2×C4⋊C4—262no—
625C2×C4⋊C4—262no—
626C2×C4⋊C4—521no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4—134no—
636C2×C22⋊C4—134no—
637C2×C22⋊C4—262no—
638C2×C22⋊C4—262no—
639C2×C22⋊C4—262no—
640C2×C22⋊C4—262no—
641C2×C22⋊C4—262no—
642C2×C22⋊C4—262no—
643C2×C22⋊C4—521no—
644C2×C22⋊C4C4×D1314yes—
645C2×C42—134no—
646C2×C42—262no—
647C2×C42—262no—
648C2×C42—262no—
649C2×C42—262no—
650C2×C42—262no—
651C2×C42—262no—
652C2×C42—262no—
653C2×C42—262no—
654C2×C42—262no—
655C2×C42—521no—
656C2×C42—521no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—262no—
661#95—262no—
662#95—262no—
663#95—262no—
664#95—262no—
665#95—262no—
666#95—262no—
667#95—262no—
668#95—262no—
669#95—262no—
670#95—262no—
671#95—262no—
672#95—262no—
673C2×C13—44no—
674C2×C13C2×#39011yescharacteristic
675C2×C13C4×C22⋊Q811yescharacteristic
676C2×C13#232311yescharacteristic
677C2×C13#233911yescharacteristic
678C2×C13Q8×C22⋊C411yescharacteristic
679C2×C13#236011yescharacteristic
680C2×C13#236211yescharacteristic
681C2×C13#241511yescharacteristic
682C2×C13#241711yescharacteristic
683C2×C13#242711yescharacteristic
684C2×C13#242911yescharacteristic
685C2×C13#248911yescharacteristic
686C2×C13#249211yescharacteristic
687C2×C13#254011yescharacteristic
688C2×C13#254211yescharacteristic
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24C2×C4×D1312yes—
702C24#612912yes—
703C24Q8×D1312yes—
704C24C23×D1311yescharacteristic
705C2×Q8—268no—
706C2×Q8—268no—
707C2×Q8—268no—
708C2×Q8—524no—
709C2×Q8—524no—
710C2×Q8—524no—
711C2×Q8—524no—
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—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—132no—
748C22×C4—132no—
749C22×C4—132no—
750C22×C4—132no—
751C22×C4—132no—
752C22×C4—132no—
753C22×C4—132no—
754C22×C4—132no—
755C22×C4—132no—
756C22×C4—132no—
757C22×C4—132no—
758C22×C4—132no—
759C22×C4—132no—
760C22×C4—132no—
761C22×C4—132no—
762C22×C4—132no—
763C22×C4—132no—
764C22×C4—268no—
765C22×C4—268no—
766C22×C4—268no—
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×C4—261no—
788C22×C4—261no—
789C22×C4—261no—
790C22×C4—261no—
791C22×C4—261no—
792C22×C4—261no—
793C22×C4—261no—
794C22×C4—261no—
795C22×C4—261no—
796C22×C4—261no—
797C22×C4—261no—
798C22×C4—261no—
799C22×C4—261no—
800C22×C4—261no—
801C22×C4—261no—
802C22×C4—261no—
803C22×C4—261no—
804C22×C4—261no—
805C22×C4—261no—
806C22×C4—524no—
807C22×C4—524no—
808C22×C4—524no—
809C22×C4—524no—
810C22×C4C2×C4×D1312yes—
811C22×C4C2×C4×D1312yes—
812C22×C4D4×D1312yes—
813C22×C4D4×D1312yes—
814C22×C4D4×D1312yes—
815C22×C4D4×D1312yes—
816C22×C4#612912yes—
817C4⋊C4—44no—
818C4⋊C4—1316no—
819C4⋊C4—268no—
820C4⋊C4—268no—
821C4⋊C4—268no—
822C4⋊C4—524no—
823C4⋊C4—524no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—44no—
827C22⋊C4—268no—
828C22⋊C4—268no—
829C22⋊C4—524no—
830C42—268no—
831C42—524no—
832C42—524no—
833C42—524no—
834C13#1399711yescharacteristic, complemented, Sylow
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23#8814114yes—
870C23C22×C4×D1311yescharacteristic
871C23C2×D4×D1311yescharacteristic
872C23C2×D4×D1311yescharacteristic
873C23C2×D4×D1311yescharacteristic
874C23C2×D4×D1311yescharacteristic
875C23C2×#612911yescharacteristic
876C23C2×#612911yescharacteristic
877C23#8825111yescharacteristic
878C23C2×Q8×D1311yescharacteristic
879C23#41×D1311yescharacteristic
880C23#41×D1311yescharacteristic
881C23#41×D1311yescharacteristic
882C23#8825711yescharacteristic
883C23#8825711yescharacteristic
884C23#8825711yescharacteristic
885Q8—5216no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—134no—
928C2×C4—134no—
929C2×C4—134no—
930C2×C4—134no—
931C2×C4—134no—
932C2×C4—134no—
933C2×C4—134no—
934C2×C4—134no—
935C2×C4—134no—
936C2×C4—262no—
937C2×C4—262no—
938C2×C4—262no—
939C2×C4—262no—
940C2×C4—262no—
941C2×C4—262no—
942C2×C4—262no—
943C2×C4—262no—
944C2×C4—262no—
945C2×C4—262no—
946C2×C4—262no—
947C2×C4—262no—
948C2×C4—262no—
949C2×C4—262no—
950C2×C4—262no—
951C2×C4—262no—
952C2×C4—262no—
953C2×C4—262no—
954C2×C4—262no—
955C2×C4—262no—
956C2×C4—262no—
957C2×C4—262no—
958C2×C4—262no—
959C2×C4—262no—
960C2×C4—5216no—
961C2×C4—521no—
962C2×C4—521no—
963C2×C4—521no—
964C2×C4—521no—
965C2×C4—521no—
966C2×C4—521no—
967C2×C4—521no—
968C2×C4—521no—
969C2×C4—521no—
970C2×C4—521no—
971C2×C4—521no—
972C2×C4—521no—
973C2×C4—521no—
974C2×C4—521no—
975C2×C4—521no—
976C2×C4—521no—
977C2×C4—521no—
978C2×C4—521no—
979C2×C4—521no—
980C2×C4—521no—
981C2×C4—521no—
982C2×C4—521no—
983C2×C4—521no—
984C2×C4C22⋊C4×D1314yes—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22C2×C22⋊C4×D1311yescharacteristic
1001C22C2×#8814111yescharacteristic
1002C22#1171922111yescharacteristic
1003C22C4×#612911yescharacteristic
1004C22C4×D4×D1311yescharacteristic
1005C22C4×D4×D1311yescharacteristic
1006C22#1171925111yescharacteristic
1007C22#1171929111yescharacteristic
1008C22#1171929611yescharacteristic
1009C22#1171929611yescharacteristic
1010C22#1171930311yescharacteristic
1011C22#1171930311yescharacteristic
1012C22#1171930311yescharacteristic
1013C22D13×#12111yescharacteristic
1014C22D13×#12111yescharacteristic
1015C22#1171931311yescharacteristic
1016C22#1171931511yescharacteristic
1017C22#1171931611yescharacteristic
1018C22#1171932711yescharacteristic
1019C22D13×C22⋊Q811yescharacteristic
1020C22#1171933711yescharacteristic
1021C22#1171933711yescharacteristic
1022C22#1171933711yescharacteristic
1023C22#1171934111yescharacteristic
1024C22#1171935311yescharacteristic
1025C22#1171935411yescharacteristic
1026C22#1171935511yescharacteristic
1027C22#1171936011yescharacteristic
1028C22#1171936011yescharacteristic
1029C22#1171937411yescharacteristic
1030C22#1171937611yescharacteristic
1031C22D13×#12411yescharacteristic
1032C22#1171940611yescharacteristic
1033C22#1171941311yescharacteristic
1034C22D13×#12711yescharacteristic
1035C4—24no—
1036C4—42no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—81no—
1041C4—138no—
1042C4—264no—
1043C4—264no—
1044C4—522no—
1045C4—522no—
1046C4—522no—
1047C4—522no—
1048C4—1041no—
1049C2—44no—
1050C2D13×#39011yescharacteristic
1051C2#1311736811yescharacteristic
1052C2#1311751511yescharacteristic
1053C2#1311766211yescharacteristic
1054C2#1311766811yescharacteristic
1055C2#1311783611yescharacteristic
1056C2#1311786611yescharacteristic
1057C2#1311825811yescharacteristic
1058C2#1311828011yescharacteristic
1059C2#1311840611yescharacteristic
1060C2#1311842811yescharacteristic
1061C2#1311917011yescharacteristic
1062C2#1311920311yescharacteristic
1063C2#1311976911yescharacteristic
1064C2#1311978411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#13997
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#11718307C2semidirect
3. C2×#11718307C2semidirect
4. C2×#11718633C2semidirect
6. C2×#11718310C2semidirect
8. #13113103C2semidirect
9. #13113102C2semidirect
13. #13113065C2semidirect
14. #13113064C2semidirect
37. C2×#88132C4semidirect
109. C2×C22⋊Dic13Q8semidirect
298. #6101C22⋊C4semidirect
464. C2×Dic13C22⋊Q8semidirect
834. C13#13997semidirect

Maximal subgroups

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

subgroupindex
C22×#881322
C2×#117183072
C2×#117186332
C2×#117186032
C2×#117183102
C2×C22⋊C4×Dic132
#131131032
#131131022
#131130792
#131130732
#131130652
#131130642
C13×#14392
#1399713