Finite Group Databasebeta

← #15786052

Subgroups — #15786052

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×#88150C211yesmaximal, characteristic
2C2×#11718307C211yesmaximal, characteristic, complemented
3C2×#11718307C211yesmaximal, characteristic, complemented
4C2×#11718633C211yesmaximal, characteristic, complemented
5C2×#11718328C211yesmaximal, characteristic
6C2×C4×#6101C211yesmaximal, characteristic, complemented
7C2×#11718327C211yesmaximal, characteristic
8#13113104C211yesmaximal, characteristic, complemented
9#13113102C211yesmaximal, characteristic, complemented
10#13113080C211yesmaximal, characteristic
11#13113078C211yesmaximal, characteristic
12#13113074C211yesmaximal, characteristic
13#13113072C211yesmaximal, characteristic
14#13113064C211yesmaximal, characteristic, complemented
15C13×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C2×#88150—24no—
36C2×#88150—24no—
37C2×#88150C418yescomplemented
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
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—
55C4×#6101—24no—
56#11718328—24no—
57#11718327—24no—
58#11718307—24no—
59#11718307—24no—
60C24×D13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C22×C4×D13—22no—
76C22×C4×D13—22no—
77C22×C4×D13—22no—
78C22×C4×D13—22no—
79C22×C4×D13—22no—
80C22×C4×D13—22no—
81C22×C4×D13C2×C414yes—
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—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—41no—
94C2×C13×C4⋊C4C2×C414yes—
95C2×C42×C13—22no—
96C2×C42×C13—22no—
97C2×C42×C13—41no—
98C2×#6103—22no—
99C2×#6103—22no—
100C2×#6103—22no—
101C2×#6103—22no—
102C2×#6103—22no—
103C2×#6103—22no—
104C2×#6103—22no—
105C2×#6103—22no—
106C2×#6103—22no—
107C2×#6103—22no—
108C2×#6103—22no—
109C2×#6103—22no—
110C2×#6103—22no—
111C2×#6103—41no—
112C2×#6103—41no—
113C2×#6103C2×C414yes—
114C2×#6103C2×C414yes—
115C2×#6103Q814yescomplemented
116C2×#6101—22no—
117C2×#6101—22no—
118C2×#6101—22no—
119C2×#6101—22no—
120C2×#6101—22no—
121C2×#6101—22no—
122C2×#6101—22no—
123C2×#6101—22no—
124C2×#6101—22no—
125C2×#6101—41no—
126C2×#6101C2×C414yes—
127C2×#6101C2×C414yes—
128C2×#6101D414yes—
129C2×#6101D414yes—
130C2×#6101D414yes—
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—22no—
138C2×C4×Dic13—41no—
139C2×C4×Dic13D414yes—
140#88150—232no—
141C13×#95—22no—
142C13×#95—22no—
143C13×#95—22no—
144C13×#95—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×C13C2411yescharacteristic
159C23×D13—21no—
160C23×D13—21no—
161C23×D13—21no—
162C23×D13—21no—
163C23×D13—21no—
164C23×D13—21no—
165C23×D13—21no—
166C23×D13—21no—
167C23×D13—21no—
168C23×D13—21no—
169C23×D13—21no—
170C23×D13—21no—
171C23×D13C22×C412yes—
172C23×D13C2×Q812yes—
173C23×D13#4112yes—
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×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13C22×C412yes—
214C22×C4×C13C22×C412yes—
215C22×C4×C13C22×C412yes—
216C22×C4×C13C2×D412yes—
217C22×C4×C13C2×D412yes—
218C22×C4×C13C2×D412yes—
219C22×C4×C13C2×D412yes—
220C22×C4×C13C2×Q812yes—
221C22×C4×C13#4112yes—
222C22×C4×C13#4112yes—
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×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×D412yes—
268C22×Dic13C2×D412yes—
269C22×Dic13C2×Q812yes—
270C22×Dic13#4112yes—
271C22×Dic13#4112yes—
272C2×C4×D13—28no—
273C2×C4×D13—28no—
274C2×C4×D13—28no—
275C2×C4×D13—44no—
276C2×C4×D13—44no—
277C2×C4×D13—44no—
278C2×C4×D13—44no—
279C2×Dic26—28no—
280C2×Dic26—28no—
281C2×Dic26—28no—
282C2×Dic26—44no—
283C2×Dic26—44no—
284C2×Dic26—44no—
285C2×Dic26—44no—
286C13×C4⋊C4—28no—
287C13×C4⋊C4—44no—
288C42×C13—44no—
289#6103—28no—
290#6103—28no—
291#6103—28no—
292#6103—28no—
293#6103—44no—
294#6103—44no—
295#6101—28no—
296#6101—28no—
297#6101—44no—
298#6101—44no—
299#6101C22⋊C4116yescomplemented
300C4×Dic13—28no—
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#1439—131no—
314#1437—131no—
315#1437—131no—
316C4⋊#95—131no—
317C4⋊#95D1311yescharacteristic, complemented
318C23×C13C23×C411yescharacteristic
319C23×C13C22×D411yescharacteristic
320C23×C13C22×D411yescharacteristic
321C23×C13C22×D411yescharacteristic
322C23×C13C22×D411yescharacteristic
323C23×C13C22×Q811yescharacteristic
324C23×C13C2×#4111yescharacteristic
325C23×C13C2×#4111yescharacteristic
326C23×C13C2×#4111yescharacteristic
327C23×C13C2×#4111yescharacteristic
328C23×C13C2×#4111yescharacteristic
329C23×C13H(5,𝔽2)11yescharacteristic
330C23×C132−1+411yescharacteristic
331C23×C132−1+411yescharacteristic
332C23×C132−1+411yescharacteristic
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—22no—
338C22×D13—22no—
339C22×D13—22no—
340C22×D13—22no—
341C22×D13—22no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—22no—
345C22×D13—22no—
346C22×D13—22no—
347C22×D13—22no—
348C22×D13—22no—
349C22×D13—22no—
350C22×D13—22no—
351C22×D13—41no—
352C22×D13—41no—
353C22×D13—41no—
354C22×D13—41no—
355C22×D13—41no—
356C22×D13—41no—
357C22×D13—41no—
358C22×D13—41no—
359C22×D13—41no—
360C22×D13—41no—
361C22×D13—41no—
362C22×D13—41no—
363C22×D13—41no—
364C22×D13—41no—
365C22×D13—41no—
366C22×D13—41no—
367C22×D13C4×Q814yes—
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—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
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×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13C2×C22⋊C414yes—
416C2×C4×C13C22⋊Q814yescomplemented
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—22no—
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—41no—
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×Dic13#12414yes—
465C2×Dic13#12714yes—
466C4×D13—416no—
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⋊C4C2×D1311yescharacteristic
479C22×C4⋊C4C2×D1311yescharacteristic
480C22×C22⋊C4—131no—
481C22×C22⋊C4—131no—
482C22×C22⋊C4—131no—
483C22×C22⋊C4—131no—
484C22×C22⋊C4—131no—
485C22×C22⋊C4—131no—
486C22×C42—131no—
487C22×C42—131no—
488C22×C42—131no—
489C22×C42C2×D1311yescharacteristic
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×#95C2×D1311yescharacteristic
509C2×#95C2×D1311yescharacteristic
510C2×#95C2×D1311yescharacteristic
511C2×#95C2×D1311yescharacteristic
512C22×C13C22×C22⋊C411yescharacteristic
513C22×C13C2×C4×D411yescharacteristic
514C22×C13C2×C4×D411yescharacteristic
515C22×C13C2×C4×Q811yescharacteristic
516C22×C13C4×#4111yescharacteristic
517C22×C13#51911yescharacteristic
518C22×C13#52011yescharacteristic
519C22×C13C2×#12111yescharacteristic
520C22×C13C2×#12111yescharacteristic
521C22×C13C2×C22⋊Q811yescharacteristic
522C22×C13#52511yescharacteristic
523C22×C13C2×#12411yescharacteristic
524C22×C13#52911yescharacteristic
525C22×C13C2×#12711yescharacteristic
526C22×C13#53311yescharacteristic
527C22×C13#53611yescharacteristic
528C22×C13#53711yescharacteristic
529C22×C13#54111yescharacteristic
530C22×C13#54211yescharacteristic
531C22×C13#54611yescharacteristic
532C22×C13#54611yescharacteristic
533C22×C13#54611yescharacteristic
534C22×C13#54711yescharacteristic
535C22×C13#54711yescharacteristic
536C22×C13#54711yescharacteristic
537C22×C13#54811yescharacteristic
538C22×C13#54811yescharacteristic
539C22×C13#54811yescharacteristic
540C22×C13D4×Q811yescharacteristic
541C22×C13D4×Q811yescharacteristic
542C22×C13D4×Q811yescharacteristic
543C22×C13#55211yescharacteristic
544C22×C13#55211yescharacteristic
545C22×C13#55411yescharacteristic
546C22×C13#55611yescharacteristic
547C2×D13—24no—
548C2×D13—24no—
549C2×D13—24no—
550C2×D13—42no—
551C2×D13—42no—
552C2×D13—42no—
553C2×D13—42no—
554C2×D13—42no—
555C2×D13—42no—
556C2×D13—42no—
557C2×D13—42no—
558C2×D13—42no—
559C2×D13—42no—
560C2×D13—42no—
561C2×D13—42no—
562C4×C13—24no—
563C4×C13—24no—
564C4×C13—42no—
565C4×C13—42no—
566C4×C13—42no—
567C4×C13—42no—
568C4×C13—81no—
569Dic13—24no—
570Dic13—42no—
571Dic13—42no—
572Dic13—42no—
573Dic13—42no—
574Dic13—81no—
575Dic13#39018yes—
576C25—131no—
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—131no—
588C23×C4—131no—
589C23×C4—131no—
590C23×C4—134no—
591C23×C4—131no—
592C23×C4—262no—
593C23×C4—262no—
594C23×C4—262no—
595C23×C4—262no—
596C23×C4—262no—
597C23×C4—262no—
598C23×C4C22×D1311yescharacteristic
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—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—134no—
612C2×C4⋊C4—134no—
613C2×C4⋊C4—134no—
614C2×C4⋊C4—134no—
615C2×C4⋊C4—134no—
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—521no—
626C2×C4⋊C4C4×D1314yes—
627C2×C22⋊C4—134no—
628C2×C22⋊C4—134no—
629C2×C22⋊C4—134no—
630C2×C22⋊C4—262no—
631C2×C22⋊C4—262no—
632C2×C22⋊C4—262no—
633C2×C22⋊C4—262no—
634C2×C22⋊C4—262no—
635C2×C22⋊C4—262no—
636C2×C22⋊C4—262no—
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⋊C4—521no—
645C2×C42—22no—
646C2×C42—22no—
647C2×C42—41no—
648C2×C42—134no—
649C2×C42—262no—
650C2×C42—262no—
651C2×C42—262no—
652C2×C42—262no—
653C2×C42—262no—
654C2×C42—262no—
655C2×C42—262no—
656C2×C42—521no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
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×C13C2×#39011yescharacteristic
674C2×C13C4×C22⋊Q811yescharacteristic
675C2×C13#232311yescharacteristic
676C2×C13#233911yescharacteristic
677C2×C13Q8×C22⋊C411yescharacteristic
678C2×C13#236011yescharacteristic
679C2×C13#236211yescharacteristic
680C2×C13#241511yescharacteristic
681C2×C13#241711yescharacteristic
682C2×C13#242711yescharacteristic
683C2×C13#242911yescharacteristic
684C2×C13#248911yescharacteristic
685C2×C13#249211yescharacteristic
686C2×C13#254011yescharacteristic
687C2×C13#254211yescharacteristic
688D13—44no—
689C24—132no—
690C24—132no—
691C24—132no—
692C24—261no—
693C24—261no—
694C24—261no—
695C24—261no—
696C24—261no—
697C24—261no—
698C24—261no—
699C24—261no—
700C24—261no—
701C24—261no—
702C24—261no—
703C24—261no—
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—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
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—132no—
765C22×C4—268no—
766C22×C4—268no—
767C22×C4—268no—
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—524no—
804C22×C4—524no—
805C22×C4—524no—
806C22×C4—524no—
807C22×C4C2×C4×D1312yes—
808C22×C4C2×C4×D1312yes—
809C22×C4C2×C4×D1312yes—
810C22×C4#612712yes—
811C22×C4#612712yes—
812C22×C4D4×D1312yes—
813C22×C4D4×D1312yes—
814C22×C4D4×D1312yes—
815C22×C4D4×D1312yes—
816C22×C4Q8×D1312yes—
817C4⋊C4—28no—
818C4⋊C4—44no—
819C4⋊C4—1316no—
820C4⋊C4—268no—
821C4⋊C4—268no—
822C4⋊C4—524no—
823C4⋊C4—524no—
824C22⋊C4—268no—
825C22⋊C4—268no—
826C22⋊C4—268no—
827C22⋊C4—268no—
828C22⋊C4—524no—
829C22⋊C4—524no—
830C42—44no—
831C42—268no—
832C42—524no—
833C42—524no—
834C13#1399711yescharacteristic, complemented, Sylow
835C23—134no—
836C23—262no—
837C23—262no—
838C23—262no—
839C23—262no—
840C23—262no—
841C23—262no—
842C23—262no—
843C23—262no—
844C23—262no—
845C23—262no—
846C23—262no—
847C23—262no—
848C23—262no—
849C23—262no—
850C23—262no—
851C23—262no—
852C23—262no—
853C23—262no—
854C23—521no—
855C23—521no—
856C23—521no—
857C23—521no—
858C23—521no—
859C23—521no—
860C23—521no—
861C23—521no—
862C23—521no—
863C23—521no—
864C23—521no—
865C23—521no—
866C23—521no—
867C23—521no—
868C23—521no—
869C23—521no—
870C23C22×C4×D1311yescharacteristic
871C23C2×#612711yescharacteristic
872C23C2×#612711yescharacteristic
873C23C2×D4×D1311yescharacteristic
874C23C2×D4×D1311yescharacteristic
875C23C2×D4×D1311yescharacteristic
876C23C2×D4×D1311yescharacteristic
877C23#8825111yescharacteristic
878C23C2×Q8×D1311yescharacteristic
879C23#8825411yescharacteristic
880C23#8825411yescharacteristic
881C23#41×D1311yescharacteristic
882C23#41×D1311yescharacteristic
883C23#41×D1311yescharacteristic
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—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
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—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—134no—
934C2×C4—134no—
935C2×C4—134no—
936C2×C4—134no—
937C2×C4—134no—
938C2×C4—134no—
939C2×C4—134no—
940C2×C4—134no—
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—5216no—
960C2×C4—521no—
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×C4C22⋊C4×D1314yes—
984C2×C4#8815014yescomplemented
985C22—264no—
986C22—264no—
987C22—264no—
988C22—522no—
989C22—522no—
990C22—522no—
991C22—522no—
992C22—522no—
993C22—522no—
994C22—522no—
995C22—522no—
996C22—522no—
997C22—522no—
998C22—522no—
999C22—522no—
1000C22C4×#612711yescharacteristic
1001C22C2×C22⋊C4×D1311yescharacteristic
1002C22#1171919511yescharacteristic
1003C22#1171919511yescharacteristic
1004C22#1171920911yescharacteristic
1005C22#1171921211yescharacteristic
1006C22#1171921211yescharacteristic
1007C22#1171921211yescharacteristic
1008C22C2×#8815011yescharacteristic
1009C22#1171923311yescharacteristic
1010C22#1171923611yescharacteristic
1011C22C4×D4×D1311yescharacteristic
1012C22C4×D4×D1311yescharacteristic
1013C22#1171925211yescharacteristic
1014C22#1171925711yescharacteristic
1015C22#1171927311yescharacteristic
1016C22C4×Q8×D1311yescharacteristic
1017C22#1171927711yescharacteristic
1018C22#1171928311yescharacteristic
1019C22#1171930211yescharacteristic
1020C22D13×#12111yescharacteristic
1021C22D13×#12111yescharacteristic
1022C22#1171931511yescharacteristic
1023C22#1171933711yescharacteristic
1024C22#1171933811yescharacteristic
1025C22#1171934111yescharacteristic
1026C22#1171934511yescharacteristic
1027C22D13×#12411yescharacteristic
1028C22#1171938211yescharacteristic
1029C22#1171939811yescharacteristic
1030C22#1171940111yescharacteristic
1031C22D13×#12711yescharacteristic
1032C22#1171942911yescharacteristic
1033C22#1171943211yescharacteristic
1034C22#1171943211yescharacteristic
1035C4—24no—
1036C4—24no—
1037C4—42no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—81no—
1042C4—138no—
1043C4—264no—
1044C4—522no—
1045C4—522no—
1046C4—522no—
1047C4—522no—
1048C4—1041no—
1049C2—524no—
1050C2D13×#39011yescharacteristic
1051C2C4×#8815011yescharacteristic
1052C2#1311751311yescharacteristic
1053C2#1311766311yescharacteristic
1054C2#1311767011yescharacteristic
1055C2#1311783811yescharacteristic
1056C2#1311786411yescharacteristic
1057C2#1311826411yescharacteristic
1058C2#1311828611yescharacteristic
1059C2#1311841211yescharacteristic
1060C2#1311843411yescharacteristic
1061C2#1311917611yescharacteristic
1062C2#1311920911yescharacteristic
1063C2#1311977311yescharacteristic
1064C2#1311978811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4⋊#95D13
hypocenterC13#13997
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

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×C4×#6101C2semidirect
8. #13113104C2semidirect
9. #13113102C2semidirect
14. #13113064C2semidirect
15. C13×C4⋊#95C2semidirect
37. C2×#88150C4semidirect
115. C2×#6103Q8semidirect
299. #6101C22⋊C4semidirect
317. C4⋊#95D13semidirect
416. C2×C4×C13C22⋊Q8semidirect
834. C13#13997semidirect
984. C2×C4#88150semidirect

Maximal subgroups

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

subgroupindex
C22×#881502
C2×#117183072
C2×#117186332
C2×#117183282
C2×C4×#61012
C2×#117183272
#131131042
#131131022
#131130802
#131130782
#131130742
#131130722
#131130642
C13×C4⋊#952
#1399713