Finite Group Databasebeta

← #15788216

Subgroups — #15788216

Order 3328.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88141C211yesmaximal, characteristic, complemented
2C2×#11718608C211yesmaximal, characteristic
3C2×#11718871C211yesmaximal, characteristic
4C2×C4×C22⋊Dic13C211yesmaximal, characteristic
5#13113106C211yesmaximal, characteristic, complemented
6#13113099C211yesmaximal, characteristic, complemented
7#13113079C211yesmaximal, characteristic
8#13113073C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113071C211yesmaximal, characteristic, complemented
11#13113068C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13#13113067C211yesmaximal, characteristic, complemented
14#13113060C211yesmaximal, characteristic, complemented
15C2×C13×#385C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×#88141—24no—
34C2×#88141—24no—
35C2×#88141—24no—
36C13×#385—24no—
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39#11718871—24no—
40C4×C22⋊Dic13—24no—
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
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718608C418yescomplemented
58C25×C13C2311yescharacteristic
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—41no—
65C23×C4×C13—41no—
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C22×Dic26—22no—
81C22×Dic26—22no—
82C22×Dic26—22no—
83C22×Dic26—22no—
84C22×Dic26—22no—
85C22×Dic26—22no—
86C22×Dic26C2×C414yescomplemented
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—41no—
92C2×C13×C4⋊C4D414yes—
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—41no—
98C2×C13×C22⋊C4C2×C414yes—
99C2×C22⋊Dic13—22no—
100C2×C22⋊Dic13—22no—
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⋊Dic13C2×C414yes—
110C2×C22⋊Dic13Q814yescomplemented
111C2×#6101—22no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101—22no—
116C2×#6101—22no—
117C2×#6101—22no—
118C2×#6101—41no—
119C2×#6101D414yes—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
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—41no—
130C2×C4×Dic13—41no—
131C2×C4×Dic13D414yes—
132#88141—232no—
133C13×#95—22no—
134C13×#95—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—22no—
143#88071—22no—
144#88071—41no—
145#88071—41no—
146#88071—41no—
147#88071—41no—
148#88071C2×C414yescomplemented
149#88071C2×C414yescomplemented
150#88071C2×C414yescomplemented
151#14172—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×Q812yes—
166C24×C13#4112yes—
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—28no—
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—44no—
203C22×C4×C13—44no—
204C22×C4×C13—44no—
205C22×C4×C13—44no—
206C22×C4×C13—44no—
207C22×C4×C13—44no—
208C22×C4×C13C22×C412yes—
209C22×C4×C13C22×C412yes—
210C22×C4×C13C2×D412yes—
211C22×C4×C13C2×D412yes—
212C22×C4×C13C2×D412yes—
213C22×C4×C13C2×D412yes—
214C22×C4×C13C2×D412yes—
215C22×C4×C13#4112yes—
216C22×C4×C13#4112yes—
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—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×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13C22×C412yes—
261C22×Dic13C22×C412yes—
262C22×Dic13C22×C412yes—
263C22×Dic13C22×C412yes—
264C22×Dic13C2×D412yes—
265C22×Dic13C2×D412yes—
266C22×Dic13C2×D412yes—
267C22×Dic13C2×D412yes—
268C22×Dic13C2×Q812yes—
269C22×Dic13C2×Q812yes—
270C22×Dic13#4112yes—
271C22×Dic13#4112yes—
272C22×Dic13#4112yes—
273C2×Dic26—28no—
274C2×Dic26—28no—
275C2×Dic26—28no—
276C2×Dic26—28no—
277C2×Dic26—28no—
278C2×Dic26—28no—
279C2×Dic26—28no—
280C13×C4⋊C4—28no—
281C13×C4⋊C4—44no—
282C13×C22⋊C4—28no—
283C13×C22⋊C4—44no—
284C22⋊Dic13—28no—
285C22⋊Dic13—28no—
286C22⋊Dic13—28no—
287C22⋊Dic13—44no—
288#6101—28no—
289#6101—28no—
290#6101—44no—
291C4×Dic13—28no—
292C4×Dic13—28no—
293C4×Dic13—28no—
294C4×Dic13—44no—
295C22×C4×Q8—131no—
296C2×#393—131no—
297C2×#385—131no—
298C2×#385D1311yescharacteristic
299C2×C4×C22⋊C4—131no—
300#1446—131no—
301#1444—131no—
302#1439—131no—
303#1437—131no—
304#1437—131no—
305#1436—131no—
306#1436—131no—
307#1436—131no—
308#1436—131no—
309#1434—131no—
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—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
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×C13—41no—
341C23×C13—41no—
342C23×C13—41no—
343C23×C13—41no—
344C23×C13C4×Q814yescomplemented
345C23×C13C23×C411yescharacteristic
346C23×C13C22×D411yescharacteristic
347C23×C13C22×D411yescharacteristic
348C23×C13C22×D411yescharacteristic
349C23×C13C22×Q811yescharacteristic
350C23×C13C2×#4111yescharacteristic
351C23×C13C2×#4111yescharacteristic
352C23×C13C2×#4111yescharacteristic
353C23×C13C2×#4111yescharacteristic
354C23×C13C2×#4111yescharacteristic
355C23×C13C2×#4111yescharacteristic
356C23×C13H(5,𝔽2)11yescharacteristic
357C23×C13H(5,𝔽2)11yescharacteristic
358C23×C132−1+411yescharacteristic
359C23×C132−1+411yescharacteristic
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—416no—
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×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13C4×D414yes—
402C2×C4×C13#12014yes—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
423C2×Dic13—22no—
424C2×Dic13—22no—
425C2×Dic13—22no—
426C2×Dic13—22no—
427C2×Dic13—22no—
428C2×Dic13—22no—
429C2×Dic13—22no—
430C2×Dic13—22no—
431C2×Dic13—22no—
432C2×Dic13—22no—
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×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×Dic13C4×D414yes—
457C2×Dic13C4×D414yes—
458C2×Dic13C22⋊Q814yes—
459Dic26—232no—
460C23×Q8—131no—
461C24×C4C2×D1311yescharacteristic
462C2×C4×Q8—264no—
463C2×C4×Q8—264no—
464C2×C4×Q8—264no—
465C22×C4⋊C4—131no—
466C22×C4⋊C4—131no—
467C22×C4⋊C4—131no—
468C22×C4⋊C4C2×D1311yescharacteristic
469C22×C4⋊C4C2×D1311yescharacteristic
470C22×C22⋊C4—131no—
471C22×C22⋊C4—131no—
472C22×C22⋊C4—131no—
473C22×C22⋊C4—131no—
474C22×C22⋊C4C2×D1311yescharacteristic
475C22×C22⋊C4C2×D1311yescharacteristic
476C22×C42—131no—
477C22×C42—131no—
478C22×C42—131no—
479C22×C42—131no—
480#393—138no—
481#385—24no—
482#385—264no—
483C4×C22⋊C4—264no—
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×#95—131no—
495C2×#95—131no—
496C2×#95—131no—
497C2×#95—131no—
498C2×#95—131no—
499C2×#95—131no—
500C2×#95C2×D1311yescharacteristic
501C2×#95C2×D1311yescharacteristic
502C22×C13—24no—
503C22×C13—24no—
504C22×C13—24no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13—42no—
512C22×C13—42no—
513C22×C13—42no—
514C22×C13—42no—
515C22×C13—42no—
516C22×C13—42no—
517C22×C13C2×C4×D411yescharacteristic
518C22×C13C2×C4×D411yescharacteristic
519C22×C13C2×C4×D411yescharacteristic
520C22×C13C2×C4×Q811yescharacteristic
521C22×C13C4×#4111yescharacteristic
522C22×C13#52011yescharacteristic
523C22×C13#52011yescharacteristic
524C22×C13C2×#12011yescharacteristic
525C22×C13C2×C22⋊Q811yescharacteristic
526C22×C13#52511yescharacteristic
527C22×C13#52511yescharacteristic
528C22×C13#52511yescharacteristic
529C22×C13#52511yescharacteristic
530C22×C13#52911yescharacteristic
531C22×C13#53311yescharacteristic
532C22×C13#53511yescharacteristic
533C22×C13#53611yescharacteristic
534C22×C13#54211yescharacteristic
535C22×C13#54211yescharacteristic
536C22×C13#54611yescharacteristic
537C22×C13#54611yescharacteristic
538C22×C13#54611yescharacteristic
539C22×C13#54611yescharacteristic
540C22×C13#54811yescharacteristic
541C22×C13#54811yescharacteristic
542C22×C13D4×Q811yescharacteristic
543C22×C13D4×Q811yescharacteristic
544C22×C13#55211yescharacteristic
545C22×C13#55211yescharacteristic
546C22×C13#55411yescharacteristic
547C22×C13#55411yescharacteristic
548C22×C13#55611yescharacteristic
549C22×C13#55611yescharacteristic
550C22×C13#55911yescharacteristic
551C22×C13#55911yescharacteristic
552C4×C13—24no—
553C4×C13—24no—
554C4×C13—42no—
555C4×C13—42no—
556C4×C13—42no—
557C4×C13—81no—
558Dic13—24no—
559Dic13—24no—
560Dic13—24no—
561Dic13—42no—
562Dic13—42no—
563Dic13—42no—
564Dic13—42no—
565Dic13—81no—
566C25C22×D1311yescharacteristic
567C22×Q8—134no—
568C22×Q8—262no—
569C22×Q8—262no—
570C22×Q8—262no—
571C22×Q8—262no—
572C22×Q8—262no—
573C22×Q8—262no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—41no—
580C23×C4—41no—
581C23×C4—131no—
582C23×C4—131no—
583C23×C4—131no—
584C23×C4—131no—
585C23×C4—131no—
586C23×C4—131no—
587C23×C4—131no—
588C23×C4—131no—
589C23×C4C22×D1311yescharacteristic
590C23×C4C22×D1311yescharacteristic
591C23×C4C22×D1311yescharacteristic
592C23×C4C22×D1311yescharacteristic
593C23×C4C22×D1311yescharacteristic
594C23×C4C22×D1311yescharacteristic
595C4×Q8—2632no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—134no—
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—262no—
609C2×C4⋊C4—521no—
610C2×C4⋊C4C22⋊D1314yes—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—134no—
617C2×C22⋊C4—134no—
618C2×C22⋊C4—134no—
619C2×C22⋊C4—262no—
620C2×C22⋊C4—262no—
621C2×C22⋊C4—262no—
622C2×C22⋊C4—262no—
623C2×C22⋊C4—262no—
624C2×C22⋊C4—262no—
625C2×C22⋊C4—262no—
626C2×C22⋊C4—262no—
627C2×C22⋊C4—521no—
628C2×C22⋊C4C4×D1314yes—
629C2×C42—134no—
630C2×C42—262no—
631C2×C42—262no—
632C2×C42—262no—
633C2×C42—262no—
634C2×C42—262no—
635C2×C42—262no—
636C2×C42—262no—
637C2×C42—262no—
638C2×C42—262no—
639C2×C42—521no—
640C2×C42—521no—
641#95—22no—
642#95—22no—
643#95—134no—
644#95—134no—
645#95—134no—
646#95—262no—
647#95—262no—
648#95—262no—
649#95—262no—
650#95—262no—
651#95—262no—
652#95—262no—
653#95—262no—
654#95—262no—
655#95—521no—
656#95—521no—
657#95—521no—
658#95—521no—
659C2×C13—44no—
660C2×C13C4×#12011yescharacteristic
661C2×C13C4×C22⋊Q811yescharacteristic
662C2×C13#232611yescharacteristic
663C2×C13#236011yescharacteristic
664C2×C13#236011yescharacteristic
665C2×C13#236711yescharacteristic
666C2×C13#236711yescharacteristic
667C2×C13#240411yescharacteristic
668C2×C13#240911yescharacteristic
669C2×C13#245811yescharacteristic
670C2×C13#245811yescharacteristic
671C2×C13#246511yescharacteristic
672C2×C13#246511yescharacteristic
673C2×C13#258011yescharacteristic
674C2×C13#259911yescharacteristic
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×C4×D1312yes—
688C24#612912yes—
689C24Q8×D1312yes—
690C24C23×D1311yescharacteristic
691C2×Q8—268no—
692C2×Q8—268no—
693C2×Q8—268no—
694C2×Q8—268no—
695C2×Q8—268no—
696C2×Q8—268no—
697C2×Q8—268no—
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—28no—
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—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—132no—
739C22×C4—132no—
740C22×C4—132no—
741C22×C4—132no—
742C22×C4—132no—
743C22×C4—132no—
744C22×C4—132no—
745C22×C4—132no—
746C22×C4—132no—
747C22×C4—132no—
748C22×C4—132no—
749C22×C4—132no—
750C22×C4—132no—
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×C4—261no—
788C22×C4—261no—
789C22×C4—261no—
790C22×C4—261no—
791C22×C4—261no—
792C22×C4—261no—
793C22×C4—261no—
794C22×C4C2×C4×D1312yes—
795C22×C4C2×C4×D1312yes—
796C22×C4#612712yes—
797C22×C4D4×D1312yes—
798C22×C4D4×D1312yes—
799C22×C4#612912yes—
800C22×C4C2×C22⋊D1312yes—
801C22×C4C2×C22⋊D1312yes—
802C22×C4C2×C22⋊D1312yes—
803C4⋊C4—28no—
804C4⋊C4—44no—
805C4⋊C4—268no—
806C4⋊C4—268no—
807C4⋊C4—524no—
808C22⋊C4—28no—
809C22⋊C4—44no—
810C22⋊C4—268no—
811C22⋊C4—268no—
812C22⋊C4—268no—
813C22⋊C4—524no—
814C42—268no—
815C42—268no—
816C42—268no—
817C42—524no—
818C13#1417211yescharacteristic, complemented, Sylow
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23#8814114yescomplemented
854C23C22×C4×D1311yescharacteristic
855C23C2×#612711yescharacteristic
856C23C2×D4×D1311yescharacteristic
857C23C2×D4×D1311yescharacteristic
858C23C2×#612911yescharacteristic
859C23C2×#612911yescharacteristic
860C23#8825111yescharacteristic
861C23#8825111yescharacteristic
862C23C2×Q8×D1311yescharacteristic
863C23#8825411yescharacteristic
864C23#41×D1311yescharacteristic
865C23#41×D1311yescharacteristic
866C23#41×D1311yescharacteristic
867C23#8825711yescharacteristic
868C23C22×C22⋊D1311yescharacteristic
869Q8—2632no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—416no—
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—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—134no—
912C2×C4—134no—
913C2×C4—134no—
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—262no—
933C2×C4—262no—
934C2×C4—262no—
935C2×C4—262no—
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—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—
959C2×C4—521no—
960C2×C4—521no—
961C2×C4—521no—
962C2×C4—521no—
963C2×C4—521no—
964C2×C4—521no—
965C2×C4—521no—
966C2×C4—521no—
967C2×C4C4×C22⋊D1314yes—
968C2×C4#8819114yes—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22C2×#8814111yescharacteristic
985C22#1171920911yescharacteristic
986C22#1171921611yescharacteristic
987C22#1171921811yescharacteristic
988C22C4×#612911yescharacteristic
989C22#1171924711yescharacteristic
990C22C4×D4×D1311yescharacteristic
991C22C4×D4×D1311yescharacteristic
992C22#1171925111yescharacteristic
993C22#1171925211yescharacteristic
994C22#1171925211yescharacteristic
995C22#1171926411yescharacteristic
996C22#1171929111yescharacteristic
997C22#1171929611yescharacteristic
998C22#1171929611yescharacteristic
999C22#1171929711yescharacteristic
1000C22#1171932711yescharacteristic
1001C22D13×C22⋊Q811yescharacteristic
1002C22#1171933311yescharacteristic
1003C22#1171933711yescharacteristic
1004C22#1171933811yescharacteristic
1005C22#1171934111yescharacteristic
1006C22#1171934511yescharacteristic
1007C22#1171934611yescharacteristic
1008C22#1171935411yescharacteristic
1009C22#1171935511yescharacteristic
1010C22#1171936711yescharacteristic
1011C22#1171936911yescharacteristic
1012C22C2×C4×C22⋊D1311yescharacteristic
1013C22C2×#8819111yescharacteristic
1014C22#1171951111yescharacteristic
1015C22#1171951111yescharacteristic
1016C22Q8×C22⋊D1311yescharacteristic
1017C22#1171953311yescharacteristic
1018C22#1171953611yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—264no—
1026C4—264no—
1027C4—264no—
1028C4—522no—
1029C4—522no—
1030C4—522no—
1031C4—522no—
1032C4—1041no—
1033C2—44no—
1034C2C4×#8819111yescharacteristic
1035C2#1311736811yescharacteristic
1036C2#1311754211yescharacteristic
1037C2#1311783611yescharacteristic
1038C2#1311784111yescharacteristic
1039C2#1311790411yescharacteristic
1040C2#1311790911yescharacteristic
1041C2#1311815211yescharacteristic
1042C2#1311819711yescharacteristic
1043C2#1311875411yescharacteristic
1044C2#1311876211yescharacteristic
1045C2#1311885311yescharacteristic
1046C2#1311886111yescharacteristic
1047C2#1312019311yescharacteristic
1048C2#1312040911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#385C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#385D13
hypocenterC13#14172
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#88141C2semidirect
5. #13113106C2semidirect
6. #13113099C2semidirect
10. #13113071C2semidirect
11. #13113068C2semidirect
12. #13113068C2semidirect
13. #13113067C2semidirect
14. #13113060C2semidirect
57. #11718608C4semidirect
86. C22×Dic26C2×C4semidirect
110. C2×C22⋊Dic13Q8semidirect
148. #88071C2×C4semidirect
149. #88071C2×C4semidirect
150. #88071C2×C4semidirect
344. C23×C13C4×Q8semidirect
818. C13#14172semidirect
853. C23#88141semidirect

Maximal subgroups

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

subgroupindex
C22×#881412
C2×#117186082
C2×#117188712
C2×C4×C22⋊Dic132
#131131062
#131130992
#131130792
#131130732
#131130712
#131130682
#131130672
#131130602
C2×C13×#3852
#1417213