Finite Group Databasebeta

← #15788217

Subgroups — #15788217

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×C4×Dic26C211yesmaximal, characteristic, complemented
2C2×#11718608C211yesmaximal, characteristic
3C2×#11718611C211yesmaximal, characteristic
4C2×#11718607C211yesmaximal, characteristic
5C2×C22⋊C4×Dic13C211yesmaximal, characteristic
6#13113106C211yesmaximal, characteristic, complemented
7#13113100C211yesmaximal, characteristic, complemented
8#13113079C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic, complemented
11#13113070C211yesmaximal, characteristic, complemented
12#13113069C211yesmaximal, characteristic, complemented
13#13113067C211yesmaximal, characteristic, complemented
14#13113062C211yesmaximal, characteristic, complemented
15C13×#1437C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×C4×Dic26—24no—
34C2×C4×Dic26—24no—
35C2×C4×Dic26—24no—
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
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#11718611—24no—
55#11718608C418yescomplemented
56#11718607—24no—
57C22⋊C4×Dic13—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×Dic13—22no—
70C23×Dic13—41no—
71C23×Dic13—41no—
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×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—22no—
92C2×C13×C22⋊C4—22no—
93C2×C13×C22⋊C4—41no—
94C2×C13×C22⋊C4C2×C414yes—
95C2×C13×C22⋊C4Q814yescomplemented
96C2×C42×C13—22no—
97C2×C42×C13—22no—
98C2×C42×C13—22no—
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—41no—
106C2×C22⋊Dic13C2×C414yes—
107C2×C22⋊Dic13C2×C414yes—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13—22no—
111C2×C4⋊Dic13—22no—
112C2×C4⋊Dic13—41no—
113C2×C4⋊Dic13D414yes—
114C2×#6101—22no—
115C2×#6101—22no—
116C2×#6101—22no—
117C2×#6101—22no—
118C2×#6101—22no—
119C2×#6101—22no—
120C2×#6101—22no—
121C2×#6101—41no—
122C2×#6101D414yes—
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—
132C4×Dic26—232no—
133C13×#95—22no—
134C13×#95—22no—
135C13×#95—41no—
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—22no—
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—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×C13C22×C412yes—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13C2×D412yes—
206C22×C4×C13C2×Q812yes—
207C22×C4×C13C2×Q812yes—
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—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—28no—
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—44no—
255C22×Dic13—44no—
256C22×Dic13—44no—
257C22×Dic13—44no—
258C22×Dic13—44no—
259C22×Dic13—44no—
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×D412yes—
269C22×Dic13C2×D412yes—
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×C22⋊C4—28no—
281C13×C22⋊C4—28no—
282C13×C22⋊C4—44no—
283C42×C13—28no—
284C22⋊Dic13—28no—
285C22⋊Dic13—28no—
286C22⋊Dic13—44no—
287C4⋊Dic13—28no—
288C4⋊Dic13—44no—
289#6101—28no—
290#6101—28no—
291#6101—44no—
292C4×Dic13—28no—
293C4×Dic13—28no—
294C4×Dic13—44no—
295C22×C4×Q8—131no—
296C2×#393—131no—
297C2×#385—131no—
298C2×#385—131no—
299C2×C4×C22⋊C4—131no—
300#1446—131no—
301#1444—131no—
302#1439—131no—
303#1437—131no—
304#1437D1311yescharacteristic
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—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13C4×D414yes—
401C2×C4×C13C22⋊Q814yes—
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—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—416no—
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×Dic13#12014yes—
459Dic26—232no—
460C23×Q8—131no—
461C24×C4—131no—
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⋊C4—131no—
469C22×C4⋊C4—131no—
470C22×C22⋊C4—131no—
471C22×C22⋊C4—131no—
472C22×C22⋊C4—131no—
473C22×C22⋊C4C2×D1311yescharacteristic
474C22×C22⋊C4C2×D1311yescharacteristic
475C22×C22⋊C4C2×D1311yescharacteristic
476C22×C42—131no—
477C22×C42—131no—
478C22×C42—131no—
479C22×C42C2×D1311yescharacteristic
480#393—138no—
481#385—264no—
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×#95C2×D1311yescharacteristic
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—131no—
575C23×C4—131no—
576C23×C4—131no—
577C23×C4—131no—
578C23×C4—131no—
579C23×C4—131no—
580C23×C4—131no—
581C23×C4—131no—
582C23×C4—262no—
583C23×C4—262no—
584C23×C4—262no—
585C23×C4—262no—
586C23×C4—262no—
587C23×C4—521no—
588C23×C4—521no—
589C23×C4C22×D1311yescharacteristic
590C23×C4C22×D1311yescharacteristic
591C23×C4C22×D1311yescharacteristic
592C23×C4C22×D1311yescharacteristic
593C23×C4C22×D1311yescharacteristic
594C23×C4C22×D1311yescharacteristic
595C4×Q8—2632no—
596C2×C4⋊C4—134no—
597C2×C4⋊C4—134no—
598C2×C4⋊C4—262no—
599C2×C4⋊C4—262no—
600C2×C4⋊C4—262no—
601C2×C4⋊C4—262no—
602C2×C4⋊C4—262no—
603C2×C4⋊C4—262no—
604C2×C4⋊C4—262no—
605C2×C4⋊C4—262no—
606C2×C4⋊C4—262no—
607C2×C4⋊C4—262no—
608C2×C4⋊C4—262no—
609C2×C4⋊C4—521no—
610C2×C4⋊C4—521no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—134no—
619C2×C22⋊C4—134no—
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—521no—
627C2×C22⋊C4Dic2614yescomplemented
628C2×C22⋊C4C4×D1314yes—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—134no—
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—41no—
644#95—134no—
645#95—134no—
646#95—134no—
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—262no—
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×Dic2612yes—
688C24C2×C4×D1312yes—
689C24#612712yes—
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—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
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—132no—
740C22×C4—132no—
741C22×C4—132no—
742C22×C4—132no—
743C22×C4—132no—
744C22×C4—261no—
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—268no—
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—524no—
789C22×C4—524no—
790C22×C4—524no—
791C22×C4—524no—
792C22×C4—524no—
793C22×C4—524no—
794C22×C4C2×Dic2612yes—
795C22×C4C2×Dic2612yes—
796C22×C4C2×C4×D1312yes—
797C22×C4C2×C4×D1312yes—
798C22×C4D4×D1312yes—
799C22×C4D4×D1312yes—
800C22×C4D4×D1312yes—
801C22×C4#612912yes—
802C22×C4#612912yes—
803C4⋊C4—268no—
804C4⋊C4—268no—
805C4⋊C4—268no—
806C4⋊C4—524no—
807C4⋊C4—524no—
808C22⋊C4—28no—
809C22⋊C4—28no—
810C22⋊C4—44no—
811C22⋊C4—268no—
812C22⋊C4—268no—
813C22⋊C4—524no—
814C42—28no—
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—
853C23C4×Dic2614yescomplemented
854C23C22×Dic2611yescharacteristic
855C23C22×C4×D1311yescharacteristic
856C23C2×#612711yescharacteristic
857C23C2×D4×D1311yescharacteristic
858C23C2×D4×D1311yescharacteristic
859C23C2×D4×D1311yescharacteristic
860C23C2×#612911yescharacteristic
861C23C2×#612911yescharacteristic
862C23#8825111yescharacteristic
863C23#41×D1311yescharacteristic
864C23#41×D1311yescharacteristic
865C23#41×D1311yescharacteristic
866C23#8825611yescharacteristic
867C23#8825711yescharacteristic
868C23#8825711yescharacteristic
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—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—134no—
911C2×C4—134no—
912C2×C4—134no—
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—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—5216no—
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×C4#8813214yes—
968C2×C4#8813514yes—
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×C4×Dic2611yescharacteristic
985C22C2×#8813211yescharacteristic
986C22C2×#8813511yescharacteristic
987C22#1171919511yescharacteristic
988C22#1171922211yescharacteristic
989C22#1171922811yescharacteristic
990C22#1171923611yescharacteristic
991C22C4×#612911yescharacteristic
992C22D4×Dic2611yescharacteristic
993C22D4×Dic2611yescharacteristic
994C22#1171924311yescharacteristic
995C22#1171924411yescharacteristic
996C22#1171924611yescharacteristic
997C22#1171924811yescharacteristic
998C22C4×D4×D1311yescharacteristic
999C22C4×D4×D1311yescharacteristic
1000C22#1171925111yescharacteristic
1001C22#1171925211yescharacteristic
1002C22#1171925511yescharacteristic
1003C22D13×#12011yescharacteristic
1004C22#1171930311yescharacteristic
1005C22#1171930311yescharacteristic
1006C22#1171931111yescharacteristic
1007C22#1171931111yescharacteristic
1008C22#1171931211yescharacteristic
1009C22#1171931711yescharacteristic
1010C22#1171935311yescharacteristic
1011C22#1171935911yescharacteristic
1012C22#1171936111yescharacteristic
1013C22#1171937411yescharacteristic
1014C22#1171937611yescharacteristic
1015C22#1171938611yescharacteristic
1016C22#1171940711yescharacteristic
1017C22#1171941511yescharacteristic
1018C22#1171941811yescharacteristic
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—
1034C2#1311734111yescharacteristic
1035C2C4×#8813211yescharacteristic
1036C2#1311754511yescharacteristic
1037C2#1311783911yescharacteristic
1038C2#1311784211yescharacteristic
1039C2#1311790611yescharacteristic
1040C2#1311791011yescharacteristic
1041C2#1311815311yescharacteristic
1042C2#1311819811yescharacteristic
1043C2#1311875511yescharacteristic
1044C2#1311876311yescharacteristic
1045C2#1311885411yescharacteristic
1046C2#1311886211yescharacteristic
1047C2#1312019211yescharacteristic
1048C2#1312041011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1437C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1437D13
hypocenterC13#14172
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic26C2semidirect
6. #13113106C2semidirect
7. #13113100C2semidirect
10. #13113070C2semidirect
11. #13113070C2semidirect
12. #13113069C2semidirect
13. #13113067C2semidirect
14. #13113062C2semidirect
55. #11718608C4semidirect
86. C22×Dic26C2×C4semidirect
95. C2×C13×C22⋊C4Q8semidirect
148. #88071C2×C4semidirect
149. #88071C2×C4semidirect
150. #88071C2×C4semidirect
344. C23×C13C4×Q8semidirect
627. C2×C22⋊C4Dic26semidirect
818. C13#14172semidirect
853. C23C4×Dic26semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic262
C2×#117186082
C2×#117186112
C2×#117186072
C2×C22⋊C4×Dic132
#131131062
#131131002
#131130792
#131130732
#131130702
#131130692
#131130672
#131130622
C13×#14372
#1417213