Finite Group Databasebeta

← #15784424

Subgroups — #15784424

Order 3328.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718329C211yesmaximal, characteristic
2C2×#11718650C211yesmaximal, characteristic
3C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
4C2×C4×#6103C211yesmaximal, characteristic
5C2×#11718327C211yesmaximal, characteristic
6C2×#11718327C211yesmaximal, characteristic
7C2×D13×#95C211yesmaximal, characteristic
8#13113071C211yesmaximal, characteristic, complemented
9#13113070C211yesmaximal, characteristic, complemented
10#13113067C211yesmaximal, characteristic, complemented
11#13113064C211yesmaximal, characteristic, complemented
12#13113061C211yesmaximal, characteristic, complemented
13#13113057C211yesmaximal, characteristic
14C4×#88071C211yesmaximal, characteristic, complemented
15C13×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C23×C4×D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51#11718650C418yescomplemented
52C4⋊C4×Dic13—24no—
53C4×#6103—24no—
54#11718329C418yescomplemented
55#11718327—24no—
56#11718327C418yescomplemented
57D13×#95—24no—
58C24×D13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C22×C4×D13—22no—
74C22×C4×D13—22no—
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×D13—22no—
82C22×C4×D13—22no—
83C22×C4×D13—22no—
84C22×C4×D13—22no—
85C22×C4×D13—41no—
86C22×C4×D13—41no—
87C22×C4×D13—41no—
88C22×C4×D13—41no—
89C22×C4×D13—41no—
90C22×C4×D13—41no—
91C22×C4×D13C2×C414yes—
92C22×C4×D13C2×C414yes—
93C22×C4×D13C2×C414yes—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4C2×C414yescomplemented
97C2×C42×C13—22no—
98C2×C42×C13—22no—
99C2×C42×C13—41no—
100C2×#6103—22no—
101C2×#6103—22no—
102C2×#6103—22no—
103C2×#6103—22no—
104C2×#6103C2×C414yes—
105C2×#6103C2×C414yes—
106C2×#6103C2×C414yes—
107C2×#6103C2×C414yes—
108C2×#6103C2×C414yes—
109C2×#6103C2×C414yes—
110C2×#6103D414yes—
111C2×#6103Q814yes—
112C2×C4⋊Dic13—22no—
113C2×C4⋊Dic13—22no—
114C2×C4⋊Dic13C2×C414yescomplemented
115C2×#6101—41no—
116C2×#6101—41no—
117C2×#6101—41no—
118C2×#6101—41no—
119C2×#6101C2×C414yescomplemented
120C2×#6101C2×C414yescomplemented
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×Dic13—41no—
132C2×C4×Dic13—41no—
133C2×C4×Dic13—41no—
134C2×C4×Dic13C2×C414yescomplemented
135C2×C4×Dic13C2×C414yescomplemented
136C13×#95—22no—
137C13×#95—22no—
138C13×#95—41no—
139C13×#95C2×C414yescomplemented
140C13×#95C2×C414yescomplemented
141#88071—22no—
142#88071—22no—
143#88071—22no—
144#88071—22no—
145#88071—22no—
146#88071—22no—
147#88071—22no—
148#88071—41no—
149#88071C2×C414yescomplemented
150#88071C2×C414yescomplemented
151#88071C2×C414yescomplemented
152#88071C2×C414yescomplemented
153#88071D414yes—
154#13814—131nomaximal, Sylow
155C24×C13C2411yescharacteristic
156C23×D13—21no—
157C23×D13—21no—
158C23×D13—21no—
159C23×D13—21no—
160C23×D13—21no—
161C23×D13—21no—
162C23×D13—21no—
163C23×D13—21no—
164C23×D13C22×C412yes—
165C23×D13C22×C412yes—
166C23×D13C22×C412yes—
167C23×D13C2×D412yes—
168C23×D13C2×Q812yes—
169C23×D13#4112yes—
170C23×D13#4112yes—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13C22×C412yes—
208C22×C4×C13C22×C412yes—
209C22×C4×C13C22×C412yes—
210C22×C4×C13C22×C412yes—
211C22×C4×C13C22×C412yes—
212C22×C4×C13C22×C412yes—
213C22×C4×C13C22×C412yes—
214C22×C4×C13C22×C412yes—
215C22×C4×C13C22×C412yes—
216C22×C4×C13C2×D412yes—
217C22×C4×C13C2×D412yes—
218C22×C4×C13C2×Q812yes—
219C22×C4×C13#4112yes—
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×Dic13C22×C412yes—
255C22×Dic13C22×C412yes—
256C22×Dic13C22×C412yes—
257C22×Dic13C22×C412yes—
258C22×Dic13C22×C412yes—
259C22×Dic13C22×C412yes—
260C22×Dic13C22×C412yes—
261C22×Dic13C22×C412yes—
262C22×Dic13C22×C412yes—
263C22×Dic13C2×D412yes—
264C22×Dic13C2×D412yes—
265C22×Dic13C2×D412yes—
266C22×Dic13C2×Q812yes—
267C22×Dic13#4112yes—
268C22×Dic13#4112yes—
269C2×C4×D13—28no—
270C2×C4×D13—28no—
271C2×C4×D13—28no—
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×C4×D13—44no—
280C2×C4×D13—44no—
281C2×C4×D13—44no—
282C2×C4×D13—44no—
283C2×C4×D13—44no—
284C2×C4×D13—44no—
285C2×C4×D13—44no—
286C2×C4×D13—44no—
287C2×C4×D13—44no—
288C2×C4×D13—44no—
289C2×C4×D13—44no—
290C13×C4⋊C4—28no—
291C42×C13—44no—
292#6103—28no—
293#6103—28no—
294#6103C42116yescomplemented
295#6103C4⋊C4116yescomplemented
296C4⋊Dic13—28no—
297#6101—44no—
298#6101—44no—
299C4×Dic13—28no—
300C4×Dic13—44no—
301C4×Dic13—44no—
302C4×Dic13—44no—
303C4×Dic13—44no—
304C2×#385—131no—
305C2×#385—131no—
306C2×C4×C4⋊C4—131no—
307C2×C4×C22⋊C4—131no—
308C2×C4×C22⋊C4—131no—
309C2×C4×C22⋊C4—131no—
310C22×#95—131no—
311#1436—131no—
312#1436—131no—
313#1436—131no—
314#1436D1311yescharacteristic, complemented
315C4⋊#95—131no—
316#1434—131no—
317C22⋊#95—131no—
318C4×#95—131no—
319C23×C13C23×C411yescharacteristic
320C23×C13C23×C411yescharacteristic
321C23×C13C23×C411yescharacteristic
322C23×C13C22×D411yescharacteristic
323C23×C13C22×D411yescharacteristic
324C23×C13C22×Q811yescharacteristic
325C23×C13C2×#4111yescharacteristic
326C23×C13C2×#4111yescharacteristic
327C23×C13C2×#4111yescharacteristic
328C23×C13C2×#4111yescharacteristic
329C23×C13C2×#4111yescharacteristic
330C23×C13H(5,𝔽2)11yescharacteristic
331C23×C13H(5,𝔽2)11yescharacteristic
332C23×C13H(5,𝔽2)11yescharacteristic
333C23×C132−1+411yescharacteristic
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—22no—
352C22×D13—22no—
353C22×D13—22no—
354C22×D13—22no—
355C22×D13—22no—
356C22×D13—22no—
357C22×D13—22no—
358C22×D13—22no—
359C22×D13—22no—
360C22×D13—22no—
361C22×D13—22no—
362C22×D13C2×C4214yes—
363C22×D13C2×C4⋊C414yes—
364C22×D13#11714yes—
365C22×D13C4×D414yes—
366C22×D13C4×D414yes—
367C22×D13C4×Q814yes—
368C22×D13C4×Q814yes—
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—22no—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—22no—
398C2×C4×C13—22no—
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×C4214yes—
416C2×C4×C13C2×C4⋊C414yes—
417C2×C4×C13C4×D414yes—
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—22no—
436C2×Dic13—22no—
437C2×Dic13—22no—
438C2×Dic13—22no—
439C2×Dic13—22no—
440C2×Dic13—22no—
441C2×Dic13—22no—
442C2×Dic13—22no—
443C2×Dic13—22no—
444C2×Dic13—22no—
445C2×Dic13—22no—
446C2×Dic13—22no—
447C2×Dic13—22no—
448C2×Dic13—22no—
449C2×Dic13—22no—
450C2×Dic13—22no—
451C2×Dic13—41no—
452C2×Dic13—41no—
453C2×Dic13—41no—
454C2×Dic13—41no—
455C2×Dic13—41no—
456C2×Dic13—41no—
457C2×Dic13—41no—
458C2×Dic13—41no—
459C2×Dic13—41no—
460C2×Dic13—41no—
461C2×Dic13—41no—
462C2×Dic13—41no—
463C2×Dic13C2×C4214yes—
464C2×Dic13C2×C4⋊C414yes—
465C2×Dic13C4×D414yes—
466C2×Dic13C4×D414yes—
467C4×D13—416no—
468C4×D13—416no—
469C4×D13—416no—
470C24×C4—131no—
471C24×C4—131no—
472C24×C4—131no—
473C22×C4⋊C4—131no—
474C22×C4⋊C4—131no—
475C22×C4⋊C4—131no—
476C22×C4⋊C4C2×D1311yescharacteristic
477C22×C22⋊C4—131no—
478C22×C22⋊C4—131no—
479C22×C22⋊C4—131no—
480C22×C22⋊C4—131no—
481C22×C42—131no—
482C22×C42—131no—
483C22×C42—131no—
484C22×C42—131no—
485C22×C42—131no—
486C22×C42C2×D1311yescharacteristic
487#385—138no—
488#385—138no—
489C4×C4⋊C4—264no—
490C4×C22⋊C4—138no—
491C4×C22⋊C4—264no—
492C4×C22⋊C4—264no—
493C2×#95—131no—
494C2×#95—131no—
495C2×#95—131no—
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—264no—
507C2×#95C2×D1311yescharacteristic
508C2×#95C2×D1311yescharacteristic
509C2×#95C2×D1311yescharacteristic
510C2×#95C2×D1311yescharacteristic
511C2×#95C2×D1311yescharacteristic
512C22×C13C22×C4211yescharacteristic
513C22×C13C22×C4⋊C411yescharacteristic
514C22×C13C2×#11711yescharacteristic
515C22×C13C2×C4×D411yescharacteristic
516C22×C13C2×C4×D411yescharacteristic
517C22×C13C2×C4×D411yescharacteristic
518C22×C13C2×C4×D411yescharacteristic
519C22×C13C2×C4×D411yescharacteristic
520C22×C13C2×C4×Q811yescharacteristic
521C22×C13C2×C4×Q811yescharacteristic
522C22×C13C4×#4111yescharacteristic
523C22×C13C4×#4111yescharacteristic
524C22×C13C4×#4111yescharacteristic
525C22×C13#51811yescharacteristic
526C22×C13#51811yescharacteristic
527C22×C13#51811yescharacteristic
528C22×C13#52011yescharacteristic
529C22×C13#52011yescharacteristic
530C22×C13#52011yescharacteristic
531C22×C13D4211yescharacteristic
532C22×C13#54611yescharacteristic
533C22×C13#54611yescharacteristic
534C22×C13#54611yescharacteristic
535C22×C13#54611yescharacteristic
536C22×C13#54711yescharacteristic
537C22×C13D4×Q811yescharacteristic
538C22×C13#55111yescharacteristic
539C22×C13#55111yescharacteristic
540C22×C13#55111yescharacteristic
541C22×C13#55111yescharacteristic
542C22×C13#55211yescharacteristic
543C22×C13#55211yescharacteristic
544C22×C13#55411yescharacteristic
545C22×C13#55411yescharacteristic
546C22×C13#55411yescharacteristic
547C2×D13—24no—
548C2×D13—24no—
549C2×D13—24no—
550C2×D13—24no—
551C2×D13—24no—
552C2×D13—24no—
553C2×D13—24no—
554C2×D13—24no—
555C2×D13—24no—
556C2×D13—24no—
557C2×D13—24no—
558C2×D13—24no—
559C2×D13—24no—
560C2×D13—24no—
561C2×D13C4×C4⋊C418yescomplemented
562C4×C13—24no—
563C4×C13—24no—
564C4×C13—24no—
565C4×C13—42no—
566C4×C13—42no—
567C4×C13—42no—
568C4×C13—42no—
569Dic13—24no—
570Dic13—24no—
571Dic13—24no—
572Dic13—24no—
573Dic13—42no—
574Dic13—42no—
575Dic13—42no—
576C25—131no—
577C23×C4—131no—
578C23×C4—131no—
579C23×C4—131no—
580C23×C4—131no—
581C23×C4—131no—
582C23×C4—131no—
583C23×C4—131no—
584C23×C4—134no—
585C23×C4—134no—
586C23×C4—134no—
587C23×C4—262no—
588C23×C4—262no—
589C23×C4—262no—
590C23×C4—262no—
591C23×C4—262no—
592C23×C4—262no—
593C23×C4—262no—
594C23×C4—262no—
595C23×C4—262no—
596C23×C4—262no—
597C23×C4—262no—
598C23×C4—262no—
599C23×C4—521no—
600C23×C4—521no—
601C23×C4—521no—
602C23×C4—521no—
603C23×C4—521no—
604C23×C4—521no—
605C23×C4C22×D1311yescharacteristic
606C23×C4C22×D1311yescharacteristic
607C23×C4C22×D1311yescharacteristic
608C23×C4C22×D1311yescharacteristic
609C23×C4C22×D1311yescharacteristic
610C23×C4C22×D1311yescharacteristic
611C23×C4C22×D1311yescharacteristic
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—134no—
615C2×C4⋊C4—134no—
616C2×C4⋊C4—134no—
617C2×C4⋊C4—262no—
618C2×C4⋊C4—262no—
619C2×C4⋊C4—521no—
620C2×C4⋊C4—521no—
621C2×C4⋊C4—521no—
622C2×C4⋊C4—521no—
623C2×C4⋊C4C4×D1314yescomplemented
624C2×C22⋊C4—134no—
625C2×C22⋊C4—134no—
626C2×C22⋊C4—134no—
627C2×C22⋊C4—134no—
628C2×C22⋊C4—134no—
629C2×C22⋊C4—134no—
630C2×C22⋊C4—134no—
631C2×C22⋊C4—134no—
632C2×C22⋊C4—262no—
633C2×C22⋊C4—262no—
634C2×C22⋊C4—262no—
635C2×C22⋊C4—262no—
636C2×C42—22no—
637C2×C42—22no—
638C2×C42—41no—
639C2×C42—134no—
640C2×C42—134no—
641C2×C42—262no—
642C2×C42—262no—
643C2×C42—262no—
644C2×C42—262no—
645C2×C42—262no—
646C2×C42—262no—
647C2×C42—262no—
648C2×C42—262no—
649C2×C42—521no—
650C2×C42—521no—
651C2×C42—521no—
652C2×C42—521no—
653C2×C42—521no—
654#95—22no—
655#95—22no—
656#95—41no—
657#95—134no—
658#95—134no—
659#95—134no—
660#95—134no—
661#95—134no—
662#95—262no—
663#95—262no—
664#95—262no—
665#95—262no—
666#95—262no—
667#95—262no—
668#95—262no—
669#95—521no—
670#95C4×D1314yescomplemented
671#95C4×D1314yescomplemented
672C2×C13C2×C4×C4⋊C411yescharacteristic
673C2×C13C42×D411yescharacteristic
674C2×C13#227511yescharacteristic
675C2×C13#234211yescharacteristic
676C2×C13#234311yescharacteristic
677C2×C13D4×C4⋊C411yescharacteristic
678C2×C13#234911yescharacteristic
679C2×C13#235811yescharacteristic
680C2×C13#235811yescharacteristic
681C2×C13#235911yescharacteristic
682C2×C13#235911yescharacteristic
683C2×C13#236011yescharacteristic
684C2×C13#236011yescharacteristic
685C2×C13#236811yescharacteristic
686C2×C13#236811yescharacteristic
687D13—28no—
688C24—132no—
689C24—132no—
690C24—132no—
691C24—132no—
692C24—132no—
693C24—132no—
694C24—132no—
695C24—261no—
696C24—261no—
697C24—261no—
698C24—261no—
699C24—261no—
700C24—261no—
701C24—261no—
702C24—261no—
703C24C23×D1311yescharacteristic
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—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—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—132no—
752C22×C4—132no—
753C22×C4—132no—
754C22×C4—132no—
755C22×C4—268no—
756C22×C4—268no—
757C22×C4—268no—
758C22×C4—268no—
759C22×C4—268no—
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×C4—268no—
795C22×C4—524no—
796C22×C4—524no—
797C22×C4—524no—
798C22×C4—524no—
799C22×C4—524no—
800C22×C4—524no—
801C22×C4—524no—
802C22×C4—524no—
803C22×C4—524no—
804C22×C4—524no—
805C22×C4—524no—
806C22×C4—524no—
807C22×C4—524no—
808C22×C4—524no—
809C22×C4—524no—
810C22×C4C2×C4×D1312yes—
811C22×C4C2×C4×D1312yes—
812C22×C4C2×C4×D1312yes—
813C22×C4C2×C4×D1312yes—
814C22×C4C2×C4×D1312yes—
815C22×C4C2×C4×D1312yes—
816C22×C4C2×C4×D1312yes—
817C22×C4C2×C4×D1312yes—
818C22×C4C2×C4×D1312yes—
819C22×C4D4×D1312yes—
820C22×C4D4×D1312yes—
821C22×C4#612912yes—
822C22×C4Q8×D1312yes—
823C4⋊C4—28no—
824C4⋊C4—268no—
825C4⋊C4—524no—
826C4⋊C4—524no—
827C22⋊C4—1316no—
828C22⋊C4—1316no—
829C22⋊C4—268no—
830C22⋊C4—268no—
831C42—44no—
832C42—268no—
833C42—524no—
834C42—524no—
835C42—524no—
836C42—524no—
837C13#1381411yescharacteristic, complemented, Sylow
838C23—134no—
839C23—134no—
840C23—134no—
841C23—134no—
842C23—134no—
843C23—134no—
844C23—134no—
845C23—262no—
846C23—262no—
847C23—262no—
848C23—262no—
849C23—262no—
850C23—262no—
851C23—262no—
852C23—262no—
853C23—262no—
854C23—262no—
855C23—262no—
856C23—262no—
857C23—262no—
858C23—262no—
859C23—262no—
860C23—262no—
861C23—262no—
862C23—262no—
863C23—262no—
864C23—262no—
865C23—262no—
866C23—262no—
867C23—262no—
868C23—262no—
869C23—262no—
870C23—262no—
871C23—262no—
872C23—262no—
873C23C22×C4×D1311yescharacteristic
874C23C22×C4×D1311yescharacteristic
875C23C22×C4×D1311yescharacteristic
876C23C2×D4×D1311yescharacteristic
877C23C2×D4×D1311yescharacteristic
878C23C2×#612911yescharacteristic
879C23#8825111yescharacteristic
880C23C2×Q8×D1311yescharacteristic
881C23#8825411yescharacteristic
882C23#41×D1311yescharacteristic
883C23#41×D1311yescharacteristic
884C23#41×D1311yescharacteristic
885C23#41×D1311yescharacteristic
886C23#8825611yescharacteristic
887C23#8825611yescharacteristic
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—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
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—41no—
934C2×C4—134no—
935C2×C4—134no—
936C2×C4—134no—
937C2×C4—134no—
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—262no—
961C2×C4—262no—
962C2×C4—262no—
963C2×C4—262no—
964C2×C4—262no—
965C2×C4—262no—
966C2×C4—262no—
967C2×C4—262no—
968C2×C4—262no—
969C2×C4—262no—
970C2×C4—262no—
971C2×C4—5216no—
972C2×C4—5216no—
973C2×C4—5216no—
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×C4—521no—
985C2×C4—521no—
986C2×C4C42×D1314yes—
987C2×C4#8813514yes—
988C2×C4C4⋊C4×D1314yes—
989C22—138no—
990C22—264no—
991C22—264no—
992C22—264no—
993C22—264no—
994C22—264no—
995C22—264no—
996C22—264no—
997C22—264no—
998C22—264no—
999C22—264no—
1000C22—264no—
1001C22—264no—
1002C22—264no—
1003C22—264no—
1004C22C2×C42×D1311yescharacteristic
1005C22C2×#8813511yescharacteristic
1006C22C2×C4⋊C4×D1311yescharacteristic
1007C22#1171920911yescharacteristic
1008C22D13×#11711yescharacteristic
1009C22#1171922611yescharacteristic
1010C22#1171922711yescharacteristic
1011C22C4×#612911yescharacteristic
1012C22C4×#612911yescharacteristic
1013C22C4×D4×D1311yescharacteristic
1014C22C4×D4×D1311yescharacteristic
1015C22C4×D4×D1311yescharacteristic
1016C22C4×D4×D1311yescharacteristic
1017C22#1171925011yescharacteristic
1018C22#1171925011yescharacteristic
1019C22C4×Q8×D1311yescharacteristic
1020C22C4×Q8×D1311yescharacteristic
1021C22#1171927911yescharacteristic
1022C22#1171927911yescharacteristic
1023C22#1171929611yescharacteristic
1024C22#1171931411yescharacteristic
1025C22#1171931511yescharacteristic
1026C22#1171933611yescharacteristic
1027C22#1171934011yescharacteristic
1028C22#1171934111yescharacteristic
1029C22#1171934411yescharacteristic
1030C22#1171935911yescharacteristic
1031C22#1171936311yescharacteristic
1032C22#1171936411yescharacteristic
1033C22#1171938111yescharacteristic
1034C22#1171939511yescharacteristic
1035C22#1171939811yescharacteristic
1036C22#1171941011yescharacteristic
1037C22#1171941011yescharacteristic
1038C22#1171943211yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—264no—
1047C4—264no—
1048C4—264no—
1049C4—264no—
1050C4—522no—
1051C4—522no—
1052C4—522no—
1053C2—268no—
1054C2C4×C4⋊C4×D1311yescharacteristic
1055C2C4×#8813511yescharacteristic
1056C2#1311719611yescharacteristic
1057C2#1311768411yescharacteristic
1058C2#1311769111yescharacteristic
1059C2#1311773711yescharacteristic
1060C2#1311774211yescharacteristic
1061C2#1311781411yescharacteristic
1062C2#1311781611yescharacteristic
1063C2#1311782111yescharacteristic
1064C2#1311783111yescharacteristic
1065C2#1311783811yescharacteristic
1066C2#1311784611yescharacteristic
1067C2#1311791311yescharacteristic
1068C2#1311791811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC13×#1436C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1436D13
hypocenterC13#13814
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic13C2semidirect
8. #13113071C2semidirect
9. #13113070C2semidirect
10. #13113067C2semidirect
11. #13113064C2semidirect
12. #13113061C2semidirect
14. C4×#88071C2semidirect
15. C13×#1436C2semidirect
51. #11718650C4semidirect
54. #11718329C4semidirect
56. #11718327C4semidirect
96. C2×C13×C4⋊C4C2×C4semidirect
114. C2×C4⋊Dic13C2×C4semidirect
119. C2×#6101C2×C4semidirect
120. C2×#6101C2×C4semidirect
134. C2×C4×Dic13C2×C4semidirect
135. C2×C4×Dic13C2×C4semidirect
139. C13×#95C2×C4semidirect
140. C13×#95C2×C4semidirect
149. #88071C2×C4semidirect
150. #88071C2×C4semidirect
151. #88071C2×C4semidirect
152. #88071C2×C4semidirect
294. #6103C42semidirect
295. #6103C4⋊C4semidirect
314. #1436D13semidirect
561. C2×D13C4×C4⋊C4semidirect
623. C2×C4⋊C4C4×D13semidirect
670. #95C4×D13semidirect
671. #95C4×D13semidirect
837. C13#13814semidirect

Maximal subgroups

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

subgroupindex
C2×#117183292
C2×#117186502
C2×C4⋊C4×Dic132
C2×C4×#61032
C2×#117183272
C2×D13×#952
#131130712
#131130702
#131130672
#131130642
#131130612
#131130572
C4×#880712
C13×#14362
#1381413