Finite Group Databasebeta

← #15786124

Subgroups — #15786124

Order 3328.

2106 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×#11718633C211yesmaximal, characteristic, complemented
2C2×#11718871C211yesmaximal, characteristic
3C2×#11718607C211yesmaximal, characteristic
4C2×#11718603C211yesmaximal, characteristic
5C2×C22⋊C4×Dic13C211yesmaximal, characteristic
6C22×#88071C211yesmaximal, characteristic
7#13113099C211yesmaximal, characteristic, complemented
8#13113091C211yesmaximal, characteristic, complemented
9#13113087C211yesmaximal, characteristic, complemented
10#13113086C211yesmaximal, characteristic, complemented
11#13113071C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13#13113064C211yesmaximal, characteristic, complemented
14#13113058C211yesmaximal, characteristic
15C2×C13×#385C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C24×Dic13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C13×#385—24no—
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36#11718871—24no—
37C2×#88071—24no—
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
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54#11718633—24no—
55#11718607C418yescomplemented
56#11718603—24no—
57C22⋊C4×Dic13—24no—
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×Dic13—22no—
73C23×Dic13—22no—
74C23×Dic13—22no—
75C23×Dic13—22no—
76C23×Dic13—22no—
77C23×Dic13—22no—
78C23×Dic13—22no—
79C23×Dic13—22no—
80C23×Dic13—41no—
81C23×Dic13—41no—
82C23×Dic13—41no—
83C23×Dic13—41no—
84C23×Dic13C2×C414yes—
85C23×Dic13Q814yes—
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—41no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—22no—
102C2×C13×C22⋊C4—22no—
103C2×C13×C22⋊C4—22no—
104C2×C13×C22⋊C4C2×C414yes—
105C2×C13×C22⋊C4D414yes—
106C2×C22⋊Dic13—22no—
107C2×C22⋊Dic13—22no—
108C2×C22⋊Dic13—22no—
109C2×C22⋊Dic13C2×C414yes—
110C2×C22⋊Dic13D414yes—
111C2×C22⋊Dic13Q814yes—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101—22no—
116C2×#6101—22no—
117C2×#6101—22no—
118C2×#6101—22no—
119C2×#6101—22no—
120C2×#6101—22no—
121C2×#6101—22no—
122C2×#6101—41no—
123C2×#6101—41no—
124C2×#6101—41no—
125C2×#6101—41no—
126C2×#6101—41no—
127C2×#6101—41no—
128C2×#6101C2×C414yescomplemented
129C2×#6101C2×C414yescomplemented
130C2×C4×Dic13—22no—
131C2×C4×Dic13—22no—
132C2×C4×Dic13—22no—
133C2×C4×Dic13—22no—
134C2×C4×Dic13—41no—
135C2×C4×Dic13—41no—
136C13×#95—22no—
137C13×#95—22no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—22no—
143#88071—22no—
144#88071—22no—
145#88071—22no—
146#88071—22no—
147#88071—22no—
148#88071—22no—
149#88071—41no—
150#88071—41no—
151#88071C2×C414yescomplemented
152#88071C2×C414yescomplemented
153#88071D414yes—
154#14004—131nomaximal, Sylow
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×C13C22×C412yes—
164C24×C13C2×D412yes—
165C24×C13C2×D412yes—
166C24×C13C2×Q812yes—
167C24×C13C2×Q812yes—
168C24×C13#4112yes—
169C24×C13#4112yes—
170C24×C13C2411yescharacteristic
171C22×C4×C13—28no—
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×C13—21no—
208C22×C4×C13—44no—
209C22×C4×C13—44no—
210C22×C4×C13—44no—
211C22×C4×C13—44no—
212C22×C4×C13—44no—
213C22×C4×C13—44no—
214C22×C4×C13C22×C412yes—
215C22×C4×C13C22×C412yes—
216C22×C4×C13C2×D412yes—
217C22×C4×C13C2×D412yes—
218C22×C4×C13C2×D412yes—
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—28no—
237C22×Dic13—28no—
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—28no—
251C22×Dic13—28no—
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×Dic13—21no—
261C22×Dic13—21no—
262C22×Dic13—21no—
263C22×Dic13—21no—
264C22×Dic13—21no—
265C22×Dic13—21no—
266C22×Dic13—44no—
267C22×Dic13—44no—
268C22×Dic13—44no—
269C22×Dic13—44no—
270C22×Dic13—44no—
271C22×Dic13—44no—
272C22×Dic13—44no—
273C22×Dic13—44no—
274C22×Dic13—44no—
275C22×Dic13—44no—
276C22×Dic13C22×C412yes—
277C22×Dic13C22×C412yes—
278C22×Dic13C22×C412yes—
279C22×Dic13C22×C412yes—
280C22×Dic13C2×D412yes—
281C22×Dic13C2×D412yes—
282C22×Dic13C2×D412yes—
283C22×Dic13C2×D412yes—
284C22×Dic13C2×Q812yes—
285C22×Dic13C2×Q812yes—
286C22×Dic13C2×Q812yes—
287C22×Dic13C2×Q812yes—
288C22×Dic13#4112yes—
289C22×Dic13#4112yes—
290C13×C4⋊C4—44no—
291C13×C4⋊C4—44no—
292C13×C22⋊C4—28no—
293C13×C22⋊C4—28no—
294C22⋊Dic13—44no—
295C22⋊Dic13C4⋊C4116yescomplemented
296#6101—28no—
297#6101—44no—
298#6101—44no—
299#6101—44no—
300#6101—44no—
301#6101—44no—
302C4×Dic13—44no—
303C4×Dic13—44no—
304C2×#389—131no—
305C2×#385—131no—
306C2×#385—131no—
307C2×#385D1311yescharacteristic
308C2×#380—131no—
309C2×C4×C22⋊C4—131no—
310C22×#95—131no—
311#1444—131no—
312#1442—131no—
313#1441—131no—
314#1441—131no—
315#1436—131no—
316#1436—131no—
317C4⋊#95—131no—
318C22⋊#95—131no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13—22no—
340C23×C13—22no—
341C23×C13—22no—
342C23×C13—22no—
343C23×C13—22no—
344C23×C13—22no—
345C23×C13—22no—
346C23×C13—22no—
347C23×C13C2×C4⋊C414yes—
348C23×C13C4×D414yes—
349C23×C13C4×Q814yes—
350C23×C13#12114yes—
351C23×C13C22⋊Q814yes—
352C23×C13#12514yes—
353C23×C13C4⋊Q814yes—
354C23×C13C23×C411yescharacteristic
355C23×C13C22×D411yescharacteristic
356C23×C13C22×D411yescharacteristic
357C23×C13C22×D411yescharacteristic
358C23×C13C22×Q811yescharacteristic
359C23×C13C22×Q811yescharacteristic
360C23×C13C2×#4111yescharacteristic
361C23×C13C2×#4111yescharacteristic
362C23×C13C2×#4111yescharacteristic
363C23×C13C2×#4111yescharacteristic
364C23×C13C2×#4111yescharacteristic
365C23×C13H(5,𝔽2)11yescharacteristic
366C23×C13H(5,𝔽2)11yescharacteristic
367C23×C13H(5,𝔽2)11yescharacteristic
368C23×C132−1+411yescharacteristic
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—416no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
423C2×Dic13—22no—
424C2×Dic13—22no—
425C2×Dic13—22no—
426C2×Dic13—22no—
427C2×Dic13—22no—
428C2×Dic13—22no—
429C2×Dic13—22no—
430C2×Dic13—22no—
431C2×Dic13—22no—
432C2×Dic13—22no—
433C2×Dic13—22no—
434C2×Dic13—22no—
435C2×Dic13—22no—
436C2×Dic13—22no—
437C2×Dic13—22no—
438C2×Dic13—22no—
439C2×Dic13—22no—
440C2×Dic13—22no—
441C2×Dic13—22no—
442C2×Dic13—416no—
443C2×Dic13—416no—
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×Dic13—41no—
459C2×Dic13—41no—
460C2×Dic13—41no—
461C2×Dic13—41no—
462C2×Dic13—41no—
463C2×Dic13—41no—
464C2×Dic13—41no—
465C2×Dic13—41no—
466C2×Dic13C2×C4⋊C414yes—
467C2×Dic13C2×C4⋊C414yes—
468C2×Dic13C4×D414yes—
469C2×Dic13C22⋊Q814yes—
470C24×C4—131no—
471C24×C4—131no—
472C24×C4C2×D1311yescharacteristic
473C22×C4⋊C4—131no—
474C22×C4⋊C4—131no—
475C22×C4⋊C4—131no—
476C22×C4⋊C4—131no—
477C22×C4⋊C4—131no—
478C22×C4⋊C4—131no—
479C22×C4⋊C4C2×D1311yescharacteristic
480C22×C4⋊C4C2×D1311yescharacteristic
481C22×C22⋊C4—131no—
482C22×C22⋊C4—131no—
483C22×C22⋊C4C2×D1311yescharacteristic
484C22×C22⋊C4C2×D1311yescharacteristic
485C22×C42—131no—
486C22×C42—131no—
487#389—264no—
488#385—24no—
489#385—138no—
490#385—264no—
491#380—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—131no—
507C2×#95—131no—
508C2×#95—131no—
509C2×#95—264no—
510C2×#95C2×D1311yescharacteristic
511C2×#95C2×D1311yescharacteristic
512C22×C13—24no—
513C22×C13—24no—
514C22×C13—24no—
515C22×C13—24no—
516C22×C13—24no—
517C22×C13—24no—
518C22×C13—24no—
519C22×C13—24no—
520C22×C13—24no—
521C22×C13—24no—
522C22×C13—24no—
523C22×C13—24no—
524C22×C13—24no—
525C22×C13—24no—
526C22×C13#38918yescomplemented
527C22×C13C22×C4⋊C411yescharacteristic
528C22×C13C2×C4×D411yescharacteristic
529C22×C13C2×C4×D411yescharacteristic
530C22×C13C2×C4×Q811yescharacteristic
531C22×C13C4×#4111yescharacteristic
532C22×C13#51811yescharacteristic
533C22×C13#52011yescharacteristic
534C22×C13C2×#12111yescharacteristic
535C22×C13C2×C22⋊Q811yescharacteristic
536C22×C13C2×C22⋊Q811yescharacteristic
537C22×C13#52511yescharacteristic
538C22×C13C2×#12511yescharacteristic
539C22×C13#52911yescharacteristic
540C22×C13C2×C4⋊Q811yescharacteristic
541C22×C13#53311yescharacteristic
542C22×C13#53811yescharacteristic
543C22×C13#53911yescharacteristic
544C22×C13#54311yescharacteristic
545C22×C13#54411yescharacteristic
546C22×C13D4211yescharacteristic
547C22×C13D4211yescharacteristic
548C22×C13#54611yescharacteristic
549C22×C13#54611yescharacteristic
550C22×C13#54611yescharacteristic
551C22×C13#54611yescharacteristic
552C22×C13#54611yescharacteristic
553C22×C13#54711yescharacteristic
554C22×C13#54711yescharacteristic
555C22×C13D4×Q811yescharacteristic
556C22×C13#55111yescharacteristic
557C22×C13#55111yescharacteristic
558C22×C13#55211yescharacteristic
559C22×C13#55411yescharacteristic
560C22×C13#55411yescharacteristic
561C22×C13#55411yescharacteristic
562C4×C13—42no—
563C4×C13—42no—
564C4×C13—42no—
565C4×C13—42no—
566C4×C13—42no—
567C4×C13—42no—
568Dic13—24no—
569Dic13—24no—
570Dic13—24no—
571Dic13—24no—
572Dic13—42no—
573Dic13—42no—
574Dic13—81no—
575Dic13—81no—
576C25C22×D1311yescharacteristic
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4—131no—
585C23×C4—131no—
586C23×C4—131no—
587C23×C4—131no—
588C23×C4—131no—
589C23×C4—131no—
590C23×C4—134no—
591C23×C4—134no—
592C23×C4—131no—
593C23×C4—131no—
594C23×C4—262no—
595C23×C4—262no—
596C23×C4—262no—
597C23×C4—262no—
598C23×C4—262no—
599C23×C4—262no—
600C23×C4—262no—
601C23×C4—262no—
602C23×C4—521no—
603C23×C4—521no—
604C23×C4—521no—
605C23×C4—521no—
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—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—134no—
619C2×C4⋊C4—134no—
620C2×C4⋊C4—262no—
621C2×C4⋊C4—262no—
622C2×C4⋊C4—262no—
623C2×C4⋊C4—262no—
624C2×C4⋊C4—262no—
625C2×C4⋊C4—262no—
626C2×C4⋊C4—262no—
627C2×C4⋊C4—262no—
628C2×C4⋊C4—262no—
629C2×C4⋊C4—262no—
630C2×C4⋊C4—521no—
631C2×C4⋊C4—521no—
632C2×C4⋊C4—521no—
633C2×C4⋊C4—521no—
634C2×C4⋊C4—521no—
635C2×C4⋊C4—521no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—134no—
641C2×C22⋊C4—134no—
642C2×C22⋊C4—134no—
643C2×C22⋊C4—262no—
644C2×C22⋊C4—262no—
645C2×C22⋊C4—262no—
646C2×C22⋊C4C4×D1314yes—
647C2×C22⋊C4C22⋊D1314yes—
648C2×C42—262no—
649C2×C42—262no—
650C2×C42—262no—
651C2×C42—262no—
652C2×C42—521no—
653C2×C42—521no—
654#95—22no—
655#95—22no—
656#95—134no—
657#95—134no—
658#95—134no—
659#95—262no—
660#95—262no—
661#95—262no—
662#95—262no—
663#95—262no—
664#95—262no—
665#95—262no—
666#95—262no—
667#95—262no—
668#95—262no—
669#95—262no—
670#95—521no—
671#95—521no—
672C2×C13—28no—
673C2×C13C2×#38911yescharacteristic
674C2×C13C4×C22⋊Q811yescharacteristic
675C2×C13#232911yescharacteristic
676C2×C13D4×C4⋊C411yescharacteristic
677C2×C13#234911yescharacteristic
678C2×C13#235811yescharacteristic
679C2×C13#235911yescharacteristic
680C2×C13#242411yescharacteristic
681C2×C13#242511yescharacteristic
682C2×C13#243711yescharacteristic
683C2×C13#243811yescharacteristic
684C2×C13#244011yescharacteristic
685C2×C13#247311yescharacteristic
686C2×C13#250511yescharacteristic
687C2×C13#254911yescharacteristic
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24C2×C4×D1312yes—
697C24#612712yes—
698C24D4×D1312yes—
699C24#612912yes—
700C24Q8×D1312yes—
701C24Q8×D1312yes—
702C24C2×C22⋊D1312yes—
703C24C23×D1311yescharacteristic
704C22×C4—28no—
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—21no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—132no—
748C22×C4—132no—
749C22×C4—132no—
750C22×C4—132no—
751C22×C4—132no—
752C22×C4—132no—
753C22×C4—132no—
754C22×C4—132no—
755C22×C4—132no—
756C22×C4—132no—
757C22×C4—132no—
758C22×C4—132no—
759C22×C4—132no—
760C22×C4—132no—
761C22×C4—268no—
762C22×C4—268no—
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—268no—
780C22×C4—268no—
781C22×C4—261no—
782C22×C4—261no—
783C22×C4—261no—
784C22×C4—261no—
785C22×C4—261no—
786C22×C4—261no—
787C22×C4—261no—
788C22×C4—261no—
789C22×C4—261no—
790C22×C4—261no—
791C22×C4—261no—
792C22×C4—261no—
793C22×C4—261no—
794C22×C4—261no—
795C22×C4—261no—
796C22×C4—261no—
797C22×C4—261no—
798C22×C4—261no—
799C22×C4—261no—
800C22×C4—261no—
801C22×C4—261no—
802C22×C4—261no—
803C22×C4—261no—
804C22×C4—261no—
805C22×C4—261no—
806C22×C4—261no—
807C22×C4—524no—
808C22×C4—524no—
809C22×C4—524no—
810C22×C4—524no—
811C22×C4—524no—
812C22×C4—524no—
813C22×C4—524no—
814C22×C4—524no—
815C22×C4—524no—
816C22×C4—524no—
817C22×C4C2×C4×D1312yes—
818C22×C4C2×C4×D1312yes—
819C22×C4D4×D1312yes—
820C22×C4#612912yes—
821C22×C4C2×C22⋊D1312yes—
822C22×C4C2×C22⋊D1312yes—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—268no—
826C4⋊C4—524no—
827C4⋊C4—524no—
828C4⋊C4—524no—
829C4⋊C4—524no—
830C4⋊C4—524no—
831C22⋊C4—28no—
832C22⋊C4—28no—
833C22⋊C4—1316no—
834C22⋊C4—524no—
835C42—524no—
836C42—524no—
837C13#1400411yescharacteristic, complemented, Sylow
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23#8814114yes—
867C23#8814314yes—
868C23C4⋊C4×D1314yes—
869C23#8815014yes—
870C23C4×C22⋊D1314yes—
871C23#8819314yes—
872C23#8819814yes—
873C23C22×C4×D1311yescharacteristic
874C23C2×#612711yescharacteristic
875C23C2×D4×D1311yescharacteristic
876C23C2×D4×D1311yescharacteristic
877C23C2×#612911yescharacteristic
878C23C2×#612911yescharacteristic
879C23#8825111yescharacteristic
880C23#8825111yescharacteristic
881C23C2×Q8×D1311yescharacteristic
882C23C2×Q8×D1311yescharacteristic
883C23#41×D1311yescharacteristic
884C23#41×D1311yescharacteristic
885C23#8825611yescharacteristic
886C23#8825711yescharacteristic
887C23C22×C22⋊D1311yescharacteristic
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—416no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—134no—
932C2×C4—134no—
933C2×C4—134no—
934C2×C4—134no—
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—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—5216no—
966C2×C4—5216no—
967C2×C4—521no—
968C2×C4—521no—
969C2×C4—521no—
970C2×C4—521no—
971C2×C4—521no—
972C2×C4—521no—
973C2×C4—521no—
974C2×C4—521no—
975C2×C4—521no—
976C2×C4—521no—
977C2×C4—521no—
978C2×C4—521no—
979C2×C4—521no—
980C2×C4—521no—
981C2×C4—521no—
982C2×C4—521no—
983C2×C4—521no—
984C2×C4—521no—
985C2×C4—521no—
986C2×C4—521no—
987C2×C4—521no—
988C2×C4—521no—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22#1171863318yescomplemented
1004C22C2×#8814111yescharacteristic
1005C22C2×#8814311yescharacteristic
1006C22C2×C4⋊C4×D1311yescharacteristic
1007C22C2×#8815011yescharacteristic
1008C22C4×#612911yescharacteristic
1009C22#1171924611yescharacteristic
1010C22C4×D4×D1311yescharacteristic
1011C22#1171925011yescharacteristic
1012C22#1171925111yescharacteristic
1013C22#1171925511yescharacteristic
1014C22#1171926111yescharacteristic
1015C22#1171926111yescharacteristic
1016C22#1171929111yescharacteristic
1017C22#1171929511yescharacteristic
1018C22#1171929611yescharacteristic
1019C22#1171929811yescharacteristic
1020C22#1171932711yescharacteristic
1021C22#1171932811yescharacteristic
1022C22D13×C22⋊Q811yescharacteristic
1023C22#1171933711yescharacteristic
1024C22#1171933911yescharacteristic
1025C22#1171934011yescharacteristic
1026C22#1171934111yescharacteristic
1027C22#1171934111yescharacteristic
1028C22#1171935411yescharacteristic
1029C22#1171935911yescharacteristic
1030C22#1171936011yescharacteristic
1031C22#1171937011yescharacteristic
1032C22C2×C4×C22⋊D1311yescharacteristic
1033C22D4×C22⋊D1311yescharacteristic
1034C22C2×#8819311yescharacteristic
1035C22#1171951111yescharacteristic
1036C22C2×#8819811yescharacteristic
1037C22#1171952911yescharacteristic
1038C22#1171953411yescharacteristic
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—264no—
1046C4—264no—
1047C4—264no—
1048C4—264no—
1049C4—522no—
1050C4—522no—
1051C4—1041no—
1052C4—1041no—
1053C2—28no—
1054C2C2×#1171863311yescharacteristic
1055C2#1311736811yescharacteristic
1056C2#1311756711yescharacteristic
1057C2#1311773411yescharacteristic
1058C2#1311774211yescharacteristic
1059C2#1311781311yescharacteristic
1060C2#1311782211yescharacteristic
1061C2#1311837611yescharacteristic
1062C2#1311839111yescharacteristic
1063C2#1311850111yescharacteristic
1064C2#1311851611yescharacteristic
1065C2#1311853511yescharacteristic
1066C2#1311897411yescharacteristic
1067C2#1311933511yescharacteristic
1068C2#1311984411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#385C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#385D13
hypocenterC13#14004
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#11718633C2semidirect
7. #13113099C2semidirect
8. #13113091C2semidirect
9. #13113087C2semidirect
10. #13113086C2semidirect
11. #13113071C2semidirect
12. #13113068C2semidirect
13. #13113064C2semidirect
55. #11718607C4semidirect
128. C2×#6101C2×C4semidirect
129. C2×#6101C2×C4semidirect
151. #88071C2×C4semidirect
152. #88071C2×C4semidirect
295. C22⋊Dic13C4⋊C4semidirect
526. C22×C13#389semidirect
837. C13#14004semidirect
1003. C22#11718633semidirect

Maximal subgroups

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

subgroupindex
C2×#117186332
C2×#117188712
C2×#117186072
C2×#117186032
C2×C22⋊C4×Dic132
C22×#880712
#131130992
#131130912
#131130872
#131130862
#131130712
#131130682
#131130642
#131130582
C2×C13×#3852
#1400413