Finite Group Databasebeta

← #15789905

Subgroups — #15789905

Order 3328.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718608C211yesmaximal, characteristic
2C2×#11718307C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic13C211yesmaximal, characteristic
4#13113106C211yesmaximal, characteristic, complemented
5#13113100C211yesmaximal, characteristic, complemented
6#13113097C211yesmaximal, characteristic, complemented
7#13113097C211yesmaximal, characteristic, complemented
8#13113081C211yesmaximal, characteristic
9#13113079C211yesmaximal, characteristic
10#13113079C211yesmaximal, characteristic
11#13113070C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13#13113062C211yesmaximal, characteristic, complemented
14#13113059C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C4×C22⋊Dic13—24no—
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
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
52#11718608C418yescomplemented
53#11718307—24no—
54C25×C13C2311yescharacteristic
55C23×C4×C13—22no—
56C23×C4×C13—22no—
57C23×C4×C13—41no—
58C23×C4×C13—41no—
59C23×C4×C13—41no—
60C23×C4×C13—41no—
61C23×C4×C13Q814yescomplemented
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C22×Dic26—22no—
77C22×Dic26—22no—
78C22×Dic26—41no—
79C22×Dic26—41no—
80C22×Dic26—41no—
81C22×Dic26—41no—
82C22×Dic26C2×C414yescomplemented
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—41no—
85C2×C13×C22⋊C4—41no—
86C2×C13×C22⋊C4—41no—
87C2×C13×C22⋊C4—41no—
88C2×C13×C22⋊C4C2×C414yes—
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—22no—
95C2×C22⋊Dic13—41no—
96C2×C22⋊Dic13—41no—
97C2×C22⋊Dic13—41no—
98C2×C22⋊Dic13—41no—
99C2×C22⋊Dic13C2×C414yes—
100C2×C22⋊Dic13C2×C414yes—
101C2×C4⋊Dic13—22no—
102C2×C4⋊Dic13—41no—
103C2×C4⋊Dic13—41no—
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—41no—
107C2×#6101—41no—
108C2×#6101—41no—
109C2×#6101—41no—
110C2×C4×Dic13—22no—
111C2×C4×Dic13—41no—
112C2×C4×Dic13—41no—
113C2×C4×Dic13—41no—
114C2×C4×Dic13—41no—
115C2×C4×Dic13D414yes—
116C13×#95—22no—
117C13×#95—22no—
118C13×#95—41no—
119C13×#95—41no—
120#88071—22no—
121#88071—22no—
122#88071—22no—
123#88071—22no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—41no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071—41no—
132#88071—41no—
133#88071—41no—
134#88071—41no—
135#88071C2×C414yescomplemented
136#88071C2×C414yescomplemented
137#88071C2×C414yescomplemented
138#14319—131nomaximal, Sylow
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13C22×C412yes—
152C24×C13C2×Q812yes—
153C24×C13#4112yes—
154C24×C13C2411yescharacteristic
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
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—28no—
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—44no—
193C22×C4×C13—44no—
194C22×C4×C13—44no—
195C22×C4×C13—44no—
196C22×C4×C13—44no—
197C22×C4×C13—44no—
198C22×C4×C13C22×C412yes—
199C22×C4×C13C22×C412yes—
200C22×C4×C13C2×D412yes—
201C22×C4×C13C2×Q812yes—
202C22×C4×C13C2×Q812yes—
203C22×C4×C13#4112yes—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
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—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×Dic13C22×C412yes—
253C22×Dic13C22×C412yes—
254C22×Dic13C22×C412yes—
255C22×Dic13C22×C412yes—
256C22×Dic13C2×D412yes—
257C22×Dic13C2×D412yes—
258C22×Dic13#4112yes—
259C22×Dic13#4112yes—
260C2×Dic26—28no—
261C2×Dic26—44no—
262C2×Dic26—44no—
263C2×Dic26—44no—
264C2×Dic26—44no—
265C2×Dic26—44no—
266C2×Dic26—44no—
267C13×C22⋊C4—44no—
268C13×C22⋊C4—44no—
269C22⋊Dic13—28no—
270C22⋊Dic13—28no—
271C22⋊Dic13—44no—
272C22⋊Dic13—44no—
273C4⋊Dic13—44no—
274#6101—44no—
275#6101—44no—
276C4×Dic13—44no—
277C4×Dic13—44no—
278C2×#393—131no—
279C2×#391—131no—
280C2×C4×C22⋊C4—131no—
281#1446—131no—
282#1444—131no—
283#1443—131no—
284#1443—131no—
285#1439—131no—
286#1439—131no—
287#1439—131no—
288#1436—131no—
289#1436—131no—
290#1434—131no—
291C22⋊#95—131no—
292C22⋊#95D1311yescharacteristic
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13C4×Q814yes—
328C23×C13C23×C411yescharacteristic
329C23×C13C22×D411yescharacteristic
330C23×C13C22×Q811yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13C2×#4111yescharacteristic
335C23×C13H(5,𝔽2)11yescharacteristic
336C23×C13H(5,𝔽2)11yescharacteristic
337C23×C13H(5,𝔽2)11yescharacteristic
338C23×C13H(5,𝔽2)11yescharacteristic
339C23×C13H(5,𝔽2)11yescharacteristic
340C23×C13H(5,𝔽2)11yescharacteristic
341C23×C132−1+411yescharacteristic
342C23×C132−1+411yescharacteristic
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—416no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13C22⋊Q814yes—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—41no—
408C2×Dic13—41no—
409C2×Dic13—41no—
410C2×Dic13—41no—
411C2×Dic13—41no—
412C2×Dic13—41no—
413C2×Dic13—41no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C2×Dic13—41no—
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×Dic13C4×D414yes—
442Dic26—416no—
443C23×Q8—131no—
444C24×C4C2×D1311yescharacteristic
445C22×C4⋊C4—131no—
446C22×C4⋊C4—131no—
447C22×C4⋊C4—131no—
448C22×C22⋊C4—131no—
449C22×C22⋊C4—131no—
450C22×C22⋊C4—131no—
451C22×C22⋊C4—131no—
452C22×C22⋊C4C2×D1311yescharacteristic
453C22×C22⋊C4C2×D1311yescharacteristic
454C22×C42—131no—
455C22×C42—131no—
456#393—138no—
457#391—264no—
458C4×C22⋊C4—264no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95—131no—
464C2×#95—131no—
465C2×#95—131no—
466C2×#95—131no—
467C2×#95—131no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95C2×D1311yescharacteristic
478C2×#95C2×D1311yescharacteristic
479C2×#95C2×D1311yescharacteristic
480C2×#95C2×D1311yescharacteristic
481C22×C13—24no—
482C22×C13—24no—
483C22×C13—24no—
484C22×C13—42no—
485C22×C13—42no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13C2×C4×D411yescharacteristic
497C22×C13C2×C4×Q811yescharacteristic
498C22×C13C4×#4111yescharacteristic
499C22×C13#51811yescharacteristic
500C22×C13#51811yescharacteristic
501C22×C13#52011yescharacteristic
502C22×C13#52011yescharacteristic
503C22×C13C2×C22⋊Q811yescharacteristic
504C22×C13#52511yescharacteristic
505C22×C13#52911yescharacteristic
506C22×C13#53311yescharacteristic
507C22×C13#53411yescharacteristic
508C22×C13#53511yescharacteristic
509C22×C13#53511yescharacteristic
510C22×C13#53611yescharacteristic
511C22×C13#53811yescharacteristic
512C22×C13#53811yescharacteristic
513C22×C13#53811yescharacteristic
514C22×C13#53811yescharacteristic
515C22×C13#53811yescharacteristic
516C22×C13#53811yescharacteristic
517C22×C13#53811yescharacteristic
518C22×C13#53811yescharacteristic
519C22×C13#53911yescharacteristic
520C22×C13#53911yescharacteristic
521C22×C13#54211yescharacteristic
522C22×C13#54211yescharacteristic
523C22×C13#54211yescharacteristic
524C22×C13#54211yescharacteristic
525C22×C13#54211yescharacteristic
526C22×C13#54211yescharacteristic
527C22×C13#54311yescharacteristic
528C22×C13#54311yescharacteristic
529C22×C13#54411yescharacteristic
530C22×C13#54411yescharacteristic
531C4×C13—24no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—81no—
536C4×C13—81no—
537Dic13—24no—
538Dic13—42no—
539Dic13—42no—
540Dic13—42no—
541Dic13—42no—
542Dic13—42no—
543Dic13—81no—
544Dic13—81no—
545C25C22×D1311yescharacteristic
546C22×Q8—134no—
547C22×Q8—262no—
548C22×Q8—262no—
549C22×Q8—521no—
550C22×Q8—521no—
551C22×Q8—521no—
552C22×Q8—521no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—41no—
556C23×C4—41no—
557C23×C4—41no—
558C23×C4—41no—
559C23×C4—131no—
560C23×C4—131no—
561C23×C4—131no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4—131no—
567C23×C4Dic2614yescomplemented
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C23×C4C22×D1311yescharacteristic
573C23×C4C22×D1311yescharacteristic
574C2×C4⋊C4—262no—
575C2×C4⋊C4—262no—
576C2×C4⋊C4—262no—
577C2×C4⋊C4—521no—
578C2×C4⋊C4—521no—
579C2×C4⋊C4—521no—
580C2×C4⋊C4—521no—
581C2×C4⋊C4—521no—
582C2×C4⋊C4—521no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—134no—
589C2×C22⋊C4—134no—
590C2×C22⋊C4—262no—
591C2×C22⋊C4—262no—
592C2×C22⋊C4—262no—
593C2×C22⋊C4—262no—
594C2×C22⋊C4—262no—
595C2×C22⋊C4—262no—
596C2×C22⋊C4—521no—
597C2×C22⋊C4—521no—
598C2×C22⋊C4—521no—
599C2×C22⋊C4—521no—
600C2×C22⋊C4C4×D1314yes—
601C2×C42—134no—
602C2×C42—262no—
603C2×C42—521no—
604C2×C42—521no—
605C2×C42—521no—
606C2×C42—521no—
607#95—22no—
608#95—22no—
609#95—41no—
610#95—41no—
611#95—134no—
612#95—134no—
613#95—134no—
614#95—262no—
615#95—262no—
616#95—262no—
617#95—262no—
618#95—262no—
619#95—262no—
620#95—262no—
621#95—521no—
622#95—521no—
623#95—521no—
624#95—521no—
625#95—521no—
626#95—521no—
627#95—521no—
628#95—521no—
629C2×C13—44no—
630C2×C13C4×C22⋊Q811yescharacteristic
631C2×C13#232111yescharacteristic
632C2×C13#232611yescharacteristic
633C2×C13#232911yescharacteristic
634C2×C13#232911yescharacteristic
635C2×C13#233711yescharacteristic
636C2×C13#233711yescharacteristic
637C2×C13#262611yescharacteristic
638C2×C13#262811yescharacteristic
639C2×C13#263111yescharacteristic
640C2×C13#263811yescharacteristic
641C2×C13#265311yescharacteristic
642C2×C13#265311yescharacteristic
643C2×C13#266511yescharacteristic
644C2×C13#266511yescharacteristic
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24C2×Dic2612yes—
658C24C2×C4×D1312yes—
659C24#612712yes—
660C24C23×D1311yescharacteristic
661C2×Q8—268no—
662C2×Q8—524no—
663C2×Q8—524no—
664C2×Q8—524no—
665C2×Q8—524no—
666C2×Q8—524no—
667C2×Q8—524no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—28no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—132no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
715C22×C4—132no—
716C22×C4—132no—
717C22×C4—132no—
718C22×C4—132no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
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—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×C4C2×Dic2612yes—
768C22×C4C2×Dic2612yes—
769C22×C4C2×C4×D1312yes—
770C22×C4C2×C4×D1312yes—
771C22×C4D4×D1312yes—
772C22×C4#612912yes—
773C4⋊C4—524no—
774C4⋊C4—524no—
775C4⋊C4—524no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4—268no—
779C22⋊C4—268no—
780C22⋊C4—524no—
781C22⋊C4—524no—
782C42—524no—
783C42—524no—
784C13#1431911yescharacteristic, complemented, Sylow
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23C4×Dic2614yes—
820C23C22×Dic2611yescharacteristic
821C23C22×C4×D1311yescharacteristic
822C23C2×#612711yescharacteristic
823C23C2×D4×D1311yescharacteristic
824C23C2×#612911yescharacteristic
825C23#8825111yescharacteristic
826C23#8825111yescharacteristic
827C23#8825111yescharacteristic
828C23#8825111yescharacteristic
829C23#8825111yescharacteristic
830C23#8825411yescharacteristic
831C23#41×D1311yescharacteristic
832C23#41×D1311yescharacteristic
833C23#8825611yescharacteristic
834C23#8825711yescharacteristic
835Q8—5216no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—416no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—134no—
879C2×C4—262no—
880C2×C4—262no—
881C2×C4—262no—
882C2×C4—262no—
883C2×C4—262no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—262no—
894C2×C4—262no—
895C2×C4—262no—
896C2×C4—262no—
897C2×C4—262no—
898C2×C4—262no—
899C2×C4—262no—
900C2×C4—521no—
901C2×C4—521no—
902C2×C4—521no—
903C2×C4—521no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4#8813214yes—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22C2×C4×Dic2611yescharacteristic
951C22C2×#8813211yescharacteristic
952C22#1171918811yescharacteristic
953C22#1171918811yescharacteristic
954C22#1171919111yescharacteristic
955C22#1171919911yescharacteristic
956C22#1171920511yescharacteristic
957C22#1171920911yescharacteristic
958C22#1171922011yescharacteristic
959C22#1171922211yescharacteristic
960C22#1171922411yescharacteristic
961C22C4×#612911yescharacteristic
962C22#1171924311yescharacteristic
963C22C4×D4×D1311yescharacteristic
964C22#1171925011yescharacteristic
965C22#1171925111yescharacteristic
966C22#1171925211yescharacteristic
967C22#1171926511yescharacteristic
968C22#1171926911yescharacteristic
969C22#1171929411yescharacteristic
970C22#1171929711yescharacteristic
971C22#1171929811yescharacteristic
972C22#1171929811yescharacteristic
973C22#1171930811yescharacteristic
974C22#1171931211yescharacteristic
975C22#1171931811yescharacteristic
976C22#1171931811yescharacteristic
977C22#1171933311yescharacteristic
978C22#1171934511yescharacteristic
979C22#1171934511yescharacteristic
980C22#1171934811yescharacteristic
981C22#1171936211yescharacteristic
982C22#1171936211yescharacteristic
983C22#1171936711yescharacteristic
984C22#1171936711yescharacteristic
985C4—24no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—81no—
990C4—81no—
991C4—264no—
992C4—522no—
993C4—522no—
994C4—522no—
995C4—522no—
996C4—522no—
997C4—1041no—
998C4—1041no—
999C2—44no—
1000C2C4×#8813211yescharacteristic
1001C2#1311749211yescharacteristic
1002C2#1311754211yescharacteristic
1003C2#1311756411yescharacteristic
1004C2#1311756911yescharacteristic
1005C2#1311764511yescharacteristic
1006C2#1311765011yescharacteristic
1007C2#1312064511yescharacteristic
1008C2#1312066111yescharacteristic
1009C2#1312069211yescharacteristic
1010C2#1312075711yescharacteristic
1011C2#1312089911yescharacteristic
1012C2#1312090111yescharacteristic
1013C2#1312100811yescharacteristic
1014C2#1312100911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C22⋊#95C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22⋊#95D13
hypocenterC13#14319
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#11718307C2semidirect
4. #13113106C2semidirect
5. #13113100C2semidirect
6. #13113097C2semidirect
7. #13113097C2semidirect
11. #13113070C2semidirect
12. #13113067C2semidirect
13. #13113062C2semidirect
52. #11718608C4semidirect
61. C23×C4×C13Q8semidirect
82. C22×Dic26C2×C4semidirect
135. #88071C2×C4semidirect
136. #88071C2×C4semidirect
137. #88071C2×C4semidirect
567. C23×C4Dic26semidirect
784. C13#14319semidirect

Maximal subgroups

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

subgroupindex
C2×#117186082
C2×#117183072
C2×C4×C22⋊Dic132
#131131062
#131131002
#131130972
#131130812
#131130792
#131130702
#131130672
#131130622
#131130592
C13×C22⋊#952
#1431913