Finite Group Databasebeta

← #15790943

Subgroups — #15790943

Order 3328.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718633C211yesmaximal, characteristic, complemented
2C2×#11718605C211yesmaximal, characteristic
3C2×#11718605C211yesmaximal, characteristic
4C2×#11718607C211yesmaximal, characteristic
5C2×#11718603C211yesmaximal, characteristic
6#13113100C211yesmaximal, characteristic, complemented
7#13113094C211yesmaximal, characteristic, complemented
8#13113087C211yesmaximal, characteristic, complemented
9#13113086C211yesmaximal, characteristic, complemented
10#13113081C211yesmaximal, characteristic
11#13113070C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13#13113064C211yesmaximal, characteristic, complemented
14#13113058C211yesmaximal, characteristic
15C13×#1439C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
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
51#11718633—24no—
52#11718607C418yescomplemented
53#11718605—24no—
54#11718605—24no—
55#11718603—24no—
56C25×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13—22no—
64C23×Dic13—22no—
65C23×Dic13—41no—
66C23×Dic13—41no—
67C23×Dic13—41no—
68C23×Dic13—41no—
69C23×Dic13C2×C414yes—
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—41no—
80C2×C13×C4⋊C4—41no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—41no—
86C2×C13×C22⋊C4—41no—
87C2×C13×C22⋊C4—41no—
88C2×C13×C22⋊C4—41no—
89C2×C13×C22⋊C4C2×C414yes—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—41no—
95C2×C22⋊Dic13—41no—
96C2×C22⋊Dic13C2×C414yes—
97C2×C22⋊Dic13D414yes—
98C2×C22⋊Dic13Q814yes—
99C2×C4⋊Dic13—22no—
100C2×C4⋊Dic13—41no—
101C2×C4⋊Dic13—41no—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101—41no—
110C2×#6101—41no—
111C2×#6101—41no—
112C2×#6101—41no—
113C2×#6101—41no—
114C2×#6101—41no—
115C2×#6101—41no—
116C2×#6101—41no—
117C2×#6101C2×C414yes—
118C2×#6101C2×C414yes—
119C2×#6101D414yes—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—22no—
124C2×C4×Dic13—41no—
125C2×C4×Dic13—41no—
126C13×#95—22no—
127C13×#95—41no—
128C13×#95—41no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—41no—
139#88071—41no—
140#88071—41no—
141#88071—41no—
142#88071C2×C414yes—
143#88071C2×C414yes—
144#14408—131nomaximal, Sylow
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13C22×C412yes—
158C24×C13C2×D412yes—
159C24×C13C2×Q812yes—
160C24×C13C2411yescharacteristic
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—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×C13C22×C412yes—
200C22×C4×C13C22×C412yes—
201C22×C4×C13C2×D412yes—
202C22×C4×C13#4112yes—
203C22×Dic13—21no—
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—28no—
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—44no—
249C22×Dic13—44no—
250C22×Dic13—44no—
251C22×Dic13—44no—
252C22×Dic13—44no—
253C22×Dic13—44no—
254C22×Dic13C22×C412yes—
255C22×Dic13C22×C412yes—
256C22×Dic13C22×C412yes—
257C22×Dic13C22×C412yes—
258C22×Dic13C2×D412yes—
259C22×Dic13C2×D412yes—
260C22×Dic13C2×D412yes—
261C22×Dic13C2×D412yes—
262C22×Dic13C2×Q812yes—
263C22×Dic13C2×Q812yes—
264C22×Dic13#4112yes—
265C22×Dic13#4112yes—
266C13×C4⋊C4—44no—
267C13×C22⋊C4—44no—
268C13×C22⋊C4—44no—
269C13×C22⋊C4—44no—
270C22⋊Dic13—44no—
271C22⋊Dic13—44no—
272C22⋊Dic13C4⋊C4116yescomplemented
273C4⋊Dic13—44no—
274#6101—28no—
275#6101—44no—
276#6101—44no—
277#6101—44no—
278#6101—44no—
279#6101—44no—
280C4×Dic13—44no—
281C4×Dic13—44no—
282C2×#389—131no—
283C2×#388—131no—
284C2×#388—131no—
285C2×#385—131no—
286C2×#380—131no—
287#1444—131no—
288#1442—131no—
289#1441—131no—
290#1441—131no—
291#1439—131no—
292#1439D1311yescharacteristic
293#1436—131no—
294#1436—131no—
295C4⋊#95—131no—
296C22⋊#95—131no—
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—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
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×C13—41no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13C2×C4⋊C414yes—
332C23×C13C23×C411yescharacteristic
333C23×C13C22×D411yescharacteristic
334C23×C13C22×D411yescharacteristic
335C23×C13C22×Q811yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13C2×#4111yescharacteristic
338C23×C13C2×#4111yescharacteristic
339C23×C13H(5,𝔽2)11yescharacteristic
340C23×C13H(5,𝔽2)11yescharacteristic
341C23×C13H(5,𝔽2)11yescharacteristic
342C23×C13H(5,𝔽2)11yescharacteristic
343C23×C13H(5,𝔽2)11yescharacteristic
344C23×C132−1+411yescharacteristic
345C23×C132−1+411yescharacteristic
346C23×C132−1+411yescharacteristic
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—22no—
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×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
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—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—416no—
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×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13C2×C4⋊C414yes—
444C2×Dic13C2×C4⋊C414yes—
445C2×Dic13C4×D414yes—
446C24×C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4—131no—
451C22×C4⋊C4—131no—
452C22×C4⋊C4—131no—
453C22×C4⋊C4—131no—
454C22×C4⋊C4C2×D1311yescharacteristic
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C22⋊C4—131no—
458C22×C22⋊C4C2×D1311yescharacteristic
459C22×C22⋊C4C2×D1311yescharacteristic
460C22×C22⋊C4C2×D1311yescharacteristic
461C22×C42—131no—
462C22×C42—131no—
463#389—264no—
464#388—264no—
465#388—264no—
466#385—138no—
467#380—264no—
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×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95C2×D1311yescharacteristic
484C2×#95C2×D1311yescharacteristic
485C2×#95C2×D1311yescharacteristic
486C22×C13—24no—
487C22×C13—24no—
488C22×C13—24no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13—42no—
497C22×C13—42no—
498C22×C13—42no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13C22×C4⋊C411yescharacteristic
502C22×C13C2×C4×D411yescharacteristic
503C22×C13C4×#4111yescharacteristic
504C22×C13#51811yescharacteristic
505C22×C13#51811yescharacteristic
506C22×C13#51911yescharacteristic
507C22×C13#52011yescharacteristic
508C22×C13#53411yescharacteristic
509C22×C13#53511yescharacteristic
510C22×C13#53711yescharacteristic
511C22×C13#53711yescharacteristic
512C22×C13#53811yescharacteristic
513C22×C13#53811yescharacteristic
514C22×C13#53811yescharacteristic
515C22×C13#53911yescharacteristic
516C22×C13#54011yescharacteristic
517C22×C13#54211yescharacteristic
518C22×C13#54411yescharacteristic
519C22×C13#54411yescharacteristic
520C22×C13D4211yescharacteristic
521C22×C13#54611yescharacteristic
522C22×C13#54611yescharacteristic
523C22×C13#54711yescharacteristic
524C22×C13#54711yescharacteristic
525C22×C13#54811yescharacteristic
526C22×C13D4×Q811yescharacteristic
527C22×C13#55211yescharacteristic
528C22×C13#55411yescharacteristic
529C22×C13#55411yescharacteristic
530C22×C13#55411yescharacteristic
531C22×C13#55611yescharacteristic
532C22×C13#56211yescharacteristic
533C22×C13#56211yescharacteristic
534C22×C13#56311yescharacteristic
535C22×C13#56311yescharacteristic
536C4×C13—42no—
537C4×C13—42no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—81no—
541C4×C13—81no—
542Dic13—24no—
543Dic13—24no—
544Dic13—24no—
545Dic13—42no—
546Dic13—42no—
547Dic13—42no—
548Dic13—81no—
549Dic13—81no—
550C25C22×D1311yescharacteristic
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—131no—
556C23×C4—131no—
557C23×C4—134no—
558C23×C4—131no—
559C23×C4—131no—
560C23×C4—262no—
561C23×C4—262no—
562C23×C4—521no—
563C23×C4—521no—
564C23×C4—521no—
565C23×C4—521no—
566C23×C4C22×D1311yescharacteristic
567C23×C4C22×D1311yescharacteristic
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C2×C4⋊C4—22no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—134no—
576C2×C4⋊C4—134no—
577C2×C4⋊C4—134no—
578C2×C4⋊C4—262no—
579C2×C4⋊C4—262no—
580C2×C4⋊C4—262no—
581C2×C4⋊C4—262no—
582C2×C4⋊C4—262no—
583C2×C4⋊C4—262no—
584C2×C4⋊C4—262no—
585C2×C4⋊C4—262no—
586C2×C4⋊C4—521no—
587C2×C4⋊C4—521no—
588C2×C4⋊C4—521no—
589C2×C4⋊C4—521no—
590C2×C4⋊C4—521no—
591C2×C4⋊C4—521no—
592C2×C4⋊C4—521no—
593C2×C4⋊C4—521no—
594C2×C4⋊C4—521no—
595C2×C4⋊C4—521no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—134no—
605C2×C22⋊C4—134no—
606C2×C22⋊C4—134no—
607C2×C22⋊C4—262no—
608C2×C22⋊C4—262no—
609C2×C22⋊C4—262no—
610C2×C22⋊C4—262no—
611C2×C22⋊C4—521no—
612C2×C22⋊C4—521no—
613C2×C22⋊C4C4×D1314yes—
614C2×C42—262no—
615C2×C42—262no—
616C2×C42—262no—
617C2×C42—262no—
618C2×C42—521no—
619C2×C42—521no—
620#95—22no—
621#95—41no—
622#95—41no—
623#95—134no—
624#95—134no—
625#95—262no—
626#95—262no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—521no—
635#95—521no—
636#95—521no—
637#95—521no—
638C2×C13—44no—
639C2×C13#231611yescharacteristic
640C2×C13#232111yescharacteristic
641C2×C13#233511yescharacteristic
642C2×C13D4×C4⋊C411yescharacteristic
643C2×C13#234911yescharacteristic
644C2×C13#236211yescharacteristic
645C2×C13#237811yescharacteristic
646C2×C13#267111yescharacteristic
647C2×C13#267611yescharacteristic
648C2×C13#269511yescharacteristic
649C2×C13#271511yescharacteristic
650C2×C13#272011yescharacteristic
651C2×C13#272911yescharacteristic
652C2×C13#276811yescharacteristic
653C2×C13#278811yescharacteristic
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24C2×C4×D1312yes—
667C24D4×D1312yes—
668C24Q8×D1312yes—
669C24C23×D1311yescharacteristic
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—21no—
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—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—132no—
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—132no—
720C22×C4—268no—
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—524no—
766C22×C4—524no—
767C22×C4—524no—
768C22×C4—524no—
769C22×C4—524no—
770C22×C4—524no—
771C22×C4C2×C4×D1312yes—
772C22×C4C2×C4×D1312yes—
773C22×C4D4×D1312yes—
774C22×C4#612912yes—
775C4⋊C4—44no—
776C4⋊C4—268no—
777C4⋊C4—524no—
778C4⋊C4—524no—
779C4⋊C4—524no—
780C4⋊C4—524no—
781C4⋊C4—524no—
782C4⋊C4—524no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—1316no—
787C22⋊C4—524no—
788C22⋊C4—524no—
789C42—524no—
790C42—524no—
791C13#1440811yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C4⋊C4×D1314yes—
827C23C22×C4×D1311yescharacteristic
828C23C2×D4×D1311yescharacteristic
829C23C2×D4×D1311yescharacteristic
830C23C2×#612911yescharacteristic
831C23#8825111yescharacteristic
832C23#8825111yescharacteristic
833C23#8825111yescharacteristic
834C23#8825111yescharacteristic
835C23C2×Q8×D1311yescharacteristic
836C23#41×D1311yescharacteristic
837C23#41×D1311yescharacteristic
838C23#8825611yescharacteristic
839C23#8825711yescharacteristic
840C23#8825711yescharacteristic
841C23#8825711yescharacteristic
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—22no—
852C2×C4—22no—
853C2×C4—22no—
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—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—134no—
885C2×C4—134no—
886C2×C4—134no—
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—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—262no—
905C2×C4—262no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—262no—
909C2×C4—262no—
910C2×C4—262no—
911C2×C4—262no—
912C2×C4—262no—
913C2×C4—262no—
914C2×C4—5216no—
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—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4—521no—
939C2×C4—521no—
940C2×C4—521no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22#1171919111yescharacteristic
957C22C2×C4⋊C4×D1311yescharacteristic
958C22#1171922111yescharacteristic
959C22C4×#612911yescharacteristic
960C22C4×D4×D1311yescharacteristic
961C22#1171925011yescharacteristic
962C22#1171925111yescharacteristic
963C22#1171929411yescharacteristic
964C22#1171929511yescharacteristic
965C22#1171929611yescharacteristic
966C22#1171930211yescharacteristic
967C22#1171930211yescharacteristic
968C22#1171930711yescharacteristic
969C22#1171931211yescharacteristic
970C22#1171931611yescharacteristic
971C22#1171931811yescharacteristic
972C22#1171931811yescharacteristic
973C22#1171932611yescharacteristic
974C22#1171932811yescharacteristic
975C22#1171932811yescharacteristic
976C22#1171933711yescharacteristic
977C22#1171934011yescharacteristic
978C22#1171934111yescharacteristic
979C22#1171934111yescharacteristic
980C22#1171935511yescharacteristic
981C22#1171935911yescharacteristic
982C22#1171936011yescharacteristic
983C22#1171936211yescharacteristic
984C22#1171937211yescharacteristic
985C22#1171937411yescharacteristic
986C22#1171937711yescharacteristic
987C22#1171938211yescharacteristic
988C22#1171940711yescharacteristic
989C22#1171941711yescharacteristic
990C22#1171942411yescharacteristic
991C4—42no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C4—264no—
998C4—264no—
999C4—264no—
1000C4—522no—
1001C4—522no—
1002C4—522no—
1003C4—1041no—
1004C4—1041no—
1005C2—44no—
1006C2#1311745311yescharacteristic
1007C2#1311749211yescharacteristic
1008C2#1311762311yescharacteristic
1009C2#1311773411yescharacteristic
1010C2#1311774211yescharacteristic
1011C2#1311786011yescharacteristic
1012C2#1311799611yescharacteristic
1013C2#1312107411yescharacteristic
1014C2#1312113911yescharacteristic
1015C2#1312137011yescharacteristic
1016C2#1312164611yescharacteristic
1017C2#1312172211yescharacteristic
1018C2#1312182311yescharacteristic
1019C2#1312231811yescharacteristic
1020C2#1312257511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#14408
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#11718633C2semidirect
6. #13113100C2semidirect
7. #13113094C2semidirect
8. #13113087C2semidirect
9. #13113086C2semidirect
11. #13113070C2semidirect
12. #13113067C2semidirect
13. #13113064C2semidirect
52. #11718607C4semidirect
272. C22⋊Dic13C4⋊C4semidirect
791. C13#14408semidirect

Maximal subgroups

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

subgroupindex
C2×#117186332
C2×#117186052
C2×#117186072
C2×#117186032
#131131002
#131130942
#131130872
#131130862
#131130812
#131130702
#131130672
#131130642
#131130582
C13×#14392
#1440813