Finite Group Databasebeta

← #15790930

Subgroups — #15790930

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×#11718601C211yesmaximal, characteristic
2C2×#11718651C211yesmaximal, characteristic
3C2×#11718650C211yesmaximal, characteristic
4C2×#11718648C211yesmaximal, characteristic
5#13113100C211yesmaximal, characteristic, complemented
6#13113095C211yesmaximal, characteristic, complemented
7#13113089C211yesmaximal, characteristic, complemented
8#13113086C211yesmaximal, characteristic, complemented
9#13113080C211yesmaximal, characteristic
10#13113078C211yesmaximal, characteristic
11#13113069C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13#13113064C211yesmaximal, characteristic, complemented
14#13113057C211yesmaximal, characteristic
15C2×C13×#389C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C13×#389—24no—
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
51C2×#88071C2211yescharacteristic
52#11718651—24no—
53#11718650C418yescomplemented
54#11718648—24no—
55#11718601—24no—
56C24×D13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C22×C4×D13—22no—
72C22×C4×D13—22no—
73C22×C4×D13—41no—
74C22×C4×D13—41no—
75C22×C4×D13—41no—
76C22×C4×D13—41no—
77C22×C4×D13C2×C414yes—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—41no—
84C2×C13×C4⋊C4—41no—
85C2×C13×C4⋊C4—41no—
86C2×C13×C4⋊C4—41no—
87C2×C13×C4⋊C4—41no—
88C2×C13×C4⋊C4C2×C414yes—
89C2×C13×C4⋊C4D414yes—
90C2×C42×C13—22no—
91C2×C42×C13—22no—
92C2×C42×C13—41no—
93C2×#6103—22no—
94C2×#6103—22no—
95C2×#6103—22no—
96C2×#6103—22no—
97C2×#6103—22no—
98C2×#6103—22no—
99C2×#6103—22no—
100C2×#6103—22no—
101C2×#6103—41no—
102C2×#6103—41no—
103C2×#6103—41no—
104C2×#6103—41no—
105C2×#6103—41no—
106C2×#6103—41no—
107C2×#6103C2×C414yes—
108C2×#6103C2×C414yes—
109C2×#6103D414yes—
110C2×#6103Q814yes—
111C2×C4⋊Dic13—22no—
112C2×C4⋊Dic13—41no—
113C2×C4⋊Dic13—41no—
114C2×#6101—22no—
115C2×#6101—22no—
116C2×#6101—22no—
117C2×#6101—41no—
118C2×#6101—41no—
119C2×#6101—41no—
120C2×#6101—41no—
121C2×#6101—41no—
122C2×#6101C2×C414yes—
123C2×C4×Dic13—22no—
124C2×C4×Dic13—22no—
125C2×C4×Dic13—41no—
126C13×#95—22no—
127C13×#95—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—41no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#88071—41no—
141#88071—41no—
142#88071C2×C414yes—
143#88071C2×C414yes—
144#14408—131nomaximal, Sylow
145C24×C13C2411yescharacteristic
146C23×D13—21no—
147C23×D13—21no—
148C23×D13—21no—
149C23×D13—21no—
150C23×D13—21no—
151C23×D13—21no—
152C23×D13—21no—
153C23×D13—21no—
154C23×D13—21no—
155C23×D13—21no—
156C23×D13—21no—
157C23×D13—21no—
158C23×D13C22×C412yes—
159C23×D13C2×D412yes—
160C23×D13C2×Q812yes—
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×C13—21no—
200C22×C4×C13C22×C412yes—
201C22×C4×C13C22×C412yes—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13C2×D412yes—
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×Q812yes—
208C22×C4×C13#4112yes—
209C22×C4×C13#4112yes—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—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×Dic13C22×C412yes—
254C22×Dic13C22×C412yes—
255C22×Dic13C22×C412yes—
256C22×Dic13C2×D412yes—
257C22×Dic13C2×Q812yes—
258C22×Dic13#4112yes—
259C2×C4×D13—28no—
260C2×C4×D13—44no—
261C2×C4×D13—44no—
262C2×C4×D13—44no—
263C2×C4×D13—44no—
264C2×C4×D13—44no—
265C2×C4×D13—44no—
266C13×C4⋊C4—28no—
267C13×C4⋊C4—44no—
268C13×C4⋊C4—44no—
269C13×C4⋊C4—44no—
270C42×C13—44no—
271#6103—44no—
272#6103—44no—
273#6103—44no—
274#6103—44no—
275#6103—44no—
276#6103C4⋊C4116yescomplemented
277C4⋊Dic13—44no—
278#6101—44no—
279#6101—44no—
280#6101—44no—
281C4×Dic13—44no—
282C2×#389D1311yescharacteristic, complemented
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#1439—131no—
293#1436—131no—
294#1436—131no—
295C4⋊#95—131no—
296C22⋊#95—131no—
297C23×C13C23×C411yescharacteristic
298C23×C13C22×D411yescharacteristic
299C23×C13C22×D411yescharacteristic
300C23×C13C22×Q811yescharacteristic
301C23×C13C2×#4111yescharacteristic
302C23×C13C2×#4111yescharacteristic
303C23×C13C2×#4111yescharacteristic
304C23×C13H(5,𝔽2)11yescharacteristic
305C23×C13H(5,𝔽2)11yescharacteristic
306C23×C13H(5,𝔽2)11yescharacteristic
307C23×C13H(5,𝔽2)11yescharacteristic
308C23×C13H(5,𝔽2)11yescharacteristic
309C23×C132−1+411yescharacteristic
310C23×C132−1+411yescharacteristic
311C23×C132−1+411yescharacteristic
312C22×D13—22no—
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—22no—
322C22×D13—22no—
323C22×D13—22no—
324C22×D13—22no—
325C22×D13—22no—
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—41no—
331C22×D13—41no—
332C22×D13—41no—
333C22×D13—41no—
334C22×D13—41no—
335C22×D13—41no—
336C22×D13—41no—
337C22×D13—41no—
338C22×D13—41no—
339C22×D13—41no—
340C22×D13—41no—
341C22×D13—41no—
342C22×D13—41no—
343C22×D13—41no—
344C22×D13—41no—
345C22×D13—41no—
346C22×D13C2×C4⋊C414yes—
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—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—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×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13C2×C4⋊C414yes—
395C2×C4×C13C4×D414yes—
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—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×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13C2×C4⋊C414yes—
445C4×D13—416no—
446C24×C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4—131no—
451C22×C4⋊C4C2×D1311yescharacteristic
452C22×C4⋊C4C2×D1311yescharacteristic
453C22×C4⋊C4C2×D1311yescharacteristic
454C22×C4⋊C4C2×D1311yescharacteristic
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C22⋊C4—131no—
458C22×C22⋊C4—131no—
459C22×C22⋊C4—131no—
460C22×C22⋊C4—131no—
461C22×C42—131no—
462C22×C42C2×D1311yescharacteristic
463#389—24no—
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×#95—131no—
484C2×#95C2×D1311yescharacteristic
485C2×#95C2×D1311yescharacteristic
486C22×C13C22×C4⋊C411yescharacteristic
487C22×C13C2×C4×D411yescharacteristic
488C22×C13C4×#4111yescharacteristic
489C22×C13#51811yescharacteristic
490C22×C13#51811yescharacteristic
491C22×C13#51911yescharacteristic
492C22×C13#52011yescharacteristic
493C22×C13#53411yescharacteristic
494C22×C13#53511yescharacteristic
495C22×C13#53711yescharacteristic
496C22×C13#53711yescharacteristic
497C22×C13#53811yescharacteristic
498C22×C13#53811yescharacteristic
499C22×C13#53811yescharacteristic
500C22×C13#53911yescharacteristic
501C22×C13#54011yescharacteristic
502C22×C13#54211yescharacteristic
503C22×C13#54411yescharacteristic
504C22×C13#54411yescharacteristic
505C22×C13D4211yescharacteristic
506C22×C13#54611yescharacteristic
507C22×C13#54611yescharacteristic
508C22×C13#54711yescharacteristic
509C22×C13#54711yescharacteristic
510C22×C13#54811yescharacteristic
511C22×C13D4×Q811yescharacteristic
512C22×C13#55211yescharacteristic
513C22×C13#55411yescharacteristic
514C22×C13#55411yescharacteristic
515C22×C13#55411yescharacteristic
516C22×C13#55611yescharacteristic
517C22×C13#56211yescharacteristic
518C22×C13#56211yescharacteristic
519C22×C13#56311yescharacteristic
520C22×C13#56311yescharacteristic
521C2×D13—24no—
522C2×D13—24no—
523C2×D13—24no—
524C2×D13—42no—
525C2×D13—42no—
526C2×D13—42no—
527C2×D13—42no—
528C2×D13—42no—
529C2×D13—42no—
530C2×D13—42no—
531C2×D13—42no—
532C2×D13—42no—
533C2×D13—42no—
534C2×D13—42no—
535C2×D13—42no—
536C4×C13—24no—
537C4×C13—24no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—42no—
542C4×C13—81no—
543Dic13—24no—
544Dic13—42no—
545Dic13—42no—
546Dic13—42no—
547Dic13—81no—
548Dic13—81no—
549Dic13—81no—
550C25—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—134no—
556C23×C4—131no—
557C23×C4—131no—
558C23×C4—131no—
559C23×C4—262no—
560C23×C4—262no—
561C23×C4—521no—
562C23×C4—521no—
563C23×C4—521no—
564C23×C4—521no—
565C23×C4C22×D1311yescharacteristic
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—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—134no—
583C2×C4⋊C4—262no—
584C2×C4⋊C4—262no—
585C2×C4⋊C4—262no—
586C2×C4⋊C4—262no—
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⋊C4C4×D1314yes—
595C2×C4⋊C4C22⋊D1314yes—
596C2×C22⋊C4—134no—
597C2×C22⋊C4—134no—
598C2×C22⋊C4—134no—
599C2×C22⋊C4—134no—
600C2×C22⋊C4—262no—
601C2×C22⋊C4—262no—
602C2×C22⋊C4—262no—
603C2×C22⋊C4—262no—
604C2×C22⋊C4—262no—
605C2×C22⋊C4—262no—
606C2×C22⋊C4—262no—
607C2×C22⋊C4—262no—
608C2×C22⋊C4—521no—
609C2×C22⋊C4—521no—
610C2×C22⋊C4—521no—
611C2×C22⋊C4—521no—
612C2×C22⋊C4—521no—
613C2×C22⋊C4—521no—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—41no—
617C2×C42—262no—
618C2×C42—262no—
619C2×C42—521no—
620#95—22no—
621#95—22no—
622#95—134no—
623#95—134no—
624#95—262no—
625#95—262no—
626#95—262no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—521no—
633#95—521no—
634#95—521no—
635#95—521no—
636#95—521no—
637#95—521no—
638C2×C13#231611yescharacteristic
639C2×C13#232111yescharacteristic
640C2×C13#233511yescharacteristic
641C2×C13D4×C4⋊C411yescharacteristic
642C2×C13#234911yescharacteristic
643C2×C13#236211yescharacteristic
644C2×C13#237811yescharacteristic
645C2×C13#267111yescharacteristic
646C2×C13#267611yescharacteristic
647C2×C13#269511yescharacteristic
648C2×C13#271511yescharacteristic
649C2×C13#272011yescharacteristic
650C2×C13#272911yescharacteristic
651C2×C13#276811yescharacteristic
652C2×C13#278811yescharacteristic
653D13—44no—
654C24—132no—
655C24—132no—
656C24—132no—
657C24—261no—
658C24—261no—
659C24—261no—
660C24—261no—
661C24—261no—
662C24—261no—
663C24—261no—
664C24—261no—
665C24—261no—
666C24—261no—
667C24—261no—
668C24—261no—
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—21no—
709C22×C4—132no—
710C22×C4—132no—
711C22×C4—132no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
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—268no—
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—524no—
760C22×C4—524no—
761C22×C4—524no—
762C22×C4—524no—
763C22×C4—524no—
764C22×C4—524no—
765C22×C4C2×C4×D1312yes—
766C22×C4C2×C4×D1312yes—
767C22×C4C2×C4×D1312yes—
768C22×C4#612712yes—
769C22×C4D4×D1312yes—
770C22×C4Q8×D1312yes—
771C22×C4#613112yes—
772C22×C4C2×C22⋊D1312yes—
773C22×C4C2×C22⋊D1312yes—
774C22×C4C2×C22⋊D1312yes—
775C4⋊C4—28no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—524no—
780C4⋊C4—524no—
781C4⋊C4—524no—
782C4⋊C4—524no—
783C22⋊C4—1316no—
784C22⋊C4—524no—
785C22⋊C4—524no—
786C22⋊C4—524no—
787C22⋊C4—524no—
788C22⋊C4—524no—
789C42—44no—
790C42—524no—
791C13#1440811yescharacteristic, complemented, Sylow
792C23—134no—
793C23—262no—
794C23—262no—
795C23—262no—
796C23—262no—
797C23—262no—
798C23—262no—
799C23—262no—
800C23—262no—
801C23—262no—
802C23—262no—
803C23—262no—
804C23—262no—
805C23—262no—
806C23—262no—
807C23—262no—
808C23—262no—
809C23—262no—
810C23—262no—
811C23—521no—
812C23—521no—
813C23—521no—
814C23—521no—
815C23—521no—
816C23—521no—
817C23—521no—
818C23—521no—
819C23—521no—
820C23—521no—
821C23—521no—
822C23—521no—
823C23—521no—
824C23—521no—
825C23—521no—
826C23—521no—
827C23C22×C4×D1311yescharacteristic
828C23C2×#612711yescharacteristic
829C23C2×D4×D1311yescharacteristic
830C23#8825111yescharacteristic
831C23#8825111yescharacteristic
832C23#8825111yescharacteristic
833C23C2×Q8×D1311yescharacteristic
834C23C2×#613111yescharacteristic
835C23#8825411yescharacteristic
836C23#8825411yescharacteristic
837C23#41×D1311yescharacteristic
838C23#8825611yescharacteristic
839C23#8825611yescharacteristic
840C23#8825711yescharacteristic
841C23C22×C22⋊D1311yescharacteristic
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—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
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—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—134no—
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—5216no—
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—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4—521no—
939C2×C4C4⋊C4×D1314yes—
940C2×C4C4×C22⋊D1314yes—
941C22—264no—
942C22—264no—
943C22—264no—
944C22—522no—
945C22—522no—
946C22—522no—
947C22—522no—
948C22—522no—
949C22—522no—
950C22—522no—
951C22—522no—
952C22—522no—
953C22—522no—
954C22—522no—
955C22—522no—
956C22C2×C4⋊C4×D1311yescharacteristic
957C22#1171920911yescharacteristic
958C22#1171921211yescharacteristic
959C22#1171921611yescharacteristic
960C22#1171925011yescharacteristic
961C22#1171925011yescharacteristic
962C22#1171926511yescharacteristic
963C22#1171926511yescharacteristic
964C22#1171927711yescharacteristic
965C22C4×#613111yescharacteristic
966C22#1171928611yescharacteristic
967C22#1171928911yescharacteristic
968C22#1171931311yescharacteristic
969C22#1171931711yescharacteristic
970C22#1171932011yescharacteristic
971C22#1171932611yescharacteristic
972C22#1171933411yescharacteristic
973C22#1171933511yescharacteristic
974C22#1171934911yescharacteristic
975C22#1171935211yescharacteristic
976C22#1171939411yescharacteristic
977C22#1171939511yescharacteristic
978C22#1171939711yescharacteristic
979C22#1171940411yescharacteristic
980C22#1171943411yescharacteristic
981C22#1171943511yescharacteristic
982C22#1171943811yescharacteristic
983C22#1171944011yescharacteristic
984C22C2×C4×C22⋊D1311yescharacteristic
985C22D4×C22⋊D1311yescharacteristic
986C22#1171950911yescharacteristic
987C22Q8×C22⋊D1311yescharacteristic
988C22#1171952211yescharacteristic
989C22#1171952911yescharacteristic
990C22#1171953511yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—81no—
998C4—264no—
999C4—522no—
1000C4—522no—
1001C4—522no—
1002C4—1041no—
1003C4—1041no—
1004C4—1041no—
1005C2—524no—
1006C2#1311745111yescharacteristic
1007C2#1311749011yescharacteristic
1008C2#1311762911yescharacteristic
1009C2C4⋊C4×C22⋊D1311yescharacteristic
1010C2#1311774511yescharacteristic
1011C2#1311785911yescharacteristic
1012C2#1311799811yescharacteristic
1013C2#1312106811yescharacteristic
1014C2#1312113311yescharacteristic
1015C2#1312137211yescharacteristic
1016C2#1312164811yescharacteristic
1017C2#1312171211yescharacteristic
1018C2#1312181211yescharacteristic
1019C2#1312231911yescharacteristic
1020C2#1312258011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#389D13
hypocenterC13#14408
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
5. #13113100C2semidirect
6. #13113095C2semidirect
7. #13113089C2semidirect
8. #13113086C2semidirect
11. #13113069C2semidirect
12. #13113068C2semidirect
13. #13113064C2semidirect
15. C2×C13×#389C2semidirect
53. #11718650C4semidirect
276. #6103C4⋊C4semidirect
282. C2×#389D13semidirect
791. C13#14408semidirect

Maximal subgroups

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

subgroupindex
C2×#117186012
C2×#117186512
C2×#117186502
C2×#117186482
#131131002
#131130952
#131130892
#131130862
#131130802
#131130782
#131130692
#131130682
#131130642
#131130572
C2×C13×#3892
#1440813