Finite Group Databasebeta

← #15790887

Subgroups — #15790887

Order 3328.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718633C211yesmaximal, characteristic, complemented
2C2×#11718601C211yesmaximal, characteristic
3C2×#11718651C211yesmaximal, characteristic
4C2×#11718650C211yesmaximal, characteristic
5C2×#11718650C211yesmaximal, characteristic
6C2×#11718650C211yesmaximal, characteristic
7#13113099C211yesmaximal, characteristic, complemented
8#13113099C211yesmaximal, characteristic, complemented
9#13113095C211yesmaximal, characteristic, complemented
10#13113086C211yesmaximal, characteristic, complemented
11#13113078C211yesmaximal, characteristic
12#13113078C211yesmaximal, characteristic
13#13113068C211yesmaximal, characteristic, complemented
14#13113063C211yesmaximal, characteristic, complemented
15C2×C13×#384C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C13×#384—24no—
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#11718650—24no—
54#11718650—24no—
55#11718650—24no—
56#11718633—24no—
57#11718601C418yescomplemented
58C24×D13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C22×C4×D13—22no—
74C22×C4×D13—22no—
75C22×C4×D13—22no—
76C22×C4×D13—41no—
77C22×C4×D13—41no—
78C22×C4×D13—41no—
79C22×C4×D13—41no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—41no—
90C2×C13×C4⋊C4—41no—
91C2×C13×C4⋊C4—41no—
92C2×C13×C4⋊C4—41no—
93C2×C13×C4⋊C4—41no—
94C2×C13×C4⋊C4—41no—
95C2×C13×C4⋊C4—41no—
96C2×C13×C4⋊C4—41no—
97C2×C13×C4⋊C4D414yes—
98C2×C42×C13—22no—
99C2×C42×C13—22no—
100C2×C42×C13C2×C414yescomplemented
101C2×#6103—22no—
102C2×#6103—22no—
103C2×#6103—22no—
104C2×#6103—22no—
105C2×#6103—22no—
106C2×#6103—22no—
107C2×#6103—22no—
108C2×#6103—22no—
109C2×#6103—22no—
110C2×#6103—41no—
111C2×#6103—41no—
112C2×#6103—41no—
113C2×#6103—41no—
114C2×#6103C2×C414yes—
115C2×#6103C2×C414yes—
116C2×#6103C2×C414yes—
117C2×#6103D414yes—
118C2×#6103Q814yes—
119C2×#6101—22no—
120C2×#6101—22no—
121C2×#6101—22no—
122C2×#6101—22no—
123C2×#6101—22no—
124C2×#6101—22no—
125C2×#6101—22no—
126C2×#6101—41no—
127C2×#6101—41no—
128C2×#6101—41no—
129C2×#6101—41no—
130C2×#6101C2×C414yescomplemented
131C2×C4×Dic13—22no—
132C2×C4×Dic13—22no—
133C2×C4×Dic13—41no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—22no—
143#88071—22no—
144#88071—41no—
145#88071—41no—
146#88071—41no—
147#88071C2×C414yescomplemented
148#88071C2×C414yescomplemented
149#88071D414yes—
150#14405—131nomaximal, Sylow
151C24×C13C2411yescharacteristic
152C23×D13—21no—
153C23×D13—21no—
154C23×D13—21no—
155C23×D13—21no—
156C23×D13—21no—
157C23×D13—21no—
158C23×D13—21no—
159C23×D13—21no—
160C23×D13—21no—
161C23×D13—21no—
162C23×D13—21no—
163C23×D13—21no—
164C23×D13C22×C412yes—
165C23×D13C2×D412yes—
166C23×D13C2×Q812yes—
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×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13C22×C412yes—
206C22×C4×C13C22×C412yes—
207C22×C4×C13C22×C412yes—
208C22×C4×C13C2×D412yes—
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2×D412yes—
211C22×C4×C13C2×D412yes—
212C22×C4×C13C2×D412yes—
213C22×C4×C13C2×Q812yes—
214C22×C4×C13#4112yes—
215C22×C4×C13#4112yes—
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×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13C22×C412yes—
259C22×Dic13C22×C412yes—
260C22×Dic13C22×C412yes—
261C22×Dic13C2×D412yes—
262C22×Dic13C2×D412yes—
263C22×Dic13C2×D412yes—
264C22×Dic13C2×Q812yes—
265C2×C4×D13—44no—
266C2×C4×D13—44no—
267C2×C4×D13—44no—
268C2×C4×D13—44no—
269C2×C4×D13—44no—
270C2×C4×D13—44no—
271C2×C4×D13—44no—
272C13×C4⋊C4—44no—
273C13×C4⋊C4—44no—
274C13×C4⋊C4—44no—
275C13×C4⋊C4—44no—
276C13×C4⋊C4—44no—
277C13×C4⋊C4—44no—
278C42×C13—28no—
279#6103—28no—
280#6103—28no—
281#6103—44no—
282#6103—44no—
283#6103—44no—
284#6103C4⋊C4116yescomplemented
285#6101—28no—
286#6101—44no—
287#6101—44no—
288#6101—44no—
289C4×Dic13—44no—
290C2×#389—131no—
291C2×#388—131no—
292C2×#388—131no—
293C2×#385—131no—
294C2×#385—131no—
295C2×#385—131no—
296C2×#384D1311yescharacteristic, complemented
297#1444—131no—
298#1444—131no—
299#1442—131no—
300#1441—131no—
301#1439—131no—
302#1439—131no—
303#1436—131no—
304#1434—131no—
305C23×C13C23×C411yescharacteristic
306C23×C13C22×D411yescharacteristic
307C23×C13C22×D411yescharacteristic
308C23×C13C22×D411yescharacteristic
309C23×C13C22×Q811yescharacteristic
310C23×C13C2×#4111yescharacteristic
311C23×C13C2×#4111yescharacteristic
312C23×C13H(5,𝔽2)11yescharacteristic
313C23×C13H(5,𝔽2)11yescharacteristic
314C23×C13H(5,𝔽2)11yescharacteristic
315C23×C13H(5,𝔽2)11yescharacteristic
316C23×C132−1+411yescharacteristic
317C23×C132−1+411yescharacteristic
318C23×C132−1+411yescharacteristic
319C23×C132−1+411yescharacteristic
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—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—22no—
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×D13—41no—
347C22×D13—41no—
348C22×D13—41no—
349C22×D13—41no—
350C22×D13—41no—
351C22×D13—41no—
352C22×D13—41no—
353C22×D13—41no—
354C22×D13C2×C4⋊C414yes—
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—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—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×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×C13C2×C4⋊C414yes—
402C2×C4×C13C4×D414yes—
403C2×C4×C13C4×D414yes—
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—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
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×Dic13—41no—
445C2×Dic13—41no—
446C2×Dic13—41no—
447C2×Dic13—41no—
448C2×Dic13—41no—
449C2×Dic13—41no—
450C2×Dic13—41no—
451C2×Dic13—41no—
452C2×Dic13C2×C4⋊C414yes—
453C4×D13—416no—
454C24×C4—131no—
455C22×C4⋊C4—131no—
456C22×C4⋊C4—131no—
457C22×C4⋊C4—131no—
458C22×C4⋊C4—131no—
459C22×C4⋊C4C2×D1311yescharacteristic
460C22×C4⋊C4C2×D1311yescharacteristic
461C22×C4⋊C4C2×D1311yescharacteristic
462C22×C4⋊C4C2×D1311yescharacteristic
463C22×C4⋊C4C2×D1311yescharacteristic
464C22×C4⋊C4C2×D1311yescharacteristic
465C22×C22⋊C4—131no—
466C22×C22⋊C4—131no—
467C22×C22⋊C4—131no—
468C22×C22⋊C4—131no—
469C22×C22⋊C4—131no—
470C22×C22⋊C4—131no—
471C22×C42—131no—
472C22×C42C2×D1311yescharacteristic
473#389—264no—
474#388—138no—
475#388—264no—
476#385—264no—
477#385—264no—
478#385—264no—
479#384—24no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95—131no—
490C2×#95—131no—
491C2×#95—131no—
492C2×#95—131no—
493C2×#95—131no—
494C2×#95—131no—
495C2×#95—131no—
496C22×C13C22×C4⋊C411yescharacteristic
497C22×C13C2×C4×D411yescharacteristic
498C22×C13C2×C4×D411yescharacteristic
499C22×C13#52011yescharacteristic
500C22×C13#52011yescharacteristic
501C22×C13#52011yescharacteristic
502C22×C13#52011yescharacteristic
503C22×C13#53411yescharacteristic
504C22×C13#53511yescharacteristic
505C22×C13#53511yescharacteristic
506C22×C13#53611yescharacteristic
507C22×C13#53611yescharacteristic
508C22×C13#53611yescharacteristic
509C22×C13#53911yescharacteristic
510C22×C13#53911yescharacteristic
511C22×C13#54211yescharacteristic
512C22×C13#54211yescharacteristic
513C22×C13#54411yescharacteristic
514C22×C13#54411yescharacteristic
515C22×C13D4211yescharacteristic
516C22×C13D4211yescharacteristic
517C22×C13D4211yescharacteristic
518C22×C13#54711yescharacteristic
519C22×C13#54711yescharacteristic
520C22×C13#54711yescharacteristic
521C22×C13#54811yescharacteristic
522C22×C13D4×Q811yescharacteristic
523C22×C13D4×Q811yescharacteristic
524C22×C13#55311yescharacteristic
525C22×C13#55411yescharacteristic
526C22×C13#55411yescharacteristic
527C22×C13#56011yescharacteristic
528C22×C13#56311yescharacteristic
529C22×C13#56311yescharacteristic
530C22×C13#56311yescharacteristic
531C2×D13—24no—
532C2×D13—24no—
533C2×D13—24no—
534C2×D13—42no—
535C2×D13—42no—
536C2×D13—42no—
537C2×D13—42no—
538C2×D13—42no—
539C2×D13—42no—
540C2×D13—42no—
541C2×D13—42no—
542C2×D13—42no—
543C2×D13—42no—
544C2×D13—42no—
545C2×D13—42no—
546C4×C13—24no—
547C4×C13—24no—
548C4×C13—24no—
549C4×C13—42no—
550C4×C13—42no—
551C4×C13—81no—
552C4×C13—81no—
553Dic13—24no—
554Dic13—42no—
555Dic13—42no—
556Dic13—42no—
557Dic13—42no—
558Dic13—81no—
559Dic13—81no—
560C25—131no—
561C23×C4—131no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4—131no—
567C23×C4—131no—
568C23×C4—262no—
569C23×C4—262no—
570C23×C4—262no—
571C23×C4—521no—
572C23×C4—521no—
573C23×C4—521no—
574C23×C4—521no—
575C23×C4C22×D1311yescharacteristic
576C23×C4C22×D1311yescharacteristic
577C23×C4C22×D1311yescharacteristic
578C23×C4C22×D1311yescharacteristic
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—134no—
600C2×C4⋊C4—262no—
601C2×C4⋊C4—262no—
602C2×C4⋊C4—262no—
603C2×C4⋊C4—262no—
604C2×C4⋊C4—262no—
605C2×C4⋊C4—262no—
606C2×C4⋊C4—262no—
607C2×C4⋊C4—521no—
608C2×C4⋊C4—521no—
609C2×C4⋊C4—521no—
610C2×C4⋊C4—521no—
611C2×C4⋊C4C22⋊D1314yes—
612C2×C22⋊C4—134no—
613C2×C22⋊C4—134no—
614C2×C22⋊C4—134no—
615C2×C22⋊C4—134no—
616C2×C22⋊C4—134no—
617C2×C22⋊C4—262no—
618C2×C22⋊C4—262no—
619C2×C22⋊C4—262no—
620C2×C22⋊C4—262no—
621C2×C22⋊C4—262no—
622C2×C22⋊C4—262no—
623C2×C22⋊C4—262no—
624C2×C22⋊C4—262no—
625C2×C22⋊C4—262no—
626C2×C22⋊C4—521no—
627C2×C22⋊C4—521no—
628C2×C22⋊C4—521no—
629C2×C22⋊C4—521no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—262no—
633C2×C42—262no—
634C2×C42—521no—
635C2×C42C4×D1314yescomplemented
636#95—134no—
637#95—134no—
638#95—134no—
639#95—262no—
640#95—262no—
641#95—262no—
642#95—262no—
643#95—262no—
644#95—262no—
645#95—262no—
646#95—262no—
647#95—262no—
648#95—262no—
649#95—521no—
650#95—521no—
651#95—521no—
652C2×C13#231711yescharacteristic
653C2×C13#232211yescharacteristic
654C2×C13#232611yescharacteristic
655C2×C13D4×C4⋊C411yescharacteristic
656C2×C13D4×C4⋊C411yescharacteristic
657C2×C13#236111yescharacteristic
658C2×C13#238311yescharacteristic
659C2×C13#266911yescharacteristic
660C2×C13#267411yescharacteristic
661C2×C13#267711yescharacteristic
662C2×C13#268011yescharacteristic
663C2×C13#271811yescharacteristic
664C2×C13#272011yescharacteristic
665C2×C13#272911yescharacteristic
666C2×C13#279011yescharacteristic
667D13—44no—
668C24—132no—
669C24—132no—
670C24—132no—
671C24—261no—
672C24—261no—
673C24—261no—
674C24—261no—
675C24—261no—
676C24—261no—
677C24—261no—
678C24—261no—
679C24—261no—
680C24—261no—
681C24—261no—
682C24—261no—
683C24C23×D1311yescharacteristic
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—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—132no—
723C22×C4—132no—
724C22×C4—132no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—132no—
728C22×C4—132no—
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×C4—261no—
768C22×C4—261no—
769C22×C4—261no—
770C22×C4—261no—
771C22×C4—524no—
772C22×C4—524no—
773C22×C4—524no—
774C22×C4—524no—
775C22×C4—524no—
776C22×C4—524no—
777C22×C4—524no—
778C22×C4C2×C4×D1312yes—
779C22×C4C2×C4×D1312yes—
780C22×C4C2×C4×D1312yes—
781C22×C4#612712yes—
782C22×C4D4×D1312yes—
783C22×C4D4×D1312yes—
784C22×C4Q8×D1312yes—
785C22×C4#613112yes—
786C22×C4C2×C22⋊D1312yes—
787C22×C4C2×C22⋊D1312yes—
788C22×C4C2×C22⋊D1312yes—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—268no—
796C4⋊C4—524no—
797C4⋊C4—524no—
798C4⋊C4—524no—
799C22⋊C4—1316no—
800C22⋊C4—268no—
801C22⋊C4—268no—
802C22⋊C4—524no—
803C22⋊C4—524no—
804C22⋊C4—524no—
805C42—28no—
806C42—524no—
807C13#1440511yescharacteristic, complemented, Sylow
808C23—134no—
809C23—262no—
810C23—262no—
811C23—262no—
812C23—262no—
813C23—262no—
814C23—262no—
815C23—262no—
816C23—262no—
817C23—262no—
818C23—262no—
819C23—262no—
820C23—262no—
821C23—262no—
822C23—262no—
823C23—262no—
824C23—262no—
825C23—262no—
826C23—262no—
827C23—521no—
828C23—521no—
829C23—521no—
830C23—521no—
831C23—521no—
832C23—521no—
833C23—521no—
834C23—521no—
835C23—521no—
836C23—521no—
837C23—521no—
838C23—521no—
839C23—521no—
840C23—521no—
841C23—521no—
842C23—521no—
843C23C22×C4×D1311yescharacteristic
844C23C2×#612711yescharacteristic
845C23C2×D4×D1311yescharacteristic
846C23C2×D4×D1311yescharacteristic
847C23#8825111yescharacteristic
848C23#8825111yescharacteristic
849C23#8825111yescharacteristic
850C23#8825111yescharacteristic
851C23C2×Q8×D1311yescharacteristic
852C23C2×#613111yescharacteristic
853C23#8825411yescharacteristic
854C23#8825411yescharacteristic
855C23#8825411yescharacteristic
856C23#8825411yescharacteristic
857C23C22×C22⋊D1311yescharacteristic
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—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—134no—
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—262no—
915C2×C4—262no—
916C2×C4—262no—
917C2×C4—262no—
918C2×C4—262no—
919C2×C4—262no—
920C2×C4—262no—
921C2×C4—262no—
922C2×C4—262no—
923C2×C4—5216no—
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—
941C2×C4—521no—
942C2×C4—521no—
943C2×C4—521no—
944C2×C4—521no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
949C2×C4—521no—
950C2×C4—521no—
951C2×C4—521no—
952C2×C4—521no—
953C2×C4—521no—
954C2×C4C4⋊C4×D1314yes—
955C2×C4#8814714yes—
956C2×C4C4×C22⋊D1314yes—
957C22—264no—
958C22—264no—
959C22—264no—
960C22—522no—
961C22—522no—
962C22—522no—
963C22—522no—
964C22—522no—
965C22—522no—
966C22—522no—
967C22—522no—
968C22—522no—
969C22—522no—
970C22—522no—
971C22—522no—
972C22C2×C4⋊C4×D1311yescharacteristic
973C22C2×#8814711yescharacteristic
974C22#1171920911yescharacteristic
975C22#1171920911yescharacteristic
976C22#1171920911yescharacteristic
977C22#1171920911yescharacteristic
978C22#1171921211yescharacteristic
979C22#1171921211yescharacteristic
980C22#1171921611yescharacteristic
981C22#1171921911yescharacteristic
982C22#1171922011yescharacteristic
983C22#1171922011yescharacteristic
984C22#1171942011yescharacteristic
985C22#1171942011yescharacteristic
986C22#1171942211yescharacteristic
987C22#1171942511yescharacteristic
988C22#1171942911yescharacteristic
989C22#1171942911yescharacteristic
990C22#1171943111yescharacteristic
991C22#1171943211yescharacteristic
992C22#1171943411yescharacteristic
993C22#1171943411yescharacteristic
994C22#1171943511yescharacteristic
995C22#1171943811yescharacteristic
996C22#1171943811yescharacteristic
997C22#1171944011yescharacteristic
998C22#1171944011yescharacteristic
999C22#1171944011yescharacteristic
1000C22C2×C4×C22⋊D1311yescharacteristic
1001C22D4×C22⋊D1311yescharacteristic
1002C22D4×C22⋊D1311yescharacteristic
1003C22#1171950911yescharacteristic
1004C22Q8×C22⋊D1311yescharacteristic
1005C22#1171952111yescharacteristic
1006C22#1171952211yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—81no—
1013C4—81no—
1014C4—264no—
1015C4—522no—
1016C4—522no—
1017C4—522no—
1018C4—522no—
1019C4—1041no—
1020C4—1041no—
1021C2—524no—
1022C2#1311745711yescharacteristic
1023C2#1311750511yescharacteristic
1024C2#1311754411yescharacteristic
1025C2C4⋊C4×C22⋊D1311yescharacteristic
1026C2#1311773611yescharacteristic
1027C2#1311785211yescharacteristic
1028C2#1311802911yescharacteristic
1029C2#1312104911yescharacteristic
1030C2#1312111211yescharacteristic
1031C2#1312114611yescharacteristic
1032C2#1312117611yescharacteristic
1033C2#1312168111yescharacteristic
1034C2#1312171111yescharacteristic
1035C2#1312181211yescharacteristic
1036C2#1312260211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#384C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#384D13
hypocenterC13#14405
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
1. C2×#11718633C2semidirect
7. #13113099C2semidirect
8. #13113099C2semidirect
9. #13113095C2semidirect
10. #13113086C2semidirect
13. #13113068C2semidirect
14. #13113063C2semidirect
15. C2×C13×#384C2semidirect
57. #11718601C4semidirect
100. C2×C42×C13C2×C4semidirect
130. C2×#6101C2×C4semidirect
147. #88071C2×C4semidirect
148. #88071C2×C4semidirect
284. #6103C4⋊C4semidirect
296. C2×#384D13semidirect
635. C2×C42C4×D13semidirect
807. C13#14405semidirect

Maximal subgroups

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

subgroupindex
C2×#117186332
C2×#117186012
C2×#117186512
C2×#117186502
#131130992
#131130952
#131130862
#131130782
#131130682
#131130632
C2×C13×#3842
#1440513