Finite Group Databasebeta

← #15790894

Subgroups — #15790894

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×#11718634C211yesmaximal, characteristic, complemented
2C2×#11718612C211yesmaximal, characteristic
3C2×#11718612C211yesmaximal, characteristic
4C2×#11718871C211yesmaximal, characteristic
5C2×#11718871C211yesmaximal, characteristic
6C2×#11718637C211yesmaximal, characteristic, complemented
7#13113100C211yesmaximal, characteristic, complemented
8#13113099C211yesmaximal, characteristic, complemented
9#13113095C211yesmaximal, characteristic, complemented
10#13113088C211yesmaximal, characteristic, complemented
11#13113079C211yesmaximal, characteristic
12#13113079C211yesmaximal, characteristic
13#13113067C211yesmaximal, characteristic, complemented
14#13113062C211yesmaximal, characteristic, complemented
15C2×C13×#385C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C13×#385—24no—
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38#11718871—24no—
39#11718871—24no—
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54#11718637—24no—
55#11718634—24no—
56#11718612—24no—
57#11718612C418yescomplemented
58C25×C13C2311yescharacteristic
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—41no—
63C23×C4×C13—41no—
64C23×C4×C13—41no—
65C23×C4×C13—41no—
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—41no—
85C2×C13×C4⋊C4—41no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—41no—
88C2×C13×C22⋊C4—41no—
89C2×C13×C22⋊C4C2×C414yes—
90C2×C13×C22⋊C4D414yes—
91C2×C13×C22⋊C4Q814yes—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—22no—
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—22no—
97C2×C22⋊Dic13—22no—
98C2×C22⋊Dic13—22no—
99C2×C22⋊Dic13—22no—
100C2×C22⋊Dic13—41no—
101C2×C22⋊Dic13—41no—
102C2×C22⋊Dic13C2×C414yes—
103C2×C22⋊Dic13C2×C414yes—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—22no—
107C2×C4⋊Dic13—22no—
108C2×C4⋊Dic13—41no—
109C2×C4⋊Dic13C2×C414yescomplemented
110C2×#6101—22no—
111C2×#6101—22no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101—22no—
116C2×#6101—22no—
117C2×#6101—22no—
118C2×#6101—41no—
119C2×#6101—41no—
120C2×#6101—41no—
121C2×#6101—41no—
122C2×#6101—41no—
123C2×#6101—41no—
124C2×#6101—41no—
125C2×#6101—41no—
126C2×#6101—41no—
127C2×#6101D414yes—
128C2×C4×Dic13—22no—
129C2×C4×Dic13—22no—
130C2×C4×Dic13—22no—
131C2×C4×Dic13—22no—
132C2×C4×Dic13—41no—
133C2×C4×Dic13C2×C414yescomplemented
134C13×#95—22no—
135C13×#95—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×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13C22×C412yes—
164C24×C13C2×D412yes—
165C24×C13C2×Q812yes—
166C24×C13C2411yescharacteristic
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—44no—
202C22×C4×C13—44no—
203C22×C4×C13—44no—
204C22×C4×C13—44no—
205C22×C4×C13—44no—
206C22×C4×C13—44no—
207C22×C4×C13—44no—
208C22×C4×C13C22×C412yes—
209C22×C4×C13C22×C412yes—
210C22×C4×C13C2×D412yes—
211C22×C4×C13C2×D412yes—
212C22×C4×C13C2×D412yes—
213C22×C4×C13C2×D412yes—
214C22×C4×C13C2×Q812yes—
215C22×C4×C13C2×Q812yes—
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×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13—21no—
261C22×Dic13—21no—
262C22×Dic13C22×C412yes—
263C22×Dic13C22×C412yes—
264C22×Dic13C22×C412yes—
265C22×Dic13C22×C412yes—
266C22×Dic13C2×D412yes—
267C22×Dic13C2×D412yes—
268C22×Dic13C2×D412yes—
269C22×Dic13C2×D412yes—
270C22×Dic13#4112yes—
271C22×Dic13#4112yes—
272C13×C4⋊C4—44no—
273C13×C4⋊C4—44no—
274C13×C22⋊C4—44no—
275C13×C22⋊C4C4⋊C4116yescomplemented
276C22⋊Dic13—28no—
277C22⋊Dic13—28no—
278C22⋊Dic13—44no—
279C22⋊Dic13—44no—
280C4⋊Dic13—28no—
281C4⋊Dic13—44no—
282#6101—44no—
283#6101—44no—
284#6101—44no—
285#6101—44no—
286#6101—44no—
287#6101—44no—
288C4×Dic13—28no—
289C4×Dic13—44no—
290C2×#389—131no—
291C2×#388—131no—
292C2×#388—131no—
293C2×#385—131no—
294C2×#385—131no—
295C2×#385D1311yescharacteristic
296C2×#384—131no—
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×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—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
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×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—41no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13—41no—
339C23×C13C2×C4⋊C414yes—
340C23×C13C23×C411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C23×C13C22×D411yescharacteristic
343C23×C13C22×D411yescharacteristic
344C23×C13C22×Q811yescharacteristic
345C23×C13C2×#4111yescharacteristic
346C23×C13C2×#4111yescharacteristic
347C23×C13H(5,𝔽2)11yescharacteristic
348C23×C13H(5,𝔽2)11yescharacteristic
349C23×C13H(5,𝔽2)11yescharacteristic
350C23×C13H(5,𝔽2)11yescharacteristic
351C23×C132−1+411yescharacteristic
352C23×C132−1+411yescharacteristic
353C23×C132−1+411yescharacteristic
354C23×C132−1+411yescharacteristic
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—416no—
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×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13C2×C4⋊C414yes—
397C2×C4×C13C2×C4⋊C414yes—
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—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×Dic13C4×D414yes—
453C2×Dic13C4×D414yes—
454C24×C4C2×D1311yescharacteristic
455C22×C4⋊C4—131no—
456C22×C4⋊C4—131no—
457C22×C4⋊C4—131no—
458C22×C4⋊C4—131no—
459C22×C4⋊C4—131no—
460C22×C4⋊C4—131no—
461C22×C4⋊C4—131no—
462C22×C4⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
470C22×C22⋊C4C2×D1311yescharacteristic
471C22×C42—131no—
472C22×C42—131no—
473#389—264no—
474#388—138no—
475#388—264no—
476#385—24no—
477#385—264no—
478#385—264no—
479#384—264no—
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×#95C2×D1311yescharacteristic
495C2×#95C2×D1311yescharacteristic
496C22×C13—24no—
497C22×C13—24no—
498C22×C13—24no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13C22×C4⋊C411yescharacteristic
512C22×C13C2×C4×D411yescharacteristic
513C22×C13C2×C4×D411yescharacteristic
514C22×C13#52011yescharacteristic
515C22×C13#52011yescharacteristic
516C22×C13#52011yescharacteristic
517C22×C13#52011yescharacteristic
518C22×C13#53411yescharacteristic
519C22×C13#53511yescharacteristic
520C22×C13#53511yescharacteristic
521C22×C13#53611yescharacteristic
522C22×C13#53611yescharacteristic
523C22×C13#53611yescharacteristic
524C22×C13#53911yescharacteristic
525C22×C13#53911yescharacteristic
526C22×C13#54211yescharacteristic
527C22×C13#54211yescharacteristic
528C22×C13#54411yescharacteristic
529C22×C13#54411yescharacteristic
530C22×C13D4211yescharacteristic
531C22×C13D4211yescharacteristic
532C22×C13D4211yescharacteristic
533C22×C13#54711yescharacteristic
534C22×C13#54711yescharacteristic
535C22×C13#54711yescharacteristic
536C22×C13#54811yescharacteristic
537C22×C13D4×Q811yescharacteristic
538C22×C13D4×Q811yescharacteristic
539C22×C13#55311yescharacteristic
540C22×C13#55411yescharacteristic
541C22×C13#55411yescharacteristic
542C22×C13#56011yescharacteristic
543C22×C13#56311yescharacteristic
544C22×C13#56311yescharacteristic
545C22×C13#56311yescharacteristic
546C4×C13—24no—
547C4×C13—24no—
548C4×C13—42no—
549C4×C13—42no—
550C4×C13—81no—
551C4×C13—81no—
552Dic13—24no—
553Dic13—24no—
554Dic13—42no—
555Dic13—42no—
556Dic13—42no—
557Dic13—42no—
558Dic13—81no—
559Dic13—81no—
560C25C22×D1311yescharacteristic
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—41no—
565C23×C4—41no—
566C23×C4—41no—
567C23×C4—41no—
568C23×C4—131no—
569C23×C4—131no—
570C23×C4—131no—
571C23×C4—131no—
572C23×C4—131no—
573C23×C4—131no—
574C23×C4—131no—
575C23×C4—131no—
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—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—134no—
589C2×C4⋊C4—134no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C4⋊C4—262no—
597C2×C4⋊C4—262no—
598C2×C4⋊C4—262no—
599C2×C4⋊C4—262no—
600C2×C4⋊C4—262no—
601C2×C4⋊C4—262no—
602C2×C4⋊C4—521no—
603C2×C4⋊C4—521no—
604C2×C4⋊C4—521no—
605C2×C4⋊C4—521no—
606C2×C4⋊C4—521no—
607C2×C4⋊C4—521no—
608C2×C4⋊C4—521no—
609C2×C4⋊C4—521no—
610C2×C4⋊C4—521no—
611C2×C4⋊C4—521no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—41no—
614C2×C22⋊C4—41no—
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—521no—
626C2×C22⋊C4—521no—
627C2×C22⋊C4Dic2614yes—
628C2×C22⋊C4C4×D1314yes—
629C2×C22⋊C4C22⋊D1314yes—
630C2×C42—134no—
631C2×C42—262no—
632C2×C42—262no—
633C2×C42—262no—
634C2×C42—262no—
635C2×C42—521no—
636#95—22no—
637#95—22no—
638#95—134no—
639#95—134no—
640#95—134no—
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—44no—
653C2×C13#231711yescharacteristic
654C2×C13#232211yescharacteristic
655C2×C13#232611yescharacteristic
656C2×C13D4×C4⋊C411yescharacteristic
657C2×C13D4×C4⋊C411yescharacteristic
658C2×C13#236111yescharacteristic
659C2×C13#238311yescharacteristic
660C2×C13#266911yescharacteristic
661C2×C13#267411yescharacteristic
662C2×C13#267711yescharacteristic
663C2×C13#268011yescharacteristic
664C2×C13#271811yescharacteristic
665C2×C13#272011yescharacteristic
666C2×C13#272911yescharacteristic
667C2×C13#279011yescharacteristic
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C2×Dic2612yes—
681C24C2×C4×D1312yes—
682C24C2×C22⋊D1312yes—
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—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—132no—
728C22×C4—132no—
729C22×C4—132no—
730C22×C4—132no—
731C22×C4—132no—
732C22×C4—132no—
733C22×C4—132no—
734C22×C4—132no—
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—261no—
772C22×C4—261no—
773C22×C4—261no—
774C22×C4—261no—
775C22×C4—261no—
776C22×C4—261no—
777C22×C4—261no—
778C22×C4—261no—
779C22×C4—261no—
780C22×C4—261no—
781C22×C4C2×Dic2612yes—
782C22×C4C2×Dic2612yes—
783C22×C4C2×C4×D1312yes—
784C22×C4C2×C4×D1312yes—
785C22×C4D4×D1312yes—
786C22×C4D4×D1312yes—
787C22×C4C2×C22⋊D1312yes—
788C22×C4C2×C22⋊D1312yes—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—268no—
792C4⋊C4—524no—
793C4⋊C4—524no—
794C4⋊C4—524no—
795C4⋊C4—524no—
796C4⋊C4—524no—
797C4⋊C4—524no—
798C4⋊C4—524no—
799C22⋊C4—44no—
800C22⋊C4—268no—
801C22⋊C4—268no—
802C22⋊C4—524no—
803C22⋊C4—524no—
804C22⋊C4#6101116yescomplemented
805C42—268no—
806C42—524no—
807C13#1440511yescharacteristic, complemented, Sylow
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×#610114yes—
843C23C22×Dic2611yescharacteristic
844C23C22×C4×D1311yescharacteristic
845C23C2×D4×D1311yescharacteristic
846C23C2×D4×D1311yescharacteristic
847C23#8825111yescharacteristic
848C23#8825111yescharacteristic
849C23#8825111yescharacteristic
850C23#8825111yescharacteristic
851C23#8825411yescharacteristic
852C23#8825411yescharacteristic
853C23#41×D1311yescharacteristic
854C23#41×D1311yescharacteristic
855C23#8825711yescharacteristic
856C23#8825711yescharacteristic
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—416no—
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—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—134no—
900C2×C4—134no—
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—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—262no—
924C2×C4—262no—
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×C4—521no—
955C2×C4C2×#610114yes—
956C2×C4C2×#610114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22#1171920511yescharacteristic
973C22#1171920511yescharacteristic
974C22#1171920911yescharacteristic
975C22#1171920911yescharacteristic
976C22D4×Dic2611yescharacteristic
977C22D4×Dic2611yescharacteristic
978C22#1171924411yescharacteristic
979C22#1171924411yescharacteristic
980C22C4×D4×D1311yescharacteristic
981C22C4×D4×D1311yescharacteristic
982C22#1171925111yescharacteristic
983C22#1171925111yescharacteristic
984C22#1171929411yescharacteristic
985C22#1171929511yescharacteristic
986C22#1171929711yescharacteristic
987C22#1171930011yescharacteristic
988C22#1171933311yescharacteristic
989C22#1171933311yescharacteristic
990C22#1171933611yescharacteristic
991C22#1171933811yescharacteristic
992C22#1171934311yescharacteristic
993C22#1171934511yescharacteristic
994C22#1171935111yescharacteristic
995C22#1171935111yescharacteristic
996C22#1171935611yescharacteristic
997C22#1171936511yescharacteristic
998C22#1171936611yescharacteristic
999C22#1171936711yescharacteristic
1000C22C22×#610111yescharacteristic
1001C22D4×C22⋊D1311yescharacteristic
1002C22D4×C22⋊D1311yescharacteristic
1003C22#1171951011yescharacteristic
1004C22#1171952111yescharacteristic
1005C22#1171952911yescharacteristic
1006C22#1171952911yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—264no—
1014C4—264no—
1015C4—522no—
1016C4—522no—
1017C4—522no—
1018C4—522no—
1019C4—1041no—
1020C4—1041no—
1021C2—44no—
1022C2#1311746011yescharacteristic
1023C2#1311750311yescharacteristic
1024C2#1311754211yescharacteristic
1025C2D4×#610111yescharacteristic
1026C2D4×#610111yescharacteristic
1027C2#1311785511yescharacteristic
1028C2#1311802411yescharacteristic
1029C2#1312105011yescharacteristic
1030C2#1312111311yescharacteristic
1031C2#1312115111yescharacteristic
1032C2#1312117511yescharacteristic
1033C2#1312168211yescharacteristic
1034C2#1312171711yescharacteristic
1035C2#1312182211yescharacteristic
1036C2#1312260911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#385C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#385D13
hypocenterC13#14405
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#11718634C2semidirect
6. C2×#11718637C2semidirect
7. #13113100C2semidirect
8. #13113099C2semidirect
9. #13113095C2semidirect
10. #13113088C2semidirect
13. #13113067C2semidirect
14. #13113062C2semidirect
57. #11718612C4semidirect
109. C2×C4⋊Dic13C2×C4semidirect
133. C2×C4×Dic13C2×C4semidirect
147. #88071C2×C4semidirect
148. #88071C2×C4semidirect
275. C13×C22⋊C4C4⋊C4semidirect
804. C22⋊C4#6101semidirect
807. C13#14405semidirect

Maximal subgroups

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

subgroupindex
C2×#117186342
C2×#117186122
C2×#117188712
C2×#117186372
#131131002
#131130992
#131130952
#131130882
#131130792
#131130672
#131130622
C2×C13×#3852
#1440513