Finite Group Databasebeta

← #15790909

Subgroups — #15790909

Order 3328.

1390 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718646C211yesmaximal, characteristic
2C2×#11718589C211yesmaximal, characteristic
3C2×#11718642C211yesmaximal, characteristic
4C2×#11718637C211yesmaximal, characteristic
5#13113100C211yesmaximal, characteristic
6#13113100C211yesmaximal, characteristic
7#13113100C211yesmaximal, characteristic
8#13113099C211yesmaximal, characteristic
9#13113092C211yesmaximal, characteristic
10#13113088C211yesmaximal, characteristic
11#13113069C211yesmaximal, characteristic
12#13113067C211yesmaximal, characteristic
13#13113067C211yesmaximal, characteristic
14#13113062C211yesmaximal, characteristic
15C2×C13×#387C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C13×#387—24no—
32C2×C13×#95C2211yescharacteristic
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
51C2×#88071C2211yescharacteristic
52#11718646—24no—
53#11718642C418yescomplemented
54#11718637—24no—
55#11718589—24no—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—41no—
74C2×C13×C4⋊C4C2×C414yes—
75C2×C13×C4⋊C4D414yes—
76C2×C13×C4⋊C4Q814yes—
77C2×C42×C13—22no—
78C2×C42×C13—22no—
79C2×C42×C13—41no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—41no—
88C2×C4⋊Dic13—41no—
89C2×C4⋊Dic13—41no—
90C2×C4⋊Dic13—41no—
91C2×C4⋊Dic13C2×C414yes—
92C2×#6101—22no—
93C2×#6101—22no—
94C2×#6101—22no—
95C2×#6101—22no—
96C2×#6101—22no—
97C2×#6101—22no—
98C2×#6101—41no—
99C2×#6101—41no—
100C2×#6101—41no—
101C2×#6101—41no—
102C2×#6101—41no—
103C2×#6101—41no—
104C2×#6101—41no—
105C2×#6101—41no—
106C2×#6101—41no—
107C2×#6101—41no—
108C2×#6101—41no—
109C2×#6101D414yes—
110C2×C4×Dic13—22no—
111C2×C4×Dic13—22no—
112C2×C4×Dic13—22no—
113C2×C4×Dic13—41no—
114C2×C4×Dic13—41no—
115C2×C4×Dic13C2×C414yes—
116C13×#95—22no—
117C13×#95—22no—
118C13×#95—22no—
119C13×#95—22no—
120#88071—22no—
121#88071—22no—
122#88071—22no—
123#88071—22no—
124#88071—22no—
125#88071—22no—
126#88071—41no—
127#88071—41no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071C2×C414yes—
132#88071C2×C414yes—
133#88071C2×C414yes—
134#88071C2×C414yes—
135#88071Q814yes—
136#14406—131nomaximal, Sylow
137C24×C13C2411yescharacteristic
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13C22×C412yes—
177C22×C4×C13C22×C412yes—
178C22×C4×C13C22×C412yes—
179C22×C4×C13C2×D412yes—
180C22×C4×C13C2×D412yes—
181C22×C4×C13C2×D412yes—
182C22×C4×C13C2×D412yes—
183C22×C4×C13C2×Q812yes—
184C22×C4×C13C2×Q812yes—
185C22×C4×C13C2×Q812yes—
186C22×C4×C13C2×Q812yes—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
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×Dic13C22×C412yes—
234C22×Dic13C22×C412yes—
235C22×Dic13C22×C412yes—
236C22×Dic13C22×C412yes—
237C22×Dic13C2×D412yes—
238C22×Dic13C2×D412yes—
239C22×Dic13C2×Q812yes—
240C22×Dic13C2×Q812yes—
241C22×Dic13#4112yes—
242C22×Dic13#4112yes—
243C13×C4⋊C4—44no—
244C13×C4⋊C4C4⋊C4116yescomplemented
245C42×C13—44no—
246C4⋊Dic13—28no—
247C4⋊Dic13—44no—
248C4⋊Dic13—44no—
249C4⋊Dic13—44no—
250#6101—44no—
251#6101—44no—
252#6101—44no—
253#6101—44no—
254#6101—44no—
255#6101—44no—
256C4×Dic13—28no—
257C4×Dic13—44no—
258C2×#389—131no—
259C2×#389—131no—
260C2×#387—131no—
261C2×#387D1311yescharacteristic
262C2×#384—131no—
263#1444—131no—
264#1444—131no—
265#1444—131no—
266#1444—131no—
267#1442—131no—
268#1441—131no—
269#1436—131no—
270#1436—131no—
271#1436—131no—
272#1434—131no—
273C23×C13C23×C411yescharacteristic
274C23×C13C22×D411yescharacteristic
275C23×C13C22×D411yescharacteristic
276C23×C13C22×Q811yescharacteristic
277C23×C13C22×Q811yescharacteristic
278C23×C13C2×#4111yescharacteristic
279C23×C13C2×#4111yescharacteristic
280C23×C13H(5,𝔽2)11yescharacteristic
281C23×C13H(5,𝔽2)11yescharacteristic
282C23×C13H(5,𝔽2)11yescharacteristic
283C23×C13H(5,𝔽2)11yescharacteristic
284C23×C132−1+411yescharacteristic
285C23×C132−1+411yescharacteristic
286C23×C132−1+411yescharacteristic
287C23×C132−1+411yescharacteristic
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—41no—
330C2×C4×C13—41no—
331C2×C4×C13—41no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
334C2×C4×C13C2×C4⋊C414yes—
335C2×C4×C13C2×C4⋊C414yes—
336C2×C4×C13C2×C4⋊C414yes—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—41no—
362C2×Dic13—41no—
363C2×Dic13—41no—
364C2×Dic13—41no—
365C2×Dic13—41no—
366C2×Dic13—41no—
367C2×Dic13—41no—
368C2×Dic13—41no—
369C2×Dic13—41no—
370C2×Dic13—41no—
371C2×Dic13—41no—
372C2×Dic13—41no—
373C2×Dic13—41no—
374C2×Dic13—41no—
375C2×Dic13—41no—
376C2×Dic13—41no—
377C2×Dic13—41no—
378C2×Dic13—41no—
379C2×Dic13—41no—
380C2×Dic13—41no—
381C2×Dic13—41no—
382C2×Dic13—41no—
383C2×Dic13—41no—
384C2×Dic13—41no—
385C2×Dic13—41no—
386C2×Dic13—41no—
387C2×Dic13—41no—
388C2×Dic13—41no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13C4×D414yes—
392C2×Dic13C4×Q814yes—
393C22×C4⋊C4—131no—
394C22×C4⋊C4—131no—
395C22×C4⋊C4—131no—
396C22×C4⋊C4—131no—
397C22×C4⋊C4—131no—
398C22×C4⋊C4—131no—
399C22×C4⋊C4—131no—
400C22×C4⋊C4—131no—
401C22×C4⋊C4—131no—
402C22×C4⋊C4—131no—
403C22×C4⋊C4C2×D1311yescharacteristic
404C22×C4⋊C4C2×D1311yescharacteristic
405C22×C42—131no—
406C22×C42—131no—
407C22×C42C2×D1311yescharacteristic
408#389—264no—
409#389—264no—
410#387—24no—
411#387—138no—
412#384—264no—
413C2×#95—131no—
414C2×#95—131no—
415C2×#95—131no—
416C2×#95—131no—
417C2×#95—131no—
418C2×#95—131no—
419C2×#95—131no—
420C2×#95—131no—
421C2×#95—131no—
422C2×#95—131no—
423C2×#95—131no—
424C2×#95—131no—
425C2×#95—131no—
426C2×#95—131no—
427C2×#95—131no—
428C2×#95—131no—
429C2×#95C2×D1311yescharacteristic
430C2×#95C2×D1311yescharacteristic
431C2×#95C2×D1311yescharacteristic
432C2×#95C2×D1311yescharacteristic
433C22×C13C22×C4⋊C411yescharacteristic
434C22×C13C2×C4×D411yescharacteristic
435C22×C13C2×C4×Q811yescharacteristic
436C22×C13#52011yescharacteristic
437C22×C13#52011yescharacteristic
438C22×C13#52011yescharacteristic
439C22×C13#52011yescharacteristic
440C22×C13#53411yescharacteristic
441C22×C13#53511yescharacteristic
442C22×C13#53611yescharacteristic
443C22×C13#53611yescharacteristic
444C22×C13#53911yescharacteristic
445C22×C13#53911yescharacteristic
446C22×C13#54011yescharacteristic
447C22×C13#54111yescharacteristic
448C22×C13#54411yescharacteristic
449C22×C13#54411yescharacteristic
450C22×C13#54411yescharacteristic
451C22×C13#54411yescharacteristic
452C22×C13D4211yescharacteristic
453C22×C13#54611yescharacteristic
454C22×C13#54711yescharacteristic
455C22×C13D4×Q811yescharacteristic
456C22×C13D4×Q811yescharacteristic
457C22×C13D4×Q811yescharacteristic
458C22×C13#55011yescharacteristic
459C22×C13#55211yescharacteristic
460C22×C13#55411yescharacteristic
461C22×C13#55411yescharacteristic
462C22×C13#55711yescharacteristic
463C22×C13Q8211yescharacteristic
464C22×C13#56011yescharacteristic
465C22×C13#56311yescharacteristic
466C22×C13#56311yescharacteristic
467C22×C13#56311yescharacteristic
468C4×C13—24no—
469C4×C13—24no—
470C4×C13—24no—
471C4×C13—42no—
472C4×C13—42no—
473C4×C13—81no—
474C4×C13—81no—
475Dic13—24no—
476Dic13—24no—
477Dic13—42no—
478Dic13—42no—
479Dic13—42no—
480Dic13—42no—
481Dic13—81no—
482Dic13—81no—
483C23×C4—131no—
484C23×C4—131no—
485C23×C4—131no—
486C23×C4—131no—
487C23×C4—131no—
488C23×C4—131no—
489C23×C4—131no—
490C23×C4—131no—
491C23×C4C22×D1311yescharacteristic
492C23×C4C22×D1311yescharacteristic
493C23×C4C22×D1311yescharacteristic
494C23×C4C22×D1311yescharacteristic
495C23×C4C22×D1311yescharacteristic
496C23×C4C22×D1311yescharacteristic
497C23×C4C22×D1311yescharacteristic
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—134no—
502C2×C4⋊C4—134no—
503C2×C4⋊C4—262no—
504C2×C4⋊C4—262no—
505C2×C4⋊C4—262no—
506C2×C4⋊C4—262no—
507C2×C4⋊C4—262no—
508C2×C4⋊C4—262no—
509C2×C4⋊C4—262no—
510C2×C4⋊C4—262no—
511C2×C4⋊C4—262no—
512C2×C4⋊C4—262no—
513C2×C4⋊C4—262no—
514C2×C4⋊C4—262no—
515C2×C4⋊C4—262no—
516C2×C4⋊C4—521no—
517C2×C4⋊C4—521no—
518C2×C4⋊C4—521no—
519C2×C4⋊C4—521no—
520C2×C4⋊C4—521no—
521C2×C4⋊C4—521no—
522C2×C4⋊C4—521no—
523C2×C4⋊C4—521no—
524C2×C4⋊C4—521no—
525C2×C4⋊C4—521no—
526C2×C4⋊C4—521no—
527C2×C4⋊C4—521no—
528C2×C4⋊C4—521no—
529C2×C4⋊C4—521no—
530C2×C4⋊C4—521no—
531C2×C4⋊C4Dic2614yes—
532C2×C4⋊C4C4×D1314yes—
533C2×C4⋊C4C22⋊D1314yes—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—41no—
537C2×C42—134no—
538C2×C42—262no—
539C2×C42—262no—
540C2×C42—262no—
541C2×C42—521no—
542C2×C42—521no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—134no—
548#95—134no—
549#95—134no—
550#95—134no—
551#95—134no—
552#95—262no—
553#95—262no—
554#95—262no—
555#95—262no—
556#95—262no—
557#95—262no—
558#95—521no—
559#95—521no—
560#95—521no—
561#95—521no—
562#95—521no—
563C2×C13#231711yescharacteristic
564C2×C13#232211yescharacteristic
565C2×C13#233011yescharacteristic
566C2×C13D4×C4⋊C411yescharacteristic
567C2×C13Q8×C4⋊C411yescharacteristic
568C2×C13#236011yescharacteristic
569C2×C13#238311yescharacteristic
570C2×C13#267311yescharacteristic
571C2×C13#267711yescharacteristic
572C2×C13#271311yescharacteristic
573C2×C13#272011yescharacteristic
574C2×C13#272111yescharacteristic
575C2×C13#273411yescharacteristic
576C2×C13#279111yescharacteristic
577C2×C13#279211yescharacteristic
578C24C23×D1311yescharacteristic
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—132no—
618C22×C4—132no—
619C22×C4—132no—
620C22×C4—132no—
621C22×C4—132no—
622C22×C4—132no—
623C22×C4—132no—
624C22×C4—132no—
625C22×C4—132no—
626C22×C4—132no—
627C22×C4—261no—
628C22×C4—261no—
629C22×C4—261no—
630C22×C4—261no—
631C22×C4—261no—
632C22×C4—261no—
633C22×C4—261no—
634C22×C4—261no—
635C22×C4—261no—
636C22×C4—261no—
637C22×C4—261no—
638C22×C4—261no—
639C22×C4—261no—
640C22×C4—261no—
641C22×C4—261no—
642C22×C4—261no—
643C22×C4—261no—
644C22×C4—261no—
645C22×C4—261no—
646C22×C4—261no—
647C22×C4—261no—
648C22×C4—261no—
649C22×C4—261no—
650C22×C4—261no—
651C22×C4—261no—
652C22×C4—261no—
653C22×C4—261no—
654C22×C4—261no—
655C22×C4—261no—
656C22×C4—261no—
657C22×C4—261no—
658C22×C4—261no—
659C22×C4—261no—
660C22×C4—261no—
661C22×C4—261no—
662C22×C4—261no—
663C22×C4—261no—
664C22×C4—261no—
665C22×C4—261no—
666C22×C4—261no—
667C22×C4—261no—
668C22×C4—261no—
669C22×C4—261no—
670C22×C4—261no—
671C22×C4—261no—
672C22×C4—261no—
673C22×C4C2×Dic2612yes—
674C22×C4C2×Dic2612yes—
675C22×C4C2×Dic2612yes—
676C22×C4C2×C4×D1312yes—
677C22×C4C2×C4×D1312yes—
678C22×C4C2×C4×D1312yes—
679C22×C4D4×D1312yes—
680C22×C4Q8×D1312yes—
681C22×C4C2×C22⋊D1312yes—
682C22×C4C2×C22⋊D1312yes—
683C22×C4C2×C22⋊D1312yes—
684C4⋊C4—44no—
685C4⋊C4—268no—
686C4⋊C4—524no—
687C4⋊C4—524no—
688C4⋊C4—524no—
689C4⋊C4—524no—
690C4⋊C4—524no—
691C4⋊C4—524no—
692C4⋊C4—524no—
693C4⋊C4—524no—
694C4⋊C4—524no—
695C4⋊C4#6101116yescomplemented
696C42—44no—
697C42—268no—
698C42—524no—
699C13#1440611yescharacteristic, complemented, Sylow
700C23C22×Dic2611yescharacteristic
701C23C22×C4×D1311yescharacteristic
702C23C2×D4×D1311yescharacteristic
703C23#8825111yescharacteristic
704C23C2×Q8×D1311yescharacteristic
705C23#8825411yescharacteristic
706C23#41×D1311yescharacteristic
707C23#41×D1311yescharacteristic
708C23#8825611yescharacteristic
709C23#8825611yescharacteristic
710C23#8825611yescharacteristic
711C23#8825711yescharacteristic
712C23#8825711yescharacteristic
713C23#8825711yescharacteristic
714C23C22×C22⋊D1311yescharacteristic
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—134no—
762C2×C4—134no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—262no—
766C2×C4—262no—
767C2×C4—262no—
768C2×C4—262no—
769C2×C4—262no—
770C2×C4—262no—
771C2×C4—262no—
772C2×C4—262no—
773C2×C4—262no—
774C2×C4—262no—
775C2×C4—262no—
776C2×C4—262no—
777C2×C4—262no—
778C2×C4—262no—
779C2×C4—262no—
780C2×C4—262no—
781C2×C4—262no—
782C2×C4—262no—
783C2×C4—262no—
784C2×C4—262no—
785C2×C4—262no—
786C2×C4—262no—
787C2×C4—521no—
788C2×C4—521no—
789C2×C4—521no—
790C2×C4—521no—
791C2×C4—521no—
792C2×C4—521no—
793C2×C4—521no—
794C2×C4—521no—
795C2×C4—521no—
796C2×C4—521no—
797C2×C4—521no—
798C2×C4—521no—
799C2×C4—521no—
800C2×C4—521no—
801C2×C4—521no—
802C2×C4—521no—
803C2×C4—521no—
804C2×C4—521no—
805C2×C4—521no—
806C2×C4—521no—
807C2×C4—521no—
808C2×C4—521no—
809C2×C4—521no—
810C2×C4—521no—
811C2×C4—521no—
812C2×C4—521no—
813C2×C4—521no—
814C2×C4—521no—
815C2×C4—521no—
816C2×C4—521no—
817C2×C4C2×#610114yes—
818C2×C4C2×#610114yes—
819C2×C4C2×#610114yes—
820C22#1171922411yescharacteristic
821C22#1171922411yescharacteristic
822C22#1171922811yescharacteristic
823C22#1171922811yescharacteristic
824C22D4×Dic2611yescharacteristic
825C22#1171924411yescharacteristic
826C22C4×D4×D1311yescharacteristic
827C22#1171925111yescharacteristic
828C22Q8×Dic2611yescharacteristic
829C22#1171927411yescharacteristic
830C22C4×Q8×D1311yescharacteristic
831C22#1171927911yescharacteristic
832C22#1171932811yescharacteristic
833C22#1171933311yescharacteristic
834C22#1171933711yescharacteristic
835C22#1171935111yescharacteristic
836C22#1171935811yescharacteristic
837C22#1171935911yescharacteristic
838C22#1171936811yescharacteristic
839C22#1171937111yescharacteristic
840C22#1171939411yescharacteristic
841C22#1171939511yescharacteristic
842C22#1171939711yescharacteristic
843C22#1171940411yescharacteristic
844C22#1171940611yescharacteristic
845C22#1171941211yescharacteristic
846C22#1171941311yescharacteristic
847C22#1171941711yescharacteristic
848C22C22×#610111yescharacteristic
849C22D4×C22⋊D1311yescharacteristic
850C22Q8×C22⋊D1311yescharacteristic
851C22#1171952911yescharacteristic
852C22#1171953011yescharacteristic
853C22#1171953511yescharacteristic
854C22#1171953911yescharacteristic
855C4—24no—
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—264no—
863C4—264no—
864C4—522no—
865C4—522no—
866C4—522no—
867C4—522no—
868C4—1041no—
869C4—1041no—
870C2#1311745611yescharacteristic
871C2#1311750911yescharacteristic
872C2#1311757211yescharacteristic
873C2D4×#610111yescharacteristic
874C2Q8×#610111yescharacteristic
875C2#1311784411yescharacteristic
876C2#1311802611yescharacteristic
877C2#1312110211yescharacteristic
878C2#1312114711yescharacteristic
879C2#1312162111yescharacteristic
880C2#1312171211yescharacteristic
881C2#1312172711yescharacteristic
882C2#1312186911yescharacteristic
883C2#1312262411yescharacteristic
884C2#1312263311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#387C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#387D13
hypocenterC13#14406
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
53. #11718642C4semidirect
244. C13×C4⋊C4C4⋊C4semidirect
695. C4⋊C4#6101semidirect
699. C13#14406semidirect

Maximal subgroups

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

subgroupindex
C2×#117186462
C2×#117185892
C2×#117186422
C2×#117186372
#131131002
#131130992
#131130922
#131130882
#131130692
#131130672
#131130622
C2×C13×#3872
#1440613