Finite Group Databasebeta

← C2×#13122934 #16069126

Subgroups — C2×#13122934 #16069126

Order 3328.

2542 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13122934C2116yesmaximal, direct product factor
2C2×#11718321C211yesmaximal, characteristic, complemented
3C2×#11718643C211yesmaximal, characteristic, complemented
4C2×#11718610C211yesmaximal, characteristic, complemented
5C2×#11718335C211yesmaximal, characteristic, complemented
6C2×#11718614C211yesmaximal, characteristic, complemented
7C2×#11718609C211yesmaximal, characteristic, complemented
8C2×#11718655C211yesmaximal, characteristic, complemented
9C2×#11718622C211yesmaximal, characteristic, complemented
10C2×#11718620C211yesmaximal, characteristic, complemented
11C2×#11718620C211yesmaximal, characteristic, complemented
12C2×#11718884C211yesmaximal, characteristic
13C2×#11718881C211yesmaximal, characteristic, complemented
14C2×#11718619C211yesmaximal, characteristic, complemented
15C2×#11718611C211yesmaximal, characteristic, complemented
16C2×C13×#394C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C13×#394C2218yescomplemented
43C2×C13×#95C2211yescharacteristic
44#11718884C2218yes—
45#11718881C2218yescomplemented
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718655C2218yescomplemented
56#11718643C2218yescomplemented
57#11718622C2218yescomplemented
58#11718620C2218yescomplemented
59#11718620C2218yescomplemented
60#11718619C2218yescomplemented
61#11718614C2218yescomplemented
62#11718611C2218yescomplemented
63#11718610C2218yescomplemented
64#11718609C2218yescomplemented
65#11718335C2218yescomplemented
66#11718321C2218yescomplemented
67C25×C13C2311yescharacteristic
68C25×C13C2311yescharacteristic
69C24×D13C2311yescharacteristic
70C22×D4×C13—24no—
71C22×D4×C13—42no—
72C22×D4×C13—42no—
73C22×D4×C13C2314yes—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×C22⋊D13—24no—
80C22×C22⋊D13—42no—
81C22×C22⋊D13—42no—
82C22×C22⋊D13—42no—
83C22×C22⋊D13—42no—
84C22×C22⋊D13—42no—
85C22×C22⋊D13C2314yes—
86C22×C22⋊D13C2314yes—
87C23×Dic13—42no—
88C23×Dic13—42no—
89C23×Dic13—42no—
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2314yes—
98C2×C13×C4⋊C4—42no—
99C2×C13×C4⋊C4C2314yes—
100C2×C13×C22⋊C4—24no—
101C2×C13×C22⋊C4—42no—
102C2×C13×C22⋊C4—42no—
103C2×C13×C22⋊C4—42no—
104C2×C13×C22⋊C4C2314yes—
105C2×C13×C22⋊C4C2314yes—
106C2×C13×C22⋊C4C2314yes—
107C2×C13×C22⋊C4C2314yes—
108C2×C22⋊Dic13—42no—
109C2×C22⋊Dic13—42no—
110C2×C22⋊Dic13—42no—
111C2×C22⋊Dic13—42no—
112C2×C22⋊Dic13—42no—
113C2×C22⋊Dic13C2314yes—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116C2×C22⋊Dic13C2314yes—
117C2×C22⋊Dic13C2314yes—
118C2×#6103—42no—
119C2×#6103—42no—
120C2×#6103—42no—
121C2×#6103—42no—
122C2×#6103—42no—
123C2×#6103C2314yes—
124C2×#6103C2314yes—
125C2×#6103C2314yes—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×C4⋊Dic13—42no—
129C2×C4⋊Dic13—42no—
130C2×C4⋊Dic13—42no—
131C2×C4⋊Dic13C2314yes—
132C2×C4⋊Dic13C2314yes—
133C2×C4⋊Dic13C2314yes—
134C2×#6101—42no—
135C2×#6101—42no—
136C2×#6101—42no—
137C2×#6101C2314yes—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C13×#95C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2826—131nomaximal, Sylow
151C24×C13—22no—
152C24×C13—22no—
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13—22no—
158C24×C13—22no—
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13#4114yes—
165C24×C13C2412yes—
166C24×C13C2412yes—
167C24×C13C2411yescharacteristic
168C23×D13—22no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—22no—
173C23×D13—22no—
174C23×D13—22no—
175C23×D13C2412yes—
176C2×D4×C13—28no—
177C2×D4×C13—44no—
178C2×D4×C13—44no—
179C2×D4×C13—416no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—22no—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—22no—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C22×C4×C13C2412yes—
199C22×C4×C13C2412yes—
200C2×C22⋊D13—28no—
201C2×C22⋊D13—44no—
202C2×C22⋊D13—44no—
203C2×C22⋊D13—44no—
204C2×C22⋊D13—44no—
205C2×C22⋊D13—44no—
206C2×C22⋊D13—416no—
207C2×C22⋊D13—416no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—22no—
224C22×Dic13—22no—
225C22×Dic13—22no—
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—22no—
229C22×Dic13—44no—
230C22×Dic13—44no—
231C22×Dic13—44no—
232C22×Dic13—416no—
233C22×Dic13C2412yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C13×C4⋊C4—44no—
241C13×C22⋊C4—28no—
242C13×C22⋊C4—44no—
243C13×C22⋊C4—44no—
244C13×C22⋊C4—44no—
245C22⋊Dic13—44no—
246C22⋊Dic13—44no—
247C22⋊Dic13—44no—
248C22⋊Dic13—44no—
249C22⋊Dic13—44no—
250#6103—44no—
251#6103—44no—
252#6103—44no—
253#6103—44no—
254#6103—44no—
255C4⋊Dic13—44no—
256C4⋊Dic13—44no—
257C4⋊Dic13—44no—
258#6101—44no—
259#6101—44no—
260#6101—44no—
261#2826—1316no—
262C2×#400—131no—
263C2×#400—131no—
264C2×#399—131no—
265C2×#397—131no—
266C2×#397—131no—
267C2×#396—131no—
268C2×#396—131no—
269C2×#394—131no—
270C2×#394—131no—
271C2×#394—131no—
272C2×#394D1311yescharacteristic, complemented
273C2×#392—131no—
274C2×#386—131no—
275C2×#386—131no—
276C2×#385—131no—
277C23×C13—28no—
278C23×C13—28no—
279C23×C13—28no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—44no—
294C23×C13—44no—
295C23×C13—44no—
296C23×C13—44no—
297C23×C13—44no—
298C23×C13—44no—
299C23×C13—44no—
300C23×C13—44no—
301C23×C13—44no—
302C23×C13—44no—
303C23×C13—44no—
304C23×C13C2×#4114yes—
305C23×C13C2×#4112yes—
306C23×C13H(5,𝔽2)12yes—
307C23×C13H(5,𝔽2)12yes—
308C23×C13H(5,𝔽2)12yes—
309C23×C13H(5,𝔽2)12yes—
310C23×C13H(5,𝔽2)12yes—
311C23×C132−1+412yes—
312C23×C13C2511yescharacteristic
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—44no—
321C22×D13—44no—
322C22×D13—44no—
323C22×D13—44no—
324C22×D13—44no—
325C22×D13—44no—
326C22×D13—44no—
327D4×C13—416no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—44no—
344C2×C4×C13—44no—
345C2×C4×C13—44no—
346C2×C4×C13—44no—
347C2×C4×C13—44no—
348C22⋊D13—416no—
349C22⋊D13—416no—
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—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—416no—
372C2×Dic13—44no—
373C2×Dic13—44no—
374C2×Dic13—44no—
375C2×Dic13—44no—
376C2×Dic13—44no—
377C2×Dic13—44no—
378C2×Dic13—44no—
379C23×D4—131no—
380C23×D4—131no—
381C23×D4C2×D1311yescharacteristic
382C24×C4—131no—
383C22×C4⋊C4—131no—
384C22×C4⋊C4—131no—
385C22×C4⋊C4—131no—
386C22×C4⋊C4—131no—
387C22×C4⋊C4—131no—
388C22×C4⋊C4—131no—
389C22×C4⋊C4C2×D1311yescharacteristic
390C22×C22⋊C4—131no—
391C22×C22⋊C4—131no—
392C22×C22⋊C4—131no—
393C22×C22⋊C4—131no—
394C22×C22⋊C4—131no—
395C22×C22⋊C4—131no—
396C22×C22⋊C4—131no—
397C22×C22⋊C4—131no—
398C22×C22⋊C4—131no—
399C22×C22⋊C4—131no—
400C22×C22⋊C4C2×D1311yescharacteristic
401C22×C22⋊C4C2×D1311yescharacteristic
402C22×C22⋊C4C2×D1311yescharacteristic
403C22×C22⋊C4C2×D1311yescharacteristic
404#400—138no—
405#400—138no—
406#399—138no—
407#397—138no—
408#397—138no—
409#396—138no—
410#396—138no—
411#394—138no—
412#394—138no—
413#394—138no—
414#394C2×D1318yescomplemented
415#392—138no—
416#386—138no—
417#386—138no—
418#385—138no—
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×#95C2×D1311yescharacteristic
429C22×C13—24no—
430C22×C13—24no—
431C22×C13—24no—
432C22×C13—416no—
433C22×C13—42no—
434C22×C13—42no—
435C22×C13—42no—
436C22×C13—42no—
437C22×C13—42no—
438C22×C13—42no—
439C22×C13—42no—
440C22×C13—42no—
441C22×C13—42no—
442C22×C13—42no—
443C22×C13—42no—
444C22×C13—88no—
445C22×C13#53814yes—
446C22×C13#53814yes—
447C22×C13#53914yes—
448C22×C13#56014yes—
449C22×C13#56014yes—
450C22×C13#56214yes—
451C22×C13#56214yes—
452C22×C13C22×#4111yescharacteristic
453C22×C13C2×H(5,𝔽2)11yescharacteristic
454C22×C13C2×H(5,𝔽2)11yescharacteristic
455C22×C13C2×H(5,𝔽2)11yescharacteristic
456C22×C13C2×H(5,𝔽2)11yescharacteristic
457C22×C13C2×H(5,𝔽2)11yescharacteristic
458C22×C13C2×2−1+411yescharacteristic
459C2×D13—42no—
460C2×D13—42no—
461C2×D13—42no—
462C2×D13—42no—
463C2×D13—42no—
464C2×D13—42no—
465C2×D13—42no—
466C2×D13—88no—
467C4×C13—42no—
468C4×C13—42no—
469C4×C13—42no—
470C4×C13—42no—
471C4×C13—42no—
472Dic13—42no—
473Dic13—42no—
474Dic13—42no—
475Dic13—42no—
476Dic13—42no—
477Dic13—42no—
478Dic13—42no—
479C25—131no—
480C25C22×D1311yescharacteristic
481C25C22×D1311yescharacteristic
482C22×D4—24no—
483C22×D4—42no—
484C22×D4—42no—
485C22×D4—134no—
486C22×D4—134no—
487C22×D4—264no—
488C22×D4—522no—
489C22×D4—522no—
490C22×D4—522no—
491C22×D4—522no—
492C22×D4—522no—
493C22×D4C22×D1314yes—
494C23×C4—131no—
495C23×C4—131no—
496C23×C4—131no—
497C23×C4—131no—
498C23×C4—131no—
499C23×C4—131no—
500C23×C4—131no—
501C23×C4—134no—
502C23×C4—522no—
503C23×C4—522no—
504C23×C4—522no—
505C23×C4C22×D1311yescharacteristic
506C23×C4C22×D1311yescharacteristic
507C23×C4C22×D1311yescharacteristic
508C23×C4C22×D1311yescharacteristic
509C23×C4C22×D1311yescharacteristic
510C2×C4⋊C4—42no—
511C2×C4⋊C4—134no—
512C2×C4⋊C4—134no—
513C2×C4⋊C4—134no—
514C2×C4⋊C4—134no—
515C2×C4⋊C4—134no—
516C2×C4⋊C4—134no—
517C2×C4⋊C4—522no—
518C2×C4⋊C4—522no—
519C2×C4⋊C4—522no—
520C2×C4⋊C4—522no—
521C2×C4⋊C4—522no—
522C2×C4⋊C4—522no—
523C2×C4⋊C4C22×D1314yes—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—134no—
529C2×C22⋊C4—134no—
530C2×C22⋊C4—134no—
531C2×C22⋊C4—134no—
532C2×C22⋊C4—134no—
533C2×C22⋊C4—134no—
534C2×C22⋊C4—134no—
535C2×C22⋊C4—134no—
536C2×C22⋊C4—134no—
537C2×C22⋊C4—134no—
538C2×C22⋊C4—522no—
539C2×C22⋊C4—522no—
540C2×C22⋊C4—522no—
541C2×C22⋊C4—522no—
542C2×C22⋊C4—522no—
543C2×C22⋊C4—522no—
544C2×C22⋊C4—522no—
545C2×C22⋊C4—522no—
546C2×C22⋊C4—522no—
547C2×C22⋊C4—522no—
548C2×C22⋊C4C22×D1314yes—
549C2×C22⋊C4C22×D1314yes—
550C2×C22⋊C4C22×D1314yes—
551C2×C22⋊C4C22×D1314yes—
552#95—134no—
553#95—134no—
554#95—134no—
555#95—134no—
556#95—134no—
557#95—134no—
558#95—134no—
559#95—134no—
560#95—134no—
561#95C22×D1314yes—
562C2×C13—44no—
563C2×C13—82no—
564C2×C13#282618yescomplemented
565C2×C13C2×#53811yescharacteristic
566C2×C13C2×#53811yescharacteristic
567C2×C13C2×#53911yescharacteristic
568C2×C13C2×#56011yescharacteristic
569C2×C13C2×#56011yescharacteristic
570C2×C13C2×#56211yescharacteristic
571C2×C13C2×#56211yescharacteristic
572D13—82no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—132no—
587C24—262no—
588C24—262no—
589C24—262no—
590C24—262no—
591C24—262no—
592C24—262no—
593C24—262no—
594C24#612914yes—
595C24C23×D1312yes—
596C24C23×D1312yes—
597C24C23×D1311yescharacteristic
598C2×D4—28no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—416no—
602C2×D4—268no—
603C2×D4—524no—
604C2×D4—524no—
605C2×D4—524no—
606C2×D4—524no—
607C2×D4—524no—
608C2×D4—5216no—
609C2×D4—5216no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—132no—
626C22×C4—132no—
627C22×C4—132no—
628C22×C4—132no—
629C22×C4—132no—
630C22×C4—132no—
631C22×C4—132no—
632C22×C4—262no—
633C22×C4—262no—
634C22×C4—262no—
635C22×C4—262no—
636C22×C4—262no—
637C22×C4—262no—
638C22×C4—262no—
639C22×C4—262no—
640C22×C4—262no—
641C22×C4—262no—
642C22×C4—262no—
643C22×C4—262no—
644C22×C4—262no—
645C22×C4—262no—
646C22×C4—262no—
647C22×C4—262no—
648C22×C4—262no—
649C22×C4—262no—
650C22×C4—262no—
651C22×C4—262no—
652C22×C4—262no—
653C22×C4—524no—
654C22×C4—524no—
655C22×C4—524no—
656C22×C4—5216no—
657C22×C4C23×D1312yes—
658C22×C4C23×D1312yes—
659C22×C4C23×D1312yes—
660C22×C4C23×D1312yes—
661C22×C4C23×D1312yes—
662C4⋊C4—44no—
663C4⋊C4—524no—
664C4⋊C4—524no—
665C4⋊C4—524no—
666C4⋊C4—524no—
667C4⋊C4—524no—
668C4⋊C4—524no—
669C22⋊C4—28no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—524no—
674C22⋊C4—524no—
675C22⋊C4—524no—
676C22⋊C4—524no—
677C22⋊C4—524no—
678C22⋊C4—524no—
679C22⋊C4—524no—
680C22⋊C4—524no—
681C22⋊C4—524no—
682C22⋊C4—524no—
683C13C2×#282611yescharacteristic, complemented, Sylow
684C23—28no—
685C23—28no—
686C23—28no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—262no—
712C23—262no—
713C23—262no—
714C23—262no—
715C23—262no—
716C23—262no—
717C23—262no—
718C23—524no—
719C23—524no—
720C23—524no—
721C23—524no—
722C23—524no—
723C23—524no—
724C23—524no—
725C23C2×#612914yes—
726C23C2×#612912yes—
727C23#8825112yes—
728C23#8825112yes—
729C23#8825112yes—
730C23#8825612yes—
731C23#8825612yes—
732C23#8825712yes—
733C23C24×D1311yescharacteristic
734D4—416no—
735D4—5216no—
736D4—5216no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
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—5216no—
779C2×C4—524no—
780C2×C4—524no—
781C2×C4—524no—
782C2×C4—524no—
783C2×C4—524no—
784C2×C4—524no—
785C2×C4—524no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—42no—
790C22—416no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—88no—
802C22—522no—
803C22—522no—
804C22—522no—
805C22—522no—
806C22—522no—
807C22—522no—
808C22—522no—
809C22—1048no—
810C22#1171929814yes—
811C22#1171932214yes—
812C22#1171932514yes—
813C22#1171932614yes—
814C22#1171937014yes—
815C22#1171937114yes—
816C22#1171938914yes—
817C22C22×#612911yescharacteristic
818C22C2×#8825111yescharacteristic
819C22C2×#8825111yescharacteristic
820C22C2×#8825111yescharacteristic
821C22C2×#8825611yescharacteristic
822C22C2×#8825611yescharacteristic
823C22C2×#8825711yescharacteristic
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—522no—
830C4—522no—
831C4—522no—
832C4—522no—
833C4—522no—
834C4—522no—
835C4—522no—
836C2—44no—
837C2—82no—
838C2—1042no—
839C2#1312293418yesdirect product factor
840C2C2×#1171929811yescharacteristic
841C2C2×#1171932211yescharacteristic
842C2C2×#1171937011yescharacteristic
843C2C2×#1171932511yescharacteristic
844C2C2×#1171937111yescharacteristic
845C2C2×#1171938911yescharacteristic
846C2C2×#1171932611yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#394C2
socleC24×C13C24
prime radicalC2×#11718884C2
hypercenterC2×#394D13
hypocenterC13C2×#2826
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #13122934C2direct (N × H)
2. C2×#11718321C2semidirect
3. C2×#11718643C2semidirect
4. C2×#11718610C2semidirect
5. C2×#11718335C2semidirect
6. C2×#11718614C2semidirect
7. C2×#11718609C2semidirect
8. C2×#11718655C2semidirect
9. C2×#11718622C2semidirect
10. C2×#11718620C2semidirect
11. C2×#11718620C2semidirect
13. C2×#11718881C2semidirect
14. C2×#11718619C2semidirect
15. C2×#11718611C2semidirect
16. C2×C13×#394C2semidirect
42. C13×#394C22semidirect
45. #11718881C22semidirect
55. #11718655C22semidirect
56. #11718643C22semidirect
57. #11718622C22semidirect
58. #11718620C22semidirect
59. #11718620C22semidirect
60. #11718619C22semidirect
61. #11718614C22semidirect
62. #11718611C22semidirect
63. #11718610C22semidirect
64. #11718609C22semidirect
65. #11718335C22semidirect
66. #11718321C22semidirect
272. C2×#394D13semidirect
414. #394C2×D13semidirect
564. C2×C13#2826semidirect
683. C13C2×#2826semidirect
839. C2#13122934direct (N × H)

Maximal subgroups

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

subgroupindex
#131229342
C2×#117183212
C2×#117186432
C2×#117186102
C2×#117183352
C2×#117186142
C2×#117186092
C2×#117186552
C2×#117186222
C2×#117186202
C2×#117188842
C2×#117188812
C2×#117186192
C2×#117186112
C2×C13×#3942
C2×#282613