Finite Group Databasebeta

← C2×#13122975 #16069237

Subgroups — C2×#13122975 #16069237

Order 3328.

2434 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13122975C2116yesmaximal, direct product factor
2C2×#11718644C211yesmaximal, characteristic, complemented
3C2×#11718336C211yesmaximal, characteristic, complemented
4C2×#11718613C211yesmaximal, characteristic, complemented
5C2×#11718337C211yesmaximal, characteristic, complemented
6C2×#11718655C211yesmaximal, characteristic, complemented
7C2×#11718652C211yesmaximal, characteristic, complemented
8C2×#11718652C211yesmaximal, characteristic, complemented
9C2×#11718622C211yesmaximal, characteristic, complemented
10C2×#11718620C211yesmaximal, characteristic, complemented
11C2×#11718620C211yesmaximal, characteristic, complemented
12C2×#11718621C211yesmaximal, characteristic
13C2×#11718618C211yesmaximal, characteristic, complemented
14C2×#11718651C211yesmaximal, characteristic, complemented
15C2×#11718639C211yesmaximal, characteristic, complemented
16C2×C13×#399C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×D52C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×#6103C2211yescharacteristic
36C22×#6103C2211yescharacteristic
37C22×#6103C2211yescharacteristic
38C22×C4⋊Dic13C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×#6101C2211yescharacteristic
41C22×#6101C2211yescharacteristic
42C22×#6101C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C13×#399C2218yescomplemented
45C2×C13×#95C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53#11718655C2218yescomplemented
54#11718652C2218yescomplemented
55#11718652C2218yescomplemented
56#11718651C2218yescomplemented
57#11718644C2218yescomplemented
58#11718639C2218yescomplemented
59#11718622C2218yescomplemented
60#11718621C2218yes—
61#11718620C2218yescomplemented
62#11718620C2218yescomplemented
63#11718618C2218yescomplemented
64#11718613C2218yescomplemented
65#11718337C2218yescomplemented
66#11718336C2218yescomplemented
67C25×C13C2311yescharacteristic
68C24×D13C2311yescharacteristic
69C24×D13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C22×C22⋊D13—24no—
77C22×C22⋊D13—42no—
78C22×C22⋊D13—42no—
79C22×C22⋊D13—42no—
80C22×C22⋊D13—42no—
81C22×C22⋊D13—42no—
82C22×C22⋊D13C2314yes—
83C22×C22⋊D13C2314yes—
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C23×Dic13C2311yescharacteristic
89C23×Dic13C2311yescharacteristic
90C22×D52—42no—
91C22×D52—42no—
92C22×D52—42no—
93C22×D52C2314yes—
94C2×C13×C4⋊C4—42no—
95C2×C13×C4⋊C4—42no—
96C2×C13×C4⋊C4—42no—
97C2×C13×C4⋊C4C2314yes—
98C2×C13×C4⋊C4C2314yes—
99C2×C13×C4⋊C4C2314yes—
100C2×C13×C22⋊C4—42no—
101C2×C13×C22⋊C4—42no—
102C2×C13×C22⋊C4—42no—
103C2×C13×C22⋊C4C2314yes—
104C2×C13×C22⋊C4C2314yes—
105C2×C13×C22⋊C4C2314yes—
106C2×C22⋊Dic13—42no—
107C2×C22⋊Dic13—42no—
108C2×C22⋊Dic13C2314yes—
109C2×C22⋊Dic13C2314yes—
110C2×#6103—24no—
111C2×#6103—42no—
112C2×#6103—42no—
113C2×#6103—42no—
114C2×#6103—42no—
115C2×#6103—42no—
116C2×#6103—42no—
117C2×#6103—42no—
118C2×#6103—42no—
119C2×#6103—42no—
120C2×#6103C2314yes—
121C2×#6103C2314yes—
122C2×#6103C2314yes—
123C2×#6103C2314yes—
124C2×#6103C2314yes—
125C2×#6103C2314yes—
126C2×#6103C2314yes—
127C2×#6103C2314yes—
128C2×#6103C2314yes—
129C2×#6103C2314yes—
130C2×C4⋊Dic13—42no—
131C2×C4⋊Dic13C2314yes—
132C2×#6101—24no—
133C2×#6101—42no—
134C2×#6101—42no—
135C2×#6101—42no—
136C2×#6101C2314yes—
137C2×#6101C2314yes—
138C2×#6101C2314yes—
139C2×#6101C2314yes—
140C2×C4×Dic13—42no—
141C2×C4×Dic13C2314yes—
142C13×#95C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2829—131nomaximal, Sylow
151C24×C13—22no—
152C24×C13—22no—
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13—22no—
158C24×C13C2412yes—
159C24×C13C2411yescharacteristic
160C23×D13—22no—
161C23×D13—22no—
162C23×D13—22no—
163C23×D13—22no—
164C23×D13—22no—
165C23×D13—22no—
166C23×D13—22no—
167C23×D13—22no—
168C23×D13—22no—
169C23×D13—22no—
170C23×D13—22no—
171C23×D13—22no—
172C23×D13—22no—
173C23×D13—22no—
174C23×D13C2412yes—
175C23×D13C2412yes—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
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×C13C2412yes—
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#4114yes—
226C22×Dic13C2412yes—
227C22×Dic13C2412yes—
228C22×Dic13C2412yes—
229C22×Dic13C2412yes—
230C22×Dic13C2412yes—
231C22×Dic13C2412yes—
232C2×D52—44no—
233C2×D52—44no—
234C2×D52—44no—
235C2×D52—416no—
236C13×C4⋊C4—44no—
237C13×C4⋊C4—44no—
238C13×C4⋊C4—44no—
239C13×C22⋊C4—44no—
240C13×C22⋊C4—44no—
241C13×C22⋊C4—44no—
242C22⋊Dic13—44no—
243C22⋊Dic13—44no—
244#6103—28no—
245#6103—44no—
246#6103—44no—
247#6103—44no—
248#6103—44no—
249#6103—44no—
250#6103—44no—
251#6103—44no—
252#6103—44no—
253#6103—44no—
254C4⋊Dic13—44no—
255#6101—28no—
256#6101—44no—
257#6101—44no—
258#6101—44no—
259C4×Dic13—44no—
260#2829—1316no—
261C2×#399D1311yescharacteristic, complemented
262C2×#398—131no—
263C2×#397—131no—
264C2×#397—131no—
265C2×#396—131no—
266C2×#396—131no—
267C2×#394—131no—
268C2×#394—131no—
269C2×#394—131no—
270C2×#394—131no—
271C2×#394—131no—
272C2×#392—131no—
273C2×#390—131no—
274C2×#388—131no—
275C2×#387—131no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—44no—
284C23×C13—44no—
285C23×C13—44no—
286C23×C13—44no—
287C23×C13—44no—
288C23×C13—44no—
289C23×C13—44no—
290C23×C13C2×#4112yes—
291C23×C13H(5,𝔽2)12yes—
292C23×C13H(5,𝔽2)12yes—
293C23×C13H(5,𝔽2)12yes—
294C23×C13H(5,𝔽2)12yes—
295C23×C13H(5,𝔽2)12yes—
296C23×C132−1+412yes—
297C23×C13C2511yescharacteristic
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—22no—
302C22×D13—22no—
303C22×D13—22no—
304C22×D13—22no—
305C22×D13—22no—
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—44no—
313C22×D13—44no—
314C22×D13—44no—
315C22×D13—44no—
316C22×D13—44no—
317C22×D13—44no—
318C22×D13—44no—
319C22×D13—44no—
320C22×D13—44no—
321C22×D13—44no—
322C22×D13—44no—
323C22×D13—44no—
324C22×D13—44no—
325C22×D13—44no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
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—22no—
344C2×C4×C13—44no—
345C2×C4×C13—44no—
346C2×C4×C13—44no—
347C2×C4×C13—44no—
348C2×C4×C13—44no—
349C2×C4×C13—44no—
350C22⋊D13—416no—
351C22⋊D13—416no—
352C2×Dic13—28no—
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—44no—
371C2×Dic13—44no—
372C2×Dic13—44no—
373C2×Dic13—44no—
374C2×Dic13—44no—
375C2×Dic13C2×#4114yes—
376D52—416no—
377C23×D4—131no—
378C23×D4—131no—
379C23×D4—131no—
380C22×C4⋊C4—131no—
381C22×C4⋊C4—131no—
382C22×C4⋊C4—131no—
383C22×C4⋊C4—131no—
384C22×C4⋊C4—131no—
385C22×C4⋊C4C2×D1311yescharacteristic
386C22×C4⋊C4C2×D1311yescharacteristic
387C22×C4⋊C4C2×D1311yescharacteristic
388C22×C22⋊C4—131no—
389C22×C22⋊C4—131no—
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×C42—131no—
404#399C2×D1318yescomplemented
405#398—138no—
406#397—138no—
407#397—138no—
408#396—138no—
409#396—138no—
410#394—138no—
411#394—138no—
412#394—138no—
413#394—138no—
414#394—138no—
415#392—138no—
416#390—138no—
417#388—138no—
418#387—138no—
419C2×#95—131no—
420C2×#95—131no—
421C2×#95—131no—
422C2×#95—131no—
423C2×#95—131no—
424C2×#95—131no—
425C2×#95—131no—
426C2×#95C2×D1311yescharacteristic
427C22×C13—42no—
428C22×C13—42no—
429C22×C13—42no—
430C22×C13—42no—
431C22×C13—42no—
432C22×C13—42no—
433C22×C13—42no—
434C22×C13—88no—
435C22×C13#53814yes—
436C22×C13#54014yes—
437C22×C13#54214yes—
438C22×C13#56014yes—
439C22×C13#56014yes—
440C22×C13#56214yes—
441C22×C13#56214yes—
442C22×C13C22×#4111yescharacteristic
443C22×C13C2×H(5,𝔽2)11yescharacteristic
444C22×C13C2×H(5,𝔽2)11yescharacteristic
445C22×C13C2×H(5,𝔽2)11yescharacteristic
446C22×C13C2×H(5,𝔽2)11yescharacteristic
447C22×C13C2×H(5,𝔽2)11yescharacteristic
448C22×C13C2×2−1+411yescharacteristic
449C2×D13—42no—
450C2×D13—42no—
451C2×D13—42no—
452C2×D13—42no—
453C2×D13—42no—
454C2×D13—42no—
455C2×D13—42no—
456C2×D13—42no—
457C2×D13—42no—
458C2×D13—42no—
459C2×D13—42no—
460C2×D13—42no—
461C2×D13—42no—
462C2×D13—42no—
463C2×D13—88no—
464C2×D13—88no—
465C4×C13—42no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13—42no—
469C4×C13—42no—
470C4×C13—42no—
471Dic13—24no—
472Dic13—42no—
473Dic13—42no—
474Dic13—42no—
475Dic13—42no—
476Dic13—42no—
477C25—131no—
478C25—131no—
479C25C22×D1311yescharacteristic
480C22×D4—134no—
481C22×D4—134no—
482C22×D4—134no—
483C22×D4—264no—
484C22×D4—522no—
485C22×D4—522no—
486C22×D4—522no—
487C22×D4—522no—
488C22×D4—522no—
489C22×D4—522no—
490C22×D4—522no—
491C22×D4—522no—
492C23×C4—131no—
493C23×C4—131no—
494C23×C4—131no—
495C23×C4—131no—
496C23×C4—131no—
497C23×C4—131no—
498C23×C4C22×D1311yescharacteristic
499C23×C4C22×D1311yescharacteristic
500C23×C4C22×D1311yescharacteristic
501C23×C4C22×D1311yescharacteristic
502C23×C4C22×D1311yescharacteristic
503C23×C4C22×D1311yescharacteristic
504C2×C4⋊C4—42no—
505C2×C4⋊C4—42no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—134no—
508C2×C4⋊C4—134no—
509C2×C4⋊C4—134no—
510C2×C4⋊C4—134no—
511C2×C4⋊C4—134no—
512C2×C4⋊C4—264no—
513C2×C4⋊C4—522no—
514C2×C4⋊C4—522no—
515C2×C4⋊C4—522no—
516C2×C4⋊C4—522no—
517C2×C4⋊C4C22×D1314yes—
518C2×C4⋊C4C22×D1314yes—
519C2×C4⋊C4C22×D1314yes—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—134no—
524C2×C22⋊C4—134no—
525C2×C22⋊C4—134no—
526C2×C22⋊C4—134no—
527C2×C22⋊C4—134no—
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—264no—
536C2×C22⋊C4—522no—
537C2×C22⋊C4—522no—
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⋊C4C22×D1314yes—
548C2×C22⋊C4C22×D1314yes—
549C2×C22⋊C4C22×D1314yes—
550C2×C42—134no—
551C2×C42—522no—
552#95—134no—
553#95—134no—
554#95—134no—
555#95—134no—
556#95—134no—
557#95—134no—
558#95—134no—
559#95C22×D1314yes—
560C2×C13—82no—
561C2×C13#282918yescomplemented
562C2×C13C2×#53811yescharacteristic
563C2×C13C2×#54011yescharacteristic
564C2×C13C2×#54211yescharacteristic
565C2×C13C2×#56011yescharacteristic
566C2×C13C2×#56011yescharacteristic
567C2×C13C2×#56211yescharacteristic
568C2×C13C2×#56211yescharacteristic
569D13—82no—
570D13—82no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—132no—
579C24—132no—
580C24—262no—
581C24—262no—
582C24—262no—
583C24—262no—
584C24—262no—
585C24—262no—
586C24—262no—
587C24—262no—
588C24—262no—
589C24—262no—
590C24—262no—
591C24—262no—
592C24—262no—
593C24—262no—
594C24C23×D1312yes—
595C24C23×D1311yescharacteristic
596C2×D4—268no—
597C2×D4—524no—
598C2×D4—524no—
599C2×D4—524no—
600C2×D4—5216no—
601C2×D4—524no—
602C2×D4—524no—
603C2×D4—524no—
604C2×D4—524no—
605C2×D4—524no—
606C2×D4—5216no—
607C2×D4—5216no—
608C22×C4—22no—
609C22×C4—22no—
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—22no—
626C22×C4—134no—
627C22×C4—132no—
628C22×C4—132no—
629C22×C4—132no—
630C22×C4—132no—
631C22×C4—132no—
632C22×C4—132no—
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×C4C23×D1312yes—
651C22×C4C23×D1312yes—
652C22×C4C23×D1312yes—
653C22×C4C23×D1312yes—
654C22×C4C23×D1312yes—
655C22×C4C23×D1312yes—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—268no—
660C4⋊C4—524no—
661C4⋊C4—524no—
662C4⋊C4—524no—
663C4⋊C4—524no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—268no—
668C22⋊C4—524no—
669C22⋊C4—524no—
670C22⋊C4—524no—
671C22⋊C4—524no—
672C22⋊C4—524no—
673C22⋊C4—524no—
674C22⋊C4—524no—
675C22⋊C4—524no—
676C22⋊C4—524no—
677C22⋊C4—524no—
678C22⋊C4—524no—
679C42—524no—
680C13C2×#282911yescharacteristic, complemented, Sylow
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—262no—
696C23—262no—
697C23—262no—
698C23—262no—
699C23—262no—
700C23—262no—
701C23—262no—
702C23—262no—
703C23—262no—
704C23—262no—
705C23—262no—
706C23—262no—
707C23—262no—
708C23—262no—
709C23—524no—
710C23—524no—
711C23—524no—
712C23—524no—
713C23—524no—
714C23—524no—
715C23—524no—
716C23—524no—
717C23—524no—
718C23—524no—
719C23—524no—
720C23—524no—
721C23—524no—
722C23—524no—
723C23#8825112yes—
724C23#8825112yes—
725C23#8825112yes—
726C23#8825412yes—
727C23#41×D1312yes—
728C23#8825612yes—
729C23#8825612yes—
730C23C24×D1311yescharacteristic
731D4—5216no—
732D4—5216no—
733D4—5216no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
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—44no—
758C2×C4—134no—
759C2×C4—268no—
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—524no—
778C2×C4—524no—
779C2×C4—524no—
780C2×C4—524no—
781C2×C4—524no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—88no—
790C22—522no—
791C22—522no—
792C22—522no—
793C22—522no—
794C22—522no—
795C22—522no—
796C22—522no—
797C22—522no—
798C22—522no—
799C22—522no—
800C22—522no—
801C22—522no—
802C22—522no—
803C22—522no—
804C22—1048no—
805C22—1048no—
806C22#1171934514yes—
807C22#1171935214yes—
808C22#1171935214yes—
809C22#1171936214yes—
810C22#1171936814yes—
811C22#1171937114yes—
812C22#1171942514yes—
813C22C2×#8825111yescharacteristic
814C22C2×#8825111yescharacteristic
815C22C2×#8825111yescharacteristic
816C22C2×#8825411yescharacteristic
817C22C2×#41×D1311yescharacteristic
818C22C2×#8825611yescharacteristic
819C22C2×#8825611yescharacteristic
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—264no—
827C4—522no—
828C4—522no—
829C4—522no—
830C4—522no—
831C4—522no—
832C2—82no—
833C2—1042no—
834C2—1042no—
835C2#1312297518yesdirect product factor
836C2C2×#1171936211yescharacteristic
837C2C2×#1171936811yescharacteristic
838C2C2×#1171934511yescharacteristic
839C2C2×#1171942511yescharacteristic
840C2C2×#1171937111yescharacteristic
841C2C2×#1171935211yescharacteristic
842C2C2×#1171935211yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#399C2
socleC24×C13C24
prime radicalC2×#11718621C2
hypercenterC2×#399D13
hypocenterC13C2×#2829
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. #13122975C2direct (N × H)
2. C2×#11718644C2semidirect
3. C2×#11718336C2semidirect
4. C2×#11718613C2semidirect
5. C2×#11718337C2semidirect
6. C2×#11718655C2semidirect
7. C2×#11718652C2semidirect
8. C2×#11718652C2semidirect
9. C2×#11718622C2semidirect
10. C2×#11718620C2semidirect
11. C2×#11718620C2semidirect
13. C2×#11718618C2semidirect
14. C2×#11718651C2semidirect
15. C2×#11718639C2semidirect
16. C2×C13×#399C2semidirect
44. C13×#399C22semidirect
53. #11718655C22semidirect
54. #11718652C22semidirect
55. #11718652C22semidirect
56. #11718651C22semidirect
57. #11718644C22semidirect
58. #11718639C22semidirect
59. #11718622C22semidirect
61. #11718620C22semidirect
62. #11718620C22semidirect
63. #11718618C22semidirect
64. #11718613C22semidirect
65. #11718337C22semidirect
66. #11718336C22semidirect
261. C2×#399D13semidirect
404. #399C2×D13semidirect
561. C2×C13#2829semidirect
680. C13C2×#2829semidirect
835. C2#13122975direct (N × H)

Maximal subgroups

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

subgroupindex
#131229752
C2×#117186442
C2×#117183362
C2×#117186132
C2×#117183372
C2×#117186552
C2×#117186522
C2×#117186222
C2×#117186202
C2×#117186212
C2×#117186182
C2×#117186512
C2×#117186392
C2×C13×#3992
C2×#282913