Finite Group Databasebeta

← C2×#13122930 #16069124

Subgroups — C2×#13122930 #16069124

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#13122930C2116yesmaximal, direct product factor
2C2×#11718320C211yesmaximal, characteristic, complemented
3C2×#11718643C211yesmaximal, characteristic, complemented
4C2×#11718653C211yesmaximal, characteristic, complemented
5C2×#11718613C211yesmaximal, characteristic, complemented
6C2×#11718654C211yesmaximal, characteristic, complemented
7C2×#11718655C211yesmaximal, characteristic, complemented
8C2×#11718652C211yesmaximal, characteristic, complemented
9C2×#11718622C211yesmaximal, characteristic, complemented
10C2×#11718620C211yesmaximal, characteristic, complemented
11C2×#11718620C211yesmaximal, characteristic, complemented
12C2×#11718621C211yesmaximal, characteristic
13C2×#11718326C211yesmaximal, characteristic, complemented
14C2×#11718617C211yesmaximal, characteristic, complemented
15C2×#11718650C211yesmaximal, characteristic, complemented
16C2×C13×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D13C2211yescharacteristic
18C23×C22⋊D13C2211yescharacteristic
19C23×D52C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
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
42C13×#396C2218yescomplemented
43C2×C13×#95C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53#11718655C2218yescomplemented
54#11718654C2218yescomplemented
55#11718653C2218yescomplemented
56#11718652C2218yescomplemented
57#11718650C2218yescomplemented
58#11718643C2218yescomplemented
59#11718622C2218yescomplemented
60#11718621C2218yes—
61#11718620C2218yescomplemented
62#11718620C2218yescomplemented
63#11718617C2218yescomplemented
64#11718613C2218yescomplemented
65#11718326C2218yescomplemented
66#11718320C2218yescomplemented
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—24no—
91C22×D52—42no—
92C22×D52—42no—
93C22×D52C2314yes—
94C22×C4×D13—42no—
95C22×C4×D13—42no—
96C22×C4×D13—42no—
97C22×C4×D13C2314yes—
98C2×C13×C4⋊C4—42no—
99C2×C13×C4⋊C4—42no—
100C2×C13×C4⋊C4—42no—
101C2×C13×C4⋊C4C2314yes—
102C2×C13×C4⋊C4C2314yes—
103C2×C13×C4⋊C4C2314yes—
104C2×C13×C22⋊C4—42no—
105C2×C13×C22⋊C4—42no—
106C2×C13×C22⋊C4—42no—
107C2×C13×C22⋊C4C2314yes—
108C2×C13×C22⋊C4C2314yes—
109C2×C13×C22⋊C4C2314yes—
110C2×C22⋊Dic13—42no—
111C2×C22⋊Dic13—42no—
112C2×C22⋊Dic13C2314yes—
113C2×C22⋊Dic13C2314yes—
114C2×#6103—24no—
115C2×#6103—42no—
116C2×#6103—42no—
117C2×#6103—42no—
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×#6103C2314yes—
129C2×#6103C2314yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×C4⋊Dic13—42no—
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×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#4114yes—
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—22no—
226C22×Dic13C2412yes—
227C22×Dic13C2412yes—
228C22×Dic13C2412yes—
229C22×Dic13C2412yes—
230C22×Dic13C2412yes—
231C22×Dic13C2412yes—
232C2×D52—28no—
233C2×D52—44no—
234C2×D52—44no—
235C2×D52—416no—
236C2×C4×D13—44no—
237C2×C4×D13—44no—
238C2×C4×D13—44no—
239C2×C4×D13—416no—
240C13×C4⋊C4—44no—
241C13×C4⋊C4—44no—
242C13×C4⋊C4—44no—
243C13×C22⋊C4—44no—
244C13×C22⋊C4—44no—
245C13×C22⋊C4—44no—
246C22⋊Dic13—44no—
247C22⋊Dic13—44no—
248#6103—28no—
249#6103—44no—
250#6103—44no—
251#6103—44no—
252#6103—44no—
253#6103—44no—
254#6103—44no—
255#6103—44no—
256#6103—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×#396D1311yescharacteristic, complemented
269C2×#394—131no—
270C2×#394—131no—
271C2×#394—131no—
272C2×#394—131no—
273C2×#392—131no—
274C2×#386—131no—
275C2×#386—131no—
276C2×#385—131no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—44no—
285C23×C13—44no—
286C23×C13—44no—
287C23×C13—44no—
288C23×C13—44no—
289C23×C13—44no—
290C23×C13—44no—
291C23×C13C2×#4112yes—
292C23×C13H(5,𝔽2)12yes—
293C23×C13H(5,𝔽2)12yes—
294C23×C13H(5,𝔽2)12yes—
295C23×C13H(5,𝔽2)12yes—
296C23×C13H(5,𝔽2)12yes—
297C23×C132−1+412yes—
298C23×C13C2511yescharacteristic
299C22×D13—28no—
300C22×D13—28no—
301C22×D13—28no—
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—22no—
313C22×D13—22no—
314C22×D13—22no—
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—
326C22×D13C2×#4114yes—
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—22no—
345C2×C4×C13—44no—
346C2×C4×C13—44no—
347C2×C4×C13—44no—
348C2×C4×C13—44no—
349C2×C4×C13—44no—
350C2×C4×C13—44no—
351C22⋊D13—416no—
352C22⋊D13—416no—
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—44no—
372C2×Dic13—44no—
373C2×Dic13—44no—
374C2×Dic13—44no—
375C2×Dic13—44no—
376C2×Dic13—44no—
377D52—416no—
378C4×D13—416no—
379C23×D4—131no—
380C23×D4—131no—
381C23×D4—131no—
382C24×C4—131no—
383C22×C4⋊C4—131no—
384C22×C4⋊C4—131no—
385C22×C4⋊C4—131no—
386C22×C4⋊C4—131no—
387C22×C4⋊C4C2×D1311yescharacteristic
388C22×C4⋊C4C2×D1311yescharacteristic
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⋊C4—131no—
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#396C2×D1318yescomplemented
411#394—138no—
412#394—138no—
413#394—138no—
414#394—138no—
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—42no—
430C22×C13—42no—
431C22×C13—42no—
432C22×C13—42no—
433C22×C13—42no—
434C22×C13—42no—
435C22×C13—42no—
436C22×C13—88no—
437C22×C13#53814yes—
438C22×C13#53814yes—
439C22×C13#53914yes—
440C22×C13#56014yes—
441C22×C13#56014yes—
442C22×C13#56214yes—
443C22×C13#56214yes—
444C22×C13C22×#4111yescharacteristic
445C22×C13C2×H(5,𝔽2)11yescharacteristic
446C22×C13C2×H(5,𝔽2)11yescharacteristic
447C22×C13C2×H(5,𝔽2)11yescharacteristic
448C22×C13C2×H(5,𝔽2)11yescharacteristic
449C22×C13C2×H(5,𝔽2)11yescharacteristic
450C22×C13C2×2−1+411yescharacteristic
451C2×D13—24no—
452C2×D13—24no—
453C2×D13—24no—
454C2×D13—416no—
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—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—
472C4×C13—42no—
473Dic13—42no—
474Dic13—42no—
475Dic13—42no—
476Dic13—42no—
477Dic13—42no—
478Dic13—42no—
479C25—131no—
480C25—131no—
481C25C22×D1311yescharacteristic
482C22×D4—134no—
483C22×D4—134no—
484C22×D4—134no—
485C22×D4—264no—
486C22×D4—264no—
487C22×D4—522no—
488C22×D4—522no—
489C22×D4—522no—
490C22×D4—522no—
491C22×D4—522no—
492C22×D4—522no—
493C22×D4—522no—
494C23×C4—131no—
495C23×C4—131no—
496C23×C4—131no—
497C23×C4—131no—
498C23×C4—131no—
499C23×C4—131no—
500C23×C4—134no—
501C23×C4—522no—
502C23×C4—522no—
503C23×C4—522no—
504C23×C4C22×D1311yescharacteristic
505C23×C4C22×D1311yescharacteristic
506C23×C4C22×D1311yescharacteristic
507C23×C4C22×D1311yescharacteristic
508C23×C4C22×D1311yescharacteristic
509C23×C4C22×D1311yescharacteristic
510C2×C4⋊C4—42no—
511C2×C4⋊C4—42no—
512C2×C4⋊C4—42no—
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⋊C4C22×D1314yes—
522C2×C4⋊C4C22×D1314yes—
523C2×C4⋊C4C22×D1314yes—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
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—134no—
536C2×C22⋊C4—134no—
537C2×C22⋊C4—134no—
538C2×C22⋊C4—264no—
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⋊C4—522no—
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—82no—
563C2×C13#282618yescomplemented
564C2×C13C2×#53811yescharacteristic
565C2×C13C2×#53811yescharacteristic
566C2×C13C2×#53911yescharacteristic
567C2×C13C2×#56011yescharacteristic
568C2×C13C2×#56011yescharacteristic
569C2×C13C2×#56211yescharacteristic
570C2×C13C2×#56211yescharacteristic
571D13—44no—
572D13—82no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—134no—
581C24—132no—
582C24—132no—
583C24—262no—
584C24—262no—
585C24—262no—
586C24—262no—
587C24—262no—
588C24—262no—
589C24—262no—
590C24—262no—
591C24—262no—
592C24—262no—
593C24—262no—
594C24—262no—
595C24—262no—
596C24C23×D1312yes—
597C24C23×D1311yescharacteristic
598C2×D4—268no—
599C2×D4—268no—
600C2×D4—524no—
601C2×D4—524no—
602C2×D4—5216no—
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—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—132no—
629C22×C4—132no—
630C22×C4—132no—
631C22×C4—132no—
632C22×C4—132no—
633C22×C4—132no—
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—524no—
653C22×C4—524no—
654C22×C4—524no—
655C22×C4—5216no—
656C22×C4C23×D1312yes—
657C22×C4C23×D1312yes—
658C22×C4C23×D1312yes—
659C22×C4C23×D1312yes—
660C22×C4C23×D1312yes—
661C22×C4C23×D1312yes—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—524no—
666C4⋊C4—524no—
667C4⋊C4—524no—
668C4⋊C4—524no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—268no—
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—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—134no—
699C23—268no—
700C23—268no—
701C23—262no—
702C23—262no—
703C23—262no—
704C23—262no—
705C23—262no—
706C23—262no—
707C23—268no—
708C23—262no—
709C23—262no—
710C23—262no—
711C23—262no—
712C23—262no—
713C23—262no—
714C23—262no—
715C23—524no—
716C23—524no—
717C23—524no—
718C23—524no—
719C23—524no—
720C23—524no—
721C23—524no—
722C23—524no—
723C23—524no—
724C23—524no—
725C23—524no—
726C23#8825112yes—
727C23#8825112yes—
728C23#8825112yes—
729C23#8825412yes—
730C23#41×D1312yes—
731C23#8825612yes—
732C23#8825612yes—
733C23C24×D1311yescharacteristic
734D4—5216no—
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—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
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—262no—
779C2×C4—5216no—
780C2×C4—524no—
781C2×C4—524no—
782C2×C4—524no—
783C2×C4—524no—
784C2×C4—524no—
785C2×C4—524no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—88no—
794C22—264no—
795C22—264no—
796C22—264no—
797C22—522no—
798C22—522no—
799C22—5216no—
800C22—522no—
801C22—522no—
802C22—522no—
803C22—522no—
804C22—522no—
805C22—522no—
806C22—522no—
807C22—522no—
808C22—522no—
809C22—1048no—
810C22#1171931814yes—
811C22#1171932514yes—
812C22#1171932514yes—
813C22#1171934314yes—
814C22#1171935214yes—
815C22#1171935214yes—
816C22#1171940914yes—
817C22C2×#8825111yescharacteristic
818C22C2×#8825111yescharacteristic
819C22C2×#8825111yescharacteristic
820C22C2×#8825411yescharacteristic
821C22C2×#41×D1311yescharacteristic
822C22C2×#8825611yescharacteristic
823C22C2×#8825611yescharacteristic
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—522no—
831C4—522no—
832C4—522no—
833C4—522no—
834C4—522no—
835C4—522no—
836C2—82no—
837C2—524no—
838C2—1042no—
839C2#1312293018yesdirect product factor
840C2C2×#1171931811yescharacteristic
841C2C2×#1171940911yescharacteristic
842C2C2×#1171934311yescharacteristic
843C2C2×#1171932511yescharacteristic
844C2C2×#1171932511yescharacteristic
845C2C2×#1171935211yescharacteristic
846C2C2×#1171935211yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#396C2
socleC24×C13C24
prime radicalC2×#11718621C2
hypercenterC2×#396D13
hypocenterC13C2×#2826
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #13122930C2direct (N × H)
2. C2×#11718320C2semidirect
3. C2×#11718643C2semidirect
4. C2×#11718653C2semidirect
5. C2×#11718613C2semidirect
6. C2×#11718654C2semidirect
7. C2×#11718655C2semidirect
8. C2×#11718652C2semidirect
9. C2×#11718622C2semidirect
10. C2×#11718620C2semidirect
11. C2×#11718620C2semidirect
13. C2×#11718326C2semidirect
14. C2×#11718617C2semidirect
15. C2×#11718650C2semidirect
16. C2×C13×#396C2semidirect
42. C13×#396C22semidirect
53. #11718655C22semidirect
54. #11718654C22semidirect
55. #11718653C22semidirect
56. #11718652C22semidirect
57. #11718650C22semidirect
58. #11718643C22semidirect
59. #11718622C22semidirect
61. #11718620C22semidirect
62. #11718620C22semidirect
63. #11718617C22semidirect
64. #11718613C22semidirect
65. #11718326C22semidirect
66. #11718320C22semidirect
268. C2×#396D13semidirect
410. #396C2×D13semidirect
563. C2×C13#2826semidirect
683. C13C2×#2826semidirect
839. C2#13122930direct (N × H)

Maximal subgroups

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

subgroupindex
#131229302
C2×#117183202
C2×#117186432
C2×#117186532
C2×#117186132
C2×#117186542
C2×#117186552
C2×#117186522
C2×#117186222
C2×#117186202
C2×#117186212
C2×#117183262
C2×#117186172
C2×#117186502
C2×C13×#3962
C2×#282613