Finite Group Databasebeta

← C2×#13120824 #16029378

Subgroups — C2×#13120824 #16029378

Order 3328.

2654 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#13120824C2116yesmaximal, direct product factor
2C2×#11718319C211yesmaximal, characteristic, complemented
3C2×#11718335C211yesmaximal, characteristic, complemented
4C2×#11718614C211yesmaximal, characteristic, complemented
5C2×#11718609C211yesmaximal, characteristic, complemented
6C2×#11718622C211yesmaximal, characteristic, complemented
7C2×#11718620C211yesmaximal, characteristic, complemented
8C2×#11718883C211yesmaximal, characteristic, complemented
9C2×#11718884C211yesmaximal, characteristic
10C2×#11718618C211yesmaximal, characteristic, complemented
11C2×#11718612C211yesmaximal, characteristic, complemented
12C2×#11718330C211yesmaximal, characteristic, complemented
13C2×#11718316C211yesmaximal, characteristic, complemented
14C2×#11718874C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#386C211yesmaximal, characteristic, complemented
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C23×C22⋊D13C2211yescharacteristic
20C23×C22⋊D13C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×#6103C2211yescharacteristic
33C22×#6103C2211yescharacteristic
34C22×#6103C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C13×#386C2218yescomplemented
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45#11718884C2218yes—
46#11718883C2218yescomplemented
47#11718874C2218yescomplemented
48C4×C22⋊Dic13C2218yescomplemented
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718622C2218yescomplemented
58#11718620C2218yescomplemented
59#11718618C2218yescomplemented
60#11718614C2218yescomplemented
61#11718612C2218yescomplemented
62#11718609C2218yescomplemented
63#11718335C2218yescomplemented
64#11718330C2218yescomplemented
65#11718319C2218yescomplemented
66#11718316C2218yescomplemented
67C25×C13C2311yescharacteristic
68C25×C13C2311yescharacteristic
69C24×D13C2311yescharacteristic
70C22×D4×C13—24no—
71C22×D4×C13—42no—
72C22×D4×C13—42no—
73C22×D4×C13C2314yes—
74C23×C4×C13—24no—
75C23×C4×C13—42no—
76C23×C4×C13—42no—
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2314yes—
83C22×C22⋊D13—24no—
84C22×C22⋊D13—24no—
85C22×C22⋊D13—42no—
86C22×C22⋊D13—42no—
87C22×C22⋊D13—42no—
88C22×C22⋊D13—42no—
89C22×C22⋊D13C2314yes—
90C22×C22⋊D13C2314yes—
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C2×C13×C22⋊C4—24no—
99C2×C13×C22⋊C4—42no—
100C2×C13×C22⋊C4—42no—
101C2×C13×C22⋊C4C2314yes—
102C2×C13×C22⋊C4C2314yes—
103C2×C13×C22⋊C4C2314yes—
104C2×C22⋊Dic13—24no—
105C2×C22⋊Dic13—24no—
106C2×C22⋊Dic13—42no—
107C2×C22⋊Dic13—42no—
108C2×C22⋊Dic13—42no—
109C2×C22⋊Dic13—42no—
110C2×C22⋊Dic13C2314yes—
111C2×C22⋊Dic13C2314yes—
112C2×C22⋊Dic13C2314yes—
113C2×C22⋊Dic13C2314yes—
114C2×C22⋊Dic13C2314yes—
115C2×C22⋊Dic13C2314yes—
116C2×#6103—24no—
117C2×#6103—42no—
118C2×#6103—42no—
119C2×#6103—42no—
120C2×#6103—42no—
121C2×#6103C2314yes—
122C2×#6103C2314yes—
123C2×#6103C2314yes—
124C2×#6103C2314yes—
125C2×#6103C2314yes—
126C2×C4⋊Dic13—42no—
127C2×C4⋊Dic13—42no—
128C2×C4⋊Dic13C2314yes—
129C2×C4⋊Dic13C2314yes—
130C2×#6101—24no—
131C2×#6101—42no—
132C2×#6101—42no—
133C2×#6101C2314yes—
134C2×#6101C2314yes—
135C2×#6101C2314yes—
136C2×C4×Dic13—42no—
137C2×C4×Dic13—42no—
138C2×C4×Dic13C2314yes—
139C2×C4×Dic13C2314yes—
140C13×#95C2314yes—
141C13×#95C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2648—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—28no—
195C22×C4×C13—44no—
196C22×C4×C13—44no—
197C22×C4×C13—416no—
198C22×C4×C13#4114yes—
199C22×C4×C13C2412yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C2×C22⋊D13—28no—
205C2×C22⋊D13—28no—
206C2×C22⋊D13—44no—
207C2×C22⋊D13—44no—
208C2×C22⋊D13—44no—
209C2×C22⋊D13—44no—
210C2×C22⋊D13—416no—
211C2×C22⋊D13—416no—
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—22no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13#4114yes—
233C22×Dic13C2412yes—
234C22×Dic13C2412yes—
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C13×C22⋊C4—28no—
241C13×C22⋊C4—44no—
242C13×C22⋊C4—44no—
243C22⋊Dic13—28no—
244C22⋊Dic13—28no—
245C22⋊Dic13—44no—
246C22⋊Dic13—44no—
247C22⋊Dic13—44no—
248C22⋊Dic13—44no—
249#6103—28no—
250#6103—44no—
251#6103—44no—
252#6103—44no—
253#6103—44no—
254C4⋊Dic13—44no—
255C4⋊Dic13—44no—
256#6101—28no—
257#6101—44no—
258#6101—44no—
259C4×Dic13—44no—
260C4×Dic13—44no—
261#2648—1316no—
262C2×#400—131no—
263C2×#397—131no—
264C2×#397—131no—
265C2×#396—131no—
266C2×#394—131no—
267C2×#394—131no—
268C2×#394—131no—
269C2×#392—131no—
270C2×#390—131no—
271C2×#388—131no—
272C2×#388—131no—
273C2×#387—131no—
274C2×#386—131no—
275C2×#386D1311yescharacteristic, complemented
276C2×C4×C22⋊C4—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×C13C2×#4112yes—
307C23×C13C2×#4112yes—
308C23×C13H(5,𝔽2)12yes—
309C23×C13H(5,𝔽2)12yes—
310C23×C13H(5,𝔽2)12yes—
311C23×C13H(5,𝔽2)12yes—
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—28no—
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—416no—
344C2×C4×C13—44no—
345C2×C4×C13—44no—
346C2×C4×C13—44no—
347C2×C4×C13—44no—
348C2×C4×C13C2×#4114yes—
349C22⋊D13—416no—
350C22⋊D13—416no—
351C2×Dic13—28no—
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—22no—
372C2×Dic13—44no—
373C2×Dic13—44no—
374C2×Dic13—44no—
375C2×Dic13—44no—
376C2×Dic13—44no—
377C2×Dic13—44no—
378C2×Dic13C2×#4114yes—
379C23×D4—131no—
380C23×D4—131no—
381C23×D4C2×D1311yescharacteristic
382C24×C4C2×D1311yescharacteristic
383C22×C4⋊C4—131no—
384C22×C4⋊C4—131no—
385C22×C4⋊C4—131no—
386C22×C4⋊C4—131no—
387C22×C4⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
400C22×C22⋊C4C2×D1311yescharacteristic
401C22×C22⋊C4C2×D1311yescharacteristic
402C22×C42—131no—
403C22×C42—131no—
404#400—138no—
405#397—138no—
406#397—138no—
407#396—138no—
408#394—138no—
409#394—138no—
410#394—138no—
411#392—138no—
412#390—138no—
413#388—138no—
414#388—138no—
415#387—138no—
416#386—138no—
417#386C2×D1318yescomplemented
418C4×C22⋊C4—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×#95C2×D1311yescharacteristic
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#52914yes—
446C22×C13#53814yes—
447C22×C13#53814yes—
448C22×C13#53814yes—
449C22×C13#53814yes—
450C22×C13#54014yes—
451C22×C13#54014yes—
452C22×C13C22×#4111yescharacteristic
453C22×C13C22×#4111yescharacteristic
454C22×C13C22×#4111yescharacteristic
455C22×C13C2×H(5,𝔽2)11yescharacteristic
456C22×C13C2×H(5,𝔽2)11yescharacteristic
457C22×C13C2×H(5,𝔽2)11yescharacteristic
458C22×C13C2×H(5,𝔽2)11yescharacteristic
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—24no—
468C4×C13—42no—
469C4×C13—42no—
470C4×C13—42no—
471C4×C13—42no—
472Dic13—24no—
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—264no—
489C22×D4—522no—
490C22×D4—522no—
491C22×D4—522no—
492C22×D4—522no—
493C22×D4C22×D1314yes—
494C23×C4—24no—
495C23×C4—42no—
496C23×C4—42no—
497C23×C4—131no—
498C23×C4—131no—
499C23×C4—131no—
500C23×C4—131no—
501C23×C4—131no—
502C23×C4—131no—
503C23×C4—131no—
504C23×C4C22×D1311yescharacteristic
505C23×C4C22×D1311yescharacteristic
506C23×C4C22×D1311yescharacteristic
507C23×C4C22×D1311yescharacteristic
508C23×C4C22×D1311yescharacteristic
509C23×C4C22×D1314yes—
510C2×C4⋊C4—134no—
511C2×C4⋊C4—134no—
512C2×C4⋊C4—134no—
513C2×C4⋊C4—134no—
514C2×C4⋊C4—134no—
515C2×C4⋊C4—264no—
516C2×C4⋊C4—522no—
517C2×C4⋊C4—522no—
518C2×C4⋊C4—522no—
519C2×C4⋊C4—522no—
520C2×C22⋊C4—24no—
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—264no—
535C2×C22⋊C4—264no—
536C2×C22⋊C4—264no—
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⋊C4C22×D1314yes—
546C2×C22⋊C4C22×D1314yes—
547C2×C22⋊C4C22×D1314yes—
548C2×C42—134no—
549C2×C42—134no—
550C2×C42—522no—
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#95—134no—
560#95C22×D1314yes—
561#95C22×D1314yes—
562C2×C13—44no—
563C2×C13—82no—
564C2×C13#264818yescomplemented
565C2×C13C2×#52911yescharacteristic
566C2×C13C2×#53811yescharacteristic
567C2×C13C2×#53811yescharacteristic
568C2×C13C2×#53811yescharacteristic
569C2×C13C2×#53811yescharacteristic
570C2×C13C2×#54011yescharacteristic
571C2×C13C2×#54011yescharacteristic
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#612714yes—
595C24C23×D1312yes—
596C24C23×D1312yes—
597C24C23×D1311yescharacteristic
598C2×D4—28no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—416no—
602C2×D4—268no—
603C2×D4—268no—
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—28no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—416no—
628C22×C4—134no—
629C22×C4—132no—
630C22×C4—132no—
631C22×C4—132no—
632C22×C4—132no—
633C22×C4—132no—
634C22×C4—132no—
635C22×C4—132no—
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—262no—
654C22×C4—262no—
655C22×C4—262no—
656C22×C4#612914yes—
657C22×C4C23×D1312yes—
658C22×C4C23×D1312yes—
659C22×C4C23×D1312yes—
660C22×C4C23×D1312yes—
661C22×C4C23×D1312yes—
662C4⋊C4—268no—
663C4⋊C4—524no—
664C4⋊C4—524no—
665C4⋊C4—524no—
666C4⋊C4—524no—
667C22⋊C4—28no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—268no—
671C22⋊C4—268no—
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—
681C42—524no—
682C42—524no—
683C13C2×#264811yescharacteristic, 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×#612714yes—
726C23C2×#612712yes—
727C23C2×#612912yes—
728C23#8825112yes—
729C23#8825112yes—
730C23#8825112yes—
731C23#41×D1312yes—
732C23#8825612yes—
733C23C24×D1311yescharacteristic
734D4—416no—
735D4—5216no—
736D4—5216no—
737C2×C4—28no—
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—416no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—134no—
758C2×C4—268no—
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—262no—
779C2×C4—524no—
780C2×C4—524no—
781C2×C4—524no—
782C2×C4—524no—
783C2×C4—524no—
784C2×C4—524no—
785C2×C4C2×#612914yes—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—42no—
790C22—42no—
791C22—416no—
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#1171919914yes—
811C22#1171924314yes—
812C22#1171926514yes—
813C22#1171929814yes—
814C22#1171931814yes—
815C22#1171932414yes—
816C22#1171936814yes—
817C22C22×#612711yescharacteristic
818C22C22×#612911yescharacteristic
819C22C2×#8825111yescharacteristic
820C22C2×#8825111yescharacteristic
821C22C2×#8825111yescharacteristic
822C22C2×#41×D1311yescharacteristic
823C22C2×#8825611yescharacteristic
824C4—24no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—264no—
830C4—522no—
831C4—522no—
832C4—522no—
833C4—522no—
834C4—522no—
835C4—522no—
836C2—44no—
837C2—82no—
838C2—1042no—
839C2#1312082418yesdirect product factor
840C2C2×#1171924311yescharacteristic
841C2C2×#1171931811yescharacteristic
842C2C2×#1171926511yescharacteristic
843C2C2×#1171929811yescharacteristic
844C2C2×#1171919911yescharacteristic
845C2C2×#1171936811yescharacteristic
846C2C2×#1171932411yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#386C2
socleC24×C13C24
prime radicalC2×#11718884C2
hypercenterC2×#386D13
hypocenterC13C2×#2648
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. #13120824C2direct (N × H)
2. C2×#11718319C2semidirect
3. C2×#11718335C2semidirect
4. C2×#11718614C2semidirect
5. C2×#11718609C2semidirect
6. C2×#11718622C2semidirect
7. C2×#11718620C2semidirect
8. C2×#11718883C2semidirect
10. C2×#11718618C2semidirect
11. C2×#11718612C2semidirect
12. C2×#11718330C2semidirect
13. C2×#11718316C2semidirect
14. C2×#11718874C2semidirect
15. C2×C4×C22⋊Dic13C2semidirect
16. C2×C13×#386C2semidirect
42. C13×#386C22semidirect
46. #11718883C22semidirect
47. #11718874C22semidirect
48. C4×C22⋊Dic13C22semidirect
57. #11718622C22semidirect
58. #11718620C22semidirect
59. #11718618C22semidirect
60. #11718614C22semidirect
61. #11718612C22semidirect
62. #11718609C22semidirect
63. #11718335C22semidirect
64. #11718330C22semidirect
65. #11718319C22semidirect
66. #11718316C22semidirect
275. C2×#386D13semidirect
417. #386C2×D13semidirect
564. C2×C13#2648semidirect
683. C13C2×#2648semidirect
839. C2#13120824direct (N × H)

Maximal subgroups

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

subgroupindex
#131208242
C2×#117183192
C2×#117183352
C2×#117186142
C2×#117186092
C2×#117186222
C2×#117186202
C2×#117188832
C2×#117188842
C2×#117186182
C2×#117186122
C2×#117183302
C2×#117183162
C2×#117188742
C2×C4×C22⋊Dic132
C2×C13×#3862
C2×#264813