Finite Group Databasebeta

← C2×#13120825 #16029379

Subgroups — C2×#13120825 #16029379

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#13120825C2116yesmaximal, direct product factor
2C2×#11718321C211yesmaximal, characteristic, complemented
3C2×#11718613C211yesmaximal, characteristic, complemented
4C2×#11718613C211yesmaximal, characteristic, complemented
5C2×#11718609C211yesmaximal, characteristic, complemented
6C2×#11718883C211yesmaximal, characteristic, complemented
7C2×#11718883C211yesmaximal, characteristic, complemented
8C2×#11718883C211yesmaximal, characteristic, complemented
9C2×#11718882C211yesmaximal, characteristic, complemented
10C2×#11718606C211yesmaximal, characteristic, complemented
11C2×#11718605C211yesmaximal, characteristic, complemented
12C2×#11718313C211yesmaximal, characteristic, complemented
13C2×#11718881C211yesmaximal, characteristic, complemented
14C2×#11718881C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#392C211yesmaximal, characteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C23×D4×C13C2211yescharacteristic
20C24×Dic13C2211yescharacteristic
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×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C22⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C13×#392C2218yes—
43C2×C13×#95C2211yescharacteristic
44#11718883C2218yescomplemented
45#11718883C2218yescomplemented
46#11718883C2218yescomplemented
47#11718882C2218yescomplemented
48#11718881C2218yescomplemented
49#11718881C2218yescomplemented
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58C2×#88071C2211yescharacteristic
59#11718613C2218yescomplemented
60#11718613C2218yescomplemented
61#11718609C2218yescomplemented
62#11718606C2218yescomplemented
63#11718605C2218yescomplemented
64C22⋊C4×Dic13C2218yescomplemented
65#11718321C2218yescomplemented
66#11718313C2218yescomplemented
67C25×C13C2311yescharacteristic
68C25×C13C2311yescharacteristic
69C25×C13C2311yescharacteristic
70C22×D4×C13—24no—
71C22×D4×C13—24no—
72C22×D4×C13—24no—
73C22×D4×C13—42no—
74C22×D4×C13—42no—
75C22×D4×C13—42no—
76C22×D4×C13—42no—
77C22×D4×C13—42no—
78C22×D4×C13—42no—
79C22×D4×C13C2314yes—
80C22×D4×C13C2314yes—
81C22×D4×C13C2314yes—
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×Dic13—24no—
87C23×Dic13—42no—
88C23×Dic13—42no—
89C23×Dic13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C23×Dic13C2311yescharacteristic
94C23×Dic13C2311yescharacteristic
95C23×Dic13C2311yescharacteristic
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2314yes—
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—24no—
107C2×C22⋊Dic13—42no—
108C2×C22⋊Dic13—42no—
109C2×C22⋊Dic13—42no—
110C2×C22⋊Dic13—42no—
111C2×C22⋊Dic13—42no—
112C2×C22⋊Dic13—42no—
113C2×C22⋊Dic13—42no—
114C2×C22⋊Dic13—42no—
115C2×C22⋊Dic13C2314yes—
116C2×C22⋊Dic13C2314yes—
117C2×C22⋊Dic13C2314yes—
118C2×C22⋊Dic13C2314yes—
119C2×C22⋊Dic13C2314yes—
120C2×C22⋊Dic13C2314yes—
121C2×C22⋊Dic13C2314yes—
122C2×C22⋊Dic13C2314yes—
123C2×C22⋊Dic13C2314yes—
124C2×C22⋊Dic13C2314yes—
125C2×C22⋊Dic13C2314yes—
126C2×C4⋊Dic13—42no—
127C2×C4⋊Dic13C2314yes—
128C2×#6101—24no—
129C2×#6101—42no—
130C2×#6101—42no—
131C2×#6101—42no—
132C2×#6101C2314yes—
133C2×#6101C2314yes—
134C2×#6101C2314yes—
135C2×#6101C2314yes—
136C2×C4×Dic13—42no—
137C2×C4×Dic13—42no—
138C2×C4×Dic13C2314yes—
139C2×C4×Dic13C2314yes—
140C13×#95C2314yes—
141#88071C2314yes—
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—22no—
165C24×C13—22no—
166C24×C13—22no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—22no—
171C24×C13#4114yes—
172C24×C13C2412yes—
173C24×C13C2412yes—
174C24×C13C2412yes—
175C24×C13C2411yescharacteristic
176C2×D4×C13—28no—
177C2×D4×C13—28no—
178C2×D4×C13—28no—
179C2×D4×C13—44no—
180C2×D4×C13—44no—
181C2×D4×C13—44no—
182C2×D4×C13—44no—
183C2×D4×C13—44no—
184C2×D4×C13—44no—
185C2×D4×C13—416no—
186C2×D4×C13—416no—
187C2×D4×C13—416no—
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×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13#4114yes—
200C22×C4×C13C2412yes—
201C22×C4×C13C2412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2412yes—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
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—28no—
228C22×Dic13—44no—
229C22×Dic13—44no—
230C22×Dic13—416no—
231C22×Dic13#4114yes—
232C22×Dic13C2412yes—
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—28no—
246C22⋊Dic13—44no—
247C22⋊Dic13—44no—
248C22⋊Dic13—44no—
249C22⋊Dic13—44no—
250C22⋊Dic13—44no—
251C22⋊Dic13—44no—
252C22⋊Dic13—44no—
253C22⋊Dic13—44no—
254C4⋊Dic13—44no—
255#6101—28no—
256#6101—44no—
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×#392D1311yescharacteristic
270C2×#390—131no—
271C2×#388—131no—
272C2×#388—131no—
273C2×#387—131no—
274C2×#386—131no—
275C2×#386—131no—
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—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—44no—
301C23×C13—44no—
302C23×C13—44no—
303C23×C13—44no—
304C23×C13—44no—
305C23×C13—44no—
306C23×C13—44no—
307C23×C13—44no—
308C23×C13—44no—
309C23×C13—44no—
310C23×C13—44no—
311C23×C13—44no—
312C23×C13—44no—
313C23×C13—44no—
314C23×C13—44no—
315C23×C13—44no—
316C23×C13—44no—
317C23×C13—44no—
318C23×C13C2×#4114yes—
319C23×C13C2×#4112yes—
320C23×C13C2×#4112yes—
321C23×C13C2×#4112yes—
322C23×C13H(5,𝔽2)12yes—
323C23×C13H(5,𝔽2)12yes—
324C23×C13H(5,𝔽2)12yes—
325C23×C13H(5,𝔽2)12yes—
326C23×C13C2511yescharacteristic
327D4×C13—416no—
328D4×C13—416no—
329D4×C13—416no—
330C2×C4×C13—28no—
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—44no—
343C2×C4×C13—44no—
344C2×C4×C13—44no—
345C2×C4×C13C2×#4114yes—
346C2×Dic13—28no—
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—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—416no—
371C2×Dic13—44no—
372C2×Dic13—44no—
373C2×Dic13—44no—
374C2×Dic13—44no—
375C2×Dic13—44no—
376C2×Dic13—44no—
377C2×Dic13—44no—
378C2×Dic13C2×#4114yes—
379C23×D4C2×D1311yescharacteristic
380C23×D4C2×D1311yescharacteristic
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×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#392C2×D1318yes—
412#390—138no—
413#388—138no—
414#388—138no—
415#387—138no—
416#386—138no—
417#386—138no—
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×#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—42no—
445C22×C13—42no—
446C22×C13—42no—
447C22×C13—42no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—88no—
452C22×C13—88no—
453C22×C13#52914yes—
454C22×C13#53814yes—
455C22×C13#53814yes—
456C22×C13#53814yes—
457C22×C13#53814yes—
458C22×C13#54014yes—
459C22×C13#54014yes—
460C22×C13C22×#4111yescharacteristic
461C22×C13C22×#4111yescharacteristic
462C22×C13C22×#4111yescharacteristic
463C22×C13C2×H(5,𝔽2)11yescharacteristic
464C22×C13C2×H(5,𝔽2)11yescharacteristic
465C22×C13C2×H(5,𝔽2)11yescharacteristic
466C22×C13C2×H(5,𝔽2)11yescharacteristic
467C4×C13—24no—
468C4×C13—42no—
469C4×C13—42no—
470C4×C13—42no—
471Dic13—24no—
472Dic13—42no—
473Dic13—42no—
474Dic13—42no—
475Dic13—42no—
476Dic13—42no—
477Dic13—42no—
478Dic13—42no—
479C25C22×D1311yescharacteristic
480C25C22×D1311yescharacteristic
481C25C22×D1311yescharacteristic
482C22×D4—24no—
483C22×D4—24no—
484C22×D4—24no—
485C22×D4—42no—
486C22×D4—42no—
487C22×D4—42no—
488C22×D4—42no—
489C22×D4—42no—
490C22×D4—42no—
491C22×D4C22×D1314yes—
492C22×D4C22×D1314yes—
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—131no—
502C23×C4—134no—
503C23×C4—264no—
504C23×C4—522no—
505C23×C4—522no—
506C23×C4C22×D1311yescharacteristic
507C23×C4C22×D1311yescharacteristic
508C23×C4C22×D1311yescharacteristic
509C23×C4C22×D1311yescharacteristic
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#95—134no—
561#95C22×D1314yes—
562C2×C13—44no—
563C2×C13—82no—
564C2×C13—82no—
565C2×C13#264818yescomplemented
566C2×C13C2×#52911yescharacteristic
567C2×C13C2×#53811yescharacteristic
568C2×C13C2×#53811yescharacteristic
569C2×C13C2×#53811yescharacteristic
570C2×C13C2×#53811yescharacteristic
571C2×C13C2×#54011yescharacteristic
572C2×C13C2×#54011yescharacteristic
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—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24#612914yes—
594C24C23×D1312yes—
595C24C23×D1312yes—
596C24C23×D1312yes—
597C24C23×D1311yescharacteristic
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—28no—
601C2×D4—44no—
602C2×D4—44no—
603C2×D4—44no—
604C2×D4—44no—
605C2×D4—44no—
606C2×D4—44no—
607C2×D4—416no—
608C2×D4—416no—
609C2×D4—416no—
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—134no—
622C22×C4—132no—
623C22×C4—132no—
624C22×C4—132no—
625C22×C4—132no—
626C22×C4—132no—
627C22×C4—132no—
628C22×C4—132no—
629C22×C4—132no—
630C22×C4—268no—
631C22×C4—262no—
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—262no—
654C22×C4—524no—
655C22×C4—524no—
656C22×C4—5216no—
657C22×C4#612914yes—
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—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23C2×#612914yes—
726C23C2×#612912yes—
727C23C2×#612912yes—
728C23#8825112yes—
729C23#8825112yes—
730C23#8825112yes—
731C23#8825112yes—
732C23#41×D1312yes—
733C23C24×D1311yescharacteristic
734D4—416no—
735D4—416no—
736D4—416no—
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—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—134no—
753C2×C4—268no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
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—5216no—
778C2×C4—524no—
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—416no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—88no—
809C22—88no—
810C22#1171929814yes—
811C22#1171929814yes—
812C22#1171929814yes—
813C22#1171930514yes—
814C22#1171931814yes—
815C22#1171932014yes—
816C22#1171942414yes—
817C22C22×#612911yescharacteristic
818C22C22×#612911yescharacteristic
819C22C2×#8825111yescharacteristic
820C22C2×#8825111yescharacteristic
821C22C2×#8825111yescharacteristic
822C22C2×#8825111yescharacteristic
823C22C2×#41×D1311yescharacteristic
824C4—24no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—264no—
829C4—522no—
830C4—522no—
831C4—522no—
832C4—522no—
833C4—522no—
834C4—522no—
835C4—522no—
836C2—44no—
837C2—82no—
838C2—82no—
839C2#1312082518yesdirect product factor
840C2C2×#1171930511yescharacteristic
841C2C2×#1171931811yescharacteristic
842C2C2×#1171929811yescharacteristic
843C2C2×#1171929811yescharacteristic
844C2C2×#1171929811yescharacteristic
845C2C2×#1171932011yescharacteristic
846C2C2×#1171942411yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
Fitting, prime radicalC2×C13×#392C2
socleC24×C13C24
hypercenterC2×#392D13
hypocenterC13C2×#2648
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. #13120825C2direct (N × H)
2. C2×#11718321C2semidirect
3. C2×#11718613C2semidirect
4. C2×#11718613C2semidirect
5. C2×#11718609C2semidirect
6. C2×#11718883C2semidirect
7. C2×#11718883C2semidirect
8. C2×#11718883C2semidirect
9. C2×#11718882C2semidirect
10. C2×#11718606C2semidirect
11. C2×#11718605C2semidirect
12. C2×#11718313C2semidirect
13. C2×#11718881C2semidirect
14. C2×#11718881C2semidirect
15. C2×C22⋊C4×Dic13C2semidirect
44. #11718883C22semidirect
45. #11718883C22semidirect
46. #11718883C22semidirect
47. #11718882C22semidirect
48. #11718881C22semidirect
49. #11718881C22semidirect
59. #11718613C22semidirect
60. #11718613C22semidirect
61. #11718609C22semidirect
62. #11718606C22semidirect
63. #11718605C22semidirect
64. C22⋊C4×Dic13C22semidirect
65. #11718321C22semidirect
66. #11718313C22semidirect
565. C2×C13#2648semidirect
683. C13C2×#2648semidirect
839. C2#13120825direct (N × H)

Maximal subgroups

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

subgroupindex
#131208252
C2×#117183212
C2×#117186132
C2×#117186092
C2×#117188832
C2×#117188822
C2×#117186062
C2×#117186052
C2×#117183132
C2×#117188812
C2×C22⋊C4×Dic132
C2×C13×#3922
C2×#264813