Finite Group Databasebeta

← C2×#13118505 #16031558

Subgroups — C2×#13118505 #16031558

Order 3328.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88200C211yesmaximal, characteristic
2C22×#88146C211yesmaximal, characteristic
3#13118505C2116yesmaximal, direct product factor
4C2×#11718321C211yesmaximal, characteristic, complemented
5C2×#11718645C211yesmaximal, characteristic, complemented
6C2×#11718322C211yesmaximal, characteristic, complemented
7C2×#11718891C211yesmaximal, characteristic, complemented
8C2×#11718633C211yesmaximal, characteristic, complemented
9C2×#11718642C211yesmaximal, characteristic, complemented
10C2×#11718314C211yesmaximal, characteristic, complemented
11C2×#11718329C211yesmaximal, characteristic
12C2×#11718650C211yesmaximal, characteristic
13C2×#11718325C211yesmaximal, characteristic
14C2×#11718648C211yesmaximal, characteristic
15C2×D13×#95C211yesmaximal, characteristic
16C2×C13×#395C211yesmaximal, characteristic, complemented
17C23×Q8×C13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C2×#88200—28no—
25C2×#88200C2218yes—
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C2×#88146—28no—
41C2×#88146C2218yes—
42C13×#395C2218yescomplemented
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46#11718891C2218yescomplemented
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718650C2218yes—
59#11718648C2218yes—
60#11718645C2218yescomplemented
61#11718642C2218yescomplemented
62#11718633C2218yescomplemented
63#11718329C2218yes—
64#11718325C2218yes—
65D13×#95C2218yes—
66#11718322C2218yescomplemented
67#11718321C2218yescomplemented
68#11718314C2218yescomplemented
69C24×D13C2311yescharacteristic
70C22×Q8×C13—24no—
71C22×Q8×C13—24no—
72C22×Q8×C13—42no—
73C22×Q8×C13C2314yes—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C22×C4×D13—24no—
89C22×C4×D13—24no—
90C22×C4×D13—24no—
91C22×C4×D13—24no—
92C22×C4×D13—24no—
93C22×C4×D13—24no—
94C22×C4×D13—42no—
95C22×C4×D13—42no—
96C22×C4×D13Q818yescomplemented
97C22×C4×D13C2314yes—
98C22×C4×D13C2314yes—
99C22×C4×D13C2314yes—
100C2×C13×C4⋊C4—24no—
101C2×C13×C4⋊C4—24no—
102C2×C13×C4⋊C4—42no—
103C2×C13×C4⋊C4C2314yes—
104C2×C13×C4⋊C4C2314yes—
105C2×C13×C4⋊C4C2314yes—
106#88200—232no—
107C2×#6103—24no—
108C2×#6103—24no—
109C2×#6103—24no—
110C2×#6103D418yes—
111C2×#6103C2314yes—
112C2×#6103C2314yes—
113C2×#6103C2314yes—
114C2×#6103C2314yes—
115C2×C4⋊Dic13—24no—
116C2×C4⋊Dic13—24no—
117C2×C4⋊Dic13—24no—
118C2×C4⋊Dic13—42no—
119C2×C4⋊Dic13C2314yes—
120C2×C4⋊Dic13C2314yes—
121C2×C4⋊Dic13C2314yes—
122C2×C4⋊Dic13C2314yes—
123C2×#6101—24no—
124C2×#6101—24no—
125C2×#6101—24no—
126C2×#6101—42no—
127C2×#6101C2314yes—
128C2×#6101C2314yes—
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×C4×Dic13—24no—
132C2×C4×Dic13—24no—
133C2×C4×Dic13C2314yes—
134C2×C4×Dic13C2314yes—
135#88146—232no—
136C13×#95C2314yes—
137C13×#95C2314yes—
138C13×#95C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2438—131nomaximal, Sylow
151C24×C13C2411yescharacteristic
152C23×D13—22no—
153C23×D13—22no—
154C23×D13—22no—
155C23×D13—22no—
156C23×D13C2×D414yes—
157C23×D13C2×Q814yes—
158C23×D13#4114yes—
159C23×D13C2412yes—
160C2×Q8×C13—28no—
161C2×Q8×C13—28no—
162C2×Q8×C13—44no—
163C2×Q8×C13—416no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13C2×D414yes—
182C22×C4×C13C2×Q814yes—
183C22×C4×C13#4114yes—
184C22×C4×C13#4114yes—
185C22×C4×C13C2412yes—
186C22×C4×C13C2412yes—
187C22×C4×C13C2412yes—
188C22×C4×C13C2412yes—
189C22×C4×C13C2412yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2412yes—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13C2×D414yes—
212C22×Dic13C2×Q814yes—
213C22×Dic13C2412yes—
214C22×Dic13C2412yes—
215C22×Dic13C2412yes—
216C22×Dic13C2412yes—
217C22×Dic13C2412yes—
218C22×Dic13C2412yes—
219C22×Dic13C2412yes—
220C2×C4×D13—232no—
221C2×C4×D13—28no—
222C2×C4×D13—28no—
223C2×C4×D13—28no—
224C2×C4×D13—28no—
225C2×C4×D13—28no—
226C2×C4×D13—28no—
227C2×C4×D13—44no—
228C2×C4×D13—44no—
229C2×C4×D13—416no—
230C2×C4×D13—416no—
231C2×C4×D13C2×Q8116yescomplemented
232C13×C4⋊C4—28no—
233C13×C4⋊C4—28no—
234C13×C4⋊C4—44no—
235#6103—28no—
236#6103—28no—
237#6103—28no—
238#6103C2×D4116yes—
239C4⋊Dic13—28no—
240C4⋊Dic13—28no—
241C4⋊Dic13—28no—
242C4⋊Dic13—44no—
243#6101—28no—
244#6101—28no—
245#6101—28no—
246#6101—44no—
247C4×Dic13—28no—
248C4×Dic13—28no—
249C22×C22⋊Q8—131no—
250C22×#117—131no—
251#2438—1316no—
252C2×#400—131no—
253C2×#398—131no—
254C2×#398—131no—
255C2×#395D1311yescharacteristic, complemented
256C2×#391—131no—
257C2×#389—131no—
258C2×#387—131no—
259C2×#387—131no—
260C2×#385—131no—
261C2×#385—131no—
262C2×#381—131no—
263C2×#380—131no—
264C22×#95—131no—
265C23×C13C22×D412yes—
266C23×C13C22×Q812yes—
267C23×C13C2×#4112yes—
268C23×C13C2×#4112yes—
269C23×C13C2×#4112yes—
270C23×C13H(5,𝔽2)12yes—
271C23×C132−1+412yes—
272C23×C13C2511yescharacteristic
273C22×D13—28no—
274C22×D13—28no—
275C22×D13—28no—
276C22×D13—28no—
277C22×D13—28no—
278C22×D13—28no—
279C22×D13—22no—
280C22×D13—22no—
281C22×D13—22no—
282C22×D13—22no—
283C22×D13C22⋊Q8116yes—
284C22×D13C22×D414yes—
285C22×D13C22×Q814yes—
286C22×D13C2×#4114yes—
287Q8×C13—416no—
288C2×C4×C13—28no—
289C2×C4×C13—28no—
290C2×C4×C13—28no—
291C2×C4×C13—28no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—44no—
310C2×C4×C13—44no—
311C2×C4×C13—44no—
312C2×C4×C13C22×D414yes—
313C2×C4×C13C22×Q814yes—
314C2×C4×C13C2×#4114yes—
315C2×C4×C13C2×#4114yes—
316C2×Dic13—28no—
317C2×Dic13—28no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—44no—
338C2×Dic13—44no—
339C2×Dic13—44no—
340C2×Dic13—44no—
341C2×Dic13—44no—
342C2×Dic13C22×D414yes—
343C2×Dic13C22×Q814yes—
344C4×D13—232no—
345C4×D13—416no—
346C4×D13—416no—
347C23×Q8C2×D1311yescharacteristic
348C24×C4—131no—
349C24×C4—131no—
350C24×C4—131no—
351C2×C22⋊Q8—138no—
352C2×C22⋊Q8—268no—
353C2×#117—138no—
354C2×#117—268no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4—131no—
357C22×C4⋊C4—131no—
358C22×C4⋊C4—131no—
359C22×C4⋊C4—131no—
360C22×C4⋊C4—131no—
361C22×C4⋊C4—131no—
362C22×C4⋊C4—131no—
363C22×C4⋊C4C2×D1311yescharacteristic
364C22×C4⋊C4C2×D1311yescharacteristic
365C22×C4⋊C4C2×D1311yescharacteristic
366C22×C22⋊C4—131no—
367C22×C22⋊C4—131no—
368C22×C22⋊C4—131no—
369C22×C22⋊C4—131no—
370C22×C42—131no—
371C22×C42—131no—
372#400—138no—
373#398—138no—
374#398—138no—
375#395C2×D1318yescomplemented
376#391—138no—
377#389—138no—
378#387—138no—
379#387—138no—
380#385—138no—
381#385—138no—
382#381—138no—
383#380—138no—
384C2×#95—131no—
385C2×#95—131no—
386C2×#95—131no—
387C2×#95—131no—
388C2×#95—131no—
389C2×#95—131no—
390C2×#95—131no—
391C2×#95—131no—
392C2×#95—131no—
393C2×#95—131no—
394C2×#95—131no—
395C2×#95—138no—
396C2×#95C2×D1311yescharacteristic
397C2×#95C2×D1311yescharacteristic
398C2×#95C2×D1311yescharacteristic
399C22×C13C2×C22⋊Q814yes—
400C22×C13#53314yes—
401C22×C13#54414yes—
402C22×C13#54614yes—
403C22×C13#54714yes—
404C22×C13#55114yes—
405C22×C13#55214yes—
406C22×C13C23×D411yescharacteristic
407C22×C13C23×Q811yescharacteristic
408C22×C13C22×#4111yescharacteristic
409C22×C13C22×#4111yescharacteristic
410C22×C13C22×#4111yescharacteristic
411C22×C13C2×H(5,𝔽2)11yescharacteristic
412C22×C13C2×2−1+411yescharacteristic
413C2×D13—24no—
414C2×D13—24no—
415C2×D13—232no—
416C2×D13—24no—
417C2×D13—24no—
418C2×D13—24no—
419C2×D13—24no—
420C2×D13C2×C22⋊Q818yes—
421C4×C13—24no—
422C4×C13—24no—
423C4×C13—24no—
424C4×C13—24no—
425C4×C13—42no—
426C4×C13—42no—
427C4×C13—42no—
428Dic13—24no—
429Dic13—24no—
430Dic13—42no—
431Dic13—42no—
432Dic13—42no—
433Dic13—42no—
434Dic13—42no—
435C25—131no—
436C22×Q8—24no—
437C22×Q8—24no—
438C22×Q8—42no—
439C22×Q8C22×D1314yes—
440C23×C4—131no—
441C23×C4—131no—
442C23×C4—138no—
443C23×C4—134no—
444C23×C4—131no—
445C23×C4—131no—
446C23×C4—131no—
447C23×C4—131no—
448C23×C4—131no—
449C23×C4—134no—
450C23×C4—134no—
451C23×C4—264no—
452C23×C4—264no—
453C23×C4—264no—
454C23×C4—264no—
455C23×C4—264no—
456C23×C4—264no—
457C23×C4—522no—
458C23×C4—522no—
459C23×C4C22×D1311yescharacteristic
460C23×C4C22×D1311yescharacteristic
461C23×C4C22×D1311yescharacteristic
462C23×C4C22×D1311yescharacteristic
463C23×C4C22×D1311yescharacteristic
464C23×C4C22×D1311yescharacteristic
465C23×C4C22×D1311yescharacteristic
466C22⋊Q8—2632no—
467#117—2632no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—134no—
472C2×C4⋊C4—134no—
473C2×C4⋊C4—134no—
474C2×C4⋊C4—134no—
475C2×C4⋊C4—134no—
476C2×C4⋊C4—134no—
477C2×C4⋊C4—134no—
478C2×C4⋊C4—134no—
479C2×C4⋊C4—264no—
480C2×C4⋊C4—264no—
481C2×C4⋊C4—264no—
482C2×C4⋊C4—264no—
483C2×C4⋊C4—264no—
484C2×C4⋊C4—264no—
485C2×C4⋊C4—522no—
486C2×C4⋊C4—522no—
487C2×C4⋊C4C22×D1314yes—
488C2×C4⋊C4C22×D1314yes—
489C2×C4⋊C4C22×D1314yes—
490C2×C22⋊C4—138no—
491C2×C22⋊C4—134no—
492C2×C22⋊C4—134no—
493C2×C22⋊C4—134no—
494C2×C22⋊C4—134no—
495C2×C22⋊C4—264no—
496C2×C22⋊C4—264no—
497C2×C22⋊C4—264no—
498C2×C42—134no—
499C2×C42—134no—
500C2×C42—264no—
501C2×C42—264no—
502#95—134no—
503#95—134no—
504#95—134no—
505#95—134no—
506#95—134no—
507#95—134no—
508#95—134no—
509#95—134no—
510#95—134no—
511#95—134no—
512#95—134no—
513#95C22×D1314yes—
514#95C22×D1314yes—
515#95C22×D1314yes—
516C2×C13#243818yescomplemented
517C2×C13C22×C22⋊Q811yescharacteristic
518C2×C13C2×#53311yescharacteristic
519C2×C13C2×#54411yescharacteristic
520C2×C13C2×#54611yescharacteristic
521C2×C13C2×#54711yescharacteristic
522C2×C13C2×#55111yescharacteristic
523C2×C13C2×#55211yescharacteristic
524D13—28no—
525C24—134no—
526C24—134no—
527C24—134no—
528C24—132no—
529C24—262no—
530C24—262no—
531C24—262no—
532C24—262no—
533C24C23×D1311yescharacteristic
534C2×Q8—28no—
535C2×Q8—28no—
536C2×Q8—44no—
537C2×Q8—416no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—134no—
556C22×C4—134no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—1316no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—132no—
563C22×C4—132no—
564C22×C4—132no—
565C22×C4—268no—
566C22×C4—2632no—
567C22×C4—268no—
568C22×C4—268no—
569C22×C4—268no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—262no—
576C22×C4—262no—
577C22×C4—262no—
578C22×C4—262no—
579C22×C4—262no—
580C22×C4—262no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—268no—
590C22×C4—268no—
591C22×C4—524no—
592C22×C4—524no—
593C22×C4—5216no—
594C22×C4—5216no—
595C22×C4D4×D1314yes—
596C22×C4#612914yes—
597C22×C4Q8×D1314yes—
598C22×C4#613114yes—
599C22×C4C23×D1312yes—
600C22×C4C23×D1312yes—
601C22×C4C23×D1312yes—
602C22×C4C23×D1312yes—
603C22×C4C23×D1312yes—
604C22×C4C23×D1312yes—
605C22×C4C23×D1312yes—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—44no—
609C4⋊C4—268no—
610C4⋊C4—268no—
611C4⋊C4—268no—
612C4⋊C4—268no—
613C4⋊C4—268no—
614C4⋊C4—268no—
615C4⋊C4—524no—
616C4⋊C4—524no—
617C22⋊C4—1316no—
618C22⋊C4—268no—
619C22⋊C4—268no—
620C22⋊C4—268no—
621C42—268no—
622C42—268no—
623C13C2×#243811yescharacteristic, complemented, Sylow
624C23—1316no—
625C23—134no—
626C23—134no—
627C23—134no—
628C23—268no—
629C23—268no—
630C23—268no—
631C23—268no—
632C23—268no—
633C23—268no—
634C23—262no—
635C23—262no—
636C23—262no—
637C23—262no—
638C23C2×D4×D1312yes—
639C23C2×#612912yes—
640C23#8825112yes—
641C23C2×Q8×D1312yes—
642C23C2×#613112yes—
643C23#8825412yes—
644C23#41×D1312yes—
645C23C24×D1311yescharacteristic
646Q8—416no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—134no—
672C2×C4—134no—
673C2×C4—2632no—
674C2×C4—268no—
675C2×C4—268no—
676C2×C4—262no—
677C2×C4—262no—
678C2×C4—262no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—262no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—262no—
695C2×C4—5216no—
696C2×C4—5216no—
697C2×C4—524no—
698C2×C4—524no—
699C2×C4—524no—
700C2×C4—524no—
701C2×C4—524no—
702C2×C4C2×D4×D1314yes—
703C2×C4C2×#612914yes—
704C2×C4C2×Q8×D1314yes—
705C2×C4C2×#613114yes—
706C22—138no—
707C22—2632no—
708C22—264no—
709C22—264no—
710C22—264no—
711C22—264no—
712C22—264no—
713C22—264no—
714C22#1171929614yes—
715C22D13×C22⋊Q814yes—
716C22#1171934214yes—
717C22#1171934414yes—
718C22#1171943114yes—
719C22#1171943314yes—
720C22#1171943414yes—
721C22C22×D4×D1311yescharacteristic
722C22C22×#612911yescharacteristic
723C22C2×#8825111yescharacteristic
724C22C22×Q8×D1311yescharacteristic
725C22C22×#613111yescharacteristic
726C22C2×#8825411yescharacteristic
727C22C2×#41×D1311yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—264no—
736C4—264no—
737C4—522no—
738C4—522no—
739C4—522no—
740C4—522no—
741C4—522no—
742C2—268no—
743C2#1311850518yesdirect product factor
744C2C2×D13×C22⋊Q811yescharacteristic
745C2C2×#1171943311yescharacteristic
746C2C2×#1171943411yescharacteristic
747C2C2×#1171929611yescharacteristic
748C2C2×#1171943111yescharacteristic
749C2C2×#1171934211yescharacteristic
750C2C2×#1171934411yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#395C2
socleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#395D13
hypocenterC13C2×#2438
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
3. #13118505C2direct (N × H)
4. C2×#11718321C2semidirect
5. C2×#11718645C2semidirect
6. C2×#11718322C2semidirect
7. C2×#11718891C2semidirect
8. C2×#11718633C2semidirect
9. C2×#11718642C2semidirect
10. C2×#11718314C2semidirect
16. C2×C13×#395C2semidirect
42. C13×#395C22semidirect
46. #11718891C22semidirect
60. #11718645C22semidirect
61. #11718642C22semidirect
62. #11718633C22semidirect
66. #11718322C22semidirect
67. #11718321C22semidirect
68. #11718314C22semidirect
96. C22×C4×D13Q8semidirect
231. C2×C4×D13C2×Q8semidirect
255. C2×#395D13semidirect
375. #395C2×D13semidirect
516. C2×C13#2438semidirect
623. C13C2×#2438semidirect
743. C2#13118505direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882002
C22×#881462
#131185052
C2×#117183212
C2×#117186452
C2×#117183222
C2×#117188912
C2×#117186332
C2×#117186422
C2×#117183142
C2×#117183292
C2×#117186502
C2×#117183252
C2×#117186482
C2×D13×#952
C2×C13×#3952
C2×#243813