Finite Group Databasebeta

← C2×#13118978 #16030506

Subgroups — C2×#13118978 #16030506

Order 3328.

2942 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88143C211yesmaximal, characteristic, complemented
2C22×C4⋊C4×D13C211yesmaximal, characteristic
3#13118978C2116yesmaximal, direct product factor
4C2×#11718319C211yesmaximal, characteristic, complemented
5C2×#11718318C211yesmaximal, characteristic, complemented
6C2×#11718645C211yesmaximal, characteristic, complemented
7C2×#11718646C211yesmaximal, characteristic, complemented
8C2×#11718316C211yesmaximal, characteristic, complemented
9C2×#11718642C211yesmaximal, characteristic, complemented
10C2×#11718329C211yesmaximal, characteristic
11C2×#11718329C211yesmaximal, characteristic
12C2×#11718650C211yesmaximal, characteristic
13C2×#11718650C211yesmaximal, characteristic
14C2×#11718648C211yesmaximal, characteristic
15C2×#11718327C211yesmaximal, characteristic
16C2×C13×#398C211yesmaximal, characteristic, complemented
17C23×C4×D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C2×C4⋊C4×D13—28no—
41C2×C4⋊C4×D13C2218yes—
42C2×#88143—28no—
43C2×#88143C2218yescomplemented
44C13×#398C2218yescomplemented
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718650C2218yes—
58#11718650C2218yes—
59#11718648C2218yes—
60#11718646C2218yescomplemented
61#11718645C2218yescomplemented
62#11718642C2218yescomplemented
63#11718329C2218yes—
64#11718329C2218yes—
65#11718327C2218yes—
66#11718319C2218yescomplemented
67#11718318C2218yescomplemented
68#11718316C2218yescomplemented
69C24×D13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C22×C4×D13—24no—
85C22×C4×D13—24no—
86C22×C4×D13—24no—
87C22×C4×D13—24no—
88C22×C4×D13—24no—
89C22×C4×D13—24no—
90C22×C4×D13—24no—
91C22×C4×D13—42no—
92C22×C4×D13—42no—
93C22×C4×D13C2314yes—
94C22×C4×D13C2314yes—
95C22×C4×D13C2314yes—
96C2×C13×C4⋊C4—24no—
97C2×C13×C4⋊C4—24no—
98C2×C13×C4⋊C4—24no—
99C2×C13×C4⋊C4—24no—
100C2×C13×C4⋊C4C2314yes—
101C2×C13×C4⋊C4C2314yes—
102C2×C13×C4⋊C4C2314yes—
103C2×C13×C4⋊C4C2314yes—
104C2×#6103—24no—
105C2×#6103—24no—
106C2×#6103—24no—
107C2×#6103Q818yes—
108C2×#6103C2314yes—
109C2×#6103C2314yes—
110C2×#6103C2314yes—
111C2×#6103C2314yes—
112C2×C4⋊Dic13—24no—
113C2×C4⋊Dic13—24no—
114C2×C4⋊Dic13—42no—
115C2×C4⋊Dic13—42no—
116C2×C4⋊Dic13C2314yes—
117C2×C4⋊Dic13C2314yes—
118C2×C4⋊Dic13C2314yes—
119C2×C4⋊Dic13C2314yes—
120C2×#6101—24no—
121C2×#6101—24no—
122C2×#6101—24no—
123C2×#6101—24no—
124C2×#6101—42no—
125C2×#6101D418yes—
126C2×#6101C2314yes—
127C2×#6101C2314yes—
128C2×#6101C2314yes—
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×C4×Dic13—24no—
133C2×C4×Dic13—42no—
134C2×C4×Dic13C2314yes—
135C2×C4×Dic13C2314yes—
136C4⋊C4×D13—232no—
137#88143—232no—
138C13×#95C2314yes—
139C13×#95C2314yes—
140C13×#95C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146#88071C2314yes—
147#88071C2314yes—
148#88071C2314yes—
149#88071C2314yes—
150C2×#2473—131nomaximal, Sylow
151C24×C13C2411yescharacteristic
152C23×D13—22no—
153C23×D13—22no—
154C23×D13—22no—
155C23×D13—22no—
156C23×D13C2×Q814yes—
157C23×D13#4114yes—
158C23×D13#4114yes—
159C23×D13C2412yes—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
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×C13C2×D414yes—
179C22×C4×C13C2×Q814yes—
180C22×C4×C13#4114yes—
181C22×C4×C13C2412yes—
182C22×C4×C13C2412yes—
183C22×C4×C13C2412yes—
184C22×C4×C13C2412yes—
185C22×C4×C13C2412yes—
186C22×C4×C13C2412yes—
187C22×C4×C13C2412yes—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
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×Dic13C2×D414yes—
207C22×Dic13C2×D414yes—
208C22×Dic13C2×Q814yes—
209C22×Dic13C2412yes—
210C22×Dic13C2412yes—
211C22×Dic13C2412yes—
212C22×Dic13C2412yes—
213C22×Dic13C2412yes—
214C22×Dic13C2412yes—
215C22×Dic13C2412yes—
216C2×C4×D13—232no—
217C2×C4×D13—28no—
218C2×C4×D13—28no—
219C2×C4×D13—28no—
220C2×C4×D13—28no—
221C2×C4×D13—28no—
222C2×C4×D13—28no—
223C2×C4×D13—28no—
224C2×C4×D13—44no—
225C2×C4×D13—44no—
226C2×C4×D13—416no—
227C2×C4×D13—416no—
228C13×C4⋊C4—28no—
229C13×C4⋊C4—28no—
230C13×C4⋊C4—28no—
231C13×C4⋊C4—28no—
232#6103—28no—
233#6103—28no—
234#6103—28no—
235#6103C2×Q8116yes—
236C4⋊Dic13—28no—
237C4⋊Dic13—28no—
238C4⋊Dic13—44no—
239C4⋊Dic13—44no—
240#6101—28no—
241#6101—28no—
242#6101—28no—
243#6101—28no—
244#6101—44no—
245#6101C2×D4116yes—
246C4×Dic13—28no—
247C4×Dic13—44no—
248C22×#125—131no—
249C23×C4⋊C4—131no—
250#2473—1316no—
251C2×#400—131no—
252C2×#398—131no—
253C2×#398—131no—
254C2×#398D1311yescharacteristic, complemented
255C2×#389—131no—
256C2×#387—131no—
257C2×#387—131no—
258C2×#385—131no—
259C2×#385—131no—
260C2×#385—131no—
261C2×#385—131no—
262C2×#380—131no—
263C2×C4×C22⋊C4—131no—
264C23×C13C22×D412yes—
265C23×C13C22×Q812yes—
266C23×C13C2×#4112yes—
267C23×C13C2×#4112yes—
268C23×C13C2×#4112yes—
269C23×C13H(5,𝔽2)12yes—
270C23×C132−1+412yes—
271C23×C13C2511yescharacteristic
272C22×D13—28no—
273C22×D13—28no—
274C22×D13—28no—
275C22×D13—28no—
276C22×D13—28no—
277C22×D13—28no—
278C22×D13—22no—
279C22×D13—22no—
280C22×D13—22no—
281C22×D13—22no—
282C22×D13#125116yescomplemented
283C22×D13C22×Q814yes—
284C22×D13C2×#4114yes—
285C22×D13C2×#4114yes—
286C2×C4×C13—28no—
287C2×C4×C13—28no—
288C2×C4×C13—28no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
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—44no—
308C2×C4×C13—44no—
309C2×C4×C13—44no—
310C2×C4×C13—44no—
311C2×C4×C13C22×D414yes—
312C2×C4×C13C22×Q814yes—
313C2×C4×C13C2×#4114yes—
314C2×Dic13—28no—
315C2×Dic13—28no—
316C2×Dic13—28no—
317C2×Dic13—22no—
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—44no—
336C2×Dic13—44no—
337C2×Dic13—44no—
338C2×Dic13—44no—
339C2×Dic13C22×D414yes—
340C2×Dic13C22×D414yes—
341C2×Dic13C22×Q814yes—
342C4×D13—232no—
343C4×D13—416no—
344C4×D13—416no—
345C24×C4—131no—
346C24×C4—131no—
347C24×C4—131no—
348C2×#125—138no—
349C2×#125—268no—
350C22×C4⋊C4—131no—
351C22×C4⋊C4—131no—
352C22×C4⋊C4—131no—
353C22×C4⋊C4—131no—
354C22×C4⋊C4—131no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4—131no—
357C22×C4⋊C4—131no—
358C22×C4⋊C4—131no—
359C22×C4⋊C4—131no—
360C22×C4⋊C4—138no—
361C22×C4⋊C4—268no—
362C22×C4⋊C4C2×D1311yescharacteristic
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#398C2×D1318yescomplemented
376#389—138no—
377#387—138no—
378#387—138no—
379#385—138no—
380#385—138no—
381#385—138no—
382#385—138no—
383#380—138no—
384C4×C22⋊C4—138no—
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×#95C2×D1311yescharacteristic
395C2×#95C2×D1311yescharacteristic
396C2×#95C2×D1311yescharacteristic
397C22×C13#52514yes—
398C22×C13C2×#12514yes—
399C22×C13#53914yes—
400C22×C13#54614yes—
401C22×C13D4×Q814yes—
402C22×C13#55214yes—
403C22×C13#55414yes—
404C22×C13C23×D411yescharacteristic
405C22×C13C23×Q811yescharacteristic
406C22×C13C22×#4111yescharacteristic
407C22×C13C22×#4111yescharacteristic
408C22×C13C22×#4111yescharacteristic
409C22×C13C2×H(5,𝔽2)11yescharacteristic
410C22×C13C2×2−1+411yescharacteristic
411C2×D13—24no—
412C2×D13—24no—
413C2×D13—24no—
414C2×D13—24no—
415C2×D13—24no—
416C2×D13—24no—
417C2×D13—232no—
418C2×D13C2×#12518yescomplemented
419C4×C13—24no—
420C4×C13—24no—
421C4×C13—24no—
422C4×C13—42no—
423C4×C13—42no—
424C4×C13—42no—
425C4×C13—42no—
426Dic13—24no—
427Dic13—24no—
428Dic13—24no—
429Dic13—42no—
430Dic13—42no—
431Dic13—42no—
432Dic13—42no—
433C25—131no—
434C23×C4—131no—
435C23×C4—131no—
436C23×C4—131no—
437C23×C4—131no—
438C23×C4—131no—
439C23×C4—131no—
440C23×C4—131no—
441C23×C4—134no—
442C23×C4—134no—
443C23×C4—134no—
444C23×C4—264no—
445C23×C4—264no—
446C23×C4—264no—
447C23×C4—264no—
448C23×C4—264no—
449C23×C4—264no—
450C23×C4—264no—
451C23×C4—522no—
452C23×C4—522no—
453C23×C4C22×D1311yescharacteristic
454C23×C4C22×D1311yescharacteristic
455C23×C4C22×D1311yescharacteristic
456C23×C4C22×D1311yescharacteristic
457C23×C4C22×D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459C23×C4C22×D1311yescharacteristic
460#125—2632no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—138no—
466C2×C4⋊C4—134no—
467C2×C4⋊C4—134no—
468C2×C4⋊C4—134no—
469C2×C4⋊C4—134no—
470C2×C4⋊C4—134no—
471C2×C4⋊C4—134no—
472C2×C4⋊C4—134no—
473C2×C4⋊C4—134no—
474C2×C4⋊C4—134no—
475C2×C4⋊C4—134no—
476C2×C4⋊C4—2632no—
477C2×C4⋊C4—264no—
478C2×C4⋊C4—264no—
479C2×C4⋊C4—264no—
480C2×C4⋊C4—264no—
481C2×C4⋊C4—264no—
482C2×C4⋊C4—264no—
483C2×C4⋊C4—522no—
484C2×C4⋊C4—522no—
485C2×C4⋊C4—522no—
486C2×C4⋊C4C22×D1314yes—
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—522no—
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#95C22×D1314yes—
512#95C22×D1314yes—
513#95C22×D1314yes—
514C2×C13#247318yescomplemented
515C2×C13C2×#52511yescharacteristic
516C2×C13C22×#12511yescharacteristic
517C2×C13C2×#53911yescharacteristic
518C2×C13C2×#54611yescharacteristic
519C2×C13C2×D4×Q811yescharacteristic
520C2×C13C2×#55211yescharacteristic
521C2×C13C2×#55411yescharacteristic
522D13—28no—
523C24—134no—
524C24—134no—
525C24—134no—
526C24—132no—
527C24—262no—
528C24—262no—
529C24—262no—
530C24—262no—
531C24C23×D1311yescharacteristic
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
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—134no—
551C22×C4—134no—
552C22×C4—134no—
553C22×C4—132no—
554C22×C4—132no—
555C22×C4—132no—
556C22×C4—132no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—132no—
560C22×C4—268no—
561C22×C4—268no—
562C22×C4—268no—
563C22×C4—2632no—
564C22×C4—268no—
565C22×C4—268no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—268no—
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—268no—
586C22×C4—524no—
587C22×C4—524no—
588C22×C4—5216no—
589C22×C4—5216no—
590C22×C4D4×D1314yes—
591C22×C4#612914yes—
592C22×C4Q8×D1314yes—
593C22×C4C23×D1312yes—
594C22×C4C23×D1312yes—
595C22×C4C23×D1312yes—
596C22×C4C23×D1312yes—
597C22×C4C23×D1312yes—
598C22×C4C23×D1312yes—
599C22×C4C23×D1312yes—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—28no—
604C4⋊C4—1316no—
605C4⋊C4—268no—
606C4⋊C4—268no—
607C4⋊C4—268no—
608C4⋊C4—268no—
609C4⋊C4—268no—
610C4⋊C4—268no—
611C4⋊C4—524no—
612C4⋊C4—524no—
613C4⋊C4—524no—
614C22⋊C4—1316no—
615C22⋊C4—268no—
616C22⋊C4—268no—
617C22⋊C4—268no—
618C42—268no—
619C42—524no—
620C13C2×#247311yescharacteristic, complemented, Sylow
621C23—134no—
622C23—134no—
623C23—134no—
624C23—1316no—
625C23—268no—
626C23—268no—
627C23—268no—
628C23—268no—
629C23—268no—
630C23—262no—
631C23—262no—
632C23—262no—
633C23—262no—
634C23—268no—
635C23C2×D4×D1312yes—
636C23C2×#612912yes—
637C23C2×Q8×D1312yes—
638C23#8825412yes—
639C23#41×D1312yes—
640C23#41×D1312yes—
641C23#8825612yes—
642C23C24×D1311yescharacteristic
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
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—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—134no—
669C2×C4—134no—
670C2×C4—134no—
671C2×C4—2632no—
672C2×C4—268no—
673C2×C4—268no—
674C2×C4—268no—
675C2×C4—262no—
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—5216no—
694C2×C4—5216no—
695C2×C4—524no—
696C2×C4—524no—
697C2×C4—524no—
698C2×C4—524no—
699C2×C4C2×D4×D1314yes—
700C2×C4C2×#612914yes—
701C2×C4C2×Q8×D1314yes—
702C22—138no—
703C22—2632no—
704C22—264no—
705C22—264no—
706C22—264no—
707C22—264no—
708C22—264no—
709C22—264no—
710C22#1171931114yes—
711C22#1171934014yes—
712C22#1171934414yes—
713C22#1171935914yes—
714C22D13×#12514yes—
715C22#1171939714yes—
716C22#1171943214yes—
717C22C22×D4×D1311yescharacteristic
718C22C22×#612911yescharacteristic
719C22C22×Q8×D1311yescharacteristic
720C22C2×#8825411yescharacteristic
721C22C2×#41×D1311yescharacteristic
722C22C2×#41×D1311yescharacteristic
723C22C2×#8825611yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—264no—
732C4—264no—
733C4—264no—
734C4—522no—
735C4—522no—
736C4—522no—
737C4—522no—
738C2—268no—
739C2#1311897818yesdirect product factor
740C2C2×#1171931111yescharacteristic
741C2C2×D13×#12511yescharacteristic
742C2C2×#1171939711yescharacteristic
743C2C2×#1171935911yescharacteristic
744C2C2×#1171943211yescharacteristic
745C2C2×#1171934411yescharacteristic
746C2C2×#1171934011yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#398C2
socleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#398D13
hypocenterC13C2×#2473
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#88143C2semidirect
3. #13118978C2direct (N × H)
4. C2×#11718319C2semidirect
5. C2×#11718318C2semidirect
6. C2×#11718645C2semidirect
7. C2×#11718646C2semidirect
8. C2×#11718316C2semidirect
9. C2×#11718642C2semidirect
16. C2×C13×#398C2semidirect
43. C2×#88143C22semidirect
44. C13×#398C22semidirect
60. #11718646C22semidirect
61. #11718645C22semidirect
62. #11718642C22semidirect
66. #11718319C22semidirect
67. #11718318C22semidirect
68. #11718316C22semidirect
254. C2×#398D13semidirect
282. C22×D13#125semidirect
375. #398C2×D13semidirect
418. C2×D13C2×#125semidirect
514. C2×C13#2473semidirect
620. C13C2×#2473semidirect
739. C2#13118978direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881432
C22×C4⋊C4×D132
#131189782
C2×#117183192
C2×#117183182
C2×#117186452
C2×#117186462
C2×#117183162
C2×#117186422
C2×#117183292
C2×#117186502
C2×#117186482
C2×#117183272
C2×C13×#3982
C2×#247313