Finite Group Databasebeta

← C2×#13128755 #16771423

Subgroups — C2×#13128755 #16771423

Order 3328.

7238 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128755C2132yesmaximal, direct product factor
2C2×#11719319C214yesmaximal, complemented
3C2×#11719366C214yesmaximal, complemented
4C2×#11719306C214yesmaximal, complemented
5C2×#11719355C214yesmaximal, complemented
6C2×#11719402C211yesmaximal, characteristic, complemented
7C2×#11719223C211yesmaximal, characteristic, complemented
8C2×#11719424C211yesmaximal, characteristic, complemented
9C2×#11719313C212yesmaximal, complemented
10C2×#11719421C211yesmaximal, characteristic, complemented
11C2×#11719262C212yesmaximal, complemented
12C2×#11719305C212yesmaximal, complemented
13C2×D13×#125C211yesmaximal, characteristic, complemented
14C2×#11719251C212yesmaximal, complemented
15C2×#11719227C211yesmaximal, characteristic, complemented
16C2×C13×#540C211yesmaximal, characteristic, complemented
17C22×#6129C2212yes—
18C22×#6127C2211yescharacteristic
19C13×#540C22116yescomplemented
20C2×C13×#127C2211yescharacteristic
21C2×C13×#125C2211yescharacteristic
22C2×C13×#123C2214yes—
23C2×C13×#121C2214yes—
24C2×C13×#121C2212yes—
25C2×C4×D4×C13C2212yes—
26C2×C13×#117C2211yescharacteristic
27C2×#88193C2214yes—
28C2×#88193C2214yes—
29C2×#88192C2212yes—
30C2×#88192C2214yes—
31C2×#88192C2214yes—
32C2×#88190C2212yes—
33C2×#88189C2214yes—
34C2×#88189C2214yes—
35C2×D4×Dic13C2212yes—
36C2×D4×Dic13C2214yes—
37C2×D4×Dic13C2214yes—
38C2×C4×C22⋊D13C2214yes—
39C2×C4×C22⋊D13C2214yes—
40C2×#88180C2214yes—
41C2×#88178C2212yes—
42C22×#6101C2214yes—
43C22×C4×Dic13C2211yescharacteristic
44#11719424C22116yescomplemented
45#11719421C22116yescomplemented
46#11719402C22116yescomplemented
47D13×#125C22116yescomplemented
48#11719366C22164yescomplemented
49#11719355C22164yescomplemented
50#11719319C22164yescomplemented
51#11719313C22132yescomplemented
52#11719306C22164yescomplemented
53#11719305C22132yescomplemented
54#11719262C22132yescomplemented
55#11719251C22132yescomplemented
56#11719227C22116yescomplemented
57#11719223C22116yescomplemented
58C2×#88152C2214yes—
59C2×#88151C2212yes—
60C2×#88147C2212yes—
61C2×C4⋊C4×D13C2212yes—
62C2×C4⋊C4×D13C2214yes—
63C2×#88144C2214yes—
64C2×#88144C2212yes—
65C2×#88143C2214yes—
66C2×#88143C2214yes—
67C2×#88141C2212yes—
68C2×#88141C2212yes—
69C2×#88138C2214yes—
70C2×#88137C2214yes—
71C2×#88135C2212yes—
72C2×#88135C2212yes—
73C2×#88135C2214yes—
74C2×#88133C2214yes—
75C2×#88133C2214yes—
76C2×#88133C2214yes—
77C2×#88132C2214yes—
78C2×#88131C2214yes—
79C2×#88131C2214yes—
80C2×#88126C2211yescharacteristic
81C2×#88126C2211yescharacteristic
82C2×C42×D13C2211yescharacteristic
83C2×C42×D13C2211yescharacteristic
84C2×#88124C2211yescharacteristic
85C2×#88123C2211yescharacteristic
86C2×C4×Dic26C2212yes—
87C22×D4×C13C2312yes—
88C22×D4×C13C2314yes—
89C22×D4×C13C2314yes—
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2314yes—
92C22×C22⋊D13C2311yescharacteristic
93C22×C22⋊D13C2311yescharacteristic
94C22×C22⋊D13C2314yes—
95C22×C22⋊D13C2314yes—
96C23×Dic13C2314yes—
97C23×Dic13C2314yes—
98C23×Dic13C2312yes—
99C2×#6129—216no—
100C2×#6129C23116yes—
101C2×#6127—28no—
102C2×#6127C2318yes—
103C22×D52C2311yescharacteristic
104C22×C4×D13C2311yescharacteristic
105C22×C4×D13C2312yes—
106C22×C4×D13C2312yes—
107C22×C4×D13C2314yes—
108C22×C4×D13C2311yescharacteristic
109C22×Dic26C2312yes—
110C22×Dic26C2311yescharacteristic
111C13×#127C2318yes—
112C13×#125C2318yes—
113C13×#123C23132yes—
114C13×#121C23116yes—
115C13×#121C23132yes—
116C4×D4×C13C23116yes—
117C13×#117C2318yes—
118C2×C13×C4⋊C4C2312yes—
119C2×C13×C4⋊C4C2312yes—
120C2×C13×C4⋊C4C2314yes—
121C2×C13×C22⋊C4C2314yes—
122C2×C13×C22⋊C4C2314yes—
123C2×C13×C22⋊C4C2312yes—
124C2×C42×C13C2311yescharacteristic
125C2×C42×C13C2311yescharacteristic
126C2×C22⋊Dic13C2314yes—
127C2×C22⋊Dic13C2314yes—
128C2×C22⋊Dic13C2314yes—
129C2×C22⋊Dic13C2314yes—
130C2×C22⋊Dic13C2314yes—
131#88193C23132yes—
132#88193C23132yes—
133#88192C23116yes—
134#88192C23132yes—
135#88192C23132yes—
136#88190C23116yes—
137#88189C23132yes—
138#88189C23132yes—
139D4×Dic13C23116yes—
140D4×Dic13C23132yes—
141D4×Dic13C23132yes—
142C4×C22⋊D13C23132yes—
143C4×C22⋊D13C23132yes—
144C2×#6103C2312yes—
145C2×#6103C2312yes—
146C2×#6103C2314yes—
147#88180C23132yes—
148C2×C4⋊Dic13C2312yes—
149C2×C4⋊Dic13C2314yes—
150C2×C4⋊Dic13C2314yes—
151C2×C4⋊Dic13C2314yes—
152#88178C23116yes—
153C2×#6101C2314yes—
154C2×#6101C2314yes—
155C2×#6101C2312yes—
156C2×#6101C2312yes—
157C2×#6101C2314yes—
158C2×#6101C2314yes—
159C2×#6101C2314yes—
160C2×#6101C2314yes—
161C2×#6101C23132yes—
162C2×C4×Dic13C2314yes—
163C2×C4×Dic13C2311yescharacteristic
164C2×C4×Dic13C2312yes—
165C2×C4×Dic13C2312yes—
166C2×C4×Dic13C2311yescharacteristic
167C2×C4×Dic13C2312yes—
168C2×C4×Dic13C2314yes—
169C2×C4×Dic13C2318yes—
170#88152C23132yes—
171#88151C23116yes—
172#88147C23116yes—
173C4⋊C4×D13C23116yes—
174C4⋊C4×D13C23132yes—
175#88144C23116yes—
176#88144C23132yes—
177#88143C23132yes—
178#88143C23132yes—
179#88141C23116yes—
180#88141C23116yes—
181#88138C23132yes—
182#88137C23132yes—
183#88135C23116yes—
184#88135C23116yes—
185#88135C23132yes—
186#88133C23132yes—
187#88133C23132yes—
188#88133C23132yes—
189#88132C23132yes—
190#88131C23132yes—
191#88131C23132yes—
192#88126C2318yes—
193#88126C2318yes—
194C42×D13C2318yes—
195C42×D13C2318yes—
196#88124C2318yes—
197#88123C2318yes—
198C4×Dic26C23116yes—
199C2×#3512—131nomaximal, Sylow
200C24×C13C2414yes—
201C24×C13C2411yescharacteristic
202C23×D13C2411yescharacteristic
203C23×D13C2411yescharacteristic
204C2×D4×C13—28no—
205C2×D4×C13—48no—
206C2×D4×C13—48no—
207C2×D4×C13C2418yes—
208C2×D4×C13C24116yes—
209C2×D4×C13C24116yes—
210C22×C4×C13—24no—
211C22×C4×C13—48no—
212C22×C4×C13C2412yes—
213C22×C4×C13C2411yescharacteristic
214C22×C4×C13C2414yes—
215C22×C4×C13C2412yes—
216C22×C4×C13C2414yes—
217C22×C4×C13C24116yes—
218C22×C4×C13C2411yescharacteristic
219C2×C22⋊D13—24no—
220C2×C22⋊D13—216no—
221C2×C22⋊D13—24no—
222C2×C22⋊D13—48no—
223C2×C22⋊D13C2414yes—
224C2×C22⋊D13C2414yes—
225C2×C22⋊D13C24116yes—
226C2×C22⋊D13C24116yes—
227C22×Dic13—216no—
228C22×Dic13—44no—
229C22×Dic13—48no—
230C22×Dic13C24116yes—
231C22×Dic13C2412yes—
232C22×Dic13C2412yes—
233C22×Dic13C2414yes—
234C22×Dic13C2411yescharacteristic
235C22×Dic13C2414yes—
236C22×Dic13C24116yes—
237C22×Dic13C2418yes—
238C22×Dic13C2411yescharacteristic
239#6129—264no—
240#6127—232no—
241C2×D52—24no—
242C2×D52C2414yes—
243C2×C4×D13—24no—
244C2×C4×D13—44no—
245C2×C4×D13—44no—
246C2×C4×D13—48no—
247C2×C4×D13#4118yes—
248C2×C4×D13C2414yes—
249C2×C4×D13C2418yes—
250C2×C4×D13C2418yes—
251C2×C4×D13C24116yes—
252C2×C4×D13C2414yes—
253C2×Dic26—28no—
254C2×Dic26—24no—
255C2×Dic26C2418yes—
256C2×Dic26C2414yes—
257C13×C4⋊C4C2418yes—
258C13×C4⋊C4C2418yes—
259C13×C4⋊C4C24116yes—
260C13×C22⋊C4C24116yes—
261C13×C22⋊C4C24116yes—
262C13×C22⋊C4C2418yes—
263C42×C13C2414yes—
264C42×C13C2414yes—
265C22⋊Dic13C24116yes—
266C22⋊Dic13C24116yes—
267C22⋊Dic13C24116yes—
268C22⋊Dic13C24116yes—
269C22⋊Dic13C24116yes—
270#6103C2418yes—
271#6103C2418yes—
272#6103C24116yes—
273C4⋊Dic13C2418yes—
274C4⋊Dic13C24116yes—
275C4⋊Dic13C24116yes—
276C4⋊Dic13C24116yes—
277#6101C24116yes—
278#6101C24116yes—
279#6101C2418yes—
280#6101C2418yes—
281#6101C24116yes—
282#6101C24116yes—
283#6101C24116yes—
284#6101C24116yes—
285C4×Dic13C24116yes—
286C4×Dic13C2414yes—
287C4×Dic13C2418yes—
288C4×Dic13C2418yes—
289C4×Dic13C2414yes—
290C4×Dic13C2418yes—
291C4×Dic13C24116yes—
292#3512—1332no—
293C2×#553—134no—
294C2×#553—134no—
295C2×#553—134no—
296C2×#552—134no—
297C2×#541—131no—
298C2×#541—131no—
299C2×#540—131no—
300C2×#540D1311yescharacteristic, complemented
301C2×#537—132no—
302C2×#532—131no—
303C2×#529—132no—
304C2×#529—132no—
305C22×#125—131no—
306C2×#520—132no—
307C2×C4×#41—131no—
308C23×C13—28no—
309C23×C13—22no—
310C23×C13—28no—
311C23×C13—24no—
312C23×C13—28no—
313C23×C13C2518yes—
314C23×C13C2512yes—
315C23×C13C2511yescharacteristic
316C22×D13—24no—
317C22×D13—22no—
318C22×D13—24no—
319C22×D13C2×#4114yes—
320C22×D13C2512yes—
321C22×D13C2512yes—
322D4×C13—216no—
323D4×C13—416no—
324D4×C13—416no—
325C2×C4×C13—22no—
326C2×C4×C13—24no—
327C2×C4×C13—28no—
328C2×C4×C13—24no—
329C2×C4×C13—28no—
330C2×C4×C13—416no—
331C2×C4×C13C2×#4114yes—
332C2×C4×C13C2514yes—
333C2×C4×C13C2512yes—
334C2×C4×C13C2514yes—
335C2×C4×C13C2518yes—
336C2×C4×C13C2512yes—
337C22⋊D13—28no—
338C22⋊D13—232no—
339C22⋊D13—28no—
340C22⋊D13—416no—
341C2×Dic13—22no—
342C2×Dic13—28no—
343C2×Dic13—24no—
344C2×Dic13—28no—
345C2×Dic13—24no—
346C2×Dic13—232no—
347C2×Dic13—48no—
348C2×Dic13—416no—
349C2×Dic13C2×#4114yes—
350C2×Dic13C2514yes—
351C2×Dic13C2514yes—
352C2×Dic13C2518yes—
353C2×Dic13C2512yes—
354C2×Dic13C2518yes—
355C2×Dic13C2512yes—
356D52—28no—
357C4×D13—28no—
358C4×D13—48no—
359C4×D13—48no—
360C4×D13—416no—
361C4×D13C2×#41116yes—
362Dic26—216no—
363Dic26—28no—
364C22×#41—132no—
365C22×#41—131no—
366#553—1364no—
367#553—1364no—
368#553—1364no—
369#552—1364no—
370#541—1316no—
371#541—1316no—
372#540—1316no—
373#540C2×D13116yescomplemented
374#537—1332no—
375#532—1316no—
376C2×C4⋊Q8—131no—
377C2×#127C2×D1311yescharacteristic
378#529—1332no—
379#529—1332no—
380C2×#126—134no—
381C2×#126—134no—
382C2×#126—134no—
383C2×#126—134no—
384C2×#125—1316no—
385C2×#125—134no—
386C2×#125—134no—
387C2×#125—132no—
388C2×#125—134no—
389C2×#125—131no—
390C2×#125C2×D1311yescharacteristic
391C2×#124—132no—
392C2×#123—134no—
393C2×#123—134no—
394C2×#123—134no—
395C2×#123C2×D1314yes—
396C2×C22⋊Q8—132no—
397C2×C22⋊Q8—132no—
398C2×C22⋊Q8—134no—
399C2×#121—132no—
400C2×#121—134no—
401C2×#121—134no—
402C2×#121—134no—
403C2×#121—134no—
404C2×#121—134no—
405C2×#121C2×D1312yes—
406C2×#121C2×D1314yes—
407#520—1332no—
408C4×#41—1316no—
409C2×C4×Q8—132no—
410C2×C4×Q8—132no—
411C2×C4×Q8—132no—
412C2×C4×D4—132no—
413C2×C4×D4—134no—
414C2×C4×D4—134no—
415C2×C4×D4—134no—
416C2×C4×D4—134no—
417C2×C4×D4—132no—
418C2×C4×D4—132no—
419C2×C4×D4—132no—
420C2×C4×D4—134no—
421C2×C4×D4C2×D1312yes—
422C2×#117—134no—
423C2×#117—134no—
424C2×#117—134no—
425C2×#117—131no—
426C2×#117—131no—
427C2×#117C2×D1311yescharacteristic
428C22×C4⋊C4—134no—
429C22×C4⋊C4—132no—
430C22×C4⋊C4—134no—
431C22×C42—131no—
432C22×C42—131no—
433C22×C42—131no—
434C22×C13—28no—
435C22×C13—22no—
436C22×C13—28no—
437C22×C13—24no—
438C22×C13—28no—
439C22×C13—416no—
440C22×C13—44no—
441C22×C13C22×#4112yes—
442C22×C13#58514yes—
443C22×C13C2611yescharacteristic
444C2×D13—24no—
445C2×D13—28no—
446C2×D13—22no—
447C2×D13—24no—
448C2×D13—44no—
449C2×D13C22×#4114yes—
450C4×C13—22no—
451C4×C13—24no—
452C4×C13—28no—
453C4×C13—24no—
454C4×C13C22×#4114yes—
455Dic13—22no—
456Dic13—28no—
457Dic13—24no—
458Dic13—28no—
459Dic13—24no—
460Dic13C22×#4114yes—
461C2×#41—1316no—
462C2×#41—138no—
463C2×#41—268no—
464C2×#41—2616no—
465C22×Q8—131no—
466C22×Q8—132no—
467C22×D4—131no—
468C22×D4—134no—
469C22×D4—131no—
470C22×D4—134no—
471C22×D4—131no—
472C22×D4C22×D1312yes—
473C22×D4C22×D1314yes—
474C22×D4C22×D1314yes—
475C23×C4—131no—
476C23×C4—134no—
477C23×C4—134no—
478C23×C4—132no—
479C23×C4—131no—
480C23×C4—134no—
481C23×C4—132no—
482C23×C4—132no—
483C23×C4C22×D1311yescharacteristic
484C23×C4C22×D1314yes—
485C4⋊Q8—138no—
486#127C22×D1318yes—
487#126—1332no—
488#126—1332no—
489#126—1332no—
490#126—1332no—
491#125—1316no—
492#125—1332no—
493#125—1332no—
494#125—1332no—
495#125—138no—
496#125C22×D1318yes—
497#124—1316no—
498#123—1332no—
499#123—1332no—
500#123—1332no—
501#123C22×D13132yes—
502C22⋊Q8—1316no—
503C22⋊Q8—1316no—
504C22⋊Q8—1332no—
505#121—1316no—
506#121—1332no—
507#121—1332no—
508#121—1332no—
509#121—1332no—
510#121—1332no—
511#121C22×D13116yes—
512#121C22×D13132yes—
513C4×Q8—1316no—
514C4×Q8—1316no—
515C4×Q8—1316no—
516C4×D4—1316no—
517C4×D4—1332no—
518C4×D4—1332no—
519C4×D4—1332no—
520C4×D4—1332no—
521C4×D4—1316no—
522C4×D4—1316no—
523C4×D4—1316no—
524C4×D4—1332no—
525C4×D4C22×D13116yes—
526#117—1332no—
527#117—1332no—
528#117—1332no—
529#117—138no—
530#117—138no—
531#117C22×D1318yes—
532C2×C4⋊C4—132no—
533C2×C4⋊C4—134no—
534C2×C4⋊C4—134no—
535C2×C4⋊C4—134no—
536C2×C4⋊C4—132no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—134no—
539C2×C4⋊C4—1332no—
540C2×C4⋊C4—134no—
541C2×C4⋊C4—132no—
542C2×C4⋊C4—134no—
543C2×C4⋊C4—134no—
544C2×C4⋊C4—134no—
545C2×C4⋊C4—1316no—
546C2×C4⋊C4—1332no—
547C2×C4⋊C4C22×D1312yes—
548C2×C4⋊C4C22×D1314yes—
549C2×C4⋊C4C22×D1312yes—
550C2×C22⋊C4—134no—
551C2×C22⋊C4—134no—
552C2×C22⋊C4—134no—
553C2×C22⋊C4—134no—
554C2×C22⋊C4—134no—
555C2×C22⋊C4—132no—
556C2×C22⋊C4—132no—
557C2×C22⋊C4—134no—
558C2×C22⋊C4C22×D1314yes—
559C2×C22⋊C4C22×D1314yes—
560C2×C22⋊C4C22×D1312yes—
561C2×C42—131no—
562C2×C42—134no—
563C2×C42—134no—
564C2×C42—132no—
565C2×C42—132no—
566C2×C42—132no—
567C2×C42—138no—
568C2×C42—131no—
569C2×C42—138no—
570C2×C42—138no—
571C2×C42C22×D1311yescharacteristic
572C2×C42C22×D1311yescharacteristic
573C2×C13—48no—
574C2×C13—42no—
575C2×C13#351214yescomplemented
576C2×C13C23×#4111yescharacteristic
577C2×C13C2×#58512yes—
578D13—24no—
579D13—42no—
580C24—131no—
581C24—131no—
582C24C23×D1311yescharacteristic
583C24C23×D1314yes—
584#41—2632no—
585#41—2664no—
586C2×Q8—134no—
587C2×Q8—138no—
588C2×Q8—264no—
589C2×Q8—268no—
590C2×D4—28no—
591C2×D4—48no—
592C2×D4—48no—
593C2×D4—134no—
594C2×D4—1316no—
595C2×D4—134no—
596C2×D4—1316no—
597C2×D4—134no—
598C2×D4—264no—
599C2×D4—264no—
600C2×D4—264no—
601C2×D4—2616no—
602C2×D4—528no—
603C2×D4C23×D1318yes—
604C2×D4C23×D13116yes—
605C2×D4C23×D13116yes—
606C22×C4—24no—
607C22×C4—48no—
608C22×C4—131no—
609C22×C4—138no—
610C22×C4—134no—
611C22×C4—1316no—
612C22×C4—132no—
613C22×C4—132no—
614C22×C4—134no—
615C22×C4—131no—
616C22×C4—134no—
617C22×C4—138no—
618C22×C4—1316no—
619C22×C4—134no—
620C22×C4—138no—
621C22×C4—138no—
622C22×C4—1316no—
623C22×C4—2616no—
624C22×C4—264no—
625C22×C4—524no—
626C22×C4—528no—
627C22×C4—524no—
628C22×C4—524no—
629C22×C4—528no—
630C22×C4C23×D1314yes—
631C22×C4C23×D1312yes—
632C22×C4C23×D1311yescharacteristic
633C22×C4C23×D1312yes—
634C22×C4C23×D1314yes—
635C22×C4C23×D13116yes—
636C22×C4C23×D1311yescharacteristic
637C4⋊C4—138no—
638C4⋊C4—1316no—
639C4⋊C4—1316no—
640C4⋊C4—1316no—
641C4⋊C4—138no—
642C4⋊C4—1316no—
643C4⋊C4—1316no—
644C4⋊C4—1316no—
645C4⋊C4—138no—
646C4⋊C4—1316no—
647C4⋊C4—1316no—
648C4⋊C4—1316no—
649C4⋊C4C23×D1318yes—
650C4⋊C4C23×D13116yes—
651C4⋊C4C23×D1318yes—
652C22⋊C4—1316no—
653C22⋊C4—1316no—
654C22⋊C4—1316no—
655C22⋊C4—1316no—
656C22⋊C4—1316no—
657C22⋊C4—138no—
658C22⋊C4—138no—
659C22⋊C4—1316no—
660C22⋊C4C23×D13116yes—
661C22⋊C4C23×D13116yes—
662C22⋊C4C23×D1318yes—
663C42—134no—
664C42—134no—
665C42—138no—
666C42—138no—
667C42—138no—
668C42—1316no—
669C42—1316no—
670C42C23×D1314yes—
671C42C23×D1314yes—
672C13C2×#351211yescharacteristic, complemented, Sylow
673C23—22no—
674C23—28no—
675C23—28no—
676C23—24no—
677C23—28no—
678C23—134no—
679C23—132no—
680C23—132no—
681C23—264no—
682C23—262no—
683C23—264no—
684C23C24×D1312yes—
685C23C24×D1318yes—
686C23C24×D1311yescharacteristic
687Q8—268no—
688Q8—2616no—
689D4—216no—
690D4—416no—
691D4—416no—
692D4—268no—
693D4—268no—
694D4—268no—
695D4—2632no—
696D4—5216no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—134no—
704C2×C4—132no—
705C2×C4—1316no—
706C2×C4—134no—
707C2×C4—134no—
708C2×C4—132no—
709C2×C4—138no—
710C2×C4—138no—
711C2×C4—2632no—
712C2×C4—262no—
713C2×C4—268no—
714C2×C4—264no—
715C2×C4—264no—
716C2×C4—268no—
717C2×C4—268no—
718C2×C4—528no—
719C2×C4—5216no—
720C2×C4—528no—
721C2×C4—528no—
722C2×C4—5216no—
723C2×C4#41×D1314yes—
724C2×C4C24×D1314yes—
725C2×C4C24×D1312yes—
726C2×C4C24×D1314yes—
727C2×C4C24×D1318yes—
728C2×C4C24×D1312yes—
729C22—22no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—44no—
735C22—416no—
736C22—134no—
737C22—268no—
738C22—264no—
739C22—262no—
740C22—264no—
741C22—524no—
742C22C2×#41×D1312yes—
743C22#1171965014yes—
744C22C25×D1311yescharacteristic
745C4—22no—
746C4—24no—
747C4—28no—
748C4—24no—
749C4—134no—
750C4—262no—
751C4—268no—
752C4—264no—
753C4—264no—
754C4—268no—
755C4C2×#41×D1314yes—
756C2—42no—
757C2—48no—
758C2—264no—
759C2—522no—
760C2#1312875514yesdirect product factor
761C2C22×#41×D1311yescharacteristic
762C2C2×#1171965012yes—
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#540C2
socleC23×C13C25
hypercenterC2×#540D13
hypocenterC13C2×#3512
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #13128755C2direct (N × H)
2. C2×#11719319C2semidirect
3. C2×#11719366C2semidirect
4. C2×#11719306C2semidirect
5. C2×#11719355C2semidirect
6. C2×#11719402C2semidirect
7. C2×#11719223C2semidirect
8. C2×#11719424C2semidirect
9. C2×#11719313C2semidirect
10. C2×#11719421C2semidirect
11. C2×#11719262C2semidirect
12. C2×#11719305C2semidirect
13. C2×D13×#125C2semidirect
14. C2×#11719251C2semidirect
15. C2×#11719227C2semidirect
16. C2×C13×#540C2semidirect
19. C13×#540C22semidirect
44. #11719424C22semidirect
45. #11719421C22semidirect
46. #11719402C22semidirect
47. D13×#125C22semidirect
48. #11719366C22semidirect
49. #11719355C22semidirect
50. #11719319C22semidirect
51. #11719313C22semidirect
52. #11719306C22semidirect
53. #11719305C22semidirect
54. #11719262C22semidirect
55. #11719251C22semidirect
56. #11719227C22semidirect
57. #11719223C22semidirect
300. C2×#540D13semidirect
373. #540C2×D13semidirect
575. C2×C13#3512semidirect
672. C13C2×#3512semidirect
760. C2#13128755direct (N × H)

Maximal subgroups

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

subgroupindex
#131287552
C2×#117193192
C2×#117193662
C2×#117193062
C2×#117193552
C2×#117194022
C2×#117192232
C2×#117194242
C2×#117193132
C2×#117194212
C2×#117192622
C2×#117193052
C2×D13×#1252
C2×#117192512
C2×#117192272
C2×C13×#5402
C2×#351213