Finite Group Databasebeta

← C2×#13129446 #16770297

Subgroups — C2×#13129446 #16770297

Order 3328.

6458 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
1#13129446C2132yesmaximal, direct product factor
2C2×C13⋊#564C212yesmaximal, complemented
3C2×#11719404C212yesmaximal, complemented
4C2×#11719274C212yesmaximal, complemented
5C2×#11719340C212yesmaximal, complemented
6C2×#11719347C212yesmaximal, complemented
7C2×#11719286C212yesmaximal, complemented
8C2×#11719236C214yesmaximal, complemented
9C2×#11719328C212yesmaximal, complemented
10C2×#11719434C212yesmaximal, complemented
11C2×#11719436C212yesmaximal, complemented
12C2×#11719288C214yesmaximal, complemented
13C2×#11719350C212yesmaximal
14C2×#11719184C211yesmaximal, characteristic
15C22×#88124C211yesmaximal, characteristic, complemented
16C2×C13×#533C211yesmaximal, characteristic, complemented
17C13×#533C22116yescomplemented
18C2×C13×C4⋊Q8C2211yescharacteristic
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#125C2212yes—
21C2×C13×C22⋊Q8C2212yes—
22C2×C13×C22⋊Q8C2212yes—
23C2×C4×Q8×C13C2212yes—
24C2×C4×Q8×C13C2212yes—
25C2×C13×#117C2212yes—
26C22×C42×C13C2211yescharacteristic
27C2×#88200C2214yes—
28C2×#88200C2212yes—
29C2×#88200C2212yes—
30C2×Q8×Dic13C2212yes—
31C2×Q8×Dic13C2212yes—
32C2×#88198C2214yes—
33C2×#88184C2211yescharacteristic
34C2×#88183C2212yes—
35C2×C4×C22⋊D13C2212yes—
36C22×C4⋊Dic13C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C2×#88178C2211yescharacteristic
39C22×#6101C2212yes—
40C22×#6101C2212yes—
41#11719436C22132yescomplemented
42#11719434C22132yescomplemented
43#11719404C22132yescomplemented
44C13⋊#564C22132yescomplemented
45#11719350C22132yes—
46#11719347C22132yescomplemented
47#11719340C22132yescomplemented
48#11719328C22132yescomplemented
49#11719288C22164yescomplemented
50#11719286C22132yescomplemented
51#11719274C22132yescomplemented
52#11719236C22164yescomplemented
53C2×#88152C2214yes—
54C2×#88152C2214yes—
55C2×#88152C2214yes—
56C2×#88151C2214yes—
57C2×#88150C2214yes—
58C2×#88148C2214yes—
59C2×#88146C2212yes—
60C2×C4⋊C4×D13C2212yes—
61C2×#88144C2214yes—
62C2×#88144C2214yes—
63C2×#88144C2212yes—
64C2×#88143C2214yes—
65C2×#88143C2214yes—
66C2×#88143C2214yes—
67C2×#88143C2214yes—
68C2×#88143C2214yes—
69C2×#88142C2214yes—
70C2×#88142C2212yes—
71C2×#88140C2214yes—
72C2×#88135C2214yes—
73C2×#88132C2214yes—
74C2×#88131C2214yes—
75#11719184C22116yes—
76C2×#88130C2212yes—
77C2×#88130C2214yes—
78C2×#88129C2211yescharacteristic
79C2×C4×D52C2211yescharacteristic
80C2×#88126C2214yes—
81C2×#88126C2212yes—
82C2×#88124C2212yes—
83C2×#88124C2214yes—
84C2×#88124C2212yes—
85C2×#88124C2212yes—
86C2×#88124C2211yescharacteristic
87C2×#88124C2212yes—
88C2×#88124C22116yescomplemented
89C2×C4×Dic26C2214yes—
90C2×C4×Dic26C2211yescharacteristic
91C22×Q8×C13C2312yes—
92C22×Q8×C13C2312yes—
93C23×C4×C13C2311yescharacteristic
94C23×C4×C13C2311yescharacteristic
95C23×C4×C13C2311yescharacteristic
96C22×C22⋊D13C2312yes—
97C23×Dic13C2312yes—
98C23×Dic13C2312yes—
99C22×D52C2311yescharacteristic
100C22×C4×D13C2312yes—
101C22×C4×D13C2314yes—
102C22×Dic26C2311yescharacteristic
103C22×Dic26C2314yes—
104C13×C4⋊Q8C2318yes—
105C13×C4⋊Q8C2318yes—
106C13×#125C23116yes—
107C13×C22⋊Q8C23116yes—
108C13×C22⋊Q8C23116yes—
109C4×Q8×C13C23116yes—
110C4×Q8×C13C23116yes—
111C13×#117C23116yes—
112C2×C13×C4⋊C4C2314yes—
113C2×C13×C4⋊C4C2312yes—
114C2×C13×C4⋊C4C2312yes—
115C2×C13×C4⋊C4C2312yes—
116C2×C13×C4⋊C4C2312yes—
117C2×C13×C4⋊C4C2314yes—
118C2×C13×C22⋊C4C2314yes—
119C2×C42×C13C2311yescharacteristic
120C2×C42×C13C2314yes—
121C2×C42×C13C2311yescharacteristic
122C2×C42×C13C2311yescharacteristic
123C2×C42×C13C2311yescharacteristic
124C2×C42×C13C2318yes—
125C2×C22⋊Dic13C2312yes—
126#88200C23132yes—
127#88200C23116yes—
128#88200C23116yes—
129Q8×Dic13C23116yes—
130Q8×Dic13C23116yes—
131#88198C23132yes—
132#88184C2318yes—
133#88183C23116yes—
134C4×C22⋊D13C23116yes—
135C2×#6103C2312yes—
136C2×#6103C2312yes—
137C2×#6103C2312yes—
138C2×#6103C2314yes—
139C2×#6103C2312yes—
140C2×#6103C2314yes—
141C2×#6103C2314yes—
142C2×C4⋊Dic13C2311yescharacteristic
143C2×C4⋊Dic13C2314yes—
144C2×C4⋊Dic13C2312yes—
145C2×C4⋊Dic13C2312yes—
146C2×C4⋊Dic13C2312yes—
147C2×C4⋊Dic13C2312yes—
148C2×C4⋊Dic13C2311yescharacteristic
149C2×C4⋊Dic13C2314yes—
150C2×C4⋊Dic13C2314yes—
151C2×C4⋊Dic13C2318yes—
152C2×C4⋊Dic13C2318yes—
153#88178C2318yes—
154C2×#6101C2312yes—
155C2×#6101C2314yes—
156C2×#6101C2314yes—
157C2×#6101C2314yes—
158C2×#6101C2314yes—
159C2×#6101C2312yes—
160C2×#6101C2312yes—
161C2×#6101C2314yes—
162C2×#6101C2314yes—
163C2×#6101C23116yes—
164C2×#6101C23116yes—
165C2×#6101C2312yes—
166C2×#6101C2314yes—
167C2×#6101C2314yes—
168C2×#6101C2314yes—
169C2×C4×Dic13C2312yes—
170C2×C4×Dic13C2314yes—
171C2×C4×Dic13C2314yes—
172C2×C4×Dic13C2314yes—
173#88152C23132yes—
174#88152C23132yes—
175#88152C23132yes—
176#88151C23132yes—
177#88150C23132yes—
178#88148C23132yes—
179#88146C23116yes—
180C4⋊C4×D13C23116yes—
181#88144C23116yes—
182#88144C23132yes—
183#88144C23132yes—
184#88143C23132yes—
185#88143C23132yes—
186#88143C23132yes—
187#88143C23132yes—
188#88143C23132yes—
189#88142C23116yes—
190#88142C23132yes—
191#88140C23132yes—
192#88135C23132yes—
193#88132C23132yes—
194#88131C23132yes—
195#88130C23116yes—
196#88130C23132yes—
197#88129C2318yes—
198C4×D52C2318yes—
199#88126C23116yes—
200#88126C23132yes—
201#88124C23116yes—
202#88124C23116yes—
203#88124C23116yes—
204#88124C23116yes—
205#88124C2318yes—
206#88124C23132yes—
207C4×Dic26C2318yes—
208C4×Dic26C23132yes—
209C2×#3563—131nomaximal, Sylow
210C24×C13C2411yescharacteristic
211C23×D13C2412yes—
212C2×Q8×C13—28no—
213C2×Q8×C13—44no—
214C2×Q8×C13C2418yes—
215C2×Q8×C13C2418yes—
216C22×C4×C13—24no—
217C22×C4×C13—24no—
218C22×C4×C13—42no—
219C22×C4×C13C2414yes—
220C22×C4×C13C2414yes—
221C22×C4×C13C2411yescharacteristic
222C22×C4×C13C2411yescharacteristic
223C22×C4×C13C2411yescharacteristic
224C22×C4×C13C2411yescharacteristic
225C22×C4×C13C2414yes—
226C22×C4×C13C2411yescharacteristic
227C22×C4×C13C2414yes—
228C22×C4×C13C2414yes—
229C22×C4×C13C2411yescharacteristic
230C2×C22⋊D13—28no—
231C2×C22⋊D13C2418yes—
232C22×Dic13—28no—
233C22×Dic13—44no—
234C22×Dic13C2418yes—
235C22×Dic13C2412yes—
236C22×Dic13C2412yes—
237C22×Dic13C2412yes—
238C22×Dic13C2414yes—
239C22×Dic13C2414yes—
240C22×Dic13C2418yes—
241C2×D52—42no—
242C2×D52C2414yes—
243C2×C4×D13—28no—
244C2×C4×D13—48no—
245C2×C4×D13C2418yes—
246C2×C4×D13C24116yes—
247C2×Dic26—42no—
248C2×Dic26—48no—
249C2×Dic26C2414yes—
250C2×Dic26C24116yes—
251C13×C4⋊C4C24116yes—
252C13×C4⋊C4C2418yes—
253C13×C4⋊C4C2418yes—
254C13×C4⋊C4C2418yes—
255C13×C4⋊C4C2418yes—
256C13×C4⋊C4C24116yes—
257C13×C22⋊C4C24116yes—
258C42×C13C2414yes—
259C42×C13C24116yes—
260C42×C13C2414yes—
261C42×C13C2414yes—
262C42×C13C2414yes—
263C22⋊Dic13C2418yes—
264#6103C2418yes—
265#6103C2418yes—
266#6103C2418yes—
267#6103C24116yes—
268#6103C2418yes—
269#6103C24116yes—
270#6103C24116yes—
271C4⋊Dic13C2414yes—
272C4⋊Dic13C24116yes—
273C4⋊Dic13C2418yes—
274C4⋊Dic13C2418yes—
275C4⋊Dic13C2418yes—
276C4⋊Dic13C2418yes—
277C4⋊Dic13C2414yes—
278C4⋊Dic13C24116yes—
279C4⋊Dic13C24116yes—
280#6101C2418yes—
281#6101C24116yes—
282#6101C24116yes—
283#6101C24116yes—
284#6101C24116yes—
285#6101C2418yes—
286#6101C2418yes—
287#6101C24116yes—
288#6101C24116yes—
289#6101C2418yes—
290#6101C24116yes—
291#6101C24116yes—
292#6101C24116yes—
293C4×Dic13C2418yes—
294C4×Dic13C24116yes—
295C4×Dic13C24116yes—
296C4×Dic13C24116yes—
297#3563—1332no—
298C2×#564—132no—
299C2×#563—132no—
300C2×#557—132no—
301C2×#554—132no—
302C2×#552—132no—
303C2×#552—132no—
304C2×#552—134no—
305C2×#544—132no—
306C2×#544—132no—
307C2×#541—132no—
308C2×#541—134no—
309C2×#539—132no—
310C2×#533D1311yescharacteristic, complemented
311C2×#529—131no—
312C22×#125—131no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C132−1+414yes—
316C23×C13C2512yes—
317C23×C13C2511yescharacteristic
318C22×D13—24no—
319C22×D13—24no—
320C22×D13—24no—
321C22×D13C2514yes—
322Q8×C13—216no—
323Q8×C13—48no—
324C2×C4×C13—28no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—28no—
329C2×C4×C13—28no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—28no—
333C2×C4×C13—44no—
334C2×C4×C132−1+414yes—
335C2×C4×C13C2518yes—
336C2×C4×C13C2518yes—
337C2×C4×C13C2512yes—
338C2×C4×C13C2512yes—
339C2×C4×C13C2512yes—
340C2×C4×C13C2512yes—
341C2×C4×C13C2512yes—
342C2×C4×C13C2512yes—
343C22⋊D13—216no—
344C2×Dic13—24no—
345C2×Dic13—216no—
346C2×Dic13—28no—
347C2×Dic13—24no—
348C2×Dic13—24no—
349C2×Dic13—28no—
350C2×Dic13—48no—
351C2×Dic13C2514yes—
352C2×Dic13C2514yes—
353C2×Dic13C2514yes—
354C2×Dic13C2518yes—
355C2×Dic13C2518yes—
356D52—44no—
357C4×D13—216no—
358C4×D13—416no—
359Dic26—44no—
360Dic26—416no—
361#564—1332no—
362#563—1332no—
363#557—1332no—
364#554—1332no—
365#552—1332no—
366#552—1332no—
367#552—1364no—
368#544—1332no—
369#544—1332no—
370#541—1332no—
371#541—1364no—
372#539—1332no—
373#533C2×D13116yescomplemented
374C2×C4⋊Q8—134no—
375C2×C4⋊Q8—132no—
376C2×C4⋊Q8—134no—
377C2×C4⋊Q8C2×D1311yescharacteristic
378C2×C4⋊Q8C2×D1311yescharacteristic
379#529—1316no—
380C2×#126—134no—
381C2×#126—134no—
382C2×#126—134no—
383C2×#126—132no—
384C2×#126—134no—
385C2×#125—134no—
386C2×#125—134no—
387C2×#125—134no—
388C2×#125—134no—
389C2×#125—134no—
390C2×#125—134no—
391C2×#125—134no—
392C2×#125—132no—
393C2×#125—132no—
394C2×#125—132no—
395C2×#125—132no—
396C2×#125—132no—
397C2×#125—131no—
398C2×#125—134no—
399C2×#125—1316no—
400C2×#125C2×D1312yes—
401C2×#124—131no—
402C2×#123—132no—
403C2×#123—134no—
404C2×#123—134no—
405C2×C22⋊Q8—134no—
406C2×C22⋊Q8—132no—
407C2×C22⋊Q8—132no—
408C2×C22⋊Q8—131no—
409C2×C22⋊Q8—134no—
410C2×C22⋊Q8—134no—
411C2×C22⋊Q8—134no—
412C2×C22⋊Q8C2×D1312yes—
413C2×C22⋊Q8C2×D1312yes—
414C2×#121—131no—
415C2×C4×Q8—132no—
416C2×C4×Q8—132no—
417C2×C4×Q8—131no—
418C2×C4×Q8—134no—
419C2×C4×Q8C2×D1312yes—
420C2×C4×Q8C2×D1312yes—
421C2×C4×D4—132no—
422C2×C4×D4—134no—
423C2×C4×D4—131no—
424C2×#117—132no—
425C2×#117—134no—
426C2×#117—132no—
427C2×#117—134no—
428C2×#117C2×D1312yes—
429C22×C4⋊C4—132no—
430C22×C4⋊C4—132no—
431C22×C4⋊C4—131no—
432C22×C4⋊C4—131no—
433C22×C4⋊C4—132no—
434C22×C42C2×D1311yescharacteristic
435C22×C13—22no—
436C22×C13—22no—
437C22×C13—28no—
438C22×C13C2×2−1+414yes—
439C22×C13C2×2−1+412yes—
440C22×C13C2×2−1+412yes—
441C22×C13#58512yes—
442C22×C13C2611yescharacteristic
443C2×D13—24no—
444C2×D13—24no—
445C2×D13—24no—
446C2×D13—48no—
447C4×C13—22no—
448C4×C13—22no—
449C4×C13—22no—
450C4×C13—28no—
451C4×C13—28no—
452C4×C13—22no—
453C4×C13—22no—
454C4×C13C2×2−1+414yes—
455Dic13—24no—
456Dic13—28no—
457Dic13—24no—
458Dic13—24no—
459Dic13—28no—
460C22×Q8—134no—
461C22×Q8—131no—
462C22×Q8C22×D1312yes—
463C22×Q8C22×D1312yes—
464C22×D4—132no—
465C22×D4—131no—
466C23×C4—132no—
467C23×C4—132no—
468C23×C4—132no—
469C23×C4—134no—
470C23×C4C22×D1311yescharacteristic
471C23×C4C22×D1311yescharacteristic
472C23×C4C22×D1311yescharacteristic
473C4⋊Q8—1332no—
474C4⋊Q8—1316no—
475C4⋊Q8—1332no—
476C4⋊Q8C22×D1318yes—
477C4⋊Q8C22×D1318yes—
478#126—1332no—
479#126—1332no—
480#126—1332no—
481#126—1316no—
482#126—1332no—
483#125—1332no—
484#125—1332no—
485#125—1332no—
486#125—1332no—
487#125—1332no—
488#125—1316no—
489#125—1332no—
490#125—1332no—
491#125—1316no—
492#125—1316no—
493#125—1316no—
494#125—1316no—
495#125—138no—
496#125—1332no—
497#125C22×D13116yes—
498#124—138no—
499#123—1316no—
500#123—1332no—
501#123—1332no—
502C22⋊Q8—1332no—
503C22⋊Q8—1316no—
504C22⋊Q8—1316no—
505C22⋊Q8—138no—
506C22⋊Q8—1332no—
507C22⋊Q8—1332no—
508C22⋊Q8—1332no—
509C22⋊Q8C22×D13116yes—
510C22⋊Q8C22×D13116yes—
511#121—138no—
512C4×Q8—1316no—
513C4×Q8—1316no—
514C4×Q8—138no—
515C4×Q8—1332no—
516C4×Q8C22×D13116yes—
517C4×Q8C22×D13116yes—
518C4×D4—1316no—
519C4×D4—1332no—
520C4×D4—138no—
521#117—1316no—
522#117—1332no—
523#117—1316no—
524#117—1332no—
525#117C22×D13116yes—
526C2×C4⋊C4—132no—
527C2×C4⋊C4—132no—
528C2×C4⋊C4—134no—
529C2×C4⋊C4—132no—
530C2×C4⋊C4—134no—
531C2×C4⋊C4—134no—
532C2×C4⋊C4—134no—
533C2×C4⋊C4—134no—
534C2×C4⋊C4—132no—
535C2×C4⋊C4—1316no—
536C2×C4⋊C4—1316no—
537C2×C4⋊C4—138no—
538C2×C4⋊C4—138no—
539C2×C4⋊C4—134no—
540C2×C4⋊C4—134no—
541C2×C4⋊C4—134no—
542C2×C4⋊C4—132no—
543C2×C4⋊C4—132no—
544C2×C4⋊C4—131no—
545C2×C4⋊C4—134no—
546C2×C4⋊C4—132no—
547C2×C4⋊C4—132no—
548C2×C4⋊C4—131no—
549C2×C4⋊C4—134no—
550C2×C4⋊C4—134no—
551C2×C4⋊C4—134no—
552C2×C4⋊C4—1316no—
553C2×C4⋊C4C22×D1312yes—
554C2×C4⋊C4C22×D1312yes—
555C2×C4⋊C4C22×D1312yes—
556C2×C4⋊C4C22×D1314yes—
557C2×C4⋊C4C22×D1314yes—
558C2×C4⋊C4C22×D1312yes—
559C2×C22⋊C4—132no—
560C2×C22⋊C4—132no—
561C2×C22⋊C4—132no—
562C2×C22⋊C4—134no—
563C2×C22⋊C4—132no—
564C2×C22⋊C4—134no—
565C2×C22⋊C4—134no—
566C2×C22⋊C4—132no—
567C2×C22⋊C4C22×D1314yes—
568C2×C42—134no—
569C2×C42—132no—
570C2×C42—134no—
571C2×C42—134no—
572C2×C42C22×D1311yescharacteristic
573C2×C42C22×D1314yes—
574C2×C42C22×D1311yescharacteristic
575C2×C42C22×D1311yescharacteristic
576C2×C42C22×D1311yescharacteristic
577C2×C42C22×D1318yes—
578C2×C13—24no—
579C2×C13#356314yescomplemented
580C2×C13C22×2−1+411yescharacteristic
581C2×C13C22×2−1+411yescharacteristic
582C2×C13C2×#58511yescharacteristic
583D13—44no—
584C24—132no—
585C24C23×D1311yescharacteristic
586C2×Q8—28no—
587C2×Q8—44no—
588C2×Q8—1316no—
589C2×Q8—134no—
590C2×Q8—522no—
591C2×Q8—528no—
592C2×Q8C23×D1318yes—
593C2×Q8C23×D1318yes—
594C2×D4—138no—
595C2×D4—134no—
596C2×D4—268no—
597C2×D4—522no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—42no—
601C22×C4—138no—
602C22×C4—132no—
603C22×C4—132no—
604C22×C4—134no—
605C22×C4—132no—
606C22×C4—134no—
607C22×C4—138no—
608C22×C4—138no—
609C22×C4—1316no—
610C22×C4—268no—
611C22×C4—268no—
612C22×C4—528no—
613C22×C4—524no—
614C22×C4C23×D1314yes—
615C22×C4C23×D1314yes—
616C22×C4C23×D1314yes—
617C22×C4C23×D1314yes—
618C22×C4C23×D1311yescharacteristic
619C22×C4C23×D1311yescharacteristic
620C22×C4C23×D1311yescharacteristic
621C22×C4C23×D1311yescharacteristic
622C22×C4C23×D1311yescharacteristic
623C22×C4C23×D1314yes—
624C22×C4C23×D1311yescharacteristic
625C4⋊C4—138no—
626C4⋊C4—138no—
627C4⋊C4—1316no—
628C4⋊C4—138no—
629C4⋊C4—1316no—
630C4⋊C4—1316no—
631C4⋊C4—1316no—
632C4⋊C4—1316no—
633C4⋊C4—138no—
634C4⋊C4—1316no—
635C4⋊C4—1316no—
636C4⋊C4—1316no—
637C4⋊C4—138no—
638C4⋊C4—138no—
639C4⋊C4—134no—
640C4⋊C4—1316no—
641C4⋊C4—138no—
642C4⋊C4—138no—
643C4⋊C4—134no—
644C4⋊C4—1316no—
645C4⋊C4—1316no—
646C4⋊C4—1316no—
647C4⋊C4C23×D1318yes—
648C4⋊C4C23×D1318yes—
649C4⋊C4C23×D1318yes—
650C4⋊C4C23×D13116yes—
651C4⋊C4C23×D13116yes—
652C4⋊C4C23×D1318yes—
653C22⋊C4—138no—
654C22⋊C4—138no—
655C22⋊C4—138no—
656C22⋊C4—1316no—
657C22⋊C4—138no—
658C22⋊C4—1316no—
659C22⋊C4—1316no—
660C22⋊C4—138no—
661C22⋊C4C23×D13116yes—
662C42—1316no—
663C42—138no—
664C42—1316no—
665C42—1316no—
666C42C23×D1314yes—
667C42C23×D1314yes—
668C42C23×D1314yes—
669C42C23×D1314yes—
670C42C23×D13116yes—
671C13C2×#356311yescharacteristic, complemented, Sylow
672C23—22no—
673C23—22no—
674C23—134no—
675C23—264no—
676C23—264no—
677C23—264no—
678C23#8825414yes—
679C23C24×D1312yes—
680C23C24×D1311yescharacteristic
681Q8—216no—
682Q8—48no—
683Q8—524no—
684Q8—5216no—
685D4—2616no—
686D4—524no—
687C2×C4—28no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—28no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—44no—
697C2×C4—134no—
698C2×C4—134no—
699C2×C4—134no—
700C2×C4—138no—
701C2×C4—138no—
702C2×C4—2616no—
703C2×C4—268no—
704C2×C4—264no—
705C2×C4—264no—
706C2×C4—268no—
707C2×C4—264no—
708C2×C4—2616no—
709C2×C4—5216no—
710C2×C4—528no—
711C2×C4#8825714yes—
712C2×C4C24×D1318yes—
713C2×C4C24×D1318yes—
714C2×C4C24×D1312yes—
715C2×C4C24×D1312yes—
716C2×C4C24×D1312yes—
717C2×C4C24×D1312yes—
718C2×C4C24×D1312yes—
719C2×C4C24×D1312yes—
720C22—22no—
721C22—22no—
722C22—28no—
723C22—264no—
724C22—264no—
725C22—264no—
726C22—528no—
727C22C2×#8825414yes—
728C22C2×#8825412yes—
729C22C2×#8825712yes—
730C22#1171964812yes—
731C22C25×D1311yescharacteristic
732C4—22no—
733C4—28no—
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—28no—
739C4—264no—
740C4—268no—
741C4—264no—
742C4—268no—
743C4—264no—
744C4C2×#8825714yes—
745C2—24no—
746C2—524no—
747C2#1312944614yesdirect product factor
748C2C22×#8825711yescharacteristic
749C2C22×#8825411yescharacteristic
750C2C2×#1171964811yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#533C2
socleC23×C13C25
prime radicalC2×#88184C22
hypercenterC2×#533D13
hypocenterC13C2×#3563
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #13129446C2direct (N × H)
2. C2×C13⋊#564C2semidirect
3. C2×#11719404C2semidirect
4. C2×#11719274C2semidirect
5. C2×#11719340C2semidirect
6. C2×#11719347C2semidirect
7. C2×#11719286C2semidirect
8. C2×#11719236C2semidirect
9. C2×#11719328C2semidirect
10. C2×#11719434C2semidirect
11. C2×#11719436C2semidirect
12. C2×#11719288C2semidirect
15. C22×#88124C2semidirect
16. C2×C13×#533C2semidirect
17. C13×#533C22semidirect
41. #11719436C22semidirect
42. #11719434C22semidirect
43. #11719404C22semidirect
44. C13⋊#564C22semidirect
46. #11719347C22semidirect
47. #11719340C22semidirect
48. #11719328C22semidirect
49. #11719288C22semidirect
50. #11719286C22semidirect
51. #11719274C22semidirect
52. #11719236C22semidirect
88. C2×#88124C22semidirect
310. C2×#533D13semidirect
373. #533C2×D13semidirect
579. C2×C13#3563semidirect
671. C13C2×#3563semidirect
747. C2#13129446direct (N × H)

Maximal subgroups

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

subgroupindex
#131294462
C2×C13⋊#5642
C2×#117194042
C2×#117192742
C2×#117193402
C2×#117193472
C2×#117192862
C2×#117192362
C2×#117193282
C2×#117194342
C2×#117194362
C2×#117192882
C2×#117193502
C2×#117191842
C22×#881242
C2×C13×#5332
C2×#356313