Finite Group Databasebeta

← C2×#13129370 #16770286

Subgroups — C2×#13129370 #16770286

Order 3328.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129370C2132yesmaximal, direct product factor
2C2×#11719404C212yesmaximal, complemented
3C2×#11719405C212yesmaximal, complemented
4C2×#11719395C212yesmaximal, complemented
5C2×#11719400C212yesmaximal, complemented
6C2×#11719219C212yesmaximal, complemented
7C2×#11719212C214yesmaximal, complemented
8C2×#11719212C212yesmaximal, complemented
9C2×#11719394C212yesmaximal, complemented
10C2×#11719403C212yesmaximal, complemented
11C2×#11719397C214yesmaximal, complemented
12C2×#11719220C212yesmaximal, complemented
13C2×#11719215C212yesmaximal, complemented
14C2×#11719182C211yesmaximal, characteristic, complemented
15C2×#11719184C211yesmaximal, characteristic, complemented
16C22×C13×#125C211yesmaximal, characteristic, complemented
17C22×#6127C2212yes—
18C22×#6127C2214yes—
19C2×C13×#125C2212yes—
20C2×C13×#125C2212yes—
21C2×C13×#125C2212yes—
22C2×C13×#125C2212yes—
23C2×C13×#125C22116yescomplemented
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2212yes—
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2212yes—
28C22×C42×C13C2211yescharacteristic
29C2×#88184C2212yes—
30C2×#88184C2214yes—
31C2×#88184C2211yescharacteristic
32C2×#88184C2212yes—
33C2×#88183C2212yes—
34C2×#88183C2214yes—
35C2×C4×C22⋊D13C2212yes—
36C2×C4×C22⋊D13C2214yes—
37C2×#88178C2211yescharacteristic
38#11719405C22132yescomplemented
39#11719404C22132yescomplemented
40#11719403C22132yescomplemented
41#11719400C22132yescomplemented
42#11719397C22164yescomplemented
43#11719395C22132yescomplemented
44#11719394C22132yescomplemented
45#11719220C22132yescomplemented
46#11719219C22132yescomplemented
47C2×#88152C2214yes—
48C2×#88152C2214yes—
49#11719215C22132yescomplemented
50C2×#88151C2214yes—
51C2×#88151C2214yes—
52C2×#88150C2214yes—
53C2×#88150C2214yes—
54C2×#88150C2214yes—
55C2×#88150C2214yes—
56#11719212C22132yescomplemented
57#11719212C22164yescomplemented
58C2×#88149C2214yes—
59C2×#88149C2214yes—
60C2×#88149C2212yes—
61C2×#88149C2212yes—
62C2×#88149C2214yes—
63C2×#88148C2214yes—
64C2×#88148C2214yes—
65C2×#88148C2214yes—
66C2×#88148C2214yes—
67C2×#88148C2214yes—
68C2×#88147C2212yes—
69C2×#88147C2212yes—
70C2×#88147C2214yes—
71C2×#88146C2212yes—
72C2×C4⋊C4×D13C2212yes—
73C2×C4⋊C4×D13C2214yes—
74C2×#88144C2212yes—
75C2×#88143C2214yes—
76C2×#88142C2214yes—
77C2×#88142C2212yes—
78#11719184C22116yescomplemented
79C2×#88130C2212yes—
80#11719182C22116yescomplemented
81C2×#88129C2211yescharacteristic
82C2×#88129C2212yes—
83C2×#88128C2211yescharacteristic
84C2×C4×D52C2211yescharacteristic
85C2×C4×D52C2212yes—
86C2×C4×D52C2212yes—
87C2×#88126C2212yes—
88C2×#88124C2211yescharacteristic
89C2×#88123C2211yescharacteristic
90C2×C4×Dic26C2211yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C23×C4×C13C2311yescharacteristic
93C23×C4×C13C2312yes—
94C23×C4×C13C2311yescharacteristic
95C23×C4×C13C2312yes—
96C22×C22⋊D13C2312yes—
97C22×C22⋊D13C2314yes—
98C2×#6127—48no—
99C2×#6127—416no—
100C2×#6127C23116yes—
101C2×#6127C23132yes—
102C22×D52C2312yes—
103C22×D52C2312yes—
104C22×D52C2311yescharacteristic
105C22×D52C2312yes—
106C22×D52C2314yes—
107C22×D52C2314yes—
108C22×C4×D13C2312yes—
109C22×C4×D13C2314yes—
110C22×C4×D13C2314yes—
111C22×C4×D13C2314yes—
112C22×C4×D13C2314yes—
113C22×Dic26C2311yescharacteristic
114C22×Dic26C2312yes—
115C22×Dic26C2314yes—
116C13×#125C23116yes—
117C13×#125C23116yes—
118C13×#125C23116yes—
119C13×#125C23116yes—
120C2×C13×C4⋊C4C2312yes—
121C2×C13×C4⋊C4C2314yes—
122C2×C13×C4⋊C4C2314yes—
123C2×C13×C4⋊C4C2312yes—
124C2×C13×C4⋊C4C2314yes—
125C2×C13×C4⋊C4C2312yes—
126C2×C13×C4⋊C4C2312yes—
127C2×C13×C4⋊C4C2314yes—
128C2×C13×C4⋊C4C2318yes—
129C2×C13×C4⋊C4C23116yes—
130C2×C13×C4⋊C4C23116yes—
131C2×C13×C4⋊C4C2318yes—
132C2×C42×C13C2311yescharacteristic
133C2×C42×C13C2311yescharacteristic
134C2×C42×C13C2311yescharacteristic
135C2×C42×C13C2311yescharacteristic
136C2×C42×C13C2318yes—
137C2×C22⋊Dic13C2312yes—
138#88184C23116yes—
139#88184C23116yes—
140#88184C2318yes—
141#88184C23132yes—
142#88183C23116yes—
143#88183C23132yes—
144C4×C22⋊D13C23116yes—
145C4×C22⋊D13C23132yes—
146C2×#6103C2312yes—
147C2×#6103C2312yes—
148C2×#6103C2314yes—
149C2×#6103C2314yes—
150C2×#6103C2312yes—
151C2×#6103C2312yes—
152C2×#6103C2314yes—
153C2×#6103C2314yes—
154C2×#6103C2314yes—
155C2×#6103C2314yes—
156C2×#6103C2314yes—
157C2×C4⋊Dic13C2311yescharacteristic
158C2×C4⋊Dic13C2312yes—
159C2×C4⋊Dic13C2312yes—
160C2×C4⋊Dic13C2311yescharacteristic
161C2×C4⋊Dic13C2314yes—
162#88178C2318yes—
163C2×#6101C2312yes—
164C2×#6101C2312yes—
165C2×#6101C2312yes—
166C2×#6101C2312yes—
167C2×#6101C2314yes—
168C2×#6101C2314yes—
169C2×#6101C2314yes—
170C2×C4×Dic13C2312yes—
171C2×C4×Dic13C2314yes—
172#88152C23132yes—
173#88152C23132yes—
174#88151C23132yes—
175#88151C23132yes—
176#88150C23132yes—
177#88150C23132yes—
178#88150C23132yes—
179#88150C23132yes—
180#88149C23116yes—
181#88149C23132yes—
182#88149C23132yes—
183#88149C23132yes—
184#88149C23116yes—
185#88148C23132yes—
186#88148C23132yes—
187#88148C23132yes—
188#88148C23132yes—
189#88148C23132yes—
190#88147C23116yes—
191#88147C23132yes—
192#88147C23116yes—
193#88146C23116yes—
194C4⋊C4×D13C23116yes—
195C4⋊C4×D13C23132yes—
196#88144C23116yes—
197#88143C23132yes—
198#88142C23116yes—
199#88142C23132yes—
200#88130C23116yes—
201#88129C23116yes—
202#88129C2318yes—
203#88128C2318yes—
204C4×D52C23116yes—
205C4×D52C23116yes—
206C4×D52C2318yes—
207#88126C23116yes—
208#88124C2318yes—
209#88123C2318yes—
210C4×Dic26C2318yes—
211C2×#3559—131nomaximal, Sylow
212C24×C13C2411yescharacteristic
213C23×D13C2412yes—
214C23×D13C2414yes—
215C22×C4×C13—24no—
216C22×C4×C13—28no—
217C22×C4×C13—24no—
218C22×C4×C13—42no—
219C22×C4×C13—44no—
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×C13C2418yes—
230C22×C4×C13C2414yes—
231C22×C4×C13C2418yes—
232C22×C4×C13C2411yescharacteristic
233C2×C22⋊D13—216no—
234C2×C22⋊D13—28no—
235C2×C22⋊D13C2418yes—
236C2×C22⋊D13C24116yes—
237C22×Dic13C2412yes—
238C22×Dic13C2412yes—
239C22×Dic13C2412yes—
240C22×Dic13C2414yes—
241#6127—432no—
242#6127—464no—
243C2×D52—28no—
244C2×D52—42no—
245C2×D52—48no—
246C2×D52—44no—
247C2×D52—44no—
248C2×D52—48no—
249C2×D52C2418yes—
250C2×D52C2418yes—
251C2×D52C2414yes—
252C2×D52C2418yes—
253C2×D52C24116yes—
254C2×D52C24116yes—
255C2×C4×D13—28no—
256C2×C4×D13—48no—
257C2×C4×D13—48no—
258C2×C4×D13—48no—
259C2×C4×D13—48no—
260C2×C4×D13C2418yes—
261C2×C4×D13C24116yes—
262C2×C4×D13C24116yes—
263C2×C4×D13C24116yes—
264C2×C4×D13C24116yes—
265C2×Dic26—42no—
266C2×Dic26—44no—
267C2×Dic26—48no—
268C2×Dic26C2414yes—
269C2×Dic26C2418yes—
270C2×Dic26C24116yes—
271C13×C4⋊C4C2418yes—
272C13×C4⋊C4C24116yes—
273C13×C4⋊C4C24116yes—
274C13×C4⋊C4C2418yes—
275C13×C4⋊C4C24116yes—
276C13×C4⋊C4C2418yes—
277C13×C4⋊C4C2418yes—
278C13×C4⋊C4C24116yes—
279C42×C13C2414yes—
280C42×C13C2414yes—
281C42×C13C2414yes—
282C42×C13C2414yes—
283C22⋊Dic13C2418yes—
284#6103C2418yes—
285#6103C2418yes—
286#6103C24116yes—
287#6103C24116yes—
288#6103C2418yes—
289#6103C2418yes—
290#6103C24116yes—
291#6103C24116yes—
292#6103C24116yes—
293#6103C24116yes—
294#6103C24116yes—
295C4⋊Dic13C2414yes—
296C4⋊Dic13C2418yes—
297C4⋊Dic13C2418yes—
298C4⋊Dic13C2414yes—
299C4⋊Dic13C24116yes—
300#6101C2418yes—
301#6101C2418yes—
302#6101C2418yes—
303#6101C2418yes—
304#6101C24116yes—
305#6101C24116yes—
306#6101C24116yes—
307C4×Dic13C2418yes—
308C4×Dic13C24116yes—
309#3559—1332no—
310C2×#563—132no—
311C2×#562—132no—
312C2×#554—132no—
313C2×#553—132no—
314C2×#553—132no—
315C2×#547—134no—
316C2×#547—132no—
317C2×#544—132no—
318C2×#540—132no—
319C2×#539—134no—
320C2×#539—132no—
321C2×#537—132no—
322C2×#532—131no—
323C2×#529—131no—
324C22×#125D1311yescharacteristic, complemented
325C23×C13—22no—
326C23×C13—22no—
327C23×C13H(5,𝔽2)14yes—
328C23×C13C2512yes—
329C23×C13C2511yescharacteristic
330C22×D13—24no—
331C22×D13—28no—
332C22×D13—24no—
333C22×D13—28no—
334C22×D13—28no—
335C22×D13—24no—
336C22×D13C2514yes—
337C22×D13C2518yes—
338C2×C4×C13—22no—
339C2×C4×C13—28no—
340C2×C4×C13—22no—
341C2×C4×C13—28no—
342C2×C4×C13—216no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—28no—
346C2×C4×C13—22no—
347C2×C4×C13—28no—
348C2×C4×C13—44no—
349C2×C4×C13—48no—
350C2×C4×C132−1+414yes—
351C2×C4×C13C2518yes—
352C2×C4×C13C2512yes—
353C2×C4×C13C2512yes—
354C2×C4×C13C2512yes—
355C2×C4×C13C2512yes—
356C2×C4×C13C2518yes—
357C2×C4×C13C2512yes—
358C2×C4×C13C2512yes—
359C22⋊D13—232no—
360C22⋊D13—216no—
361C2×Dic13—28no—
362C2×Dic13—24no—
363C2×Dic13—24no—
364C2×Dic13—24no—
365C2×Dic13C2514yes—
366C2×Dic13C2514yes—
367C2×Dic13C2514yes—
368C2×Dic13C2518yes—
369D52—216no—
370D52—44no—
371D52—416no—
372D52—48no—
373D52—48no—
374D52—416no—
375C4×D13—216no—
376C4×D13—416no—
377C4×D13—416no—
378C4×D13—416no—
379C4×D13—416no—
380Dic26—44no—
381Dic26—48no—
382Dic26—416no—
383C22×#41—132no—
384C22×#41—134no—
385#563—1332no—
386#562—1332no—
387#554—1332no—
388#553—1332no—
389#553—1332no—
390#547—1364no—
391#547—1332no—
392#544—1332no—
393#540—1332no—
394#539—1364no—
395#539—1332no—
396#537—1332no—
397#532—1316no—
398C2×C4⋊Q8—132no—
399C2×C4⋊Q8—134no—
400C2×C4⋊Q8—131no—
401C2×#127—131no—
402#529—1316no—
403C2×#126—134no—
404C2×#126—134no—
405C2×#126—132no—
406C2×#125—134no—
407C2×#125—132no—
408C2×#125—131no—
409C2×#125C2×D1312yes—
410C2×#125C2×D1312yes—
411C2×#125C2×D1312yes—
412C2×#125C2×D1312yes—
413C2×#125C2×D13116yescomplemented
414C2×#124—131no—
415C2×#124—132no—
416C2×#123—132no—
417C2×#123—134no—
418C2×#123—134no—
419C2×#123—134no—
420C2×#123—134no—
421C2×#123—134no—
422C2×#123—134no—
423C2×C22⋊Q8—131no—
424C2×C22⋊Q8—134no—
425C2×C22⋊Q8—134no—
426C2×C22⋊Q8—134no—
427C2×C22⋊Q8—134no—
428C2×C22⋊Q8—134no—
429C2×C22⋊Q8—134no—
430C2×#121—131no—
431C2×#121—132no—
432C2×#121—132no—
433C2×#121—134no—
434C2×#121—134no—
435C2×#121—134no—
436C2×#121—132no—
437C2×#121—134no—
438C2×#121—132no—
439C2×C4×Q8—131no—
440C2×C4×D4—132no—
441C2×C4×D4—134no—
442C2×C4×D4—134no—
443C2×C4×D4—132no—
444C2×C4×D4—132no—
445C2×C4×D4—131no—
446C2×C4×D4—132no—
447C2×C4×D4—132no—
448C2×#117—132no—
449C2×#117—132no—
450C22×C4⋊C4—134no—
451C22×C4⋊C4—132no—
452C22×C4⋊C4C2×D1312yes—
453C22×C4⋊C4C2×D1311yescharacteristic
454C22×C4⋊C4C2×D1312yes—
455C22×C4⋊C4C2×D1311yescharacteristic
456C22×C42C2×D1311yescharacteristic
457C22×C13—22no—
458C22×C13—22no—
459C22×C13—28no—
460C22×C13C2×H(5,𝔽2)14yes—
461C22×C13C2×H(5,𝔽2)12yes—
462C22×C13C2×2−1+412yes—
463C22×C13#58512yes—
464C22×C13C2611yescharacteristic
465C2×D13—24no—
466C2×D13—28no—
467C2×D13—24no—
468C2×D13—28no—
469C2×D13—28no—
470C2×D13—24no—
471C2×D13—48no—
472C2×D13—416no—
473C4×C13—22no—
474C4×C13—28no—
475C4×C13—22no—
476C4×C13—22no—
477C4×C13—22no—
478C4×C13—28no—
479C4×C13—22no—
480C4×C13C2×2−1+414yes—
481Dic13—28no—
482Dic13—24no—
483Dic13—24no—
484Dic13—24no—
485C2×#41—1316no—
486C2×#41—1332no—
487C2×#41—528no—
488C2×#41—5216no—
489C22×Q8—131no—
490C22×Q8—134no—
491C22×Q8—132no—
492C22×D4—132no—
493C22×D4—134no—
494C22×D4—132no—
495C22×D4—134no—
496C22×D4—131no—
497C22×D4—132no—
498C22×D4—134no—
499C22×D4—132no—
500C23×C4—132no—
501C23×C4—134no—
502C23×C4—134no—
503C23×C4—134no—
504C23×C4—134no—
505C23×C4C22×D1312yes—
506C23×C4C22×D1311yescharacteristic
507C23×C4C22×D1311yescharacteristic
508C23×C4C22×D1312yes—
509C23×C4C22×D1311yescharacteristic
510C4⋊Q8—1316no—
511C4⋊Q8—1332no—
512C4⋊Q8—138no—
513#127—138no—
514#126—1332no—
515#126—1332no—
516#126—1316no—
517#125—1332no—
518#125—1316no—
519#125—138no—
520#125C22×D13116yes—
521#125C22×D13116yes—
522#125C22×D13116yes—
523#125C22×D13116yes—
524#124—138no—
525#124—1316no—
526#123—1316no—
527#123—1332no—
528#123—1332no—
529#123—1332no—
530#123—1332no—
531#123—1332no—
532#123—1332no—
533C22⋊Q8—138no—
534C22⋊Q8—1332no—
535C22⋊Q8—1332no—
536C22⋊Q8—1332no—
537C22⋊Q8—1332no—
538C22⋊Q8—1332no—
539C22⋊Q8—1332no—
540#121—138no—
541#121—1316no—
542#121—1316no—
543#121—1332no—
544#121—1332no—
545#121—1332no—
546#121—1316no—
547#121—1332no—
548#121—1316no—
549C4×Q8—138no—
550C4×D4—1316no—
551C4×D4—1332no—
552C4×D4—1332no—
553C4×D4—1316no—
554C4×D4—1316no—
555C4×D4—138no—
556C4×D4—1316no—
557C4×D4—1316no—
558#117—1316no—
559#117—1316no—
560C2×C4⋊C4—132no—
561C2×C4⋊C4—132no—
562C2×C4⋊C4—134no—
563C2×C4⋊C4—134no—
564C2×C4⋊C4—134no—
565C2×C4⋊C4—132no—
566C2×C4⋊C4—132no—
567C2×C4⋊C4—132no—
568C2×C4⋊C4—134no—
569C2×C4⋊C4—132no—
570C2×C4⋊C4—131no—
571C2×C4⋊C4—131no—
572C2×C4⋊C4—1332no—
573C2×C4⋊C4—1316no—
574C2×C4⋊C4C22×D1312yes—
575C2×C4⋊C4C22×D1314yes—
576C2×C4⋊C4C22×D1312yes—
577C2×C4⋊C4C22×D1314yes—
578C2×C4⋊C4C22×D1314yes—
579C2×C4⋊C4C22×D1314yes—
580C2×C4⋊C4C22×D1312yes—
581C2×C4⋊C4C22×D1312yes—
582C2×C4⋊C4C22×D13116yes—
583C2×C4⋊C4C22×D1318yes—
584C2×C4⋊C4C22×D13116yes—
585C2×C4⋊C4C22×D1318yes—
586C2×C22⋊C4—132no—
587C2×C22⋊C4—132no—
588C2×C22⋊C4—134no—
589C2×C22⋊C4—132no—
590C2×C22⋊C4—132no—
591C2×C22⋊C4—134no—
592C2×C22⋊C4—134no—
593C2×C22⋊C4—134no—
594C2×C22⋊C4—134no—
595C2×C22⋊C4—134no—
596C2×C22⋊C4—134no—
597C2×C22⋊C4—132no—
598C2×C42—132no—
599C2×C42—134no—
600C2×C42C22×D1311yescharacteristic
601C2×C42C22×D1311yescharacteristic
602C2×C42C22×D1311yescharacteristic
603C2×C42C22×D1311yescharacteristic
604C2×C42C22×D1318yes—
605C2×C13—24no—
606C2×C13#355914yescomplemented
607C2×C13C22×H(5,𝔽2)11yescharacteristic
608C2×C13C22×2−1+411yescharacteristic
609C2×C13C2×#58511yescharacteristic
610D13—44no—
611D13—48no—
612C24—132no—
613C24—134no—
614C24C23×D1311yescharacteristic
615#41—5232no—
616#41—5264no—
617C2×Q8—134no—
618C2×Q8—1316no—
619C2×Q8—138no—
620C2×Q8—528no—
621C2×Q8—524no—
622C2×Q8—522no—
623C2×D4—138no—
624C2×D4—1316no—
625C2×D4—138no—
626C2×D4—1316no—
627C2×D4—134no—
628C2×D4—138no—
629C2×D4—1316no—
630C2×D4—138no—
631C2×D4—268no—
632C2×D4—2616no—
633C2×D4—268no—
634C2×D4—528no—
635C2×D4—524no—
636C2×D4—528no—
637C2×D4—524no—
638C2×D4—522no—
639C22×C4—24no—
640C22×C4—28no—
641C22×C4—24no—
642C22×C4—44no—
643C22×C4—42no—
644C22×C4—132no—
645C22×C4—132no—
646C22×C4—132no—
647C22×C4—134no—
648C22×C4—138no—
649C22×C4—1316no—
650C22×C4—1316no—
651C22×C4—1316no—
652C22×C4—1316no—
653C22×C4—268no—
654C22×C4—528no—
655C22×C4—528no—
656C22×C4—528no—
657C22×C4—528no—
658C22×C4C23×D1314yes—
659C22×C4C23×D1314yes—
660C22×C4C23×D1318yes—
661C22×C4C23×D1314yes—
662C22×C4C23×D1311yescharacteristic
663C22×C4C23×D1311yescharacteristic
664C22×C4C23×D1311yescharacteristic
665C22×C4C23×D1311yescharacteristic
666C22×C4C23×D1311yescharacteristic
667C22×C4C23×D1314yes—
668C22×C4C23×D1314yes—
669C22×C4C23×D1318yes—
670C22×C4C23×D1311yescharacteristic
671C4⋊C4—138no—
672C4⋊C4—138no—
673C4⋊C4—1316no—
674C4⋊C4—1316no—
675C4⋊C4—1316no—
676C4⋊C4—138no—
677C4⋊C4—138no—
678C4⋊C4—138no—
679C4⋊C4—1316no—
680C4⋊C4—138no—
681C4⋊C4—134no—
682C4⋊C4—134no—
683C4⋊C4C23×D1318yes—
684C4⋊C4C23×D13116yes—
685C4⋊C4C23×D1318yes—
686C4⋊C4C23×D13116yes—
687C4⋊C4C23×D13116yes—
688C4⋊C4C23×D13116yes—
689C4⋊C4C23×D1318yes—
690C4⋊C4C23×D1318yes—
691C22⋊C4—138no—
692C22⋊C4—138no—
693C22⋊C4—1316no—
694C22⋊C4—138no—
695C22⋊C4—138no—
696C22⋊C4—1316no—
697C22⋊C4—1316no—
698C22⋊C4—1316no—
699C22⋊C4—1316no—
700C22⋊C4—1316no—
701C22⋊C4—1316no—
702C22⋊C4—138no—
703C42—138no—
704C42—1316no—
705C42C23×D1314yes—
706C42C23×D1314yes—
707C42C23×D1314yes—
708C42C23×D1314yes—
709C13C2×#355911yescharacteristic, complemented, Sylow
710C23—22no—
711C23—22no—
712C23—134no—
713C23—138no—
714C23—264no—
715C23—268no—
716C23—264no—
717C23—268no—
718C23—268no—
719C23—264no—
720C23#8825614yes—
721C23C24×D1312yes—
722C23C24×D1311yescharacteristic
723Q8—524no—
724Q8—5216no—
725Q8—528no—
726D4—2616no—
727D4—2632no—
728D4—2616no—
729D4—5216no—
730D4—528no—
731D4—524no—
732D4—5216no—
733D4—528no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—22no—
738C2×C4—28no—
739C2×C4—216no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—28no—
744C2×C4—48no—
745C2×C4—44no—
746C2×C4—134no—
747C2×C4—134no—
748C2×C4—134no—
749C2×C4—138no—
750C2×C4—264no—
751C2×C4—264no—
752C2×C4—268no—
753C2×C4—264no—
754C2×C4—2616no—
755C2×C4—5216no—
756C2×C4—5216no—
757C2×C4—5216no—
758C2×C4—5216no—
759C2×C4#8825414yes—
760C2×C4C24×D1318yes—
761C2×C4C24×D1312yes—
762C2×C4C24×D1312yes—
763C2×C4C24×D1312yes—
764C2×C4C24×D1312yes—
765C2×C4C24×D1312yes—
766C2×C4C24×D1318yes—
767C2×C4C24×D1312yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—264no—
772C22—268no—
773C22—264no—
774C22—268no—
775C22—268no—
776C22—264no—
777C22—528no—
778C22—5216no—
779C22C2×#8825412yes—
780C22C2×#8825614yes—
781C22C2×#8825612yes—
782C22#1171964812yes—
783C22C25×D1311yescharacteristic
784C4—22no—
785C4—28no—
786C4—22no—
787C4—22no—
788C4—28no—
789C4—22no—
790C4—22no—
791C4—264no—
792C4—268no—
793C4—264no—
794C4—264no—
795C4C2×#8825414yes—
796C2—24no—
797C2—524no—
798C2—528no—
799C2#1312937014yesdirect product factor
800C2C22×#8825611yescharacteristic
801C2C22×#8825411yescharacteristic
802C2C2×#1171964811yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC22×C13×#125C2
socleC23×C13C25
hypercenterC22×#125D13
hypocenterC13C2×#3559
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #13129370C2direct (N × H)
2. C2×#11719404C2semidirect
3. C2×#11719405C2semidirect
4. C2×#11719395C2semidirect
5. C2×#11719400C2semidirect
6. C2×#11719219C2semidirect
7. C2×#11719212C2semidirect
8. C2×#11719212C2semidirect
9. C2×#11719394C2semidirect
10. C2×#11719403C2semidirect
11. C2×#11719397C2semidirect
12. C2×#11719220C2semidirect
13. C2×#11719215C2semidirect
14. C2×#11719182C2semidirect
15. C2×#11719184C2semidirect
16. C22×C13×#125C2semidirect
23. C2×C13×#125C22semidirect
38. #11719405C22semidirect
39. #11719404C22semidirect
40. #11719403C22semidirect
41. #11719400C22semidirect
42. #11719397C22semidirect
43. #11719395C22semidirect
44. #11719394C22semidirect
45. #11719220C22semidirect
46. #11719219C22semidirect
49. #11719215C22semidirect
56. #11719212C22semidirect
57. #11719212C22semidirect
78. #11719184C22semidirect
80. #11719182C22semidirect
324. C22×#125D13semidirect
413. C2×#125C2×D13semidirect
606. C2×C13#3559semidirect
709. C13C2×#3559semidirect
799. C2#13129370direct (N × H)

Maximal subgroups

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

subgroupindex
#131293702
C2×#117194042
C2×#117194052
C2×#117193952
C2×#117194002
C2×#117192192
C2×#117192122
C2×#117193942
C2×#117194032
C2×#117193972
C2×#117192202
C2×#117192152
C2×#117191822
C2×#117191842
C22×C13×#1252
C2×#355913