Finite Group Databasebeta

← #16771469

Subgroups — #16771469

Order 3328.

11346 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719648C212yesmaximal, complemented
2#13128628C214yesmaximal, complemented
3#13128625C214yesmaximal, complemented
4#13128618C214yesmaximal, complemented
5#13128611C214yesmaximal, complemented
6#13128605C214yesmaximal, complemented
7#13128599C214yesmaximal, complemented
8#13128597C218yesmaximal, complemented
9#13128319C2116yesmaximal, complemented
10#13128169C211yesmaximal, characteristic, complemented
11#13128163C214yesmaximal, complemented
12C2×#11719537C212yesmaximal, complemented
13D13×#532C214yesmaximal, complemented
14C2×#11719227C211yesmaximal, characteristic, complemented
15C13×#3449C211yesmaximal, characteristic, complemented
16C22×C13×#41C2212yescomplemented
17#11719648—232no—
18C2×#88257C2214yescomplemented
19C2×#88257C2214yescomplemented
20C2×#88256C2214yescomplemented
21C2×#88256C2214yescomplemented
22C2×#41×D13C2218yescomplemented
23C2×#41×D13C2218yescomplemented
24C2×#88254C2214yescomplemented
25C2×#88251C2218yescomplemented
26C2×#88251C2214yescomplemented
27C22×#6127C2211yescharacteristic
28C22×#6127C2218yescomplemented
29C22×#6127C2212yescomplemented
30C13×#537C2214yescomplemented
31C13×#536C2214yescomplemented
32C13×#535C2214yescomplemented
33C13×#534C2214yescomplemented
34C13×#532C2214yescomplemented
35C13×#525C2218yescomplemented
36C2×C13×#117C2211yescharacteristic, complemented
37#11719537C2218yescomplemented
38#11719537C2218yescomplemented
39#11719537C2214yescomplemented
40#11719537C2214yescomplemented
41#11719537C2214yescomplemented
42#11719537C2214yescomplemented
43C2×#88201C2212yescomplemented
44C2×#88198C2212yescomplemented
45C2×#88194C2212yescomplemented
46C2×#88193C2218yescomplemented
47C2×#88190C2212yescomplemented
48C2×C4×C22⋊D13C2218yescomplemented
49C22×C4×Dic13C2211yescharacteristic, complemented
50#11719430C2214yescomplemented
51#11719429C2218yescomplemented
52D13×C4⋊Q8C2214yescomplemented
53#11719421C2214yescomplemented
54#11719420C2218yescomplemented
55D13×#127C2214yescomplemented
56#11719380C2218yescomplemented
57#11719379C2218yescomplemented
58D13×#124C2218yescomplemented
59#11719373C2218yescomplemented
60#11719360C22132yescomplemented
61#11719359C22132yescomplemented
62#11719338C22116yescomplemented
63#11719337C22116yescomplemented
64#11719336C22116yescomplemented
65#11719335C22116yescomplemented
66#11719317C22116yescomplemented
67#11719314C22116yescomplemented
68#11719310C22116yescomplemented
69D13×#121C22116yescomplemented
70#11719304C22116yescomplemented
71#11719303C22116yescomplemented
72#11719302C22116yescomplemented
73#11719301C22116yescomplemented
74#11719296C22132yescomplemented
75#11719295C22132yescomplemented
76#11719253C22116yescomplemented
77#11719252C22132yescomplemented
78C4×D4×D13C22116yescomplemented
79#11719231C2214yescomplemented
80#11719230C2214yescomplemented
81#11719229C2218yescomplemented
82#11719227C2218yescomplemented
83#11719227C2214yescomplemented
84#11719227C2214yescomplemented
85#11719215C2214yescomplemented
86C2×#88147C2212yescomplemented
87C2×#88141C2212yescomplemented
88#11719198C2214yescomplemented
89C2×#88135C2214yescomplemented
90#11719182C2214yescomplemented
91C2×#88126C2212yescomplemented
92C2×C42×D13C2212yescomplemented
93C2×C13×#41—216no—
94C2×C13×#41C2314yes—
95C2×C13×#41C2314yes—
96C2×C13×#41C2314yes—
97C2×C13×#41C2314yes—
98C22×Q8×C13C2312yes—
99C22×D4×C13C2312yes—
100C22×D4×C13C2314yes—
101C23×C4×C13C2314yes—
102C23×C4×C13C2311yescharacteristic
103C22×C22⋊D13C2314yes—
104C22×C22⋊D13C23116yes—
105C22×C22⋊D13C2318yes—
106C22×C22⋊D13C2312yes—
107C23×Dic13C2312yes—
108#88257—232no—
109#88257—232no—
110#88256—232no—
111#88256—232no—
112#41×D13—264no—
113#41×D13—264no—
114#88254—232no—
115C2×#6131C2318yes—
116C2×#6131C2318yes—
117C2×Q8×D13C2318yes—
118C2×Q8×D13C2318yes—
119#88251—264no—
120#88251—232no—
121C2×#6129C23116yes—
122C2×#6129C23116yes—
123C2×#6129C2318yes—
124C2×#6129C2318yes—
125C2×D4×D13C23116yes—
126C2×D4×D13C23116yes—
127C2×D4×D13C2318yes—
128C2×D4×D13C2318yes—
129C2×D4×D13C23116yes—
130C2×#6127—216no—
131C2×#6127—264no—
132C2×#6127D4116yescomplemented
133C2×#6127C2314yes—
134C2×#6127C2314yes—
135C2×#6127C2314yes—
136C2×#6127C2314yes—
137C2×#6127C23116yes—
138C2×#6127C2318yes—
139C2×#6127C2318yes—
140C2×#6127C23116yes—
141C2×#6127C2314yes—
142C2×#6127C2314yes—
143C22×D52C2312yes—
144C22×D52C2318yes—
145C22×D52C2311yescharacteristic
146C22×C4×D13C2314yes—
147C22×C4×D13C23116yes—
148C22×C4×D13C2314yes—
149C22×C4×D13C2312yes—
150C22×Dic26C2312yes—
151C22×Dic26C2318yes—
152C22×Dic26C2311yescharacteristic
153C13×C4⋊Q8C2314yes—
154C13×#127C2314yes—
155C13×#124C2318yes—
156C13×#123C23116yes—
157C13×C22⋊Q8C23116yes—
158C13×#121C23116yes—
159C13×#121C23116yes—
160C13×#120C23116yes—
161C4×D4×C13C23116yes—
162C13×#117C2314yes—
163C13×#117C2314yes—
164C2×C13×C4⋊C4C2312yes—
165C2×C13×C22⋊C4C2312yes—
166C2×C42×C13C2312yes—
167C2×C22⋊Dic13C2318yes—
168#88201C2314yes—
169#88201C2314yes—
170#88201C2318yes—
171#88198C2314yes—
172#88198C2314yes—
173#88198C2318yes—
174#88194C2318yes—
175#88194C2314yes—
176#88194C2314yes—
177#88194C23116yes—
178#88193C23116yes—
179#88193C23116yes—
180#88193C23116yes—
181#88193C23116yes—
182#88193C23132yes—
183#88192C23116yes—
184#88191C23132yes—
185#88190C2318yes—
186#88190C2314yes—
187#88190C2314yes—
188D4×Dic13C23116yes—
189#88184C23116yes—
190C4×C22⋊D13C23116yes—
191C4×C22⋊D13C23116yes—
192C4×C22⋊D13C23116yes—
193C4×C22⋊D13C23116yes—
194C2×#6103C2314yes—
195C2×#6103C2318yes—
196C2×#6101C2314yes—
197C2×#6101C2318yes—
198C2×C4×Dic13C2311yescharacteristic
199C2×C4×Dic13C2314yes—
200C2×C4×Dic13C2311yescharacteristic
201C2×C4×Dic13C2312yes—
202C2×C4×Dic13C2314yes—
203C2×C4×Dic13C2312yes—
204C2×C4×Dic13C2312yes—
205#88151C23116yes—
206#88150C23132yes—
207#88149C23116yes—
208#88149C23116yes—
209#88148C23132yes—
210#88147C23116yes—
211#88147C2318yes—
212#88147C2318yes—
213C4⋊C4×D13C23116yes—
214#88142C23116yes—
215#88141C2318yes—
216#88141C2318yes—
217#88140C23116yes—
218#88139C23132yes—
219#88138C23132yes—
220#88138C23132yes—
221#88137C23132yes—
222#88136C23116yes—
223#88136C23132yes—
224#88135C23116yes—
225#88135C23116yes—
226#88135C23132yes—
227C22⋊C4×D13C23132yes—
228#88132C23132yes—
229#88129C2318yes—
230#88128C2314yes—
231C4×D52C23116yes—
232#88126C2318yes—
233#88126C2318yes—
234C42×D13C2314yes—
235C42×D13C2314yes—
236C42×D13C2318yes—
237#88123C2314yes—
238#62812—131nomaximal, Sylow
239C24×C13C2414yes—
240C24×C13C2411yescharacteristic
241C23×D13C24116yes—
242C23×D13C2414yes—
243C23×D13C2412yes—
244C13×#41—216no—
245C13×#41—216no—
246C13×#41—216no—
247C13×#41—216no—
248C2×Q8×C13—28no—
249C2×Q8×C13C2414yes—
250C2×Q8×C13C2414yes—
251C2×D4×C13—216no—
252C2×D4×C13—28no—
253C2×D4×C13C2414yes—
254C2×D4×C13C2414yes—
255C2×D4×C13C2418yes—
256C2×D4×C13C2418yes—
257C2×D4×C13C24116yes—
258C22×C4×C13—216no—
259C22×C4×C13C2×D418yescomplemented
260C22×C4×C13C2414yes—
261C22×C4×C13C2418yes—
262C22×C4×C13C2418yes—
263C22×C4×C13C2414yes—
264C22×C4×C13C2411yescharacteristic
265C22×C4×C13C2411yescharacteristic
266C22×C4×C13C2412yes—
267C22×C4×C13C2412yes—
268C2×C22⋊D13—216no—
269C2×C22⋊D13—264no—
270C2×C22⋊D13—416no—
271C2×C22⋊D13C2×D4116yescomplemented
272C2×C22⋊D13C24116yes—
273C2×C22⋊D13C2418yes—
274C2×C22⋊D13C24116yes—
275C2×C22⋊D13C24116yes—
276C2×C22⋊D13C2418yes—
277C2×C22⋊D13C24116yes—
278C2×C22⋊D13C2418yes—
279C22×Dic13—44no—
280C22×Dic13C24116yes—
281C22×Dic13C2414yes—
282C22×Dic13C2414yes—
283C22×Dic13C2412yes—
284C22×Dic13C2414yes—
285C22×Dic13C2412yes—
286C22×Dic13C2412yes—
287#6131—232no—
288#6131—232no—
289Q8×D13—232no—
290Q8×D13—232no—
291#6129—264no—
292#6129—264no—
293#6129—232no—
294#6129—232no—
295D4×D13—264no—
296D4×D13—264no—
297D4×D13—232no—
298D4×D13—232no—
299D4×D13—432no—
300#6127—216no—
301#6127—216no—
302#6127—216no—
303#6127—216no—
304#6127—264no—
305#6127—232no—
306#6127—264no—
307#6127—232no—
308#6127C2×D4132yescomplemented
309#6127C2×D4132yescomplemented
310C2×D52—28no—
311C2×D52—232no—
312C2×D52C2×D418yescomplemented
313C2×D52C2414yes—
314C2×D52C24116yes—
315C2×D52C2414yes—
316C2×D52C24116yes—
317C2×D52C2414yes—
318C2×C4×D13—216no—
319C2×C4×D13—264no—
320C2×C4×D13—48no—
321C2×C4×D13C2×D4116yescomplemented
322C2×C4×D13C2418yes—
323C2×C4×D13C2418yes—
324C2×C4×D13C24116yes—
325C2×C4×D13C24116yes—
326C2×C4×D13C2418yes—
327C2×C4×D13C2418yes—
328C2×C4×D13C2414yes—
329C2×C4×D13C2414yes—
330C2×Dic26—28no—
331C2×Dic26—232no—
332C2×Dic26C2×D418yescomplemented
333C2×Dic26C2414yes—
334C2×Dic26C24116yes—
335C2×Dic26C2414yes—
336C2×Dic26C2414yes—
337C13×C4⋊C4C2418yes—
338C13×C4⋊C4C24116yes—
339C13×C22⋊C4C24132yes—
340C13×C22⋊C4C2418yes—
341C42×C13C2414yes—
342C42×C13C2414yes—
343C22⋊Dic13C24116yes—
344C22⋊Dic13C24116yes—
345#6103C24116yes—
346#6103C24132yes—
347#6103C24116yes—
348#6103C24116yes—
349C4⋊Dic13C24116yes—
350#6101C24116yes—
351#6101C24116yes—
352#6101C24116yes—
353C4×Dic13C2412yes—
354C4×Dic13C2411yescharacteristic
355C4×Dic13C2411yescharacteristic
356C4×Dic13C2418yes—
357C4×Dic13C2418yes—
358C4×Dic13C2412yes—
359C4×Dic13C2412yes—
360C4×Dic13C2414yes—
361C4×Dic13C2414yes—
362C2×#585—132no—
363#3500—134no—
364#3500—134no—
365#3499—134no—
366#3498—134no—
367#3497—134no—
368#3496—134no—
369#3496—138no—
370D4×#41—1316no—
371#3449—134no—
372#3449—131no—
373#3449D1311yescharacteristic, complemented
374C2×#532—132no—
375C2×#532—134no—
376C2×C4×#41—131no—
377C23×C13—28no—
378C23×C13—42no—
379C23×C13—48no—
380C23×C13C22×D414yes—
381C23×C13C2518yes—
382C23×C13C2512yes—
383C23×C13C2511yescharacteristic
384C22×D13—28no—
385C22×D13—232no—
386C22×D13—44no—
387C22×D13—432no—
388C22×D13—48no—
389C22×D13C22×D418yes—
390C22×D13C2518yes—
391C22×D13C2514yes—
392Q8×C13—28no—
393Q8×C13—28no—
394D4×C13—216no—
395D4×C13—216no—
396D4×C13—28no—
397D4×C13—28no—
398D4×C13—416no—
399C2×C4×C13—28no—
400C2×C4×C13—216no—
401C2×C4×C13—216no—
402C2×C4×C13—44no—
403C2×C4×C13C22×D418yes—
404C2×C4×C13C22×D414yes—
405C2×C4×C13C22×D418yes—
406C2×C4×C13C22×D414yes—
407C2×C4×C13C2518yes—
408C2×C4×C13C2518yes—
409C2×C4×C13C2511yescharacteristic
410C2×C4×C13C2512yes—
411C2×C4×C13C2511yescharacteristic
412C22⋊D13—216no—
413C22⋊D13—216no—
414C22⋊D13—232no—
415C22⋊D13—232no—
416C22⋊D13—232no—
417C22⋊D13—416no—
418C22⋊D13C22×D4132yes—
419C2×Dic13—28no—
420C2×Dic13—232no—
421C2×Dic13—24no—
422C2×Dic13—28no—
423C2×Dic13—44no—
424C2×Dic13—42no—
425C2×Dic13C22×D418yes—
426C2×Dic13C2512yes—
427C2×Dic13C2514yes—
428C2×Dic13C2518yes—
429C2×Dic13C2514yes—
430C2×Dic13C2512yes—
431D52—232no—
432D52—28no—
433D52—28no—
434D52—416no—
435D52C22×D4116yes—
436C4×D13—232no—
437C4×D13—216no—
438C4×D13—216no—
439C4×D13—232no—
440C4×D13—216no—
441C4×D13—48no—
442C4×D13C22×D4116yes—
443C4×D13C22×D4116yes—
444Dic26—28no—
445Dic26—28no—
446Dic26—232no—
447Dic26C22×D4116yes—
448#585—2632no—
449C2×2−1+4—134no—
450C2×2−1+4—134no—
451C2×2−1+4—134no—
452C2×H(5,𝔽2)—134no—
453C2×H(5,𝔽2)—134no—
454C2×H(5,𝔽2)—138no—
455C2×H(5,𝔽2)—134no—
456C22×#41—138no—
457C22×#41—138no—
458C22×#41—131no—
459C22×#41—132no—
460C22×#41—138no—
461C22×#41C2×D1312yescomplemented
462#550—1316no—
463D4×Q8—1316no—
464#548—1316no—
465#548—1316no—
466#547—1332no—
467#547—1316no—
468#546—1332no—
469#546—1316no—
470#546—1316no—
471#546—1332no—
472D42—1316no—
473D42—1332no—
474#537—1316no—
475#537—134no—
476#537C2×D1314yescomplemented
477#536—138no—
478#536—138no—
479#536—134no—
480#536C2×D1314yescomplemented
481#535—138no—
482#535—138no—
483#535—134no—
484#535C2×D1314yescomplemented
485#534—1316no—
486#534—134no—
487#534C2×D1314yescomplemented
488#532—134no—
489#532—134no—
490#532—138no—
491#532—138no—
492#532—134no—
493#532—134no—
494#532—134no—
495#532—134no—
496#532—138no—
497#532—1316no—
498#532—1316no—
499#532—134no—
500#532C2×D1314yescomplemented
501C2×C4⋊Q8—132no—
502C2×C4⋊Q8—134no—
503C2×#127—132no—
504C2×#127—134no—
505C2×#124—132no—
506C2×#124—132no—
507C2×#124—138no—
508#525—1332no—
509#525—138no—
510#525C2×D1318yescomplemented
511C2×#121—138no—
512C2×#121—1316no—
513C4×#41—138no—
514C4×#41—134no—
515C4×#41—134no—
516C2×C4×Q8—132no—
517C2×C4×D4—138no—
518C2×C4×D4—1316no—
519C2×C4×D4—132no—
520C2×C4×D4—134no—
521C2×#117—132no—
522C2×#117C2×D1311yescharacteristic, complemented
523C22×C42—131no—
524C22×C42—132no—
525C22×C13—22no—
526C22×C13—24no—
527C22×C13—28no—
528C22×C13—216no—
529C22×C13—44no—
530C22×C13—88no—
531C22×C13C23×D414yes—
532C22×C13C23×D412yes—
533C22×C13C2611yescharacteristic
534C2×D13—28no—
535C2×D13—28no—
536C2×D13—216no—
537C2×D13—48no—
538C2×D13—832no—
539C2×D13—88no—
540C2×D13C23×D418yes—
541C4×C13—28no—
542C4×C13—28no—
543C4×C13C23×D412yes—
544C4×C13C23×D414yes—
545C4×C13C23×D412yes—
546Dic13—28no—
547Dic13—22no—
548Dic13—24no—
549Dic13C23×D418yes—
550Dic13#58514yescomplemented
5512−1+4—2632no—
5522−1+4—2632no—
5532−1+4—2632no—
554H(5,𝔽2)—2664no—
555H(5,𝔽2)—2632no—
556H(5,𝔽2)—2632no—
557H(5,𝔽2)—2632no—
558C2×#41—216no—
559C2×#41—138no—
560C2×#41—138no—
561C2×#41—138no—
562C2×#41—1316no—
563C2×#41—1316no—
564C2×#41—138no—
565C2×#41—1316no—
566C2×#41—134no—
567C2×#41—134no—
568C2×#41—1316no—
569C2×#41—134no—
570C2×#41—134no—
571C2×#41—134no—
572C2×#41—134no—
573C2×#41—138no—
574C2×#41—1316no—
575C2×#41—138no—
576C2×#41—2664no—
577C2×#41—2664no—
578C2×#41—2664no—
579C2×#41—2616no—
580C2×#41C22×D1314yes—
581C2×#41C22×D1314yes—
582C2×#41C22×D1314yes—
583C2×#41C22×D1314yes—
584C22×Q8—138no—
585C22×Q8—138no—
586C22×Q8—131no—
587C22×Q8—132no—
588C22×Q8—138no—
589C22×Q8C22×D1312yes—
590C22×D4—132no—
591C22×D4—134no—
592C22×D4—1316no—
593C22×D4—138no—
594C22×D4—1316no—
595C22×D4—138no—
596C22×D4—1316no—
597C22×D4—138no—
598C22×D4—1316no—
599C22×D4—131no—
600C22×D4—132no—
601C22×D4—138no—
602C22×D4C22×D1314yes—
603C22×D4C22×D1312yes—
604C23×C4—132no—
605C23×C4—132no—
606C23×C4—1316no—
607C23×C4—134no—
608C23×C4—134no—
609C23×C4C22×D1314yes—
610C23×C4C22×D1311yescharacteristic
611C4⋊Q8—134no—
612C4⋊Q8—134no—
613C4⋊Q8—138no—
614C4⋊Q8—1316no—
615C4⋊Q8—134no—
616C4⋊Q8C22×D1314yes—
617#127—134no—
618#127—134no—
619#127—1316no—
620#127—138no—
621#127—134no—
622#127C22×D1314yes—
623#124—134no—
624#124—134no—
625#124—138no—
626#124—134no—
627#124—134no—
628#124—138no—
629#124—1332no—
630#124—138no—
631#124C22×D1318yes—
632#123—1332no—
633#123—1332no—
634#123—1316no—
635#123C22×D13116yes—
636C22⋊Q8—1332no—
637C22⋊Q8—1316no—
638C22⋊Q8—1332no—
639C22⋊Q8C22×D13116yes—
640#121—1316no—
641#121—1316no—
642#121—1316no—
643#121—1316no—
644#121—1316no—
645#121—1332no—
646#121—1316no—
647#121—1316no—
648#121—1316no—
649#121—1332no—
650#121—1332no—
651#121C22×D13116yes—
652#121C22×D13116yes—
653#120—1332no—
654#120—1332no—
655#120—1316no—
656#120C22×D13116yes—
657C4×Q8—138no—
658C4×Q8—138no—
659C4×D4—1316no—
660C4×D4—1316no—
661C4×D4—1316no—
662C4×D4—1316no—
663C4×D4—1316no—
664C4×D4—138no—
665C4×D4—138no—
666C4×D4—1316no—
667C4×D4—1316no—
668C4×D4—1316no—
669C4×D4—1332no—
670C4×D4—1316no—
671C4×D4C22×D13116yes—
672#117—138no—
673#117—138no—
674#117C22×D1314yes—
675#117C22×D1314yes—
676C2×C4⋊C4—134no—
677C2×C4⋊C4—138no—
678C2×C4⋊C4—1316no—
679C2×C4⋊C4C22×D1312yes—
680C2×C22⋊C4—138no—
681C2×C22⋊C4—134no—
682C2×C22⋊C4—138no—
683C2×C22⋊C4—1332no—
684C2×C22⋊C4C22×D1312yes—
685C2×C42—131no—
686C2×C42—134no—
687C2×C42—134no—
688C2×C42—132no—
689C2×C42—132no—
690C2×C42—132no—
691C2×C42—131no—
692C2×C42—138no—
693C2×C42—134no—
694C2×C42—134no—
695C2×C42C22×D1312yes—
696C2×C13—22no—
697C2×C13—24no—
698C2×C13—48no—
699C2×C13C24×D411yescharacteristic
700C2×C13C2×#58512yes—
701D13—28no—
702D13—48no—
703C24—132no—
704C24—1316no—
705C24—134no—
706C24C23×D1314yes—
707C24C23×D1311yescharacteristic
708#41—216no—
709#41—216no—
710#41—216no—
711#41—216no—
712#41—1332no—
713#41—1332no—
714#41—2664no—
715#41—2664no—
716#41—2632no—
717#41—2632no—
718#41—2664no—
719#41—2632no—
720#41—2632no—
721#41—2664no—
722#41—2632no—
723#41—2632no—
724#41—2616no—
725#41—2616no—
726#41—2616no—
727#41—2616no—
728C2×Q8—28no—
729C2×Q8—138no—
730C2×Q8—134no—
731C2×Q8—1316no—
732C2×Q8—134no—
733C2×Q8—134no—
734C2×Q8—2632no—
735C2×Q8—2632no—
736C2×Q8—2632no—
737C2×Q8—268no—
738C2×Q8C23×D1314yes—
739C2×Q8C23×D1314yes—
740C2×D4—216no—
741C2×D4—28no—
742C2×D4—1316no—
743C2×D4—138no—
744C2×D4—1316no—
745C2×D4—1316no—
746C2×D4—138no—
747C2×D4—138no—
748C2×D4—1316no—
749C2×D4—1316no—
750C2×D4—138no—
751C2×D4—134no—
752C2×D4—1316no—
753C2×D4—134no—
754C2×D4—134no—
755C2×D4—1316no—
756C2×D4—2632no—
757C2×D4—2632no—
758C2×D4—2664no—
759C2×D4—2632no—
760C2×D4—2664no—
761C2×D4—2664no—
762C2×D4—2616no—
763C2×D4—268no—
764C2×D4—5232no—
765C2×D4—5216no—
766C2×D4C23×D1318yes—
767C2×D4C23×D1318yes—
768C2×D4C23×D1314yes—
769C2×D4C23×D1314yes—
770C2×D4C23×D13116yes—
771C22×C4—216no—
772C22×C4—132no—
773C22×C4—1316no—
774C22×C4—134no—
775C22×C4—134no—
776C22×C4—132no—
777C22×C4—134no—
778C22×C4—134no—
779C22×C4—1316no—
780C22×C4—134no—
781C22×C4—132no—
782C22×C4—138no—
783C22×C4—1316no—
784C22×C4—1316no—
785C22×C4—138no—
786C22×C4—138no—
787C22×C4—138no—
788C22×C4—2664no—
789C22×C4—2616no—
790C22×C4—528no—
791C22×C4—524no—
792C22×C4D4×D1318yescomplemented
793C22×C4C23×D1314yes—
794C22×C4C23×D1318yes—
795C22×C4C23×D1318yes—
796C22×C4C23×D1314yes—
797C22×C4C23×D1311yescharacteristic
798C22×C4C23×D1312yes—
799C22×C4C23×D1311yescharacteristic
800C22×C4C23×D1312yes—
801C4⋊C4—1316no—
802C4⋊C4—1316no—
803C4⋊C4—1316no—
804C4⋊C4—1316no—
805C4⋊C4C23×D13116yes—
806C4⋊C4C23×D1318yes—
807C22⋊C4—1316no—
808C22⋊C4—1316no—
809C22⋊C4—1316no—
810C22⋊C4—1316no—
811C22⋊C4—1316no—
812C22⋊C4—1332no—
813C22⋊C4C23×D13132yes—
814C22⋊C4C23×D1318yes—
815C42—131no—
816C42—131no—
817C42—132no—
818C42—138no—
819C42—134no—
820C42—138no—
821C42—134no—
822C42—132no—
823C42—132no—
824C42C23×D1314yes—
825C42C23×D1314yes—
826C13#6281211yescharacteristic, complemented, Sylow
827C23—28no—
828C23—42no—
829C23—48no—
830C23—134no—
831C23—138no—
832C23—138no—
833C23—2632no—
834C23—268no—
835C23—524no—
836C23—528no—
837C23—5232no—
838C23C2×D4×D1314yes—
839C23C24×D1318yes—
840C23C24×D1312yes—
841C23C24×D1311yescharacteristic
842Q8—28no—
843Q8—28no—
844Q8—1316no—
845Q8—2632no—
846Q8—268no—
847Q8—268no—
848D4—216no—
849D4—216no—
850D4—28no—
851D4—28no—
852D4—416no—
853D4—1332no—
854D4—1316no—
855D4—2632no—
856D4—2632no—
857D4—2632no—
858D4—2632no—
859D4—2616no—
860D4—2616no—
861D4—268no—
862D4—268no—
863D4—5216no—
864D4—5216no—
865C2×C4—28no—
866C2×C4—216no—
867C2×C4—216no—
868C2×C4—44no—
869C2×C4—138no—
870C2×C4—132no—
871C2×C4—134no—
872C2×C4—1316no—
873C2×C4—1316no—
874C2×C4—132no—
875C2×C4—134no—
876C2×C4—138no—
877C2×C4—2632no—
878C2×C4—2616no—
879C2×C4—2632no—
880C2×C4—2632no—
881C2×C4—264no—
882C2×C4—268no—
883C2×C4—268no—
884C2×C4—2616no—
885C2×C4—2616no—
886C2×C4—528no—
887C2×C4—524no—
888C2×C4—522no—
889C2×C4C2×D4×D1318yes—
890C2×C4C2×D4×D1314yes—
891C2×C4C2×D4×D1318yes—
892C2×C4C2×D4×D1314yes—
893C2×C4C24×D1318yes—
894C2×C4C24×D1318yes—
895C2×C4C24×D1311yescharacteristic
896C2×C4C24×D1312yes—
897C2×C4C24×D1311yescharacteristic
898C22—22no—
899C22—24no—
900C22—28no—
901C22—216no—
902C22—44no—
903C22—88no—
904C22—138no—
905C22—268no—
906C22—268no—
907C22—2616no—
908C22—528no—
909C22—1048no—
910C22—10432no—
911C22C22×D4×D1314yes—
912C22C22×D4×D1312yes—
913C22C25×D1311yescharacteristic
914C4—28no—
915C4—28no—
916C4—138no—
917C4—134no—
918C4—268no—
919C4—262no—
920C4—264no—
921C4C22×D4×D1312yes—
922C4C22×D4×D1314yes—
923C4C22×D4×D1312yes—
924C2—24no—
925C2—22no—
926C2—48no—
927C2—268no—
928C2—528no—
929C2C23×D4×D1311yescharacteristic
930C2D13×#58512yes—
subgroupG/H
centerC2×C4C24×D13
commutator, socle, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC13×#3449C2
hypercenter#3449D13
hypocenterC13#62812
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#11719648C2semidirect
2. #13128628C2semidirect
3. #13128625C2semidirect
4. #13128618C2semidirect
5. #13128611C2semidirect
6. #13128605C2semidirect
7. #13128599C2semidirect
8. #13128597C2semidirect
9. #13128319C2semidirect
10. #13128169C2semidirect
11. #13128163C2semidirect
12. C2×#11719537C2semidirect
13. D13×#532C2semidirect
14. C2×#11719227C2semidirect
15. C13×#3449C2semidirect
16. C22×C13×#41C22semidirect
18. C2×#88257C22semidirect
19. C2×#88257C22semidirect
20. C2×#88256C22semidirect
21. C2×#88256C22semidirect
22. C2×#41×D13C22semidirect
23. C2×#41×D13C22semidirect
24. C2×#88254C22semidirect
25. C2×#88251C22semidirect
26. C2×#88251C22semidirect
28. C22×#6127C22semidirect
29. C22×#6127C22semidirect
30. C13×#537C22semidirect
31. C13×#536C22semidirect
32. C13×#535C22semidirect
33. C13×#534C22semidirect
34. C13×#532C22semidirect
35. C13×#525C22semidirect
36. C2×C13×#117C22semidirect
37. #11719537C22semidirect
38. #11719537C22semidirect
39. #11719537C22semidirect
40. #11719537C22semidirect
41. #11719537C22semidirect
42. #11719537C22semidirect
43. C2×#88201C22semidirect
44. C2×#88198C22semidirect
45. C2×#88194C22semidirect
46. C2×#88193C22semidirect
47. C2×#88190C22semidirect
48. C2×C4×C22⋊D13C22semidirect
49. C22×C4×Dic13C22semidirect
50. #11719430C22semidirect
51. #11719429C22semidirect
52. D13×C4⋊Q8C22semidirect
53. #11719421C22semidirect
54. #11719420C22semidirect
55. D13×#127C22semidirect
56. #11719380C22semidirect
57. #11719379C22semidirect
58. D13×#124C22semidirect
59. #11719373C22semidirect
60. #11719360C22semidirect
61. #11719359C22semidirect
62. #11719338C22semidirect
63. #11719337C22semidirect
64. #11719336C22semidirect
65. #11719335C22semidirect
66. #11719317C22semidirect
67. #11719314C22semidirect
68. #11719310C22semidirect
69. D13×#121C22semidirect
70. #11719304C22semidirect
71. #11719303C22semidirect
72. #11719302C22semidirect
73. #11719301C22semidirect
74. #11719296C22semidirect
75. #11719295C22semidirect
76. #11719253C22semidirect
77. #11719252C22semidirect
78. C4×D4×D13C22semidirect
79. #11719231C22semidirect
80. #11719230C22semidirect
81. #11719229C22semidirect
82. #11719227C22semidirect
83. #11719227C22semidirect
84. #11719227C22semidirect
85. #11719215C22semidirect
86. C2×#88147C22semidirect
87. C2×#88141C22semidirect
88. #11719198C22semidirect
89. C2×#88135C22semidirect
90. #11719182C22semidirect
91. C2×#88126C22semidirect
92. C2×C42×D13C22semidirect
132. C2×#6127D4semidirect
259. C22×C4×C13C2×D4semidirect
271. C2×C22⋊D13C2×D4semidirect
308. #6127C2×D4semidirect
309. #6127C2×D4semidirect
312. C2×D52C2×D4semidirect
321. C2×C4×D13C2×D4semidirect
332. C2×Dic26C2×D4semidirect
373. #3449D13semidirect
461. C22×#41C2×D13semidirect
476. #537C2×D13semidirect
480. #536C2×D13semidirect
484. #535C2×D13semidirect
487. #534C2×D13semidirect
500. #532C2×D13semidirect
510. #525C2×D13semidirect
522. C2×#117C2×D13semidirect
550. Dic13#585semidirect
792. C22×C4D4×D13semidirect
826. C13#62812semidirect

Maximal subgroups

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

subgroupindex
C2×#117196482
#131286282
#131286252
#131286182
#131286112
#131286052
#131285992
#131285972
#131283192
#131281692
#131281632
C2×#117195372
D13×#5322
C2×#117192272
C13×#34492
#6281213