Finite Group Databasebeta

← #16731339

Subgroups — #16731339

Order 3328.

2138 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128132C211yesmaximal, characteristic
2C22×C4×Dic26C211yesmaximal, characteristic, complemented
3#13125009C214yesmaximal, complemented
4#13124967C212yesmaximal, complemented
5#13124959C212yesmaximal, complemented
6#13124918C214yesmaximal, complemented
7#13124876C212yesmaximal, complemented
8#13124868C212yesmaximal, complemented
9#13124761C212yesmaximal, complemented
10#13124643C212yesmaximal, complemented
11#13124310C212yesmaximal, complemented
12#13124073C212yesmaximal, complemented
13C4×#88163C214yesmaximal, complemented
14C13×#2920C211yesmaximal, characteristic, complemented
15C23×Dic26C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17#11719496—21no—
18#11719496—21no—
19#11719496C2212yes—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101—21no—
22C22×C4×Dic13—21no—
23C2×#88163C2214yes—
24#11719184—21no—
25#11719184—21no—
26#11719184—21no—
27#11719184—21no—
28#11719184C2212yes—
29#11719184C2212yes—
30#11719182C2211yescharacteristic
31#11719182C2211yescharacteristic
32#11719182C2211yescharacteristic
33C4×#6127—21no—
34C4×#6127—21no—
35C4×#6127C2212yes—
36#11719175C2211yescharacteristic
37#11719175C2211yescharacteristic
38#11719175C2211yescharacteristic
39C2×C4×Dic26—21no—
40C2×C4×Dic26—21no—
41C2×C4×Dic26—21no—
42C2×C4×Dic26—21no—
43C2×C4×Dic26—21no—
44C2×C4×Dic26—21no—
45C2×C4×Dic26C2212yes—
46C2×C4×Dic26C2212yes—
47C2×C4×Dic26C2212yes—
48C2×C4×Dic26C2212yes—
49C2×C4×Dic26C2212yes—
50C2×C4×Dic26C2212yes—
51C13×#432C2212yes—
52C13×#432C2212yes—
53C13×#431C2212yes—
54C13×#431C2212yes—
55C13×#423C2212yes—
56C13×#407C2212yes—
57C4×C13×M16C2212yes—
58#11718794C2214yes—
59#11718782C2214yes—
60#11718781C2214yes—
61#11718512C2214yescomplemented
62#11718511C2214yescomplemented
63#11718510C2214yescomplemented
64#11718509C2214yescomplemented
65#11718506C2218yescomplemented
66#11718490C2218yescomplemented
67#11718400C2214yes—
68#11718400C2214yes—
69#11718399C2214yes—
70#11718399C2214yes—
71#11718397C2214yes—
72#11718396C2214yes—
73#11718383C2214yes—
74#11718382C2214yes—
75#11718377C2218yescomplemented
76#11718371C2218yescomplemented
77C4×Dic52C2218yescomplemented
78C4×#6095C2218yescomplemented
79C23×C4×C13D411yescharacteristic
80C23×C4×C13D411yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×Dic13—21no—
83C23×Dic13—21no—
84C2×#6127—21no—
85C2×#6127—21no—
86C2×#6127C2312yes—
87C22×Dic26—21no—
88C22×Dic26—21no—
89C22×Dic26—21no—
90C22×Dic26—28no—
91C22×Dic26C2312yes—
92C22×Dic26C2312yes—
93C22×Dic26C2312yes—
94C2×C13×M16C2314yes—
95C2×C42×C13D411yescharacteristic
96C2×C42×C13D411yescharacteristic
97C2×C42×C13D411yescharacteristic
98C2×C42×C13D411yescharacteristic
99C2×C42×C13D411yescharacteristic
100C2×C42×C13D411yescharacteristic
101C2×C42×C13C2311yescharacteristic
102C2×C42×C13C2311yescharacteristic
103C2×C42×C13C2311yescharacteristic
104C2×C42×C13C2311yescharacteristic
105C2×C42×C13C2311yescharacteristic
106C2×C42×C13C2311yescharacteristic
107#88207—22no—
108#88184—21no—
109#88184—21no—
110#88184—21no—
111#88184—21no—
112#88184C2312yes—
113#88184C2312yes—
114#88183—22no—
115#88183—22no—
116#88183—22no—
117C4×C22⋊D13—22no—
118C4×C22⋊D13—22no—
119C4×C22⋊D13—22no—
120C4×C22⋊D13—22no—
121C4×C22⋊D13—22no—
122C4×C22⋊D13—22no—
123#88180—21no—
124#88180—21no—
125#88180C2312yes—
126C2×C4⋊Dic13—21no—
127C2×C4⋊Dic13—21no—
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13C2312yes—
130C2×C4⋊Dic13C2312yes—
131C2×C4⋊Dic13C2312yes—
132#88178—21no—
133#88178—21no—
134#88178—21no—
135#88178—21no—
136#88178C2312yes—
137#88178C2312yes—
138C2×#6101—22no—
139C2×#6101—22no—
140C2×#6101—22no—
141C2×#6101—22no—
142C2×#6101—22no—
143C2×#6101—22no—
144C2×C4×Dic13—22no—
145C2×C4×Dic13—22no—
146C2×C4×Dic13—22no—
147C2×C4×Dic13—22no—
148C2×C4×Dic13—22no—
149C2×C4×Dic13—22no—
150#88163—216no—
151C2×Dic52C2318yes—
152C2×#6095C2318yes—
153#88130—22no—
154#88130—22no—
155#88129—21no—
156#88129—21no—
157#88129C2312yes—
158#88128C2311yescharacteristic
159C4×D52—21no—
160C4×D52—21no—
161C4×D52—21no—
162C4×D52—21no—
163C4×D52C2312yes—
164C4×D52C2312yes—
165#88126—22no—
166#88126—22no—
167#88126—22no—
168C42×D13—22no—
169#88124—21no—
170#88124—21no—
171#88124C2312yes—
172#88123C2311yescharacteristic
173#88123C2311yescharacteristic
174#88123C2311yescharacteristic
175C4×Dic26—22no—
176C4×Dic26—22no—
177C4×Dic26—22no—
178C4×Dic26—22no—
179C4×Dic26—22no—
180C4×Dic26—22no—
181C4×Dic26—22no—
182C4×Dic26—22no—
183C4×Dic26—22no—
184C4×Dic26—22no—
185C4×Dic26—22no—
186C4×Dic26—22no—
187C4×Dic26—21no—
188C4×Dic26—21no—
189C4×Dic26—21no—
190C4×Dic26—21no—
191C4×Dic26C2314yes—
192C4×Dic26C2314yes—
193C4×Dic26C2314yes—
194C4×Dic26C2314yes—
195C4×Dic26C2312yes—
196C4×Dic26C2312yes—
197C13×C4⋊C8C2314yes—
198C13×C4⋊C8C2314yes—
199C13×C22⋊C8C2314yes—
200C13×C22⋊C8C2314yes—
201C13×#97C2314yes—
202C4×C8×C13C2314yes—
203#88061C2318yes—
204#88058C2318yes—
205#88057C2318yes—
206#88056C2318yes—
207#88056C2318yes—
208#88056C2318yes—
209#60560—131nomaximal, Sylow
210C24×C13C2×D411yescharacteristic
211C22×C4×C13—24no—
212C22×C4×C13—24no—
213C22×C4×C13—42no—
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2×D411yescharacteristic
220C22×C4×C13C2×D411yescharacteristic
221C22×C4×C13C2×D411yescharacteristic
222C22×C4×C13C2×D411yescharacteristic
223C22×C4×C13C2×D411yescharacteristic
224C22×C4×C13C2×D411yescharacteristic
225C22×C4×C13C2×D411yescharacteristic
226C22×C4×C13C2×D411yescharacteristic
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2411yescharacteristic
230C22×C4×C13C2411yescharacteristic
231C22×C4×C13C2411yescharacteristic
232C2×C22⋊D13—22no—
233C2×C22⋊D13—22no—
234C2×C22⋊D13—22no—
235C22×Dic13—28no—
236C22×Dic13—22no—
237C22×Dic13—22no—
238C22×Dic13—22no—
239C22×Dic13—22no—
240C22×Dic13—22no—
241C22×Dic13—22no—
242C22×Dic13—44no—
243#6127—28no—
244#6127—44no—
245#6127—44no—
246C2×D52—21no—
247C2×D52—21no—
248C2×D52C2412yes—
249C2×C4×D13—22no—
250C2×C4×D13—22no—
251C2×C4×D13—22no—
252C2×Dic26—28no—
253C2×Dic26—28no—
254C2×Dic26—28no—
255C2×Dic26—22no—
256C2×Dic26—22no—
257C2×Dic26—22no—
258C2×Dic26—24no—
259C2×Dic26—28no—
260C2×Dic26—28no—
261C2×Dic26—21no—
262C2×Dic26—21no—
263C2×Dic26#4118yescomplemented
264C2×Dic26C2412yes—
265C2×Dic26C2414yes—
266C13×M16—28no—
267C2×C8×C13C2418yes—
268C42×C13C2×D411yescharacteristic
269C42×C13C2×D411yescharacteristic
270C42×C13C2×D411yescharacteristic
271C42×C13C2×D411yescharacteristic
272C42×C13C2×D411yescharacteristic
273C42×C13C2×D411yescharacteristic
274C42×C13C2×D411yescharacteristic
275C42×C13C2×D411yescharacteristic
276C42×C13C2×D411yescharacteristic
277C42×C13C2×D411yescharacteristic
278C42×C13C2×D411yescharacteristic
279C42×C13C2×D411yescharacteristic
280C42×C13C2411yescharacteristic
281C42×C13C2411yescharacteristic
282C42×C13C2411yescharacteristic
283C42×C13C2411yescharacteristic
284C22⋊Dic13—22no—
285C22⋊Dic13—22no—
286C22⋊Dic13—22no—
287#6103—22no—
288#6103—22no—
289#6103—22no—
290#6103—22no—
291#6103—22no—
292#6103—22no—
293C4⋊Dic13—22no—
294C4⋊Dic13—22no—
295C4⋊Dic13—22no—
296C4⋊Dic13—21no—
297C4⋊Dic13—21no—
298C4⋊Dic13—21no—
299C4⋊Dic13—21no—
300C4⋊Dic13C2414yes—
301C4⋊Dic13C2412yes—
302C4⋊Dic13C2412yes—
303#6101—24no—
304#6101—24no—
305#6101—24no—
306#6101—24no—
307#6101—22no—
308#6101—22no—
309#6101—22no—
310#6101—22no—
311#6101—22no—
312#6101—22no—
313C4×Dic13—24no—
314C4×Dic13—24no—
315C4×Dic13—24no—
316C4×Dic13—24no—
317C4×Dic13—22no—
318C4×Dic13—22no—
319C4×Dic13—22no—
320Dic52—216no—
321#6095—216no—
322#3444—131no—
323C22×C4×Q8—131no—
324#3117—134no—
325#3113—132no—
326#3112—132no—
327#3108—134no—
328#3104—132no—
329#3103—132no—
330#3092—132no—
331#3078—132no—
332#3037—132no—
333#3004—132no—
334C4×#137—134no—
335#2920D1311yescharacteristic, complemented
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13C22×D411yescharacteristic
340C23×C13C22×D411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C22×D13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13#13714yescomplemented
360C2×C4×C13C22×D411yescharacteristic
361C2×C4×C13C22×D411yescharacteristic
362C2×C4×C13C22×D411yescharacteristic
363C2×C4×C13C22×D411yescharacteristic
364C2×C4×C13C22×D411yescharacteristic
365C2×C4×C13C22×D411yescharacteristic
366C2×C4×C13C22×D411yescharacteristic
367C2×C4×C13C22×D411yescharacteristic
368C2×C4×C13C22×D411yescharacteristic
369C2×C4×C13C22×D411yescharacteristic
370C2×C4×C13C22×D411yescharacteristic
371C2×C4×C13C2×#4114yes—
372C2×C4×C13C2511yescharacteristic
373C22⋊D13—44no—
374C22⋊D13—44no—
375C22⋊D13—44no—
376C2×Dic13—28no—
377C2×Dic13—28no—
378C2×Dic13—28no—
379C2×Dic13—24no—
380C2×Dic13—24no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—44no—
385C2×Dic13—44no—
386C2×Dic13—44no—
387D52—24no—
388D52—42no—
389D52—42no—
390C4×D13—44no—
391C4×D13—44no—
392C4×D13—44no—
393Dic26—28no—
394Dic26—28no—
395Dic26—28no—
396Dic26—24no—
397Dic26—24no—
398Dic26—42no—
399Dic26—42no—
400Dic26C2×#4118yes—
401C8×C13—28no—
402C23×Q8—131no—
403C2×#137—134no—
404#533—131no—
405#533—131no—
406#533—131no—
407#532—131no—
408#532—131no—
409#532—131no—
410#529—132no—
411#529—132no—
412#529—261no—
413#529—261no—
414#529—261no—
415#529—261no—
416#525—132no—
417#525—261no—
418#525—261no—
419C4×#41—132no—
420C4×#41—261no—
421C4×#41—261no—
422C2×C4×Q8—132no—
423C2×C4×Q8—132no—
424C2×C4×Q8—132no—
425C2×C4×Q8—132no—
426C2×C4×Q8—132no—
427C2×C4×Q8—132no—
428C2×C4×Q8—261no—
429C2×C4×Q8—261no—
430C2×C4×Q8—261no—
431C2×C4×Q8—261no—
432C2×C4×Q8—261no—
433C2×C4×Q8—261no—
434C22×C4⋊C4—131no—
435C22×C4⋊C4—261no—
436C22×C42—261no—
437C22×C42C2×D1311yescharacteristic
438#484—134no—
439#483—134no—
440#481—134no—
441#480—134no—
442#479—138no—
443#477—134no—
444#475—134no—
445#464—138no—
446#462—134no—
447#460—134no—
448#451—134no—
449#451—134no—
450#448—134no—
451#448—134no—
452#441—138no—
453#440—138no—
454C4×Q16—138no—
455C4×SD16—138no—
456#432C2×D1312yes—
457#432C2×D1312yes—
458#431C2×D1312yes—
459#431C2×D1312yes—
460#428—134no—
461#423C2×D1312yes—
462#419—134no—
463#417—134no—
464#407C2×D1312yes—
465C4×M16C2×D1312yes—
466C22×C13—28no—
467C22×C13—21no—
468C22×C13—21no—
469C22×C13—21no—
470C22×C13—21no—
471C22×C13—21no—
472C22×C13—21no—
473C22×C13#52512yes—
474C22×C13C2×#13712yes—
475C22×C13#57512yes—
476C22×C13C23×D411yescharacteristic
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—42no—
480C4×C13—21no—
481C4×C13—21no—
482C4×C13—21no—
483C4×C13—21no—
484C4×C13—21no—
485C4×C13—21no—
486C4×C13—21no—
487C4×C13—21no—
488C4×C13#52512yes—
489C4×C13C2×#13712yes—
490C4×C13C2×#13712yes—
491C4×C13C22×#4112yes—
492Dic13—28no—
493Dic13—42no—
494Dic13—42no—
495Dic13—42no—
496Dic13—44no—
497C2×#41—132no—
498C2×#41—261no—
499C2×#41—261no—
500C22×Q8—132no—
501C22×Q8—132no—
502C22×Q8—132no—
503C22×Q8—268no—
504C22×Q8—261no—
505C22×Q8—261no—
506C22×Q8—261no—
507C23×C4—261no—
508C23×C4—261no—
509C23×C4D5211yescharacteristic
510C23×C4D5211yescharacteristic
511C23×C4C22×D1311yescharacteristic
512#137—2616no—
513C2×Q16—138no—
514C2×SD16—138no—
515C2×M16C22×D1314yes—
516C4⋊Q8—131no—
517C4⋊Q8—131no—
518C4⋊Q8—131no—
519#127—131no—
520#126—262no—
521#126—262no—
522#125—132no—
523#125—261no—
524#125—261no—
525#124—132no—
526#124—261no—
527#124—261no—
528#123—262no—
529#123—262no—
530#123—262no—
531C22⋊Q8—132no—
532C22⋊Q8—132no—
533C22⋊Q8—261no—
534C22⋊Q8—261no—
535C22⋊Q8—261no—
536C22⋊Q8—261no—
537#121—132no—
538#121—132no—
539#121—261no—
540#121—261no—
541#121—261no—
542#121—261no—
543#120—262no—
544C4×Q8—134no—
545C4×Q8—134no—
546C4×Q8—134no—
547C4×Q8—134no—
548C4×Q8—132no—
549C4×Q8—132no—
550C4×Q8—262no—
551C4×Q8—262no—
552C4×Q8—262no—
553C4×Q8—262no—
554C4×Q8—262no—
555C4×Q8—262no—
556C4×Q8—262no—
557C4×Q8—262no—
558C4×Q8—262no—
559C4×Q8—262no—
560C4×Q8—262no—
561C4×Q8—262no—
562C4×Q8—261no—
563C4×Q8—261no—
564C4×Q8—261no—
565C4×Q8—261no—
566C4×D4—132no—
567C4×D4—132no—
568C4×D4—262no—
569C4×D4—262no—
570C4×D4—262no—
571C4×D4—262no—
572C4×D4—262no—
573C4×D4—262no—
574C4×D4—261no—
575C4×D4—261no—
576C4×D4—261no—
577C4×D4—261no—
578#117—132no—
579#117—261no—
580#117—261no—
581#117—262no—
582#117—262no—
583#117—262no—
584C2×C4⋊C4—132no—
585C2×C4⋊C4—132no—
586C2×C4⋊C4—132no—
587C2×C4⋊C4—261no—
588C2×C4⋊C4—261no—
589C2×C4⋊C4—261no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C42—262no—
597C2×C42—262no—
598C2×C42—262no—
599C2×C42—262no—
600C2×C42—262no—
601C2×C42—262no—
602C2×C42—262no—
603C2×C42D5211yescharacteristic
604C2×C42D5211yescharacteristic
605C2×C42D5211yescharacteristic
606C2×C42D5211yescharacteristic
607C2×C42D5211yescharacteristic
608C2×C42D5211yescharacteristic
609C2×C42C22×D1311yescharacteristic
610C2×C42C22×D1311yescharacteristic
611C2×C42C22×D1311yescharacteristic
612C2×C42C22×D1311yescharacteristic
613C2×C42C22×D1311yescharacteristic
614C2×C42C22×D1311yescharacteristic
615#107—138no—
616#106—138no—
617C4⋊C8C22×D1314yes—
618C4⋊C8C22×D1314yes—
619#103—138no—
620#103—138no—
621#103—138no—
622#102—138no—
623C22⋊C8C22×D1314yes—
624C22⋊C8C22×D1314yes—
625#97C22×D1314yes—
626C4×C8C22×D1314yes—
627C2×C13—22no—
628C2×C13—22no—
629C2×C13—22no—
630C2×C13C2×#52511yescharacteristic
631C2×C13C22×#13711yescharacteristic
632C2×C13C2×#57511yescharacteristic
633D13—82no—
634C24C2×D5211yescharacteristic
635#41—268no—
636#41—524no—
637#41—524no—
638C2×Q8—138no—
639C2×Q8—134no—
640C2×Q8—132no—
641C2×Q8—268no—
642C2×Q8—268no—
643C2×Q8—268no—
644C2×Q8—268no—
645C2×Q8—268no—
646C2×Q8—262no—
647C2×Q8—262no—
648C2×Q8—262no—
649C2×Q8—261no—
650C2×Q8—261no—
651C2×Q8—264no—
652C2×D4—132no—
653C2×D4—262no—
654C2×D4—262no—
655C2×D4—262no—
656C2×D4—261no—
657C2×D4—261no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—42no—
661C22×C4—268no—
662C22×C4—262no—
663C22×C4—262no—
664C22×C4—262no—
665C22×C4—262no—
666C22×C4—262no—
667C22×C4—262no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—262no—
671C22×C4—524no—
672C22×C4C2×D5211yescharacteristic
673C22×C4C2×D5211yescharacteristic
674C22×C4C2×D5211yescharacteristic
675C22×C4C2×D5211yescharacteristic
676C22×C4C2×D5211yescharacteristic
677C22×C4C2×D5211yescharacteristic
678C22×C4C2×D5211yescharacteristic
679C22×C4C2×D5211yescharacteristic
680C22×C4C2×D5211yescharacteristic
681C22×C4C2×D5211yescharacteristic
682C22×C4C2×D5211yescharacteristic
683C22×C4C2×D5211yescharacteristic
684C22×C4C2×D5211yescharacteristic
685C22×C4C2×D5211yescharacteristic
686C22×C4C2×D5211yescharacteristic
687C22×C4C23×D1311yescharacteristic
688C22×C4C23×D1311yescharacteristic
689C22×C4C23×D1311yescharacteristic
690Q16—2616no—
691SD16—2616no—
692M16—28no—
693C2×C8C23×D1318yes—
694C4⋊C4—134no—
695C4⋊C4—132no—
696C4⋊C4—132no—
697C4⋊C4—262no—
698C4⋊C4—262no—
699C4⋊C4—262no—
700C4⋊C4—264no—
701C4⋊C4—264no—
702C4⋊C4—264no—
703C4⋊C4—264no—
704C4⋊C4—262no—
705C4⋊C4—262no—
706C4⋊C4—261no—
707C4⋊C4—261no—
708C4⋊C4—261no—
709C4⋊C4—261no—
710C4⋊C4—262no—
711C4⋊C4—262no—
712C4⋊C4—262no—
713C4⋊C4—262no—
714C22⋊C4—262no—
715C22⋊C4—262no—
716C22⋊C4—262no—
717C22⋊C4—262no—
718C22⋊C4—262no—
719C22⋊C4—262no—
720C22⋊C4—262no—
721C22⋊C4—262no—
722C22⋊C4—262no—
723C42—264no—
724C42—264no—
725C42—264no—
726C42—262no—
727C42—262no—
728C42—264no—
729C42—262no—
730C42C2×D5211yescharacteristic
731C42C2×D5211yescharacteristic
732C42C2×D5211yescharacteristic
733C42C2×D5211yescharacteristic
734C42C2×D5211yescharacteristic
735C42C2×D5211yescharacteristic
736C42C2×D5211yescharacteristic
737C42C2×D5211yescharacteristic
738C42C2×D5211yescharacteristic
739C42C2×D5211yescharacteristic
740C42C2×D5211yescharacteristic
741C42C2×D5211yescharacteristic
742C42C23×D1311yescharacteristic
743C42C23×D1311yescharacteristic
744C42C23×D1311yescharacteristic
745C42C23×D1311yescharacteristic
746C13#6056011yescharacteristic, complemented, Sylow
747C23—22no—
748C23—22no—
749C23—22no—
750C23—262no—
751C23C22×D5211yescharacteristic
752C23C22×D5211yescharacteristic
753C23C22×D5211yescharacteristic
754Q8—138no—
755Q8—268no—
756Q8—268no—
757Q8—268no—
758Q8—264no—
759Q8—264no—
760Q8—522no—
761Q8—522no—
762D4—264no—
763D4—522no—
764D4—524no—
765D4—524no—
766D4—524no—
767D4—522no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—268no—
785C2×C4—268no—
786C2×C4—268no—
787C2×C4—264no—
788C2×C4—264no—
789C2×C4—262no—
790C2×C4—262no—
791C2×C4—262no—
792C2×C4—524no—
793C2×C4—524no—
794C2×C4—524no—
795C2×C4—524no—
796C2×C4—524no—
797C2×C4—524no—
798C2×C4#8816314yescomplemented
799C2×C4C22×D5211yescharacteristic
800C2×C4C22×D5211yescharacteristic
801C2×C4C22×D5211yescharacteristic
802C2×C4C22×D5211yescharacteristic
803C2×C4C22×D5211yescharacteristic
804C2×C4C22×D5211yescharacteristic
805C2×C4C22×D5211yescharacteristic
806C2×C4C22×D5211yescharacteristic
807C2×C4C22×D5211yescharacteristic
808C2×C4C22×D5211yescharacteristic
809C2×C4C22×D5211yescharacteristic
810C2×C4#41×D1314yes—
811C2×C4C24×D1311yescharacteristic
812C8—28no—
813C22—28no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—522no—
821C22—522no—
822C22—522no—
823C22#1171922912yes—
824C22C2×#8816312yes—
825C22#1171945312yes—
826C22C23×D5211yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—268no—
836C4—522no—
837C4—524no—
838C4—522no—
839C4—522no—
840C4#1171922912yes—
841C4C2×#8816312yes—
842C4C2×#8816312yes—
843C4C2×#41×D1312yes—
844C2—22no—
845C2—22no—
846C2—22no—
847C2—1042no—
848C2C2×#1171922911yescharacteristic
849C2C22×#8816311yescharacteristic
850C2C2×#1171945311yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#2920C2
socleC22×C13C23×D4
prime radical#13128132C2
hypercenter#2920D13
hypocenterC13#60560
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic26C2semidirect
3. #13125009C2semidirect
4. #13124967C2semidirect
5. #13124959C2semidirect
6. #13124918C2semidirect
7. #13124876C2semidirect
8. #13124868C2semidirect
9. #13124761C2semidirect
10. #13124643C2semidirect
11. #13124310C2semidirect
12. #13124073C2semidirect
13. C4×#88163C2semidirect
14. C13×#2920C2semidirect
61. #11718512C22semidirect
62. #11718511C22semidirect
63. #11718510C22semidirect
64. #11718509C22semidirect
65. #11718506C22semidirect
66. #11718490C22semidirect
75. #11718377C22semidirect
76. #11718371C22semidirect
77. C4×Dic52C22semidirect
78. C4×#6095C22semidirect
263. C2×Dic26#41semidirect
335. #2920D13semidirect
359. C2×C4×C13#137semidirect
746. C13#60560semidirect
798. C2×C4#88163semidirect

Maximal subgroups

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

subgroupindex
#131281322
C22×C4×Dic262
#131250092
#131249672
#131249592
#131249182
#131248762
#131248682
#131247612
#131246432
#131243102
#131240732
C4×#881632
C13×#29202
#6056013