Finite Group Databasebeta

← #16731368

Subgroups — #16731368

Order 3328.

2148 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719175C211yesmaximal, characteristic, complemented
2C2×C4×#6127C211yesmaximal, characteristic
3#13124999C214yesmaximal, complemented
4#13124967C212yesmaximal, complemented
5#13124936C212yesmaximal, complemented
6#13124908C214yesmaximal, complemented
7#13124876C212yesmaximal, complemented
8#13124845C212yesmaximal, complemented
9#13124785C212yesmaximal, complemented
10#13124652C212yesmaximal, complemented
11#13124324C212yesmaximal, complemented
12#13124098C212yesmaximal
13C4×#88163C214yesmaximal, complemented
14C13×#2920C211yesmaximal, characteristic, complemented
15C22×#6127C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C2×C4×C22⋊D13—21no—
18C2×C4×C22⋊D13—21no—
19C2×#88180—21no—
20C2×#88180C2211yescharacteristic
21C2×#88178—21no—
22C2×#88178C2212yes—
23C2×#88163C2214yes—
24C4×#6127—21no—
25C4×#6127—21no—
26C4×#6127—21no—
27C4×#6127—21no—
28C4×#6127C2212yes—
29C4×#6127C2212yes—
30C4×#6127C2212yes—
31C4×#6127C2212yes—
32C2×C4×D52C2211yescharacteristic
33C2×C4×D52C2211yescharacteristic
34C2×#88126—21no—
35C2×C42×D13—21no—
36#11719175—21no—
37#11719175—21no—
38#11719175—21no—
39#11719175—21no—
40#11719175C2212yes—
41#11719175C2212yes—
42#11719175C2212yescomplemented
43#11719175C2212yescomplemented
44C2×#88124—21no—
45C2×#88123C2211yescharacteristic, complemented
46C2×#88123C2211yescharacteristic, complemented
47C2×C4×Dic26—21no—
48C2×C4×Dic26C2211yescharacteristic
49C2×C4×Dic26C2211yescharacteristic
50C2×C4×Dic26C2212yescomplemented
51C13×#432C2212yes—
52C13×#432C2212yescomplemented
53C13×#431C2212yes—
54C13×#431C2212yescomplemented
55C13×#423C2212yescomplemented
56C13×#407C2212yes—
57C4×C13×M16C2212yescomplemented
58#11718794C2214yes—
59#11718782C2214yescomplemented
60#11718781C2214yescomplemented
61#11718512C2214yescomplemented
62#11718511C2214yescomplemented
63#11718510C2214yescomplemented
64#11718510C2214yescomplemented
65#11718507C2214yescomplemented
66#11718503C2214yescomplemented
67#11718502C2214yescomplemented
68#11718502C2214yescomplemented
69#11718400C2214yes—
70#11718394C2218yes—
71#11718392C2214yes—
72#11718384C2218yescomplemented
73#11718383C2214yes—
74#11718382C2214yes—
75#11718377C2218yescomplemented
76#11718371C2218yescomplemented
77C4×Dic52C2218yescomplemented
78C4×#6095C2218yescomplemented
79C23×C4×C13D411yescharacteristic
80C23×C4×C13D411yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C22×C22⋊D13—21no—
83C2×#6127—21no—
84C2×#6127—21no—
85C2×#6127—28no—
86C2×#6127C2312yes—
87C2×#6127C2312yes—
88C22×D52C2311yescharacteristic
89C22×C4×D13—21no—
90C22×C4×D13—21no—
91C22×C4×D13—21no—
92C22×Dic26—21no—
93C22×Dic26C2311yescharacteristic
94C22×Dic26C2312yes—
95C2×C13×M16C2314yes—
96C2×C42×C13D411yescharacteristic
97C2×C42×C13D411yescharacteristic
98C2×C42×C13D411yescharacteristic
99C2×C42×C13D411yescharacteristic
100C2×C42×C13D411yescharacteristic
101C2×C42×C13D411yescharacteristic
102C2×C42×C13C2311yescharacteristic
103C2×C42×C13C2311yescharacteristic
104C2×C42×C13C2311yescharacteristic
105C2×C42×C13C2311yescharacteristic
106C2×C42×C13C2311yescharacteristic
107C2×C42×C13C2311yescharacteristic
108C2×C22⋊Dic13—22no—
109C2×C22⋊Dic13—21no—
110C4×C22⋊D13—22no—
111C4×C22⋊D13—22no—
112C4×C22⋊D13—22no—
113C4×C22⋊D13—22no—
114C4×C22⋊D13—22no—
115C4×C22⋊D13—22no—
116C4×C22⋊D13—22no—
117C4×C22⋊D13—22no—
118C2×#6103—21no—
119C2×#6103—21no—
120#88180—22no—
121#88180—22no—
122#88180—22no—
123#88180—22no—
124#88180—21no—
125#88180—21no—
126#88180C2312yes—
127#88180C2312yes—
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13—21no—
130C2×C4⋊Dic13—21no—
131C2×C4⋊Dic13C2311yescharacteristic
132C2×C4⋊Dic13C2311yescharacteristic
133C2×C4⋊Dic13C2312yes—
134#88178—22no—
135#88178—22no—
136#88178—22no—
137#88178—22no—
138#88178—22no—
139#88178—22no—
140#88178C2314yes—
141#88178C2314yes—
142C2×#6101—22no—
143C2×#6101—21no—
144C2×#6101—21no—
145C2×#6101—22no—
146C2×C4×Dic13—22no—
147C2×C4×Dic13—21no—
148C2×C4×Dic13—21no—
149C2×C4×Dic13—21no—
150#88163—216no—
151C2×Dic52C2318yes—
152C2×#6095C2318yes—
153C4×D52—21no—
154C4×D52—21no—
155C4×D52—21no—
156C4×D52—21no—
157C4×D52C2312yes—
158C4×D52C2312yes—
159C4×D52C2312yes—
160C4×D52C2312yes—
161#88126—22no—
162#88126—22no—
163#88126—22no—
164#88126—22no—
165C42×D13—22no—
166C42×D13—22no—
167C42×D13—22no—
168C42×D13—22no—
169#88124—22no—
170#88124—22no—
171#88124—22no—
172#88124—22no—
173#88123—21no—
174#88123—21no—
175#88123—21no—
176#88123—21no—
177#88123C2312yes—
178#88123C2312yes—
179#88123C2312yes—
180#88123C2312yes—
181C4×Dic26—22no—
182C4×Dic26—22no—
183C4×Dic26—22no—
184C4×Dic26—22no—
185C4×Dic26—21no—
186C4×Dic26—21no—
187C4×Dic26—21no—
188C4×Dic26—21no—
189C4×Dic26—22no—
190C4×Dic26—22no—
191C4×Dic26C2312yes—
192C4×Dic26C2312yes—
193C4×Dic26C2312yes—
194C4×Dic26C2312yes—
195C4×Dic26C2314yes—
196C4×Dic26C2314yes—
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#60562—131nomaximal, Sylow
210C24×C13C2×D411yescharacteristic
211C23×D13—21no—
212C22×C4×C13—24no—
213C22×C4×C13—24no—
214C22×C4×C13—42no—
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×C13C2×D411yescharacteristic
230C22×C4×C13C2411yescharacteristic
231C22×C4×C13C2411yescharacteristic
232C22×C4×C13C2411yescharacteristic
233C2×C22⋊D13—28no—
234C2×C22⋊D13—22no—
235C2×C22⋊D13—22no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—22no—
240C22×Dic13—22no—
241#6127—28no—
242#6127—28no—
243#6127—24no—
244#6127—24no—
245#6127—24no—
246#6127#4118yes—
247C2×D52—21no—
248C2×D52—24no—
249C2×D52C2412yes—
250C2×C4×D13—28no—
251C2×C4×D13—22no—
252C2×C4×D13—22no—
253C2×C4×D13—22no—
254C2×C4×D13—22no—
255C2×C4×D13—22no—
256C2×C4×D13—22no—
257C2×C4×D13—44no—
258C2×C4×D13—44no—
259C2×Dic26—21no—
260C2×Dic26—24no—
261C2×Dic26—28no—
262C2×Dic26—22no—
263C2×Dic26—22no—
264C2×Dic26—22no—
265C2×Dic26—44no—
266C2×Dic26C2414yes—
267C2×Dic26C2412yes—
268C13×M16—28no—
269C2×C8×C13C2418yes—
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×C13C2×D411yescharacteristic
281C42×C13C2×D411yescharacteristic
282C42×C13C2411yescharacteristic
283C42×C13C2411yescharacteristic
284C42×C13C2411yescharacteristic
285C42×C13C2411yescharacteristic
286C22⋊Dic13—24no—
287C22⋊Dic13—24no—
288C22⋊Dic13—22no—
289C22⋊Dic13—22no—
290#6103—22no—
291#6103—22no—
292#6103—22no—
293#6103—22no—
294C4⋊Dic13—22no—
295C4⋊Dic13—22no—
296C4⋊Dic13—22no—
297C4⋊Dic13—21no—
298C4⋊Dic13—21no—
299C4⋊Dic13—22no—
300C4⋊Dic13—22no—
301C4⋊Dic13—22no—
302C4⋊Dic13—22no—
303C4⋊Dic13C2414yes—
304C4⋊Dic13C2412yes—
305C4⋊Dic13C2412yes—
306#6101—24no—
307#6101—24no—
308#6101—24no—
309#6101—24no—
310#6101—22no—
311#6101—22no—
312#6101—22no—
313#6101—22no—
314C4×Dic13—24no—
315C4×Dic13—24no—
316C4×Dic13—22no—
317C4×Dic13—22no—
318C4×Dic13—22no—
319C4×Dic13—22no—
320C4×Dic13—22no—
321C4×Dic13—22no—
322Dic52—216no—
323#6095—216no—
324C2×#533—131no—
325C2×C4×#41—131no—
326#3116—134no—
327#3113—132no—
328#3110—132no—
329#3107—134no—
330#3104—132no—
331#3101—132no—
332#3095—132no—
333#3079—132no—
334#3039—132no—
335#3007—132no—
336C4×#137—134no—
337#2920D1311yescharacteristic, complemented
338C23×C13—22no—
339C23×C13—22no—
340C23×C13—41no—
341C23×C13C22×D411yescharacteristic
342C23×C13C22×D411yescharacteristic
343C23×C13C22×D411yescharacteristic
344C22×D13—24no—
345C22×D13—22no—
346C22×D13—42no—
347C22×D13—42no—
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—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13#13714yescomplemented
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×C13C22×D411yescharacteristic
372C2×C4×C13C22×D411yescharacteristic
373C2×C4×C13C22×D411yescharacteristic
374C2×C4×C13C22×D411yescharacteristic
375C2×C4×C13C22×D411yescharacteristic
376C2×C4×C13C2×#4114yes—
377C2×C4×C13C2511yescharacteristic
378C22⋊D13—28no—
379C22⋊D13—28no—
380C2×Dic13—24no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—24no—
385C2×Dic13—24no—
386C2×Dic13—44no—
387C2×Dic13—42no—
388C2×Dic13—44no—
389C2×Dic13—42no—
390D52—24no—
391D52—22no—
392D52C2×#4114yes—
393C4×D13—28no—
394C4×D13—28no—
395C4×D13—44no—
396C4×D13—44no—
397C4×D13—44no—
398C4×D13—44no—
399Dic26—24no—
400Dic26—22no—
401Dic26—28no—
402Dic26—44no—
403Dic26—44no—
404Dic26—44no—
405Dic26C2×#4114yes—
406C8×C13—28no—
407C22×#41—131no—
408C2×#137—134no—
409#533—132no—
410#533—132no—
411#533—132no—
412#533—132no—
413#533—261no—
414#533—261no—
415#533—261no—
416#533—261no—
417C2×C4⋊Q8—131no—
418C2×C4⋊Q8—131no—
419C2×#125—261no—
420C2×C22⋊Q8—132no—
421C2×C22⋊Q8—261no—
422C4×#41—132no—
423C4×#41—132no—
424C4×#41—132no—
425C4×#41—132no—
426C4×#41—261no—
427C4×#41—261no—
428C4×#41—261no—
429C4×#41—261no—
430C2×C4×Q8—131no—
431C2×C4×Q8—131no—
432C2×C4×Q8—132no—
433C2×C4×Q8—261no—
434C2×C4×D4—131no—
435C2×C4×D4—131no—
436C2×C4×D4—261no—
437C2×C4×D4—261no—
438C2×#117—131no—
439C2×#117—261no—
440C2×#117—261no—
441C22×C42—261no—
442C22×C42C2×D1311yescharacteristic
443#485—138no—
444#484—134no—
445#483—134no—
446#477—134no—
447#476—134no—
448#475—134no—
449#474—134no—
450#462—134no—
451#462—134no—
452#461—134no—
453#461—134no—
454#452—138no—
455#451—134no—
456#450—134no—
457#441—138no—
458#440—138no—
459C4×Q16—138no—
460C4×SD16—138no—
461#432C2×D1312yes—
462#432C2×D1312yescomplemented
463#431C2×D1312yes—
464#431C2×D1312yescomplemented
465#428—134no—
466#423C2×D1312yescomplemented
467#419—134no—
468#417—134no—
469#407C2×D1312yes—
470C4×M16C2×D1312yescomplemented
471C22×C13—21no—
472C22×C13—21no—
473C22×C13—21no—
474C22×C13—21no—
475C22×C13—21no—
476C22×C13—21no—
477C22×C13—21no—
478C22×C13—44no—
479C22×C13#52512yes—
480C22×C13C2×#13712yes—
481C22×C13C23×D411yescharacteristic
482C2×D13—24no—
483C2×D13—48no—
484C2×D13—42no—
485C2×D13—42no—
486C4×C13—21no—
487C4×C13—21no—
488C4×C13—21no—
489C4×C13—21no—
490C4×C13—21no—
491C4×C13—21no—
492C4×C13—21no—
493C4×C13#52512yes—
494C4×C13C2×#13712yes—
495C4×C13C2×#13712yes—
496C4×C13#57512yes—
497C4×C13C22×#4112yes—
498Dic13—24no—
499Dic13—44no—
500Dic13—42no—
501Dic13—44no—
502Dic13—42no—
503C2×#41—132no—
504C2×#41—132no—
505C2×#41—268no—
506C2×#41—261no—
507C2×#41—261no—
508C22×Q8—131no—
509C22×Q8—132no—
510C22×Q8—261no—
511C22×D4—131no—
512C22×D4—261no—
513C23×C4—261no—
514C23×C4—261no—
515C23×C4—261no—
516C23×C4D5211yescharacteristic
517C23×C4D5211yescharacteristic
518C23×C4C22×D1311yescharacteristic
519#137—2616no—
520C2×Q16—138no—
521C2×SD16—138no—
522C2×M16C22×D1314yes—
523C4⋊Q8—132no—
524C4⋊Q8—132no—
525C4⋊Q8—132no—
526C4⋊Q8—132no—
527C4⋊Q8—261no—
528C4⋊Q8—261no—
529C4⋊Q8—261no—
530C4⋊Q8—261no—
531#125—262no—
532#125—262no—
533#125—262no—
534#125—262no—
535C22⋊Q8—134no—
536C22⋊Q8—134no—
537C22⋊Q8—262no—
538C22⋊Q8—262no—
539C22⋊Q8—262no—
540C22⋊Q8—262no—
541C22⋊Q8—262no—
542C22⋊Q8—262no—
543C4×Q8—132no—
544C4×Q8—132no—
545C4×Q8—132no—
546C4×Q8—132no—
547C4×Q8—134no—
548C4×Q8—134no—
549C4×Q8—261no—
550C4×Q8—261no—
551C4×Q8—261no—
552C4×Q8—261no—
553C4×Q8—262no—
554C4×Q8—262no—
555C4×Q8—262no—
556C4×Q8—262no—
557C4×Q8—262no—
558C4×Q8—262no—
559C4×D4—132no—
560C4×D4—132no—
561C4×D4—132no—
562C4×D4—132no—
563C4×D4—262no—
564C4×D4—262no—
565C4×D4—262no—
566C4×D4—262no—
567C4×D4—262no—
568C4×D4—262no—
569C4×D4—262no—
570C4×D4—262no—
571C4×D4—261no—
572C4×D4—261no—
573C4×D4—261no—
574C4×D4—261no—
575#117—132no—
576#117—132no—
577#117—261no—
578#117—261no—
579#117—262no—
580#117—262no—
581#117—262no—
582#117—262no—
583#117—262no—
584#117—262no—
585#117—262no—
586#117—262no—
587C2×C4⋊C4—131no—
588C2×C4⋊C4—131no—
589C2×C4⋊C4—132no—
590C2×C4⋊C4—261no—
591C2×C4⋊C4—261no—
592C2×C4⋊C4—261no—
593C2×C4⋊C4—261no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C4⋊C4—261no—
597C2×C22⋊C4—261no—
598C2×C22⋊C4—262no—
599C2×C22⋊C4—261no—
600C2×C22⋊C4—261no—
601C2×C42—261no—
602C2×C42—262no—
603C2×C42—261no—
604C2×C42—261no—
605C2×C42—262no—
606C2×C42—262no—
607C2×C42—262no—
608C2×C42—262no—
609C2×C42D5211yescharacteristic
610C2×C42D5211yescharacteristic
611C2×C42D5211yescharacteristic
612C2×C42D5211yescharacteristic
613C2×C42D5211yescharacteristic
614C2×C42D5211yescharacteristic
615C2×C42C22×D1311yescharacteristic
616C2×C42C22×D1311yescharacteristic
617C2×C42C22×D1311yescharacteristic
618C2×C42C22×D1311yescharacteristic
619C2×C42C22×D1311yescharacteristic
620C2×C42C22×D1311yescharacteristic
621#107—138no—
622#106—138no—
623C4⋊C8C22×D1314yes—
624C4⋊C8C22×D1314yes—
625#103—138no—
626#103—138no—
627#103—138no—
628#102—138no—
629C22⋊C8C22×D1314yes—
630C22⋊C8C22×D1314yes—
631#97C22×D1314yes—
632C4×C8C22×D1314yes—
633C2×C13—22no—
634C2×C13—22no—
635C2×C13—41no—
636C2×C13C2×#52511yescharacteristic
637C2×C13C22×#13711yescharacteristic
638C2×C13C2×#57511yescharacteristic
639D13—44no—
640C24—261no—
641C24C2×D5211yescharacteristic
642#41—138no—
643#41—264no—
644#41—264no—
645#41—268no—
646#41—268no—
647#41—264no—
648C2×Q8—132no—
649C2×Q8—134no—
650C2×Q8—264no—
651C2×Q8—261no—
652C2×Q8—262no—
653C2×Q8—262no—
654C2×Q8—262no—
655C2×Q8—268no—
656C2×Q8—524no—
657C2×D4—132no—
658C2×D4—264no—
659C2×D4—268no—
660C2×D4—262no—
661C2×D4—262no—
662C2×D4—261no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—42no—
666C22×C4—268no—
667C22×C4—261no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—261no—
671C22×C4—261no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—262no—
675C22×C4—262no—
676C22×C4—262no—
677C22×C4—262no—
678C22×C4—524no—
679C22×C4—524no—
680C22×C4C2×D5211yescharacteristic
681C22×C4C2×D5211yescharacteristic
682C22×C4C2×D5211yescharacteristic
683C22×C4C2×D5211yescharacteristic
684C22×C4C2×D5211yescharacteristic
685C22×C4C2×D5211yescharacteristic
686C22×C4C2×D5211yescharacteristic
687C22×C4C2×D5211yescharacteristic
688C22×C4C2×D5211yescharacteristic
689C22×C4C2×D5211yescharacteristic
690C22×C4C2×D5211yescharacteristic
691C22×C4C2×D5211yescharacteristic
692C22×C4C2×D5211yescharacteristic
693C22×C4C2×D5211yescharacteristic
694C22×C4C2×D5211yescharacteristic
695C22×C4C23×D1311yescharacteristic
696C22×C4C23×D1311yescharacteristic
697C22×C4C23×D1311yescharacteristic
698Q16—2616no—
699SD16—2616no—
700M16—28no—
701C2×C8C23×D1318yes—
702C4⋊C4—134no—
703C4⋊C4—132no—
704C4⋊C4—132no—
705C4⋊C4—261no—
706C4⋊C4—261no—
707C4⋊C4—262no—
708C4⋊C4—262no—
709C4⋊C4—262no—
710C4⋊C4—262no—
711C4⋊C4—262no—
712C4⋊C4—262no—
713C4⋊C4—262no—
714C4⋊C4—262no—
715C4⋊C4—262no—
716C4⋊C4—264no—
717C4⋊C4—264no—
718C4⋊C4—264no—
719C4⋊C4—264no—
720C4⋊C4—262no—
721C4⋊C4—262no—
722C22⋊C4—262no—
723C22⋊C4—262no—
724C22⋊C4—264no—
725C22⋊C4—264no—
726C22⋊C4—262no—
727C22⋊C4—262no—
728C22⋊C4—262no—
729C22⋊C4—262no—
730C42—262no—
731C42—262no—
732C42—262no—
733C42—262no—
734C42—262no—
735C42—264no—
736C42—262no—
737C42—264no—
738C42C2×D5211yescharacteristic
739C42C2×D5211yescharacteristic
740C42C2×D5211yescharacteristic
741C42C2×D5211yescharacteristic
742C42C2×D5211yescharacteristic
743C42C2×D5211yescharacteristic
744C42C2×D5211yescharacteristic
745C42C2×D5211yescharacteristic
746C42C2×D5211yescharacteristic
747C42C2×D5211yescharacteristic
748C42C2×D5211yescharacteristic
749C42C2×D5211yescharacteristic
750C42C23×D1311yescharacteristic
751C42C23×D1311yescharacteristic
752C42C23×D1311yescharacteristic
753C42C23×D1311yescharacteristic
754C13#6056211yescharacteristic, complemented, Sylow
755C23—22no—
756C23—22no—
757C23—41no—
758C23—264no—
759C23—262no—
760C23—522no—
761C23—522no—
762C23C22×D5211yescharacteristic
763C23C22×D5211yescharacteristic
764C23C22×D5211yescharacteristic
765Q8—134no—
766Q8—264no—
767Q8—262no—
768Q8—268no—
769Q8—524no—
770Q8—524no—
771Q8—524no—
772D4—134no—
773D4—264no—
774D4—268no—
775D4—268no—
776D4—262no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—268no—
794C2×C4—264no—
795C2×C4—262no—
796C2×C4—268no—
797C2×C4—262no—
798C2×C4—262no—
799C2×C4—264no—
800C2×C4—264no—
801C2×C4—524no—
802C2×C4—522no—
803C2×C4—524no—
804C2×C4—522no—
805C2×C4—524no—
806C2×C4—524no—
807C2×C4—524no—
808C2×C4—524no—
809C2×C4#8816314yescomplemented
810C2×C4C22×D5211yescharacteristic
811C2×C4C22×D5211yescharacteristic
812C2×C4C22×D5211yescharacteristic
813C2×C4C22×D5211yescharacteristic
814C2×C4C22×D5211yescharacteristic
815C2×C4C22×D5211yescharacteristic
816C2×C4C22×D5211yescharacteristic
817C2×C4C22×D5211yescharacteristic
818C2×C4C22×D5211yescharacteristic
819C2×C4C22×D5211yescharacteristic
820C2×C4C22×D5211yescharacteristic
821C2×C4#41×D1314yes—
822C2×C4C24×D1311yescharacteristic
823C8—28no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—44no—
832C22—264no—
833C22—528no—
834C22—522no—
835C22—522no—
836C22#1171922912yes—
837C22C2×#8816312yes—
838C22C23×D5211yescharacteristic
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—264no—
847C4—522no—
848C4—522no—
849C4—524no—
850C4—524no—
851C4#1171922912yes—
852C4C2×#8816312yes—
853C4C2×#8816312yes—
854C4#1171945312yes—
855C4C2×#41×D1312yes—
856C2—22no—
857C2—22no—
858C2—41no—
859C2—524no—
860C2C2×#1171922911yescharacteristic
861C2C22×#8816311yescharacteristic
862C2C2×#1171945311yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#2920C2
socleC22×C13C23×D4
prime radicalC22×#6127C22
hypercenter#2920D13
hypocenterC13#60562
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
1. C2×#11719175C2semidirect
3. #13124999C2semidirect
4. #13124967C2semidirect
5. #13124936C2semidirect
6. #13124908C2semidirect
7. #13124876C2semidirect
8. #13124845C2semidirect
9. #13124785C2semidirect
10. #13124652C2semidirect
11. #13124324C2semidirect
13. C4×#88163C2semidirect
14. C13×#2920C2semidirect
42. #11719175C22semidirect
43. #11719175C22semidirect
45. C2×#88123C22semidirect
46. C2×#88123C22semidirect
50. C2×C4×Dic26C22semidirect
52. C13×#432C22semidirect
54. C13×#431C22semidirect
55. C13×#423C22semidirect
57. C4×C13×M16C22semidirect
59. #11718782C22semidirect
60. #11718781C22semidirect
61. #11718512C22semidirect
62. #11718511C22semidirect
63. #11718510C22semidirect
64. #11718510C22semidirect
65. #11718507C22semidirect
66. #11718503C22semidirect
67. #11718502C22semidirect
68. #11718502C22semidirect
72. #11718384C22semidirect
75. #11718377C22semidirect
76. #11718371C22semidirect
77. C4×Dic52C22semidirect
78. C4×#6095C22semidirect
337. #2920D13semidirect
364. C2×C4×C13#137semidirect
462. #432C2×D13semidirect
464. #431C2×D13semidirect
466. #423C2×D13semidirect
470. C4×M16C2×D13semidirect
754. C13#60562semidirect
809. C2×C4#88163semidirect

Maximal subgroups

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

subgroupindex
C2×#117191752
C2×C4×#61272
#131249992
#131249672
#131249362
#131249082
#131248762
#131248452
#131247852
#131246522
#131243242
#131240982
C4×#881632
C13×#29202
#6056213