Finite Group Databasebeta

← C2×#13125677 #16733549

Subgroups — C2×#13125677 #16733549

Order 3328.

2362 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719332C211yesmaximal, characteristic, complemented
2C2×#11719533C211yesmaximal, characteristic, complemented
3#13125677C2116yesmaximal, direct product factor
4C2×#11718475C211yesmaximal, characteristic, complemented
5C2×#11718706C211yesmaximal, characteristic, complemented
6C2×#11718398C211yesmaximal, characteristic, complemented
7C2×#11718440C211yesmaximal, characteristic, complemented
8C2×#11718850C211yesmaximal, characteristic, complemented
9C2×#11718443C211yesmaximal, characteristic, complemented
10C2×#11718473C211yesmaximal, characteristic, complemented
11C2×#11718835C211yesmaximal, characteristic, complemented
12C2×#11718848C211yesmaximal, characteristic, complemented
13C2×#11718899C211yesmaximal, characteristic, complemented
14C2×#11718833C211yesmaximal, characteristic, complemented
15C2×#11718387C211yesmaximal, characteristic, complemented
16C2×C13×#452C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C22×#6131C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C22×C13×Q16C2211yescharacteristic, complemented
21C22×C13×SD16C2211yescharacteristic, complemented
22C2×C13×C22⋊Q8C2211yescharacteristic
23#11719533—24no—
24#11719533C2218yescomplemented
25C2×#88200C2211yescharacteristic
26C2×#88200C2211yescharacteristic
27C2×#88200C2211yescharacteristic
28C22×#6106C2211yescharacteristic, complemented
29C2×#88192C2211yescharacteristic
30C2×#88192C2211yescharacteristic
31C2×#88191—21no—
32C2×#88189—21no—
33C22×#6104C2211yescharacteristic, complemented
34C2×#88184C2211yescharacteristic
35C2×C4×C22⋊D13—21no—
36C2×C4×C22⋊D13—21no—
37C2×#88180C2211yescharacteristic
38C22×#6094C2211yescharacteristic
39C22×#6094C2211yescharacteristic
40#11719332—24no—
41#11719332C2218yescomplemented
42C2×#88149C2211yescharacteristic
43C2×#88148—21no—
44C2×#88147—21no—
45C2×#88146C2211yescharacteristic
46C2×#88136—21no—
47C2×#88135—21no—
48C13×#452C2218yescomplemented
49C2×C13×#103C2211yescharacteristic, complemented
50C2×C13×#102C2211yescharacteristic, complemented
51C2×C13×C22⋊C8C2211yescharacteristic
52#11718899C2218yescomplemented
53C2×#88075C2211yescharacteristic, complemented
54C2×#88075C2211yescharacteristic, complemented
55C2×#88075C2211yescharacteristic, complemented
56C2×#88072C2211yescharacteristic, complemented
57C2×C22⋊#1055C2211yescharacteristic
58#11718850C2218yescomplemented
59#11718848C2218yescomplemented
60#11718835C2218yescomplemented
61#11718833C2218yescomplemented
62C2×#88061C2211yescharacteristic, complemented
63C2×#88061C2211yescharacteristic, complemented
64C2×#88060C2211yescharacteristic
65C2×#88060C2211yescharacteristic
66C2×#88058C2211yescharacteristic, complemented
67C2×#88057C2211yescharacteristic, complemented
68#11718706C2218yescomplemented
69C2×#88048C2211yescharacteristic, complemented
70C2×#88047C2211yescharacteristic, complemented
71#11718475C2218yescomplemented
72#11718473C2218yescomplemented
73#11718443C2218yescomplemented
74#11718440C2218yescomplemented
75#11718398C2218yescomplemented
76#11718387C2218yescomplemented
77C24×D13D411yescharacteristic
78C2×C13×#41—22no—
79C2×C13×#41—42no—
80C2×C13×#41—42no—
81C2×C13×#41C2314yes—
82C22×Q8×C13C2311yescharacteristic
83C22×Q8×C13C2311yescharacteristic
84C22×D4×C13—21no—
85C22×D4×C13C2311yescharacteristic
86C23×C4×C13—21no—
87C23×C4×C13C2311yescharacteristic
88C22×C22⋊D13—21no—
89C22×C22⋊D13—21no—
90C22×C22⋊D13—21no—
91C23×Dic13D411yescharacteristic
92C2×#6131—22no—
93C2×#6131—42no—
94C2×#6131—42no—
95C2×#6131C2314yes—
96C22×D52—21no—
97C22×D52—21no—
98C22×D52C2311yescharacteristic
99C22×C4×D13—21no—
100C22×C4×D13—42no—
101C22×C4×D13—42no—
102C22×C4×D13D411yescharacteristic
103C22×C4×D13D411yescharacteristic
104C22×C4×D13D414yes—
105C22×C4×D13C2311yescharacteristic
106C22×C4×D13C2311yescharacteristic
107C22×C4×D13C2314yes—
108C2×C13×Q16—42no—
109C2×C13×Q16C2314yescomplemented
110C2×C13×SD16—42no—
111C2×C13×SD16C2314yescomplemented
112C22×C8×C13C2311yescharacteristic
113C22×C8×C13C2311yescharacteristic
114C13×C22⋊Q8—22no—
115C13×C22⋊Q8C2314yes—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4C2311yescharacteristic
118C2×C13×C22⋊C4—21no—
119C2×C22⋊Dic13—21no—
120C2×C22⋊Dic13—21no—
121C2×C22⋊Dic13—21no—
122#88200—22no—
123#88200—22no—
124#88200—22no—
125#88200C2314yes—
126#88200C2314yes—
127#88200C2314yes—
128C2×#6106—42no—
129C2×#6106C2314yescomplemented
130#88192—22no—
131#88192—22no—
132#88192C2314yes—
133#88192C2314yes—
134#88191—28no—
135#88189—28no—
136C2×#6104—42no—
137C2×#6104C2314yescomplemented
138#88184—22no—
139#88184C2314yes—
140C4×C22⋊D13—28no—
141C4×C22⋊D13—28no—
142C2×#6103—21no—
143C2×#6103—21no—
144C2×#6103—21no—
145C2×#6103—21no—
146C2×#6103—21no—
147C2×#6103—21no—
148#88180—22no—
149#88180C2314yes—
150C2×C4⋊Dic13C2311yescharacteristic
151C2×C4⋊Dic13C2311yescharacteristic
152C2×C4⋊Dic13C2311yescharacteristic
153C2×#6101—21no—
154C2×#6101—21no—
155C2×#6101—21no—
156C2×C4×Dic13—21no—
157C2×C4×Dic13—21no—
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C2×#6094—42no—
161C2×#6094—42no—
162C2×#6094C2314yes—
163C2×#6094C2314yes—
164#88149—22no—
165#88149C2314yes—
166#88148—28no—
167#88147—28no—
168#88146—22no—
169#88146C2314yes—
170#88136—28no—
171#88135—28no—
172C13×#103C2314yescomplemented
173C13×#102C2314yescomplemented
174C13×C22⋊C8C2314yes—
175#88075C2314yescomplemented
176#88075C2314yescomplemented
177#88075C2314yescomplemented
178#88072C2314yescomplemented
179C22⋊#1055C2314yes—
180#88061C2314yescomplemented
181#88061C2314yescomplemented
182#88060C2314yes—
183#88060C2314yes—
184#88058C2314yescomplemented
185#88057C2314yescomplemented
186#88048C2314yescomplemented
187#88047C2314yescomplemented
188C2×#3197—131nomaximal, Sylow
189C24×C13—21no—
190C24×C13C2×D411yescharacteristic
191C23×D13—21no—
192C23×D13—42no—
193C23×D13—42no—
194C23×D13—42no—
195C23×D13C2×D411yescharacteristic
196C23×D13C2×D411yescharacteristic
197C23×D13C2×D414yes—
198C13×#41—44no—
199C13×#41—44no—
200C13×#41—48no—
201C2×Q8×C13—21no—
202C2×Q8×C13—21no—
203C2×Q8×C13—22no—
204C2×Q8×C13—22no—
205C2×Q8×C13—22no—
206C2×Q8×C13—22no—
207C2×Q8×C13C2412yes—
208C2×Q8×C13C2412yes—
209C2×D4×C13—24no—
210C2×D4×C13—21no—
211C2×D4×C13—22no—
212C2×D4×C13—22no—
213C2×D4×C13—44no—
214C2×D4×C13C2412yes—
215C22×C4×C13—22no—
216C22×C4×C13—22no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—24no—
221C22×C4×C13—44no—
222C22×C4×C13C2×D411yescharacteristic
223C22×C4×C13C2×D412yes—
224C22×C4×C13C2412yes—
225C22×C4×C13C2411yescharacteristic
226C2×C22⋊D13—24no—
227C2×C22⋊D13—24no—
228C2×C22⋊D13—24no—
229C2×C22⋊D13—44no—
230C2×C22⋊D13—44no—
231C2×C22⋊D13—44no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—42no—
236C22×Dic13C2×D411yescharacteristic
237C22×Dic13C2×D411yescharacteristic
238C22×Dic13C2×D414yes—
239#6131—44no—
240#6131—44no—
241#6131—48no—
242C2×D52—22no—
243C2×D52—22no—
244C2×D52—24no—
245C2×D52—24no—
246C2×D52—21no—
247C2×D52—44no—
248C2×D52—44no—
249C2×D52C2412yes—
250C2×C4×D13—22no—
251C2×C4×D13—22no—
252C2×C4×D13—22no—
253C2×C4×D13—22no—
254C2×C4×D13—24no—
255C2×C4×D13—48no—
256C2×C4×D13—44no—
257C2×C4×D13—44no—
258C2×C4×D13—42no—
259C2×C4×D13—42no—
260C2×C4×D13—44no—
261C2×C4×D13C2×D412yes—
262C2×C4×D13C2×D412yes—
263C2×C4×D13C2×D414yes—
264C2×C4×D13C2×D414yes—
265C2×C4×D13C2412yes—
266C2×C4×D13C2412yes—
267C13×Q16—44no—
268C13×SD16—44no—
269C2×C8×C13—22no—
270C2×C8×C13—22no—
271C2×C8×C13C2412yes—
272C2×C8×C13C2412yes—
273C13×C4⋊C4—21no—
274C13×C4⋊C4—24no—
275C13×C4⋊C4C2412yes—
276C13×C22⋊C4—24no—
277C22⋊Dic13—24no—
278C22⋊Dic13—24no—
279C22⋊Dic13—24no—
280#6106—44no—
281#6104—44no—
282#6103—24no—
283#6103—24no—
284#6103—24no—
285#6103—24no—
286#6103—24no—
287#6103—24no—
288C4⋊Dic13—21no—
289C4⋊Dic13—21no—
290C4⋊Dic13—21no—
291C4⋊Dic13C2412yes—
292C4⋊Dic13C2412yes—
293C4⋊Dic13C2412yes—
294#6101—24no—
295#6101—24no—
296#6101—24no—
297C4×Dic13—24no—
298C4×Dic13—24no—
299C2×#1055—22no—
300C2×#1055—22no—
301C2×#1055C2412yes—
302C2×#1055C2412yes—
303#6094—44no—
304#6094—44no—
305C2×#525—131no—
306C2×#525—131no—
307#3197—1316no—
308C2×#485—131no—
309C2×#485—131no—
310C2×#482—131no—
311C2×#482—131no—
312C2×#470—131no—
313C2×#469—131no—
314C2×#468—131no—
315C2×#468—131no—
316C2×#452—131no—
317C2×#452D1311yescharacteristic, complemented
318C2×#449—131no—
319C2×#449—131no—
320C2×#407—131no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—42no—
326C23×C13—42no—
327C23×C13—42no—
328C23×C13C22×D412yes—
329C23×C13C22×D411yescharacteristic
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—44no—
338C22×D13—44no—
339C22×D13—44no—
340C22×D13—416no—
341C22×D13—42no—
342C22×D13—42no—
343C22×D13—42no—
344C22×D13C22×D412yes—
345C22×D13C22×D412yes—
346Q8×C13—22no—
347Q8×C13—22no—
348Q8×C13—22no—
349Q8×C13—22no—
350Q8×C13—42no—
351Q8×C13—42no—
352D4×C13—22no—
353D4×C13—22no—
354D4×C13—48no—
355D4×C13—42no—
356C2×C4×C13—22no—
357C2×C4×C13—24no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—48no—
364C2×C4×C13—42no—
365C2×C4×C13—42no—
366C2×C4×C13—42no—
367C2×C4×C13C22×D412yes—
368C2×C4×C13C22×D411yescharacteristic
369C2×C4×C13H(5,𝔽2)12yes—
370C2×C4×C13H(5,𝔽2)12yes—
371C2×C4×C13C2511yescharacteristic
372C22⋊D13—48no—
373C22⋊D13—48no—
374C22⋊D13—48no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—44no—
381C2×Dic13—42no—
382C2×Dic13—42no—
383C2×Dic13—42no—
384C2×Dic13C22×D412yes—
385C2×Dic13C22×D412yes—
386D52—22no—
387D52—22no—
388D52—48no—
389D52—48no—
390D52—42no—
391C4×D13—24no—
392C4×D13—24no—
393C4×D13—22no—
394C4×D13—22no—
395C4×D13—22no—
396C4×D13—22no—
397C4×D13—44no—
398C4×D13—44no—
399C4×D13—48no—
400C8×C13—22no—
401C8×C13—22no—
402#1055—22no—
403#1055—22no—
404C22×#41—131no—
405C22×#41C2×D1311yescharacteristic
406C24×C4—131no—
407C22×Q16C2×D1311yescharacteristic, complemented
408C22×SD16—131no—
409C22×SD16C2×D1311yescharacteristic, complemented
410C22×D8—131no—
411C22×M16—131no—
412C22×M16—131no—
413#525—138no—
414#525—138no—
415#525—264no—
416#525—264no—
417C2×#123—261no—
418C2×#123—261no—
419C2×C22⋊Q8—131no—
420C2×C22⋊Q8—131no—
421C2×C22⋊Q8—131no—
422C2×C22⋊Q8C2×D1311yescharacteristic
423C2×#121—131no—
424C2×#121—131no—
425C2×#121—131no—
426C2×#121—131no—
427C2×#120—261no—
428C2×#120—261no—
429C2×C4×D4—261no—
430C2×C4×D4—261no—
431C2×C4×D4—261no—
432C2×C4×D4—261no—
433C2×#117—131no—
434C2×#117—131no—
435#485—138no—
436#485—138no—
437#482—138no—
438#482—138no—
439#470—138no—
440#469—138no—
441#468—138no—
442#468—138no—
443#452—138no—
444#452C2×D1318yescomplemented
445#449—138no—
446#449—138no—
447C2×#107—131no—
448C2×#107—131no—
449C2×#106—131no—
450C2×#106—131no—
451C2×#103—131no—
452C2×#103—131no—
453C2×#103—131no—
454C2×#103C2×D1311yescharacteristic, complemented
455C2×#102—131no—
456C2×#102—131no—
457C2×#102—131no—
458C2×#102C2×D1311yescharacteristic, complemented
459#407—138no—
460C2×C22⋊C8—131no—
461C2×C22⋊C8—131no—
462C2×C22⋊C8—131no—
463C2×C22⋊C8C2×D1311yescharacteristic
464C22×C13—22no—
465C22×C13—22no—
466C22×C13—22no—
467C22×C13—44no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—84no—
472C22×C13#53412yes—
473C22×C13#57512yes—
474C22×C13#57512yes—
475C22×C13C23×D411yescharacteristic
476C2×D13—22no—
477C2×D13—22no—
478C2×D13—22no—
479C2×D13—22no—
480C2×D13—22no—
481C2×D13—22no—
482C2×D13—416no—
483C2×D13—44no—
484C2×D13—44no—
485C2×D13—42no—
486C2×D13—42no—
487C2×D13—42no—
488C2×D13—84no—
489C4×C13—22no—
490C4×C13—42no—
491C4×C13—42no—
492C4×C13—42no—
493C4×C13#53412yes—
494C4×C13C2×H(5,𝔽2)11yescharacteristic
495C4×C13C2×H(5,𝔽2)11yescharacteristic
496Dic13—22no—
497Dic13—22no—
498Dic13—42no—
499Dic13—42no—
500Dic13—42no—
501C25—131no—
502C2×#41—22no—
503C2×#41—42no—
504C2×#41—42no—
505C2×#41—134no—
506C2×#41—262no—
507C2×#41—522no—
508C2×#41—522no—
509C2×#41C22×D1314yes—
510C22×Q8C22×D1311yescharacteristic
511C22×Q8C22×D1311yescharacteristic
512C22×D4—21no—
513C22×D4—131no—
514C22×D4—261no—
515C22×D4—261no—
516C22×D4—261no—
517C22×D4—261no—
518C22×D4—261no—
519C22×D4C22×D1311yescharacteristic
520C23×C4—21no—
521C23×C4—131no—
522C23×C4—131no—
523C23×C4—131no—
524C23×C4—131no—
525C23×C4—131no—
526C23×C4—134no—
527C23×C4—134no—
528C23×C4—261no—
529C23×C4—522no—
530C23×C4—522no—
531C23×C4C22×D1311yescharacteristic
532C2×Q16—42no—
533C2×Q16C22×D1314yescomplemented
534C2×SD16—42no—
535C2×SD16—134no—
536C2×SD16—522no—
537C2×SD16C22×D1314yescomplemented
538C2×D8—134no—
539C2×D8—522no—
540C2×M16—134no—
541C2×M16—134no—
542C2×M16—522no—
543C2×M16—522no—
544C22×C8—131no—
545C22×C8—131no—
546C22×C8C22×D1311yescharacteristic
547C22×C8C22×D1311yescharacteristic
548#123—268no—
549#123—268no—
550C22⋊Q8—22no—
551C22⋊Q8—134no—
552C22⋊Q8—134no—
553C22⋊Q8—134no—
554C22⋊Q8—262no—
555C22⋊Q8—262no—
556C22⋊Q8—262no—
557C22⋊Q8C22×D1314yes—
558#121—134no—
559#121—134no—
560#121—134no—
561#121—134no—
562#121—262no—
563#121—262no—
564#121—262no—
565#121—262no—
566#120—268no—
567#120—268no—
568C4×D4—268no—
569C4×D4—268no—
570C4×D4—268no—
571C4×D4—268no—
572#117—134no—
573#117—134no—
574#117—262no—
575#117—262no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—131no—
578C2×C4⋊C4—131no—
579C2×C4⋊C4—131no—
580C2×C4⋊C4—261no—
581C2×C4⋊C4—261no—
582C2×C4⋊C4—261no—
583C2×C4⋊C4C22×D1311yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—261no—
586C2×C22⋊C4—261no—
587C2×C22⋊C4—261no—
588C2×C22⋊C4—261no—
589C2×C22⋊C4—261no—
590C2×C22⋊C4—261no—
591C2×C22⋊C4—261no—
592C2×C22⋊C4—261no—
593C2×C22⋊C4—261no—
594C2×C42—261no—
595C2×C42—261no—
596#107—134no—
597#107—134no—
598#106—134no—
599#106—134no—
600#103—134no—
601#103—134no—
602#103—134no—
603#103C22×D1314yescomplemented
604#102—134no—
605#102—134no—
606#102—134no—
607#102C22×D1314yescomplemented
608C22⋊C8—134no—
609C22⋊C8—134no—
610C22⋊C8—134no—
611C22⋊C8C22×D1314yes—
612C2×C13—42no—
613C2×C13—82no—
614C2×C13#319714yescomplemented
615C2×C13C2×#53411yescharacteristic
616C2×C13C2×#57511yescharacteristic
617C2×C13C2×#57511yescharacteristic
618D13—42no—
619D13—42no—
620D13—82no—
621C24—21no—
622C24—131no—
623C24—131no—
624C24—134no—
625C24—261no—
626C24—522no—
627C24—522no—
628C24—522no—
629C24D4×D1311yescharacteristic
630#41—44no—
631#41—44no—
632#41—48no—
633#41—524no—
634#41—524no—
635#41—528no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8C23×D1312yes—
643C2×Q8C23×D1312yes—
644C2×D4—24no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—44no—
649C2×D4—132no—
650C2×D4—264no—
651C2×D4—264no—
652C2×D4—264no—
653C2×D4—264no—
654C2×D4—264no—
655C2×D4—261no—
656C2×D4—262no—
657C2×D4—262no—
658C2×D4—524no—
659C2×D4—524no—
660C2×D4—524no—
661C2×D4—524no—
662C2×D4—524no—
663C2×D4C23×D1312yes—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—24no—
670C22×C4—44no—
671C22×C4—131no—
672C22×C4—131no—
673C22×C4—134no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—134no—
679C22×C4—134no—
680C22×C4—264no—
681C22×C4—262no—
682C22×C4—262no—
683C22×C4—262no—
684C22×C4—262no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4—528no—
689C22×C4—524no—
690C22×C4—524no—
691C22×C4—522no—
692C22×C4—522no—
693C22×C4—524no—
694C22×C4—522no—
695C22×C4D4×D1312yes—
696C22×C4D4×D1311yescharacteristic
697C22×C4C23×D1312yes—
698C22×C4C23×D1311yescharacteristic
699Q16—44no—
700SD16—44no—
701SD16—524no—
702D8—524no—
703M16—524no—
704M16—524no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—132no—
708C2×C8—132no—
709C2×C8—262no—
710C2×C8—262no—
711C2×C8C23×D1312yes—
712C2×C8C23×D1312yes—
713C4⋊C4—24no—
714C4⋊C4—21no—
715C4⋊C4—132no—
716C4⋊C4—132no—
717C4⋊C4—132no—
718C4⋊C4—264no—
719C4⋊C4—264no—
720C4⋊C4—264no—
721C4⋊C4—261no—
722C4⋊C4—261no—
723C4⋊C4—261no—
724C4⋊C4C23×D1312yes—
725C22⋊C4—24no—
726C22⋊C4—264no—
727C22⋊C4—264no—
728C22⋊C4—264no—
729C22⋊C4—264no—
730C22⋊C4—264no—
731C22⋊C4—264no—
732C22⋊C4—264no—
733C22⋊C4—264no—
734C22⋊C4—264no—
735C42—264no—
736C42—264no—
737C13C2×#319711yescharacteristic, complemented, Sylow
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—132no—
746C23—132no—
747C23—262no—
748C23—262no—
749C23—262no—
750C23—262no—
751C23—262no—
752C23—262no—
753C23—262no—
754C23—524no—
755C23—524no—
756C23—524no—
757C23—5216no—
758C23—522no—
759C23—522no—
760C23—522no—
761C23C2×D4×D1312yes—
762C23C2×D4×D1311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—42no—
768Q8—42no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—42no—
773D4—262no—
774D4—262no—
775D4—528no—
776D4—528no—
777D4—528no—
778D4—528no—
779D4—528no—
780D4—522no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—48no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—132no—
793C2×C4—132no—
794C2×C4—262no—
795C2×C4—262no—
796C2×C4—264no—
797C2×C4—264no—
798C2×C4—262no—
799C2×C4—262no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—262no—
803C2×C4—262no—
804C2×C4—262no—
805C2×C4—524no—
806C2×C4—524no—
807C2×C4—528no—
808C2×C4—524no—
809C2×C4—522no—
810C2×C4—522no—
811C2×C4—522no—
812C2×C4C2×D4×D1312yes—
813C2×C4C2×D4×D1311yescharacteristic
814C2×C4#8825112yes—
815C2×C4#8825112yes—
816C2×C4C24×D1311yescharacteristic
817C8—22no—
818C8—22no—
819C8—262no—
820C8—262no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—84no—
829C22—262no—
830C22—262no—
831C22—262no—
832C22—262no—
833C22—262no—
834C22—262no—
835C22—5216no—
836C22—524no—
837C22—524no—
838C22—522no—
839C22—522no—
840C22—522no—
841C22—1044no—
842C22#1171929412yes—
843C22#1171947312yes—
844C22#1171948212yes—
845C22C22×D4×D1311yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—262no—
851C4—262no—
852C4—522no—
853C4—522no—
854C4—522no—
855C4#1171929412yes—
856C4C2×#8825111yescharacteristic
857C4C2×#8825111yescharacteristic
858C2—42no—
859C2—82no—
860C2—522no—
861C2—522no—
862C2—1042no—
863C2#1312567714yesdirect product factor
864C2C2×#1171929411yescharacteristic
865C2C2×#1171947311yescharacteristic
866C2C2×#1171948211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#452C2
socleC23×C13C22×D4
hypercenterC2×#452D13
hypocenterC13C2×#3197
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#11719332C2semidirect
2. C2×#11719533C2semidirect
3. #13125677C2direct (N × H)
4. C2×#11718475C2semidirect
5. C2×#11718706C2semidirect
6. C2×#11718398C2semidirect
7. C2×#11718440C2semidirect
8. C2×#11718850C2semidirect
9. C2×#11718443C2semidirect
10. C2×#11718473C2semidirect
11. C2×#11718835C2semidirect
12. C2×#11718848C2semidirect
13. C2×#11718899C2semidirect
14. C2×#11718833C2semidirect
15. C2×#11718387C2semidirect
16. C2×C13×#452C2semidirect
20. C22×C13×Q16C22semidirect
21. C22×C13×SD16C22semidirect
24. #11719533C22semidirect
28. C22×#6106C22semidirect
33. C22×#6104C22semidirect
41. #11719332C22semidirect
48. C13×#452C22semidirect
49. C2×C13×#103C22semidirect
50. C2×C13×#102C22semidirect
52. #11718899C22semidirect
53. C2×#88075C22semidirect
54. C2×#88075C22semidirect
55. C2×#88075C22semidirect
56. C2×#88072C22semidirect
58. #11718850C22semidirect
59. #11718848C22semidirect
60. #11718835C22semidirect
61. #11718833C22semidirect
62. C2×#88061C22semidirect
63. C2×#88061C22semidirect
66. C2×#88058C22semidirect
67. C2×#88057C22semidirect
68. #11718706C22semidirect
69. C2×#88048C22semidirect
70. C2×#88047C22semidirect
71. #11718475C22semidirect
72. #11718473C22semidirect
73. #11718443C22semidirect
74. #11718440C22semidirect
75. #11718398C22semidirect
76. #11718387C22semidirect
109. C2×C13×Q16C23semidirect
111. C2×C13×SD16C23semidirect
129. C2×#6106C23semidirect
137. C2×#6104C23semidirect
172. C13×#103C23semidirect
173. C13×#102C23semidirect
175. #88075C23semidirect
176. #88075C23semidirect
177. #88075C23semidirect
178. #88072C23semidirect
180. #88061C23semidirect
181. #88061C23semidirect
184. #88058C23semidirect
185. #88057C23semidirect
186. #88048C23semidirect
187. #88047C23semidirect
317. C2×#452D13semidirect
407. C22×Q16C2×D13semidirect
409. C22×SD16C2×D13semidirect
444. #452C2×D13semidirect
454. C2×#103C2×D13semidirect
458. C2×#102C2×D13semidirect
533. C2×Q16C22×D13semidirect
537. C2×SD16C22×D13semidirect
603. #103C22×D13semidirect
607. #102C22×D13semidirect
614. C2×C13#3197semidirect
737. C13C2×#3197semidirect
863. C2#13125677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193322
C2×#117195332
#131256772
C2×#117184752
C2×#117187062
C2×#117183982
C2×#117184402
C2×#117188502
C2×#117184432
C2×#117184732
C2×#117188352
C2×#117188482
C2×#117188992
C2×#117188332
C2×#117183872
C2×C13×#4522
C2×#319713