Finite Group Databasebeta

← C2×#13124787 #16730739

Subgroups — C2×#13124787 #16730739

Order 3328.

2362 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719312C211yesmaximal, characteristic
2C2×#11719209C211yesmaximal, characteristic, complemented
3#13124787C2116yesmaximal, direct product factor
4C2×#11718629C211yesmaximal, characteristic, complemented
5C2×#11718438C211yesmaximal, characteristic, complemented
6C2×#11718546C211yesmaximal, characteristic, complemented
7C2×#11718398C211yesmaximal, characteristic, complemented
8C2×#11718445C211yesmaximal, characteristic, complemented
9C2×#11718696C211yesmaximal, characteristic, complemented
10C2×#11718543C211yesmaximal, characteristic, complemented
11C2×#11718542C211yesmaximal, characteristic, complemented
12C2×#11718541C211yesmaximal, characteristic, complemented
13C2×#11718431C211yesmaximal, characteristic, complemented
14C2×D13×#102C211yesmaximal, characteristic, complemented
15C2×#11718388C211yesmaximal, characteristic, complemented
16C2×C13×#480C211yesmaximal, characteristic, complemented
17C22×D4×D13C2211yescharacteristic
18C22×#6127C2211yescharacteristic
19C2×C13×#121C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic, complemented
21C2×#88194—21no—
22C2×#88192C2211yescharacteristic
23C2×#88191—21no—
24C2×#88184C2211yescharacteristic
25C2×C4×C22⋊D13—21no—
26C2×C4×C22⋊D13—21no—
27C2×#88180C2211yescharacteristic, complemented
28C22×#6094C2211yescharacteristic
29C22×C8×D13C2211yescharacteristic
30#11719312—24no—
31#11719312C2218yes—
32C2×#88149C2211yescharacteristic
33#11719209—24no—
34#11719209C2218yescomplemented
35C2×#88147—21no—
36C2×#88146C2211yescharacteristic
37C2×#88146C2211yescharacteristic
38C2×#88146C2211yescharacteristic, complemented
39C2×C4⋊C4×D13C2211yescharacteristic
40C2×C4⋊C4×D13C2211yescharacteristic, complemented
41C2×#88141—21no—
42C2×#88139—21no—
43C2×#88136—21no—
44C13×#480C2218yescomplemented
45C2×C13×#107C2211yescharacteristic, complemented
46C2×C13×#107C2211yescharacteristic, complemented
47C2×C13×#102C2211yescharacteristic
48C2×C13×#102C2211yescharacteristic
49C2×C13×C22⋊C8C2211yescharacteristic, complemented
50C2×#88072C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×C22⋊#1055C2211yescharacteristic, complemented
53C2×#88061C2211yescharacteristic
54C2×#88061C2211yescharacteristic
55C2×#88060C2211yescharacteristic, complemented
56C2×#88060C2211yescharacteristic, complemented
57C2×#88058C2211yescharacteristic, complemented
58C2×#88057C2211yescharacteristic, complemented
59#11718696C2218yescomplemented
60#11718629C2218yescomplemented
61C2×#88049C2211yescharacteristic
62C2×#88049C2211yescharacteristic
63C2×#88048C2211yescharacteristic, complemented
64C2×#88048C2211yescharacteristic, complemented
65C2×#88048C2211yescharacteristic, complemented
66C2×#88047C2211yescharacteristic, complemented
67#11718546C2218yescomplemented
68#11718543C2218yescomplemented
69#11718542C2218yescomplemented
70#11718541C2218yescomplemented
71#11718445C2218yescomplemented
72#11718438C2218yescomplemented
73#11718431C2218yescomplemented
74D13×#102C2218yescomplemented
75#11718398C2218yescomplemented
76#11718388C2218yescomplemented
77C24×D13—21no—
78C22×D4×C13—21no—
79C22×D4×C13C2311yescharacteristic
80C23×C4×C13—21no—
81C23×C4×C13C2311yescharacteristic
82C22×C22⋊D13—21no—
83C22×C22⋊D13—21no—
84C22×C22⋊D13—21no—
85C22×C22⋊D13D411yescharacteristic
86C22×C22⋊D13D411yescharacteristic
87C2×D4×D13—22no—
88C2×D4×D13—24no—
89C2×D4×D13—24no—
90C2×D4×D13C2314yes—
91C2×#6127—24no—
92C2×#6127—24no—
93C2×#6127D414yes—
94C2×#6127C2314yes—
95C22×D52—21no—
96C22×D52D411yescharacteristic
97C22×D52C2311yescharacteristic
98C22×C4×D13—21no—
99C22×C4×D13—21no—
100C22×C4×D13C2311yescharacteristic
101C22×C4×D13C2311yescharacteristic
102C22×Dic26D411yescharacteristic
103C22×C8×C13C2311yescharacteristic
104C22×C8×C13C2311yescharacteristic
105C13×#121—22no—
106C13×#121C2314yes—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—22no—
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C4⋊C4C2311yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C4⋊C4C2314yescomplemented
113C2×C13×C22⋊C4—21no—
114C2×C22⋊Dic13—21no—
115C2×C22⋊Dic13—21no—
116#88194—28no—
117#88192—22no—
118#88192C2314yes—
119#88191—28no—
120#88184—22no—
121#88184C2314yes—
122C4×C22⋊D13—28no—
123C4×C22⋊D13—28no—
124C2×#6103—21no—
125C2×#6103—21no—
126C2×#6103—21no—
127C2×#6103—21no—
128C2×#6103—21no—
129#88180—22no—
130#88180C2314yescomplemented
131C2×C4⋊Dic13C2311yescharacteristic
132C2×C4⋊Dic13C2311yescharacteristic
133C2×C4⋊Dic13C2311yescharacteristic
134C2×#6101—21no—
135C2×#6101—21no—
136C2×C4×Dic13—21no—
137C2×C4×Dic13—21no—
138C2×C4×Dic13—21no—
139C2×C4×Dic13—21no—
140C22×#1055C2311yescharacteristic
141C22×#1055C2311yescharacteristic
142C2×#6094—24no—
143C2×#6094C2314yes—
144C2×C8×D13—24no—
145C2×C8×D13C2314yes—
146#88149—22no—
147#88149C2314yes—
148#88147—28no—
149#88146—22no—
150#88146—22no—
151#88146—22no—
152#88146C2314yes—
153#88146C2314yes—
154#88146C2314yescomplemented
155C4⋊C4×D13—22no—
156C4⋊C4×D13—22no—
157C4⋊C4×D13C2314yes—
158C4⋊C4×D13C2314yescomplemented
159#88141—28no—
160#88139—28no—
161#88136—28no—
162C13×#107C2314yescomplemented
163C13×#107C2314yescomplemented
164C13×#102C2314yes—
165C13×#102C2314yes—
166C13×C22⋊C8C2314yescomplemented
167#88072C2314yes—
168#88072C2314yes—
169C22⋊#1055C2314yescomplemented
170#88061C2314yes—
171#88061C2314yes—
172#88060C2314yescomplemented
173#88060C2314yescomplemented
174#88058C2314yescomplemented
175#88057C2314yescomplemented
176#88049C2314yes—
177#88049C2314yes—
178#88048C2314yescomplemented
179#88048C2314yescomplemented
180#88048C2314yescomplemented
181#88047C2314yescomplemented
182C2×#3096—131nomaximal, Sylow
183C24×C13—21no—
184C24×C13C2×D411yescharacteristic
185C23×D13—21no—
186C23×D13—24no—
187C23×D13—44no—
188C23×D13—82no—
189C23×D13—82no—
190C23×D13C2×D411yescharacteristic
191C23×D13C2×D411yescharacteristic
192C2×D4×C13—24no—
193C2×D4×C13—21no—
194C2×D4×C13—22no—
195C2×D4×C13—22no—
196C2×D4×C13—82no—
197C2×D4×C13C2412yes—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—24no—
204C22×C4×C13—82no—
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2412yes—
208C22×C4×C13C2411yescharacteristic
209C2×C22⋊D13—24no—
210C2×C22⋊D13—24no—
211C2×C22⋊D13—24no—
212C2×C22⋊D13—24no—
213C2×C22⋊D13—24no—
214C2×C22⋊D13—44no—
215C2×C22⋊D13—82no—
216C2×C22⋊D13—82no—
217C2×C22⋊D13C2×D414yes—
218C2×C22⋊D13C2×D414yes—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13C2×D411yescharacteristic
223C22×Dic13C2×D411yescharacteristic
224D4×D13—28no—
225D4×D13—28no—
226D4×D13—48no—
227#6127—216no—
228#6127—28no—
229#6127—28no—
230C2×D52—24no—
231C2×D52—22no—
232C2×D52—22no—
233C2×D52—21no—
234C2×D52—24no—
235C2×D52—82no—
236C2×D52C2×D414yes—
237C2×D52C2412yes—
238C2×C4×D13—22no—
239C2×C4×D13—22no—
240C2×C4×D13—24no—
241C2×C4×D13—24no—
242C2×C4×D13—82no—
243C2×C4×D13—82no—
244C2×C4×D13C2×D412yes—
245C2×C4×D13C2×D412yes—
246C2×C4×D13#4114yes—
247C2×C4×D13#4114yes—
248C2×C4×D13C2412yes—
249C2×C4×D13C2412yes—
250C2×Dic26—24no—
251C2×Dic26C2×D414yes—
252C2×C8×C13—22no—
253C2×C8×C13—22no—
254C2×C8×C13C2412yes—
255C2×C8×C13C2412yes—
256C13×C4⋊C4—24no—
257C13×C4⋊C4—21no—
258C13×C4⋊C4—21no—
259C13×C4⋊C4—21no—
260C13×C4⋊C4C2412yes—
261C13×C4⋊C4C2412yes—
262C13×C4⋊C4C2412yes—
263C13×C22⋊C4—24no—
264C22⋊Dic13—24no—
265C22⋊Dic13—24no—
266#6103—24no—
267#6103—24no—
268#6103—24no—
269#6103—24no—
270#6103—24no—
271C4⋊Dic13—21no—
272C4⋊Dic13—21no—
273C4⋊Dic13—21no—
274C4⋊Dic13C2412yes—
275C4⋊Dic13C2412yes—
276C4⋊Dic13C2412yes—
277#6101—24no—
278#6101—24no—
279C4×Dic13—24no—
280C4×Dic13—24no—
281C4×Dic13—24no—
282C4×Dic13—24no—
283C2×#1055—22no—
284C2×#1055—22no—
285C2×#1055C2412yes—
286C2×#1055C2412yes—
287#6094—28no—
288C8×D13—28no—
289C2×#535—131no—
290C2×#520—131no—
291#3096—1316no—
292C2×#481—131no—
293C2×#481—131no—
294C2×#482—131no—
295C2×#482—131no—
296C2×#482—131no—
297C2×#482—131no—
298C2×#480—131no—
299C2×#480D1311yescharacteristic, complemented
300C2×#428—131no—
301C2×#427—131no—
302C2×#418—131no—
303C22×#102—131no—
304C2×#408—131no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—42no—
310C23×C13—42no—
311C23×C13—42no—
312C23×C13C22×D412yes—
313C23×C13C22×D411yescharacteristic
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—42no—
321C22×D13—42no—
322C22×D13—42no—
323C22×D13—48no—
324C22×D13—84no—
325C22×D13—84no—
326C22×D13—816no—
327C22×D13#12314yes—
328C22×D13C22×D412yes—
329C22×D13C22×D412yes—
330D4×C13—22no—
331D4×C13—22no—
332D4×C13—42no—
333D4×C13—84no—
334C2×C4×C13—22no—
335C2×C4×C13—24no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—42no—
342C2×C4×C13—42no—
343C2×C4×C13—42no—
344C2×C4×C13—84no—
345C2×C4×C13C22×D412yes—
346C2×C4×C13C22×D411yescharacteristic
347C2×C4×C13C2×#4112yes—
348C2×C4×C13C2×#4112yes—
349C2×C4×C13C2511yescharacteristic
350C22⋊D13—28no—
351C22⋊D13—28no—
352C22⋊D13—48no—
353C22⋊D13—84no—
354C22⋊D13—84no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—42no—
360C2×Dic13—42no—
361C2×Dic13—42no—
362C2×Dic13#12314yes—
363C2×Dic13C22×D412yes—
364C2×Dic13C22×D412yes—
365D52—28no—
366D52—22no—
367D52—22no—
368D52—42no—
369D52—84no—
370C4×D13—24no—
371C4×D13—22no—
372C4×D13—22no—
373C4×D13—84no—
374C4×D13—84no—
375C4×D13#12318yes—
376C4×D13C2×#4114yes—
377C4×D13C2×#4114yes—
378Dic26—28no—
379C8×C13—22no—
380C8×C13—22no—
381#1055—22no—
382#1055—22no—
383C22×#41—131no—
384C23×D4—131no—
385C22×M16—131no—
386C23×C8—131no—
387#535—138no—
388#535—264no—
389C2×#127—261no—
390C2×#124—261no—
391C2×#121—131no—
392C2×#121—131no—
393C2×#121—131no—
394C2×#121C2×D1311yescharacteristic
395C2×#120—261no—
396C2×#120—261no—
397#520—138no—
398#520—264no—
399C2×C4×Q8—261no—
400C2×C4×D4—261no—
401C2×C4×D4—261no—
402C2×C4×D4—261no—
403C2×#117—131no—
404C2×#117—131no—
405C2×#117—131no—
406C2×#117—131no—
407C22×C4⋊C4—131no—
408C22×C4⋊C4—131no—
409C22×C4⋊C4C2×D1311yescharacteristic, complemented
410#482—138no—
411#482—138no—
412#482—138no—
413#482—138no—
414#481—138no—
415#481—138no—
416#480—138no—
417#480C2×D1318yescomplemented
418#428—138no—
419#427—138no—
420C2×#107—131no—
421C2×#107—131no—
422C2×#107C2×D1311yescharacteristic, complemented
423C2×#107C2×D1311yescharacteristic, complemented
424C2×#106—131no—
425C2×#106—131no—
426C2×#106—131no—
427C2×#106—131no—
428#418—138no—
429C2×#102—131no—
430C2×#102—131no—
431C2×#102—131no—
432C2×#102—131no—
433C2×#102—131no—
434C2×#102—131no—
435C2×#102—138no—
436C2×#102C2×D1311yescharacteristic
437C2×#102C2×D1311yescharacteristic
438#408—138no—
439C2×C22⋊C8—131no—
440C2×C22⋊C8—131no—
441C2×C22⋊C8—131no—
442C2×C22⋊C8C2×D1311yescharacteristic, complemented
443C22×C13—22no—
444C22×C13—22no—
445C22×C13—22no—
446C22×C13—44no—
447C22×C13—42no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—84no—
451C22×C13C2×#12312yes—
452C22×C13#57612yes—
453C22×C13#57712yes—
454C22×C13C23×D411yescharacteristic
455C2×D13—28no—
456C2×D13—22no—
457C2×D13—22no—
458C2×D13—22no—
459C2×D13—22no—
460C2×D13—22no—
461C2×D13—44no—
462C2×D13—42no—
463C2×D13—42no—
464C2×D13—42no—
465C2×D13—816no—
466C2×D13—84no—
467C2×D13C2×#12314yes—
468C4×C13—22no—
469C4×C13—42no—
470C4×C13—42no—
471C4×C13—42no—
472C4×C13C2×#12312yes—
473C4×C13C22×#4111yescharacteristic
474C4×C13C22×#4111yescharacteristic
475Dic13—22no—
476Dic13—42no—
477Dic13—42no—
478Dic13—42no—
479Dic13C2×#12314yes—
480C25—261no—
481C2×#41—134no—
482C2×#41—134no—
483C2×#41—264no—
484C2×#41—264no—
485C22×Q8—131no—
486C22×D4—21no—
487C22×D4—131no—
488C22×D4—131no—
489C22×D4—134no—
490C22×D4—131no—
491C22×D4—131no—
492C22×D4—261no—
493C22×D4—264no—
494C22×D4—264no—
495C22×D4—262no—
496C22×D4—261no—
497C22×D4—261no—
498C22×D4—261no—
499C22×D4C22×D1311yescharacteristic
500C23×C4—21no—
501C23×C4—131no—
502C23×C4—131no—
503C23×C4—261no—
504C23×C4—261no—
505C23×C4C22×D1311yescharacteristic
506C2×M16—134no—
507C2×M16—264no—
508C22×C8—131no—
509C22×C8—131no—
510C22×C8—134no—
511C22×C8—264no—
512C22×C8C22×D1311yescharacteristic
513C22×C8C22×D1311yescharacteristic
514#127—268no—
515#124—268no—
516#121—22no—
517#121—134no—
518#121—134no—
519#121—134no—
520#121—262no—
521#121—262no—
522#121—262no—
523#121C22×D1314yes—
524#120—268no—
525#120—268no—
526C4×Q8—268no—
527C4×D4—268no—
528C4×D4—268no—
529C4×D4—268no—
530#117—134no—
531#117—134no—
532#117—134no—
533#117—134no—
534#117—262no—
535#117—262no—
536#117—262no—
537#117—262no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—131no—
541C2×C4⋊C4—131no—
542C2×C4⋊C4—131no—
543C2×C4⋊C4—134no—
544C2×C4⋊C4—134no—
545C2×C4⋊C4—262no—
546C2×C4⋊C4—262no—
547C2×C4⋊C4—261no—
548C2×C4⋊C4—261no—
549C2×C4⋊C4C22×D1311yescharacteristic
550C2×C4⋊C4C22×D1311yescharacteristic
551C2×C4⋊C4C22×D1311yescharacteristic
552C2×C4⋊C4C22×D1314yescomplemented
553C2×C22⋊C4—21no—
554C2×C22⋊C4—261no—
555C2×C22⋊C4—261no—
556C2×C22⋊C4—261no—
557C2×C22⋊C4—261no—
558C2×C22⋊C4—261no—
559C2×C22⋊C4—261no—
560C2×C22⋊C4—261no—
561C2×C42—261no—
562C2×C42—261no—
563C2×C42—261no—
564C2×C42—261no—
565#107—134no—
566#107—134no—
567#107C22×D1314yescomplemented
568#107C22×D1314yescomplemented
569#106—134no—
570#106—134no—
571#106—134no—
572#106—134no—
573#102—134no—
574#102—134no—
575#102—134no—
576#102—134no—
577#102—134no—
578#102—134no—
579#102C22×D1314yes—
580#102C22×D1314yes—
581C22⋊C8—134no—
582C22⋊C8—134no—
583C22⋊C8—134no—
584C22⋊C8C22×D1314yescomplemented
585C2×C13—42no—
586C2×C13—82no—
587C2×C13#309614yescomplemented
588C2×C13C22×#12311yescharacteristic
589C2×C13C2×#57611yescharacteristic
590C2×C13C2×#57711yescharacteristic
591D13—24no—
592D13—42no—
593D13—82no—
594C24—21no—
595C24—131no—
596C24—131no—
597C24—264no—
598C24—261no—
599C24—524no—
600C24—1042no—
601C24—1042no—
602C24D4×D1311yescharacteristic
603#41—2616no—
604#41—268no—
605#41—268no—
606C2×Q8—134no—
607C2×Q8—264no—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—82no—
613C2×D4—134no—
614C2×D4—134no—
615C2×D4—134no—
616C2×D4—132no—
617C2×D4—264no—
618C2×D4—264no—
619C2×D4—268no—
620C2×D4—268no—
621C2×D4—264no—
622C2×D4—264no—
623C2×D4—264no—
624C2×D4—264no—
625C2×D4—264no—
626C2×D4—261no—
627C2×D4—262no—
628C2×D4—262no—
629C2×D4—528no—
630C2×D4—524no—
631C2×D4—1042no—
632C2×D4—1042no—
633C2×D4—1042no—
634C2×D4C23×D1312yes—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—82no—
642C22×C4—131no—
643C22×C4—132no—
644C22×C4—134no—
645C22×C4—134no—
646C22×C4—132no—
647C22×C4—131no—
648C22×C4—132no—
649C22×C4—132no—
650C22×C4—264no—
651C22×C4—264no—
652C22×C4—262no—
653C22×C4—262no—
654C22×C4—261no—
655C22×C4—261no—
656C22×C4—261no—
657C22×C4—1042no—
658C22×C4—1042no—
659C22×C4D4×D1312yes—
660C22×C4D4×D1311yescharacteristic
661C22×C4C23×D1312yes—
662C22×C4C23×D1311yescharacteristic
663M16—268no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—132no—
667C2×C8—132no—
668C2×C8—268no—
669C2×C8—262no—
670C2×C8—262no—
671C2×C8C23×D1312yes—
672C2×C8C23×D1312yes—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—24no—
676C4⋊C4—21no—
677C4⋊C4—132no—
678C4⋊C4—132no—
679C4⋊C4—132no—
680C4⋊C4—264no—
681C4⋊C4—264no—
682C4⋊C4—261no—
683C4⋊C4—261no—
684C4⋊C4—261no—
685C4⋊C4C23×D1312yes—
686C4⋊C4C23×D1312yes—
687C4⋊C4C23×D1312yes—
688C22⋊C4—24no—
689C22⋊C4—264no—
690C22⋊C4—264no—
691C22⋊C4—264no—
692C22⋊C4—264no—
693C22⋊C4—264no—
694C22⋊C4—264no—
695C22⋊C4—264no—
696C42—264no—
697C42—264no—
698C42—264no—
699C42—264no—
700C13C2×#309611yescharacteristic, complemented, Sylow
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—134no—
709C23—132no—
710C23—132no—
711C23—262no—
712C23—262no—
713C23—262no—
714C23—262no—
715C23—262no—
716C23—262no—
717C23—528no—
718C23—522no—
719C23—522no—
720C23—522no—
721C23—1044no—
722C23—1044no—
723C23—10416no—
724C23C2×D4×D1312yes—
725C23C2×D4×D1311yescharacteristic
726Q8—268no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—84no—
731D4—268no—
732D4—268no—
733D4—268no—
734D4—262no—
735D4—262no—
736D4—528no—
737D4—522no—
738D4—1044no—
739D4—1044no—
740D4—1044no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—84no—
752C2×C4—134no—
753C2×C4—132no—
754C2×C4—138no—
755C2×C4—134no—
756C2×C4—134no—
757C2×C4—132no—
758C2×C4—262no—
759C2×C4—264no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—522no—
766C2×C4—522no—
767C2×C4—522no—
768C2×C4—1044no—
769C2×C4—1044no—
770C2×C4C2×D4×D1312yes—
771C2×C4C2×D4×D1311yescharacteristic
772C2×C4#41×D1312yes—
773C2×C4#41×D1312yes—
774C2×C4C24×D1311yescharacteristic
775C8—22no—
776C8—22no—
777C8—262no—
778C8—262no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—134no—
788C22—262no—
789C22—262no—
790C22—268no—
791C22—262no—
792C22—262no—
793C22—262no—
794C22—524no—
795C22—522no—
796C22—522no—
797C22—522no—
798C22—10416no—
799C22—1044no—
800C22D13×#12312yes—
801C22#1171946212yes—
802C22#1171948312yes—
803C22C22×D4×D1311yescharacteristic
804C4—22no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—134no—
809C4—262no—
810C4—522no—
811C4—522no—
812C4—522no—
813C4D13×#12312yes—
814C4C2×#41×D1311yescharacteristic
815C4C2×#41×D1311yescharacteristic
816C2—42no—
817C2—82no—
818C2—264no—
819C2—522no—
820C2—1042no—
821C2#1312478714yesdirect product factor
822C2C2×D13×#12311yescharacteristic
823C2C2×#1171946211yescharacteristic
824C2C2×#1171948311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#480C2
socleC23×C13C22×D4
prime radicalC2×#11719312C2
hypercenterC2×#480D13
hypocenterC13C2×#3096
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C2×#11719209C2semidirect
3. #13124787C2direct (N × H)
4. C2×#11718629C2semidirect
5. C2×#11718438C2semidirect
6. C2×#11718546C2semidirect
7. C2×#11718398C2semidirect
8. C2×#11718445C2semidirect
9. C2×#11718696C2semidirect
10. C2×#11718543C2semidirect
11. C2×#11718542C2semidirect
12. C2×#11718541C2semidirect
13. C2×#11718431C2semidirect
14. C2×D13×#102C2semidirect
15. C2×#11718388C2semidirect
16. C2×C13×#480C2semidirect
20. C22×C13×C4⋊C4C22semidirect
27. C2×#88180C22semidirect
34. #11719209C22semidirect
38. C2×#88146C22semidirect
40. C2×C4⋊C4×D13C22semidirect
44. C13×#480C22semidirect
45. C2×C13×#107C22semidirect
46. C2×C13×#107C22semidirect
49. C2×C13×C22⋊C8C22semidirect
52. C2×C22⋊#1055C22semidirect
55. C2×#88060C22semidirect
56. C2×#88060C22semidirect
57. C2×#88058C22semidirect
58. C2×#88057C22semidirect
59. #11718696C22semidirect
60. #11718629C22semidirect
63. C2×#88048C22semidirect
64. C2×#88048C22semidirect
65. C2×#88048C22semidirect
66. C2×#88047C22semidirect
67. #11718546C22semidirect
68. #11718543C22semidirect
69. #11718542C22semidirect
70. #11718541C22semidirect
71. #11718445C22semidirect
72. #11718438C22semidirect
73. #11718431C22semidirect
74. D13×#102C22semidirect
75. #11718398C22semidirect
76. #11718388C22semidirect
112. C2×C13×C4⋊C4C23semidirect
130. #88180C23semidirect
154. #88146C23semidirect
158. C4⋊C4×D13C23semidirect
162. C13×#107C23semidirect
163. C13×#107C23semidirect
166. C13×C22⋊C8C23semidirect
169. C22⋊#1055C23semidirect
172. #88060C23semidirect
173. #88060C23semidirect
174. #88058C23semidirect
175. #88057C23semidirect
178. #88048C23semidirect
179. #88048C23semidirect
180. #88048C23semidirect
181. #88047C23semidirect
299. C2×#480D13semidirect
409. C22×C4⋊C4C2×D13semidirect
417. #480C2×D13semidirect
422. C2×#107C2×D13semidirect
423. C2×#107C2×D13semidirect
442. C2×C22⋊C8C2×D13semidirect
552. C2×C4⋊C4C22×D13semidirect
567. #107C22×D13semidirect
568. #107C22×D13semidirect
584. C22⋊C8C22×D13semidirect
587. C2×C13#3096semidirect
700. C13C2×#3096semidirect
821. C2#13124787direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193122
C2×#117192092
#131247872
C2×#117186292
C2×#117184382
C2×#117185462
C2×#117183982
C2×#117184452
C2×#117186962
C2×#117185432
C2×#117185422
C2×#117185412
C2×#117184312
C2×D13×#1022
C2×#117183882
C2×C13×#4802
C2×#309613