Finite Group Databasebeta

← C2×#13115733 #15866892

Subgroups — C2×#13115733 #15866892

Order 3328.

1474 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88204C211yesmaximal, characteristic
2C2×#11718659C211yesmaximal, characteristic, complemented
3C2×#11718800C211yesmaximal, characteristic, complemented
4C2×#11718901C211yesmaximal, characteristic, complemented
5C2×#11718667C211yesmaximal, characteristic, complemented
6C2×#11718783C211yesmaximal, characteristic, complemented
7#13115733C218yesmaximal, direct product factor
8C2×C13×#421C211yesmaximal, characteristic, complemented
9C22×C13×#41C2211yescharacteristic
10C22×#6127C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13C2×#88204—22no—
14C2×#88204—21no—
15C2×#88204—21no—
16C2×#88204—22no—
17C2×#88204—21no—
18C2×#88204—21no—
19C2×#88204C414yescomplemented
20C2×#88204C2214yes—
21C22×#6107C411yescharacteristic, complemented
22C22×#6106C411yescharacteristic, complemented
23C22×#6105C411yescharacteristic, complemented
24C22×#6104C411yescharacteristic, complemented
25C2×#88180C2211yescharacteristic
26C2×#88180C2211yescharacteristic
27C23×#1055C2211yescharacteristic
28C13×#421—22no—
29C13×#421C2214yescomplemented
30C2×C13×#104—22no—
31#11718901—22no—
32#11718901C2214yescomplemented
33C2×#88074—22no—
34#11718800—22no—
35#11718800C2214yescomplemented
36C2×#88065—22no—
37#11718783—22no—
38#11718783C2214yescomplemented
39C2×#88055—21no—
40C2×C8×Dic13—21no—
41#11718667—22no—
42#11718667C2214yescomplemented
43#11718659—22no—
44#11718659C2214yescomplemented
45C2×#88048—21no—
46C2×#88047—21no—
47C2×#88046—22no—
48C2×C13×#41—21no—
49C2×C13×#41—21no—
50C2×C13×#41—21no—
51C2×C13×#41—21no—
52C2×C13×#41—21no—
53C2×C13×#41—21no—
54C2×C13×#41—21no—
55C2×C13×#41—21no—
56C2×C13×#41—21no—
57C2×C13×#41—21no—
58C2×C13×#41C2×C412yes—
59C2×C13×#41C2312yes—
60C22×Q8×C13C2×C411yescharacteristic
61C22×D4×C13—21no—
62C22×D4×C13C2×C411yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13C2311yescharacteristic
65C22×C22⋊D13—21no—
66C2×#6127—21no—
67C2×#6127—21no—
68C2×#6127—21no—
69C2×#6127—21no—
70C2×#6127—21no—
71C2×#6127—21no—
72C2×#6127—21no—
73C2×#6127—21no—
74C2×#6127—21no—
75C2×#6127—21no—
76C2×#6127C2×C412yes—
77C2×#6127C2312yes—
78C22×D52C2×C411yescharacteristic
79C22×C4×D13—21no—
80C22×Dic26C2×C411yescharacteristic
81C2×C13×M16—21no—
82C2×C13×M16—21no—
83C2×C13×M16—21no—
84C2×C13×M16D412yes—
85C2×C13×M16D412yes—
86C2×C13×M16C2312yes—
87C22×C8×C13—21no—
88C13×#117—21no—
89C13×#117—21no—
90C13×#117—21no—
91C13×#117C2312yes—
92C2×C13×C4⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C42×C13—21no—
95C2×C22⋊Dic13—21no—
96C2×C22⋊Dic13D412yes—
97#88204—24no—
98#88204—24no—
99#88204—24no—
100#88204—24no—
101#88204—24no—
102#88204—24no—
103#88204—24no—
104#88204—24no—
105C2×#6107—22no—
106C2×#6107—21no—
107C2×#6107—21no—
108C2×#6107C2×C414yescomplemented
109C2×#6106—22no—
110C2×#6106—21no—
111C2×#6106—21no—
112C2×#6106C2×C414yescomplemented
113C2×#6105—22no—
114C2×#6105—21no—
115C2×#6105—21no—
116C2×#6105C2×C414yescomplemented
117C2×#6104—22no—
118C2×#6104—21no—
119C2×#6104—21no—
120C2×#6104C2×C414yescomplemented
121#88180—21no—
122#88180—21no—
123#88180—21no—
124#88180—21no—
125#88180—21no—
126#88180D412yes—
127#88180C2312yes—
128#88180C2312yes—
129C2×C4⋊Dic13—21no—
130C2×C4⋊Dic13—21no—
131C2×C4×Dic13—21no—
132C2×C4×Dic13—21no—
133C22×#1055C2×C411yescharacteristic
134C22×#1055C2×C411yescharacteristic
135C22×#1055C2×C412yes—
136C22×#1055D412yes—
137C22×#1055D411yescharacteristic
138C22×#1055D411yescharacteristic
139C22×#1055D412yes—
140C22×#1055D411yescharacteristic
141C22×#1055D411yescharacteristic
142C22×#1055C2312yes—
143C13×#104—28no—
144#88074—28no—
145#88065—28no—
146#88055—24no—
147C8×Dic13—24no—
148#88048—24no—
149#88047—24no—
150#88046—28no—
151C2×#1976—131nomaximal, Sylow
152C24×C13—21no—
153C24×C13C2×D411yescharacteristic
154C23×D13—21no—
155C13×#41—22no—
156C13×#41—22no—
157C13×#41—22no—
158C13×#41—22no—
159C13×#41—22no—
160C13×#41—22no—
161C13×#41—22no—
162C13×#41—22no—
163C13×#41—41no—
164C13×#41—41no—
165C13×#41—41no—
166C13×#41—41no—
167C13×#41—41no—
168C13×#41—41no—
169C13×#41—41no—
170C13×#41—41no—
171C2×Q8×C13—21no—
172C2×Q8×C13—21no—
173C2×Q8×C13—21no—
174C2×Q8×C13—21no—
175C2×Q8×C13—21no—
176C2×Q8×C13C22×C412yes—
177C2×D4×C13—22no—
178C2×D4×C13—22no—
179C2×D4×C13—21no—
180C2×D4×C13—21no—
181C2×D4×C13—21no—
182C2×D4×C13—21no—
183C2×D4×C13—21no—
184C2×D4×C13—41no—
185C2×D4×C13—41no—
186C2×D4×C13—41no—
187C2×D4×C13—41no—
188C2×D4×C13C22×C412yes—
189C22×C4×C13—21no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—41no—
193C22×C4×C13—41no—
194C22×C4×C13—41no—
195C22×C4×C13—41no—
196C22×C4×C13—41no—
197C22×C4×C13C22×C411yescharacteristic
198C22×C4×C13C22×C411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13#4111yescharacteristic
207C22×C4×C13#4111yescharacteristic
208C22×C4×C13#4111yescharacteristic
209C22×C4×C13#4111yescharacteristic
210C22×C4×C13C2411yescharacteristic
211C2×C22⋊D13—22no—
212C2×C22⋊D13—22no—
213C2×C22⋊D13—41no—
214C2×C22⋊D13—41no—
215C2×C22⋊D13—41no—
216C2×C22⋊D13—41no—
217C22×Dic13—21no—
218C22×Dic13—22no—
219C22×Dic13—41no—
220#6127—22no—
221#6127—22no—
222#6127—22no—
223#6127—22no—
224#6127—22no—
225#6127—22no—
226#6127—22no—
227#6127—22no—
228#6127—41no—
229#6127—41no—
230#6127—41no—
231#6127—41no—
232#6127—41no—
233#6127—41no—
234#6127—41no—
235#6127—41no—
236C2×D52—21no—
237C2×D52—21no—
238C2×D52—21no—
239C2×D52—21no—
240C2×D52—21no—
241C2×D52C22×C412yes—
242C2×C4×D13—22no—
243C2×C4×D13—22no—
244C2×C4×D13—41no—
245C2×C4×D13—41no—
246C2×C4×D13—41no—
247C2×C4×D13—41no—
248C2×Dic26—21no—
249C2×Dic26—21no—
250C2×Dic26—21no—
251C2×Dic26—21no—
252C2×Dic26—21no—
253C2×Dic26C22×C412yes—
254C13×M16—22no—
255C13×M16—22no—
256C13×M16—22no—
257C13×M16C2×D414yes—
258C2×C8×C13—22no—
259C2×C8×C13—22no—
260C2×C8×C13—22no—
261C13×C4⋊C4—22no—
262C13×C4⋊C4—41no—
263C13×C22⋊C4—22no—
264C13×C22⋊C4—41no—
265C42×C13—22no—
266C42×C13—41no—
267C22⋊Dic13—22no—
268C22⋊Dic13—22no—
269C22⋊Dic13—41no—
270C22⋊Dic13C2×D414yes—
271#6107—24no—
272#6107—24no—
273#6106—24no—
274#6106—24no—
275#6105—24no—
276#6105—24no—
277#6104—24no—
278#6104—24no—
279C4⋊Dic13—22no—
280C4⋊Dic13—22no—
281C4⋊Dic13—22no—
282C4⋊Dic13—41no—
283C4×Dic13—22no—
284C4×Dic13—22no—
285C4×Dic13—22no—
286C4×Dic13—41no—
287C2×#1055C22⋊C412yes—
288C2×#1055C22⋊C411yescharacteristic
289C2×#1055C22⋊C411yescharacteristic
290C2×#1055C22⋊C412yes—
291C2×#1055C22⋊C411yescharacteristic
292C2×#1055C22⋊C411yescharacteristic
293C2×#1055C22⋊C412yes—
294C2×#1055C22⋊C412yes—
295C2×#1055C22⋊C412yes—
296C2×#1055C22⋊C412yes—
297C2×#1055C22×C412yes—
298C2×#1055C22×C412yes—
299C2×#1055C2×D412yes—
300C2×#1055C2×D412yes—
301C2×#1055C2×D412yes—
302C2×#1055C2×D412yes—
303C22×#135—131no—
304C2×#427—131no—
305C2×#421—131no—
306C2×#421D1311yescharacteristic, complemented
307C2×#410—131no—
308C2×#410—131no—
309C2×#405—131no—
310#1976—138no—
311C23×C13—22no—
312C23×C13—42no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—82no—
316C23×C13C4×D411yescharacteristic
317C23×C13C4×D411yescharacteristic
318C23×C13#12111yescharacteristic
319C23×C13#12111yescharacteristic
320C23×C13#12711yescharacteristic
321C23×C13#12711yescharacteristic
322C23×C13C22×D411yescharacteristic
323C22×D13—22no—
324C22×D13—41no—
325C22×D13—41no—
326C22×D13—82no—
327Q8×C13—22no—
328Q8×C13—22no—
329Q8×C13—41no—
330Q8×C13—41no—
331D4×C13—22no—
332D4×C13—22no—
333D4×C13—42no—
334D4×C13—42no—
335D4×C13—42no—
336D4×C13—42no—
337D4×C13—41no—
338D4×C13—41no—
339C2×C4×C13—22no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—42no—
343C2×C4×C13—42no—
344C2×C4×C13—42no—
345C2×C4×C13—42no—
346C2×C4×C13—42no—
347C2×C4×C13—82no—
348C2×C4×C13C2×C22⋊C411yescharacteristic
349C2×C4×C13C2×C22⋊C411yescharacteristic
350C2×C4×C13C2×C22⋊C411yescharacteristic
351C2×C4×C13C2×C22⋊C411yescharacteristic
352C2×C4×C13C4×D411yescharacteristic
353C2×C4×C13C4×D411yescharacteristic
354C2×C4×C13C4×D411yescharacteristic
355C2×C4×C13C4×D411yescharacteristic
356C2×C4×C13C4×D411yescharacteristic
357C2×C4×C13C4×D411yescharacteristic
358C2×C4×C13#12111yescharacteristic
359C2×C4×C13#12111yescharacteristic
360C2×C4×C13#12111yescharacteristic
361C2×C4×C13#12111yescharacteristic
362C2×C4×C13#12111yescharacteristic
363C2×C4×C13#12111yescharacteristic
364C2×C4×C13#12411yescharacteristic
365C2×C4×C13#12411yescharacteristic
366C2×C4×C13#12411yescharacteristic
367C2×C4×C13#12411yescharacteristic
368C2×C4×C13#12711yescharacteristic
369C2×C4×C13#12711yescharacteristic
370C2×C4×C13C23×C411yescharacteristic
371C2×C4×C13C22×D411yescharacteristic
372C2×C4×C13C22×D411yescharacteristic
373C2×C4×C13C22×D411yescharacteristic
374C2×C4×C13C2×#4111yescharacteristic
375C2×C4×C13C2×#4111yescharacteristic
376C22⋊D13—42no—
377C22⋊D13—42no—
378C22⋊D13—42no—
379C22⋊D13—42no—
380C2×Dic13—22no—
381C2×Dic13—24no—
382C2×Dic13—44no—
383C2×Dic13—41no—
384C2×Dic13—41no—
385C2×Dic13—42no—
386C2×Dic13—82no—
387D52—22no—
388D52—22no—
389D52—41no—
390D52—41no—
391C4×D13—42no—
392C4×D13—42no—
393C4×D13—42no—
394C4×D13—42no—
395Dic26—22no—
396Dic26—22no—
397Dic26—41no—
398Dic26—41no—
399C8×C13—24no—
400#1055C2×C22⋊C412yes—
401#1055C2×C22⋊C412yes—
402#1055C2×C22⋊C412yes—
403#1055C2×C22⋊C412yes—
404C22×#41—131no—
405C22×#41C2×D1311yescharacteristic
406C2×#135—134no—
407C2×#135—134no—
408C2×#135—261no—
409C2×#135—261no—
410C2×#135—262no—
411C2×#135—261no—
412C2×#135—261no—
413C2×#135—262no—
414C22×Q16—131no—
415C22×SD16—131no—
416C22×SD16—131no—
417C22×D8—131no—
418C22×M16C2×D1311yescharacteristic
419C23×C8—131no—
420C2×#117—131no—
421C2×#117—131no—
422C2×#117C2×D1311yescharacteristic
423#427—134no—
424#427—262no—
425C2×#107—261no—
426C2×#106—261no—
427#421—22no—
428#421—134no—
429#421—262no—
430#421C2×D1314yescomplemented
431C2×#104—22no—
432C2×#104—262no—
433#410—134no—
434#410—134no—
435#410—262no—
436#410—262no—
437C2×#99—262no—
438C2×#99—262no—
439#405—134no—
440#405—262no—
441C2×#97—261no—
442C2×C4×C8—261no—
443C22×C13—22no—
444C22×C13—22no—
445C22×C13—22no—
446C22×C13—41no—
447C22×C13—41no—
448C22×C13—41no—
449C22×C13—41no—
450C22×C13—42no—
451C22×C13—82no—
452C22×C13—82no—
453C22×C13—82no—
454C22×C13#39011yescharacteristic
455C22×C13#39011yescharacteristic
456C22×C13#39011yescharacteristic
457C22×C13#39011yescharacteristic
458C22×C13C2×C4×D411yescharacteristic
459C22×C13C2×#12111yescharacteristic
460C22×C13C2×#12711yescharacteristic
461C2×D13—42no—
462C2×D13—82no—
463C2×D13—82no—
464C2×D13—82no—
465C4×C13—42no—
466C4×C13—82no—
467C4×C13#39011yescharacteristic
468C4×C13#39011yescharacteristic
469C4×C13#39011yescharacteristic
470C4×C13#39011yescharacteristic
471C4×C13C22×C22⋊C411yescharacteristic
472C4×C13C2×C4×D411yescharacteristic
473C4×C13C2×#12111yescharacteristic
474C4×C13C2×#12411yescharacteristic
475Dic13—44no—
476Dic13—42no—
477Dic13—82no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—21no—
486C2×#41—21no—
487C2×#41—21no—
488C2×#41—132no—
489C2×#41—132no—
490C2×#41—261no—
491C2×#41—261no—
492C2×#41—261no—
493C2×#41—261no—
494C2×#41—261no—
495C2×#41—261no—
496C2×#41—261no—
497C2×#41—261no—
498C2×#41—261no—
499C2×#41—261no—
500C2×#41C4×D1312yes—
501C2×#41C22×D1312yes—
502C22×Q8—131no—
503C22×Q8C4×D1311yescharacteristic
504C22×D4—21no—
505C22×D4—131no—
506C22×D4—261no—
507C22×D4C4×D1311yescharacteristic
508C23×C4—21no—
509C23×C4—261no—
510C23×C4C22×D1311yescharacteristic
511#135—264no—
512#135—264no—
513#135—264no—
514#135—264no—
515#135—264no—
516#135—264no—
517#135—264no—
518#135—264no—
519C2×Q16—134no—
520C2×Q16—261no—
521C2×Q16—261no—
522C2×Q16—262no—
523C2×SD16—134no—
524C2×SD16—134no—
525C2×SD16—261no—
526C2×SD16—261no—
527C2×SD16—262no—
528C2×SD16—261no—
529C2×SD16—261no—
530C2×SD16—262no—
531C2×D8—134no—
532C2×D8—261no—
533C2×D8—261no—
534C2×D8—262no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16C22⋊D1312yes—
539C2×M16C22⋊D1312yes—
540C2×M16C22×D1312yes—
541C22×C8—21no—
542C22×C8—131no—
543C22×C8—131no—
544C22×C8—132no—
545C22×C8—131no—
546C22×C8—131no—
547C22×C8—132no—
548C22×C8—131no—
549C22×C8—131no—
550C22×C8—132no—
551C22×C8—132no—
552#117—21no—
553#117—21no—
554#117—21no—
555#117—132no—
556#117—132no—
557#117—132no—
558#117—261no—
559#117—261no—
560#117—261no—
561#117—261no—
562#117—261no—
563#117C22×D1312yes—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—261no—
566C2×C4⋊C4—261no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—132no—
569C2×C22⋊C4—261no—
570C2×C42—21no—
571C2×C42—261no—
572C2×C42—261no—
573#107—264no—
574#106—264no—
575#104—28no—
576#104—268no—
577#99—268no—
578#99—268no—
579#97—264no—
580C4×C8—264no—
581C2×C13—21no—
582C2×C13—21no—
583C2×C13—21no—
584C2×C13—21no—
585C2×C13—21no—
586C2×C13—21no—
587C2×C13—82no—
588C2×C13#197612yescomplemented
589C2×C13C2×#39011yescharacteristic
590D13—82no—
591C24—21no—
592C24—261no—
593C24D4×D1311yescharacteristic
594#41—22no—
595#41—22no—
596#41—22no—
597#41—22no—
598#41—22no—
599#41—22no—
600#41—22no—
601#41—22no—
602#41—41no—
603#41—41no—
604#41—41no—
605#41—41no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—262no—
611#41—262no—
612#41—262no—
613#41—262no—
614#41—262no—
615#41—262no—
616#41—262no—
617#41—262no—
618#41—521no—
619#41—521no—
620#41—521no—
621#41—521no—
622#41—521no—
623#41—521no—
624#41—521no—
625#41—521no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—132no—
632C2×Q8—261no—
633C2×Q8—261no—
634C2×Q8—261no—
635C2×Q8—261no—
636C2×Q8—261no—
637C2×Q8C2×C4×D1312yes—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4—41no—
649C2×D4—132no—
650C2×D4—262no—
651C2×D4—262no—
652C2×D4—261no—
653C2×D4—261no—
654C2×D4—261no—
655C2×D4—261no—
656C2×D4—261no—
657C2×D4—521no—
658C2×D4—521no—
659C2×D4—521no—
660C2×D4—521no—
661C2×D4C2×C4×D1312yes—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—261no—
671C22×C4—262no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—521no—
675C22×C4—521no—
676C22×C4—521no—
677C22×C4—521no—
678C22×C4—521no—
679C22×C4C2×C4×D1311yescharacteristic
680C22×C4C2×C4×D1311yescharacteristic
681C22×C4#612711yescharacteristic
682C22×C4#612711yescharacteristic
683C22×C4D4×D1311yescharacteristic
684C22×C4D4×D1311yescharacteristic
685C22×C4D4×D1311yescharacteristic
686C22×C4D4×D1311yescharacteristic
687C22×C4D4×D1311yescharacteristic
688C22×C4#612911yescharacteristic
689C22×C4#612911yescharacteristic
690C22×C4C2×C22⋊D1311yescharacteristic
691C22×C4C2×C22⋊D1311yescharacteristic
692C22×C4C23×D1311yescharacteristic
693Q16—264no—
694Q16—264no—
695SD16—264no—
696SD16—264no—
697SD16—264no—
698SD16—264no—
699D8—264no—
700D8—264no—
701M16—22no—
702M16—22no—
703M16—22no—
704M16C2×C22⋊D1314yes—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—131no—
709C2×C8—131no—
710C2×C8—132no—
711C2×C8—131no—
712C2×C8—131no—
713C2×C8—132no—
714C2×C8—132no—
715C2×C8—132no—
716C2×C8—132no—
717C2×C8—132no—
718C2×C8—132no—
719C2×C8—132no—
720C2×C8—132no—
721C2×C8—132no—
722C2×C8—132no—
723C2×C8—132no—
724C4⋊C4—22no—
725C4⋊C4—41no—
726C4⋊C4—262no—
727C4⋊C4—262no—
728C4⋊C4—262no—
729C4⋊C4—521no—
730C22⋊C4—22no—
731C22⋊C4—41no—
732C22⋊C4—134no—
733C22⋊C4—262no—
734C22⋊C4—262no—
735C22⋊C4—521no—
736C42—22no—
737C42—41no—
738C42—262no—
739C42—262no—
740C42—262no—
741C42—521no—
742C13C2×#197611yescharacteristic, complemented, Sylow
743C23—22no—
744C23—42no—
745C23—41no—
746C23—41no—
747C23—82no—
748C23—262no—
749C23—521no—
750C23—521no—
751C23—1042no—
752C23#8813511yescharacteristic
753C23#8813511yescharacteristic
754C23#8813811yescharacteristic
755C23#8813811yescharacteristic
756C23#8819411yescharacteristic
757C23#8819411yescharacteristic
758C23C2×D4×D1311yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763Q8—262no—
764Q8—262no—
765Q8—521no—
766Q8—521no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—41no—
774D4—41no—
775D4—262no—
776D4—262no—
777D4—522no—
778D4—522no—
779D4—522no—
780D4—522no—
781D4—521no—
782D4—521no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—82no—
792C2×C4—262no—
793C2×C4—264no—
794C2×C4—524no—
795C2×C4—521no—
796C2×C4—521no—
797C2×C4—522no—
798C2×C4—522no—
799C2×C4—522no—
800C2×C4—522no—
801C2×C4—522no—
802C2×C4—1042no—
803C2×C4C22⋊C4×D1311yescharacteristic
804C2×C4C22⋊C4×D1311yescharacteristic
805C2×C4C22⋊C4×D1311yescharacteristic
806C2×C4C22⋊C4×D1311yescharacteristic
807C2×C4#8813511yescharacteristic
808C2×C4#8813511yescharacteristic
809C2×C4#8813811yescharacteristic
810C2×C4#8813811yescharacteristic
811C2×C4#8813911yescharacteristic
812C2×C4#8813911yescharacteristic
813C2×C4#8813911yescharacteristic
814C2×C4#8813911yescharacteristic
815C2×C4C4×C22⋊D1311yescharacteristic
816C2×C4C4×C22⋊D1311yescharacteristic
817C2×C4C4×C22⋊D1311yescharacteristic
818C2×C4C4×C22⋊D1311yescharacteristic
819C2×C4#8819311yescharacteristic
820C2×C4#8819311yescharacteristic
821C2×C4#8819311yescharacteristic
822C2×C4#8819311yescharacteristic
823C2×C4#8819411yescharacteristic
824C2×C4#8819411yescharacteristic
825C2×C4C22×C4×D1311yescharacteristic
826C2×C4C2×#612711yescharacteristic
827C2×C4C2×D4×D1311yescharacteristic
828C2×C4C2×D4×D1311yescharacteristic
829C2×C4C2×#612911yescharacteristic
830C2×C4C22×C22⋊D1311yescharacteristic
831C8—24no—
832C8—132no—
833C8—132no—
834C8—132no—
835C8—132no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—522no—
848C22—1042no—
849C22—1042no—
850C22—1042no—
851C22#1171861811yescharacteristic
852C22#1171861811yescharacteristic
853C22#1171861811yescharacteristic
854C22#1171861811yescharacteristic
855C22C2×#8813511yescharacteristic
856C22C2×#8813811yescharacteristic
857C22C2×#8819411yescharacteristic
858C4—42no—
859C4—82no—
860C4—524no—
861C4—522no—
862C4—1042no—
863C4#1171861811yescharacteristic
864C4#1171861811yescharacteristic
865C4#1171861811yescharacteristic
866C4#1171861811yescharacteristic
867C4C2×C22⋊C4×D1311yescharacteristic
868C4C2×#8813911yescharacteristic
869C4C2×C4×C22⋊D1311yescharacteristic
870C4C2×#8819311yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—21no—
875C2—21no—
876C2—21no—
877C2—82no—
878C2—1042no—
879C2#1311573312yesdirect product factor
880C2C2×#1171861811yescharacteristic
subgroupG/H
centerC2×C4#88193
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#421C2
socleC22×C13#390
prime radicalC22×#88204C2
cosocleC22×C4×C13C24
hypercenterC2×#421D13
hypocenterC13C2×#1976
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#11718659C2semidirect
3. C2×#11718800C2semidirect
4. C2×#11718901C2semidirect
5. C2×#11718667C2semidirect
6. C2×#11718783C2semidirect
7. #13115733C2direct (N × H)
8. C2×C13×#421C2semidirect
19. C2×#88204C4semidirect
21. C22×#6107C4semidirect
22. C22×#6106C4semidirect
23. C22×#6105C4semidirect
24. C22×#6104C4semidirect
29. C13×#421C22semidirect
32. #11718901C22semidirect
35. #11718800C22semidirect
38. #11718783C22semidirect
42. #11718667C22semidirect
44. #11718659C22semidirect
108. C2×#6107C2×C4semidirect
112. C2×#6106C2×C4semidirect
116. C2×#6105C2×C4semidirect
120. C2×#6104C2×C4semidirect
306. C2×#421D13semidirect
430. #421C2×D13semidirect
588. C2×C13#1976semidirect
742. C13C2×#1976semidirect
879. C2#13115733direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882042
C2×#117186592
C2×#117188002
C2×#117189012
C2×#117186672
C2×#117187832
#131157332
C2×C13×#4212
C2×#197613