Finite Group Databasebeta

← C2×#13127325 #16741502

Subgroups — C2×#13127325 #16741502

Order 3328.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719340C211yesmaximal, characteristic, complemented
2C2×#11719219C211yesmaximal, characteristic
3#13127325C2116yesmaximal, direct product factor
4C2×#11718537C211yesmaximal, characteristic, complemented
5C2×#11718396C211yesmaximal, characteristic, complemented
6C2×#11718476C211yesmaximal, characteristic, complemented
7C2×#11718543C211yesmaximal, characteristic, complemented
8C2×#11718460C211yesmaximal, characteristic, complemented
9C2×#11718551C211yesmaximal, characteristic, complemented
10C2×#11718473C211yesmaximal, characteristic, complemented
11C2×#11718709C211yesmaximal, characteristic, complemented
12C2×#11718478C211yesmaximal, characteristic, complemented
13C2×#11718391C211yesmaximal, characteristic, complemented
14C2×#11718542C211yesmaximal, characteristic, complemented
15C22×#88047C211yesmaximal, characteristic, complemented
16C2×C13×#484C211yesmaximal, characteristic, complemented
17C2×C13×C22⋊Q8C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88200C2211yescharacteristic
20C2×Q8×Dic13C2211yescharacteristic
21C22×#6106C2211yescharacteristic
22C2×#88184—21no—
23C2×#88184C2211yescharacteristic
24C2×C4×C22⋊D13—21no—
25C2×C4×C22⋊D13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C23×#1055C2211yescharacteristic
28C22×#6094C2211yescharacteristic
29#11719340—24no—
30#11719340C2218yescomplemented
31#11719219—24no—
32#11719219C2218yes—
33C2×#88152—21no—
34C2×#88151—21no—
35C2×#88149C2211yescharacteristic
36C2×#88148—21no—
37C2×#88147C2211yescharacteristic
38C2×#88146C2211yescharacteristic
39C2×C4⋊C4×D13C2211yescharacteristic
40C2×#88144C2211yescharacteristic
41C2×#88143—21no—
42C2×#88142C2211yescharacteristic
43C2×#88135—21no—
44C2×#88132—21no—
45C13×#484C2218yescomplemented
46C2×C13×#107C2211yescharacteristic
47C2×C13×#107C2211yescharacteristic
48C2×C13×#103C2211yescharacteristic
49C2×C13×#103C2211yescharacteristic
50C2×C13×C22⋊C8C2211yescharacteristic
51C2×#88075C2211yescharacteristic
52C2×#88061C2211yescharacteristic
53C2×#88061C2211yescharacteristic
54C2×#88060C2211yescharacteristic
55C2×#88057C2211yescharacteristic
56C2×#88057C2211yescharacteristic
57C2×#88055C2211yescharacteristic
58C2×#88054C2211yescharacteristic
59#11718709C2218yescomplemented
60C2×#88049C2211yescharacteristic
61C2×#88048C2211yescharacteristic
62C2×#88047C2211yescharacteristic
63C2×#88047C2211yescharacteristic
64C2×#88047C2211yescharacteristic
65C2×#88047C2211yescharacteristic
66C2×#88047C2218yescomplemented
67#11718551C2218yescomplemented
68#11718543C2218yescomplemented
69#11718542C2218yescomplemented
70#11718537C2218yescomplemented
71#11718478C2218yescomplemented
72#11718476C2218yescomplemented
73#11718473C2218yescomplemented
74#11718460C2218yescomplemented
75#11718396C2218yescomplemented
76#11718391C2218yescomplemented
77C22×Q8×C13C2311yescharacteristic
78C23×C4×C13—21no—
79C23×C4×C13C2311yescharacteristic
80C22×C22⋊D13—21no—
81C22×C22⋊D13D411yescharacteristic
82C23×Dic13—21no—
83C22×D52—21no—
84C22×D52C2311yescharacteristic
85C22×C4×D13—21no—
86C22×C4×D13—21no—
87C22×C4×D13C2311yescharacteristic
88C22×Dic26—21no—
89C22×C8×C13C2311yescharacteristic
90C22×C8×C13C2311yescharacteristic
91C13×C22⋊Q8—22no—
92C13×C22⋊Q8C2314yes—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4—21no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C13×C4⋊C4C2314yes—
100C2×C13×C22⋊C4—21no—
101C2×C22⋊Dic13D411yescharacteristic
102#88200—22no—
103#88200C2314yes—
104Q8×Dic13—22no—
105Q8×Dic13C2314yes—
106C2×#6106—24no—
107C2×#6106C2314yes—
108#88184—22no—
109#88184—28no—
110#88184C2314yes—
111C4×C22⋊D13—28no—
112C4×C22⋊D13D414yes—
113C4×C22⋊D13C2314yes—
114C2×#6103—21no—
115C2×#6103—21no—
116C2×#6103—21no—
117C2×#6103—21no—
118C2×#6103—21no—
119C2×#6103D411yescharacteristic
120C2×C4⋊Dic13—21no—
121C2×C4⋊Dic13—22no—
122C2×C4⋊Dic13—21no—
123C2×C4⋊Dic13—21no—
124C2×C4⋊Dic13C2311yescharacteristic
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4⋊Dic13C2311yescharacteristic
127C2×C4⋊Dic13C2314yes—
128C2×#6101—21no—
129C2×#6101—21no—
130C2×#6101—21no—
131C2×#6101—21no—
132C2×#6101D411yescharacteristic
133C2×C4×Dic13—21no—
134C2×C4×Dic13—21no—
135C2×C4×Dic13C2311yescharacteristic
136C22×#1055—24no—
137C22×#1055C2314yes—
138C22×#1055C2311yescharacteristic
139C22×#1055C2311yescharacteristic
140C2×#6094—24no—
141C2×#6094C2314yes—
142#88152—28no—
143#88151—28no—
144#88149—22no—
145#88149C2314yes—
146#88148—28no—
147#88147—22no—
148#88147C2314yes—
149#88146—22no—
150#88146C2314yes—
151C4⋊C4×D13—22no—
152C4⋊C4×D13C2314yes—
153#88144—22no—
154#88144C2314yes—
155#88143—28no—
156#88142—22no—
157#88142C2314yes—
158#88135—28no—
159#88132—28no—
160C13×#107C2314yes—
161C13×#107C2314yes—
162C13×#103C2314yes—
163C13×#103C2314yes—
164C13×C22⋊C8C2314yes—
165#88075C2314yes—
166#88061C2314yes—
167#88061C2314yes—
168#88060C2314yes—
169#88057C2314yes—
170#88057C2314yes—
171#88055C2314yes—
172#88054C2314yes—
173#88049C2314yes—
174#88048C2314yes—
175#88047C2314yes—
176#88047C2314yes—
177#88047C2314yes—
178#88047C2314yes—
179C2×#3346—131nomaximal, Sylow
180C24×C13C2×D411yescharacteristic
181C23×D13—21no—
182C23×D13C2×D411yescharacteristic
183C2×Q8×C13—21no—
184C2×Q8×C13—22no—
185C2×Q8×C13—22no—
186C2×Q8×C13C2412yes—
187C22×C4×C13—22no—
188C22×C4×C13—22no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—24no—
194C22×C4×C13—82no—
195C22×C4×C13C2×D411yescharacteristic
196C22×C4×C13C2×D412yes—
197C22×C4×C13C2412yes—
198C22×C4×C13C2411yescharacteristic
199C2×C22⋊D13—24no—
200C2×C22⋊D13—24no—
201C2×C22⋊D13—44no—
202C2×C22⋊D13C2×D414yes—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—24no—
207C22×Dic13—82no—
208C22×Dic13C2×D411yescharacteristic
209C22×Dic13C2×D411yescharacteristic
210C22×Dic13C2×D411yescharacteristic
211C2×D52—22no—
212C2×D52—22no—
213C2×D52—21no—
214C2×D52—24no—
215C2×D52—82no—
216C2×D52C2412yes—
217C2×C4×D13—22no—
218C2×C4×D13—22no—
219C2×C4×D13—24no—
220C2×C4×D13—24no—
221C2×C4×D13—82no—
222C2×C4×D13—82no—
223C2×C4×D13C2×D412yes—
224C2×C4×D13C2412yes—
225C2×Dic26—24no—
226C2×Dic26—82no—
227C2×C8×C13—22no—
228C2×C8×C13—22no—
229C2×C8×C13C2412yes—
230C2×C8×C13C2412yes—
231C13×C4⋊C4—21no—
232C13×C4⋊C4—24no—
233C13×C4⋊C4—21no—
234C13×C4⋊C4—21no—
235C13×C4⋊C4—24no—
236C13×C4⋊C4C2412yes—
237C13×C4⋊C4C2412yes—
238C13×C4⋊C4C2412yes—
239C13×C22⋊C4—24no—
240C22⋊Dic13C2×D414yes—
241#6106—28no—
242#6103—24no—
243#6103—24no—
244#6103—24no—
245#6103—24no—
246#6103—24no—
247#6103C2×D414yes—
248C4⋊Dic13—21no—
249C4⋊Dic13—24no—
250C4⋊Dic13—21no—
251C4⋊Dic13—21no—
252C4⋊Dic13—24no—
253C4⋊Dic13—24no—
254C4⋊Dic13C2412yes—
255C4⋊Dic13C2412yes—
256C4⋊Dic13C2412yes—
257#6101—24no—
258#6101—24no—
259#6101—24no—
260#6101—24no—
261#6101C2×D414yes—
262C4×Dic13—24no—
263C4×Dic13—24no—
264C4×Dic13C2×D412yes—
265C4×Dic13C2412yes—
266C2×#1055—22no—
267C2×#1055—28no—
268C2×#1055#4114yes—
269C2×#1055C2412yes—
270C2×#1055C2412yes—
271#6094—28no—
272C2×#554—131no—
273C2×#553—131no—
274#3346—1316no—
275C2×#501—131no—
276C2×#484D1311yescharacteristic, complemented
277C2×#481—131no—
278C2×#485—131no—
279C2×#480—131no—
280C2×#479—131no—
281C2×#474—131no—
282C2×#468—131no—
283C2×#465—131no—
284C2×#440—131no—
285C2×#435—131no—
286C2×#428—131no—
287C22×#107—131no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13#13714yes—
291C23×C13C22×D412yes—
292C23×C13C22×D411yescharacteristic
293C22×D13—22no—
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—42no—
298C22×D13—42no—
299C22×D13—42no—
300C22×D13C22×D412yes—
301Q8×C13—22no—
302Q8×C13—22no—
303Q8×C13—42no—
304C2×C4×C13—22no—
305C2×C4×C13—24no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13—84no—
317C2×C4×C13C22×D412yes—
318C2×C4×C13C22×D411yescharacteristic
319C2×C4×C13C2×#4112yes—
320C2×C4×C132−1+412yes—
321C2×C4×C13C2511yescharacteristic
322C22⋊D13—28no—
323C22⋊D13—48no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—84no—
334C2×Dic13C22×D412yes—
335C2×Dic13C22×D412yes—
336C2×Dic13C22×D412yes—
337D52—22no—
338D52—22no—
339D52—42no—
340D52—84no—
341C4×D13—24no—
342C4×D13—22no—
343C4×D13—22no—
344C4×D13—84no—
345C4×D13—84no—
346Dic26—84no—
347C8×C13—22no—
348C8×C13—22no—
349#1055—22no—
350#1055C2×#4114yes—
351C22×SD16—131no—
352C22×M16—131no—
353C23×C8—131no—
354#554—138no—
355#554—264no—
356#553—138no—
357#553—264no—
358C2×C4⋊Q8—131no—
359C2×#126—261no—
360C2×#125—131no—
361C2×#125—261no—
362C2×#123—261no—
363C2×C22⋊Q8—131no—
364C2×C22⋊Q8—261no—
365C2×C22⋊Q8—261no—
366C2×C22⋊Q8C2×D1311yescharacteristic
367C2×#121—131no—
368C2×#121—131no—
369C2×#121—261no—
370C2×C4×Q8—131no—
371C2×C4×D4—131no—
372C2×C4×D4—131no—
373C2×C4×D4—261no—
374C2×C4×D4—261no—
375C2×#117—131no—
376C22×C4⋊C4—131no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4C2×D1311yescharacteristic
379#501—138no—
380#485—138no—
381#484C2×D1318yescomplemented
382#481—138no—
383#480—138no—
384#479—138no—
385#474—138no—
386#468—138no—
387#465—138no—
388#440—138no—
389#435—138no—
390#428—138no—
391C2×#107—131no—
392C2×#107—131no—
393C2×#107—138no—
394C2×#107—131no—
395C2×#107—131no—
396C2×#107C2×D1311yescharacteristic
397C2×#107C2×D1311yescharacteristic
398C2×#106—131no—
399C2×#106—131no—
400C2×#106—131no—
401C2×C4⋊C8—131no—
402C2×#103—131no—
403C2×#103C2×D1311yescharacteristic
404C2×#103C2×D1311yescharacteristic
405C2×#102—131no—
406C2×#102—131no—
407C2×#102—131no—
408C2×C22⋊C8—131no—
409C2×C22⋊C8C2×D1311yescharacteristic
410C2×#97—131no—
411C22×C13—28no—
412C22×C13—22no—
413C22×C13—22no—
414C22×C13#54712yes—
415C22×C13C2×#13714yes—
416C22×C13C2×#13712yes—
417C22×C13#57612yes—
418C22×C13C23×D411yescharacteristic
419C2×D13—22no—
420C2×D13—22no—
421C2×D13—22no—
422C2×D13—44no—
423C2×D13—42no—
424C2×D13—42no—
425C2×D13—42no—
426C2×D13—84no—
427C4×C13—22no—
428C4×C13—42no—
429C4×C13—42no—
430C4×C13—42no—
431C4×C13—42no—
432C4×C13#54712yes—
433C4×C13C22×#4111yescharacteristic
434C4×C13C2×2−1+411yescharacteristic
435Dic13—22no—
436Dic13—22no—
437Dic13—22no—
438Dic13—42no—
439Dic13—42no—
440Dic13—42no—
441C22×Q8—261no—
442C22×Q8C22×D1311yescharacteristic
443C22×D4—131no—
444C22×D4—131no—
445C22×D4—261no—
446C22×D4—261no—
447C23×C4—21no—
448C23×C4—131no—
449C23×C4—261no—
450C23×C4—261no—
451C23×C4—261no—
452C23×C4C22×D1311yescharacteristic
453C2×SD16—134no—
454C2×SD16—264no—
455C2×M16—134no—
456C2×M16—264no—
457C22×C8—131no—
458C22×C8—131no—
459C22×C8—134no—
460C22×C8—264no—
461C22×C8C22×D1311yescharacteristic
462C22×C8C22×D1311yescharacteristic
463C4⋊Q8—134no—
464C4⋊Q8—262no—
465#126—268no—
466#125—134no—
467#125—262no—
468#125—268no—
469#123—268no—
470C22⋊Q8—22no—
471C22⋊Q8—134no—
472C22⋊Q8—268no—
473C22⋊Q8—268no—
474C22⋊Q8—262no—
475C22⋊Q8C22×D1314yes—
476#121—134no—
477#121—134no—
478#121—262no—
479#121—268no—
480#121—262no—
481C4×Q8—134no—
482C4×Q8—262no—
483C4×D4—134no—
484C4×D4—134no—
485C4×D4—134no—
486C4×D4—262no—
487C4×D4—268no—
488C4×D4—268no—
489#117—134no—
490#117—262no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—131no—
495C2×C4⋊C4—131no—
496C2×C4⋊C4—131no—
497C2×C4⋊C4—134no—
498C2×C4⋊C4—131no—
499C2×C4⋊C4—134no—
500C2×C4⋊C4—262no—
501C2×C4⋊C4—261no—
502C2×C4⋊C4—261no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—262no—
509C2×C4⋊C4C22×D1311yescharacteristic
510C2×C4⋊C4C22×D1311yescharacteristic
511C2×C4⋊C4C22×D1311yescharacteristic
512C2×C4⋊C4C22×D1314yes—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—131no—
515C2×C22⋊C4—131no—
516C2×C22⋊C4—261no—
517C2×C22⋊C4—261no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C42—131no—
522C2×C42—261no—
523C2×C42—261no—
524#107—134no—
525#107—134no—
526#107—134no—
527#107—134no—
528#107C22×D1314yes—
529#107C22×D1314yes—
530#106—134no—
531#106—134no—
532#106—134no—
533C4⋊C8—134no—
534#103—134no—
535#103C22×D1314yes—
536#103C22×D1314yes—
537#102—134no—
538#102—134no—
539#102—134no—
540C22⋊C8—134no—
541C22⋊C8C22×D1314yes—
542#97—134no—
543C2×C13—24no—
544C2×C13#334614yescomplemented
545C2×C13C2×#54711yescharacteristic
546C2×C13C22×#13711yescharacteristic
547C2×C13C2×#57611yescharacteristic
548D13—42no—
549D13—82no—
550C24—131no—
551C24—261no—
552C24D4×D1311yescharacteristic
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—264no—
557C2×Q8—1042no—
558C2×Q8C23×D1312yes—
559C2×D4—134no—
560C2×D4—132no—
561C2×D4—264no—
562C2×D4—264no—
563C2×D4—264no—
564C2×D4—261no—
565C2×D4—262no—
566C2×D4—262no—
567C2×D4—524no—
568C2×D4—1042no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—82no—
577C22×C4—131no—
578C22×C4—131no—
579C22×C4—131no—
580C22×C4—132no—
581C22×C4—132no—
582C22×C4—264no—
583C22×C4—264no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—264no—
590C22×C4—1042no—
591C22×C4—1042no—
592C22×C4—1042no—
593C22×C4D4×D1312yes—
594C22×C4D4×D1311yescharacteristic
595C22×C4C23×D1312yes—
596C22×C4C23×D1311yescharacteristic
597SD16—268no—
598M16—268no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—134no—
602C2×C8—132no—
603C2×C8—132no—
604C2×C8—268no—
605C2×C8—262no—
606C2×C8C23×D1312yes—
607C2×C8C23×D1312yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—134no—
614C4⋊C4—132no—
615C4⋊C4—132no—
616C4⋊C4—132no—
617C4⋊C4—264no—
618C4⋊C4—264no—
619C4⋊C4—264no—
620C4⋊C4—264no—
621C4⋊C4—264no—
622C4⋊C4—264no—
623C4⋊C4—261no—
624C4⋊C4—264no—
625C4⋊C4—261no—
626C4⋊C4—261no—
627C4⋊C4C23×D1312yes—
628C4⋊C4C23×D1312yes—
629C4⋊C4C23×D1312yes—
630C22⋊C4—24no—
631C22⋊C4—134no—
632C22⋊C4—134no—
633C22⋊C4—264no—
634C22⋊C4—264no—
635C22⋊C4—264no—
636C22⋊C4—264no—
637C22⋊C4—264no—
638C42—132no—
639C42—132no—
640C42—264no—
641C42—264no—
642C13C2×#334611yescharacteristic, complemented, Sylow
643C23—22no—
644C23—22no—
645C23—132no—
646C23—262no—
647C23—262no—
648C23—262no—
649C23—262no—
650C23—522no—
651C23—522no—
652C23—522no—
653C23#8817214yes—
654C23C2×D4×D1312yes—
655C23C2×D4×D1311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—1044no—
660D4—268no—
661D4—262no—
662D4—262no—
663D4—528no—
664D4—522no—
665D4—1044no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—132no—
680C2×C4—132no—
681C2×C4—132no—
682C2×C4—262no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—264no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—522no—
692C2×C4—522no—
693C2×C4—522no—
694C2×C4—1044no—
695C2×C4—1044no—
696C2×C4—1044no—
697C2×C4C2×D4×D1312yes—
698C2×C4C2×D4×D1311yescharacteristic
699C2×C4#41×D1312yes—
700C2×C4#8825712yes—
701C2×C4C24×D1311yescharacteristic
702C8—22no—
703C8—22no—
704C8—134no—
705C8—262no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—262no—
710C22—262no—
711C22—262no—
712C22—524no—
713C22—522no—
714C22—522no—
715C22—522no—
716C22—1044no—
717C22#1171936012yes—
718C22C2×#8817214yes—
719C22C2×#8817212yes—
720C22#1171947912yes—
721C22C22×D4×D1311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—262no—
728C4—262no—
729C4—262no—
730C4—522no—
731C4—522no—
732C4—522no—
733C4#1171936012yes—
734C4C2×#41×D1311yescharacteristic
735C4C2×#8825711yescharacteristic
736C2—24no—
737C2—522no—
738C2—1042no—
739C2#1312732514yesdirect product factor
740C2C2×#1171936011yescharacteristic
741C2C22×#8817211yescharacteristic
742C2C2×#1171947911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#484C2
socleC23×C13C22×D4
prime radicalC2×#11719219C2
hypercenterC2×#484D13
hypocenterC13C2×#3346
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
1. C2×#11719340C2semidirect
3. #13127325C2direct (N × H)
4. C2×#11718537C2semidirect
5. C2×#11718396C2semidirect
6. C2×#11718476C2semidirect
7. C2×#11718543C2semidirect
8. C2×#11718460C2semidirect
9. C2×#11718551C2semidirect
10. C2×#11718473C2semidirect
11. C2×#11718709C2semidirect
12. C2×#11718478C2semidirect
13. C2×#11718391C2semidirect
14. C2×#11718542C2semidirect
15. C22×#88047C2semidirect
16. C2×C13×#484C2semidirect
30. #11719340C22semidirect
45. C13×#484C22semidirect
59. #11718709C22semidirect
66. C2×#88047C22semidirect
67. #11718551C22semidirect
68. #11718543C22semidirect
69. #11718542C22semidirect
70. #11718537C22semidirect
71. #11718478C22semidirect
72. #11718476C22semidirect
73. #11718473C22semidirect
74. #11718460C22semidirect
75. #11718396C22semidirect
76. #11718391C22semidirect
276. C2×#484D13semidirect
381. #484C2×D13semidirect
544. C2×C13#3346semidirect
642. C13C2×#3346semidirect
739. C2#13127325direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193402
C2×#117192192
#131273252
C2×#117185372
C2×#117183962
C2×#117184762
C2×#117185432
C2×#117184602
C2×#117185512
C2×#117184732
C2×#117187092
C2×#117184782
C2×#117183912
C2×#117185422
C22×#880472
C2×C13×#4842
C2×#334613