Finite Group Databasebeta

← C2×#13127790 #16743456

Subgroups — C2×#13127790 #16743456

Order 3328.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719284C211yesmaximal, characteristic, complemented
2#13127790C2116yesmaximal, direct product factor
3C2×#11718726C211yesmaximal, characteristic, complemented
4C2×#11718741C211yesmaximal, characteristic, complemented
5C2×#11718725C211yesmaximal, characteristic, complemented
6C2×#11718670C211yesmaximal, characteristic, complemented
7C2×#11718670C211yesmaximal, characteristic, complemented
8C2×#11718727C211yesmaximal, characteristic, complemented
9C2×#11718727C211yesmaximal, characteristic, complemented
10C2×#11718668C211yesmaximal, characteristic, complemented
11C2×#11718748C211yesmaximal, characteristic, complemented
12C2×#11718685C211yesmaximal, characteristic, complemented
13C2×#11718675C211yesmaximal, characteristic
14C2×#11718675C211yesmaximal, characteristic
15C2×C4×#6104C211yesmaximal, characteristic
16C2×C13×#554C211yesmaximal, characteristic, complemented
17C13×#554—24no—
18C13×#554C2218yescomplemented
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#125C2211yescharacteristic
21C2×C13×#125C2211yescharacteristic
22C2×C13×C22⋊Q8—21no—
23C2×C13×C22⋊Q8—21no—
24C2×C13×C22⋊Q8—21no—
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C22×C13×C4⋊C4—21no—
30C2×#88200—21no—
31C22×#6104C2211yescharacteristic
32#11719284—24no—
33#11719284C2218yescomplemented
34C2×#88150—21no—
35C2×#88150—21no—
36C2×C4⋊C4×D13—21no—
37C2×C4×D52C2211yescharacteristic
38C2×C4×D52C2211yescharacteristic
39C2×C4×D52C2211yescharacteristic
40C2×#88124C2211yescharacteristic
41C2×#88124C2211yescharacteristic
42C2×#88123C2211yescharacteristic
43C2×#88072C2211yescharacteristic
44C2×#88072C2211yescharacteristic
45C2×#88072C2211yescharacteristic
46#11718748C2218yescomplemented
47#11718741C2218yescomplemented
48#11718727C2218yescomplemented
49#11718727C2218yescomplemented
50#11718726C2218yescomplemented
51#11718725C2218yescomplemented
52#11718685C2218yescomplemented
53#11718675C2218yes—
54#11718675C2218yes—
55C4×#6104C2218yes—
56#11718670C2218yescomplemented
57#11718670C2218yescomplemented
58#11718668C2218yescomplemented
59C2×#88049C2211yescharacteristic
60C2×#88049C2211yescharacteristic
61C2×#88049C2211yescharacteristic
62C2×#88048C2211yescharacteristic
63C2×#88048C2211yescharacteristic
64C2×#88048C2211yescharacteristic
65C2×#88048C2211yescharacteristic
66C2×#88047C2211yescharacteristic
67C2×#88047C2211yescharacteristic
68C2×#88047C2211yescharacteristic
69C2×#88047C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×C4⋊#1055C2211yescharacteristic
72C2×C4⋊#1055C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×#88043C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13—21no—
78C22×Q8×C13D411yescharacteristic
79C22×D4×C13C2311yescharacteristic
80C23×C4×C13—21no—
81C23×C4×C13—21no—
82C23×C4×C13—21no—
83C22×D52C2311yescharacteristic
84C22×C4×D13—21no—
85C22×C4×D13—21no—
86C22×C4×D13—21no—
87C22×Dic26—21no—
88C13×C4⋊Q8—22no—
89C13×C4⋊Q8C2314yes—
90C13×#125—22no—
91C13×#125—22no—
92C13×#125C2314yes—
93C13×#125C2314yes—
94C13×C22⋊Q8—28no—
95C13×C22⋊Q8—28no—
96C13×C22⋊Q8—28no—
97C4×Q8×C13D414yes—
98C4×Q8×C13C2314yes—
99C4×D4×C13—22no—
100C4×D4×C13—22no—
101C4×D4×C13—22no—
102C4×D4×C13C2314yes—
103C4×D4×C13C2314yes—
104C4×D4×C13C2314yes—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—28no—
111C2×C13×C4⋊C4D411yescharacteristic
112C2×C13×C4⋊C4D411yescharacteristic
113C2×C13×C4⋊C4D411yescharacteristic
114C2×C13×C4⋊C4C2311yescharacteristic
115C2×C13×C4⋊C4C2311yescharacteristic
116C2×C13×C4⋊C4C2311yescharacteristic
117C2×C13×C22⋊C4—21no—
118C2×C13×C22⋊C4—21no—
119C2×C13×C22⋊C4—21no—
120C2×C42×C13C2311yescharacteristic
121C2×C42×C13C2311yescharacteristic
122C2×C42×C13C2311yescharacteristic
123#88200—28no—
124C2×#6104Q818yescomplemented
125C2×#6104C2314yes—
126C2×#6103—21no—
127C2×#6103—21no—
128C2×#6103—21no—
129C2×C4⋊Dic13—21no—
130C2×C4⋊Dic13C2311yescharacteristic
131C2×C4⋊Dic13C2311yescharacteristic
132C2×C4⋊Dic13C2311yescharacteristic
133C2×#6101—21no—
134C2×#6101—21no—
135C2×#6101—21no—
136C2×#6101—21no—
137C22×#1055C2311yescharacteristic
138C22×#1055C2311yescharacteristic
139C22×#1055C2311yescharacteristic
140C22×#1055C2311yescharacteristic
141#88150—28no—
142#88150—28no—
143C4⋊C4×D13—28no—
144C4×D52—22no—
145C4×D52—22no—
146C4×D52—22no—
147C4×D52C2314yes—
148C4×D52C2314yes—
149C4×D52C2314yes—
150#88124—22no—
151#88124—22no—
152#88124C2314yes—
153#88124C2314yes—
154#88123—22no—
155#88123C2314yes—
156#88072C2314yes—
157#88072C2314yes—
158#88072C2314yes—
159#88049C2314yes—
160#88049C2314yes—
161#88049C2314yes—
162#88048C2314yes—
163#88048C2314yes—
164#88048C2314yes—
165#88048C2314yes—
166#88047C2314yes—
167#88047C2314yes—
168#88047C2314yes—
169#88047C2314yes—
170#88047C2314yes—
171C4⋊#1055C2314yes—
172C4⋊#1055C2314yes—
173C4⋊#1055C2314yes—
174#88043C2314yes—
175#88043C2314yes—
176C4×#1055C2314yes—
177C2×#3389—131nomaximal, Sylow
178C24×C13—21no—
179C23×D13—21no—
180C2×Q8×C13—24no—
181C2×Q8×C13—42no—
182C2×Q8×C13—82no—
183C2×Q8×C13C2×D414yes—
184C2×D4×C13—21no—
185C2×D4×C13—22no—
186C2×D4×C13C2×Q814yes—
187C2×D4×C13C2412yes—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—24no—
192C22×C4×C13—24no—
193C22×C4×C13—24no—
194C22×C4×C13—44no—
195C22×C4×C13—82no—
196C22×C4×C13—82no—
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2411yescharacteristic
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C2×D52—21no—
208C2×D52—22no—
209C2×D52C2×Q814yes—
210C2×D52C2412yes—
211C2×C4×D13—24no—
212C2×C4×D13—24no—
213C2×C4×D13—24no—
214C2×C4×D13—44no—
215C2×C4×D13—82no—
216C2×C4×D13—82no—
217C2×Dic26—24no—
218C2×Dic26—82no—
219C13×C4⋊C4—24no—
220C13×C4⋊C4—24no—
221C13×C4⋊C4—24no—
222C13×C4⋊C4—24no—
223C13×C4⋊C4—24no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—21no—
226C13×C4⋊C4—21no—
227C13×C4⋊C4C2×D414yes—
228C13×C4⋊C4C2×D414yes—
229C13×C4⋊C4C2×D414yes—
230C13×C4⋊C4C2412yes—
231C13×C4⋊C4C2412yes—
232C13×C4⋊C4C2412yes—
233C13×C22⋊C4—24no—
234C13×C22⋊C4—24no—
235C13×C22⋊C4—24no—
236C42×C13C2×D412yes—
237C42×C13C2×D412yes—
238C42×C13C2×D412yes—
239C42×C13C2412yes—
240C42×C13C2412yes—
241C42×C13C2412yes—
242#6104C2×Q8116yescomplemented
243#6103—24no—
244#6103—24no—
245#6103—24no—
246C4⋊Dic13—21no—
247C4⋊Dic13—21no—
248C4⋊Dic13—24no—
249C4⋊Dic13—21no—
250C4⋊Dic13C2412yes—
251C4⋊Dic13C2412yes—
252C4⋊Dic13C2412yes—
253#6101—24no—
254#6101—24no—
255#6101—24no—
256#6101—24no—
257C2×#1055—22no—
258C2×#1055—22no—
259C2×#1055—22no—
260C2×#1055C2×Q814yes—
261C2×#1055C2412yes—
262C2×#1055C2412yes—
263C2×#1055C2412yes—
264C2×#1055C2412yes—
265C2×#554—131no—
266C2×#554D1311yescharacteristic, complemented
267#3389—1316no—
268C2×#501—131no—
269C2×#501—131no—
270C2×#499—131no—
271C2×#478—131no—
272C2×#478—131no—
273C2×#478—131no—
274C2×#478—131no—
275C2×#474—131no—
276C2×#474—131no—
277C2×#446—131no—
278C2×#442—131no—
279C2×#442—131no—
280C2×C4×D8—131no—
281C23×C13—24no—
282C23×C13—22no—
283C23×C13—42no—
284C23×C13—42no—
285C23×C13C22×D411yescharacteristic
286C22×D13—24no—
287C22×D13—22no—
288C22×D13—42no—
289C22×D13—42no—
290Q8×C13—44no—
291Q8×C13—84no—
292D4×C13—24no—
293D4×C13—22no—
294D4×C13C22×Q814yes—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—48no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—42no—
308C2×C4×C13—84no—
309C2×C4×C13—84no—
310C2×C4×C13C22×D412yes—
311C2×C4×C13C22×D412yes—
312C2×C4×C13C22×D412yes—
313C2×C4×C13C22×D412yes—
314C2×C4×C13C22×D412yes—
315C2×C4×C13C22×D412yes—
316C2×C4×C13C22×D411yescharacteristic
317C2×C4×C13C22×Q812yes—
318C2×C4×C132−1+412yes—
319C2×C4×C13C2511yescharacteristic
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—42no—
324C2×Dic13—42no—
325C2×Dic13—42no—
326D52—24no—
327D52—22no—
328D52C22×Q814yes—
329C4×D13—48no—
330C4×D13—84no—
331C4×D13—84no—
332Dic26—84no—
333#1055—22no—
334#1055—22no—
335#1055—22no—
336#1055C22×Q814yes—
337C22×D8—131no—
338#554—24no—
339#554—138no—
340#554—264no—
341#554C2×D1318yescomplemented
342C2×C4⋊Q8—131no—
343C2×C4⋊Q8C2×D1311yescharacteristic
344C2×#125—131no—
345C2×#125—131no—
346C2×#125C2×D1311yescharacteristic
347C2×#125C2×D1311yescharacteristic
348C2×C22⋊Q8—21no—
349C2×C22⋊Q8—21no—
350C2×C22⋊Q8—21no—
351C2×C22⋊Q8—261no—
352C2×C22⋊Q8—261no—
353C2×C22⋊Q8—261no—
354C2×C4×Q8C2×D1311yescharacteristic
355C2×C4×D4—131no—
356C2×C4×D4—131no—
357C2×C4×D4—131no—
358C2×C4×D4C2×D1311yescharacteristic
359C2×C4×D4C2×D1311yescharacteristic
360C2×C4×D4C2×D1311yescharacteristic
361C22×C4⋊C4—21no—
362C22×C4⋊C4—261no—
363#501—138no—
364#501—138no—
365#499—138no—
366#478—138no—
367#478—138no—
368#478—138no—
369#478—138no—
370#474—138no—
371#474—138no—
372#446—138no—
373#442—138no—
374#442—138no—
375C4×D8—138no—
376C2×#107—131no—
377C2×#107—131no—
378C2×#107—131no—
379C2×#107—131no—
380C2×#107—131no—
381C2×#106—131no—
382C2×#106—131no—
383C2×#106—131no—
384C2×#106—131no—
385C2×C4⋊C8—131no—
386C2×C4⋊C8—131no—
387C2×C4⋊C8—131no—
388C2×#102—131no—
389C2×#102—131no—
390C2×#102—131no—
391C2×#102—131no—
392C2×#102—131no—
393C2×#102—131no—
394C2×#97—131no—
395C2×#97—131no—
396C2×C4×C8—131no—
397C22×C13—24no—
398C22×C13—48no—
399C22×C13—42no—
400C22×C13—42no—
401C22×C13D4×Q812yes—
402C22×C13#57512yes—
403C22×C13#57612yes—
404C22×C13C23×D411yescharacteristic
405C2×D13—24no—
406C2×D13—48no—
407C2×D13—42no—
408C2×D13—42no—
409C4×C13—22no—
410C4×C13—22no—
411C4×C13—22no—
412C4×C13—22no—
413C4×C13—22no—
414C4×C13—22no—
415C4×C13—42no—
416C4×C13—42no—
417C4×C13—42no—
418C4×C13D4×Q812yes—
419C4×C13C23×Q811yescharacteristic
420C4×C13C2×2−1+411yescharacteristic
421Dic13—42no—
422Dic13—42no—
423Dic13—42no—
424C22×Q8—21no—
425C22×Q8—261no—
426C22×Q8C22⋊D1311yescharacteristic
427C22×D4—131no—
428C22×D4C22×D1311yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—261no—
433C23×C4—261no—
434C23×C4—261no—
435C2×D8—138no—
436C2×D8—134no—
437C22×C8—131no—
438C22×C8—131no—
439C22×C8—131no—
440C22×C8—131no—
441C4⋊Q8—22no—
442C4⋊Q8—134no—
443C4⋊Q8—262no—
444C4⋊Q8C22×D1314yes—
445#125—22no—
446#125—22no—
447#125—134no—
448#125—134no—
449#125—262no—
450#125—262no—
451#125C22×D1314yes—
452#125C22×D1314yes—
453C22⋊Q8—28no—
454C22⋊Q8—28no—
455C22⋊Q8—28no—
456C22⋊Q8—268no—
457C22⋊Q8—268no—
458C22⋊Q8—268no—
459C4×Q8C22⋊D1314yes—
460C4×Q8C22×D1314yes—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—134no—
465C4×D4—134no—
466C4×D4—134no—
467C4×D4—262no—
468C4×D4—262no—
469C4×D4—262no—
470C4×D4C22×D1314yes—
471C4×D4C22×D1314yes—
472C4×D4C22×D1314yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—28no—
479C2×C4⋊C4—131no—
480C2×C4⋊C4—131no—
481C2×C4⋊C4—131no—
482C2×C4⋊C4—261no—
483C2×C4⋊C4—261no—
484C2×C4⋊C4—261no—
485C2×C4⋊C4—261no—
486C2×C4⋊C4—261no—
487C2×C4⋊C4—268no—
488C2×C4⋊C4C22⋊D1311yescharacteristic
489C2×C4⋊C4C22⋊D1311yescharacteristic
490C2×C4⋊C4C22⋊D1311yescharacteristic
491C2×C4⋊C4C22×D1311yescharacteristic
492C2×C4⋊C4C22×D1311yescharacteristic
493C2×C4⋊C4C22×D1311yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—261no—
498C2×C22⋊C4—261no—
499C2×C22⋊C4—261no—
500C2×C42C22×D1311yescharacteristic
501C2×C42C22×D1311yescharacteristic
502C2×C42C22×D1311yescharacteristic
503#107—134no—
504#107—134no—
505#107—134no—
506#107—134no—
507#107—134no—
508#106—134no—
509#106—134no—
510#106—134no—
511#106—134no—
512C4⋊C8—134no—
513C4⋊C8—134no—
514C4⋊C8—134no—
515#102—134no—
516#102—134no—
517#102—134no—
518#102—134no—
519#102—134no—
520#102—134no—
521#97—134no—
522#97—134no—
523C4×C8—134no—
524C2×C13—44no—
525C2×C13#338914yescomplemented
526C2×C13C2×D4×Q811yescharacteristic
527C2×C13C2×#57511yescharacteristic
528C2×C13C2×#57611yescharacteristic
529D13—44no—
530C24—21no—
531C24—261no—
532C2×Q8—24no—
533C2×Q8—42no—
534C2×Q8—82no—
535C2×Q8—264no—
536C2×Q8—1042no—
537C2×Q8C2×C22⋊D1314yes—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—134no—
541C2×D4—132no—
542C2×D4—262no—
543C2×D4—261no—
544C2×D4Q8×D1314yes—
545C2×D4C23×D1312yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—44no—
553C22×C4—82no—
554C22×C4—82no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—261no—
558C22×C4—264no—
559C22×C4—264no—
560C22×C4—264no—
561C22×C4—524no—
562C22×C4—1042no—
563C22×C4—1042no—
564C22×C4C2×C22⋊D1311yescharacteristic
565C22×C4C2×C22⋊D1311yescharacteristic
566C22×C4C2×C22⋊D1311yescharacteristic
567C22×C4C2×C22⋊D1311yescharacteristic
568C22×C4C2×C22⋊D1311yescharacteristic
569C22×C4C2×C22⋊D1311yescharacteristic
570C22×C4C23×D1311yescharacteristic
571D8—1316no—
572C2×C8—134no—
573C2×C8—132no—
574C2×C8—132no—
575C2×C8—132no—
576C2×C8—132no—
577C2×C8—262no—
578C2×C8—262no—
579C2×C8—262no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—132no—
589C4⋊C4—132no—
590C4⋊C4—132no—
591C4⋊C4—261no—
592C4⋊C4—261no—
593C4⋊C4—261no—
594C4⋊C4—264no—
595C4⋊C4—264no—
596C4⋊C4—264no—
597C4⋊C4—264no—
598C4⋊C4—264no—
599C4⋊C4C2×C22⋊D1314yes—
600C4⋊C4C2×C22⋊D1314yes—
601C4⋊C4C2×C22⋊D1314yes—
602C4⋊C4C23×D1312yes—
603C4⋊C4C23×D1312yes—
604C4⋊C4C23×D1312yes—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—264no—
609C22⋊C4—264no—
610C22⋊C4—264no—
611C42C2×C22⋊D1312yes—
612C42C2×C22⋊D1312yes—
613C42C2×C22⋊D1312yes—
614C42C23×D1312yes—
615C42C23×D1312yes—
616C42C23×D1312yes—
617C13C2×#338911yescharacteristic, complemented, Sylow
618C23—24no—
619C23—22no—
620C23—42no—
621C23—42no—
622C23—264no—
623C23—262no—
624C23—522no—
625C23—522no—
626C23C22×C22⋊D1311yescharacteristic
627Q8—44no—
628Q8—84no—
629Q8—1044no—
630D4—24no—
631D4—22no—
632D4—134no—
633D4—264no—
634D4—262no—
635D4C2×Q8×D1314yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—48no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—262no—
652C2×C4—262no—
653C2×C4—262no—
654C2×C4—528no—
655C2×C4—522no—
656C2×C4—522no—
657C2×C4—522no—
658C2×C4—1044no—
659C2×C4—1044no—
660C2×C4C2×Q8×D1312yes—
661C2×C4#8825412yes—
662C2×C4C22×C22⋊D1312yes—
663C2×C4C22×C22⋊D1312yes—
664C2×C4C22×C22⋊D1312yes—
665C2×C4C22×C22⋊D1312yes—
666C2×C4C22×C22⋊D1312yes—
667C2×C4C22×C22⋊D1312yes—
668C2×C4C22×C22⋊D1311yescharacteristic
669C2×C4C24×D1311yescharacteristic
670C8—134no—
671C8—262no—
672C8—262no—
673C8—262no—
674C22—24no—
675C22—42no—
676C22—48no—
677C22—42no—
678C22—264no—
679C22—522no—
680C22—528no—
681C22—522no—
682C22Q8×C22⋊D1312yes—
683C22#1171952712yes—
684C22#1171954012yes—
685C22C23×C22⋊D1311yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—522no—
696C4—522no—
697C4—522no—
698C4Q8×C22⋊D1312yes—
699C4C22×Q8×D1311yescharacteristic
700C4C2×#8825411yescharacteristic
701C2—44no—
702C2—524no—
703C2#1312779014yesdirect product factor
704C2C2×Q8×C22⋊D1311yescharacteristic
705C2C2×#1171952711yescharacteristic
706C2C2×#1171954011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#554C2
socleC23×C13C22×D4
prime radicalC22×#6104C22
hypercenterC2×#554D13
hypocenterC13C2×#3389
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#11719284C2semidirect
2. #13127790C2direct (N × H)
3. C2×#11718726C2semidirect
4. C2×#11718741C2semidirect
5. C2×#11718725C2semidirect
6. C2×#11718670C2semidirect
7. C2×#11718670C2semidirect
8. C2×#11718727C2semidirect
9. C2×#11718727C2semidirect
10. C2×#11718668C2semidirect
11. C2×#11718748C2semidirect
12. C2×#11718685C2semidirect
16. C2×C13×#554C2semidirect
18. C13×#554C22semidirect
33. #11719284C22semidirect
46. #11718748C22semidirect
47. #11718741C22semidirect
48. #11718727C22semidirect
49. #11718727C22semidirect
50. #11718726C22semidirect
51. #11718725C22semidirect
52. #11718685C22semidirect
56. #11718670C22semidirect
57. #11718670C22semidirect
58. #11718668C22semidirect
124. C2×#6104Q8semidirect
242. #6104C2×Q8semidirect
266. C2×#554D13semidirect
341. #554C2×D13semidirect
525. C2×C13#3389semidirect
617. C13C2×#3389semidirect
703. C2#13127790direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192842
#131277902
C2×#117187262
C2×#117187412
C2×#117187252
C2×#117186702
C2×#117187272
C2×#117186682
C2×#117187482
C2×#117186852
C2×#117186752
C2×C4×#61042
C2×C13×#5542
C2×#338913