Finite Group Databasebeta

← C2×#13127657 #16742678

Subgroups — C2×#13127657 #16742678

Order 3328.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719284C211yesmaximal, characteristic, complemented
2#13127657C2116yesmaximal, direct product factor
3C2×#11718743C211yesmaximal, characteristic, complemented
4C2×#11718716C211yesmaximal, characteristic, complemented
5C2×#11718717C211yesmaximal, characteristic, complemented
6C2×#11718683C211yesmaximal, characteristic, complemented
7C2×#11718681C211yesmaximal, characteristic, complemented
8C2×#11718670C211yesmaximal, characteristic, complemented
9C2×#11718718C211yesmaximal, characteristic
10C2×#11718718C211yesmaximal, characteristic
11C2×#11718744C211yesmaximal, characteristic, complemented
12C2×#11718685C211yesmaximal, characteristic, complemented
13C2×#11718675C211yesmaximal, characteristic
14C2×#11718687C211yesmaximal, characteristic, complemented
15C2×C4×#6106C211yesmaximal, characteristic, complemented
16C2×C13×#556C211yesmaximal, characteristic, complemented
17C13×#556—24no—
18C13×#556C2218yescomplemented
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#126—21no—
21C2×C13×#126—21no—
22C2×C13×#124C2211yescharacteristic
23C2×C13×#124C2211yescharacteristic
24C2×C13×C22⋊Q8—21no—
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C2×C13×#117—21no—
30C2×#88200—21no—
31C22×#6106C2211yescharacteristic
32C22×#6106C2211yescharacteristic
33C22×#6104C2211yescharacteristic
34#11719284—24no—
35#11719284C2218yescomplemented
36C2×#88150—21no—
37C2×#88150—21no—
38C2×C4⋊C4×D13—21no—
39C2×C4×D52C2211yescharacteristic
40C2×C4×D52C2211yescharacteristic
41C2×C4×D52C2211yescharacteristic
42C2×#88124C2211yescharacteristic
43C2×#88124C2211yescharacteristic
44C2×#88123C2211yescharacteristic
45C2×#88075C2211yescharacteristic
46C2×#88075C2211yescharacteristic
47C2×#88075C2211yescharacteristic
48C2×#88075C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×#88075C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×#88072C2211yescharacteristic
53C2×#88072C2211yescharacteristic
54#11718744C2218yescomplemented
55#11718743C2218yescomplemented
56#11718718C2218yes—
57#11718718C2218yes—
58#11718717C2218yescomplemented
59#11718716C2218yescomplemented
60#11718687C2218yescomplemented
61C4×#6106C2218yescomplemented
62#11718685C2218yescomplemented
63#11718683C2218yescomplemented
64#11718681C2218yescomplemented
65#11718675C2218yes—
66#11718670C2218yescomplemented
67C2×#88049C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88047C2211yescharacteristic
71C2×C4⋊#1055C2211yescharacteristic
72C2×C4⋊#1055C2211yescharacteristic
73C2×C4⋊#1055C2211yescharacteristic
74C2×#88043C2211yescharacteristic
75C2×#88043C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13D411yescharacteristic
78C22×Q8×C13C2311yescharacteristic
79C22×Q8×C13C2311yescharacteristic
80C22×D4×C13C2311yescharacteristic
81C23×C4×C13—21no—
82C22×D52C2311yescharacteristic
83C22×C4×D13—21no—
84C22×C4×D13—21no—
85C22×C4×D13—21no—
86C22×Dic26—21no—
87C13×C4⋊Q8—22no—
88C13×C4⋊Q8C2314yes—
89C13×#126—28no—
90C13×#126—28no—
91C13×#124—22no—
92C13×#124—22no—
93C13×#124C2314yes—
94C13×#124C2314yes—
95C13×C22⋊Q8—28no—
96C4×Q8×C13—22no—
97C4×Q8×C13—22no—
98C4×Q8×C13D414yes—
99C4×Q8×C13C2314yes—
100C4×Q8×C13C2314yes—
101C4×Q8×C13C2314yes—
102C4×D4×C13—22no—
103C4×D4×C13C2314yes—
104C13×#117—28no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4D411yescharacteristic
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C4⋊C4D411yescharacteristic
112C2×C13×C4⋊C4C2311yescharacteristic
113C2×C13×C22⋊C4—21no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4—21no—
118C2×C42×C13—21no—
119C2×C42×C13—21no—
120C2×C42×C13C2311yescharacteristic
121C2×C42×C13C2311yescharacteristic
122C2×C42×C13C2311yescharacteristic
123#88200—28no—
124C2×#6106—24no—
125C2×#6106—24no—
126C2×#6106C2314yes—
127C2×#6106C2314yes—
128C2×#6104—24no—
129C2×#6104C2314yes—
130C2×#6103—21no—
131C2×#6103—21no—
132C2×#6103—21no—
133C2×C4⋊Dic13—21no—
134C2×C4⋊Dic13C2311yescharacteristic
135C2×C4⋊Dic13C2311yescharacteristic
136C2×C4⋊Dic13C2311yescharacteristic
137C2×#6101—21no—
138C2×#6101—21no—
139C2×#6101—21no—
140C2×#6101—21no—
141C22×#1055C2311yescharacteristic
142C22×#1055C2311yescharacteristic
143C22×#1055C2311yescharacteristic
144C22×#1055C2311yescharacteristic
145#88150—28no—
146#88150—28no—
147C4⋊C4×D13—28no—
148C4×D52—22no—
149C4×D52—22no—
150C4×D52—22no—
151C4×D52C2314yes—
152C4×D52C2314yes—
153C4×D52C2314yes—
154#88124—22no—
155#88124—22no—
156#88124C2314yes—
157#88124C2314yes—
158#88123—22no—
159#88123C2314yes—
160#88075C2314yes—
161#88075C2314yes—
162#88075C2314yes—
163#88075C2314yes—
164#88075C2314yes—
165#88075C2314yes—
166#88072C2314yes—
167#88072C2314yes—
168#88072C2314yes—
169#88049C2314yes—
170#88048C2314yes—
171#88048C2314yes—
172#88047C2314yes—
173C4⋊#1055C2314yes—
174C4⋊#1055C2314yes—
175C4⋊#1055C2314yes—
176#88043C2314yes—
177#88043C2314yes—
178C4×#1055C2314yes—
179C2×#3376—131nomaximal, Sylow
180C24×C13—21no—
181C23×D13—21no—
182C2×Q8×C13—21no—
183C2×Q8×C13—21no—
184C2×Q8×C13—22no—
185C2×Q8×C13—22no—
186C2×Q8×C13—22no—
187C2×Q8×C13—22no—
188C2×Q8×C13—42no—
189C2×Q8×C13C2×D414yes—
190C2×Q8×C13C2412yes—
191C2×Q8×C13C2412yes—
192C2×D4×C13—21no—
193C2×D4×C13—22no—
194C2×D4×C13—22no—
195C2×D4×C13C2412yes—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—24no—
200C22×C4×C13—44no—
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2411yescharacteristic
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C2×D52—21no—
212C2×D52—22no—
213C2×D52#4114yes—
214C2×D52C2412yes—
215C2×C4×D13—24no—
216C2×C4×D13—24no—
217C2×C4×D13—24no—
218C2×C4×D13—44no—
219C2×C4×D13—82no—
220C2×C4×D13—82no—
221C2×Dic26—24no—
222C2×Dic26—82no—
223C13×C4⋊C4—24no—
224C13×C4⋊C4—24no—
225C13×C4⋊C4—24no—
226C13×C4⋊C4—24no—
227C13×C4⋊C4—21no—
228C13×C4⋊C4C2×D414yes—
229C13×C4⋊C4C2×D414yes—
230C13×C4⋊C4C2×D414yes—
231C13×C4⋊C4C2412yes—
232C13×C22⋊C4—24no—
233C13×C22⋊C4—24no—
234C13×C22⋊C4—24no—
235C13×C22⋊C4—24no—
236C13×C22⋊C4—24no—
237C42×C13—24no—
238C42×C13—24no—
239C42×C13C2×D412yes—
240C42×C13C2×D412yes—
241C42×C13C2×D412yes—
242C42×C13C2412yes—
243C42×C13C2412yes—
244C42×C13C2412yes—
245#6106—28no—
246#6106—28no—
247#6104—28no—
248#6103—24no—
249#6103—24no—
250#6103—24no—
251C4⋊Dic13—21no—
252C4⋊Dic13—21no—
253C4⋊Dic13—24no—
254C4⋊Dic13—21no—
255C4⋊Dic13C2412yes—
256C4⋊Dic13C2412yes—
257C4⋊Dic13C2412yes—
258#6101—24no—
259#6101—24no—
260#6101—24no—
261#6101—24no—
262C2×#1055—22no—
263C2×#1055—22no—
264C2×#1055—22no—
265C2×#1055—22no—
266C2×#1055C2412yes—
267C2×#1055C2412yes—
268C2×#1055C2412yes—
269C2×#1055C2412yes—
270C2×#556D1311yescharacteristic, complemented
271C2×#554—131no—
272#3376—1316no—
273C2×#491—131no—
274C2×#489—131no—
275C2×#488—131no—
276C2×#479—131no—
277C2×#475—131no—
278C2×#478—131no—
279C2×#463—131no—
280C2×#463—131no—
281C2×#461—131no—
282C2×#446—131no—
283C2×#442—131no—
284C2×#440—131no—
285C2×C4×SD16—131no—
286C23×C13—22no—
287C23×C13—42no—
288C23×C13—42no—
289C23×C13—42no—
290C23×C13C22×D411yescharacteristic
291C22×D13—24no—
292C22×D13—22no—
293C22×D13—42no—
294C22×D13—42no—
295Q8×C13—22no—
296Q8×C13—22no—
297Q8×C13—22no—
298Q8×C13—22no—
299Q8×C13—44no—
300Q8×C13—42no—
301Q8×C13—42no—
302D4×C13—22no—
303D4×C13—22no—
304D4×C13—42no—
305C2×C4×C13—22no—
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—22no—
313C2×C4×C13—22no—
314C2×C4×C13—48no—
315C2×C4×C13—42no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13C22×D412yes—
319C2×C4×C13C22×D412yes—
320C2×C4×C13C22×D412yes—
321C2×C4×C13C22×D412yes—
322C2×C4×C13C22×D412yes—
323C2×C4×C13C22×D412yes—
324C2×C4×C13C22×D411yescharacteristic
325C2×C4×C13C2×#4112yes—
326C2×C4×C132−1+412yes—
327C2×C4×C13C2511yescharacteristic
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334D52—24no—
335D52—22no—
336D52C2×#4114yes—
337C4×D13—48no—
338C4×D13—84no—
339C4×D13—84no—
340Dic26—84no—
341#1055—22no—
342#1055—22no—
343#1055—22no—
344#1055—22no—
345C22×SD16—131no—
346C22×SD16—131no—
347C22×D8—131no—
348#556—24no—
349#556C2×D1318yescomplemented
350#554—138no—
351#554—264no—
352C2×C4⋊Q8—131no—
353C2×C4⋊Q8C2×D1311yescharacteristic
354C2×#126—21no—
355C2×#126—21no—
356C2×#125—131no—
357C2×#125—131no—
358C2×#124C2×D1311yescharacteristic
359C2×#124C2×D1311yescharacteristic
360C2×C22⋊Q8—21no—
361C2×C22⋊Q8—261no—
362C2×C22⋊Q8—261no—
363C2×C22⋊Q8—261no—
364C2×C4×Q8C2×D1311yescharacteristic
365C2×C4×Q8C2×D1311yescharacteristic
366C2×C4×Q8C2×D1311yescharacteristic
367C2×C4×D4—131no—
368C2×C4×D4—131no—
369C2×C4×D4—131no—
370C2×C4×D4C2×D1311yescharacteristic
371C2×#117—21no—
372C22×C4⋊C4—261no—
373#491—138no—
374#489—138no—
375#488—138no—
376#479—138no—
377#478—138no—
378#475—138no—
379#463—138no—
380#463—138no—
381#461—138no—
382#446—138no—
383#442—138no—
384#440—138no—
385C4×SD16—138no—
386C2×#107—131no—
387C2×#106—131no—
388C2×#106—131no—
389C2×C4⋊C8—131no—
390C2×C4⋊C8—131no—
391C2×C4⋊C8—131no—
392C2×#103—131no—
393C2×#103—131no—
394C2×#103—131no—
395C2×#103—131no—
396C2×#103—131no—
397C2×#103—131no—
398C2×#102—131no—
399C2×#102—131no—
400C2×#102—131no—
401C2×#102—131no—
402C2×#97—131no—
403C2×#97—131no—
404C2×C4×C8—131no—
405C22×C13—42no—
406C22×C13—42no—
407C22×C13—42no—
408C22×C13—84no—
409C22×C13#54812yes—
410C22×C13#57512yes—
411C22×C13#57712yes—
412C22×C13C23×D411yescharacteristic
413C2×D13—24no—
414C2×D13—48no—
415C2×D13—42no—
416C2×D13—42no—
417C4×C13—22no—
418C4×C13—22no—
419C4×C13—22no—
420C4×C13—22no—
421C4×C13—22no—
422C4×C13—22no—
423C4×C13—42no—
424C4×C13—42no—
425C4×C13—42no—
426C4×C13#54812yes—
427C4×C13C22×#4111yescharacteristic
428C4×C13C2×2−1+411yescharacteristic
429Dic13—42no—
430Dic13—42no—
431Dic13—42no—
432C22×Q8—261no—
433C22×Q8C22⋊D1311yescharacteristic
434C22×Q8C22×D1311yescharacteristic
435C22×Q8C22×D1311yescharacteristic
436C22×D4—131no—
437C22×D4C22×D1311yescharacteristic
438C23×C4—21no—
439C23×C4—261no—
440C23×C4—261no—
441C23×C4—261no—
442C2×SD16—134no—
443C2×SD16—134no—
444C2×SD16—264no—
445C2×SD16—264no—
446C2×D8—134no—
447C2×D8—264no—
448C22×C8—131no—
449C22×C8—131no—
450C22×C8—131no—
451C22×C8—131no—
452C4⋊Q8—22no—
453C4⋊Q8—134no—
454C4⋊Q8—262no—
455C4⋊Q8C22×D1314yes—
456#126—28no—
457#126—28no—
458#125—134no—
459#125—134no—
460#125—262no—
461#125—262no—
462#124—22no—
463#124—22no—
464#124C22×D1314yes—
465#124C22×D1314yes—
466C22⋊Q8—28no—
467C22⋊Q8—268no—
468C22⋊Q8—268no—
469C22⋊Q8—268no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8C22⋊D1314yes—
473C4×Q8C22×D1314yes—
474C4×Q8C22×D1314yes—
475C4×Q8C22×D1314yes—
476C4×D4—22no—
477C4×D4—134no—
478C4×D4—134no—
479C4×D4—134no—
480C4×D4—262no—
481C4×D4—262no—
482C4×D4—262no—
483C4×D4C22×D1314yes—
484#117—28no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—131no—
491C2×C4⋊C4—131no—
492C2×C4⋊C4—261no—
493C2×C4⋊C4—261no—
494C2×C4⋊C4—261no—
495C2×C4⋊C4—261no—
496C2×C4⋊C4—261no—
497C2×C4⋊C4—268no—
498C2×C4⋊C4C22⋊D1311yescharacteristic
499C2×C4⋊C4C22⋊D1311yescharacteristic
500C2×C4⋊C4C22⋊D1311yescharacteristic
501C2×C4⋊C4C22×D1311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—261no—
508C2×C22⋊C4—261no—
509C2×C22⋊C4—261no—
510C2×C42—21no—
511C2×C42—21no—
512C2×C42C22×D1311yescharacteristic
513C2×C42C22×D1311yescharacteristic
514C2×C42C22×D1311yescharacteristic
515#107—134no—
516#106—134no—
517#106—134no—
518C4⋊C8—134no—
519C4⋊C8—134no—
520C4⋊C8—134no—
521#103—134no—
522#103—134no—
523#103—134no—
524#103—134no—
525#103—134no—
526#103—134no—
527#102—134no—
528#102—134no—
529#102—134no—
530#102—134no—
531#97—134no—
532#97—134no—
533C4×C8—134no—
534C2×C13—82no—
535C2×C13#337614yescomplemented
536C2×C13C2×#54811yescharacteristic
537C2×C13C2×#57511yescharacteristic
538C2×C13C2×#57711yescharacteristic
539D13—44no—
540C24—21no—
541C24—261no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—42no—
549C2×Q8—264no—
550C2×Q8—1042no—
551C2×Q8C2×C22⋊D1314yes—
552C2×Q8C23×D1312yes—
553C2×Q8C23×D1312yes—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—134no—
558C2×D4—132no—
559C2×D4—262no—
560C2×D4—261no—
561C2×D4C23×D1312yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—44no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4—264no—
571C22×C4—264no—
572C22×C4—264no—
573C22×C4—524no—
574C22×C4—1042no—
575C22×C4—1042no—
576C22×C4C2×C22⋊D1311yescharacteristic
577C22×C4C2×C22⋊D1311yescharacteristic
578C22×C4C2×C22⋊D1311yescharacteristic
579C22×C4C2×C22⋊D1311yescharacteristic
580C22×C4C2×C22⋊D1311yescharacteristic
581C22×C4C2×C22⋊D1311yescharacteristic
582C22×C4C23×D1311yescharacteristic
583SD16—268no—
584SD16—268no—
585D8—268no—
586C2×C8—132no—
587C2×C8—132no—
588C2×C8—132no—
589C2×C8—132no—
590C2×C8—262no—
591C2×C8—262no—
592C2×C8—262no—
593C2×C8—262no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—21no—
599C4⋊C4—132no—
600C4⋊C4—132no—
601C4⋊C4—132no—
602C4⋊C4—261no—
603C4⋊C4—261no—
604C4⋊C4—261no—
605C4⋊C4—264no—
606C4⋊C4—264no—
607C4⋊C4—264no—
608C4⋊C4—264no—
609C4⋊C4—264no—
610C4⋊C4C2×C22⋊D1314yes—
611C4⋊C4C2×C22⋊D1314yes—
612C4⋊C4C2×C22⋊D1314yes—
613C4⋊C4C23×D1312yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—264no—
620C22⋊C4—264no—
621C22⋊C4—264no—
622C42—24no—
623C42—24no—
624C42C2×C22⋊D1312yes—
625C42C2×C22⋊D1312yes—
626C42C2×C22⋊D1312yes—
627C42C23×D1312yes—
628C42C23×D1312yes—
629C42C23×D1312yes—
630C13C2×#337611yescharacteristic, complemented, Sylow
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—264no—
636C23—262no—
637C23—522no—
638C23—522no—
639C23C22×C22⋊D1311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—44no—
645Q8—42no—
646Q8—42no—
647Q8—1044no—
648D4—22no—
649D4—22no—
650D4—42no—
651D4—134no—
652D4—264no—
653D4—262no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—48no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—262no—
668C2×C4—262no—
669C2×C4—262no—
670C2×C4—528no—
671C2×C4—522no—
672C2×C4—522no—
673C2×C4—522no—
674C2×C4—1044no—
675C2×C4—1044no—
676C2×C4#41×D1312yes—
677C2×C4#8825712yes—
678C2×C4C22×C22⋊D1312yes—
679C2×C4C22×C22⋊D1312yes—
680C2×C4C22×C22⋊D1312yes—
681C2×C4C22×C22⋊D1312yes—
682C2×C4C22×C22⋊D1312yes—
683C2×C4C22×C22⋊D1312yes—
684C2×C4C22×C22⋊D1311yescharacteristic
685C2×C4C24×D1311yescharacteristic
686C8—262no—
687C8—262no—
688C8—262no—
689C8—262no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—264no—
695C22—522no—
696C22—522no—
697C22—528no—
698C22#1171952712yes—
699C22#1171953612yes—
700C22#1171954212yes—
701C22C23×C22⋊D1311yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—522no—
712C4—522no—
713C4—522no—
714C4#1171953612yes—
715C4C2×#41×D1311yescharacteristic
716C4C2×#8825711yescharacteristic
717C2—82no—
718C2—524no—
719C2#1312765714yesdirect product factor
720C2C2×#1171953611yescharacteristic
721C2C2×#1171952711yescharacteristic
722C2C2×#1171954211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#556C2
socleC23×C13C22×D4
prime radicalC22×#6104C22
hypercenterC2×#556D13
hypocenterC13C2×#3376
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#11719284C2semidirect
2. #13127657C2direct (N × H)
3. C2×#11718743C2semidirect
4. C2×#11718716C2semidirect
5. C2×#11718717C2semidirect
6. C2×#11718683C2semidirect
7. C2×#11718681C2semidirect
8. C2×#11718670C2semidirect
11. C2×#11718744C2semidirect
12. C2×#11718685C2semidirect
14. C2×#11718687C2semidirect
15. C2×C4×#6106C2semidirect
16. C2×C13×#556C2semidirect
18. C13×#556C22semidirect
35. #11719284C22semidirect
54. #11718744C22semidirect
55. #11718743C22semidirect
58. #11718717C22semidirect
59. #11718716C22semidirect
60. #11718687C22semidirect
61. C4×#6106C22semidirect
62. #11718685C22semidirect
63. #11718683C22semidirect
64. #11718681C22semidirect
66. #11718670C22semidirect
270. C2×#556D13semidirect
349. #556C2×D13semidirect
535. C2×C13#3376semidirect
630. C13C2×#3376semidirect
719. C2#13127657direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192842
#131276572
C2×#117187432
C2×#117187162
C2×#117187172
C2×#117186832
C2×#117186812
C2×#117186702
C2×#117187182
C2×#117187442
C2×#117186852
C2×#117186752
C2×#117186872
C2×C4×#61062
C2×C13×#5562
C2×#337613