Finite Group Databasebeta

← C2×#20254636 #27088462

Subgroups — C2×#20254636 #27088462

Order 12032.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689753C211yesmaximal, characteristic, complemented
2C2×#15689727C211yesmaximal, characteristic
3#20254636C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689522C211yesmaximal, characteristic, complemented
6C2×#15689469C211yesmaximal, characteristic, complemented
7C2×#15689440C211yesmaximal, characteristic, complemented
8C2×#15689446C211yesmaximal, characteristic, complemented
9C2×#15689445C211yesmaximal, characteristic, complemented
10C2×#15689435C211yesmaximal, characteristic, complemented
11C2×#15689425C211yesmaximal, characteristic, complemented
12C2×#15689421C211yesmaximal, characteristic, complemented
13C2×#15689411C211yesmaximal, characteristic, complemented
14C2×#15689401C211yesmaximal, characteristic, complemented
15C2×#15689185C211yesmaximal, characteristic, complemented
16C2×C47×#490C211yesmaximal, characteristic, complemented
17#15689753—24no—
18#15689753C2218yescomplemented
19#15689727—24no—
20#15689727C2218yes—
21C2×#13094024C2211yescharacteristic
22C2×#13094023—21no—
23C2×#13094023C2211yescharacteristic
24C2×#13094016C2211yescharacteristic
25C2×#13094015C2211yescharacteristic
26C2×#13094014—21no—
27C2×#13094005—21no—
28C2×#13094005—21no—
29C2×#13094004—21no—
30C2×#13094002—21no—
31C2×#13093996—21no—
32C2×#13093996—21no—
33C2×#13093995C2211yescharacteristic
34C2×#13093995C2211yescharacteristic
35C2×D4×Dic47C2211yescharacteristic
36C2×D4×Dic47C2211yescharacteristic
37C2×#13093982C2211yescharacteristic
38C2×#13093981C2211yescharacteristic
39C2×C4⋊C4×D47C2211yescharacteristic
40#15689532C2218yescomplemented
41#15689522C2218yescomplemented
42#15689469C2218yescomplemented
43#15689446C2218yescomplemented
44#15689445C2218yescomplemented
45#15689440C2218yescomplemented
46#15689435C2218yescomplemented
47#15689425C2218yescomplemented
48#15689421C2218yescomplemented
49#15689411C2218yescomplemented
50#15689401C2218yescomplemented
51#15689185C2218yescomplemented
52C2×#13093958C2211yescharacteristic
53C2×#13093958C2211yescharacteristic
54C2×#13093957C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59C2×#13093955C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C4×C47⋊C8C2211yescharacteristic
69C2×#127×C47C2211yescharacteristic
70C2×#125×C47C2211yescharacteristic
71C47×#490C2218yescomplemented
72C2×#102×C47C2211yescharacteristic
73C2×#102×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×C22⋊D47—21no—
80C22×C22⋊D47—21no—
81C23×Dic47—21no—
82C23×Dic47—21no—
83C22×C4×D47—21no—
84C22×C4×D47C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2311yescharacteristic
87#13094024—22no—
88#13094024C2314yes—
89#13094023—28no—
90#13094023—22no—
91#13094023C2314yes—
92#13094016—22no—
93#13094016C2314yes—
94#13094015—22no—
95#13094015C2314yes—
96#13094014—28no—
97#13094005—28no—
98#13094005—28no—
99#13094004—28no—
100#13094002—28no—
101#13093996—28no—
102#13093996—28no—
103#13093995—22no—
104#13093995—22no—
105#13093995C2314yes—
106#13093995C2314yes—
107D4×Dic47—22no—
108D4×Dic47—22no—
109D4×Dic47C2314yes—
110D4×Dic47C2314yes—
111#13093982—22no—
112#13093982C2314yes—
113#13093981D414yes—
114#13093981C2314yes—
115C2×C4⋊Dic47—21no—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47C2311yescharacteristic
118C2×C4⋊Dic47C2311yescharacteristic
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×Dic47⋊C4—21no—
122C2×Dic47⋊C4—21no—
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4D411yescharacteristic
127C2×Dic47⋊C4D411yescharacteristic
128C4⋊C4×D47—22no—
129C4⋊C4×D47C2314yes—
130C2×C22⋊Dic47—21no—
131C2×C22⋊Dic47—21no—
132C2×C22⋊Dic47—21no—
133C2×C22⋊Dic47—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4D411yescharacteristic
136C2×(C2×D47)⋊C4D411yescharacteristic
137C2×C4×Dic47—21no—
138C2×C4×Dic47C2311yescharacteristic
139#13093958C2314yes—
140#13093958C2314yes—
141#13093957C2314yes—
142#13093957C2314yes—
143#13093956C2314yes—
144#13093956C2314yes—
145#13093955C2314yes—
146#13093955C2314yes—
147Dic47⋊C8C2314yes—
148Dic47⋊C8C2314yes—
149#13093945C2314yes—
150#13093945C2314yes—
151#13093945C2314yes—
152#13093945C2314yes—
153(C2×D47)⋊C8C2314yes—
154(C2×D47)⋊C8C2314yes—
155C4×C47⋊C8C2314yes—
156C22×D4×C47—21no—
157C22×D4×C47—21no—
158C22×D4×C47C2311yescharacteristic
159C22×D4×C47C2311yescharacteristic
160C22×C8×C47C2311yescharacteristic
161C22×C8×C47C2311yescharacteristic
162#127×C47—22no—
163#127×C47C2314yes—
164#125×C47—22no—
165#125×C47C2314yes—
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C42×C47C2311yescharacteristic
171#102×C47C2314yes—
172#102×C47C2314yes—
173#102×C47C2314yes—
174#102×C47C2314yes—
175#97×C47C2314yes—
176C24×C47—21no—
177C24×C47—21no—
178C23×D47C2×D411yescharacteristic
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—24no—
182C2×D4×C47—24no—
183C2×D4×C47—22no—
184C2×D4×C47—22no—
185C2×D4×C47—22no—
186C2×D4×C47—22no—
187C2×D4×C47—82no—
188C2×D4×C47—82no—
189C2×D4×C47C2412yes—
190C2×D4×C47C2412yes—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—24no—
197C2×C22⋊D47—24no—
198C2×C22⋊D47—82no—
199C2×C22⋊D47—82no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—24no—
205C22×Dic47—24no—
206C22×Dic47—82no—
207C22×Dic47—82no—
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211C2×C4×D47—22no—
212C2×C4×D47—22no—
213C2×C4×D47—24no—
214C2×C4×D47—82no—
215C2×C4×D47C2×D412yes—
216C2×C4×D47C2412yes—
217C2×Dic94—24no—
218C2×Dic94—24no—
219C2×Dic94—82no—
220C2×Dic94—82no—
221C2×C8×C47—22no—
222C2×C8×C47—22no—
223C2×C8×C47C2412yes—
224C2×C8×C47C2412yes—
225C4⋊C4×C47—24no—
226C4⋊C4×C47—24no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47C2412yes—
230C4⋊C4×C47C2412yes—
231C42×C47C2×D412yes—
232C42×C47C2412yes—
233C22⋊Dic47—24no—
234C22⋊Dic47—24no—
235C22⋊Dic47—24no—
236C22⋊Dic47—24no—
237(C2×D47)⋊C4—24no—
238(C2×D47)⋊C4C2×D414yes—
239(C2×D47)⋊C4C2×D414yes—
240C4⋊Dic47—21no—
241C4⋊Dic47—24no—
242C4⋊Dic47—21no—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47—24no—
246C4⋊Dic47C2412yes—
247C4⋊Dic47C2412yes—
248C4⋊Dic47C2412yes—
249C4⋊Dic47C2412yes—
250Dic47⋊C4—24no—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4C2×D414yes—
256Dic47⋊C4C2×D414yes—
257C4×Dic47—24no—
258C4×Dic47C2×D412yes—
259C4×Dic47C2412yes—
260C2×C47⋊C8—22no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8C2412yes—
263C2×C47⋊C8C2412yes—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—42no—
267C23×C47—42no—
268C23×C47—42no—
269C23×C47—42no—
270C23×C47—42no—
271C23×C47—42no—
272C23×C47C22×D411yescharacteristic
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D47C22×D412yes—
277D4×C47—22no—
278D4×C47—22no—
279D4×C47—22no—
280D4×C47—22no—
281D4×C47—42no—
282D4×C47—42no—
283D4×C47—84no—
284D4×C47—84no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47C22×D412yes—
292C2×C4×C47C22×D412yes—
293C2×C4×C47C22×D411yescharacteristic
294C2×C4×C472−1+412yes—
295C2×C4×C472−1+412yes—
296C2×C4×C47C2511yescharacteristic
297C22⋊D47—84no—
298C22⋊D47—84no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—84no—
311C2×Dic47—84no—
312C2×Dic47C22×D412yes—
313C2×Dic47C22×D412yes—
314C2×Dic47C22×D412yes—
315C4×D47—24no—
316C4×D47—22no—
317C4×D47—22no—
318C4×D47—84no—
319Dic94—84no—
320Dic94—84no—
321C8×C47—22no—
322C8×C47—22no—
323C47⋊C8—22no—
324C47⋊C8—22no—
325C2×#3241—471nomaximal, Sylow
326C22×C47—42no—
327C22×C47—42no—
328C22×C47—42no—
329C22×C47—42no—
330C22×C47—42no—
331C22×C47—42no—
332C22×C47—84no—
333C22×C47—84no—
334C22×C47#53612yes—
335C22×C47#57612yes—
336C22×C47#57712yes—
337C22×C47C23×D411yescharacteristic
338C2×D47—22no—
339C2×D47—22no—
340C2×D47—22no—
341C2×D47—44no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—42no—
345C4×C47—42no—
346C4×C47#53612yes—
347C4×C47C2×2−1+411yescharacteristic
348C4×C47C2×2−1+411yescharacteristic
349Dic47—22no—
350Dic47—22no—
351Dic47—22no—
352Dic47—42no—
353Dic47—42no—
354Dic47—42no—
355Dic47—42no—
356C2×#544—471no—
357C2×#540—471no—
358#3241—4716no—
359C2×#501—471no—
360C2×#499—471no—
361C2×#490D4711yescharacteristic, complemented
362C2×#486—471no—
363C2×#481—471no—
364C2×#482—471no—
365C2×#482—471no—
366C2×#480—471no—
367C2×#478—471no—
368C2×#478—471no—
369C2×#476—471no—
370C2×#474—471no—
371C2×#433—471no—
372C2×C47—82no—
373C2×C47—82no—
374C2×C47#324114yescomplemented
375C2×C47C2×#53611yescharacteristic
376C2×C47C2×#57611yescharacteristic
377C2×C47C2×#57711yescharacteristic
378D47—42no—
379#544—478no—
380#544—944no—
381#540—478no—
382#540—944no—
383C2×C4⋊Q8—471no—
384C2×C4⋊Q8—471no—
385C2×C4⋊Q8—941no—
386C2×#127C2×D4711yescharacteristic
387C2×#125—471no—
388C2×#125—471no—
389C2×#125—941no—
390C2×#125C2×D4711yescharacteristic
391C2×#123—941no—
392C2×#123—941no—
393C2×C22⋊Q8—941no—
394C2×C22⋊Q8—941no—
395C2×#121—471no—
396C2×#121—471no—
397C2×#121—941no—
398C2×#121—941no—
399C2×C4×D4—471no—
400C2×C4×D4—471no—
401C2×#117—471no—
402C2×#117—471no—
403C22×C4⋊C4—471no—
404#501—478no—
405#499—478no—
406#490C2×D4718yescomplemented
407#486—478no—
408#482—478no—
409#482—478no—
410#481—478no—
411#480—478no—
412#478—478no—
413#478—478no—
414#476—478no—
415#474—478no—
416#433—478no—
417C2×#107—471no—
418C2×#107—471no—
419C2×#107—471no—
420C2×#107—471no—
421C2×#106—471no—
422C2×#106—471no—
423C2×#106—471no—
424C2×#106—471no—
425C2×C4⋊C8—471no—
426C2×C4⋊C8—471no—
427C2×#102—471no—
428C2×#102—471no—
429C2×#102—471no—
430C2×#102—471no—
431C2×#102C2×D4711yescharacteristic
432C2×#102C2×D4711yescharacteristic
433C2×#102C2×D4711yescharacteristic
434C2×#102C2×D4711yescharacteristic
435C2×C22⋊C8—471no—
436C2×C22⋊C8—471no—
437C2×#97C2×D4711yescharacteristic
438C2×C4×C8—471no—
439C47C2×#324111yescharacteristic, complemented, Sylow
440C22×Q8—941no—
441C22×Q8—941no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—941no—
445C22×D4—941no—
446C22×D4C22×D4711yescharacteristic
447C22×D4C22×D4711yescharacteristic
448C23×C4—471no—
449C23×C4—941no—
450C23×C4—941no—
451C23×C4—941no—
452C22×C8—471no—
453C22×C8—471no—
454C22×C8C22×D4711yescharacteristic
455C22×C8C22×D4711yescharacteristic
456C4⋊Q8—474no—
457C4⋊Q8—474no—
458C4⋊Q8—942no—
459C4⋊Q8—948no—
460C4⋊Q8—942no—
461#127—22no—
462#127C22×D4714yes—
463#125—22no—
464#125—474no—
465#125—474no—
466#125—942no—
467#125—948no—
468#125—942no—
469#125C22×D4714yes—
470#123—948no—
471#123—948no—
472C22⋊Q8—948no—
473C22⋊Q8—948no—
474#121—474no—
475#121—474no—
476#121—948no—
477#121—948no—
478#121—942no—
479#121—942no—
480C4×D4—474no—
481C4×D4—474no—
482C4×D4—942no—
483C4×D4—942no—
484#117—474no—
485#117—474no—
486#117—474no—
487#117—942no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—471no—
491C2×C4⋊C4—471no—
492C2×C4⋊C4—471no—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—474no—
497C2×C4⋊C4—942no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C22⋊C4—471no—
508C2×C22⋊C4—471no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C42—471no—
515C2×C42—941no—
516C2×C42C22×D4711yescharacteristic
517#107—474no—
518#107—474no—
519#107—474no—
520#107—474no—
521#106—474no—
522#106—474no—
523#106—474no—
524#106—474no—
525C4⋊C8—474no—
526C4⋊C8—474no—
527#102—474no—
528#102—474no—
529#102—474no—
530#102—474no—
531#102C22×D4714yes—
532#102C22×D4714yes—
533#102C22×D4714yes—
534#102C22×D4714yes—
535C22⋊C8—474no—
536C22⋊C8—474no—
537#97C22×D4714yes—
538C4×C8—474no—
539C24—21no—
540C24—21no—
541C24—471no—
542C2×Q8—944no—
543C2×Q8—944no—
544C2×Q8—3762no—
545C2×Q8—3762no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—944no—
557C2×D4—944no—
558C2×D4—3762no—
559C2×D4—3762no—
560C2×D4C23×D4712yes—
561C2×D4C23×D4712yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—471no—
565C22×C4—471no—
566C22×C4—471no—
567C22×C4—472no—
568C22×C4—472no—
569C22×C4—944no—
570C22×C4—944no—
571C22×C4—944no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—941no—
575C22×C4—941no—
576C22×C4—941no—
577C22×C4—941no—
578C22×C4—3762no—
579C22×C4—3762no—
580C22×C4—3762no—
581C22×C4D4×D4711yescharacteristic
582C22×C4D4×D4711yescharacteristic
583C22×C4C23×D4711yescharacteristic
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—472no—
587C2×C8—472no—
588C2×C8—942no—
589C2×C8—942no—
590C2×C8C23×D4712yes—
591C2×C8C23×D4712yes—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—474no—
597C4⋊C4—474no—
598C4⋊C4—472no—
599C4⋊C4—472no—
600C4⋊C4—472no—
601C4⋊C4—472no—
602C4⋊C4—944no—
603C4⋊C4—944no—
604C4⋊C4—944no—
605C4⋊C4—944no—
606C4⋊C4—944no—
607C4⋊C4—944no—
608C4⋊C4—941no—
609C4⋊C4—941no—
610C4⋊C4—941no—
611C4⋊C4—941no—
612C4⋊C4—944no—
613C4⋊C4C23×D4712yes—
614C4⋊C4C23×D4712yes—
615C22⋊C4—474no—
616C22⋊C4—474no—
617C22⋊C4—944no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4—944no—
621C22⋊C4—944no—
622C42—472no—
623C42—472no—
624C42—944no—
625C42D4×D4712yes—
626C42C23×D4712yes—
627C23—22no—
628C23—22no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—472no—
636C23—942no—
637C23—942no—
638C23—942no—
639C23C2×D4×D4711yescharacteristic
640Q8—3764no—
641Q8—3764no—
642D4—22no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—42no—
647D4—42no—
648D4—84no—
649D4—84no—
650D4—3764no—
651D4—3764no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—472no—
659C2×C4—472no—
660C2×C4—472no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—944no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—3764no—
672C2×C4—3764no—
673C2×C4—3764no—
674C2×C4—1882no—
675C2×C4—1882no—
676C2×C4—1882no—
677C2×C4—1882no—
678C2×C4C2×D4×D4712yes—
679C2×C4C2×D4×D4712yes—
680C2×C4C2×D4×D4711yescharacteristic
681C2×C4#1309407112yes—
682C2×C4#1309407112yes—
683C2×C4C24×D4711yescharacteristic
684C8—22no—
685C8—22no—
686C8—942no—
687C8—942no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—84no—
695C22—84no—
696C22—942no—
697C22—942no—
698C22—942no—
699C22—1884no—
700C22#1568969312yes—
701C22#1568992712yes—
702C22#1568993312yes—
703C22C22×D4×D4711yescharacteristic
704C4—22no—
705C4—22no—
706C4—42no—
707C4—42no—
708C4—942no—
709C4—942no—
710C4—942no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C4—1882no—
715C4#1568969312yes—
716C4C2×#1309407111yescharacteristic
717C4C2×#1309407111yescharacteristic
718C2—82no—
719C2—82no—
720C2—1882no—
721C2#2025463614yesdirect product factor
722C2C2×#1568969311yescharacteristic
723C2C2×#1568992711yescharacteristic
724C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#490C2
socleC23×C47C22×D4
prime radicalC2×#15689727C2
hypercenterC2×#490D47
hypocenterC47C2×#3241
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#15689753C2semidirect
3. #20254636C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689522C2semidirect
6. C2×#15689469C2semidirect
7. C2×#15689440C2semidirect
8. C2×#15689446C2semidirect
9. C2×#15689445C2semidirect
10. C2×#15689435C2semidirect
11. C2×#15689425C2semidirect
12. C2×#15689421C2semidirect
13. C2×#15689411C2semidirect
14. C2×#15689401C2semidirect
15. C2×#15689185C2semidirect
16. C2×C47×#490C2semidirect
18. #15689753C22semidirect
40. #15689532C22semidirect
41. #15689522C22semidirect
42. #15689469C22semidirect
43. #15689446C22semidirect
44. #15689445C22semidirect
45. #15689440C22semidirect
46. #15689435C22semidirect
47. #15689425C22semidirect
48. #15689421C22semidirect
49. #15689411C22semidirect
50. #15689401C22semidirect
51. #15689185C22semidirect
71. C47×#490C22semidirect
361. C2×#490D47semidirect
374. C2×C47#3241semidirect
406. #490C2×D47semidirect
439. C47C2×#3241semidirect
721. C2#20254636direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897532
C2×#156897272
#202546362
C2×#156895322
C2×#156895222
C2×#156894692
C2×#156894402
C2×#156894462
C2×#156894452
C2×#156894352
C2×#156894252
C2×#156894212
C2×#156894112
C2×#156894012
C2×#156891852
C2×C47×#4902
C2×#324147