Finite Group Databasebeta

← C2×#20254646 #27088472

Subgroups — C2×#20254646 #27088472

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×#15689724C211yesmaximal, characteristic
3#20254646C2116yesmaximal, direct product factor
4C2×#15689531C211yesmaximal, characteristic, complemented
5C2×#15689523C211yesmaximal, characteristic, complemented
6C2×#15689486C211yesmaximal, characteristic, complemented
7C2×#15689468C211yesmaximal, characteristic, complemented
8C2×#15689440C211yesmaximal, characteristic, complemented
9C2×#15689449C211yesmaximal, characteristic, complemented
10C2×#15689446C211yesmaximal, characteristic, complemented
11C2×#15689438C211yesmaximal, characteristic, complemented
12C2×#15689420C211yesmaximal, characteristic, complemented
13C2×#15689414C211yesmaximal, characteristic, complemented
14C2×#15689403C211yesmaximal, characteristic, complemented
15C2×#15689183C211yesmaximal, characteristic, complemented
16C2×C47×#478C211yesmaximal, characteristic, complemented
17#15689753—24no—
18#15689753C2218yescomplemented
19#15689724—24no—
20#15689724C2218yes—
21C2×#13094024C2211yescharacteristic
22C2×#13094023—21no—
23C2×#13094023C2211yescharacteristic
24C2×#13094020C2211yescharacteristic
25C2×#13094015C2211yescharacteristic
26C2×#13094015C2211yescharacteristic
27C2×#13094014—21no—
28C2×#13094007—21no—
29C2×#13094006—21no—
30C2×#13094004—21no—
31C2×#13094002—21no—
32C2×#13093999C2211yescharacteristic
33C2×#13093998—21no—
34C2×#13093997—21no—
35C2×#13093995C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37C2×#13093982C2211yescharacteristic
38C2×#13093981C2211yescharacteristic
39C2×C4⋊C4×D47C2211yescharacteristic
40#15689531C2218yescomplemented
41#15689523C2218yescomplemented
42#15689486C2218yescomplemented
43#15689468C2218yescomplemented
44#15689449C2218yescomplemented
45#15689446C2218yescomplemented
46#15689440C2218yescomplemented
47#15689438C2218yescomplemented
48#15689420C2218yescomplemented
49#15689414C2218yescomplemented
50#15689403C2218yescomplemented
51#15689183C2218yescomplemented
52C2×#13093957C2211yescharacteristic
53C2×#13093957C2211yescharacteristic
54C2×#13093957C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×#13093946C2211yescharacteristic
60C2×#13093946C2211yescharacteristic
61C2×#13093945C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×#125×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C47×#478C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×D188—21no—
80C22×D188C2311yescharacteristic
81C22×C22⋊D47—21no—
82C22×C22⋊D47—21no—
83C22×C22⋊D47—21no—
84C22×C4×D47—21no—
85C22×C4×D47—21no—
86C22×C4×D47C2311yescharacteristic
87C22×C47⋊C8C2311yescharacteristic
88C22×C47⋊C8C2311yescharacteristic
89#13094024—22no—
90#13094024C2314yes—
91#13094023—28no—
92#13094023—22no—
93#13094023C2314yes—
94#13094020—22no—
95#13094020C2314yes—
96#13094015—22no—
97#13094015—22no—
98#13094015C2314yes—
99#13094015C2314yes—
100#13094014—28no—
101#13094007—28no—
102#13094006—28no—
103#13094004—28no—
104#13094002—28no—
105#13093999—22no—
106#13093999C2314yes—
107#13093998—28no—
108#13093997—28no—
109#13093995—22no—
110#13093995C2314yes—
111C4×D188—22no—
112C4×D188C2314yes—
113#13093982—22no—
114#13093982C2314yes—
115#13093981D414yes—
116#13093981C2314yes—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4D411yescharacteristic
128C2×Dic47⋊C4D411yescharacteristic
129C4⋊C4×D47—22no—
130C4⋊C4×D47C2314yes—
131C2×C22⋊Dic47—21no—
132C2×(C2×D47)⋊C4—21no—
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4D411yescharacteristic
136C2×(C2×D47)⋊C4D411yescharacteristic
137C2×C4×Dic47—21no—
138C2×C4×Dic47C2311yescharacteristic
139#13093957C2314yes—
140#13093957C2314yes—
141#13093957C2314yes—
142#13093956C2314yes—
143#13093956C2314yes—
144#13093955C2314yes—
145C4⋊(C47⋊C8)C2314yes—
146#13093946C2314yes—
147#13093946C2314yes—
148#13093945C2314yes—
149#13093945C2314yes—
150#13093944C2314yes—
151#13093944C2314yes—
152(C2×D47)⋊C8C2314yes—
153(C2×D47)⋊C8C2314yes—
154#13093934C2314yes—
155C8×Dic47C2314yes—
156C22×D4×C47C2311yescharacteristic
157C23×C4×C47—21no—
158C22×C8×C47C2311yescharacteristic
159C22×C8×C47C2311yescharacteristic
160#125×C47—22no—
161#125×C47C2314yes—
162C4×D4×C47—22no—
163C4×D4×C47C2314yes—
164C2×C4⋊C4×C47—21no—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47C2311yescharacteristic
167C2×C4⋊C4×C47C2311yescharacteristic
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C22⋊C4×C47—21no—
170C2×C42×C47C2311yescharacteristic
171#107×C47C2314yes—
172#106×C47C2314yes—
173C4⋊C8×C47C2314yes—
174#102×C47C2314yes—
175#102×C47C2314yes—
176C24×C47—21no—
177C23×D47—21no—
178C23×D47C2×D411yescharacteristic
179C2×D4×C47—21no—
180C2×D4×C47—22no—
181C2×D4×C47—22no—
182C2×D4×C47C2412yes—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—24no—
187C22×C4×C47—82no—
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2411yescharacteristic
191C2×C22⋊D47—24no—
192C2×C22⋊D47—24no—
193C2×C22⋊D47—24no—
194C2×C22⋊D47—82no—
195C2×C22⋊D47—82no—
196C2×C22⋊D47—82no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47C2×D411yescharacteristic
201C22×Dic47C2×D411yescharacteristic
202C22×Dic47C2×D411yescharacteristic
203C2×D188—22no—
204C2×D188—22no—
205C2×D188—21no—
206C2×D188—24no—
207C2×D188—82no—
208C2×D188C2412yes—
209C2×C4×D47—22no—
210C2×C4×D47—22no—
211C2×C4×D47—24no—
212C2×C4×D47—24no—
213C2×C4×D47—82no—
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×C47—21no—
230C4⋊C4×C47C2412yes—
231C4⋊C4×C47C2412yes—
232C4⋊C4×C47C2412yes—
233C22⋊C4×C47—24no—
234C42×C47C2×D412yes—
235C42×C47C2412yes—
236C22⋊Dic47—24no—
237(C2×D47)⋊C4—24no—
238(C2×D47)⋊C4—24no—
239(C2×D47)⋊C4—24no—
240(C2×D47)⋊C4C2×D414yes—
241(C2×D47)⋊C4C2×D414yes—
242C4⋊Dic47—21no—
243C4⋊Dic47—24no—
244C4⋊Dic47—21no—
245C4⋊Dic47—21no—
246C4⋊Dic47—24no—
247C4⋊Dic47—24no—
248C4⋊Dic47C2412yes—
249C4⋊Dic47C2412yes—
250C4⋊Dic47C2412yes—
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—42no—
266C23×C47—42no—
267C23×C47—42no—
268C23×C47C22×D411yescharacteristic
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—42no—
274C22×D47—42no—
275C22×D47—42no—
276C22×D47C22×D412yes—
277D4×C47—22no—
278D4×C47—22no—
279D4×C47—42no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—84no—
289C2×C4×C47C22×D412yes—
290C2×C4×C47C22×D412yes—
291C2×C4×C47C22×D411yescharacteristic
292C2×C4×C472−1+412yes—
293C2×C4×C472−1+412yes—
294C2×C4×C47C2511yescharacteristic
295C22⋊D47—84no—
296C22⋊D47—84no—
297C22⋊D47—84no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47C22×D412yes—
308C2×Dic47C22×D412yes—
309C2×Dic47C22×D412yes—
310D188—22no—
311D188—22no—
312D188—42no—
313D188—84no—
314C4×D47—24no—
315C4×D47—22no—
316C4×D47—22no—
317C4×D47—84no—
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—84no—
330C22×C47#53612yes—
331C22×C47#57612yes—
332C22×C47#57712yes—
333C22×C47C23×D411yescharacteristic
334C2×D47—22no—
335C2×D47—22no—
336C2×D47—22no—
337C2×D47—44no—
338C2×D47—42no—
339C2×D47—42no—
340C2×D47—42no—
341C2×D47—84no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—42no—
345C4×C47—42no—
346C4×C47—42no—
347C4×C47#53612yes—
348C4×C47C2×2−1+411yescharacteristic
349C4×C47C2×2−1+411yescharacteristic
350Dic47—22no—
351Dic47—22no—
352Dic47—22no—
353Dic47—42no—
354Dic47—42no—
355Dic47—42no—
356C2×#544—471no—
357C2×#540—471no—
358#3241—4716no—
359C2×#501—471no—
360C2×#499—471no—
361C2×#490—471no—
362C2×#486—471no—
363C2×#481—471no—
364C2×#482—471no—
365C2×#482—471no—
366C2×#480—471no—
367C2×#478—471no—
368C2×#478D4711yescharacteristic, complemented
369C2×#476—471no—
370C2×#474—471no—
371C2×#433—471no—
372C2×C47—82no—
373C2×C47#324114yescomplemented
374C2×C47C2×#53611yescharacteristic
375C2×C47C2×#57611yescharacteristic
376C2×C47C2×#57711yescharacteristic
377D47—42no—
378D47—82no—
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×#127—471no—
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×D4C2×D4711yescharacteristic
401C2×#117—471no—
402C2×#117—471no—
403C22×C4⋊C4—471no—
404#501—478no—
405#499—478no—
406#490—478no—
407#486—478no—
408#482—478no—
409#482—478no—
410#481—478no—
411#480—478no—
412#478—478no—
413#478C2×D4718yescomplemented
414#476—478no—
415#474—478no—
416#433—478no—
417C2×#107—471no—
418C2×#107—471no—
419C2×#107—471no—
420C2×#107C2×D4711yescharacteristic
421C2×#106—471no—
422C2×#106—471no—
423C2×#106—471no—
424C2×#106C2×D4711yescharacteristic
425C2×C4⋊C8—471no—
426C2×C4⋊C8C2×D4711yescharacteristic
427C2×#102—471no—
428C2×#102—471no—
429C2×#102—471no—
430C2×#102—471no—
431C2×#102—471no—
432C2×#102—471no—
433C2×#102C2×D4711yescharacteristic
434C2×#102C2×D4711yescharacteristic
435C2×C22⋊C8—471no—
436C2×C22⋊C8—471no—
437C2×#97—471no—
438C2×C4×C8—471no—
439C47C2×#324111yescharacteristic, complemented, Sylow
440C22×Q8—941no—
441C22×Q8—941no—
442C22×D4—471no—
443C22×D4—941no—
444C22×D4—941no—
445C22×D4—941no—
446C22×D4—941no—
447C22×D4C22×D4711yescharacteristic
448C23×C4—21no—
449C23×C4—471no—
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—474no—
462#127—942no—
463#125—22no—
464#125—474no—
465#125—474no—
466#125—942no—
467#125—942no—
468#125—948no—
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—22no—
481C4×D4—474no—
482C4×D4—942no—
483C4×D4C22×D4714yes—
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—474no—
496C2×C4⋊C4—942no—
497C2×C4⋊C4—941no—
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⋊C4C22×D4711yescharacteristic
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—471no—
509C2×C22⋊C4—471no—
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#107C22×D4714yes—
521#106—474no—
522#106—474no—
523#106—474no—
524#106C22×D4714yes—
525C4⋊C8—474no—
526C4⋊C8C22×D4714yes—
527#102—474no—
528#102—474no—
529#102—474no—
530#102—474no—
531#102—474no—
532#102—474no—
533#102C22×D4714yes—
534#102C22×D4714yes—
535C22⋊C8—474no—
536C22⋊C8—474no—
537#97—474no—
538C4×C8—474no—
539C24—21no—
540C24—471no—
541C24—941no—
542C2×Q8—944no—
543C2×Q8—944no—
544C2×Q8—3762no—
545C2×Q8—3762no—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—472no—
550C2×D4—944no—
551C2×D4—944no—
552C2×D4—944no—
553C2×D4—944no—
554C2×D4—941no—
555C2×D4—942no—
556C2×D4—942no—
557C2×D4—3762no—
558C2×D4—3762no—
559C2×D4—3762no—
560C2×D4—3762no—
561C2×D4C23×D4712yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—82no—
567C22×C4—471no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4—472no—
571C22×C4—472no—
572C22×C4—944no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—941no—
576C22×C4—941no—
577C22×C4—941no—
578C22×C4—944no—
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—21no—
597C4⋊C4—474no—
598C4⋊C4—474no—
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—944no—
612C4⋊C4C23×D4712yes—
613C4⋊C4C23×D4712yes—
614C4⋊C4C23×D4712yes—
615C22⋊C4—24no—
616C22⋊C4—474no—
617C22⋊C4—474no—
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—42no—
629C23—42no—
630C23—42no—
631C23—472no—
632C23—942no—
633C23—942no—
634C23—942no—
635C23—942no—
636C23—1882no—
637C23—1882no—
638C23—1882no—
639C23C2×D4×D4711yescharacteristic
640Q8—3764no—
641Q8—3764no—
642D4—22no—
643D4—22no—
644D4—42no—
645D4—942no—
646D4—942no—
647D4—3764no—
648D4—3764no—
649D4—3764no—
650D4—3764no—
651D4—1882no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—84no—
661C2×C4—472no—
662C2×C4—472no—
663C2×C4—472no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—944no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—3764no—
674C2×C4—3764no—
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#1309407212yes—
683C2×C4C24×D4711yescharacteristic
684C8—22no—
685C8—22no—
686C8—942no—
687C8—942no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—84no—
692C22—942no—
693C22—942no—
694C22—942no—
695C22—3764no—
696C22—1882no—
697C22—1882no—
698C22—1882no—
699C22—1884no—
700C22#1568969612yes—
701C22#1568992712yes—
702C22#1568993012yes—
703C22C22×D4×D4711yescharacteristic
704C4—22no—
705C4—22no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—942no—
710C4—942no—
711C4—942no—
712C4—1882no—
713C4—1882no—
714C4—1882no—
715C4#1568969612yes—
716C4C2×#1309407111yescharacteristic
717C4C2×#1309407211yescharacteristic
718C2—82no—
719C2—3762no—
720C2—1882no—
721C2#2025464614yesdirect product factor
722C2C2×#1568969611yescharacteristic
723C2C2×#1568992711yescharacteristic
724C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#478C2
socleC23×C47C22×D4
prime radicalC2×#15689724C2
hypercenterC2×#478D47
hypocenterC47C2×#3241
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#15689753C2semidirect
3. #20254646C2direct (N × H)
4. C2×#15689531C2semidirect
5. C2×#15689523C2semidirect
6. C2×#15689486C2semidirect
7. C2×#15689468C2semidirect
8. C2×#15689440C2semidirect
9. C2×#15689449C2semidirect
10. C2×#15689446C2semidirect
11. C2×#15689438C2semidirect
12. C2×#15689420C2semidirect
13. C2×#15689414C2semidirect
14. C2×#15689403C2semidirect
15. C2×#15689183C2semidirect
16. C2×C47×#478C2semidirect
18. #15689753C22semidirect
40. #15689531C22semidirect
41. #15689523C22semidirect
42. #15689486C22semidirect
43. #15689468C22semidirect
44. #15689449C22semidirect
45. #15689446C22semidirect
46. #15689440C22semidirect
47. #15689438C22semidirect
48. #15689420C22semidirect
49. #15689414C22semidirect
50. #15689403C22semidirect
51. #15689183C22semidirect
71. C47×#478C22semidirect
368. C2×#478D47semidirect
373. C2×C47#3241semidirect
413. #478C2×D47semidirect
439. C47C2×#3241semidirect
721. C2#20254646direct (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×#156897242
#202546462
C2×#156895312
C2×#156895232
C2×#156894862
C2×#156894682
C2×#156894402
C2×#156894492
C2×#156894462
C2×#156894382
C2×#156894202
C2×#156894142
C2×#156894032
C2×#156891832
C2×C47×#4782
C2×#324147