Finite Group Databasebeta

← C2×#20254840 #27089233

Subgroups — C2×#20254840 #27089233

Order 12032.

1754 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689734C211yesmaximal, characteristic
2C2×#15689731C211yesmaximal, characteristic
3#20254840C2116yesmaximal, direct product factor
4C2×#15689432C211yesmaximal, characteristic, complemented
5C2×#15689431C211yesmaximal, characteristic, complemented
6C2×#15689430C211yesmaximal, characteristic, complemented
7C2×#15689428C211yesmaximal, characteristic, complemented
8C2×#15689380C211yesmaximal, characteristic
9C2×#15689378C211yesmaximal, characteristic
10C2×#15689363C211yesmaximal, characteristic
11C2×#15689361C211yesmaximal, characteristic
12C2×#15689331C211yesmaximal, characteristic, complemented
13C2×#15689331C211yesmaximal, characteristic, complemented
14C2×#15689330C211yesmaximal, characteristic, complemented
15C2×#15689148C211yesmaximal, characteristic
16C2×C47×#462C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689734—24no—
22#15689734C2218yes—
23#15689731—24no—
24#15689731C2218yes—
25C2×#13094022C2211yescharacteristic
26C2×#13094019—21no—
27C2×#13094019—21no—
28C2×#13094019—21no—
29C2×#13094018—21no—
30C2×#13094016—21no—
31C2×#13094016C2211yescharacteristic
32C2×#13094015C2211yescharacteristic
33C2×#13094014—21no—
34C2×#13094014—21no—
35C2×#13094014—21no—
36C2×#13094004C2211yescharacteristic
37C2×#13094000C2211yescharacteristic
38C2×#13094000C2211yescharacteristic
39C2×#13094000C2211yescharacteristic
40C2×Q8×Dic47C2211yescharacteristic
41C2×Q8×Dic47C2211yescharacteristic
42C2×C4×Dic94C2211yescharacteristic
43C2×#13093981C2211yescharacteristic
44#15689432C2218yescomplemented
45#15689431C2218yescomplemented
46#15689430C2218yescomplemented
47#15689428C2218yescomplemented
48#15689380C2218yes—
49#15689378C2218yes—
50#15689363C2218yes—
51#15689361C2218yes—
52#15689331C2218yescomplemented
53#15689331C2218yescomplemented
54#15689330C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59#15689148C2218yes—
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093948C2211yescharacteristic
67C2×#13093948C2211yescharacteristic
68C2×#13093948C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C2×C4⋊Q8×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic
73C47×#462C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94C2311yescharacteristic
78C22×C4×D47C2311yescharacteristic
79C2×#10625337—42no—
80C2×#10625337—42no—
81C2×#10625337C2314yes—
82C2×#10625337C2314yes—
83C2×#10625324—42no—
84C2×#10625324C2314yes—
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2311yescharacteristic
87C2×C8×D47—42no—
88C2×C8×D47C2314yes—
89#13094022—22no—
90#13094022C2314yes—
91#13094019—28no—
92#13094019—28no—
93#13094019—28no—
94#13094018—28no—
95#13094016—22no—
96#13094016—28no—
97#13094016C2314yes—
98#13094015—22no—
99#13094015C2314yes—
100#13094014—28no—
101#13094014—28no—
102#13094014—28no—
103#13094004—22no—
104#13094004C2314yes—
105#13094000—22no—
106#13094000—22no—
107#13094000—22no—
108#13094000C2314yes—
109#13094000C2314yes—
110#13094000C2314yes—
111Q8×Dic47—22no—
112Q8×Dic47—22no—
113Q8×Dic47C2314yes—
114Q8×Dic47C2314yes—
115C4×Dic94—22no—
116C4×Dic94C2314yes—
117#13093981D414yes—
118#13093981C2314yes—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47C2311yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4D411yescharacteristic
136C2×Dic47⋊C4D411yescharacteristic
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4D411yescharacteristic
142C2×(C2×D47)⋊C4D411yescharacteristic
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093958C2314yes—
148#13093957C2314yes—
149#13093956C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152Dic47⋊C8C2314yes—
153Dic47⋊C8C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093948C2314yes—
157#13093948C2314yes—
158#13093948C2314yes—
159#13093948C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×Q8×C47C2311yescharacteristic
162C22×Q8×C47C2311yescharacteristic
163C2×Q16×C47—42no—
164C2×Q16×C47—42no—
165C2×Q16×C47C2314yes—
166C2×Q16×C47C2314yes—
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C4⋊Q8×C47—22no—
170C4⋊Q8×C47C2314yes—
171C4×Q8×C47—22no—
172C4×Q8×C47C2314yes—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C42×C47—21no—
178C2×C42×C47C2311yescharacteristic
179C4⋊C8×C47C2314yes—
180#103×C47C2314yes—
181#103×C47C2314yes—
182C23×D47C2×D411yescharacteristic
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47C2412yes—
193C2×Q8×C47C2412yes—
194C2×Q8×C47C2412yes—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2411yescharacteristic
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209C2×C4×D47—22no—
210C2×C4×D47—22no—
211C2×C4×D47C2×D412yes—
212C2×C4×D47C2412yes—
213C2×Dic94—22no—
214C2×Dic94—22no—
215C2×Dic94—21no—
216C2×Dic94C2412yes—
217Q16×C47—44no—
218Q16×C47—44no—
219C2×C8×C47—22no—
220C2×C8×C47—22no—
221C2×C8×C47C2412yes—
222C2×C8×C47C2412yes—
223C4⋊C4×C47—24no—
224C4⋊C4×C47—24no—
225C4⋊C4×C47—24no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47C2412yes—
228C42×C47—24no—
229C42×C47C2×D412yes—
230C42×C47C2412yes—
231#10625337—44no—
232#10625337—44no—
233(C2×D47)⋊C4—24no—
234(C2×D47)⋊C4—24no—
235(C2×D47)⋊C4—24no—
236(C2×D47)⋊C4—24no—
237(C2×D47)⋊C4C2×D414yes—
238(C2×D47)⋊C4C2×D414yes—
239C4⋊Dic47—21no—
240C4⋊Dic47—21no—
241C4⋊Dic47—21no—
242C4⋊Dic47—24no—
243C4⋊Dic47—24no—
244C4⋊Dic47—24no—
245C4⋊Dic47—24no—
246C4⋊Dic47C2412yes—
247C4⋊Dic47C2412yes—
248C4⋊Dic47C2412yes—
249Dic47⋊C4—24no—
250Dic47⋊C4—24no—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4C2×D414yes—
259Dic47⋊C4C2×D414yes—
260C4×Dic47—24no—
261C4×Dic47—24no—
262C4×Dic47—24no—
263C4×Dic47C2×D412yes—
264C4×Dic47C2412yes—
265C2×C47⋊C8—22no—
266C2×C47⋊C8—22no—
267C2×C47⋊C8C2412yes—
268C2×C47⋊C8C2412yes—
269#10625324—44no—
270C8×D47—44no—
271C23×C47C22×D411yescharacteristic
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47C22×D412yes—
276Q8×C47—22no—
277Q8×C47—22no—
278Q8×C47—22no—
279Q8×C47—22no—
280Q8×C47—22no—
281Q8×C47—22no—
282Q8×C47—42no—
283Q8×C47—42no—
284Q8×C47—42no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47C22×D412yes—
296C2×C4×C47C22×D412yes—
297C2×C4×C47C22×D411yescharacteristic
298C2×C4×C47H(5,𝔽2)12yes—
299C2×C4×C472−1+412yes—
300C2×C4×C47C2511yescharacteristic
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47C22×D412yes—
313C2×Dic47C22×D412yes—
314C2×Dic47C22×D412yes—
315C4×D47—24no—
316C4×D47—22no—
317C4×D47—22no—
318Dic94—22no—
319Dic94—22no—
320Dic94—42no—
321C8×C47—22no—
322C8×C47—22no—
323C47⋊C8—22no—
324C47⋊C8—22no—
325C2×#3261—471nomaximal, Sylow
326C22×C47#53712yes—
327C22×C47#57812yes—
328C22×C47#57812yes—
329C22×C47C23×D411yescharacteristic
330C2×D47—22no—
331C2×D47—22no—
332C2×D47—22no—
333C2×D47—44no—
334C4×C47—22no—
335C4×C47—22no—
336C4×C47—42no—
337C4×C47—42no—
338C4×C47—42no—
339C4×C47—42no—
340C4×C47#53712yes—
341C4×C47C2×H(5,𝔽2)11yescharacteristic
342C4×C47C2×2−1+411yescharacteristic
343Dic47—22no—
344Dic47—22no—
345Dic47—22no—
346Dic47—42no—
347Dic47—42no—
348Dic47—42no—
349Dic47—42no—
350C2×#541—471no—
351C2×#541—471no—
352#3261—4716no—
353C2×#479—471no—
354C2×#479—471no—
355C2×#479—471no—
356C2×#479—471no—
357C2×#470—471no—
358C2×#470—471no—
359C2×#467—471no—
360C2×#467—471no—
361C2×#462—471no—
362C2×#462—471no—
363C2×#462—471no—
364C2×#462D4711yescharacteristic, complemented
365C2×#424—471no—
366C2×C47#326114yescomplemented
367C2×C47C2×#53711yescharacteristic
368C2×C47C2×#57811yescharacteristic
369C2×C47C2×#57811yescharacteristic
370D47—42no—
371C22×Q16—471no—
372C22×Q16—471no—
373C22×Q16C2×D4711yescharacteristic
374C22×Q16C2×D4711yescharacteristic
375C22×M16—471no—
376C23×C8—471no—
377#541—478no—
378#541—478no—
379#541—944no—
380#541—944no—
381C2×C4⋊Q8—471no—
382C2×C4⋊Q8C2×D4711yescharacteristic
383C2×#126—941no—
384C2×#126—941no—
385C2×#126—941no—
386C2×#126—941no—
387C2×#125—471no—
388C2×#125—471no—
389C2×#125—941no—
390C2×#125—941no—
391C2×#125—941no—
392C2×#125—941no—
393C2×C22⋊Q8—471no—
394C2×C22⋊Q8—471no—
395C2×C22⋊Q8—471no—
396C2×C22⋊Q8—471no—
397C2×C4×Q8—471no—
398C2×C4×Q8—471no—
399C2×C4×Q8—471no—
400C2×C4×Q8C2×D4711yescharacteristic
401C2×#117—471no—
402#479—478no—
403#479—478no—
404#479—478no—
405#479—478no—
406#470—478no—
407#470—478no—
408#467—478no—
409#467—478no—
410#462—478no—
411#462—478no—
412#462—478no—
413#462C2×D4718yescomplemented
414C2×#107—471no—
415C2×#107—471no—
416C2×#106—471no—
417C2×#106—471no—
418#424—478no—
419C2×C4⋊C8—471no—
420C2×C4⋊C8—471no—
421C2×C4⋊C8—471no—
422C2×C4⋊C8C2×D4711yescharacteristic
423C2×#103—471no—
424C2×#103—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103C2×D4711yescharacteristic
430C2×#103C2×D4711yescharacteristic
431C47C2×#326111yescharacteristic, complemented, Sylow
432C22×Q8—471no—
433C22×Q8C22×D4711yescharacteristic
434C22×Q8C22×D4711yescharacteristic
435C22×Q8C22×D4711yescharacteristic
436C23×C4—471no—
437C2×Q16—42no—
438C2×Q16—42no—
439C2×Q16—474no—
440C2×Q16—474no—
441C2×Q16—1882no—
442C2×Q16—1882no—
443C2×Q16C22×D4714yes—
444C2×Q16C22×D4714yes—
445C2×M16—474no—
446C2×M16—1882no—
447C22×C8—471no—
448C22×C8—471no—
449C22×C8—474no—
450C22×C8—1882no—
451C22×C8C22×D4711yescharacteristic
452C22×C8C22×D4711yescharacteristic
453C4⋊Q8—22no—
454C4⋊Q8—474no—
455C4⋊Q8—942no—
456C4⋊Q8C22×D4714yes—
457#126—948no—
458#126—948no—
459#126—948no—
460#126—948no—
461#125—474no—
462#125—474no—
463#125—948no—
464#125—942no—
465#125—948no—
466#125—948no—
467#125—948no—
468#125—942no—
469C22⋊Q8—474no—
470C22⋊Q8—474no—
471C22⋊Q8—474no—
472C22⋊Q8—474no—
473C22⋊Q8—942no—
474C22⋊Q8—942no—
475C22⋊Q8—942no—
476C22⋊Q8—942no—
477C4×Q8—22no—
478C4×Q8—474no—
479C4×Q8—474no—
480C4×Q8—474no—
481C4×Q8—942no—
482C4×Q8—942no—
483C4×Q8—942no—
484C4×Q8C22×D4714yes—
485#117—474no—
486#117—474no—
487C2×C4⋊C4—21no—
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—941no—
496C2×C4⋊C4—941no—
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⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4C22×D4711yescharacteristic
509C2×C22⋊C4—471no—
510C2×C22⋊C4—471no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C42—21no—
516C2×C42—471no—
517C2×C42—941no—
518C2×C42—941no—
519C2×C42—941no—
520C2×C42C22×D4711yescharacteristic
521#107—474no—
522#107—474no—
523#106—474no—
524#106—474no—
525C4⋊C8—474no—
526C4⋊C8—474no—
527C4⋊C8—474no—
528C4⋊C8C22×D4714yes—
529#103—474no—
530#103—474no—
531#103—474no—
532#103—474no—
533#103—474no—
534#103—474no—
535#103C22×D4714yes—
536#103C22×D4714yes—
537C24—471no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—472no—
548C2×Q8—941no—
549C2×Q8—942no—
550C2×Q8—942no—
551C2×Q8C23×D4712yes—
552C2×Q8C23×D4712yes—
553C2×Q8C23×D4712yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—471no—
559C22×C4—471no—
560C22×C4—471no—
561C22×C4—472no—
562C22×C4—472no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—941no—
569C22×C4D4×D4711yescharacteristic
570C22×C4D4×D4711yescharacteristic
571C22×C4C23×D4711yescharacteristic
572Q16—44no—
573Q16—44no—
574Q16—1884no—
575Q16—1884no—
576M16—1884no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—472no—
580C2×C8—472no—
581C2×C8—942no—
582C2×C8—942no—
583C2×C8—1884no—
584C2×C8C23×D4712yes—
585C2×C8C23×D4712yes—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—474no—
591C4⋊C4—474no—
592C4⋊C4—472no—
593C4⋊C4—472no—
594C4⋊C4—472no—
595C4⋊C4—944no—
596C4⋊C4—944no—
597C4⋊C4—944no—
598C4⋊C4—944no—
599C4⋊C4—944no—
600C4⋊C4—944no—
601C4⋊C4—944no—
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⋊C4C23×D4712yes—
612C22⋊C4—474no—
613C22⋊C4—474no—
614C22⋊C4—944no—
615C22⋊C4—944no—
616C22⋊C4—944no—
617C22⋊C4—944no—
618C42—24no—
619C42—472no—
620C42—472no—
621C42—944no—
622C42—944no—
623C42—944no—
624C42D4×D4712yes—
625C42C23×D4712yes—
626C23—472no—
627C23—942no—
628C23—942no—
629C23—942no—
630C23C2×D4×D4711yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—942no—
641Q8—942no—
642Q8—1882no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—472no—
654C2×C4—472no—
655C2×C4—472no—
656C2×C4—942no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—944no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—1882no—
667C2×C4—1882no—
668C2×C4—1882no—
669C2×C4—1882no—
670C2×C4C2×D4×D4712yes—
671C2×C4C2×D4×D4712yes—
672C2×C4C2×D4×D4711yescharacteristic
673C2×C4#1309406912yes—
674C2×C4#1309407112yes—
675C2×C4C24×D4711yescharacteristic
676C8—22no—
677C8—22no—
678C8—942no—
679C8—942no—
680C22—942no—
681C22—942no—
682C22—942no—
683C22—1884no—
684C22#1568970212yes—
685C22#1568993612yes—
686C22#1568993912yes—
687C22C22×D4×D4711yescharacteristic
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—942no—
695C4—942no—
696C4—942no—
697C4—1882no—
698C4—1882no—
699C4—1882no—
700C4—1882no—
701C4#1568970212yes—
702C4C2×#1309406911yescharacteristic
703C4C2×#1309407111yescharacteristic
704C2—1882no—
705C2#2025484014yesdirect product factor
706C2C2×#1568970211yescharacteristic
707C2C2×#1568993611yescharacteristic
708C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#462C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenterC2×#462D47
hypocenterC47C2×#3261
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #20254840C2direct (N × H)
4. C2×#15689432C2semidirect
5. C2×#15689431C2semidirect
6. C2×#15689430C2semidirect
7. C2×#15689428C2semidirect
12. C2×#15689331C2semidirect
13. C2×#15689331C2semidirect
14. C2×#15689330C2semidirect
16. C2×C47×#462C2semidirect
44. #15689432C22semidirect
45. #15689431C22semidirect
46. #15689430C22semidirect
47. #15689428C22semidirect
52. #15689331C22semidirect
53. #15689331C22semidirect
54. #15689330C22semidirect
73. C47×#462C22semidirect
364. C2×#462D47semidirect
366. C2×C47#3261semidirect
413. #462C2×D47semidirect
431. C47C2×#3261semidirect
705. C2#20254840direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897342
C2×#156897312
#202548402
C2×#156894322
C2×#156894312
C2×#156894302
C2×#156894282
C2×#156893802
C2×#156893782
C2×#156893632
C2×#156893612
C2×#156893312
C2×#156893302
C2×#156891482
C2×C47×#4622
C2×#326147