Finite Group Databasebeta

← C2×#20254643 #27088469

Subgroups — C2×#20254643 #27088469

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×#15689751C211yesmaximal, characteristic, complemented
2C2×#15689728C211yesmaximal, characteristic
3#20254643C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689525C211yesmaximal, characteristic, complemented
6C2×#15689488C211yesmaximal, characteristic, complemented
7C2×#15689470C211yesmaximal, characteristic, complemented
8C2×#15689442C211yesmaximal, characteristic, complemented
9C2×#15689448C211yesmaximal, characteristic, complemented
10C2×#15689448C211yesmaximal, characteristic, complemented
11C2×#15689437C211yesmaximal, characteristic, complemented
12C2×#15689424C211yesmaximal, characteristic, complemented
13C2×#15689424C211yesmaximal, characteristic, complemented
14C2×#15689414C211yesmaximal, characteristic, complemented
15C2×#15689404C211yesmaximal, characteristic, complemented
16C2×C47×#433C211yesmaximal, characteristic, complemented
17#15689751—24no—
18#15689751C2218yescomplemented
19#15689728—24no—
20#15689728C2218yes—
21C2×#13094024C2211yescharacteristic
22C2×#13094024C2211yescharacteristic
23C2×#13094023—21no—
24C2×#13094021C2211yescharacteristic
25C2×#13094016C2211yescharacteristic
26C2×#13094016C2211yescharacteristic
27C2×#13094016C2211yescharacteristic
28C2×#13094015—21no—
29C2×#13094009—21no—
30C2×#13094009—21no—
31C2×#13094001—21no—
32C2×#13094001—21no—
33C2×#13093998C2211yescharacteristic
34C2×#13093998C2211yescharacteristic
35C2×#13093997—21no—
36C2×#13093997—21no—
37C2×C4×D188C2211yescharacteristic
38C2×C4×D188C2211yescharacteristic
39C2×#13093983C2211yescharacteristic
40C22×C4⋊Dic47C2211yescharacteristic
41#15689532C2218yescomplemented
42#15689525C2218yescomplemented
43#15689488C2218yescomplemented
44#15689470C2218yescomplemented
45#15689448C2218yescomplemented
46#15689448C2218yescomplemented
47#15689442C2218yescomplemented
48#15689437C2218yescomplemented
49#15689424C2218yescomplemented
50#15689424C2218yescomplemented
51#15689414C2218yescomplemented
52#15689404C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093958C2211yescharacteristic
56C2×#13093958C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093956C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C2×#117×C47C2211yescharacteristic
70C47×#433C2218yescomplemented
71C2×C4⋊C8×C47C2211yescharacteristic
72C2×C4⋊C8×C47C2211yescharacteristic
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×#97×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×D188—21no—
80C22×D188—21no—
81C22×D188C2311yescharacteristic
82C22×D188C2311yescharacteristic
83C22×C22⋊D47—21no—
84C22×C22⋊D47—21no—
85C23×Dic47—21no—
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88#13094024—22no—
89#13094024—22no—
90#13094024C2314yes—
91#13094024C2314yes—
92#13094023—28no—
93#13094021—22no—
94#13094021C2314yes—
95#13094016—22no—
96#13094016—22no—
97#13094016—22no—
98#13094016C2314yes—
99#13094016C2314yes—
100#13094016C2314yes—
101#13094015—28no—
102#13094009—28no—
103#13094009—28no—
104#13094001—28no—
105#13094001—28no—
106#13093998—22no—
107#13093998—22no—
108#13093998C2314yes—
109#13093998C2314yes—
110#13093997—28no—
111#13093997—28no—
112C4×D188—22no—
113C4×D188—22no—
114C4×D188C2314yes—
115C4×D188C2314yes—
116#13093983—22no—
117#13093983C2314yes—
118C2×C4⋊Dic47—22no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47C2314yes—
123C2×C4⋊Dic47C2311yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
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×C22⋊Dic47—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×C4×Dic47—21no—
141#13093958C2314yes—
142#13093958C2314yes—
143#13093958C2314yes—
144#13093958C2314yes—
145#13093956C2314yes—
146#13093956C2314yes—
147#13093956C2314yes—
148#13093956C2314yes—
149#13093946C2314yes—
150#13093946C2314yes—
151#13093946C2314yes—
152#13093946C2314yes—
153#13093946C2314yes—
154#13093946C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157C23×C4×C47C2311yescharacteristic
158C22×C8×C47C2311yescharacteristic
159C22×C8×C47C2311yescharacteristic
160C22×C8×C47C2311yescharacteristic
161C22×C8×C47C2311yescharacteristic
162#117×C47D414yes—
163#117×C47C2314yes—
164C2×C4⋊C4×C47D411yescharacteristic
165C2×C4⋊C4×C47D411yescharacteristic
166C2×C22⋊C4×C47D411yescharacteristic
167C2×C22⋊C4×C47D411yescharacteristic
168C2×C42×C47C2311yescharacteristic
169C2×C42×C47C2311yescharacteristic
170C4⋊C8×C47C2314yes—
171C4⋊C8×C47C2314yes—
172C22⋊C8×C47C2314yes—
173C22⋊C8×C47C2314yes—
174#97×C47C2314yes—
175C4×C8×C47C2314yes—
176C24×C47C2×D411yescharacteristic
177C23×D47—21no—
178C23×D47—21no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D412yes—
187C22×C4×C47C2412yes—
188C22×C4×C47C2411yescharacteristic
189C2×C22⋊D47—24no—
190C2×C22⋊D47—24no—
191C2×C22⋊D47—82no—
192C2×C22⋊D47—82no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—24no—
200C22×Dic47—82no—
201C2×D188—22no—
202C2×D188—22no—
203C2×D188—22no—
204C2×D188—22no—
205C2×D188—21no—
206C2×D188—21no—
207C2×D188—24no—
208C2×D188—24no—
209C2×D188—82no—
210C2×D188—82no—
211C2×D188C2412yes—
212C2×D188C2412yes—
213C2×C4×D47—24no—
214C2×C4×D47—24no—
215C2×C4×D47—82no—
216C2×C4×D47—82no—
217C2×Dic94—24no—
218C2×Dic94—24no—
219C2×Dic94—82no—
220C2×Dic94—82no—
221C2×C8×C47—22no—
222C2×C8×C47—22no—
223C2×C8×C47—22no—
224C2×C8×C47—22no—
225C2×C8×C47C2412yes—
226C2×C8×C47C2412yes—
227C2×C8×C47C2412yes—
228C2×C8×C47C2412yes—
229C4⋊C4×C47C2×D414yes—
230C4⋊C4×C47C2×D414yes—
231C22⋊C4×C47C2×D414yes—
232C22⋊C4×C47C2×D414yes—
233C42×C47C2×D412yes—
234C42×C47C2×D412yes—
235C42×C47C2412yes—
236C42×C47C2412yes—
237C22⋊Dic47—24no—
238(C2×D47)⋊C4—24no—
239(C2×D47)⋊C4—24no—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242C4⋊Dic47—24no—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47—24no—
246C4⋊Dic47—24no—
247C4⋊Dic47—21no—
248C4⋊Dic47—21no—
249C4⋊Dic47—21no—
250C4⋊Dic47—21no—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253C4⋊Dic47C2412yes—
254C4⋊Dic47C2412yes—
255C4⋊Dic47C2412yes—
256C4⋊Dic47C2412yes—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263C4×Dic47—24no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47C22×D412yes—
268C23×C47C22×D411yescharacteristic
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—42no—
272C22×D47—42no—
273C22×D47—42no—
274C22×D47—42no—
275C22×D47—42no—
276C22×D47—42no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—24no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47C22×D412yes—
286C2×C4×C47C22×D412yes—
287C2×C4×C47C22×D412yes—
288C2×C4×C47C22×D412yes—
289C2×C4×C47C22×D412yes—
290C2×C4×C47C22×D411yescharacteristic
291C2×C4×C472−1+412yes—
292C2×C4×C472−1+412yes—
293C2×C4×C47C2511yescharacteristic
294C22⋊D47—84no—
295C22⋊D47—84no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—84no—
309D188—22no—
310D188—22no—
311D188—22no—
312D188—22no—
313D188—42no—
314D188—42no—
315D188—84no—
316D188—84no—
317C4×D47—84no—
318C4×D47—84no—
319Dic94—84no—
320Dic94—84no—
321C8×C47—22no—
322C8×C47—22no—
323C8×C47—22no—
324C8×C47—22no—
325C2×#3241—471nomaximal, Sylow
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—44no—
330C22×C47#53612yes—
331C22×C47#57612yes—
332C22×C47#57712yes—
333C22×C47C23×D411yescharacteristic
334C2×D47—42no—
335C2×D47—42no—
336C2×D47—42no—
337C2×D47—42no—
338C2×D47—42no—
339C2×D47—42no—
340C2×D47—84no—
341C2×D47—84no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—22no—
346C4×C47—22no—
347C4×C47#53612yes—
348C4×C47C2×2−1+411yescharacteristic
349C4×C47C2×2−1+411yescharacteristic
350Dic47—42no—
351Dic47—42no—
352Dic47—42no—
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×#478—471no—
369C2×#476—471no—
370C2×#474—471no—
371C2×#433D4711yescharacteristic, complemented
372C2×C47—42no—
373C2×C47#324114yescomplemented
374C2×C47C2×#53611yescharacteristic
375C2×C47C2×#57611yescharacteristic
376C2×C47C2×#57711yescharacteristic
377D47—82no—
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—471no—
390C2×#125—941no—
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×#117C2×D4711yescharacteristic
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#478—478no—
414#476—478no—
415#474—478no—
416#433C2×D4718yescomplemented
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⋊C8C2×D4711yescharacteristic
426C2×C4⋊C8C2×D4711yescharacteristic
427C2×#102—471no—
428C2×#102—471no—
429C2×#102—471no—
430C2×#102—471no—
431C2×#102—471no—
432C2×#102—471no—
433C2×#102—471no—
434C2×#102—471no—
435C2×C22⋊C8C2×D4711yescharacteristic
436C2×C22⋊C8C2×D4711yescharacteristic
437C2×#97C2×D4711yescharacteristic
438C2×C4×C8C2×D4711yescharacteristic
439C47C2×#324111yescharacteristic, complemented, Sylow
440C22×Q8—941no—
441C22×Q8—941no—
442C22×D4—471no—
443C22×D4—471no—
444C22×D4—941no—
445C22×D4—941no—
446C22×D4—941no—
447C22×D4—941no—
448C23×C4—941no—
449C23×C4—941no—
450C23×C4—941no—
451C23×C4C22×D4711yescharacteristic
452C22×C8C22×D4711yescharacteristic
453C22×C8C22×D4711yescharacteristic
454C22×C8C22×D4711yescharacteristic
455C22×C8C22×D4711yescharacteristic
456C4⋊Q8—474no—
457C4⋊Q8—474no—
458C4⋊Q8—948no—
459C4⋊Q8—942no—
460C4⋊Q8—942no—
461#127—474no—
462#127—942no—
463#125—474no—
464#125—474no—
465#125—474no—
466#125—948no—
467#125—942no—
468#125—942no—
469#125—942no—
470#123—948no—
471#123—948no—
472C22⋊Q8—948no—
473C22⋊Q8—948no—
474#121—474no—
475#121—474no—
476#121—942no—
477#121—942no—
478#121—948no—
479#121—948no—
480C4×D4—474no—
481C4×D4—474no—
482C4×D4—942no—
483C4×D4—942no—
484#117—474no—
485#117—942no—
486#117D18814yes—
487#117C22×D4714yes—
488C2×C4⋊C4—471no—
489C2×C4⋊C4—471no—
490C2×C4⋊C4—474no—
491C2×C4⋊C4—471no—
492C2×C4⋊C4—471no—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—941no—
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⋊C4—941no—
505C2×C4⋊C4D18811yescharacteristic
506C2×C4⋊C4D18811yescharacteristic
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4D18811yescharacteristic
513C2×C22⋊C4D18811yescharacteristic
514C2×C42—941no—
515C2×C42C22×D4711yescharacteristic
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⋊C8C22×D4714yes—
526C4⋊C8C22×D4714yes—
527#102—474no—
528#102—474no—
529#102—474no—
530#102—474no—
531#102—474no—
532#102—474no—
533#102—474no—
534#102—474no—
535C22⋊C8C22×D4714yes—
536C22⋊C8C22×D4714yes—
537#97C22×D4714yes—
538C4×C8C22×D4714yes—
539C24—941no—
540C24—941no—
541C24C2×D18811yescharacteristic
542C2×Q8—944no—
543C2×Q8—944no—
544C2×Q8—3762no—
545C2×Q8—3762no—
546C2×D4—472no—
547C2×D4—472no—
548C2×D4—944no—
549C2×D4—944no—
550C2×D4—944no—
551C2×D4—944no—
552C2×D4—941no—
553C2×D4—941no—
554C2×D4—942no—
555C2×D4—942no—
556C2×D4—942no—
557C2×D4—942no—
558C2×D4—3762no—
559C2×D4—3762no—
560C2×D4—3762no—
561C2×D4—3762no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—944no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—941no—
569C22×C4—941no—
570C22×C4—941no—
571C22×C4—944no—
572C22×C4—944no—
573C22×C4—3762no—
574C22×C4—3762no—
575C22×C4—3762no—
576C22×C4C2×D18812yes—
577C22×C4C2×D18811yescharacteristic
578C22×C4C2×D18811yescharacteristic
579C22×C4C2×D18811yescharacteristic
580C22×C4C2×D18811yescharacteristic
581C22×C4C2×D18811yescharacteristic
582C22×C4C23×D4712yes—
583C22×C4C23×D4711yescharacteristic
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8C23×D4712yes—
589C2×C8C23×D4712yes—
590C2×C8C23×D4712yes—
591C2×C8C23×D4712yes—
592C4⋊C4—472no—
593C4⋊C4—472no—
594C4⋊C4—472no—
595C4⋊C4—472no—
596C4⋊C4—472no—
597C4⋊C4—472no—
598C4⋊C4—944no—
599C4⋊C4—944no—
600C4⋊C4—944no—
601C4⋊C4—944no—
602C4⋊C4—944no—
603C4⋊C4—944no—
604C4⋊C4—944no—
605C4⋊C4—941no—
606C4⋊C4—941no—
607C4⋊C4—941no—
608C4⋊C4—941no—
609C4⋊C4—941no—
610C4⋊C4—941no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4C2×D18814yes—
614C4⋊C4C2×D18814yes—
615C22⋊C4—944no—
616C22⋊C4—944no—
617C22⋊C4—944no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4C2×D18814yes—
621C22⋊C4C2×D18814yes—
622C42—944no—
623C42C2×D18812yes—
624C42C2×D18812yes—
625C42C23×D4712yes—
626C42C23×D4712yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—942no—
631C23—942no—
632C23—1882no—
633C23—1882no—
634C23—1882no—
635C23—1882no—
636C23—1882no—
637C23—1882no—
638C23C22×D18812yes—
639C23C22×D18811yescharacteristic
640Q8—3764no—
641Q8—3764no—
642D4—942no—
643D4—942no—
644D4—942no—
645D4—942no—
646D4—3764no—
647D4—3764no—
648D4—3764no—
649D4—3764no—
650D4—1882no—
651D4—1882no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—3764no—
667C2×C4—3764no—
668C2×C4—3764no—
669C2×C4—1882no—
670C2×C4—1882no—
671C2×C4—1882no—
672C2×C4—1882no—
673C2×C4—1882no—
674C2×C4—1882no—
675C2×C4C22×D18812yes—
676C2×C4C22×D18812yes—
677C2×C4C22×D18812yes—
678C2×C4C22×D18812yes—
679C2×C4C22×D18812yes—
680C2×C4C22×D18811yescharacteristic
681C2×C4#1309407112yes—
682C2×C4#1309407112yes—
683C2×C4C24×D4711yescharacteristic
684C8—22no—
685C8—22no—
686C8—22no—
687C8—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—3764no—
693C22—3764no—
694C22—1882no—
695C22—1882no—
696C22—1882no—
697C22—1882no—
698C22—1882no—
699C22—1882no—
700C22#1568969912yes—
701C22#1568992812yes—
702C22#1568993512yes—
703C22C23×D18811yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—1882no—
710C4—1882no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C4—1882no—
715C4#1568969912yes—
716C4C2×#1309407111yescharacteristic
717C4C2×#1309407111yescharacteristic
718C2—42no—
719C2—3762no—
720C2—3762no—
721C2#2025464314yesdirect product factor
722C2C2×#1568969911yescharacteristic
723C2C2×#1568992811yescharacteristic
724C2C2×#1568993511yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#433C2
socleC23×C47C22×D4
prime radicalC2×#15689728C2
hypercenterC2×#433D47
hypocenterC47C2×#3241
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#15689751C2semidirect
3. #20254643C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689525C2semidirect
6. C2×#15689488C2semidirect
7. C2×#15689470C2semidirect
8. C2×#15689442C2semidirect
9. C2×#15689448C2semidirect
10. C2×#15689448C2semidirect
11. C2×#15689437C2semidirect
12. C2×#15689424C2semidirect
13. C2×#15689424C2semidirect
14. C2×#15689414C2semidirect
15. C2×#15689404C2semidirect
16. C2×C47×#433C2semidirect
18. #15689751C22semidirect
41. #15689532C22semidirect
42. #15689525C22semidirect
43. #15689488C22semidirect
44. #15689470C22semidirect
45. #15689448C22semidirect
46. #15689448C22semidirect
47. #15689442C22semidirect
48. #15689437C22semidirect
49. #15689424C22semidirect
50. #15689424C22semidirect
51. #15689414C22semidirect
52. #15689404C22semidirect
70. C47×#433C22semidirect
371. C2×#433D47semidirect
373. C2×C47#3241semidirect
416. #433C2×D47semidirect
439. C47C2×#3241semidirect
721. C2#20254643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897512
C2×#156897282
#202546432
C2×#156895322
C2×#156895252
C2×#156894882
C2×#156894702
C2×#156894422
C2×#156894482
C2×#156894372
C2×#156894242
C2×#156894142
C2×#156894042
C2×C47×#4332
C2×#324147