Finite Group Databasebeta

← C2×#20255848 #27094830

Subgroups — C2×#20255848 #27094830

Order 12032.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689833C211yesmaximal, characteristic
2C2×#15689814C211yesmaximal, characteristic
3#20255848C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689457C211yesmaximal, characteristic, complemented
6C2×#15689463C211yesmaximal, characteristic, complemented
7C2×#15689452C211yesmaximal, characteristic, complemented
8C2×#15689452C211yesmaximal, characteristic, complemented
9C2×#15689430C211yesmaximal, characteristic, complemented
10C2×#15689408C211yesmaximal, characteristic, complemented
11C2×#15689378C211yesmaximal, characteristic, complemented
12C2×#15689361C211yesmaximal, characteristic, complemented
13C2×#15689196C211yesmaximal, characteristic
14C2×#15689162C211yesmaximal, characteristic, complemented
15C2×#106×D47C211yesmaximal, characteristic, complemented
16C2×C47×#441C211yesmaximal, characteristic, complemented
17C22×#10625324C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19#15689833—24no—
20#15689833C2218yes—
21#15689814—24no—
22#15689814C2218yes—
23C2×#13094024C2211yescharacteristic
24C2×#13094018—21no—
25C2×#13094016—21no—
26C2×#13094016C2211yescharacteristic
27C2×#13094014—21no—
28C2×#13094009—21no—
29C2×#13094002—21no—
30C2×#13094002—21no—
31C2×#13094000C2211yescharacteristic
32C2×#13094000C2211yescharacteristic
33C2×#13094000C2211yescharacteristic
34C2×#13094000C2211yescharacteristic
35C2×C4×D188—21no—
36C2×C4×D188C2211yescharacteristic
37C2×#13093982C2211yescharacteristic
38C2×#13093981—21no—
39C2×C4⋊C4×D47C2211yescharacteristic
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689532C2218yescomplemented
43#15689463C2218yescomplemented
44#15689457C2218yescomplemented
45#15689452C2218yescomplemented
46#15689452C2218yescomplemented
47#15689430C2218yescomplemented
48#15689408C2218yescomplemented
49#15689378C2218yescomplemented
50#15689361C2218yescomplemented
51#15689196C2218yes—
52#15689162C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59C2×#13093955C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61#106×D47C2218yescomplemented
62C2×C4⋊(C47⋊C8)C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093948C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic
72C47×#441C2218yescomplemented
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×D188D411yescharacteristic
79C22×C4×D47—21no—
80C22×C4×D47—21no—
81C22×C4×D47—21no—
82C22×C4×D47C2311yescharacteristic
83C22×C4×D47C2311yescharacteristic
84C2×#10625324—24no—
85C2×#10625324C2314yes—
86C22×C47⋊C8C2311yescharacteristic
87C22×C47⋊C8C2311yescharacteristic
88C2×C8×D47—24no—
89C2×C8×D47C2314yes—
90#13094024—22no—
91#13094024C2314yes—
92#13094018—28no—
93#13094016—22no—
94#13094016—28no—
95#13094016C2314yes—
96#13094014—28no—
97#13094009—28no—
98#13094002—28no—
99#13094002—28no—
100#13094000—22no—
101#13094000—22no—
102#13094000—22no—
103#13094000—22no—
104#13094000C2314yes—
105#13094000C2314yes—
106#13094000C2314yes—
107#13094000C2314yes—
108C4×D188—28no—
109C4×D188D414yes—
110C4×D188C2314yes—
111#13093982—22no—
112#13093982C2314yes—
113#13093981—28no—
114C2×C4⋊Dic47—21no—
115C2×C4⋊Dic47D411yescharacteristic
116C2×C4⋊Dic47C2311yescharacteristic
117C2×C4⋊Dic47C2311yescharacteristic
118C2×C4⋊Dic47C2311yescharacteristic
119C2×C4⋊Dic47C2311yescharacteristic
120C2×Dic47⋊C4—21no—
121C2×Dic47⋊C4—21no—
122C2×Dic47⋊C4—21no—
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C4⋊C4×D47—22no—
130C4⋊C4×D47—22no—
131C4⋊C4×D47—22no—
132C4⋊C4×D47C2314yes—
133C4⋊C4×D47C2314yes—
134C4⋊C4×D47C2314yes—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4D411yescharacteristic
141C2×(C2×D47)⋊C4D411yescharacteristic
142C2×C4×Dic47—21no—
143#13093958C2314yes—
144#13093958C2314yes—
145#13093957C2314yes—
146#13093956C2314yes—
147#13093956C2314yes—
148#13093955C2314yes—
149#13093955C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152#13093948C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156(C2×D47)⋊C8C2314yes—
157(C2×D47)⋊C8C2314yes—
158C22×Q8×C47C2311yescharacteristic
159C22×Q8×C47C2311yescharacteristic
160C2×Q16×C47—24no—
161C2×Q16×C47C2314yes—
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164C4×Q8×C47—22no—
165C4×Q8×C47—22no—
166C4×Q8×C47C2314yes—
167C4×Q8×C47C2314yes—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C42×C47—21no—
173C2×C42×C47—21no—
174C2×C42×C47C2311yescharacteristic
175#106×C47C2314yes—
176#103×C47C2314yes—
177#103×C47C2314yes—
178#97×C47C2314yes—
179C23×D47C2×D411yescharacteristic
180C23×D47C2×D411yescharacteristic
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47—22no—
185C2×Q8×C47—22no—
186C2×Q8×C47—22no—
187C2×Q8×C47C2412yes—
188C2×Q8×C47C2412yes—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47C2×D411yescharacteristic
201C22×Dic47C2×D411yescharacteristic
202C2×D188—24no—
203C2×D188C2×D414yes—
204C2×C4×D47—22no—
205C2×C4×D47—22no—
206C2×C4×D47—22no—
207C2×C4×D47—22no—
208C2×C4×D47—24no—
209C2×C4×D47—24no—
210C2×C4×D47—24no—
211C2×C4×D47—44no—
212C2×C4×D47—82no—
213C2×C4×D47—82no—
214C2×C4×D47C2×D412yes—
215C2×C4×D47C2×D412yes—
216C2×C4×D47C2412yes—
217C2×C4×D47C2412yes—
218C2×Dic94—24no—
219C2×Dic94—82no—
220Q16×C47—28no—
221C2×C8×C47—22no—
222C2×C8×C47#4114yes—
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×C47—24no—
232C42×C47—24no—
233C42×C47C2×D412yes—
234C42×C47C2412yes—
235(C2×D47)⋊C4—24no—
236(C2×D47)⋊C4—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—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47—24no—
246C4⋊Dic47—21no—
247C4⋊Dic47C2×D414yes—
248C4⋊Dic47C2412yes—
249C4⋊Dic47C2412yes—
250C4⋊Dic47C2412yes—
251C4⋊Dic47C2412yes—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261C4×Dic47—24no—
262C2×C47⋊C8—22no—
263C2×C47⋊C8—22no—
264C2×C47⋊C8C2412yes—
265C2×C47⋊C8C2412yes—
266#10625324—28no—
267C8×D47—28no—
268C23×C47C22×D411yescharacteristic
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47#13714yes—
275C22×D47C22×D412yes—
276C22×D47C22×D412yes—
277Q8×C47—22no—
278Q8×C47—22no—
279Q8×C47—22no—
280Q8×C47—22no—
281Q8×C47—42no—
282Q8×C47—42no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
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×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47C22×D412yes—
294C2×C4×C47C22×D412yes—
295C2×C4×C47C22×D411yescharacteristic
296C2×C4×C47C2×#4112yes—
297C2×C4×C472−1+412yes—
298C2×C4×C47C2511yescharacteristic
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47C22×D412yes—
310C2×Dic47C22×D412yes—
311D188—28no—
312C4×D47—24no—
313C4×D47—24no—
314C4×D47—22no—
315C4×D47—22no—
316C4×D47—22no—
317C4×D47—22no—
318C4×D47—48no—
319C4×D47—84no—
320C4×D47—84no—
321Dic94—84no—
322C8×C47—22no—
323C8×C47C2×#4114yes—
324C47⋊C8—22no—
325C47⋊C8—22no—
326C2×#3344—471nomaximal, Sylow
327C22×C47#54712yes—
328C22×C47C2×#13712yes—
329C22×C47#57712yes—
330C22×C47C23×D411yescharacteristic
331C2×D47—28no—
332C2×D47—22no—
333C2×D47—22no—
334C2×D47—22no—
335C2×D47—22no—
336C2×D47—22no—
337C2×D47—44no—
338C2×D47C2×#13714yes—
339C4×C47—22no—
340C4×C47—22no—
341C4×C47—42no—
342C4×C47—42no—
343C4×C47—42no—
344C4×C47—42no—
345C4×C47#54712yes—
346C4×C47C22×#4111yescharacteristic
347C4×C47C2×2−1+411yescharacteristic
348Dic47—22no—
349Dic47—22no—
350Dic47—42no—
351Dic47—42no—
352Dic47—42no—
353Dic47—42no—
354C2×#554—471no—
355C2×#552—471no—
356#3344—4716no—
357C2×#501—471no—
358C2×#484—471no—
359C2×#485—471no—
360C2×#483—471no—
361C2×#483—471no—
362C2×#479—471no—
363C2×#475—471no—
364C2×#470—471no—
365C2×#467—471no—
366C2×#441D4711yescharacteristic, complemented
367C2×#435—471no—
368C2×#428—471no—
369C22×#106—471no—
370C2×C47#334414yescomplemented
371C2×C47C2×#54711yescharacteristic
372C2×C47C22×#13711yescharacteristic
373C2×C47C2×#57711yescharacteristic
374D47—24no—
375D47—42no—
376C22×Q16C2×D4711yescharacteristic
377C22×M16—471no—
378C23×C8—471no—
379#554—478no—
380#554—944no—
381#552—478no—
382#552—944no—
383C2×C4⋊Q8—471no—
384C2×#126—941no—
385C2×#125—471no—
386C2×#125—941no—
387C2×#125—941no—
388C2×#123—941no—
389C2×C22⋊Q8—471no—
390C2×C22⋊Q8—471no—
391C2×C22⋊Q8—471no—
392C2×C22⋊Q8—471no—
393C2×C22⋊Q8—941no—
394C2×C22⋊Q8—941no—
395C2×C4×Q8C2×D4711yescharacteristic
396C2×C4×Q8C2×D4711yescharacteristic
397C2×C4×D4—471no—
398C2×C4×D4—941no—
399C2×#117—471no—
400C2×#117—941no—
401C22×C4⋊C4—471no—
402C22×C4⋊C4—471no—
403C22×C4⋊C4—471no—
404#501—478no—
405#485—478no—
406#484—478no—
407#483—478no—
408#483—478no—
409#479—478no—
410#475—478no—
411#470—478no—
412#467—478no—
413#441C2×D4718yescomplemented
414#435—478no—
415#428—478no—
416C2×#107—471no—
417C2×#107—471no—
418C2×#107—471no—
419C2×#106—471no—
420C2×#106—471no—
421C2×#106—471no—
422C2×#106—471no—
423C2×#106—471no—
424C2×#106—478no—
425C2×#106C2×D4711yescharacteristic
426C2×C4⋊C8—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103—471no—
430C2×#103—471no—
431C2×#103C2×D4711yescharacteristic
432C2×#103C2×D4711yescharacteristic
433C2×C22⋊C8—471no—
434C2×C22⋊C8—471no—
435C2×#97C2×D4711yescharacteristic
436C47C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—941no—
438C22×Q8C22×D4711yescharacteristic
439C22×Q8C22×D4711yescharacteristic
440C22×D4—471no—
441C23×C4—471no—
442C23×C4—471no—
443C23×C4—941no—
444C23×C4—941no—
445C23×C4—941no—
446C2×Q16—24no—
447C2×Q16C22×D4714yes—
448C2×M16—474no—
449C2×M16—944no—
450C22×C8—471no—
451C22×C8—471no—
452C22×C8—474no—
453C22×C8—944no—
454C22×C8C22×D4711yescharacteristic
455C22×C8C22×D4711yescharacteristic
456C4⋊Q8—474no—
457C4⋊Q8—942no—
458#126—948no—
459#125—474no—
460#125—948no—
461#125—948no—
462#125—942no—
463#123—948no—
464C22⋊Q8—474no—
465C22⋊Q8—474no—
466C22⋊Q8—474no—
467C22⋊Q8—474no—
468C22⋊Q8—948no—
469C22⋊Q8—948no—
470C22⋊Q8—942no—
471C22⋊Q8—942no—
472C22⋊Q8—942no—
473C22⋊Q8—942no—
474C4×Q8—22no—
475C4×Q8—22no—
476C4×Q8C22×D4714yes—
477C4×Q8C22×D4714yes—
478C4×D4—474no—
479C4×D4—474no—
480C4×D4—948no—
481#117—474no—
482#117—948no—
483#117—942no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—471no—
488C2×C4⋊C4—471no—
489C2×C4⋊C4—471no—
490C2×C4⋊C4—471no—
491C2×C4⋊C4—474no—
492C2×C4⋊C4—474no—
493C2×C4⋊C4—474no—
494C2×C4⋊C4—942no—
495C2×C4⋊C4—942no—
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⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4C22×D4711yescharacteristic
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×C22⋊C4—941no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—941no—
519C2×C42C22×D4711yescharacteristic
520#107—474no—
521#107—474no—
522#107—474no—
523#106—474no—
524#106—474no—
525#106—474no—
526#106—474no—
527#106—474no—
528#106C22×D4714yes—
529C4⋊C8—474no—
530#103—474no—
531#103—474no—
532#103—474no—
533#103—474no—
534#103C22×D4714yes—
535#103C22×D4714yes—
536C22⋊C8—474no—
537C22⋊C8—474no—
538#97C22×D4714yes—
539C24—471no—
540C24—471no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—944no—
548C2×Q8—3762no—
549C2×Q8C23×D4712yes—
550C2×Q8C23×D4712yes—
551C2×D4—474no—
552C2×D4—944no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—471no—
558C22×C4—471no—
559C22×C4—472no—
560C22×C4—472no—
561C22×C4—472no—
562C22×C4—472no—
563C22×C4—944no—
564C22×C4—944no—
565C22×C4—944no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—941no—
571C22×C4—941no—
572C22×C4—941no—
573C22×C4—941no—
574C22×C4—3762no—
575C22×C4—3762no—
576C22×C4—1884no—
577C22×C4D4×D4711yescharacteristic
578C22×C4D4×D4711yescharacteristic
579C22×C4C23×D4711yescharacteristic
580Q16—28no—
581M16—948no—
582C2×C8—22no—
583C2×C8—472no—
584C2×C8—472no—
585C2×C8—942no—
586C2×C8—942no—
587C2×C8—948no—
588C2×C8#1062535014yes—
589C2×C8C23×D4712yes—
590C2×C8C23×D4712yes—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—474no—
596C4⋊C4—472no—
597C4⋊C4—472no—
598C4⋊C4—472no—
599C4⋊C4—472no—
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—944no—
609C4⋊C4—941no—
610C4⋊C4—941no—
611C4⋊C4—941no—
612C4⋊C4—941no—
613C4⋊C4—944no—
614C4⋊C4C23×D4712yes—
615C4⋊C4C23×D4712yes—
616C22⋊C4—474no—
617C22⋊C4—474no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4—944no—
621C22⋊C4—944no—
622C22⋊C4—944no—
623C42—24no—
624C42—24no—
625C42—944no—
626C42D4×D4712yes—
627C42C23×D4712yes—
628C23—474no—
629C23—472no—
630C23—472no—
631C23—942no—
632C23—942no—
633C23—942no—
634C23—942no—
635C23—942no—
636C23C2×D4×D4711yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—42no—
642Q8—42no—
643Q8—3764no—
644D4—948no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—472no—
656C2×C4—472no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—944no—
660C2×C4—944no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—3764no—
670C2×C4—3764no—
671C2×C4—1888no—
672C2×C4—1882no—
673C2×C4—1882no—
674C2×C4—1882no—
675C2×C4—1882no—
676C2×C4C2×D4×D4712yes—
677C2×C4C2×D4×D4712yes—
678C2×C4C2×D4×D4711yescharacteristic
679C2×C4C2×#1062535012yes—
680C2×C4#1309407112yes—
681C2×C4C24×D4711yescharacteristic
682C8—22no—
683C8—942no—
684C8—942no—
685C8C2×#1062535014yes—
686C22—474no—
687C22—942no—
688C22—942no—
689C22—948no—
690C22—942no—
691C22—942no—
692C22—942no—
693C22—1884no—
694C22#1568977812yes—
695C22#137×D4712yes—
696C22#1568993212yes—
697C22C22×D4×D4711yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—942no—
705C4—942no—
706C4—1882no—
707C4—1882no—
708C4—1882no—
709C4—1882no—
710C4#1568977812yes—
711C4C22×#1062535011yescharacteristic
712C4C2×#1309407111yescharacteristic
713C2—944no—
714C2—1882no—
715C2#2025584814yesdirect product factor
716C2C2×#1568977811yescharacteristic
717C2C2×#137×D4711yescharacteristic
718C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#441C2
socleC23×C47C22×D4
prime radicalC22×D188D4
hypercenterC2×#441D47
hypocenterC47C2×#3344
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #20255848C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689457C2semidirect
6. C2×#15689463C2semidirect
7. C2×#15689452C2semidirect
8. C2×#15689452C2semidirect
9. C2×#15689430C2semidirect
10. C2×#15689408C2semidirect
11. C2×#15689378C2semidirect
12. C2×#15689361C2semidirect
14. C2×#15689162C2semidirect
15. C2×#106×D47C2semidirect
16. C2×C47×#441C2semidirect
42. #15689532C22semidirect
43. #15689463C22semidirect
44. #15689457C22semidirect
45. #15689452C22semidirect
46. #15689452C22semidirect
47. #15689430C22semidirect
48. #15689408C22semidirect
49. #15689378C22semidirect
50. #15689361C22semidirect
52. #15689162C22semidirect
61. #106×D47C22semidirect
72. C47×#441C22semidirect
366. C2×#441D47semidirect
370. C2×C47#3344semidirect
413. #441C2×D47semidirect
436. C47C2×#3344semidirect
715. C2#20255848direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898332
C2×#156898142
#202558482
C2×#156895322
C2×#156894572
C2×#156894632
C2×#156894522
C2×#156894302
C2×#156894082
C2×#156893782
C2×#156893612
C2×#156891962
C2×#156891622
C2×#106×D472
C2×C47×#4412
C2×#334447