Finite Group Databasebeta

← C2×#20255845 #27094827

Subgroups — C2×#20255845 #27094827

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×#15689830C211yesmaximal, characteristic
2C2×#15689813C211yesmaximal, characteristic
3#20255845C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689459C211yesmaximal, characteristic, complemented
6C2×#15689465C211yesmaximal, characteristic, complemented
7C2×#15689454C211yesmaximal, characteristic, complemented
8C2×#15689454C211yesmaximal, characteristic, complemented
9C2×#15689431C211yesmaximal, characteristic, complemented
10C2×#15689409C211yesmaximal, characteristic, complemented
11C2×#15689381C211yesmaximal, characteristic, complemented
12C2×#15689364C211yesmaximal, characteristic, complemented
13C2×#15689231C211yesmaximal, characteristic, complemented
14C2×#15689165C211yesmaximal, characteristic, complemented
15C22×#13093956C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic
17C22×Dic188C2211yescharacteristic
18#15689830—24no—
19#15689830C2218yes—
20#15689813—24no—
21#15689813C2218yes—
22C2×#13094024C2211yescharacteristic
23C2×#13094017—21no—
24C2×#13094016C2211yescharacteristic
25C2×#13094015—21no—
26C2×#13094014—21no—
27C2×#13094005—21no—
28C2×#13094003C2211yescharacteristic
29C2×#13094003C2211yescharacteristic
30C2×#13094003C2211yescharacteristic
31C2×#13094003C2211yescharacteristic
32C2×#13094001—21no—
33C2×#13094001—21no—
34C2×C4×Dic94C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×D4×Dic47—21no—
37C2×#13093983C2211yescharacteristic
38C2×#13093980—21no—
39C22×C4⋊Dic47C2211yescharacteristic
40C22×C4⋊Dic47C2211yescharacteristic
41C22×C4⋊Dic47C2211yescharacteristic
42#15689532C2218yescomplemented
43#15689465C2218yescomplemented
44#15689459C2218yescomplemented
45#15689454C2218yescomplemented
46#15689454C2218yescomplemented
47#15689431C2218yescomplemented
48#15689409C2218yescomplemented
49#15689381C2218yescomplemented
50#15689364C2218yescomplemented
51#15689231C2218yescomplemented
52#15689165C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093958C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093956C2211yescharacteristic
61C2×#13093956C2211yescharacteristic
62C2×#13093956C2218yescomplemented
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093949C2211yescharacteristic
66C2×#13093949C2211yescharacteristic
67C2×#13093949C2211yescharacteristic
68C2×#13093949C2211yescharacteristic
69C22×M16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#435C2218yes—
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C23×Dic47—21no—
81C23×Dic47—21no—
82C23×Dic47—21no—
83C2×Dic188—24no—
84C2×Dic188C2314yes—
85#13094024—22no—
86#13094024C2314yes—
87#13094017—28no—
88#13094016—22no—
89#13094016C2314yes—
90#13094015—28no—
91#13094014—28no—
92#13094005—28no—
93#13094003—22no—
94#13094003—22no—
95#13094003—22no—
96#13094003—22no—
97#13094003C2314yes—
98#13094003C2314yes—
99#13094003C2314yes—
100#13094003C2314yes—
101#13094001—28no—
102#13094001—28no—
103C4×Dic94—22no—
104C4×Dic94—22no—
105C4×Dic94C2314yes—
106C4×Dic94C2314yes—
107D4×Dic47—28no—
108#13093983—22no—
109#13093983C2314yes—
110#13093980—28no—
111C2×C4⋊Dic47—22no—
112C2×C4⋊Dic47—22no—
113C2×C4⋊Dic47—22no—
114C2×C4⋊Dic47—21no—
115C2×C4⋊Dic47—21no—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47C2314yes—
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2314yes—
121C2×C4⋊Dic47C2314yes—
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2311yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
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×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143#13093958C2314yes—
144#13093958C2314yes—
145#13093958C2314yes—
146#13093956C2314yes—
147#13093956C2314yes—
148#13093956C2314yes—
149#13093956C2314yes—
150#13093956C2314yes—
151#13093956C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093949C2314yes—
157#13093949C2314yes—
158C22×D4×C47D411yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C2×M16×C47—24no—
162C2×M16×C47C2314yes—
163C22×C8×C47—24no—
164C22×C8×C47C2314yes—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C4×D4×C47D414yes—
170C4×D4×C47C2314yes—
171C2×C4⋊C4×C47D411yescharacteristic
172C2×C22⋊C4×C47D411yescharacteristic
173C2×C22⋊C4×C47D411yescharacteristic
174C2×C42×C47C2311yescharacteristic
175C4⋊C8×C47C2314yes—
176C22⋊C8×C47C2314yes—
177C22⋊C8×C47C2314yes—
178#97×C47C2314yes—
179C24×C47C2×D411yescharacteristic
180C24×C47C2×D411yescharacteristic
181C2×D4×C47—24no—
182C2×D4×C47C2×D414yes—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D412yes—
192C22×C4×C47C2×D412yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2411yescharacteristic
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—24no—
205C22×Dic47—24no—
206C22×Dic47—24no—
207C22×Dic47—44no—
208C22×Dic47—82no—
209C22×Dic47—82no—
210C2×Dic94—22no—
211C2×Dic94—22no—
212C2×Dic94—22no—
213C2×Dic94—22no—
214C2×Dic94—21no—
215C2×Dic94—21no—
216C2×Dic94—24no—
217C2×Dic94—82no—
218C2×Dic94C2412yes—
219C2×Dic94C2412yes—
220M16×C47—28no—
221C2×C8×C47—22no—
222C2×C8×C47—22no—
223C2×C8×C47—22no—
224C2×C8×C47—28no—
225C2×C8×C47#4114yes—
226C2×C8×C47C2412yes—
227C2×C8×C47C2412yes—
228C2×C8×C47C2412yes—
229C2×C8×C47C2412yes—
230C4⋊C4×C47C2×D414yes—
231C22⋊C4×C47C2×D414yes—
232C22⋊C4×C47C2×D414yes—
233C42×C47C2×D412yes—
234C42×C47C2412yes—
235C22⋊Dic47—24no—
236C22⋊Dic47—24no—
237C22⋊Dic47—24no—
238C22⋊Dic47—24no—
239C22⋊Dic47—24no—
240C4⋊Dic47—21no—
241C4⋊Dic47—21no—
242C4⋊Dic47—24no—
243C4⋊Dic47—24no—
244C4⋊Dic47—21no—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47—24no—
248C4⋊Dic47—24no—
249C4⋊Dic47—21no—
250C4⋊Dic47C2412yes—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253C4⋊Dic47C2412yes—
254C4⋊Dic47C2412yes—
255C4⋊Dic47C2412yes—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264C4×Dic47—24no—
265C4×Dic47—24no—
266C4×Dic47—24no—
267Dic188—28no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47#13714yes—
274C23×C47C22×D412yes—
275C23×C47C22×D412yes—
276C23×C47C22×D411yescharacteristic
277D4×C47—28no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—24no—
283C2×C4×C47—24no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47C22×D412yes—
289C2×C4×C47C22×D412yes—
290C2×C4×C47C22×D412yes—
291C2×C4×C47C22×D412yes—
292C2×C4×C47C22×D411yescharacteristic
293C2×C4×C47C2×#4112yes—
294C2×C4×C472−1+412yes—
295C2×C4×C47C2511yescharacteristic
296C2×Dic47—22no—
297C2×Dic47—22no—
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—48no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—84no—
314C2×Dic47—84no—
315Dic94—22no—
316Dic94—22no—
317Dic94—22no—
318Dic94—22no—
319Dic94—42no—
320Dic94—42no—
321Dic94—84no—
322C8×C47—22no—
323C8×C47—22no—
324C8×C47—22no—
325C8×C47C2×#4114yes—
326C2×#3344—471nomaximal, Sylow
327C22×C47—28no—
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—22no—
333C22×C47—44no—
334C22×C47#54712yes—
335C22×C47C2×#13714yes—
336C22×C47C2×#13712yes—
337C22×C47#57712yes—
338C22×C47C23×D411yescharacteristic
339C4×C47—22no—
340C4×C47—22no—
341C4×C47—22no—
342C4×C47—22no—
343C4×C47#54712yes—
344C4×C47C22×#4111yescharacteristic
345C4×C47C2×2−1+411yescharacteristic
346Dic47—42no—
347Dic47—42no—
348Dic47—42no—
349Dic47—42no—
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×#441—471no—
367C2×#435D4711yescharacteristic
368C2×#428—471no—
369C22×#106—471no—
370C2×C47—24no—
371C2×C47—42no—
372C2×C47#334414yescomplemented
373C2×C47C2×#54711yescharacteristic
374C2×C47C22×#13711yescharacteristic
375C2×C47C2×#57711yescharacteristic
376C22×Q16—471no—
377C22×M16C2×D4711yescharacteristic
378C23×C8C2×D4711yescharacteristic
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×Q8—471no—
396C2×C4×Q8—471no—
397C2×C4×D4—941no—
398C2×C4×D4C2×D4711yescharacteristic
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#441—478no—
414#435C2×D4718yes—
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—478no—
424C2×#106—471no—
425C2×#106—471no—
426C2×C4⋊C8C2×D4711yescharacteristic
427C2×#103—471no—
428C2×#103—471no—
429C2×#103—471no—
430C2×#103—471no—
431C2×#103—471no—
432C2×#103—471no—
433C2×C22⋊C8C2×D4711yescharacteristic
434C2×C22⋊C8C2×D4711yescharacteristic
435C2×#97C2×D4711yescharacteristic
436C47C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—471no—
438C22×Q8—471no—
439C22×Q8—941no—
440C22×D4D18811yescharacteristic
441C23×C4—941no—
442C23×C4—941no—
443C23×C4—941no—
444C23×C4C22×D4711yescharacteristic
445C23×C4C22×D4711yescharacteristic
446C2×Q16—474no—
447C2×Q16—944no—
448C2×M16—24no—
449C2×M16C22×D4714yes—
450C22×C8—24no—
451C22×C8C22×D4711yescharacteristic
452C22×C8C22×D4714yes—
453C22×C8C22×D4711yescharacteristic
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—942no—
469C22⋊Q8—942no—
470C22⋊Q8—942no—
471C22⋊Q8—942no—
472C22⋊Q8—948no—
473C22⋊Q8—948no—
474C4×Q8—474no—
475C4×Q8—474no—
476C4×Q8—942no—
477C4×Q8—942no—
478C4×D4—948no—
479C4×D4D18814yes—
480C4×D4C22×D4714yes—
481#117—474no—
482#117—942no—
483#117—948no—
484C2×C4⋊C4—471no—
485C2×C4⋊C4—471no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—471no—
488C2×C4⋊C4—471no—
489C2×C4⋊C4—474no—
490C2×C4⋊C4—474no—
491C2×C4⋊C4—474no—
492C2×C4⋊C4—471no—
493C2×C4⋊C4—941no—
494C2×C4⋊C4—941no—
495C2×C4⋊C4—941no—
496C2×C4⋊C4—942no—
497C2×C4⋊C4—942no—
498C2×C4⋊C4—942no—
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⋊C4D18811yescharacteristic
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4D18811yescharacteristic
515C2×C22⋊C4D18811yescharacteristic
516C2×C42—941no—
517C2×C42—941no—
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#106—474no—
529C4⋊C8C22×D4714yes—
530#103—474no—
531#103—474no—
532#103—474no—
533#103—474no—
534#103—474no—
535#103—474no—
536C22⋊C8C22×D4714yes—
537C22⋊C8C22×D4714yes—
538#97C22×D4714yes—
539C24C2×D18811yescharacteristic
540C24C2×D18811yescharacteristic
541C2×Q8—472no—
542C2×Q8—472no—
543C2×Q8—944no—
544C2×Q8—941no—
545C2×Q8—941no—
546C2×Q8—942no—
547C2×Q8—942no—
548C2×Q8—942no—
549C2×Q8—942no—
550C2×Q8—3762no—
551C2×D4—24no—
552C2×D4C2×D18814yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—944no—
558C22×C4—944no—
559C22×C4—944no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—3762no—
569C22×C4—3762no—
570C22×C4—1884no—
571C22×C4C2×D18812yes—
572C22×C4C2×D18812yes—
573C22×C4C2×D18811yescharacteristic
574C22×C4C2×D18811yescharacteristic
575C22×C4C2×D18811yescharacteristic
576C22×C4C2×D18811yescharacteristic
577C22×C4C23×D4712yes—
578C22×C4C23×D4712yes—
579C22×C4C23×D4711yescharacteristic
580Q16—948no—
581M16—28no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—28no—
586C2×C8#1062535214yes—
587C2×C8C23×D4712yes—
588C2×C8C23×D4712yes—
589C2×C8C23×D4712yes—
590C2×C8C23×D4712yes—
591C4⋊C4—472no—
592C4⋊C4—472no—
593C4⋊C4—472no—
594C4⋊C4—472no—
595C4⋊C4—472no—
596C4⋊C4—472no—
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—941no—
606C4⋊C4—941no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4—941no—
610C4⋊C4—941no—
611C4⋊C4—941no—
612C4⋊C4—944no—
613C4⋊C4—941no—
614C4⋊C4—944no—
615C4⋊C4C2×D18814yes—
616C22⋊C4—944no—
617C22⋊C4—944no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4—944no—
621C22⋊C4C2×D18814yes—
622C22⋊C4C2×D18814yes—
623C42—944no—
624C42—944no—
625C42—944no—
626C42C2×D18812yes—
627C42C23×D4712yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1309405714yes—
634C23C22×D18812yes—
635C23C22×D18812yes—
636C23C22×D18811yescharacteristic
637Q8—942no—
638Q8—942no—
639Q8—942no—
640Q8—942no—
641Q8—3764no—
642Q8—1882no—
643Q8—1882no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—3764no—
664C2×C4—3764no—
665C2×C4—1882no—
666C2×C4—1882no—
667C2×C4—1888no—
668C2×C4—1882no—
669C2×C4—1882no—
670C2×C4—1882no—
671C2×C4—1882no—
672C2×C4—1882no—
673C2×C4—1882no—
674C2×C4C22×D18812yes—
675C2×C4C22×D18812yes—
676C2×C4C22×D18812yes—
677C2×C4C22×D18812yes—
678C2×C4C22×D18811yescharacteristic
679C2×C4C2×#1062535212yes—
680C2×C4#1309407112yes—
681C2×C4C24×D4711yescharacteristic
682C8—22no—
683C8—22no—
684C8—22no—
685C8C2×#1062535214yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1568977712yes—
694C22C2×#1309405714yes—
695C22C2×#1309405712yes—
696C22#1568993512yes—
697C22C23×D18811yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—1882no—
703C4—1882no—
704C4—1882no—
705C4—1882no—
706C4—1882no—
707C4—1882no—
708C4—1882no—
709C4—1882no—
710C4#1568977712yes—
711C4C22×#1062535211yescharacteristic
712C4C2×#1309407111yescharacteristic
713C2—24no—
714C2—42no—
715C2#2025584514yesdirect product factor
716C2C2×#1568977711yescharacteristic
717C2C22×#1309405711yescharacteristic
718C2C2×#1568993511yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C22×D4
prime radicalC22×D4×C47D4
hypercenterC2×#435D47
hypocenterC47C2×#3344
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #20255845C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689459C2semidirect
6. C2×#15689465C2semidirect
7. C2×#15689454C2semidirect
8. C2×#15689454C2semidirect
9. C2×#15689431C2semidirect
10. C2×#15689409C2semidirect
11. C2×#15689381C2semidirect
12. C2×#15689364C2semidirect
13. C2×#15689231C2semidirect
14. C2×#15689165C2semidirect
15. C22×#13093956C2semidirect
42. #15689532C22semidirect
43. #15689465C22semidirect
44. #15689459C22semidirect
45. #15689454C22semidirect
46. #15689454C22semidirect
47. #15689431C22semidirect
48. #15689409C22semidirect
49. #15689381C22semidirect
50. #15689364C22semidirect
51. #15689231C22semidirect
52. #15689165C22semidirect
62. C2×#13093956C22semidirect
372. C2×C47#3344semidirect
436. C47C2×#3344semidirect
715. C2#20255845direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898302
C2×#156898132
#202558452
C2×#156895322
C2×#156894592
C2×#156894652
C2×#156894542
C2×#156894312
C2×#156894092
C2×#156893812
C2×#156893642
C2×#156892312
C2×#156891652
C22×#130939562
C2×C47×#4352
C2×#334447