Finite Group Databasebeta

← C2×#20255935 #27094923

Subgroups — C2×#20255935 #27094923

Order 12032.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689843C211yesmaximal, characteristic, complemented
2C2×#15689819C211yesmaximal, characteristic
3#20255935C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689465C211yesmaximal, characteristic, complemented
6C2×#15689448C211yesmaximal, characteristic, complemented
7C2×#15689448C211yesmaximal, characteristic, complemented
8C2×#15689454C211yesmaximal, characteristic, complemented
9C2×#15689431C211yesmaximal, characteristic, complemented
10C2×#15689414C211yesmaximal, characteristic, complemented
11C2×#15689369C211yesmaximal, characteristic, complemented
12C2×#15689352C211yesmaximal, characteristic, complemented
13C2×#15689225C211yesmaximal, characteristic, complemented
14C2×#15689165C211yesmaximal, characteristic, complemented
15C2×#15689161C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic, complemented
17C22×#10625325C2211yescharacteristic
18#15689843—24no—
19#15689843C2218yescomplemented
20#15689819—24no—
21#15689819C2218yes—
22C2×#13094024C2211yescharacteristic
23C2×#13094019—21no—
24C2×#13094017—21no—
25C2×#13094017—21no—
26C2×#13094016C2211yescharacteristic
27C2×#13094011—21no—
28C2×#13094006—21no—
29C2×#13094003C2211yescharacteristic
30C2×#13094003C2211yescharacteristic
31C2×#13093998C2211yescharacteristic
32C2×#13093998C2211yescharacteristic
33C2×#13093996—21no—
34C2×C4×Dic94C2211yescharacteristic
35C2×#13093989—21no—
36C2×C4×D188C2211yescharacteristic
37C2×(C22⋊D47)⋊C4—21no—
38C2×#13093983C2211yescharacteristic
39C2×#13093983C2211yescharacteristic
40C2×#13093983C2211yescharacteristic
41C22×C4⋊Dic47C2211yescharacteristic
42#15689532C2218yescomplemented
43#15689465C2218yescomplemented
44#15689454C2218yescomplemented
45#15689448C2218yescomplemented
46#15689448C2218yescomplemented
47#15689431C2218yescomplemented
48#15689414C2218yescomplemented
49#15689369C2218yescomplemented
50#15689352C2218yescomplemented
51#15689225C2218yescomplemented
52#15689165C2218yescomplemented
53#15689161C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093958C2211yescharacteristic
56C2×#13093958C2211yescharacteristic
57C2×#13093958C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093956C2211yescharacteristic
61C2×#13093956C2211yescharacteristic
62C2×#13093956C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093949C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C22×M16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#435C2218yescomplemented
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C22⋊D47—21no—
82C23×Dic47—21no—
83C22×C4×D47—21no—
84C2×#10625325—24no—
85C2×#10625325C2314yes—
86#13094024—22no—
87#13094024C2314yes—
88#13094019—28no—
89#13094017—28no—
90#13094017—28no—
91#13094016—22no—
92#13094016C2314yes—
93#13094011—28no—
94#13094006—28no—
95#13094003—22no—
96#13094003—22no—
97#13094003C2314yes—
98#13094003C2314yes—
99#13093998—22no—
100#13093998—22no—
101#13093998C2314yes—
102#13093998C2314yes—
103#13093996—28no—
104C4×Dic94—22no—
105C4×Dic94C2314yes—
106#13093989—28no—
107C4×D188—22no—
108C4×D188C2314yes—
109(C22⋊D47)⋊C4—28no—
110#13093983—22no—
111#13093983—22no—
112#13093983—22no—
113#13093983C2314yes—
114#13093983C2314yes—
115#13093983C2314yes—
116C2×C4⋊Dic47—22no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47C2314yes—
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
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×C22⋊Dic47—21no—
132C2×C22⋊Dic47—21no—
133C2×C22⋊Dic47—21no—
134C2×C22⋊Dic47—21no—
135C2×C22⋊Dic47—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143#13093958C2314yes—
144#13093958C2314yes—
145#13093958C2314yes—
146#13093958C2314yes—
147#13093956C2314yes—
148#13093956C2314yes—
149#13093956C2314yes—
150#13093956C2314yes—
151#13093956C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
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
181C23×D47—21no—
182C2×D4×C47—42no—
183C2×D4×C47C2×D414yes—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D412yes—
193C22×C4×C47C2×D412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2411yescharacteristic
197C2×C22⋊D47—24no—
198C2×C22⋊D47—24no—
199C2×C22⋊D47—44no—
200C2×C22⋊D47—82no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—24no—
209C22×Dic47—82no—
210C2×D188—22no—
211C2×D188—22no—
212C2×D188—21no—
213C2×D188C2412yes—
214C2×C4×D47—24no—
215C2×C4×D47—82no—
216C2×Dic94—22no—
217C2×Dic94—22no—
218C2×Dic94—24no—
219C2×Dic94—21no—
220C2×Dic94—44no—
221C2×Dic94C2412yes—
222M16×C47—28no—
223C2×C8×C47—22no—
224C2×C8×C47—22no—
225C2×C8×C47—22no—
226C2×C8×C47—28no—
227C2×C8×C47#4114yes—
228C2×C8×C47C2412yes—
229C2×C8×C47C2412yes—
230C2×C8×C47C2412yes—
231C2×C8×C47C2412yes—
232C4⋊C4×C47C2×D414yes—
233C22⋊C4×C47C2×D414yes—
234C22⋊C4×C47C2×D414yes—
235C42×C47C2×D412yes—
236C42×C47C2412yes—
237C22⋊Dic47—24no—
238C22⋊Dic47—24no—
239C22⋊Dic47—24no—
240C22⋊Dic47—24no—
241C22⋊Dic47—24no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47—24no—
248C4⋊Dic47—24no—
249C4⋊Dic47—21no—
250C4⋊Dic47—21no—
251C4⋊Dic47—21no—
252C4⋊Dic47—21no—
253C4⋊Dic47C2412yes—
254C4⋊Dic47C2412yes—
255C4⋊Dic47C2412yes—
256C4⋊Dic47C2412yes—
257C4⋊Dic47C2412yes—
258C4⋊Dic47C2412yes—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264C4×Dic47—24no—
265C4×Dic47—24no—
266C4×Dic47—24no—
267C4×Dic47—24no—
268#10625325—28no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47C22×D412yes—
276C23×C47C22×D412yes—
277C23×C47C22×D411yescharacteristic
278C22×D47—22no—
279C22×D47—42no—
280C22×D47—42no—
281C22×D47—42no—
282D4×C47—44no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—24no—
288C2×C4×C47—24no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47C22×D412yes—
294C2×C4×C47C22×D412yes—
295C2×C4×C47C22×D412yes—
296C2×C4×C47C22×D412yes—
297C2×C4×C47C22×D411yescharacteristic
298C2×C4×C47C2×#4112yes—
299C2×C4×C472−1+412yes—
300C2×C4×C47C2511yescharacteristic
301C22⋊D47—48no—
302C22⋊D47—84no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—84no—
318D188—22no—
319D188—22no—
320D188—42no—
321C4×D47—84no—
322Dic94—22no—
323Dic94—22no—
324Dic94—48no—
325Dic94—42no—
326C8×C47—22no—
327C8×C47—22no—
328C8×C47—22no—
329C8×C47C2×#4114yes—
330C2×#3350—471nomaximal, Sylow
331C22×C47—22no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—44no—
338C22×C47—44no—
339C22×C47#54712yes—
340C22×C47#57512yes—
341C22×C47#57712yes—
342C22×C47C23×D411yescharacteristic
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—42no—
346C2×D47—84no—
347C4×C47—22no—
348C4×C47—22no—
349C4×C47—22no—
350C4×C47—22no—
351C4×C47#54712yes—
352C4×C47C22×#4111yescharacteristic
353C4×C47C2×2−1+411yescharacteristic
354Dic47—42no—
355Dic47—42no—
356Dic47—42no—
357Dic47—42no—
358Dic47—42no—
359Dic47—42no—
360Dic47—42no—
361C2×#556—471no—
362C2×#553—471no—
363#3350—4716no—
364C2×#501—471no—
365C2×#485—471no—
366C2×#482—471no—
367C2×#482—471no—
368C2×#483—471no—
369C2×#479—471no—
370C2×#476—471no—
371C2×#468—471no—
372C2×#465—471no—
373C2×#440—471no—
374C2×#435D4711yescharacteristic, complemented
375C2×#428—471no—
376C2×#427—471no—
377C2×C47—42no—
378C2×C47—42no—
379C2×C47#335014yescomplemented
380C2×C47C2×#54711yescharacteristic
381C2×C47C2×#57511yescharacteristic
382C2×C47C2×#57711yescharacteristic
383D47—82no—
384C22×SD16—471no—
385C22×M16C2×D4711yescharacteristic
386C23×C8C2×D4711yescharacteristic
387#556—478no—
388#556—944no—
389#553—478no—
390#553—944no—
391C2×C4⋊Q8—471no—
392C2×#126—941no—
393C2×#126—941no—
394C2×#126—941no—
395C2×#125—471no—
396C2×#124—941no—
397C2×#123—941no—
398C2×C22⋊Q8—471no—
399C2×C22⋊Q8—471no—
400C2×#121—471no—
401C2×#121—471no—
402C2×#121—941no—
403C2×C4×Q8—471no—
404C2×C4×Q8—941no—
405C2×C4×D4—471no—
406C2×C4×D4—941no—
407C2×C4×D4C2×D4711yescharacteristic
408C2×#117—471no—
409C2×#117—471no—
410C2×#117—471no—
411C22×C4⋊C4—471no—
412#501—478no—
413#485—478no—
414#483—478no—
415#482—478no—
416#482—478no—
417#479—478no—
418#476—478no—
419#468—478no—
420#465—478no—
421#440—478no—
422#435C2×D4718yescomplemented
423#428—478no—
424#427—478no—
425C2×#107—471no—
426C2×#107—471no—
427C2×#107—471no—
428C2×#107—471no—
429C2×#106—471no—
430C2×#106—471no—
431C2×#106—471no—
432C2×#106—471no—
433C2×#106—471no—
434C2×C4⋊C8C2×D4711yescharacteristic
435C2×#103—471no—
436C2×#103—471no—
437C2×#103—471no—
438C2×#102—471no—
439C2×#102—471no—
440C2×#102—471no—
441C2×C22⋊C8C2×D4711yescharacteristic
442C2×C22⋊C8C2×D4711yescharacteristic
443C2×#97C2×D4711yescharacteristic
444C47C2×#335011yescharacteristic, complemented, Sylow
445C22×Q8—471no—
446C22×Q8—941no—
447C22×D4—471no—
448C22×D4—941no—
449C22×D4—941no—
450C22×D4D18811yescharacteristic
451C23×C4—941no—
452C23×C4—941no—
453C23×C4C22×D4711yescharacteristic
454C23×C4C22×D4711yescharacteristic
455C2×SD16—474no—
456C2×SD16—944no—
457C2×M16—24no—
458C2×M16C22×D4714yes—
459C22×C8—24no—
460C22×C8C22×D4711yescharacteristic
461C22×C8C22×D4714yes—
462C22×C8C22×D4711yescharacteristic
463C22×C8C22×D4711yescharacteristic
464C22×C8C22×D4711yescharacteristic
465C4⋊Q8—474no—
466C4⋊Q8—942no—
467#126—948no—
468#126—948no—
469#126—948no—
470#125—474no—
471#125—942no—
472#124—948no—
473#123—948no—
474C22⋊Q8—474no—
475C22⋊Q8—474no—
476C22⋊Q8—942no—
477C22⋊Q8—942no—
478#121—474no—
479#121—474no—
480#121—948no—
481#121—942no—
482#121—942no—
483C4×Q8—474no—
484C4×Q8—948no—
485C4×Q8—942no—
486C4×D4—474no—
487C4×D4—948no—
488C4×D4—942no—
489C4×D4D18814yes—
490C4×D4C22×D4714yes—
491#117—474no—
492#117—474no—
493#117—474no—
494#117—942no—
495#117—942no—
496#117—942no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—474no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—942no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4D18811yescharacteristic
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C22⋊C4—941no—
516C2×C22⋊C4—941no—
517C2×C22⋊C4—941no—
518C2×C22⋊C4—941no—
519C2×C22⋊C4—941no—
520C2×C22⋊C4—941no—
521C2×C22⋊C4D18811yescharacteristic
522C2×C22⋊C4D18811yescharacteristic
523C2×C42—941no—
524C2×C42—941no—
525C2×C42—941no—
526C2×C42—941no—
527C2×C42C22×D4711yescharacteristic
528#107—474no—
529#107—474no—
530#107—474no—
531#107—474no—
532#106—474no—
533#106—474no—
534#106—474no—
535#106—474no—
536#106—474no—
537C4⋊C8C22×D4714yes—
538#103—474no—
539#103—474no—
540#103—474no—
541#102—474no—
542#102—474no—
543#102—474no—
544C22⋊C8C22×D4714yes—
545C22⋊C8C22×D4714yes—
546#97C22×D4714yes—
547C24—941no—
548C24C2×D18811yescharacteristic
549C24C2×D18811yescharacteristic
550C2×Q8—472no—
551C2×Q8—941no—
552C2×Q8—944no—
553C2×Q8—942no—
554C2×Q8—942no—
555C2×Q8—1884no—
556C2×D4—42no—
557C2×D4—472no—
558C2×D4—944no—
559C2×D4—944no—
560C2×D4—941no—
561C2×D4—942no—
562C2×D4—942no—
563C2×D4—3762no—
564C2×D4—1884no—
565C2×D4C2×D18814yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—944no—
571C22×C4—941no—
572C22×C4—941no—
573C22×C4—941no—
574C22×C4—941no—
575C22×C4—941no—
576C22×C4—941no—
577C22×C4—941no—
578C22×C4—944no—
579C22×C4—3762no—
580C22×C4—3762no—
581C22×C4C2×D18812yes—
582C22×C4C2×D18812yes—
583C22×C4C2×D18811yescharacteristic
584C22×C4C2×D18811yescharacteristic
585C22×C4C2×D18811yescharacteristic
586C22×C4C2×D18811yescharacteristic
587C22×C4C23×D4712yes—
588C22×C4C23×D4712yes—
589C22×C4C23×D4711yescharacteristic
590SD16—948no—
591M16—28no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—28no—
596C2×C8#1062535214yes—
597C2×C8C23×D4712yes—
598C2×C8C23×D4712yes—
599C2×C8C23×D4712yes—
600C2×C8C23×D4712yes—
601C4⋊C4—472no—
602C4⋊C4—472no—
603C4⋊C4—472no—
604C4⋊C4—472no—
605C4⋊C4—472no—
606C4⋊C4—472no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4—941no—
613C4⋊C4—941no—
614C4⋊C4—944no—
615C4⋊C4—941no—
616C4⋊C4—941no—
617C4⋊C4—941no—
618C4⋊C4—941no—
619C4⋊C4—944no—
620C4⋊C4C2×D18814yes—
621C22⋊C4—944no—
622C22⋊C4—944no—
623C22⋊C4—944no—
624C22⋊C4—944no—
625C22⋊C4—944no—
626C22⋊C4—944no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C22⋊C4C2×D18814yes—
630C22⋊C4C2×D18814yes—
631C42—944no—
632C42—944no—
633C42—944no—
634C42—944no—
635C42C2×D18812yes—
636C42C23×D4712yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—942no—
644C23—1882no—
645C23—1882no—
646C23—1882no—
647C23C22×D18812yes—
648C23C22×D18812yes—
649C23C22×D18811yescharacteristic
650Q8—942no—
651Q8—942no—
652Q8—1888no—
653Q8—1882no—
654D4—44no—
655D4—942no—
656D4—942no—
657D4—3764no—
658D4—1888no—
659D4—1882no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—3764no—
678C2×C4—3764no—
679C2×C4—1882no—
680C2×C4—1882no—
681C2×C4—1882no—
682C2×C4—1882no—
683C2×C4—1882no—
684C2×C4—1882no—
685C2×C4—1882no—
686C2×C4C22×D18812yes—
687C2×C4C22×D18812yes—
688C2×C4C22×D18812yes—
689C2×C4C22×D18812yes—
690C2×C4C22×D18811yescharacteristic
691C2×C4C2×#1062535212yes—
692C2×C4#1309407112yes—
693C2×C4C24×D4711yescharacteristic
694C8—22no—
695C8—22no—
696C8—22no—
697C8C2×#1062535214yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—3764no—
707C22—1882no—
708C22—1882no—
709C22—1882no—
710C22#1568977712yes—
711C22#1568992312yes—
712C22#1568993512yes—
713C22C23×D18811yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—1882no—
719C4—1882no—
720C4—1882no—
721C4—1882no—
722C4—1882no—
723C4—1882no—
724C4—1882no—
725C4#1568977712yes—
726C4C22×#1062535211yescharacteristic
727C4C2×#1309407111yescharacteristic
728C2—42no—
729C2—42no—
730C2—3762no—
731C2#2025593514yesdirect product factor
732C2C2×#1568977711yescharacteristic
733C2C2×#1568992311yescharacteristic
734C2C2×#1568993511yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C22×D4
prime radicalC2×#15689819C2
hypercenterC2×#435D47
hypocenterC47C2×#3350
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
1. C2×#15689843C2semidirect
3. #20255935C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689465C2semidirect
6. C2×#15689448C2semidirect
7. C2×#15689448C2semidirect
8. C2×#15689454C2semidirect
9. C2×#15689431C2semidirect
10. C2×#15689414C2semidirect
11. C2×#15689369C2semidirect
12. C2×#15689352C2semidirect
13. C2×#15689225C2semidirect
14. C2×#15689165C2semidirect
15. C2×#15689161C2semidirect
16. C2×C47×#435C2semidirect
19. #15689843C22semidirect
42. #15689532C22semidirect
43. #15689465C22semidirect
44. #15689454C22semidirect
45. #15689448C22semidirect
46. #15689448C22semidirect
47. #15689431C22semidirect
48. #15689414C22semidirect
49. #15689369C22semidirect
50. #15689352C22semidirect
51. #15689225C22semidirect
52. #15689165C22semidirect
53. #15689161C22semidirect
72. C47×#435C22semidirect
374. C2×#435D47semidirect
379. C2×C47#3350semidirect
422. #435C2×D47semidirect
444. C47C2×#3350semidirect
731. C2#20255935direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898432
C2×#156898192
#202559352
C2×#156895322
C2×#156894652
C2×#156894482
C2×#156894542
C2×#156894312
C2×#156894142
C2×#156893692
C2×#156893522
C2×#156892252
C2×#156891652
C2×#156891612
C2×C47×#4352
C2×#335047