Finite Group Databasebeta

← C2×#20255870 #27094854

Subgroups — C2×#20255870 #27094854

Order 12032.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689834C211yesmaximal, characteristic, complemented
2C2×#15689823C211yesmaximal, characteristic
3#20255870C2116yesmaximal, direct product factor
4C2×#15689529C211yesmaximal, characteristic, complemented
5C2×#15689460C211yesmaximal, characteristic, complemented
6C2×#15689440C211yesmaximal, characteristic, complemented
7C2×#15689466C211yesmaximal, characteristic, complemented
8C2×#15689435C211yesmaximal, characteristic, complemented
9C2×#15689431C211yesmaximal, characteristic, complemented
10C2×#15689368C211yesmaximal, characteristic, complemented
11C2×#15689351C211yesmaximal, characteristic, complemented
12C2×#15689223C211yesmaximal, characteristic, complemented
13C2×#15689193C211yesmaximal, characteristic, complemented
14C2×#15689164C211yesmaximal, characteristic, complemented
15C2×#107×D47C211yesmaximal, characteristic, complemented
16C2×C47×#474C211yesmaximal, characteristic, complemented
17C22×#10625335C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20#15689834—24no—
21#15689834C2218yescomplemented
22#15689823—24no—
23#15689823C2218yes—
24C2×#13094017—21no—
25C2×#13094016C2211yescharacteristic
26C2×#13094015—21no—
27C2×#13094007—21no—
28C2×#13094004C2211yescharacteristic
29C2×#13094004C2211yescharacteristic
30C2×#13094000—21no—
31C2×#13094000—21no—
32C2×#13093997—21no—
33C2×#13093995C2211yescharacteristic
34C2×#13093995C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37C2×#13093986—21no—
38C2×C4×C22⋊D47—21no—
39C2×#13093982C2211yescharacteristic
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689529C2218yescomplemented
44#15689466C2218yescomplemented
45#15689460C2218yescomplemented
46#15689440C2218yescomplemented
47#15689435C2218yescomplemented
48#15689431C2218yescomplemented
49#15689368C2218yescomplemented
50#15689351C2218yescomplemented
51#15689223C2218yescomplemented
52#15689193C2218yescomplemented
53#15689164C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58#107×D47C2218yescomplemented
59C2×#13093956C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61C2×#13093955C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093935C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C47×#474C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94C2311yescharacteristic
78C22×D188D411yescharacteristic
79C22×C22⋊D47—21no—
80C22×C22⋊D47—21no—
81C22×C4×D47—21no—
82C22×C4×D47—21no—
83C22×C4×D47—21no—
84C22×C4×D47C2311yescharacteristic
85C22×C4×D47C2311yescharacteristic
86C2×#10625335—24no—
87C2×#10625335C2314yes—
88C2×#10625324—24no—
89C2×#10625324C2314yes—
90C22×C47⋊C8C2311yescharacteristic
91C22×C47⋊C8C2311yescharacteristic
92C2×C8×D47—24no—
93C2×C8×D47C2314yes—
94#13094017—28no—
95#13094016—22no—
96#13094016C2314yes—
97#13094015—28no—
98#13094007—28no—
99#13094004—22no—
100#13094004—22no—
101#13094004C2314yes—
102#13094004C2314yes—
103#13094000—28no—
104#13094000—28no—
105#13093997—28no—
106#13093995—22no—
107#13093995—22no—
108#13093995C2314yes—
109#13093995C2314yes—
110C4×Dic94—22no—
111C4×Dic94C2314yes—
112C4×D188D414yes—
113C4×D188C2314yes—
114#13093986—28no—
115C4×C22⋊D47—28no—
116#13093982—22no—
117#13093982C2314yes—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47D411yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2311yescharacteristic
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C4⋊C4×D47—22no—
131C4⋊C4×D47—22no—
132C4⋊C4×D47—22no—
133C4⋊C4×D47C2314yes—
134C4⋊C4×D47C2314yes—
135C4⋊C4×D47C2314yes—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—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—
145#13093958C2314yes—
146#13093957C2314yes—
147#13093957C2314yes—
148#13093957C2314yes—
149#13093956C2314yes—
150#13093955C2314yes—
151#13093955C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093947C2314yes—
155#13093945C2314yes—
156(C2×D47)⋊C8C2314yes—
157(C2×D47)⋊C8C2314yes—
158#13093935C2314yes—
159C22×Q8×C47—21no—
160C22×D4×C47C2311yescharacteristic
161C23×C4×C47—21no—
162C22×C8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164C4⋊Q8×C47—22no—
165C4⋊Q8×C47C2314yes—
166C4×D4×C47—22no—
167C4×D4×C47C2314yes—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C22⋊C4×C47—21no—
173C2×C42×C47C2311yescharacteristic
174#107×C47C2314yes—
175#107×C47C2314yes—
176C4⋊C8×C47C2314yes—
177#102×C47C2314yes—
178#102×C47C2314yes—
179C24×C47—21no—
180C23×D47C2×D411yescharacteristic
181C23×D47C2×D411yescharacteristic
182C2×Q8×C47—24no—
183C2×Q8×C47—82no—
184C2×D4×C47—21no—
185C2×D4×C47—22no—
186C2×D4×C47—22no—
187C2×D4×C47C2412yes—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—24no—
192C22×C4×C47—82no—
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—24no—
197C2×C22⋊D47—24no—
198C2×C22⋊D47—44no—
199C2×C22⋊D47—82no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D411yescharacteristic
206C2×D188—24no—
207C2×D188C2×D414yes—
208C2×C4×D47—22no—
209C2×C4×D47—22no—
210C2×C4×D47—22no—
211C2×C4×D47—22no—
212C2×C4×D47—24no—
213C2×C4×D47—24no—
214C2×C4×D47—24no—
215C2×C4×D47—82no—
216C2×C4×D47—82no—
217C2×C4×D47—82no—
218C2×C4×D47C2×D412yes—
219C2×C4×D47C2×D412yes—
220C2×C4×D47C2412yes—
221C2×C4×D47C2412yes—
222C2×Dic94—22no—
223C2×Dic94—22no—
224C2×Dic94—21no—
225C2×Dic94C2412yes—
226C2×C8×C47—22no—
227C2×C8×C47—22no—
228C2×C8×C47C2412yes—
229C2×C8×C47C2412yes—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47C2412yes—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C22⋊C4×C47—24no—
238C42×C47C2×D412yes—
239C42×C47C2412yes—
240C22⋊Dic47—24no—
241C22⋊Dic47—24no—
242#10625335—28no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4C2×D414yes—
247(C2×D47)⋊C4C2×D414yes—
248C4⋊Dic47—21no—
249C4⋊Dic47—21no—
250C4⋊Dic47—21no—
251C4⋊Dic47—24no—
252C4⋊Dic47—24no—
253C4⋊Dic47C2×D414yes—
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—
264C4×Dic47—24no—
265C2×C47⋊C8—22no—
266C2×C47⋊C8#4114yes—
267C2×C47⋊C8C2412yes—
268C2×C47⋊C8C2412yes—
269#10625324—28no—
270C8×D47—28no—
271C23×C47—22no—
272C23×C47—42no—
273C23×C47—42no—
274C23×C47—42no—
275C23×C47C22×D411yescharacteristic
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47#13714yes—
282C22×D47C22×D412yes—
283C22×D47C22×D412yes—
284Q8×C47—84no—
285D4×C47—22no—
286D4×C47—22no—
287D4×C47—42no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—84no—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D412yes—
299C2×C4×C47C22×D411yescharacteristic
300C2×C4×C47C2×#4112yes—
301C2×C4×C472−1+412yes—
302C2×C4×C47C2511yescharacteristic
303C22⋊D47—48no—
304C22⋊D47—84no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47C22×D412yes—
316C2×Dic47C22×D412yes—
317D188—28no—
318C4×D47—24no—
319C4×D47—24no—
320C4×D47—22no—
321C4×D47—22no—
322C4×D47—22no—
323C4×D47—22no—
324C4×D47—84no—
325C4×D47—84no—
326C4×D47—84no—
327Dic94—22no—
328Dic94—22no—
329Dic94—42no—
330C8×C47—22no—
331C8×C47—22no—
332C47⋊C8—22no—
333C47⋊C8C2×#4114yes—
334C2×#3346—471nomaximal, Sylow
335C22×C47—42no—
336C22×C47—42no—
337C22×C47—42no—
338C22×C47—84no—
339C22×C47#54712yes—
340C22×C47C2×#13712yes—
341C22×C47#57612yes—
342C22×C47C23×D411yescharacteristic
343C2×D47—28no—
344C2×D47—22no—
345C2×D47—22no—
346C2×D47—22no—
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—44no—
350C2×D47C2×#13714yes—
351C4×C47—22no—
352C4×C47—22no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47—42no—
356C4×C47#54712yes—
357C4×C47C22×#4111yescharacteristic
358C4×C47C2×2−1+411yescharacteristic
359Dic47—22no—
360Dic47—22no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47—42no—
365C2×#554—471no—
366C2×#553—471no—
367#3346—4716no—
368C2×#501—471no—
369C2×#484—471no—
370C2×#481—471no—
371C2×#485—471no—
372C2×#480—471no—
373C2×#479—471no—
374C2×#474D4711yescharacteristic, complemented
375C2×#468—471no—
376C2×#465—471no—
377C2×#440—471no—
378C2×#435—471no—
379C2×#428—471no—
380C22×#107—471no—
381C2×C47—82no—
382C2×C47#334614yescomplemented
383C2×C47C2×#54711yescharacteristic
384C2×C47C22×#13711yescharacteristic
385C2×C47C2×#57611yescharacteristic
386D47—24no—
387D47—42no—
388C22×SD16—471no—
389C22×M16—471no—
390C23×C8—471no—
391#554—478no—
392#554—944no—
393#553—478no—
394#553—944no—
395C2×C4⋊Q8C2×D4711yescharacteristic
396C2×#126—941no—
397C2×#125—471no—
398C2×#125—941no—
399C2×#123—941no—
400C2×C22⋊Q8—471no—
401C2×C22⋊Q8—471no—
402C2×C22⋊Q8—941no—
403C2×C22⋊Q8—941no—
404C2×#121—471no—
405C2×#121—471no—
406C2×#121—941no—
407C2×C4×Q8—471no—
408C2×C4×D4—471no—
409C2×C4×D4—941no—
410C2×C4×D4—941no—
411C2×C4×D4C2×D4711yescharacteristic
412C2×#117—471no—
413C22×C4⋊C4—471no—
414C22×C4⋊C4—471no—
415C22×C4⋊C4—471no—
416#501—478no—
417#485—478no—
418#484—478no—
419#481—478no—
420#480—478no—
421#479—478no—
422#474C2×D4718yescomplemented
423#468—478no—
424#465—478no—
425#440—478no—
426#435—478no—
427#428—478no—
428C2×#107—471no—
429C2×#107—471no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#107—478no—
433C2×#107C2×D4711yescharacteristic
434C2×#107C2×D4711yescharacteristic
435C2×#106—471no—
436C2×#106—471no—
437C2×#106—471no—
438C2×C4⋊C8C2×D4711yescharacteristic
439C2×#103—471no—
440C2×#103—471no—
441C2×#103—471no—
442C2×#102—471no—
443C2×#102C2×D4711yescharacteristic
444C2×#102C2×D4711yescharacteristic
445C2×C22⋊C8—471no—
446C2×C22⋊C8—471no—
447C2×#97—471no—
448C47C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—21no—
450C22×Q8—471no—
451C22×D4—471no—
452C22×D4—941no—
453C22×D4—941no—
454C22×D4C22×D4711yescharacteristic
455C23×C4—21no—
456C23×C4—471no—
457C23×C4—471no—
458C23×C4—941no—
459C23×C4—941no—
460C23×C4—941no—
461C2×SD16—474no—
462C2×SD16—944no—
463C2×M16—474no—
464C2×M16—944no—
465C22×C8—471no—
466C22×C8—471no—
467C22×C8—474no—
468C22×C8—944no—
469C22×C8C22×D4711yescharacteristic
470C22×C8C22×D4711yescharacteristic
471C4⋊Q8—22no—
472C4⋊Q8C22×D4714yes—
473#126—948no—
474#125—474no—
475#125—948no—
476#125—942no—
477#123—948no—
478C22⋊Q8—474no—
479C22⋊Q8—474no—
480C22⋊Q8—948no—
481C22⋊Q8—948no—
482C22⋊Q8—942no—
483C22⋊Q8—942no—
484#121—474no—
485#121—474no—
486#121—948no—
487#121—942no—
488#121—942no—
489C4×Q8—474no—
490C4×Q8—942no—
491C4×D4—22no—
492C4×D4—474no—
493C4×D4—474no—
494C4×D4—948no—
495C4×D4—948no—
496C4×D4C22×D4714yes—
497#117—474no—
498#117—942no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—474no—
505C2×C4⋊C4—474no—
506C2×C4⋊C4—474no—
507C2×C4⋊C4—942no—
508C2×C4⋊C4—942no—
509C2×C4⋊C4—942no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C4⋊C4C22×D4711yescharacteristic
520C2×C4⋊C4C22×D4711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—471no—
523C2×C22⋊C4—471no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4—941no—
529C2×C42—941no—
530C2×C42—941no—
531C2×C42C22×D4711yescharacteristic
532#107—474no—
533#107—474no—
534#107—474no—
535#107—474no—
536#107C22×D4714yes—
537#107C22×D4714yes—
538#106—474no—
539#106—474no—
540#106—474no—
541C4⋊C8C22×D4714yes—
542#103—474no—
543#103—474no—
544#103—474no—
545#102—474no—
546#102C22×D4714yes—
547#102C22×D4714yes—
548C22⋊C8—474no—
549C22⋊C8—474no—
550#97—474no—
551C24—21no—
552C24—471no—
553C24—471no—
554C2×Q8—24no—
555C2×Q8—82no—
556C2×Q8—472no—
557C2×Q8—941no—
558C2×Q8—942no—
559C2×Q8—942no—
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—474no—
564C2×D4—944no—
565C2×D4—944no—
566C2×D4—944no—
567C2×D4—3762no—
568C2×D4—1884no—
569C2×D4C23×D4712yes—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—82no—
575C22×C4—471no—
576C22×C4—471no—
577C22×C4—472no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—472no—
581C22×C4—944no—
582C22×C4—944no—
583C22×C4—944no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—3762no—
593C22×C4—3762no—
594C22×C4—3762no—
595C22×C4D4×D4711yescharacteristic
596C22×C4D4×D4711yescharacteristic
597C22×C4C23×D4711yescharacteristic
598SD16—948no—
599M16—948no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—474no—
603C2×C8—472no—
604C2×C8—472no—
605C2×C8—948no—
606C2×C8—942no—
607C2×C8C23×D4712yes—
608C2×C8C23×D4712yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—474no—
614C4⋊C4—472no—
615C4⋊C4—472no—
616C4⋊C4—472no—
617C4⋊C4—944no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—944no—
621C4⋊C4—944no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—941no—
626C4⋊C4—941no—
627C4⋊C4—941no—
628C4⋊C4C23×D4712yes—
629C4⋊C4C23×D4712yes—
630C4⋊C4C23×D4712yes—
631C22⋊C4—24no—
632C22⋊C4—474no—
633C22⋊C4—474no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C22⋊C4—944no—
639C42—944no—
640C42—944no—
641C42D4×D4712yes—
642C42C23×D4712yes—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—474no—
648C23—472no—
649C23—472no—
650C23—942no—
651C23—942no—
652C23—942no—
653C23—942no—
654C23—942no—
655C23C2×D4×D4711yescharacteristic
656Q8—84no—
657Q8—942no—
658Q8—942no—
659Q8—1882no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—948no—
664D4—3764no—
665D4—1888no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—84no—
675C2×C4—472no—
676C2×C4—472no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—944no—
680C2×C4—944no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—3764no—
690C2×C4—3764no—
691C2×C4—3764no—
692C2×C4—1882no—
693C2×C4—1882no—
694C2×C4—1882no—
695C2×C4—1882no—
696C2×C4C2×D4×D4712yes—
697C2×C4C2×D4×D4712yes—
698C2×C4C2×D4×D4711yescharacteristic
699C2×C4#41×D4712yes—
700C2×C4#1309407212yes—
701C2×C4C24×D4711yescharacteristic
702C8—22no—
703C8—22no—
704C8—474no—
705C8—942no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22—474no—
711C22—942no—
712C22—942no—
713C22—948no—
714C22—942no—
715C22—942no—
716C22—942no—
717C22—1884no—
718C22#1568977512yes—
719C22#137×D4712yes—
720C22#1568992412yes—
721C22C22×D4×D4711yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—942no—
728C4—942no—
729C4—1882no—
730C4—1882no—
731C4—1882no—
732C4—1882no—
733C4#1568977512yes—
734C4C2×#41×D4711yescharacteristic
735C4C2×#1309407211yescharacteristic
736C2—82no—
737C2—944no—
738C2—1882no—
739C2#2025587014yesdirect product factor
740C2C2×#1568977511yescharacteristic
741C2C2×#137×D4711yescharacteristic
742C2C2×#1568992411yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#474C2
socleC23×C47C22×D4
prime radicalC2×#15689823C2
hypercenterC2×#474D47
hypocenterC47C2×#3346
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#15689834C2semidirect
3. #20255870C2direct (N × H)
4. C2×#15689529C2semidirect
5. C2×#15689460C2semidirect
6. C2×#15689440C2semidirect
7. C2×#15689466C2semidirect
8. C2×#15689435C2semidirect
9. C2×#15689431C2semidirect
10. C2×#15689368C2semidirect
11. C2×#15689351C2semidirect
12. C2×#15689223C2semidirect
13. C2×#15689193C2semidirect
14. C2×#15689164C2semidirect
15. C2×#107×D47C2semidirect
16. C2×C47×#474C2semidirect
21. #15689834C22semidirect
43. #15689529C22semidirect
44. #15689466C22semidirect
45. #15689460C22semidirect
46. #15689440C22semidirect
47. #15689435C22semidirect
48. #15689431C22semidirect
49. #15689368C22semidirect
50. #15689351C22semidirect
51. #15689223C22semidirect
52. #15689193C22semidirect
53. #15689164C22semidirect
58. #107×D47C22semidirect
71. C47×#474C22semidirect
374. C2×#474D47semidirect
382. C2×C47#3346semidirect
422. #474C2×D47semidirect
448. C47C2×#3346semidirect
739. C2#20255870direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898342
C2×#156898232
#202558702
C2×#156895292
C2×#156894602
C2×#156894402
C2×#156894662
C2×#156894352
C2×#156894312
C2×#156893682
C2×#156893512
C2×#156892232
C2×#156891932
C2×#156891642
C2×#107×D472
C2×C47×#4742
C2×#334647