Finite Group Databasebeta

← C2×#20255878 #27094862

Subgroups — C2×#20255878 #27094862

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×#15689833C211yesmaximal, characteristic, complemented
2C2×#15689823C211yesmaximal, characteristic
3#20255878C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689457C211yesmaximal, characteristic, complemented
6C2×#15689440C211yesmaximal, characteristic, complemented
7C2×#15689462C211yesmaximal, characteristic, complemented
8C2×#15689435C211yesmaximal, characteristic, complemented
9C2×#15689430C211yesmaximal, characteristic, complemented
10C2×#15689403C211yesmaximal, characteristic, complemented
11C2×#15689366C211yesmaximal, characteristic, complemented
12C2×#15689349C211yesmaximal, characteristic, complemented
13C2×#15689196C211yesmaximal, characteristic, complemented
14C2×#15689164C211yesmaximal, characteristic, complemented
15C2×#107×D47C211yesmaximal, characteristic, complemented
16C2×C47×#440C211yesmaximal, characteristic, complemented
17C22×#10625324C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19#15689833—24no—
20#15689833C2218yescomplemented
21#15689823—24no—
22#15689823C2218yes—
23C2×#13094024C2211yescharacteristic
24C2×#13094017—21no—
25C2×#13094016—21no—
26C2×#13094016C2211yescharacteristic
27C2×#13094007—21no—
28C2×#13094002—21no—
29C2×#13094002—21no—
30C2×#13094000C2211yescharacteristic
31C2×#13094000C2211yescharacteristic
32C2×#13093997—21no—
33C2×#13093995C2211yescharacteristic
34C2×#13093995C2211yescharacteristic
35C2×C4×D188—21no—
36C2×C4×D188C2211yescharacteristic
37C2×C4×C22⋊D47—21no—
38C2×#13093982C2211yescharacteristic
39C2×C4⋊C4×D47C2211yescharacteristic
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689532C2218yescomplemented
43#15689462C2218yescomplemented
44#15689457C2218yescomplemented
45#15689440C2218yescomplemented
46#15689435C2218yescomplemented
47#15689430C2218yescomplemented
48#15689403C2218yescomplemented
49#15689366C2218yescomplemented
50#15689349C2218yescomplemented
51#15689196C2218yescomplemented
52#15689164C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58#107×D47C2218yescomplemented
59C2×#13093956C2211yescharacteristic
60C2×#13093956C2211yescharacteristic
61C2×#13093955C2211yescharacteristic
62C2×C4⋊(C47⋊C8)C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093945C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#440C2218yescomplemented
73C2×#107×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—21no—
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×#10625324—24no—
87C2×#10625324C2314yes—
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90C2×C8×D47—24no—
91C2×C8×D47C2314yes—
92#13094024—22no—
93#13094024C2314yes—
94#13094017—28no—
95#13094016—22no—
96#13094016—28no—
97#13094016C2314yes—
98#13094007—28no—
99#13094002—28no—
100#13094002—28no—
101#13094000—22no—
102#13094000—22no—
103#13094000C2314yes—
104#13094000C2314yes—
105#13093997—28no—
106#13093995—22no—
107#13093995—22no—
108#13093995C2314yes—
109#13093995C2314yes—
110C4×D188—28no—
111C4×D188D414yes—
112C4×D188C2314yes—
113C4×C22⋊D47—28no—
114#13093982—22no—
115#13093982C2314yes—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47D411yescharacteristic
118C2×C4⋊Dic47C2311yescharacteristic
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
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×C22⋊Dic47—21no—
136C2×C22⋊Dic47—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#13093957C2314yes—
147#13093957C2314yes—
148#13093956C2314yes—
149#13093956C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152#13093948C2314yes—
153#13093948C2314yes—
154#13093945C2314yes—
155#13093945C2314yes—
156(C2×D47)⋊C8C2314yes—
157(C2×D47)⋊C8C2314yes—
158C22×Q8×C47C2311yescharacteristic
159C22×D4×C47C2311yescharacteristic
160C23×C4×C47—21no—
161C2×SD16×C47—24no—
162C2×SD16×C47C2314yes—
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C4×Q8×C47—22no—
166C4×Q8×C47C2314yes—
167C4×D4×C47—22no—
168C4×D4×C47C2314yes—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C22⋊C4×C47—21no—
173C2×C42×C47—21no—
174C2×C42×C47C2311yescharacteristic
175#107×C47C2314yes—
176#103×C47C2314yes—
177#102×C47C2314yes—
178#97×C47C2314yes—
179C24×C47—21no—
180C23×D47C2×D411yescharacteristic
181C23×D47C2×D411yescharacteristic
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47—22no—
185C2×Q8×C47C2412yes—
186C2×D4×C47—21no—
187C2×D4×C47—22no—
188C2×D4×C47—22no—
189C2×D4×C47C2412yes—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—24no—
194C22×C4×C47—82no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198C2×C22⋊D47—24no—
199C2×C22⋊D47—24no—
200C2×C22⋊D47—44no—
201C2×C22⋊D47—82no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C2×D188—24no—
209C2×D188C2×D414yes—
210C2×C4×D47—22no—
211C2×C4×D47—22no—
212C2×C4×D47—22no—
213C2×C4×D47—22no—
214C2×C4×D47—24no—
215C2×C4×D47—24no—
216C2×C4×D47—24no—
217C2×C4×D47—82no—
218C2×C4×D47—82no—
219C2×C4×D47—82no—
220C2×C4×D47C2×D412yes—
221C2×C4×D47C2×D412yes—
222C2×C4×D47C2412yes—
223C2×C4×D47C2412yes—
224C2×Dic94—24no—
225C2×Dic94—82no—
226SD16×C47—28no—
227C2×C8×C47—22no—
228C2×C8×C47#4114yes—
229C2×C8×C47C2412yes—
230C2×C8×C47C2412yes—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47C2412yes—
235C4⋊C4×C47C2412yes—
236C22⋊C4×C47—24no—
237C42×C47—24no—
238C42×C47C2×D412yes—
239C42×C47C2412yes—
240C22⋊Dic47—24no—
241C22⋊Dic47—24no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4C2×D414yes—
246(C2×D47)⋊C4C2×D414yes—
247C4⋊Dic47—21no—
248C4⋊Dic47—21no—
249C4⋊Dic47—21no—
250C4⋊Dic47—24no—
251C4⋊Dic47—21no—
252C4⋊Dic47C2×D414yes—
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—
263Dic47⋊C4—24no—
264C4×Dic47—24no—
265C2×C47⋊C8—22no—
266C2×C47⋊C8—22no—
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—22no—
285Q8×C47—22no—
286Q8×C47—42no—
287D4×C47—22no—
288D4×C47—22no—
289D4×C47—42no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—84no—
299C2×C4×C47C22×D412yes—
300C2×C4×C47C22×D412yes—
301C2×C4×C47C22×D411yescharacteristic
302C2×C4×C47C2×#4112yes—
303C2×C4×C472−1+412yes—
304C2×C4×C47C2511yescharacteristic
305C22⋊D47—48no—
306C22⋊D47—84no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47C22×D412yes—
318C2×Dic47C22×D412yes—
319D188—28no—
320C4×D47—24no—
321C4×D47—24no—
322C4×D47—22no—
323C4×D47—22no—
324C4×D47—22no—
325C4×D47—22no—
326C4×D47—84no—
327C4×D47—84no—
328C4×D47—84no—
329Dic94—84no—
330C8×C47—22no—
331C8×C47C2×#4114yes—
332C47⋊C8—22no—
333C47⋊C8—22no—
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×#474—471no—
375C2×#468—471no—
376C2×#465—471no—
377C2×#440D4711yescharacteristic, complemented
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×SD16C2×D4711yescharacteristic
389C22×M16—471no—
390C23×C8—471no—
391#554—478no—
392#554—944no—
393#553—478no—
394#553—944no—
395C2×C4⋊Q8—471no—
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×Q8C2×D4711yescharacteristic
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#474—478no—
423#468—478no—
424#465—478no—
425#440C2×D4718yescomplemented
426#435—478no—
427#428—478no—
428C2×#107—471no—
429C2×#107—471no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#107—471no—
433C2×#107—478no—
434C2×#107C2×D4711yescharacteristic
435C2×#106—471no—
436C2×#106—471no—
437C2×#106—471no—
438C2×C4⋊C8—471no—
439C2×#103—471no—
440C2×#103—471no—
441C2×#103C2×D4711yescharacteristic
442C2×#102—471no—
443C2×#102—471no—
444C2×#102C2×D4711yescharacteristic
445C2×C22⋊C8—471no—
446C2×C22⋊C8—471no—
447C2×#97C2×D4711yescharacteristic
448C47C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—941no—
450C22×Q8C22×D4711yescharacteristic
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—24no—
462C2×SD16C22×D4714yes—
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—474no—
472C4⋊Q8—942no—
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—22no—
490C4×Q8C22×D4714yes—
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—471no—
505C2×C4⋊C4—474no—
506C2×C4⋊C4—474no—
507C2×C4⋊C4—474no—
508C2×C4⋊C4—942no—
509C2×C4⋊C4—942no—
510C2×C4⋊C4—942no—
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⋊C4—941no—
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—21no—
530C2×C42—941no—
531C2×C42C22×D4711yescharacteristic
532#107—474no—
533#107—474no—
534#107—474no—
535#107—474no—
536#107—474no—
537#107C22×D4714yes—
538#106—474no—
539#106—474no—
540#106—474no—
541C4⋊C8—474no—
542#103—474no—
543#103—474no—
544#103C22×D4714yes—
545#102—474no—
546#102—474no—
547#102C22×D4714yes—
548C22⋊C8—474no—
549C22⋊C8—474no—
550#97C22×D4714yes—
551C24—21no—
552C24—471no—
553C24—471no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—944no—
558C2×Q8—3762no—
559C2×Q8C23×D4712yes—
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—28no—
599M16—948no—
600C2×C8—22no—
601C2×C8—472no—
602C2×C8—472no—
603C2×C8—942no—
604C2×C8—942no—
605C2×C8—948no—
606C2×C8#1062535014yes—
607C2×C8C23×D4712yes—
608C2×C8C23×D4712yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—474no—
613C4⋊C4—472no—
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—941no—
625C4⋊C4—941no—
626C4⋊C4—941no—
627C4⋊C4—941no—
628C4⋊C4—944no—
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—24no—
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—22no—
657Q8—22no—
658Q8—42no—
659Q8—3764no—
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×C4C2×#1062535012yes—
700C2×C4#1309407112yes—
701C2×C4C24×D4711yescharacteristic
702C8—22no—
703C8—942no—
704C8—942no—
705C8C2×#1062535014yes—
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#1568977812yes—
719C22#137×D4712yes—
720C22#1568992712yes—
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#1568977812yes—
734C4C22×#1062535011yescharacteristic
735C4C2×#1309407111yescharacteristic
736C2—82no—
737C2—944no—
738C2—1882no—
739C2#2025587814yesdirect product factor
740C2C2×#1568977811yescharacteristic
741C2C2×#137×D4711yescharacteristic
742C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#440C2
socleC23×C47C22×D4
prime radicalC2×#15689823C2
hypercenterC2×#440D47
hypocenterC47C2×#3346
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#15689833C2semidirect
3. #20255878C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689457C2semidirect
6. C2×#15689440C2semidirect
7. C2×#15689462C2semidirect
8. C2×#15689435C2semidirect
9. C2×#15689430C2semidirect
10. C2×#15689403C2semidirect
11. C2×#15689366C2semidirect
12. C2×#15689349C2semidirect
13. C2×#15689196C2semidirect
14. C2×#15689164C2semidirect
15. C2×#107×D47C2semidirect
16. C2×C47×#440C2semidirect
20. #15689833C22semidirect
42. #15689532C22semidirect
43. #15689462C22semidirect
44. #15689457C22semidirect
45. #15689440C22semidirect
46. #15689435C22semidirect
47. #15689430C22semidirect
48. #15689403C22semidirect
49. #15689366C22semidirect
50. #15689349C22semidirect
51. #15689196C22semidirect
52. #15689164C22semidirect
58. #107×D47C22semidirect
72. C47×#440C22semidirect
377. C2×#440D47semidirect
382. C2×C47#3346semidirect
425. #440C2×D47semidirect
448. C47C2×#3346semidirect
739. C2#20255878direct (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×#156898232
#202558782
C2×#156895322
C2×#156894572
C2×#156894402
C2×#156894622
C2×#156894352
C2×#156894302
C2×#156894032
C2×#156893662
C2×#156893492
C2×#156891962
C2×#156891642
C2×#107×D472
C2×C47×#4402
C2×#334647