Finite Group Databasebeta

← C2×#20256009 #27095023

Subgroups — C2×#20256009 #27095023

Order 12032.

1930 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×#15689837C211yesmaximal, characteristic
2C2×#15689831C211yesmaximal, characteristic, complemented
3#20256009C2116yesmaximal, direct product factor
4C2×#15689527C211yesmaximal, characteristic, complemented
5C2×#15689462C211yesmaximal, characteristic, complemented
6C2×#15689461C211yesmaximal, characteristic, complemented
7C2×#15689435C211yesmaximal, characteristic, complemented
8C2×#15689434C211yesmaximal, characteristic, complemented
9C2×#15689416C211yesmaximal, characteristic, complemented
10C2×#15689411C211yesmaximal, characteristic, complemented
11C2×#15689366C211yesmaximal, characteristic, complemented
12C2×SD16×Dic47C211yesmaximal, characteristic, complemented
13C2×#15689199C211yesmaximal, characteristic, complemented
14C2×#15689165C211yesmaximal, characteristic, complemented
15C2×#15689164C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic, complemented
17C22×#10625324C2211yescharacteristic
18#15689837—24no—
19#15689837C2218yes—
20#15689831—24no—
21#15689831C2218yescomplemented
22C2×#13094023C2211yescharacteristic
23C2×#13094023C2211yescharacteristic
24C2×#13094014—21no—
25C2×#13094011—21no—
26C2×#13094010—21no—
27C2×#13094004—21no—
28C2×#13094001—21no—
29C2×#13094000C2211yescharacteristic
30C2×#13093996—21no—
31C2×#13093995C2211yescharacteristic
32C2×Q8×Dic47C2211yescharacteristic
33C2×D4×Dic47C2211yescharacteristic
34C2×C4×C22⋊D47C2211yescharacteristic
35C2×(C22⋊D47)⋊C4—21no—
36C2×#13093983C2211yescharacteristic
37C2×#13093982C2211yescharacteristic
38C2×#13093980—21no—
39C22×C4⋊Dic47C2211yescharacteristic
40C2×C4⋊C4×D47C2211yescharacteristic
41#15689527C2218yescomplemented
42#15689462C2218yescomplemented
43#15689461C2218yescomplemented
44#15689435C2218yescomplemented
45#15689434C2218yescomplemented
46#15689416C2218yescomplemented
47#15689411C2218yescomplemented
48#15689366C2218yescomplemented
49SD16×Dic47C2218yescomplemented
50#15689199C2218yescomplemented
51#15689165C2218yescomplemented
52#15689164C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#468C2218yescomplemented
74C2×#107×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×C22⋊D47—21no—
80C22×C22⋊D47D411yescharacteristic
81C23×Dic47—21no—
82C23×Dic47—21no—
83C22×C4×D47—21no—
84C22×C4×D47C2311yescharacteristic
85C2×#10625324—24no—
86C2×#10625324C2314yes—
87C22×C47⋊C8C2311yescharacteristic
88C22×C47⋊C8C2311yescharacteristic
89#13094023—22no—
90#13094023—22no—
91#13094023C2314yes—
92#13094023C2314yes—
93#13094014—28no—
94#13094011—28no—
95#13094010—28no—
96#13094004—28no—
97#13094001—28no—
98#13094000—22no—
99#13094000C2314yes—
100#13093996—28no—
101#13093995—22no—
102#13093995C2314yes—
103Q8×Dic47—22no—
104Q8×Dic47C2314yes—
105D4×Dic47—22no—
106D4×Dic47C2314yes—
107C4×C22⋊D47D414yes—
108C4×C22⋊D47C2314yes—
109(C22⋊D47)⋊C4—28no—
110#13093983—22no—
111#13093983C2314yes—
112#13093982—22no—
113#13093982C2314yes—
114#13093980—28no—
115C2×C4⋊Dic47—22no—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47C2311yescharacteristic
119C2×C4⋊Dic47C2314yes—
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4D411yescharacteristic
128C4⋊C4×D47—22no—
129C4⋊C4×D47C2314yes—
130C2×C22⋊Dic47—21no—
131C2×C22⋊Dic47—21no—
132C2×C22⋊Dic47—21no—
133C2×C22⋊Dic47D411yescharacteristic
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4D411yescharacteristic
137C2×C4×Dic47—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47C2311yescharacteristic
141#13093958C2314yes—
142#13093958C2314yes—
143#13093957C2314yes—
144#13093957C2314yes—
145#13093957C2314yes—
146#13093956C2314yes—
147#13093956C2314yes—
148#13093955C2314yes—
149Dic47⋊C8C2314yes—
150#13093948C2314yes—
151#13093948C2314yes—
152#13093945C2314yes—
153#13093945C2314yes—
154C22⋊(C47⋊C8)C2314yes—
155(C2×D47)⋊C8C2314yes—
156C8×Dic47C2314yes—
157C22×Q8×C47C2311yescharacteristic
158C22×D4×C47—21no—
159C22×D4×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C2×SD16×C47—24no—
162C2×SD16×C47C2314yes—
163C2×M16×C47—24no—
164C2×M16×C47C2314yes—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22⋊Q8×C47—22no—
168C22⋊Q8×C47C2314yes—
169#121×C47—22no—
170#121×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176#107×C47C2314yes—
177#103×C47C2314yes—
178#102×C47C2314yes—
179C24×C47—21no—
180C24×C47C2×D411yescharacteristic
181C23×D47C2×D411yescharacteristic
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47—22no—
185C2×Q8×C47C2412yes—
186C2×D4×C47—24no—
187C2×D4×C47—21no—
188C2×D4×C47—22no—
189C2×D4×C47—22no—
190C2×D4×C47—82no—
191C2×D4×C47C2412yes—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2411yescharacteristic
201C2×C22⋊D47—24no—
202C2×C22⋊D47—24no—
203C2×C22⋊D47—82no—
204C2×C22⋊D47C2×D414yes—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—24no—
210C22×Dic47—24no—
211C22×Dic47—44no—
212C22×Dic47—82no—
213C22×Dic47C2×D411yescharacteristic
214C22×Dic47C2×D411yescharacteristic
215C22×Dic47C2×D411yescharacteristic
216C2×C4×D47—22no—
217C2×C4×D47—22no—
218C2×C4×D47—24no—
219C2×C4×D47—82no—
220C2×C4×D47C2×D412yes—
221C2×C4×D47C2412yes—
222C2×Dic94—24no—
223C2×Dic94—24no—
224C2×Dic94—82no—
225C2×Dic94—82no—
226SD16×C47—28no—
227M16×C47—28no—
228C2×C8×C47—22no—
229C2×C8×C47#4114yes—
230C2×C8×C47C2412yes—
231C2×C8×C47C2412yes—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C22⋊C4×C47—24no—
238C22⋊C4×C47—24no—
239C22⋊Dic47—24no—
240C22⋊Dic47—24no—
241C22⋊Dic47—24no—
242C22⋊Dic47C2×D414yes—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4C2×D414yes—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47—24no—
249C4⋊Dic47—21no—
250C4⋊Dic47—21no—
251C4⋊Dic47—24no—
252C4⋊Dic47C2412yes—
253C4⋊Dic47C2412yes—
254C4⋊Dic47C2412yes—
255C4⋊Dic47C2412yes—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4C2×D414yes—
261C4×Dic47—24no—
262C4×Dic47—24no—
263C4×Dic47—24no—
264C4×Dic47C2×D412yes—
265C4×Dic47C2412yes—
266C2×C47⋊C8—22no—
267C2×C47⋊C8—22no—
268C2×C47⋊C8C2412yes—
269C2×C47⋊C8C2412yes—
270#10625324—28no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—42no—
276C23×C47—42no—
277C23×C47—42no—
278C23×C47C22×D412yes—
279C23×C47C22×D411yescharacteristic
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47C22×D412yes—
284Q8×C47—22no—
285Q8×C47—22no—
286Q8×C47—42no—
287D4×C47—22no—
288D4×C47—22no—
289D4×C47—42no—
290D4×C47—84no—
291C2×C4×C47—22no—
292C2×C4×C47—24no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47C22×D412yes—
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47C2×#4112yes—
304C2×C4×C472−1+412yes—
305C2×C4×C47C2511yescharacteristic
306C22⋊D47—28no—
307C22⋊D47—84no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—48no—
319C2×Dic47—84no—
320C2×Dic47#13714yes—
321C2×Dic47C22×D412yes—
322C2×Dic47C22×D412yes—
323C2×Dic47C22×D412yes—
324C4×D47—24no—
325C4×D47—22no—
326C4×D47—22no—
327C4×D47—84no—
328Dic94—84no—
329Dic94—84no—
330C8×C47—22no—
331C8×C47C2×#4114yes—
332C47⋊C8—22no—
333C47⋊C8—22no—
334C2×#3357—471nomaximal, Sylow
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—44no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—84no—
343C22×C47#54712yes—
344C22×C47C2×#13712yes—
345C22×C47#57612yes—
346C22×C47C23×D411yescharacteristic
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—44no—
351C4×C47—22no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47#54712yes—
356C4×C47C22×#4111yescharacteristic
357C4×C47C2×2−1+411yescharacteristic
358Dic47—22no—
359Dic47—22no—
360Dic47—42no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47C2×#13714yes—
365C2×#555—471no—
366C2×#554—471no—
367#3357—4716no—
368C2×#500—471no—
369C2×#485—471no—
370C2×#485—471no—
371C2×#480—471no—
372C2×#480—471no—
373C2×#477—471no—
374C2×#476—471no—
375C2×#468—471no—
376C2×#468D4711yescharacteristic, complemented
377C2×C4×SD16—471no—
378C2×#436—471no—
379C2×#428—471no—
380C2×#428—471no—
381C2×C47—42no—
382C2×C47—82no—
383C2×C47#335714yescomplemented
384C2×C47C2×#54711yescharacteristic
385C2×C47C22×#13711yescharacteristic
386C2×C47C2×#57611yescharacteristic
387D47—42no—
388C22×SD16C2×D4711yescharacteristic
389C22×M16—471no—
390C22×M16C2×D4711yescharacteristic
391#555—478no—
392#555—944no—
393#554—478no—
394#554—944no—
395C2×C4⋊Q8—471no—
396C2×C4⋊Q8—471no—
397C2×#125—941no—
398C2×#124—941no—
399C2×#124—941no—
400C2×C22⋊Q8—471no—
401C2×C22⋊Q8—941no—
402C2×C22⋊Q8—941no—
403C2×C22⋊Q8C2×D4711yescharacteristic
404C2×#121—471no—
405C2×#121—941no—
406C2×#121C2×D4711yescharacteristic
407C2×C4×Q8—471no—
408C2×C4×D4—471no—
409C2×C4×D4—471no—
410C2×C4×D4—941no—
411C2×#117—471no—
412C2×#117—471no—
413C2×#117—941no—
414C22×C4⋊C4—471no—
415C22×C4⋊C4—471no—
416#500—478no—
417#485—478no—
418#485—478no—
419#480—478no—
420#480—478no—
421#477—478no—
422#476—478no—
423#468—478no—
424#468C2×D4718yescomplemented
425C4×SD16—478no—
426#436—478no—
427#428—478no—
428#428—478no—
429C2×#107—471no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#107—471no—
433C2×#107—471no—
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×C4×C8—471no—
448C47C2×#335711yescharacteristic, complemented, Sylow
449C22×Q8—941no—
450C22×Q8—941no—
451C22×Q8C22×D4711yescharacteristic
452C22×D4—21no—
453C22×D4—471no—
454C22×D4—941no—
455C22×D4C22×D4711yescharacteristic
456C23×C4—471no—
457C23×C4—941no—
458C23×C4—941no—
459C23×C4—941no—
460C23×C4C22×D4711yescharacteristic
461C2×SD16—24no—
462C2×SD16C22×D4714yes—
463C2×M16—24no—
464C2×M16—474no—
465C2×M16—944no—
466C2×M16C22×D4714yes—
467C22×C8—471no—
468C22×C8—471no—
469C22×C8C22×D4711yescharacteristic
470C22×C8C22×D4711yescharacteristic
471C4⋊Q8—474no—
472C4⋊Q8—474no—
473C4⋊Q8—942no—
474C4⋊Q8—942no—
475#125—948no—
476#124—948no—
477#124—948no—
478C22⋊Q8—22no—
479C22⋊Q8—474no—
480C22⋊Q8—948no—
481C22⋊Q8—948no—
482C22⋊Q8—942no—
483C22⋊Q8C22×D4714yes—
484#121—22no—
485#121—474no—
486#121—942no—
487#121—948no—
488#121C22×D4714yes—
489C4×Q8—474no—
490C4×Q8—942no—
491C4×D4—474no—
492C4×D4—474no—
493C4×D4—474no—
494C4×D4—942no—
495C4×D4—948no—
496#117—474no—
497#117—474no—
498#117—948no—
499#117—942no—
500#117—942no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—474no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—474no—
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—942no—
517C2×C4⋊C4C22×D4711yescharacteristic
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—471no—
522C2×C22⋊C4—471no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—471no—
529C2×C42—941no—
530C2×C42—941no—
531C2×C42—941no—
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—
550C4×C8—474no—
551C24—21no—
552C24—471no—
553C24D4×D4711yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—944no—
558C2×Q8—944no—
559C2×Q8—3762no—
560C2×Q8—3762no—
561C2×Q8C23×D4712yes—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—82no—
567C2×D4—474no—
568C2×D4—944no—
569C2×D4—944no—
570C2×D4—3762no—
571C2×D4C23×D4712yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—471no—
578C22×C4—471no—
579C22×C4—471no—
580C22×C4—472no—
581C22×C4—472no—
582C22×C4—944no—
583C22×C4—944no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—944no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—3762no—
592C22×C4—3762no—
593C22×C4—1884no—
594C22×C4D4×D4712yes—
595C22×C4D4×D4711yescharacteristic
596C22×C4C23×D4712yes—
597C22×C4C23×D4711yescharacteristic
598SD16—28no—
599M16—28no—
600M16—948no—
601C2×C8—22no—
602C2×C8—472no—
603C2×C8—472no—
604C2×C8—942no—
605C2×C8—942no—
606C2×C8#1062535214yes—
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—941no—
623C4⋊C4—944no—
624C4⋊C4—941no—
625C4⋊C4—941no—
626C4⋊C4—941no—
627C4⋊C4C23×D4712yes—
628C4⋊C4C23×D4712yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—474no—
632C22⋊C4—474no—
633C22⋊C4—944no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C42—472no—
639C42—472no—
640C42—944no—
641C42—944no—
642C42—944no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—472no—
651C23—942no—
652C23—942no—
653C23—942no—
654C23C2×D4×D4712yes—
655C23C2×D4×D4711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—3764no—
660Q8—3764no—
661D4—22no—
662D4—22no—
663D4—42no—
664D4—84no—
665D4—948no—
666D4—3764no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—474no—
678C2×C4—472no—
679C2×C4—472no—
680C2×C4—472no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—944no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—3764no—
691C2×C4—3764no—
692C2×C4—1888no—
693C2×C4—1882no—
694C2×C4—1882no—
695C2×C4—1882no—
696C2×C4—1882no—
697C2×C4C2×D4×D4712yes—
698C2×C4C2×D4×D4711yescharacteristic
699C2×C4C2×#1062535212yes—
700C2×C4#1309407112yes—
701C2×C4C24×D4711yescharacteristic
702C8—22no—
703C8—942no—
704C8—942no—
705C8C2×#1062535214yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—942no—
715C22—942no—
716C22—942no—
717C22—1884no—
718C22#1568977312yes—
719C22#137×D4712yes—
720C22#1568992712yes—
721C22C22×D4×D4711yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—474no—
727C4—942no—
728C4—942no—
729C4—1882no—
730C4—1882no—
731C4—1882no—
732C4—1882no—
733C4#1568977312yes—
734C4C22×#1062535211yescharacteristic
735C4C2×#1309407111yescharacteristic
736C2—42no—
737C2—82no—
738C2—1882no—
739C2#2025600914yesdirect product factor
740C2C2×#1568977311yescharacteristic
741C2C2×#137×D4711yescharacteristic
742C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
prime radicalC2×#15689837C2
hypercenterC2×#468D47
hypocenterC47C2×#3357
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
2. C2×#15689831C2semidirect
3. #20256009C2direct (N × H)
4. C2×#15689527C2semidirect
5. C2×#15689462C2semidirect
6. C2×#15689461C2semidirect
7. C2×#15689435C2semidirect
8. C2×#15689434C2semidirect
9. C2×#15689416C2semidirect
10. C2×#15689411C2semidirect
11. C2×#15689366C2semidirect
12. C2×SD16×Dic47C2semidirect
13. C2×#15689199C2semidirect
14. C2×#15689165C2semidirect
15. C2×#15689164C2semidirect
16. C2×C47×#468C2semidirect
21. #15689831C22semidirect
41. #15689527C22semidirect
42. #15689462C22semidirect
43. #15689461C22semidirect
44. #15689435C22semidirect
45. #15689434C22semidirect
46. #15689416C22semidirect
47. #15689411C22semidirect
48. #15689366C22semidirect
49. SD16×Dic47C22semidirect
50. #15689199C22semidirect
51. #15689165C22semidirect
52. #15689164C22semidirect
73. C47×#468C22semidirect
376. C2×#468D47semidirect
383. C2×C47#3357semidirect
424. #468C2×D47semidirect
448. C47C2×#3357semidirect
739. C2#20256009direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898372
C2×#156898312
#202560092
C2×#156895272
C2×#156894622
C2×#156894612
C2×#156894352
C2×#156894342
C2×#156894162
C2×#156894112
C2×#156893662
C2×SD16×Dic472
C2×#156891992
C2×#156891652
C2×#156891642
C2×C47×#4682
C2×#335747