Finite Group Databasebeta

← C4×#15689374 #26222918

Subgroups — C4×#15689374 #26222918

Order 12032.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689374C211yesmaximal, characteristic
2C2×C4×#10625334C211yesmaximal, characteristic, complemented
3C2×C4×#10625329C211yesmaximal, characteristic, complemented
4C4×#13093998C211yesmaximal, characteristic, complemented
5#20244263C211yesmaximal, characteristic, complemented
6#20244128C211yesmaximal, characteristic, complemented
7#20244088C211yesmaximal, characteristic, complemented
8#20244084C211yesmaximal, characteristic, complemented
9#20243827C211yesmaximal, characteristic, complemented
10#20243824C211yesmaximal, characteristic, complemented
11#20243419C211yesmaximal, characteristic, complemented
12C4×#13093955C211yesmaximal, characteristic, complemented
13C4×#13093944C211yesmaximal, characteristic, complemented
14C4×#13093945C211yesmaximal, characteristic, complemented
15C4×#121×C47C211yesmaximal, characteristic, complemented
16C22×#10625334C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C22×#10625329C2211yescharacteristic
19C2×#13093998C2211yescharacteristic
20C2×C4×D188C2211yescharacteristic
21C2×C4×C22⋊D47—21no—
22#15689374C418yesdirect product factor
23C4×#10625334—24no—
24C2×#13093957C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×#13093955C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093945C2211yescharacteristic
30C2×#13093944C2211yescharacteristic
31C2×#13093944C2211yescharacteristic
32C2×#13093944C2211yescharacteristic
33C4×#10625329—24no—
34C2×#13093935C2211yescharacteristic
35C2×#13093935C2211yescharacteristic
36C2×C4×C47⋊C8C2211yescharacteristic
37C2×C4×C47⋊C8C2211yescharacteristic
38#15689025C2211yescharacteristic
39#15689021C2211yescharacteristic
40#15689014—21no—
41#15689002—21no—
42#15688983C2211yescharacteristic
43C4×C4⋊Dic47C2211yescharacteristic
44C4×(C2×D47)⋊C4—21no—
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51C2×#121×C47C2211yescharacteristic
52C2×C4×D4×C47—21no—
53C2×C4×D4×C47C2211yescharacteristic
54C22×C42×C47C2211yescharacteristic
55C47×#390C2211yescharacteristic
56C47×#389C2211yescharacteristic
57C47×#388—21no—
58C47×#386—21no—
59C47×#380C2211yescharacteristic
60C4×C4⋊C4×C47C2211yescharacteristic
61C4×C22⋊C4×C47—21no—
62C22×D188C2311yescharacteristic
63C22×C22⋊D47—21no—
64C22×C4×D47—21no—
65C2×#10625334—22no—
66C2×#10625334—22no—
67C2×#10625334C2×C414yescomplemented
68C2×#10625329—22no—
69C2×#10625329—22no—
70C2×#10625329—22no—
71C2×#10625329—22no—
72C2×#10625329—22no—
73C2×#10625329C2×C414yescomplemented
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78#13093998—22no—
79#13093998C2×C414yescomplemented
80C4×D188—22no—
81C4×D188—22no—
82C4×C22⋊D47—44no—
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C4⋊Dic47C2311yescharacteristic
85C2×C4⋊Dic47C2311yescharacteristic
86C2×Dic47⋊C4—21no—
87C2×C22⋊Dic47—21no—
88C2×(C2×D47)⋊C4—21no—
89C2×(C2×D47)⋊C4—21no—
90C2×(C2×D47)⋊C4—21no—
91C2×(C2×D47)⋊C4—21no—
92C2×C4×Dic47—21no—
93#13093957—22no—
94#13093955—22no—
95#13093955C2×C414yescomplemented
96#13093945—22no—
97#13093945—22no—
98#13093945C2×C414yescomplemented
99#13093944—22no—
100#13093944—22no—
101#13093944C2×C414yescomplemented
102#13093935—22no—
103#13093935—22no—
104C4×C47⋊C8—22no—
105C4×C47⋊C8D414yescomplemented
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C22×D4×C47—21no—
110C22×D4×C47C2311yescharacteristic
111C23×C4×C47—21no—
112C23×C4×C47D411yescharacteristic
113C23×C4×C47D411yescharacteristic
114C23×C4×C47C2311yescharacteristic
115#121×C47—22no—
116#121×C47C2×C414yescomplemented
117C4×D4×C47—22no—
118C4×D4×C47—22no—
119C4×D4×C47—44no—
120C2×C4⋊C4×C47—21no—
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C4⋊C4×C47C2311yescharacteristic
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C42×C47—22no—
130C2×C42×C47—22no—
131C2×C42×C47—21no—
132C2×C42×C47D411yescharacteristic
133C2×C42×C47D411yescharacteristic
134C2×C42×C47C2311yescharacteristic
135C2×C42×C47C2311yescharacteristic
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139C24×C47—21no—
140C24×C47C2×D411yescharacteristic
141C23×D47—21no—
142C2×D4×C47—24no—
143C2×D4×C47—21no—
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—42no—
149C2×D4×C47—42no—
150C2×D4×C47C22×C412yes—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—41no—
163C22×C4×C47—41no—
164C22×C4×C47—42no—
165C22×C4×C47—42no—
166C22×C4×C47—42no—
167C22×C4×C47C22×C412yes—
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47#4112yes—
174C22×C4×C47C2411yescharacteristic
175C2×C22⋊D47—24no—
176C2×C22⋊D47—42no—
177C2×C22⋊D47—42no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C2×D188—21no—
182C2×D188—21no—
183C2×D188—21no—
184C2×D188—21no—
185C2×D188—21no—
186C2×D188C22×C412yes—
187C2×C4×D47—42no—
188C2×C4×D47—42no—
189C2×C4×D47—42no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—21no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—42no—
196C4⋊C4×C47C22×C412yes—
197C22⋊C4×C47—24no—
198C22⋊C4×C47—42no—
199C22⋊C4×C47—42no—
200C22⋊C4×C47—42no—
201C22⋊C4×C47—42no—
202C42×C47—22no—
203C42×C47—22no—
204C42×C47—21no—
205C42×C47—21no—
206C42×C47—42no—
207C42×C47C2×D412yes—
208C42×C47#4112yes—
209C22⋊Dic47—42no—
210#10625334—28no—
211(C2×D47)⋊C4—24no—
212(C2×D47)⋊C4—42no—
213(C2×D47)⋊C4—42no—
214(C2×D47)⋊C4—42no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47—21no—
220C4⋊Dic47C22×C412yes—
221Dic47⋊C4—42no—
222C4×Dic47—42no—
223#10625329—28no—
224#10625329—28no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8C22×C412yes—
232C2×C47⋊C8C22×C412yes—
233C2×C47⋊C8C2×D412yes—
234C2×C47⋊C8C2×D412yes—
235C2×C47⋊C8#4112yes—
236C2×C47⋊C8#4112yes—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—22no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47C4×D412yes—
251C23×C47C22×D411yescharacteristic
252C22×D47—22no—
253C22×D47—41no—
254C22×D47—41no—
255C22×D47—41no—
256C22×D47—41no—
257C22×D47—41no—
258C22×D47—41no—
259D4×C47—22no—
260D4×C47—22no—
261D4×C47—48no—
262D4×C47—41no—
263D4×C47—41no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—44no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—44no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—84no—
290C2×C4×C47C4×D412yes—
291C2×C4×C47#12112yes—
292C2×C4×C47#12112yes—
293C2×C4×C47AGL(1,ℤ/8)12yes—
294C2×C4×C47AGL(1,ℤ/8)12yes—
295C2×C4×C47C23×C411yescharacteristic
296C2×C4×C47C22×D411yescharacteristic
297C2×C4×C47C2×#4111yescharacteristic
298C2×C4×C47C2×#4111yescharacteristic
299C2×C4×C47C2×#4111yescharacteristic
300C2×C4×C47C2×#4111yescharacteristic
301C22⋊D47—48no—
302C2×Dic47—22no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47—41no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311D188—22no—
312D188—22no—
313D188—41no—
314D188—41no—
315C4×D47—84no—
316C47⋊C8—22no—
317C47⋊C8—22no—
318C47⋊C8—22no—
319C47⋊C8C4×D414yescomplemented
320C4×#469—471nomaximal, Sylow
321C22×C47—22no—
322C22×C47—22no—
323C22×C47—22no—
324C22×C47—41no—
325C22×C47—41no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—42no—
329C22×C47—42no—
330C22×C47—42no—
331C22×C47—81no—
332C22×C47—81no—
333C22×C47—81no—
334C22×C47—81no—
335C22×C47C2×C4×D411yescharacteristic
336C22×C47C2×#12111yescharacteristic
337C22×C47#53211yescharacteristic
338C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C47#57511yescharacteristic
341C22×C47#57511yescharacteristic
342C2×D47—42no—
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—81no—
346C2×D47—81no—
347C2×D47—81no—
348C2×D47—81no—
349C4×C47—22no—
350C4×C47—22no—
351C4×C47—42no—
352C4×C47—41no—
353C4×C47—41no—
354C4×C47—81no—
355C4×C47—81no—
356C4×C47#46914yescomplemented
357C4×C47C2×C4×D411yescharacteristic
358C4×C47C4×#4111yescharacteristic
359C4×C47#52511yescharacteristic
360C4×C47#52911yescharacteristic
361Dic47—42no—
362Dic47—81no—
363Dic47—81no—
364C2×#469—471no—
365C2×C4×D8—471no—
366C2×C4×M16—471no—
367C4×#121—471no—
368C4×#121D4711yescharacteristic, complemented
369#1972—471no—
370#1944—471no—
371#1936—471no—
372#1936—471no—
373#1895—471no—
374#1895—471no—
375#1809—471no—
376C4×#106—471no—
377C4×#102—471no—
378C4×#102—471no—
379C2×C47—42no—
380C2×C47—82no—
381C2×C47C4×#12111yescharacteristic
382C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
383C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
384C2×C47C2×#46911yescharacteristic
385C2×C47#305411yescharacteristic
386C2×C47#317111yescharacteristic
387C2×C47#317111yescharacteristic
388D47—82no—
389C22×D8—471no—
390C22×M16—471no—
391C22×M16—471no—
392C2×#121—471no—
393C2×#121C2×D4711yescharacteristic
394C2×C4×D4—21no—
395C2×C4×D4—471no—
396C2×C4×D4—941no—
397C2×C4×D4C2×D4711yescharacteristic
398C22×C42C2×D4711yescharacteristic
399#469—478no—
400C4×D8—944no—
401C2×#107—471no—
402C2×#106—471no—
403C2×#106—471no—
404C2×#102—471no—
405C2×#102—471no—
406C2×#102—471no—
407C2×#102—471no—
408C2×#102—471no—
409C2×#102—471no—
410C4×M16—944no—
411C2×#97—471no—
412C2×#97—471no—
413C2×C4×C8—471no—
414C2×C4×C8—471no—
415#390—471no—
416#390C2×D4711yescharacteristic
417#389—471no—
418#389C2×D4711yescharacteristic
419#388—21no—
420#388—941no—
421#386—21no—
422#386—941no—
423#380—471no—
424#380C2×D4711yescharacteristic
425C4×C4⋊C4—471no—
426C4×C4⋊C4C2×D4711yescharacteristic
427C4×C22⋊C4—21no—
428C4×C22⋊C4—941no—
429#340—471no—
430#340—471no—
431#340—471no—
432#340—471no—
433#340—471no—
434#340—471no—
435C47C4×#46911yescharacteristic, complemented, Sylow
436C22×D4—21no—
437C22×D4—471no—
438C22×D4—941no—
439C22×D4C22×D4711yescharacteristic
440C23×C4—21no—
441C23×C4—941no—
442C23×C4C22⋊D4711yescharacteristic
443C23×C4C22⋊D4711yescharacteristic
444C23×C4C22×D4711yescharacteristic
445C2×D8—474no—
446C2×D8—942no—
447C2×D8—942no—
448C2×M16—474no—
449C2×M16—942no—
450C2×M16—942no—
451C2×M16—942no—
452C2×M16—942no—
453C2×M16—942no—
454C22×C8—471no—
455C22×C8—471no—
456C22×C8—471no—
457C22×C8—471no—
458#121—22no—
459#121—474no—
460#121—942no—
461#121C4×D4714yescomplemented
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—44no—
465C4×D4—942no—
466C4×D4—942no—
467C4×D4—1884no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—471no—
470C2×C4⋊C4—471no—
471C2×C4⋊C4—471no—
472C2×C4⋊C4—941no—
473C2×C4⋊C4C22×D4711yescharacteristic
474C2×C4⋊C4C22×D4711yescharacteristic
475C2×C4⋊C4C22×D4711yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—941no—
482C2×C22⋊C4—941no—
483C2×C22⋊C4—941no—
484C2×C22⋊C4—941no—
485C2×C22⋊C4—941no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—21no—
489C2×C42—941no—
490C2×C42C22⋊D4711yescharacteristic
491C2×C42C22⋊D4711yescharacteristic
492C2×C42C22×D4711yescharacteristic
493C2×C42C22×D4711yescharacteristic
494#107—942no—
495#106—474no—
496#106—942no—
497#102—474no—
498#102—474no—
499#102—942no—
500#102—942no—
501#102—942no—
502#102—942no—
503#97—942no—
504#97—942no—
505C4×C8—474no—
506C4×C8—942no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—941no—
511#95—941no—
512#95—941no—
513C24—21no—
514C24—941no—
515C24C2×C22⋊D4711yescharacteristic
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—472no—
525C2×D4—944no—
526C2×D4—941no—
527C2×D4—941no—
528C2×D4—941no—
529C2×D4—941no—
530C2×D4—941no—
531C2×D4—1882no—
532C2×D4—1882no—
533C2×D4C2×C4×D4712yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—941no—
551C22×C4—941no—
552C22×C4—941no—
553C22×C4—1882no—
554C22×C4—1882no—
555C22×C4—1882no—
556C22×C4C2×C4×D4712yes—
557C22×C4#1062535012yes—
558C22×C4C2×C22⋊D4711yescharacteristic
559C22×C4C2×C22⋊D4711yescharacteristic
560C22×C4C2×C22⋊D4711yescharacteristic
561C22×C4C2×C22⋊D4711yescharacteristic
562C22×C4C2×C22⋊D4711yescharacteristic
563C22×C4C23×D4711yescharacteristic
564D8—948no—
565M16—948no—
566M16—948no—
567C2×C8—472no—
568C2×C8—472no—
569C2×C8—472no—
570C2×C8—472no—
571C2×C8—472no—
572C2×C8—472no—
573C2×C8—941no—
574C2×C8—941no—
575C2×C8—941no—
576C2×C8—941no—
577C2×C8—941no—
578C2×C8—941no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—42no—
585C4⋊C4—472no—
586C4⋊C4—941no—
587C4⋊C4—941no—
588C4⋊C4—941no—
589C4⋊C4—941no—
590C4⋊C4—941no—
591C4⋊C4—1882no—
592C4⋊C4C2×C4×D4712yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—944no—
599C22⋊C4—1882no—
600C22⋊C4—1882no—
601C22⋊C4—1882no—
602C22⋊C4—1882no—
603C42—22no—
604C42—22no—
605C42—21no—
606C42—21no—
607C42—42no—
608C42—1882no—
609C42D4×D4712yes—
610C42#1062535212yes—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—942no—
625C23—1881no—
626C23—1881no—
627C23—1881no—
628C23—1881no—
629C23—1881no—
630C23—1881no—
631C23C4×C22⋊D4712yes—
632C23C22×C22⋊D4711yescharacteristic
633D4—22no—
634D4—22no—
635D4—48no—
636D4—41no—
637D4—41no—
638D4—942no—
639D4—942no—
640D4—1888no—
641D4—1881no—
642D4—1881no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—44no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—44no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—84no—
669C2×C4—942no—
670C2×C4—3764no—
671C2×C4—1881no—
672C2×C4—1881no—
673C2×C4—1881no—
674C2×C4—1881no—
675C2×C4—1881no—
676C2×C4—1881no—
677C2×C4—1881no—
678C2×C4—1881no—
679C2×C4C4×C22⋊D4712yes—
680C2×C4#1309399612yes—
681C2×C4#1309399612yes—
682C2×C4#1309404912yes—
683C2×C4#1309405012yes—
684C2×C4C22×C4×D4711yescharacteristic
685C2×C4C2×D4×D4711yescharacteristic
686C2×C4#41×D4711yescharacteristic
687C2×C4#41×D4711yescharacteristic
688C2×C4C2×#1062535211yescharacteristic
689C2×C4C2×#1062535011yescharacteristic
690C8—474no—
691C8—942no—
692C8—942no—
693C8—942no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—3761no—
709C22—3761no—
710C22—3761no—
711C22—3761no—
712C22—1882no—
713C22—1882no—
714C22—1882no—
715C22C2×C4×C22⋊D4711yescharacteristic
716C22C2×#1309399611yescharacteristic
717C22#1568966911yescharacteristic
718C22C2×#1309404911yescharacteristic
719C22C2×#1309405011yescharacteristic
720C22#1568992111yescharacteristic
721C22#1568992111yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—41no—
726C4—41no—
727C4—81no—
728C4—81no—
729C4—3761no—
730C4—3761no—
731C4—1882no—
732C4#1568937414yesdirect product factor
733C4C4×D4×D4711yescharacteristic
734C4C4×#1062535211yescharacteristic
735C4#1568963211yescharacteristic
736C4#1568965311yescharacteristic
737C2—42no—
738C2—82no—
739C2—3762no—
740C2C4×#1309399611yescharacteristic
741C2C4×#1309404911yescharacteristic
742C2C4×#1309405011yescharacteristic
743C2C2×#1568937411yescharacteristic
744C2#2025299411yescharacteristic
745C2#2025397711yescharacteristic
746C2#2025398411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#121×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689374C2
cosocleC22×C4×C47C24
hypercenterC4×#121D47
hypocenterC47C4×#469
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625334C2semidirect
3. C2×C4×#10625329C2semidirect
4. C4×#13093998C2semidirect
5. #20244263C2semidirect
6. #20244128C2semidirect
7. #20244088C2semidirect
8. #20244084C2semidirect
9. #20243827C2semidirect
10. #20243824C2semidirect
11. #20243419C2semidirect
12. C4×#13093955C2semidirect
13. C4×#13093944C2semidirect
14. C4×#13093945C2semidirect
15. C4×#121×C47C2semidirect
22. #15689374C4direct (N × H)
67. C2×#10625334C2×C4semidirect
73. C2×#10625329C2×C4semidirect
79. #13093998C2×C4semidirect
95. #13093955C2×C4semidirect
98. #13093945C2×C4semidirect
101. #13093944C2×C4semidirect
105. C4×C47⋊C8D4semidirect
116. #121×C47C2×C4semidirect
319. C47⋊C8C4×D4semidirect
356. C4×C47#469semidirect
368. C4×#121D47semidirect
435. C47C4×#469semidirect
461. #121C4×D47semidirect
732. C4#15689374direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156893742
C2×C4×#106253342
C2×C4×#106253292
C4×#130939982
#202442632
#202441282
#202440882
#202440842
#202438272
#202438242
#202434192
C4×#130939552
C4×#130939442
C4×#130939452
C4×#121×C472
C4×#46947