Finite Group Databasebeta

← C2×#20255830 #27094811

Subgroups — C2×#20255830 #27094811

Order 12032.

2094 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×#15689813C211yesmaximal, characteristic, complemented
2C2×#15689777C211yesmaximal, characteristic
3#20255830C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689459C211yesmaximal, characteristic, complemented
6C2×#15689448C211yesmaximal, characteristic, complemented
7C2×#15689454C211yesmaximal, characteristic, complemented
8C2×#15689437C211yesmaximal, characteristic, complemented
9C2×#15689419C211yesmaximal, characteristic, complemented
10C2×#15689424C211yesmaximal, characteristic, complemented
11C2×#15689369C211yesmaximal, characteristic, complemented
12C2×#15689352C211yesmaximal, characteristic, complemented
13C2×#15689225C211yesmaximal, characteristic, complemented
14C2×#15689165C211yesmaximal, characteristic, complemented
15C22×#13093958C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic, complemented
17C22×#10625352—21no—
18C22×#10625325C2211yescharacteristic
19#15689813—24no—
20#15689813C2218yescomplemented
21#15689777—24no—
22#15689777C2218yes—
23C2×#13094024C2211yescharacteristic
24C2×#13094017—21no—
25C2×#13094016C2211yescharacteristic
26C2×#13094014—21no—
27C2×#13094008—21no—
28C2×#13094008—21no—
29C2×#13094005—21no—
30C2×#13094004—21no—
31C2×#13094003C2211yescharacteristic
32C2×#13094003C2211yescharacteristic
33C2×#13093998C2211yescharacteristic
34C2×#13093998C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37C2×#13093983C2211yescharacteristic
38C2×#13093980—21no—
39C22×C4⋊Dic47C2211yescharacteristic
40C22×C4⋊Dic47C2211yescharacteristic
41C22×C4⋊Dic47C2211yescharacteristic
42#15689532C2218yescomplemented
43#15689459C2218yescomplemented
44#15689454C2218yescomplemented
45#15689448C2218yescomplemented
46#15689437C2218yescomplemented
47#15689424C2218yescomplemented
48#15689419C2218yescomplemented
49#15689369C2218yescomplemented
50#15689352C2218yescomplemented
51#15689225C2218yescomplemented
52#15689165C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093958C2211yescharacteristic
56C2×#13093958C2211yescharacteristic
57C2×#13093958C2211yescharacteristic
58C2×#13093958C2211yescharacteristic
59C2×#13093958C2218yescomplemented
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
77C2×#10625352—28no—
78C2×#10625352—48no—
79C22×Dic94—21no—
80C22×Dic94C2311yescharacteristic
81C22×D188C2311yescharacteristic
82C22×C22⋊D47—21no—
83C22×C22⋊D47—21no—
84C23×Dic47—21no—
85C23×Dic47—21no—
86C23×Dic47—21no—
87C22×C4×D47—21no—
88C2×#10625325—24no—
89C2×#10625325C2314yes—
90#13094024—22no—
91#13094024C2314yes—
92#13094017—28no—
93#13094016—22no—
94#13094016C2314yes—
95#13094014—28no—
96#13094008—28no—
97#13094008—28no—
98#13094005—28no—
99#13094004—28no—
100#13094003—22no—
101#13094003—22no—
102#13094003C2314yes—
103#13094003C2314yes—
104#13093998—22no—
105#13093998—22no—
106#13093998C2314yes—
107#13093998C2314yes—
108C4×Dic94—22no—
109C4×Dic94C2314yes—
110C4×D188—22no—
111C4×D188C2314yes—
112#13093983—22no—
113#13093983C2314yes—
114#13093980—28no—
115C2×C4⋊Dic47—22no—
116C2×C4⋊Dic47—22no—
117C2×C4⋊Dic47—22no—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47C2314yes—
123C2×C4⋊Dic47C2314yes—
124C2×C4⋊Dic47C2314yes—
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144#13093958C2314yes—
145#13093958C2314yes—
146#13093958C2314yes—
147#13093958C2314yes—
148#13093958C2314yes—
149#13093958C2314yes—
150#13093956C2314yes—
151#13093956C2314yes—
152#13093956C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
158#13093946C2314yes—
159C22×D4×C47D411yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C23×C4×C47C2311yescharacteristic
162C2×M16×C47—24no—
163C2×M16×C47C2314yes—
164C22×C8×C47—24no—
165C22×C8×C47C2314yes—
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C4×D4×C47D414yes—
171C4×D4×C47C2314yes—
172C2×C4⋊C4×C47D411yescharacteristic
173C2×C22⋊C4×C47D411yescharacteristic
174C2×C22⋊C4×C47D411yescharacteristic
175C2×C42×C47C2311yescharacteristic
176C4⋊C8×C47C2314yes—
177C22⋊C8×C47C2314yes—
178C22⋊C8×C47C2314yes—
179#97×C47C2314yes—
180C24×C47C2×D411yescharacteristic
181C24×C47C2×D411yescharacteristic
182C23×D47—21no—
183C2×D4×C47—24no—
184C2×D4×C47C2×D414yes—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D412yes—
194C22×C4×C47C2×D412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2411yescharacteristic
198C2×C22⋊D47—24no—
199C2×C22⋊D47—24no—
200C2×C22⋊D47—44no—
201C2×C22⋊D47—44no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—24no—
210C22×Dic47—24no—
211C22×Dic47—24no—
212C22×Dic47—44no—
213C22×Dic47—44no—
214C22×Dic47—44no—
215#10625352—432no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188—21no—
219C2×D188C2412yes—
220C2×C4×D47—24no—
221C2×C4×D47—44no—
222C2×Dic94—22no—
223C2×Dic94—22no—
224C2×Dic94—21no—
225C2×Dic94—24no—
226C2×Dic94—44no—
227C2×Dic94C2412yes—
228M16×C47—28no—
229C2×C8×C47—22no—
230C2×C8×C47—22no—
231C2×C8×C47—22no—
232C2×C8×C47—28no—
233C2×C8×C47#4114yescomplemented
234C2×C8×C47C2412yes—
235C2×C8×C47C2412yes—
236C2×C8×C47C2412yes—
237C2×C8×C47C2412yes—
238C4⋊C4×C47C2×D414yes—
239C22⋊C4×C47C2×D414yes—
240C22⋊C4×C47C2×D414yes—
241C42×C47C2×D412yes—
242C42×C47C2412yes—
243C22⋊Dic47—24no—
244C22⋊Dic47—24no—
245C22⋊Dic47—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249C4⋊Dic47—21no—
250C4⋊Dic47—21no—
251C4⋊Dic47—21no—
252C4⋊Dic47—21no—
253C4⋊Dic47—21no—
254C4⋊Dic47—24no—
255C4⋊Dic47—24no—
256C4⋊Dic47—24no—
257C4⋊Dic47—24no—
258C4⋊Dic47—21no—
259C4⋊Dic47C2412yes—
260C4⋊Dic47C2412yes—
261C4⋊Dic47C2412yes—
262C4⋊Dic47C2412yes—
263C4⋊Dic47C2412yes—
264C4⋊Dic47C2412yes—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268Dic47⋊C4—24no—
269Dic47⋊C4—24no—
270C4×Dic47—24no—
271C4×Dic47—24no—
272#10625325—28no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47AGL(1,ℤ/8)14yes—
279C23×C47C22×D412yes—
280C23×C47C22×D412yes—
281C23×C47C22×D411yescharacteristic
282C22×D47—22no—
283C22×D47—42no—
284C22×D47—42no—
285C22×D47—42no—
286D4×C47—28no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—24no—
292C2×C4×C47—24no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D412yes—
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—48no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—48no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—48no—
320C2×Dic47—48no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324D188—22no—
325D188—22no—
326D188—42no—
327C4×D47—48no—
328Dic94—22no—
329Dic94—22no—
330Dic94—48no—
331Dic94—42no—
332C8×C47—22no—
333C8×C47—22no—
334C8×C47—22no—
335C8×C47C2×#4114yescomplemented
336C2×#3343—471nomaximal, Sylow
337C22×C47—28no—
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—44no—
344C22×C47#54712yes—
345C22×C47C2×AGL(1,ℤ/8)14yes—
346C22×C47C2×AGL(1,ℤ/8)12yes—
347C22×C47#57812yes—
348C22×C47C23×D411yescharacteristic
349C2×D47—42no—
350C2×D47—42no—
351C2×D47—42no—
352C2×D47—84no—
353C4×C47—22no—
354C4×C47—22no—
355C4×C47—22no—
356C4×C47—22no—
357C4×C47#54712yes—
358C4×C47C22×#4111yescharacteristic
359C4×C47C2×2−1+411yescharacteristic
360Dic47—42no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47—42no—
365Dic47—42no—
366Dic47—42no—
367C2×#552—471no—
368C2×#547—471no—
369#3343—4716no—
370C2×#501—471no—
371C2×#484—471no—
372C2×#482—471no—
373C2×#483—471no—
374C2×#480—471no—
375C2×#477—471no—
376C2×#478—471no—
377C2×#468—471no—
378C2×#465—471no—
379C2×#440—471no—
380C2×#435D4711yescharacteristic, complemented
381C2×#428—471no—
382C22×#107—471no—
383C2×C47—24no—
384C2×C47—42no—
385C2×C47#334314yescomplemented
386C2×C47C2×#54711yescharacteristic
387C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
388C2×C47C2×#57811yescharacteristic
389D47—82no—
390C22×#41—941no—
391C22×SD16—471no—
392C22×M16C2×D4711yescharacteristic
393C23×C8C2×D4711yescharacteristic
394#552—478no—
395#552—944no—
396#547—478no—
397#547—944no—
398C2×C4⋊Q8—471no—
399C2×#126—941no—
400C2×#125—471no—
401C2×#125—941no—
402C2×#123—941no—
403C2×#123—941no—
404C2×#123—941no—
405C2×C22⋊Q8—471no—
406C2×C22⋊Q8—471no—
407C2×C22⋊Q8—941no—
408C2×#121—471no—
409C2×#121—471no—
410C2×C4×Q8—471no—
411C2×C4×D4—471no—
412C2×C4×D4C2×D4711yescharacteristic
413C2×#117—471no—
414C2×#117—941no—
415C22×C4⋊C4—471no—
416C22×C4⋊C4—471no—
417C22×C4⋊C4—471no—
418#501—478no—
419#484—478no—
420#483—478no—
421#482—478no—
422#480—478no—
423#478—478no—
424#477—478no—
425#468—478no—
426#465—478no—
427#440—478no—
428#435C2×D4718yescomplemented
429#428—478no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#107—471no—
433C2×#107—471no—
434C2×#107—478no—
435C2×#107—471no—
436C2×#107—471no—
437C2×#106—471no—
438C2×#106—471no—
439C2×#106—471no—
440C2×C4⋊C8C2×D4711yescharacteristic
441C2×#103—471no—
442C2×#103—471no—
443C2×#103—471no—
444C2×#102—471no—
445C2×#102—471no—
446C2×#102—471no—
447C2×C22⋊C8C2×D4711yescharacteristic
448C2×C22⋊C8C2×D4711yescharacteristic
449C2×#97C2×D4711yescharacteristic
450C47C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—948no—
452C2×#41—1888no—
453C22×Q8—471no—
454C22×Q8—941no—
455C22×D4—471no—
456C22×D4—941no—
457C22×D4—941no—
458C22×D4D18811yescharacteristic
459C23×C4—941no—
460C23×C4—941no—
461C23×C4—941no—
462C23×C4—941no—
463C23×C4C22×D4711yescharacteristic
464C23×C4C22×D4711yescharacteristic
465C2×SD16—474no—
466C2×SD16—944no—
467C2×M16—24no—
468C2×M16C22×D4714yes—
469C22×C8—24no—
470C22×C8C22×D4711yescharacteristic
471C22×C8C22×D4714yes—
472C22×C8C22×D4711yescharacteristic
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475C4⋊Q8—474no—
476C4⋊Q8—942no—
477#126—948no—
478#125—474no—
479#125—948no—
480#125—942no—
481#123—948no—
482#123—948no—
483#123—948no—
484C22⋊Q8—474no—
485C22⋊Q8—474no—
486C22⋊Q8—942no—
487C22⋊Q8—942no—
488C22⋊Q8—948no—
489#121—474no—
490#121—474no—
491#121—942no—
492#121—942no—
493C4×Q8—474no—
494C4×Q8—942no—
495C4×D4—474no—
496C4×D4—942no—
497C4×D4D18814yes—
498C4×D4C22×D4714yes—
499#117—474no—
500#117—942no—
501#117—948no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—474no—
508C2×C4⋊C4—474no—
509C2×C4⋊C4—474no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—942no—
515C2×C4⋊C4—942no—
516C2×C4⋊C4—942no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4D18811yescharacteristic
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4—941no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4D18811yescharacteristic
531C2×C22⋊C4D18811yescharacteristic
532C2×C42—941no—
533C2×C42—941no—
534C2×C42C22×D4711yescharacteristic
535#107—474no—
536#107—474no—
537#107—474no—
538#107—474no—
539#107—474no—
540#107—474no—
541#106—474no—
542#106—474no—
543#106—474no—
544C4⋊C8C22×D4714yes—
545#103—474no—
546#103—474no—
547#103—474no—
548#102—474no—
549#102—474no—
550#102—474no—
551C22⋊C8C22×D4714yes—
552C22⋊C8C22×D4714yes—
553#97C22×D4714yes—
554C24—941no—
555C24C2×D18811yescharacteristic
556C24C2×D18811yescharacteristic
557#41—18832no—
558C2×Q8—472no—
559C2×Q8—941no—
560C2×Q8—944no—
561C2×Q8—942no—
562C2×Q8—942no—
563C2×Q8—1884no—
564C2×D4—24no—
565C2×D4—472no—
566C2×D4—944no—
567C2×D4—944no—
568C2×D4—941no—
569C2×D4—942no—
570C2×D4—942no—
571C2×D4—1884no—
572C2×D4—1884no—
573C2×D4C2×D18814yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—944no—
579C22×C4—944no—
580C22×C4—944no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—941no—
587C22×C4—941no—
588C22×C4—944no—
589C22×C4—1884no—
590C22×C4—1884no—
591C22×C4—1884no—
592C22×C4—1884no—
593C22×C4C2×D18812yes—
594C22×C4C2×D18812yes—
595C22×C4C2×D18811yescharacteristic
596C22×C4C2×D18811yescharacteristic
597C22×C4C2×D18811yescharacteristic
598C22×C4C2×D18811yescharacteristic
599C22×C4C23×D4712yes—
600C22×C4C23×D4712yes—
601C22×C4C23×D4711yescharacteristic
602SD16—948no—
603M16—28no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—28no—
608C2×C8#1062535214yescomplemented
609C2×C8C23×D4712yes—
610C2×C8C23×D4712yes—
611C2×C8C23×D4712yes—
612C2×C8C23×D4712yes—
613C4⋊C4—472no—
614C4⋊C4—472no—
615C4⋊C4—472no—
616C4⋊C4—472no—
617C4⋊C4—472no—
618C4⋊C4—472no—
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⋊C4—944no—
630C4⋊C4—941no—
631C4⋊C4—944no—
632C4⋊C4—941no—
633C4⋊C4—944no—
634C4⋊C4C2×D18814yes—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C22⋊C4—944no—
639C22⋊C4—944no—
640C22⋊C4—944no—
641C22⋊C4C2×D18814yes—
642C22⋊C4C2×D18814yes—
643C42—944no—
644C42—944no—
645C42C2×D18812yes—
646C42C23×D4712yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—942no—
653C23—1882no—
654C23—1882no—
655C23—1882no—
656C23#1309405214yes—
657C23C22×D18812yes—
658C23C22×D18812yes—
659C23C22×D18811yescharacteristic
660Q8—942no—
661Q8—942no—
662Q8—1888no—
663Q8—1882no—
664D4—28no—
665D4—942no—
666D4—942no—
667D4—1888no—
668D4—1888no—
669D4—1882no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—1888no—
688C2×C4—1888no—
689C2×C4—1882no—
690C2×C4—1888no—
691C2×C4—1882no—
692C2×C4—1882no—
693C2×C4—1882no—
694C2×C4—1882no—
695C2×C4—1882no—
696C2×C4—1888no—
697C2×C4—1882no—
698C2×C4C22×D18812yes—
699C2×C4C22×D18812yes—
700C2×C4C22×D18812yes—
701C2×C4C22×D18812yes—
702C2×C4C22×D18811yescharacteristic
703C2×C4C2×#1062535212yes—
704C2×C4#1309407112yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8C2×#1062535214yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—3764no—
718C22—1882no—
719C22—1882no—
720C22—1882no—
721C22#1568977712yes—
722C22C2×#1309405214yes—
723C22C2×#1309405212yes—
724C22#1568994012yes—
725C22C23×D18811yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—1882no—
731C4—1882no—
732C4—1882no—
733C4—1882no—
734C4—1882no—
735C4—1882no—
736C4—1882no—
737C4#1568977712yes—
738C4C22×#1062535211yescharacteristic
739C4C2×#1309407111yescharacteristic
740C2—24no—
741C2—42no—
742C2—3762no—
743C2#2025583014yesdirect product factor
744C2C2×#1568977711yescharacteristic
745C2C22×#1309405211yescharacteristic
746C2C2×#1568994011yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C22×D4
prime radicalC2×#15689777C2
hypercenterC2×#435D47
hypocenterC47C2×#3343
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×#15689813C2semidirect
3. #20255830C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689459C2semidirect
6. C2×#15689448C2semidirect
7. C2×#15689454C2semidirect
8. C2×#15689437C2semidirect
9. C2×#15689419C2semidirect
10. C2×#15689424C2semidirect
11. C2×#15689369C2semidirect
12. C2×#15689352C2semidirect
13. C2×#15689225C2semidirect
14. C2×#15689165C2semidirect
15. C22×#13093958C2semidirect
16. C2×C47×#435C2semidirect
20. #15689813C22semidirect
42. #15689532C22semidirect
43. #15689459C22semidirect
44. #15689454C22semidirect
45. #15689448C22semidirect
46. #15689437C22semidirect
47. #15689424C22semidirect
48. #15689419C22semidirect
49. #15689369C22semidirect
50. #15689352C22semidirect
51. #15689225C22semidirect
52. #15689165C22semidirect
59. C2×#13093958C22semidirect
72. C47×#435C22semidirect
233. C2×C8×C47#41semidirect
335. C8×C47C2×#41semidirect
380. C2×#435D47semidirect
385. C2×C47#3343semidirect
428. #435C2×D47semidirect
450. C47C2×#3343semidirect
608. C2×C8#10625352semidirect
709. C8C2×#10625352semidirect
743. C2#20255830direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898132
C2×#156897772
#202558302
C2×#156895322
C2×#156894592
C2×#156894482
C2×#156894542
C2×#156894372
C2×#156894192
C2×#156894242
C2×#156893692
C2×#156893522
C2×#156892252
C2×#156891652
C22×#130939582
C2×C47×#4352
C2×#334347