Finite Group Databasebeta

← C2×#20254846 #27089240

Subgroups — C2×#20254846 #27089240

Order 12032.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689742C211yesmaximal, characteristic, complemented
2C2×#15689738C211yesmaximal, characteristic, complemented
3#20254846C2116yesmaximal, direct product factor
4C2×#15689419C211yesmaximal, characteristic, complemented
5C2×#15689416C211yesmaximal, characteristic, complemented
6C2×#15689403C211yesmaximal, characteristic, complemented
7C2×#15689401C211yesmaximal, characteristic, complemented
8C2×#15689368C211yesmaximal, characteristic, complemented
9C2×#15689366C211yesmaximal, characteristic, complemented
10C2×#15689363C211yesmaximal, characteristic, complemented
11C2×#15689356C211yesmaximal, characteristic
12C2×#15689343C211yesmaximal, characteristic, complemented
13C2×#15689342C211yesmaximal, characteristic, complemented
14C2×#15689336C211yesmaximal, characteristic, complemented
15C2×#15689148C211yesmaximal, characteristic, complemented
16C2×C47×#463C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625335C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689742—24no—
22#15689742C2218yescomplemented
23#15689738—24no—
24#15689738C2218yescomplemented
25C2×#13094024C2211yescharacteristic
26C2×#13094023C2211yescharacteristic
27C2×#13094017—21no—
28C2×#13094017—21no—
29C2×#13094011C2211yescharacteristic
30C2×#13094010—21no—
31C2×#13094010—21no—
32C2×#13094008—21no—
33C2×#13094007—21no—
34C2×#13094004C2211yescharacteristic
35C2×#13094003—21no—
36C2×#13094001—21no—
37C2×#13094000C2211yescharacteristic
38C2×#13093995C2211yescharacteristic
39C2×#13093995C2211yescharacteristic
40C2×Q8×Dic47C2211yescharacteristic
41C2×C4×Dic94C2211yescharacteristic
42C2×D4×Dic47C2211yescharacteristic
43C2×#13093981C2211yescharacteristic
44#15689419C2218yescomplemented
45#15689416C2218yescomplemented
46#15689403C2218yescomplemented
47#15689401C2218yescomplemented
48#15689368C2218yescomplemented
49#15689366C2218yescomplemented
50#15689363C2218yescomplemented
51#15689356C2218yes—
52#15689343C2218yescomplemented
53#15689342C2218yescomplemented
54#15689336C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093958C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093957C2211yescharacteristic
59#15689148C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093945C2211yescharacteristic
67C2×#13093945C2211yescharacteristic
68C2×#13093945C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C22×D8×C47C2211yescharacteristic
71C2×#124×C47C2211yescharacteristic
72C2×C4×D4×C47C2211yescharacteristic
73C47×#463C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×Dic94C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C22⋊D47—21no—
82C23×Dic47—21no—
83C22×C4×D47C2311yescharacteristic
84C2×#10625337—42no—
85C2×#10625337C2314yes—
86C2×#10625335—42no—
87C2×#10625335C2314yes—
88C2×#10625324—42no—
89C2×#10625324C2314yes—
90C22×C47⋊C8C2311yescharacteristic
91C22×C47⋊C8C2311yescharacteristic
92C2×C8×D47—42no—
93C2×C8×D47C2314yes—
94#13094024—22no—
95#13094024C2314yes—
96#13094023—22no—
97#13094023C2314yes—
98#13094017—28no—
99#13094017—28no—
100#13094011—22no—
101#13094011C2314yes—
102#13094010—28no—
103#13094010—28no—
104#13094008—28no—
105#13094007—28no—
106#13094004—22no—
107#13094004C2314yes—
108#13094003—28no—
109#13094001—28no—
110#13094000—22no—
111#13094000C2314yes—
112#13093995—22no—
113#13093995—22no—
114#13093995C2314yes—
115#13093995C2314yes—
116Q8×Dic47—22no—
117Q8×Dic47C2314yes—
118C4×Dic94—22no—
119C4×Dic94C2314yes—
120D4×Dic47—22no—
121D4×Dic47C2314yes—
122#13093981D414yes—
123#13093981C2314yes—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4D411yescharacteristic
134C2×Dic47⋊C4D411yescharacteristic
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4D411yescharacteristic
143C2×(C2×D47)⋊C4D411yescharacteristic
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093958C2314yes—
148#13093958C2314yes—
149#13093957C2314yes—
150#13093957C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152Dic47⋊C8C2314yes—
153Dic47⋊C8C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093948C2314yes—
157#13093945C2314yes—
158#13093945C2314yes—
159#13093945C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×D4×C47C2311yescharacteristic
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47—21no—
164C2×SD16×C47—42no—
165C2×SD16×C47C2314yes—
166C2×D8×C47—42no—
167C2×D8×C47C2314yes—
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170#124×C47—22no—
171#124×C47C2314yes—
172C4×D4×C47—22no—
173C4×D4×C47C2314yes—
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C22⋊C4×C47—21no—
178C2×C42×C47C2311yescharacteristic
179C4⋊C8×C47C2314yes—
180#103×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C24×C47—21no—
184C23×D47C2×D411yescharacteristic
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47C2412yes—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47C2412yes—
196C2×D4×C47C2412yes—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—24no—
200C22×C4×C47—82no—
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2411yescharacteristic
204C2×C22⋊D47—24no—
205C2×C22⋊D47—24no—
206C2×C22⋊D47—82no—
207C2×C22⋊D47—82no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—24no—
213C22×Dic47—82no—
214C22×Dic47C2×D411yescharacteristic
215C22×Dic47C2×D411yescharacteristic
216C22×Dic47C2×D411yescharacteristic
217C2×C4×D47—22no—
218C2×C4×D47—22no—
219C2×C4×D47C2×D412yes—
220C2×C4×D47C2412yes—
221C2×Dic94—22no—
222C2×Dic94—22no—
223C2×Dic94—21no—
224C2×Dic94—24no—
225C2×Dic94—24no—
226C2×Dic94—82no—
227C2×Dic94—82no—
228C2×Dic94C2412yes—
229SD16×C47—44no—
230D8×C47—44no—
231C2×C8×C47—22no—
232C2×C8×C47—22no—
233C2×C8×C47C2412yes—
234C2×C8×C47C2412yes—
235C4⋊C4×C47—21no—
236C4⋊C4×C47C2412yes—
237C22⋊C4×C47—24no—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—24no—
240C42×C47C2×D412yes—
241C42×C47C2412yes—
242C22⋊Dic47—24no—
243C22⋊Dic47—24no—
244C22⋊Dic47—24no—
245C22⋊Dic47—24no—
246C22⋊Dic47—24no—
247#10625337—44no—
248#10625335—44no—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4C2×D414yes—
252(C2×D47)⋊C4C2×D414yes—
253C4⋊Dic47—24no—
254C4⋊Dic47—21no—
255C4⋊Dic47—21no—
256C4⋊Dic47—21no—
257C4⋊Dic47—24no—
258C4⋊Dic47—24no—
259C4⋊Dic47C2412yes—
260C4⋊Dic47C2412yes—
261C4⋊Dic47C2412yes—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4C2×D414yes—
266Dic47⋊C4C2×D414yes—
267C4×Dic47—24no—
268C4×Dic47—24no—
269C4×Dic47C2×D412yes—
270C4×Dic47C2412yes—
271C2×C47⋊C8—22no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8C2412yes—
274C2×C47⋊C8C2412yes—
275#10625324—44no—
276C8×D47—44no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—42no—
280C23×C47—42no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47—42no—
285C23×C47C22×D411yescharacteristic
286C22×D47—22no—
287C22×D47—22no—
288C22×D47—22no—
289C22×D47C22×D412yes—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—42no—
293D4×C47—22no—
294D4×C47—22no—
295D4×C47—22no—
296D4×C47—22no—
297D4×C47—42no—
298D4×C47—42no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47—84no—
306C2×C4×C47C22×D412yes—
307C2×C4×C47C22×D412yes—
308C2×C4×C47C22×D411yescharacteristic
309C2×C4×C47H(5,𝔽2)12yes—
310C2×C4×C472−1+412yes—
311C2×C4×C47C2511yescharacteristic
312C22⋊D47—84no—
313C22⋊D47—84no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—84no—
326C2×Dic47C22×D412yes—
327C2×Dic47C22×D412yes—
328C2×Dic47C22×D412yes—
329C4×D47—24no—
330C4×D47—22no—
331C4×D47—22no—
332Dic94—22no—
333Dic94—22no—
334Dic94—42no—
335Dic94—84no—
336Dic94—84no—
337C8×C47—22no—
338C8×C47—22no—
339C47⋊C8—22no—
340C47⋊C8—22no—
341C2×#3262—471nomaximal, Sylow
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—42no—
348C22×C47—84no—
349C22×C47—84no—
350C22×C47#53712yes—
351C22×C47#57612yes—
352C22×C47#57812yes—
353C22×C47C23×D411yescharacteristic
354C2×D47—22no—
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—44no—
358C4×C47—22no—
359C4×C47—22no—
360C4×C47—42no—
361C4×C47—42no—
362C4×C47#53712yes—
363C4×C47C2×H(5,𝔽2)11yescharacteristic
364C4×C47C2×2−1+411yescharacteristic
365Dic47—22no—
366Dic47—22no—
367Dic47—22no—
368Dic47—42no—
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#542—471no—
373C2×#542—471no—
374#3262—4716no—
375C2×#477—471no—
376C2×#477—471no—
377C2×#474—471no—
378C2×#474—471no—
379C2×#468—471no—
380C2×#468—471no—
381C2×#467—471no—
382C2×#466—471no—
383C2×#464—471no—
384C2×#464—471no—
385C2×#463—471no—
386C2×#463D4711yescharacteristic, complemented
387C2×#424—471no—
388C2×C47—82no—
389C2×C47—82no—
390C2×C47#326214yescomplemented
391C2×C47C2×#53711yescharacteristic
392C2×C47C2×#57611yescharacteristic
393C2×C47C2×#57811yescharacteristic
394D47—42no—
395C22×Q16—471no—
396C22×SD16—471no—
397C22×SD16C2×D4711yescharacteristic
398C22×D8C2×D4711yescharacteristic
399C22×M16—471no—
400C23×C8—471no—
401#542—478no—
402#542—478no—
403#542—944no—
404#542—944no—
405C2×C4⋊Q8—471no—
406C2×C4⋊Q8—471no—
407C2×#126—941no—
408C2×#126—941no—
409C2×#124—471no—
410C2×#124—941no—
411C2×#124—941no—
412C2×#124C2×D4711yescharacteristic
413C2×#123—941no—
414C2×#123—941no—
415C2×C22⋊Q8—471no—
416C2×C22⋊Q8—471no—
417C2×C22⋊Q8—941no—
418C2×C22⋊Q8—941no—
419C2×#121—471no—
420C2×#121—471no—
421C2×C4×Q8—471no—
422C2×C4×Q8—471no—
423C2×C4×D4—471no—
424C2×C4×D4C2×D4711yescharacteristic
425C2×#117—471no—
426#477—478no—
427#477—478no—
428#474—478no—
429#474—478no—
430#468—478no—
431#468—478no—
432#467—478no—
433#466—478no—
434#464—478no—
435#464—478no—
436#463—478no—
437#463C2×D4718yescomplemented
438C2×#107—471no—
439C2×#107—471no—
440C2×#107—471no—
441C2×#107—471no—
442#424—478no—
443C2×C4⋊C8—471no—
444C2×C4⋊C8—471no—
445C2×C4⋊C8—471no—
446C2×C4⋊C8C2×D4711yescharacteristic
447C2×#103—471no—
448C2×#103—471no—
449C2×#103—471no—
450C2×#103C2×D4711yescharacteristic
451C2×#102—471no—
452C2×#102—471no—
453C2×#102—471no—
454C2×#102C2×D4711yescharacteristic
455C47C2×#326211yescharacteristic, complemented, Sylow
456C22×Q8—471no—
457C22×Q8—941no—
458C22×Q8—941no—
459C22×Q8C22×D4711yescharacteristic
460C22×D4—941no—
461C22×D4—941no—
462C22×D4C22×D4711yescharacteristic
463C22×D4C22×D4711yescharacteristic
464C23×C4—21no—
465C23×C4—471no—
466C23×C4—941no—
467C2×Q16—474no—
468C2×Q16—1882no—
469C2×SD16—42no—
470C2×SD16—474no—
471C2×SD16—1882no—
472C2×SD16C22×D4714yes—
473C2×D8—42no—
474C2×D8C22×D4714yes—
475C2×M16—474no—
476C2×M16—1882no—
477C22×C8—471no—
478C22×C8—471no—
479C22×C8—474no—
480C22×C8—1882no—
481C22×C8C22×D4711yescharacteristic
482C22×C8C22×D4711yescharacteristic
483C4⋊Q8—474no—
484C4⋊Q8—474no—
485C4⋊Q8—942no—
486C4⋊Q8—942no—
487#126—948no—
488#126—948no—
489#124—22no—
490#124—474no—
491#124—942no—
492#124—948no—
493#124—948no—
494#124C22×D4714yes—
495#123—948no—
496#123—948no—
497C22⋊Q8—474no—
498C22⋊Q8—474no—
499C22⋊Q8—948no—
500C22⋊Q8—942no—
501C22⋊Q8—948no—
502C22⋊Q8—942no—
503#121—474no—
504#121—474no—
505#121—942no—
506#121—942no—
507C4×Q8—474no—
508C4×Q8—474no—
509C4×Q8—942no—
510C4×Q8—942no—
511C4×D4—22no—
512C4×D4—474no—
513C4×D4—942no—
514C4×D4C22×D4714yes—
515#117—474no—
516#117—474no—
517C2×C4⋊C4—471no—
518C2×C4⋊C4—471no—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—471no—
533C2×C22⋊C4—471no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C22⋊C4—941no—
538C2×C22⋊C4—941no—
539C2×C22⋊C4—941no—
540C2×C22⋊C4—941no—
541C2×C42—471no—
542C2×C42—941no—
543C2×C42—941no—
544C2×C42C22×D4711yescharacteristic
545#107—474no—
546#107—474no—
547#107—474no—
548#107—474no—
549C4⋊C8—474no—
550C4⋊C8—474no—
551C4⋊C8—474no—
552C4⋊C8C22×D4714yes—
553#103—474no—
554#103—474no—
555#103—474no—
556#103C22×D4714yes—
557#102—474no—
558#102—474no—
559#102—474no—
560#102C22×D4714yes—
561C24—21no—
562C24—21no—
563C24—471no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—472no—
568C2×Q8—944no—
569C2×Q8—944no—
570C2×Q8—941no—
571C2×Q8—942no—
572C2×Q8—942no—
573C2×Q8—3762no—
574C2×Q8—3762no—
575C2×Q8C23×D4712yes—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—944no—
583C2×D4—944no—
584C2×D4—3762no—
585C2×D4—3762no—
586C2×D4C23×D4712yes—
587C2×D4C23×D4712yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—82no—
592C22×C4—471no—
593C22×C4—471no—
594C22×C4—471no—
595C22×C4—472no—
596C22×C4—472no—
597C22×C4—944no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—3762no—
605C22×C4D4×D4711yescharacteristic
606C22×C4D4×D4711yescharacteristic
607C22×C4C23×D4711yescharacteristic
608Q16—1884no—
609SD16—44no—
610SD16—1884no—
611D8—44no—
612M16—1884no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—472no—
616C2×C8—472no—
617C2×C8—942no—
618C2×C8—942no—
619C2×C8—1884no—
620C2×C8C23×D4712yes—
621C2×C8C23×D4712yes—
622C4⋊C4—21no—
623C4⋊C4—474no—
624C4⋊C4—474no—
625C4⋊C4—472no—
626C4⋊C4—472no—
627C4⋊C4—472no—
628C4⋊C4—944no—
629C4⋊C4—944no—
630C4⋊C4—944no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—941no—
634C4⋊C4—941no—
635C4⋊C4—941no—
636C4⋊C4—944no—
637C4⋊C4C23×D4712yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—474no—
642C22⋊C4—474no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C22⋊C4—944no—
649C22⋊C4—944no—
650C42—472no—
651C42—472no—
652C42—944no—
653C42—944no—
654C42D4×D4712yes—
655C42C23×D4712yes—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—472no—
665C23—942no—
666C23—942no—
667C23—942no—
668C23C2×D4×D4711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—942no—
673Q8—942no—
674Q8—3764no—
675Q8—3764no—
676Q8—1882no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—42no—
682D4—42no—
683D4—3764no—
684D4—3764no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—84no—
692C2×C4—472no—
693C2×C4—472no—
694C2×C4—472no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—944no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—3764no—
706C2×C4—1882no—
707C2×C4—1882no—
708C2×C4—1882no—
709C2×C4—1882no—
710C2×C4C2×D4×D4712yes—
711C2×C4C2×D4×D4712yes—
712C2×C4C2×D4×D4711yescharacteristic
713C2×C4#1309406912yes—
714C2×C4#1309407112yes—
715C2×C4C24×D4711yescharacteristic
716C8—22no—
717C8—22no—
718C8—942no—
719C8—942no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—84no—
728C22—942no—
729C22—942no—
730C22—942no—
731C22—1884no—
732C22#1568970212yes—
733C22#1568992712yes—
734C22#1568993712yes—
735C22C22×D4×D4711yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—942no—
741C4—942no—
742C4—942no—
743C4—1882no—
744C4—1882no—
745C4—1882no—
746C4—1882no—
747C4#1568970212yes—
748C4C2×#1309406911yescharacteristic
749C4C2×#1309407111yescharacteristic
750C2—82no—
751C2—82no—
752C2—1882no—
753C2#2025484614yesdirect product factor
754C2C2×#1568970211yescharacteristic
755C2C2×#1568992711yescharacteristic
756C2C2×#1568993711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#463C2
socleC23×C47C22×D4
prime radicalC2×#15689356C2
hypercenterC2×#463D47
hypocenterC47C2×#3262
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#15689742C2semidirect
2. C2×#15689738C2semidirect
3. #20254846C2direct (N × H)
4. C2×#15689419C2semidirect
5. C2×#15689416C2semidirect
6. C2×#15689403C2semidirect
7. C2×#15689401C2semidirect
8. C2×#15689368C2semidirect
9. C2×#15689366C2semidirect
10. C2×#15689363C2semidirect
12. C2×#15689343C2semidirect
13. C2×#15689342C2semidirect
14. C2×#15689336C2semidirect
15. C2×#15689148C2semidirect
16. C2×C47×#463C2semidirect
22. #15689742C22semidirect
24. #15689738C22semidirect
44. #15689419C22semidirect
45. #15689416C22semidirect
46. #15689403C22semidirect
47. #15689401C22semidirect
48. #15689368C22semidirect
49. #15689366C22semidirect
50. #15689363C22semidirect
52. #15689343C22semidirect
53. #15689342C22semidirect
54. #15689336C22semidirect
59. #15689148C22semidirect
73. C47×#463C22semidirect
386. C2×#463D47semidirect
390. C2×C47#3262semidirect
437. #463C2×D47semidirect
455. C47C2×#3262semidirect
753. C2#20254846direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897422
C2×#156897382
#202548462
C2×#156894192
C2×#156894162
C2×#156894032
C2×#156894012
C2×#156893682
C2×#156893662
C2×#156893632
C2×#156893562
C2×#156893432
C2×#156893422
C2×#156893362
C2×#156891482
C2×C47×#4632
C2×#326247