Finite Group Databasebeta

← C2×#20256468 #27097299

Subgroups — C2×#20256468 #27097299

Order 12032.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689845C211yesmaximal, characteristic, complemented
2C2×#15689843C211yesmaximal, characteristic, complemented
3#20256468C2116yesmaximal, direct product factor
4C2×#15689517C211yesmaximal, characteristic, complemented
5C2×#15689514C211yesmaximal, characteristic, complemented
6C2×#15689504C211yesmaximal, characteristic
7C2×#15689348C211yesmaximal, characteristic, complemented
8C2×#15689344C211yesmaximal, characteristic, complemented
9C2×#15689333C211yesmaximal, characteristic, complemented
10C2×#15689332C211yesmaximal, characteristic, complemented
11C2×#15689338C211yesmaximal, characteristic
12C2×#15689337C211yesmaximal, characteristic
13C2×#15689251C211yesmaximal, characteristic, complemented
14C2×#15689222C211yesmaximal, characteristic, complemented
15C2×#15689217C211yesmaximal, characteristic, complemented
16C2×C47×#440C211yesmaximal, characteristic, complemented
17C22×Dic188C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625337C2211yescharacteristic
21C22×#10625325C2211yescharacteristic
22C22×#10625325C2211yescharacteristic
23C22×#10625335C2211yescharacteristic
24C22×#10625334C2211yescharacteristic
25#15689845—24no—
26#15689845C2218yescomplemented
27#15689843—24no—
28#15689843C2218yescomplemented
29C2×#13094024C2211yescharacteristic
30C2×#13094022C2211yescharacteristic
31C2×#13094019—21no—
32C2×#13094018—21no—
33C2×#13094017—21no—
34C2×#13094017—21no—
35C2×#13094013C2211yescharacteristic
36C2×#13094012C2211yescharacteristic
37C2×#13094011C2211yescharacteristic
38C2×#13094011C2211yescharacteristic
39C2×#13094003—21no—
40C2×#13094002—21no—
41C2×C4×Dic94C2211yescharacteristic
42C2×#13093989C2211yescharacteristic
43C2×#13093989C2211yescharacteristic
44C2×#13093989C2211yescharacteristic
45C2×#13093986C2211yescharacteristic
46C2×#13093983—21no—
47C2×#13093981—21no—
48#15689517C2218yescomplemented
49#15689514C2218yescomplemented
50#15689504C2218yes—
51#15689348C2218yescomplemented
52#15689344C2218yescomplemented
53#15689338C2218yes—
54#15689337C2218yes—
55#15689333C2218yescomplemented
56#15689332C2218yescomplemented
57#15689251C2218yescomplemented
58#15689222C2218yescomplemented
59#15689217C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093947C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
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×Dic94D411yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×Dic94C2311yescharacteristic
81C22×D188C2311yescharacteristic
82C22×C4×D47—21no—
83C2×Dic188—24no—
84C2×Dic188—42no—
85C2×Dic188C2314yes—
86C2×Dic188C2314yes—
87C2×#10625337—42no—
88C2×#10625337—42no—
89C2×#10625337C2314yes—
90C2×#10625337C2314yes—
91C2×#10625325—24no—
92C2×#10625325—42no—
93C2×#10625325C2314yes—
94C2×#10625325C2314yes—
95C2×#10625335—42no—
96C2×#10625335C2314yes—
97C2×#10625334—42no—
98C2×#10625334C2314yes—
99C22×C47⋊C8C2311yescharacteristic
100C22×C47⋊C8C2311yescharacteristic
101#13094024—22no—
102#13094024C2314yes—
103#13094022—22no—
104#13094022C2314yes—
105#13094019—28no—
106#13094018—28no—
107#13094017—28no—
108#13094017—28no—
109#13094013—22no—
110#13094013C2314yes—
111#13094012—22no—
112#13094012C2314yes—
113#13094011—22no—
114#13094011—22no—
115#13094011C2314yes—
116#13094011C2314yes—
117#13094003—28no—
118#13094002—28no—
119C4×Dic94D414yes—
120C4×Dic94C2314yes—
121#13093989—22no—
122#13093989—22no—
123#13093989—22no—
124#13093989C2314yes—
125#13093989C2314yes—
126#13093989C2314yes—
127#13093986—22no—
128#13093986C2314yes—
129#13093983—28no—
130#13093981—28no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47—21no—
133C2×C4⋊Dic47D411yescharacteristic
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4D411yescharacteristic
140C2×Dic47⋊C4D411yescharacteristic
141C2×C22⋊Dic47—21no—
142C2×C22⋊Dic47—21no—
143C2×C22⋊Dic47—21no—
144C2×C22⋊Dic47—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×C4×Dic47—21no—
151C2×C4×Dic47—21no—
152C2×C4×Dic47—21no—
153C2×C4×Dic47C2311yescharacteristic
154C2×C4×Dic47C2311yescharacteristic
155C4⋊(C47⋊C8)C2314yes—
156Dic47⋊C8C2314yes—
157Dic47⋊C8C2314yes—
158#13093947C2314yes—
159#13093947C2314yes—
160#13093947C2314yes—
161#13093944C2314yes—
162#13093934C2314yes—
163C8×Dic47C2314yes—
164C22×Q8×C47C2311yescharacteristic
165C22×D4×C47C2311yescharacteristic
166C23×C4×C47—21no—
167C2×SD16×C47—24no—
168C2×SD16×C47C2314yes—
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C4×Q8×C47—22no—
172C4×Q8×C47C2314yes—
173C4×D4×C47—22no—
174C4×D4×C47C2314yes—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—21no—
179C2×C42×C47—21no—
180C2×C42×C47C2311yescharacteristic
181#107×C47C2314yes—
182#103×C47C2314yes—
183#102×C47C2314yes—
184#97×C47C2314yes—
185C24×C47—21no—
186C23×D47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47C2412yes—
191C2×D4×C47—21no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47C2412yes—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—24no—
199C22×C4×C47—44no—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2411yescharacteristic
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C2×D188—22no—
211C2×D188—22no—
212C2×D188—21no—
213C2×D188C2412yes—
214C2×C4×D47—24no—
215C2×C4×D47—44no—
216C2×Dic94—22no—
217C2×Dic94—22no—
218C2×Dic94—22no—
219C2×Dic94—22no—
220C2×Dic94—22no—
221C2×Dic94—22no—
222C2×Dic94—21no—
223C2×Dic94—21no—
224C2×Dic94—21no—
225C2×Dic94—42no—
226C2×Dic94C2×D414yes—
227C2×Dic94C2412yes—
228C2×Dic94C2412yes—
229C2×Dic94C2412yes—
230SD16×C47—28no—
231C2×C8×C47—22no—
232C2×C8×C47#4114yes—
233C2×C8×C47C2412yes—
234C2×C8×C47C2412yes—
235C4⋊C4×C47—24no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47C2412yes—
239C4⋊C4×C47C2412yes—
240C22⋊C4×C47—24no—
241C42×C47—24no—
242C42×C47C2×D412yes—
243C42×C47C2412yes—
244C22⋊Dic47—24no—
245C22⋊Dic47—24no—
246C22⋊Dic47—24no—
247C22⋊Dic47—24no—
248#10625337—44no—
249#10625337—44no—
250#10625335—44no—
251#10625334—44no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257C4⋊Dic47—24no—
258C4⋊Dic47—24no—
259C4⋊Dic47C2×D414yes—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4C2×D414yes—
266Dic47⋊C4C2×D414yes—
267C4×Dic47—24no—
268C4×Dic47—24no—
269C4×Dic47—24no—
270C4×Dic47C2×D412yes—
271C4×Dic47C2×D412yes—
272C4×Dic47C2412yes—
273C4×Dic47C2412yes—
274C2×C47⋊C8—22no—
275C2×C47⋊C8—22no—
276C2×C47⋊C8C2412yes—
277C2×C47⋊C8C2412yes—
278Dic188—28no—
279Dic188—44no—
280#10625325—28no—
281#10625325—44no—
282C23×C47—22no—
283C23×C47—42no—
284C23×C47—42no—
285C23×C47—42no—
286C23×C47C22×D411yescharacteristic
287C22×D47—22no—
288C22×D47—42no—
289C22×D47—42no—
290C22×D47—42no—
291Q8×C47—22no—
292Q8×C47—22no—
293Q8×C47—42no—
294D4×C47—22no—
295D4×C47—22no—
296D4×C47—42no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—48no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47C22×D412yes—
307C2×C4×C47C22×D412yes—
308C2×C4×C47C22×D411yescharacteristic
309C2×C4×C47C2×#4112yes—
310C2×C4×C47H(5,𝔽2)12yes—
311C2×C4×C47C2511yescharacteristic
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47C22×D412yes—
323C2×Dic47C22×D412yes—
324C2×Dic47C22×D412yes—
325C2×Dic47C22×D412yes—
326D188—22no—
327D188—22no—
328D188—42no—
329C4×D47—48no—
330Dic94—22no—
331Dic94—22no—
332Dic94—22no—
333Dic94—22no—
334Dic94—22no—
335Dic94—22no—
336Dic94—44no—
337Dic94—42no—
338Dic94—42no—
339Dic94—42no—
340C8×C47—22no—
341C8×C47C2×#4114yes—
342C47⋊C8—22no—
343C47⋊C8—22no—
344C2×#3402—471nomaximal, Sylow
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—42no—
348C22×C47—84no—
349C22×C47#55012yes—
350C22×C47#57512yes—
351C22×C47#57812yes—
352C22×C47C23×D411yescharacteristic
353C2×D47—42no—
354C2×D47—42no—
355C2×D47—42no—
356C2×D47—84no—
357C4×C47—22no—
358C4×C47—22no—
359C4×C47—42no—
360C4×C47—42no—
361C4×C47—42no—
362C4×C47#55012yes—
363C4×C47C22×#4111yescharacteristic
364C4×C47C2×H(5,𝔽2)11yescharacteristic
365Dic47—22no—
366Dic47—22no—
367Dic47—22no—
368Dic47—22no—
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#556—471no—
373C2×#556—471no—
374#3402—4716no—
375C2×#497—471no—
376C2×#497—471no—
377C2×#495—471no—
378C2×#464—471no—
379C2×#464—471no—
380C2×#462—471no—
381C2×#462—471no—
382C2×#463—471no—
383C2×#463—471no—
384C2×#446—471no—
385C2×#440—471no—
386C2×#440D4711yescharacteristic, complemented
387C2×C4×Q16—471no—
388C2×C47—82no—
389C2×C47#340214yescomplemented
390C2×C47C2×#55011yescharacteristic
391C2×C47C2×#57511yescharacteristic
392C2×C47C2×#57811yescharacteristic
393D47—82no—
394C22×Q16—471no—
395C22×Q16—471no—
396C22×Q16—471no—
397C22×Q16—471no—
398C22×SD16—471no—
399C22×SD16—471no—
400C22×SD16—471no—
401C22×SD16C2×D4711yescharacteristic
402C22×D8—471no—
403#556—478no—
404#556—478no—
405#556—944no—
406#556—944no—
407C2×C4⋊Q8—471no—
408C2×C4⋊Q8—471no—
409C2×#126—941no—
410C2×#126—941no—
411C2×#126—941no—
412C2×#126—941no—
413C2×#124—471no—
414C2×#124—471no—
415C2×#124—471no—
416C2×#124—471no—
417C2×C22⋊Q8—941no—
418C2×C22⋊Q8—941no—
419C2×C4×Q8—471no—
420C2×C4×Q8—471no—
421C2×C4×Q8—471no—
422C2×C4×Q8—471no—
423C2×C4×Q8C2×D4711yescharacteristic
424C2×C4×D4—471no—
425C2×C4×D4C2×D4711yescharacteristic
426C2×#117—941no—
427C2×#117—941no—
428#497—478no—
429#497—478no—
430#495—478no—
431#464—478no—
432#464—478no—
433#463—478no—
434#463—478no—
435#462—478no—
436#462—478no—
437#446—478no—
438#440—478no—
439#440C2×D4718yescomplemented
440C4×Q16—478no—
441C2×#107C2×D4711yescharacteristic
442C2×C4⋊C8—471no—
443C2×C4⋊C8—471no—
444C2×C4⋊C8—471no—
445C2×#103—471no—
446C2×#103—471no—
447C2×#103—471no—
448C2×#103C2×D4711yescharacteristic
449C2×#102—471no—
450C2×#102C2×D4711yescharacteristic
451C2×#97—471no—
452C2×#97C2×D4711yescharacteristic
453C2×C4×C8—471no—
454C47C2×#340211yescharacteristic, complemented, Sylow
455C22×Q8—471no—
456C22×Q8—471no—
457C22×Q8—471no—
458C22×Q8—471no—
459C22×Q8C22×D4711yescharacteristic
460C22×D4—471no—
461C22×D4C22×D4711yescharacteristic
462C23×C4—21no—
463C23×C4—941no—
464C2×Q16—474no—
465C2×Q16—474no—
466C2×Q16—474no—
467C2×Q16—474no—
468C2×Q16—944no—
469C2×Q16—1882no—
470C2×Q16—1882no—
471C2×Q16—1882no—
472C2×SD16—24no—
473C2×SD16—474no—
474C2×SD16—474no—
475C2×SD16—474no—
476C2×SD16—944no—
477C2×SD16—1882no—
478C2×SD16—1882no—
479C2×SD16C22×D4714yes—
480C2×D8—474no—
481C2×D8—1882no—
482C22×C8—471no—
483C22×C8—471no—
484C22×C8C22×D4711yescharacteristic
485C22×C8C22×D4711yescharacteristic
486C4⋊Q8—474no—
487C4⋊Q8—474no—
488C4⋊Q8—942no—
489C4⋊Q8—942no—
490#126—948no—
491#126—948no—
492#126—948no—
493#126—948no—
494#124—474no—
495#124—474no—
496#124—474no—
497#124—474no—
498#124—942no—
499#124—942no—
500#124—942no—
501#124—942no—
502C22⋊Q8—948no—
503C22⋊Q8—948no—
504C4×Q8—22no—
505C4×Q8—474no—
506C4×Q8—474no—
507C4×Q8—474no—
508C4×Q8—474no—
509C4×Q8—474no—
510C4×Q8—942no—
511C4×Q8—942no—
512C4×Q8—942no—
513C4×Q8C22×D4714yes—
514C4×D4—22no—
515C4×D4—474no—
516C4×D4—942no—
517C4×D4C22×D4714yes—
518#117—948no—
519#117—948no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—471no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4—941no—
529C2×C4⋊C4—941no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4C22×D4711yescharacteristic
532C2×C4⋊C4C22×D4711yescharacteristic
533C2×C22⋊C4—21no—
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×C22⋊C4—941no—
542C2×C22⋊C4—941no—
543C2×C42—21no—
544C2×C42—471no—
545C2×C42—471no—
546C2×C42—941no—
547C2×C42—941no—
548C2×C42—941no—
549C2×C42C22×D4711yescharacteristic
550#107C22×D4714yes—
551C4⋊C8—474no—
552C4⋊C8—474no—
553C4⋊C8—474no—
554#103—474no—
555#103—474no—
556#103—474no—
557#103C22×D4714yes—
558#102—474no—
559#102C22×D4714yes—
560#97—474no—
561#97C22×D4714yes—
562C4×C8—474no—
563C24—21no—
564C24—941no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—474no—
569C2×Q8—472no—
570C2×Q8—472no—
571C2×Q8—472no—
572C2×Q8—941no—
573C2×Q8—941no—
574C2×Q8—941no—
575C2×Q8—942no—
576C2×Q8—942no—
577C2×Q8—942no—
578C2×Q8—942no—
579C2×Q8—942no—
580C2×Q8—942no—
581C2×Q8—1882no—
582C2×Q8C23×D4712yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—472no—
587C2×D4—941no—
588C2×D4—942no—
589C2×D4—942no—
590C2×D4C23×D4712yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—471no—
597C22×C4—471no—
598C22×C4—471no—
599C22×C4—471no—
600C22×C4—944no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—1884no—
605C22×C4D4×D4711yescharacteristic
606C22×C4D4×D4711yescharacteristic
607C22×C4C23×D4711yescharacteristic
608Q16—948no—
609Q16—1884no—
610Q16—1884no—
611Q16—1884no—
612SD16—28no—
613SD16—948no—
614SD16—1884no—
615SD16—1884no—
616D8—1884no—
617C2×C8—22no—
618C2×C8—472no—
619C2×C8—472no—
620C2×C8—942no—
621C2×C8—942no—
622C2×C8#1062535014yes—
623C2×C8C23×D4712yes—
624C2×C8C23×D4712yes—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—474no—
629C4⋊C4—474no—
630C4⋊C4—474no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—944no—
634C4⋊C4—944no—
635C4⋊C4—944no—
636C4⋊C4—944no—
637C4⋊C4—944no—
638C4⋊C4C23×D4712yes—
639C4⋊C4C23×D4712yes—
640C22⋊C4—24no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C22⋊C4—944no—
649C22⋊C4—944no—
650C42—24no—
651C42—472no—
652C42—472no—
653C42—472no—
654C42—472no—
655C42—944no—
656C42—944no—
657C42—944no—
658C42D4×D4712yes—
659C42C23×D4712yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—942no—
665C23—1882no—
666C23—1882no—
667C23—1882no—
668C23C2×D4×D4711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—942no—
673Q8—942no—
674Q8—942no—
675Q8—942no—
676Q8—942no—
677Q8—942no—
678Q8—1884no—
679Q8—1882no—
680Q8—1882no—
681Q8—1882no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—942no—
686D4—942no—
687D4—1882no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—48no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—472no—
698C2×C4—472no—
699C2×C4—472no—
700C2×C4—472no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—1888no—
709C2×C4—1882no—
710C2×C4—1882no—
711C2×C4—1882no—
712C2×C4C2×D4×D4712yes—
713C2×C4C2×D4×D4712yes—
714C2×C4C2×D4×D4711yescharacteristic
715C2×C4C2×#1062535012yes—
716C2×C4#1309407012yes—
717C2×C4C24×D4711yescharacteristic
718C8—22no—
719C8—942no—
720C8—942no—
721C8C2×#1062535014yes—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—3764no—
727C22—1882no—
728C22—1882no—
729C22—1882no—
730C22#1568979412yes—
731C22#1568991912yes—
732C22#1568993912yes—
733C22C22×D4×D4711yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—942no—
740C4—942no—
741C4—942no—
742C4—942no—
743C4—1882no—
744C4—1882no—
745C4—1882no—
746C4#1568979412yes—
747C4C22×#1062535011yescharacteristic
748C4C2×#1309407011yescharacteristic
749C2—82no—
750C2—3762no—
751C2#2025646814yesdirect product factor
752C2C2×#1568979411yescharacteristic
753C2C2×#1568991911yescharacteristic
754C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#440C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
hypercenterC2×#440D47
hypocenterC47C2×#3402
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×#15689845C2semidirect
2. C2×#15689843C2semidirect
3. #20256468C2direct (N × H)
4. C2×#15689517C2semidirect
5. C2×#15689514C2semidirect
7. C2×#15689348C2semidirect
8. C2×#15689344C2semidirect
9. C2×#15689333C2semidirect
10. C2×#15689332C2semidirect
13. C2×#15689251C2semidirect
14. C2×#15689222C2semidirect
15. C2×#15689217C2semidirect
16. C2×C47×#440C2semidirect
26. #15689845C22semidirect
28. #15689843C22semidirect
48. #15689517C22semidirect
49. #15689514C22semidirect
51. #15689348C22semidirect
52. #15689344C22semidirect
55. #15689333C22semidirect
56. #15689332C22semidirect
57. #15689251C22semidirect
58. #15689222C22semidirect
59. #15689217C22semidirect
72. C47×#440C22semidirect
386. C2×#440D47semidirect
389. C2×C47#3402semidirect
439. #440C2×D47semidirect
454. C47C2×#3402semidirect
751. C2#20256468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898452
C2×#156898432
#202564682
C2×#156895172
C2×#156895142
C2×#156895042
C2×#156893482
C2×#156893442
C2×#156893332
C2×#156893322
C2×#156893382
C2×#156893372
C2×#156892512
C2×#156892222
C2×#156892172
C2×C47×#4402
C2×#340247