Finite Group Databasebeta

← C2×#20256462 #27097293

Subgroups — C2×#20256462 #27097293

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×#15689847C211yesmaximal, characteristic, complemented
2C2×#15689845C211yesmaximal, characteristic, complemented
3#20256462C2116yesmaximal, direct product factor
4C2×#15689516C211yesmaximal, characteristic, complemented
5C2×#15689515C211yesmaximal, characteristic, complemented
6C2×#15689508C211yesmaximal, characteristic
7C2×#15689348C211yesmaximal, characteristic, complemented
8C2×#15689347C211yesmaximal, characteristic, complemented
9C2×#15689331C211yesmaximal, characteristic, complemented
10C2×#15689341C211yesmaximal, characteristic
11C2×#15689339C211yesmaximal, characteristic
12C2×#15689252C211yesmaximal, characteristic, complemented
13C2×#15689226C211yesmaximal, characteristic, complemented
14C2×#15689221C211yesmaximal, characteristic, complemented
15C2×#15689215C211yesmaximal, characteristic, complemented
16C2×C47×#462C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22C22×#10625336C2211yescharacteristic
23C22×D376C2211yescharacteristic
24#15689847—24no—
25#15689847C2218yescomplemented
26#15689845—24no—
27#15689845C2218yescomplemented
28C2×#13094022C2211yescharacteristic
29C2×#13094019—21no—
30C2×#13094019—21no—
31C2×#13094019—21no—
32C2×#13094018—21no—
33C2×#13094013C2211yescharacteristic
34C2×#13094013C2211yescharacteristic
35C2×#13094013C2211yescharacteristic
36C2×#13094012C2211yescharacteristic
37C2×#13094004—21no—
38C2×#13094002—21no—
39C2×Q8×Dic47C2211yescharacteristic
40C2×Q8×Dic47C2211yescharacteristic
41C2×C4×Dic94C2211yescharacteristic
42C2×#13093989C2211yescharacteristic
43C2×C4×D188C2211yescharacteristic
44C2×#13093986C2211yescharacteristic
45C2×#13093982—21no—
46C2×#13093981—21no—
47#15689516C2218yescomplemented
48#15689515C2218yescomplemented
49#15689508C2218yes—
50#15689348C2218yescomplemented
51#15689347C2218yescomplemented
52#15689341C2218yes—
53#15689339C2218yes—
54#15689331C2218yescomplemented
55#15689252C2218yescomplemented
56#15689226C2218yescomplemented
57#15689221C2218yescomplemented
58#15689215C2218yescomplemented
59C2×#13093957C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×#13093935C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C2×C4⋊Q8×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic
73C47×#462C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94D411yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×C4×D47—21no—
82C22×C4×D47—21no—
83C2×#10625337—24no—
84C2×#10625337—42no—
85C2×#10625337C2314yes—
86C2×#10625337C2314yes—
87C2×#10625325—42no—
88C2×#10625325C2314yes—
89C2×#10625336—24no—
90C2×#10625336—24no—
91C2×#10625336—42no—
92C2×#10625336C2314yes—
93C2×#10625336C2314yes—
94C2×#10625336C2314yes—
95C2×D376—42no—
96C2×D376C2314yes—
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99#13094022—22no—
100#13094022C2314yes—
101#13094019—28no—
102#13094019—28no—
103#13094019—28no—
104#13094018—28no—
105#13094013—22no—
106#13094013—22no—
107#13094013—22no—
108#13094013C2314yes—
109#13094013C2314yes—
110#13094013C2314yes—
111#13094012—22no—
112#13094012C2314yes—
113#13094004—28no—
114#13094002—28no—
115Q8×Dic47—22no—
116Q8×Dic47—22no—
117Q8×Dic47C2314yes—
118Q8×Dic47C2314yes—
119C4×Dic94D414yes—
120C4×Dic94C2314yes—
121#13093989—22no—
122#13093989C2314yes—
123C4×D188—22no—
124C4×D188C2314yes—
125#13093986—22no—
126#13093986C2314yes—
127#13093982—28no—
128#13093981—28no—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47D411yescharacteristic
132C2×C4⋊Dic47C2311yescharacteristic
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4D411yescharacteristic
137C2×Dic47⋊C4D411yescharacteristic
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×C4×Dic47—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151C2×C4×Dic47C2311yescharacteristic
152C2×C4×Dic47C2311yescharacteristic
153#13093957C2314yes—
154Dic47⋊C8C2314yes—
155Dic47⋊C8C2314yes—
156#13093949C2314yes—
157#13093948C2314yes—
158#13093946C2314yes—
159#13093944C2314yes—
160#13093935C2314yes—
161#13093934C2314yes—
162C8×Dic47C2314yes—
163C22×Q8×C47C2311yescharacteristic
164C22×Q8×C47C2311yescharacteristic
165C22×Q8×C47C2311yescharacteristic
166C2×Q16×C47—42no—
167C2×Q16×C47—42no—
168C2×Q16×C47C2314yes—
169C2×Q16×C47C2314yes—
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C4⋊Q8×C47—22no—
173C4⋊Q8×C47C2314yes—
174C4×Q8×C47—22no—
175C4×Q8×C47C2314yes—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47—21no—
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C42×C47—21no—
181C2×C42×C47C2311yescharacteristic
182C4⋊C8×C47C2314yes—
183#103×C47C2314yes—
184#103×C47C2314yes—
185C23×D47—21no—
186C23×D47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47—22no—
193C2×Q8×C47—22no—
194C2×Q8×C47—22no—
195C2×Q8×C47—22no—
196C2×Q8×C47C2412yes—
197C2×Q8×C47C2412yes—
198C2×Q8×C47C2412yes—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2411yescharacteristic
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C2×D188—22no—
213C2×D188—22no—
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—21no—
217C2×D188—21no—
218C2×D188C2412yes—
219C2×D188C2412yes—
220C2×C4×D47—24no—
221C2×C4×D47—24no—
222C2×C4×D47—44no—
223C2×C4×D47—44no—
224C2×Dic94—22no—
225C2×Dic94—22no—
226C2×Dic94—21no—
227C2×Dic94—42no—
228C2×Dic94C2×D414yes—
229C2×Dic94C2412yes—
230Q16×C47—44no—
231Q16×C47—44no—
232C2×C8×C47—22no—
233C2×C8×C47—22no—
234C2×C8×C47C2412yes—
235C2×C8×C47C2412yes—
236C4⋊C4×C47—24no—
237C4⋊C4×C47—24no—
238C4⋊C4×C47—24no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47C2412yes—
241C42×C47—24no—
242C42×C47C2×D412yes—
243C42×C47C2412yes—
244#10625337—28no—
245#10625337—44no—
246#10625336—28no—
247#10625336—28no—
248#10625336—44no—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4—24no—
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—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259C4⋊Dic47—21no—
260C4⋊Dic47—24no—
261C4⋊Dic47—24no—
262C4⋊Dic47C2×D414yes—
263C4⋊Dic47C2412yes—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4C2×D414yes—
268Dic47⋊C4C2×D414yes—
269C4×Dic47—24no—
270C4×Dic47—24no—
271C4×Dic47—24no—
272C4×Dic47C2×D412yes—
273C4×Dic47C2×D412yes—
274C4×Dic47C2412yes—
275C4×Dic47C2412yes—
276C2×C47⋊C8—22no—
277C2×C47⋊C8#4114yes—
278C2×C47⋊C8C2412yes—
279C2×C47⋊C8C2412yes—
280D376—44no—
281#10625325—44no—
282C23×C47C22×D411yescharacteristic
283C22×D47—22no—
284C22×D47—22no—
285C22×D47—42no—
286C22×D47—42no—
287C22×D47—42no—
288C22×D47—42no—
289C22×D47—42no—
290C22×D47—42no—
291Q8×C47—22no—
292Q8×C47—22no—
293Q8×C47—22no—
294Q8×C47—22no—
295Q8×C47—22no—
296Q8×C47—22no—
297Q8×C47—42no—
298Q8×C47—42no—
299Q8×C47—42no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47C22×D412yes—
311C2×C4×C47C22×D412yes—
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C2×#4112yes—
314C2×C4×C47H(5,𝔽2)12yes—
315C2×C4×C47C2511yescharacteristic
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47C22×D412yes—
325C2×Dic47C22×D412yes—
326C2×Dic47C22×D412yes—
327C2×Dic47C22×D412yes—
328D188—22no—
329D188—22no—
330D188—22no—
331D188—22no—
332D188—42no—
333D188—42no—
334C4×D47—48no—
335C4×D47—48no—
336Dic94—22no—
337Dic94—22no—
338Dic94—44no—
339Dic94—42no—
340C8×C47—22no—
341C8×C47—22no—
342C47⋊C8—22no—
343C47⋊C8C2×#4114yes—
344C2×#3402—471nomaximal, Sylow
345C22×C47#55012yes—
346C22×C47#57512yes—
347C22×C47#57812yes—
348C22×C47C23×D411yescharacteristic
349C2×D47—42no—
350C2×D47—42no—
351C2×D47—42no—
352C2×D47—42no—
353C2×D47—42no—
354C2×D47—42no—
355C2×D47—84no—
356C2×D47—84no—
357C4×C47—22no—
358C4×C47—22no—
359C4×C47—42no—
360C4×C47—42no—
361C4×C47—42no—
362C4×C47—42no—
363C4×C47#55012yes—
364C4×C47C22×#4111yescharacteristic
365C4×C47C2×H(5,𝔽2)11yescharacteristic
366Dic47—22no—
367Dic47—22no—
368Dic47—22no—
369Dic47—22no—
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×#462D4711yescharacteristic, complemented
382C2×#463—471no—
383C2×#463—471no—
384C2×#446—471no—
385C2×#440—471no—
386C2×#440—471no—
387C2×C4×Q16—471no—
388C2×C47#340214yescomplemented
389C2×C47C2×#55011yescharacteristic
390C2×C47C2×#57511yescharacteristic
391C2×C47C2×#57811yescharacteristic
392D47—82no—
393D47—82no—
394C22×Q16—471no—
395C22×Q16—471no—
396C22×Q16C2×D4711yescharacteristic
397C22×Q16C2×D4711yescharacteristic
398C22×SD16—471no—
399C22×SD16—471no—
400C22×SD16—471no—
401C22×SD16—471no—
402C22×D8—471no—
403#556—478no—
404#556—478no—
405#556—944no—
406#556—944no—
407C2×C4⋊Q8—471no—
408C2×C4⋊Q8C2×D4711yescharacteristic
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×D4—471no—
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#462C2×D4718yescomplemented
437#446—478no—
438#440—478no—
439#440—478no—
440C4×Q16—478no—
441C2×#107—471no—
442C2×C4⋊C8—471no—
443C2×C4⋊C8—471no—
444C2×C4⋊C8C2×D4711yescharacteristic
445C2×#103—471no—
446C2×#103—471no—
447C2×#103C2×D4711yescharacteristic
448C2×#103C2×D4711yescharacteristic
449C2×#102—471no—
450C2×#102—471no—
451C2×#97—471no—
452C2×#97—471no—
453C2×C4×C8—471no—
454C47C2×#340211yescharacteristic, complemented, Sylow
455C22×Q8—471no—
456C22×Q8—471no—
457C22×Q8C22×D4711yescharacteristic
458C22×Q8C22×D4711yescharacteristic
459C22×Q8C22×D4711yescharacteristic
460C22×D4—471no—
461C22×D4—471no—
462C23×C4—941no—
463C23×C4—941no—
464C2×Q16—42no—
465C2×Q16—42no—
466C2×Q16—474no—
467C2×Q16—474no—
468C2×Q16—944no—
469C2×Q16—1882no—
470C2×Q16C22×D4714yes—
471C2×Q16C22×D4714yes—
472C2×SD16—474no—
473C2×SD16—474no—
474C2×SD16—474no—
475C2×SD16—474no—
476C2×SD16—944no—
477C2×SD16—944no—
478C2×SD16—1882no—
479C2×SD16—1882no—
480C2×D8—474no—
481C2×D8—1882no—
482C22×C8—471no—
483C22×C8—471no—
484C22×C8C22×D4711yescharacteristic
485C22×C8C22×D4711yescharacteristic
486C4⋊Q8—22no—
487C4⋊Q8—474no—
488C4⋊Q8—942no—
489C4⋊Q8C22×D4714yes—
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—474no—
515C4×D4—474no—
516C4×D4—942no—
517C4×D4—942no—
518#117—948no—
519#117—948no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—471no—
524C2×C4⋊C4—471no—
525C2×C4⋊C4—471no—
526C2×C4⋊C4—471no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4—941no—
529C2×C4⋊C4—941no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4—941no—
532C2×C4⋊C4C22×D4711yescharacteristic
533C2×C22⋊C4—941no—
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#107—474no—
551C4⋊C8—474no—
552C4⋊C8—474no—
553C4⋊C8C22×D4714yes—
554#103—474no—
555#103—474no—
556#103C22×D4714yes—
557#103C22×D4714yes—
558#102—474no—
559#102—474no—
560#97—474no—
561#97—474no—
562C4×C8—474no—
563C24—941no—
564C24—941no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—474no—
575C2×Q8—472no—
576C2×Q8—941no—
577C2×Q8—942no—
578C2×Q8—942no—
579C2×Q8—1882no—
580C2×Q8C23×D4712yes—
581C2×Q8C23×D4712yes—
582C2×Q8C23×D4712yes—
583C2×D4—472no—
584C2×D4—472no—
585C2×D4—941no—
586C2×D4—941no—
587C2×D4—942no—
588C2×D4—942no—
589C2×D4—942no—
590C2×D4—942no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—471no—
596C22×C4—471no—
597C22×C4—471no—
598C22×C4—471no—
599C22×C4—944no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—944no—
603C22×C4—1884no—
604C22×C4—1884no—
605C22×C4D4×D4711yescharacteristic
606C22×C4D4×D4711yescharacteristic
607C22×C4C23×D4711yescharacteristic
608Q16—44no—
609Q16—44no—
610Q16—948no—
611Q16—1884no—
612SD16—948no—
613SD16—948no—
614SD16—1884no—
615SD16—1884no—
616D8—1884no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—474no—
620C2×C8—472no—
621C2×C8—472no—
622C2×C8—942no—
623C2×C8C23×D4712yes—
624C2×C8C23×D4712yes—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—21no—
629C4⋊C4—474no—
630C4⋊C4—474no—
631C4⋊C4—474no—
632C4⋊C4—472no—
633C4⋊C4—944no—
634C4⋊C4—944no—
635C4⋊C4—944no—
636C4⋊C4—944no—
637C4⋊C4—944no—
638C4⋊C4—941no—
639C4⋊C4C23×D4712yes—
640C22⋊C4—944no—
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—942no—
661C23—942no—
662C23—1882no—
663C23—1882no—
664C23—1882no—
665C23—1882no—
666C23—1882no—
667C23—1882no—
668C23C2×D4×D4711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—22no—
674Q8—22no—
675Q8—42no—
676Q8—42no—
677Q8—42no—
678Q8—942no—
679Q8—942no—
680Q8—1884no—
681Q8—1882no—
682D4—942no—
683D4—942no—
684D4—942no—
685D4—942no—
686D4—1882no—
687D4—1882no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—472no—
699C2×C4—472no—
700C2×C4—472no—
701C2×C4—472no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—1888no—
709C2×C4—1888no—
710C2×C4—1882no—
711C2×C4—1882no—
712C2×C4C2×D4×D4712yes—
713C2×C4C2×D4×D4712yes—
714C2×C4C2×D4×D4711yescharacteristic
715C2×C4#41×D4712yes—
716C2×C4#1309406912yes—
717C2×C4C24×D4711yescharacteristic
718C8—22no—
719C8—22no—
720C8—474no—
721C8—942no—
722C22—3764no—
723C22—3764no—
724C22—1882no—
725C22—1882no—
726C22—1882no—
727C22—1882no—
728C22—1882no—
729C22—1882no—
730C22#1568979112yes—
731C22#1568992212yes—
732C22#1568993612yes—
733C22C22×D4×D4711yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—942no—
741C4—942no—
742C4—942no—
743C4—942no—
744C4—1882no—
745C4—1882no—
746C4#1568979112yes—
747C4C2×#41×D4711yescharacteristic
748C4C2×#1309406911yescharacteristic
749C2—3762no—
750C2—3762no—
751C2#2025646214yesdirect product factor
752C2C2×#1568979111yescharacteristic
753C2C2×#1568992211yescharacteristic
754C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#462C2
socleC23×C47C22×D4
prime radicalC22×D376C22
hypercenterC2×#462D47
hypocenterC47C2×#3402
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×#15689847C2semidirect
2. C2×#15689845C2semidirect
3. #20256462C2direct (N × H)
4. C2×#15689516C2semidirect
5. C2×#15689515C2semidirect
7. C2×#15689348C2semidirect
8. C2×#15689347C2semidirect
9. C2×#15689331C2semidirect
12. C2×#15689252C2semidirect
13. C2×#15689226C2semidirect
14. C2×#15689221C2semidirect
15. C2×#15689215C2semidirect
16. C2×C47×#462C2semidirect
25. #15689847C22semidirect
27. #15689845C22semidirect
47. #15689516C22semidirect
48. #15689515C22semidirect
50. #15689348C22semidirect
51. #15689347C22semidirect
54. #15689331C22semidirect
55. #15689252C22semidirect
56. #15689226C22semidirect
57. #15689221C22semidirect
58. #15689215C22semidirect
73. C47×#462C22semidirect
381. C2×#462D47semidirect
388. C2×C47#3402semidirect
436. #462C2×D47semidirect
454. C47C2×#3402semidirect
751. C2#20256462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898472
C2×#156898452
#202564622
C2×#156895162
C2×#156895152
C2×#156895082
C2×#156893482
C2×#156893472
C2×#156893312
C2×#156893412
C2×#156893392
C2×#156892522
C2×#156892262
C2×#156892212
C2×#156892152
C2×C47×#4622
C2×#340247