Finite Group Databasebeta

← C2×#20253676 #27084621

Subgroups — C2×#20253676 #27084621

Order 12032.

2122 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689724C211yesmaximal, characteristic
2C2×#15689599C211yesmaximal, characteristic, complemented
3#20253676C2116yesmaximal, direct product factor
4C2×#15689449C211yesmaximal, characteristic, complemented
5C2×#15689446C211yesmaximal, characteristic, complemented
6C2×#15689433C211yesmaximal, characteristic, complemented
7C2×#15689428C211yesmaximal, characteristic, complemented
8C2×#15689322C211yesmaximal, characteristic, complemented
9C2×#15689321C211yesmaximal, characteristic, complemented
10C2×#15689263C211yesmaximal, characteristic, complemented
11C2×#15689260C211yesmaximal, characteristic, complemented
12C2×#15689223C211yesmaximal, characteristic, complemented
13C2×#15689221C211yesmaximal, characteristic, complemented
14C2×C4×#10625325C211yesmaximal, characteristic, complemented
15C2×#15689182C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21#15689724—24no—
22#15689724C2218yes—
23C2×#13094020C2211yescharacteristic
24C2×#13094015C2211yescharacteristic
25C2×#13094007—21no—
26C2×#13094006—21no—
27C2×#13093999C2211yescharacteristic
28C2×#13093998—21no—
29C2×#13093997—21no—
30C2×#13093995C2211yescharacteristic
31#15689599—24no—
32#15689599C2218yescomplemented
33C2×Q8×Dic47C2211yescharacteristic
34C2×C4×Dic94—21no—
35C2×C4×Dic94C2211yescharacteristic
36C2×#13093989—21no—
37C2×#13093989C2211yescharacteristic
38C2×C4×D188C2211yescharacteristic
39C2×#13093982—21no—
40C2×#13093982C2211yescharacteristic
41C2×#13093981—21no—
42C2×#13093981C2211yescharacteristic
43#15689449C2218yescomplemented
44#15689446C2218yescomplemented
45#15689433C2218yescomplemented
46#15689428C2218yescomplemented
47#15689322C2218yescomplemented
48#15689321C2218yescomplemented
49#15689263C2218yescomplemented
50#15689260C2218yescomplemented
51#15689223C2218yescomplemented
52#15689221C2218yescomplemented
53C4×#10625325C2218yescomplemented
54#15689182C2218yescomplemented
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093935C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C4×SD16×C47C2218yescomplemented
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C2×Q8×D47—24no—
80C2×Q8×D47—22no—
81C2×Q8×D47—24no—
82C2×Q8×D47C2314yes—
83C22×D188—21no—
84C22×D188C2311yescharacteristic
85C22×C22⋊D47—21no—
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47C2311yescharacteristic
91C2×#10625325—24no—
92C2×#10625325C2314yes—
93C2×#10625335—24no—
94C2×#10625335C2314yes—
95C2×#10625336—24no—
96C2×#10625336C2314yes—
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99#13094020—22no—
100#13094020C2314yes—
101#13094015—22no—
102#13094015C2314yes—
103#13094007—28no—
104#13094006—28no—
105#13093999—22no—
106#13093999C2314yes—
107#13093998—28no—
108#13093997—28no—
109#13093995—22no—
110#13093995C2314yes—
111Q8×Dic47—22no—
112Q8×Dic47C2314yes—
113C4×Dic94—22no—
114C4×Dic94—28no—
115C4×Dic94C2314yes—
116#13093989—28no—
117#13093989—22no—
118#13093989C2314yes—
119C4×D188—22no—
120C4×D188C2314yes—
121#13093982—22no—
122#13093982—28no—
123#13093982C2314yes—
124#13093981—28no—
125#13093981D414yes—
126#13093981C2314yes—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47C2311yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4D411yescharacteristic
135C2×Dic47⋊C4D411yescharacteristic
136C2×C22⋊Dic47—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4D411yescharacteristic
141C2×(C2×D47)⋊C4D411yescharacteristic
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093957C2314yes—
148#13093957C2314yes—
149#13093956C2314yes—
150Dic47⋊C8C2314yes—
151Dic47⋊C8C2314yes—
152#13093949C2314yes—
153#13093948C2314yes—
154#13093947C2314yes—
155#13093946C2314yes—
156#13093945C2314yes—
157#13093944C2314yes—
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160#13093935C2314yes—
161C22×Q8×C47C2311yescharacteristic
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47—21no—
164C2×SD16×C47—24no—
165C2×SD16×C47C2314yes—
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168C4×Q8×C47—22no—
169C4×Q8×C47C2314yes—
170C4×D4×C47—22no—
171C4×D4×C47C2314yes—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C42×C47—21no—
177C2×C42×C47C2311yescharacteristic
178#106×C47C2314yes—
179#103×C47C2314yes—
180#102×C47C2314yes—
181C4×C8×C47C2314yes—
182C24×C47—21no—
183C23×D47—21no—
184C23×D47C2×D411yescharacteristic
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47#4114yes—
188C2×Q8×C47C2412yes—
189C2×D4×C47—21no—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47C2412yes—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—24no—
197C22×C4×C47—82no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C2×C22⋊D47—24no—
202C2×C22⋊D47—24no—
203C2×C22⋊D47—24no—
204C2×C22⋊D47—82no—
205C2×C22⋊D47—82no—
206C2×C22⋊D47—82no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213Q8×D47—216no—
214Q8×D47—28no—
215Q8×D47—28no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188—21no—
219C2×D188—24no—
220C2×D188—82no—
221C2×D188C2412yes—
222C2×C4×D47—28no—
223C2×C4×D47—24no—
224C2×C4×D47—22no—
225C2×C4×D47—22no—
226C2×C4×D47—24no—
227C2×C4×D47—82no—
228C2×C4×D47C2×D412yes—
229C2×C4×D47C2412yes—
230C2×Dic94—28no—
231C2×Dic94—21no—
232C2×Dic94—22no—
233C2×Dic94—24no—
234C2×Dic94#4114yes—
235C2×Dic94C2412yes—
236SD16×C47—28no—
237C2×C8×C47—22no—
238C2×C8×C47—22no—
239C2×C8×C47C2412yes—
240C2×C8×C47C2412yes—
241C4⋊C4×C47—24no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47C2412yes—
245C4⋊C4×C47C2412yes—
246C22⋊C4×C47—24no—
247C42×C47—24no—
248C42×C47C2×D412yes—
249C42×C47C2412yes—
250C22⋊Dic47—24no—
251#10625336—28no—
252#10625335—28no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4C2×D414yes—
257(C2×D47)⋊C4C2×D414yes—
258C4⋊Dic47—21no—
259C4⋊Dic47—21no—
260C4⋊Dic47—24no—
261C4⋊Dic47—24no—
262C4⋊Dic47C2412yes—
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×Dic47—24no—
273C4×Dic47C2×D412yes—
274C4×Dic47C2412yes—
275C2×C47⋊C8—22no—
276C2×C47⋊C8—22no—
277C2×C47⋊C8C2412yes—
278C2×C47⋊C8C2412yes—
279#10625325—28no—
280C23×C47—22no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47C22×D411yescharacteristic
285C22×D47—22no—
286C22×D47—22no—
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—42no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47C22×D412yes—
293Q8×C47—24no—
294Q8×C47—22no—
295Q8×C47C2×#4114yes—
296D4×C47—22no—
297D4×C47—22no—
298D4×C47—42no—
299C2×C4×C47—24no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47—84no—
308C2×C4×C47C22×D412yes—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D411yescharacteristic
311C2×C4×C47C2×#4112yes—
312C2×C4×C47C2×#4112yes—
313C2×C4×C47C2511yescharacteristic
314C22⋊D47—84no—
315C22⋊D47—84no—
316C22⋊D47—84no—
317C2×Dic47—22no—
318C2×Dic47—24no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—42no—
325C2×Dic47—42no—
326C2×Dic47C22×D412yes—
327C2×Dic47C22×D412yes—
328C2×Dic47C22×D412yes—
329D188—22no—
330D188—22no—
331D188—42no—
332D188—84no—
333C4×D47—216no—
334C4×D47—24no—
335C4×D47—22no—
336C4×D47—22no—
337C4×D47—84no—
338Dic94—216no—
339Dic94—24no—
340Dic94—22no—
341Dic94C2×#4114yes—
342C8×C47—22no—
343C8×C47—22no—
344C47⋊C8—22no—
345C47⋊C8—22no—
346C2×#3126—471nomaximal, Sylow
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—84no—
351C22×C47#52512yes—
352C22×C47#57712yes—
353C22×C47#57712yes—
354C22×C47C23×D411yescharacteristic
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—22no—
358C2×D47—44no—
359C2×D47—42no—
360C2×D47—42no—
361C2×D47—42no—
362C2×D47—84no—
363C4×C47—24no—
364C4×C47—22no—
365C4×C47—22no—
366C4×C47—42no—
367C4×C47—42no—
368C4×C47#52512yes—
369C4×C47C22×#4111yescharacteristic
370C4×C47C22×#4111yescharacteristic
371Dic47—22no—
372Dic47—24no—
373Dic47—22no—
374Dic47—22no—
375Dic47—42no—
376Dic47—42no—
377C2×#540—471no—
378C2×#519—471no—
379#3126—4716no—
380C2×#482—471no—
381C2×#482—471no—
382C2×#479—471no—
383C2×#479—471no—
384C2×#460—471no—
385C2×#460—471no—
386C2×#448—471no—
387C2×#448—471no—
388C2×#440—471no—
389C2×#440—471no—
390C2×C4×SD16—471no—
391C2×C4×SD16D4711yescharacteristic, complemented
392C2×#433—471no—
393C2×C47—82no—
394C2×C47#312614yescomplemented
395C2×C47C2×#52511yescharacteristic
396C2×C47C2×#57711yescharacteristic
397C2×C47C2×#57711yescharacteristic
398D47—42no—
399D47—82no—
400C23×Q8—471no—
401C22×SD16—471no—
402C22×SD16—471no—
403C22×SD16—471no—
404C22×SD16C2×D4711yescharacteristic
405#540—478no—
406#540—944no—
407C2×#127—471no—
408C2×#125—471no—
409C2×#123—941no—
410C2×#123—941no—
411C2×#121—471no—
412C2×#121—471no—
413C2×#121—941no—
414C2×#121—941no—
415#519—478no—
416#519—944no—
417C2×C4×Q8—471no—
418C2×C4×Q8—471no—
419C2×C4×Q8—471no—
420C2×C4×Q8—941no—
421C2×C4×Q8—941no—
422C2×C4×Q8C2×D4711yescharacteristic
423C2×C4×D4—471no—
424C2×C4×D4C2×D4711yescharacteristic
425C2×#117—471no—
426C2×#117—471no—
427C2×#117—941no—
428C2×#117—941no—
429#482—478no—
430#482—478no—
431#479—478no—
432#479—478no—
433#460—478no—
434#460—478no—
435#448—478no—
436#448—478no—
437#440—478no—
438#440—478no—
439C4×SD16—478no—
440C4×SD16C2×D4718yescomplemented
441#433—478no—
442C2×#107—471no—
443C2×#107—471no—
444C2×#106—471no—
445C2×#106C2×D4711yescharacteristic
446C2×C4⋊C8—471no—
447C2×C4⋊C8—471no—
448C2×#103—471no—
449C2×#103—471no—
450C2×#103—471no—
451C2×#103C2×D4711yescharacteristic
452C2×#102—471no—
453C2×#102—471no—
454C2×#102—471no—
455C2×#102C2×D4711yescharacteristic
456C2×C22⋊C8—471no—
457C2×C22⋊C8—471no—
458C2×#97—471no—
459C2×C4×C8C2×D4711yescharacteristic
460C47C2×#312611yescharacteristic, complemented, Sylow
461C22×Q8—474no—
462C22×Q8—471no—
463C22×Q8—941no—
464C22×Q8—942no—
465C22×Q8—944no—
466C22×Q8—944no—
467C22×Q8C22×D4711yescharacteristic
468C22×D4—471no—
469C22×D4—941no—
470C22×D4—941no—
471C22×D4—941no—
472C22×D4—941no—
473C22×D4C22×D4711yescharacteristic
474C23×C4—21no—
475C23×C4—471no—
476C23×C4—941no—
477C23×C4—941no—
478C2×SD16—24no—
479C2×SD16—474no—
480C2×SD16—474no—
481C2×SD16—474no—
482C2×SD16—944no—
483C2×SD16—944no—
484C2×SD16—944no—
485C2×SD16C22×D4714yes—
486C22×C8—471no—
487C22×C8—471no—
488C22×C8C22×D4711yescharacteristic
489C22×C8C22×D4711yescharacteristic
490#127—474no—
491#127—942no—
492#125—474no—
493#125—942no—
494#123—948no—
495#123—948no—
496#121—474no—
497#121—474no—
498#121—948no—
499#121—948no—
500#121—942no—
501#121—942no—
502C4×Q8—22no—
503C4×Q8—474no—
504C4×Q8—474no—
505C4×Q8—474no—
506C4×Q8—948no—
507C4×Q8—942no—
508C4×Q8—942no—
509C4×Q8—948no—
510C4×Q8—942no—
511C4×Q8C22×D4714yes—
512C4×D4—22no—
513C4×D4—474no—
514C4×D4—942no—
515C4×D4C22×D4714yes—
516#117—474no—
517#117—474no—
518#117—474no—
519#117—948no—
520#117—948no—
521#117—942no—
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×C4⋊C4C22×D4711yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—471no—
536C2×C22⋊C4—471no—
537C2×C22⋊C4—941no—
538C2×C22⋊C4—941no—
539C2×C22⋊C4—941no—
540C2×C22⋊C4—941no—
541C2×C42—21no—
542C2×C42—471no—
543C2×C42—941no—
544C2×C42—941no—
545C2×C42—941no—
546C2×C42—941no—
547C2×C42C22×D4711yescharacteristic
548#107—474no—
549#107—474no—
550#106—474no—
551#106C22×D4714yes—
552C4⋊C8—474no—
553C4⋊C8—474no—
554#103—474no—
555#103—474no—
556#103—474no—
557#103C22×D4714yes—
558#102—474no—
559#102—474no—
560#102—474no—
561#102C22×D4714yes—
562C22⋊C8—474no—
563C22⋊C8—474no—
564#97—474no—
565C4×C8C22×D4714yes—
566C24—21no—
567C24—471no—
568C24—941no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—474no—
572C2×Q8—472no—
573C2×Q8—944no—
574C2×Q8—948no—
575C2×Q8—948no—
576C2×Q8—9416no—
577C2×Q8—948no—
578C2×Q8—941no—
579C2×Q8—942no—
580C2×Q8#1062535014yes—
581C2×Q8C23×D4712yes—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—472no—
586C2×D4—944no—
587C2×D4—944no—
588C2×D4—944no—
589C2×D4—944no—
590C2×D4—941no—
591C2×D4—942no—
592C2×D4—942no—
593C2×D4—3762no—
594C2×D4—3762no—
595C2×D4—3762no—
596C2×D4—3762no—
597C2×D4C23×D4712yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—82no—
603C22×C4—471no—
604C22×C4—471no—
605C22×C4—471no—
606C22×C4—472no—
607C22×C4—472no—
608C22×C4—944no—
609C22×C4—948no—
610C22×C4—941no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—941no—
614C22×C4—941no—
615C22×C4—944no—
616C22×C4—3762no—
617C22×C4D4×D4711yescharacteristic
618C22×C4D4×D4711yescharacteristic
619C22×C4C23×D4711yescharacteristic
620SD16—28no—
621SD16—948no—
622SD16—948no—
623SD16—948no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—472no—
627C2×C8—472no—
628C2×C8—942no—
629C2×C8—942no—
630C2×C8C23×D4712yes—
631C2×C8C23×D4712yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—474no—
636C4⋊C4—474no—
637C4⋊C4—472no—
638C4⋊C4—472no—
639C4⋊C4—944no—
640C4⋊C4—944no—
641C4⋊C4—944no—
642C4⋊C4—944no—
643C4⋊C4—944no—
644C4⋊C4—941no—
645C4⋊C4—941no—
646C4⋊C4C23×D4712yes—
647C4⋊C4C23×D4712yes—
648C22⋊C4—24no—
649C22⋊C4—474no—
650C22⋊C4—474no—
651C22⋊C4—944no—
652C22⋊C4—944no—
653C22⋊C4—944no—
654C22⋊C4—944no—
655C42—24no—
656C42—472no—
657C42—472no—
658C42—944no—
659C42—944no—
660C42—944no—
661C42—944no—
662C42D4×D4712yes—
663C42C23×D4712yes—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—472no—
669C23—942no—
670C23—942no—
671C23—942no—
672C23—942no—
673C23—1882no—
674C23—1882no—
675C23—1882no—
676C23C2×D4×D4711yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—474no—
680Q8—9416no—
681Q8—944no—
682Q8—942no—
683Q8C2×#1062535014yes—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—942no—
688D4—942no—
689D4—3764no—
690D4—3764no—
691D4—3764no—
692D4—3764no—
693D4—1882no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—84no—
703C2×C4—472no—
704C2×C4—472no—
705C2×C4—472no—
706C2×C4—9416no—
707C2×C4—942no—
708C2×C4—944no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—944no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—3764no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4C2×D4×D4712yes—
721C2×C4C2×D4×D4712yes—
722C2×C4C2×D4×D4711yescharacteristic
723C2×C4#41×D4712yes—
724C2×C4C2×#1062535012yes—
725C2×C4C24×D4711yescharacteristic
726C8—22no—
727C8—22no—
728C8—942no—
729C8—942no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—942no—
735C22—942no—
736C22—942no—
737C22—3764no—
738C22—1882no—
739C22—1882no—
740C22—1882no—
741C22—1884no—
742C22#1568963212yes—
743C22#1568992912yes—
744C22#1568993012yes—
745C22C22×D4×D4711yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—942no—
752C4—942no—
753C4—942no—
754C4—944no—
755C4—1882no—
756C4—1882no—
757C4#1568963212yes—
758C4C2×#41×D4711yescharacteristic
759C4C22×#1062535011yescharacteristic
760C2—82no—
761C2—3762no—
762C2—1882no—
763C2#2025367614yesdirect product factor
764C2C2×#1568963211yescharacteristic
765C2C2×#1568992911yescharacteristic
766C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×SD16×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689724C2
hypercenterC2×C4×SD16D47
hypocenterC47C2×#3126
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#15689599C2semidirect
3. #20253676C2direct (N × H)
4. C2×#15689449C2semidirect
5. C2×#15689446C2semidirect
6. C2×#15689433C2semidirect
7. C2×#15689428C2semidirect
8. C2×#15689322C2semidirect
9. C2×#15689321C2semidirect
10. C2×#15689263C2semidirect
11. C2×#15689260C2semidirect
12. C2×#15689223C2semidirect
13. C2×#15689221C2semidirect
14. C2×C4×#10625325C2semidirect
15. C2×#15689182C2semidirect
16. C2×C4×SD16×C47C2semidirect
32. #15689599C22semidirect
43. #15689449C22semidirect
44. #15689446C22semidirect
45. #15689433C22semidirect
46. #15689428C22semidirect
47. #15689322C22semidirect
48. #15689321C22semidirect
49. #15689263C22semidirect
50. #15689260C22semidirect
51. #15689223C22semidirect
52. #15689221C22semidirect
53. C4×#10625325C22semidirect
54. #15689182C22semidirect
72. C4×SD16×C47C22semidirect
391. C2×C4×SD16D47semidirect
394. C2×C47#3126semidirect
440. C4×SD16C2×D47semidirect
460. C47C2×#3126semidirect
763. C2#20253676direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897242
C2×#156895992
#202536762
C2×#156894492
C2×#156894462
C2×#156894332
C2×#156894282
C2×#156893222
C2×#156893212
C2×#156892632
C2×#156892602
C2×#156892232
C2×#156892212
C2×C4×#106253252
C2×#156891822
C2×C4×SD16×C472
C2×#312647