Finite Group Databasebeta

← C2×#20253992 #27086053

Subgroups — C2×#20253992 #27086053

Order 12032.

1986 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689677C211yesmaximal, characteristic, complemented
2C2×#15689660C211yesmaximal, characteristic
3#20253992C2116yesmaximal, direct product factor
4C2×#15689531C211yesmaximal, characteristic, complemented
5C2×#15689516C211yesmaximal, characteristic, complemented
6C2×#15689490C211yesmaximal, characteristic, complemented
7C2×#15689484C211yesmaximal, characteristic, complemented
8C2×#15689380C211yesmaximal, characteristic, complemented
9C2×#15689378C211yesmaximal, characteristic, complemented
10C2×#15689372C211yesmaximal, characteristic
11C2×#15689370C211yesmaximal, characteristic
12C2×C4×#10625337C211yesmaximal, characteristic, complemented
13C2×C4×#10625325C211yesmaximal, characteristic, complemented
14C2×C4×#10625336C211yesmaximal, characteristic, complemented
15C2×C4×#10625324C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C47C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×#10625324C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22#15689677—24no—
23#15689677C2218yescomplemented
24C2×#13094023C2211yescharacteristic
25C2×#13094022C2211yescharacteristic
26#15689660—24no—
27#15689660C2218yes—
28C2×#13094019—21no—
29C2×#13094015C2211yescharacteristic
30C2×#13094014—21no—
31C2×#13094013C2211yescharacteristic
32C2×#13094009—21no—
33C2×#13094004C2211yescharacteristic
34C2×#13094002—21no—
35C2×#13094000C2211yescharacteristic
36C2×#13094000C2211yescharacteristic
37C2×#13093999C2211yescharacteristic
38C2×C4×Dic94—21no—
39C2×C4×Dic94C2211yescharacteristic
40C2×C4×D188—21no—
41C2×C4×D188C2211yescharacteristic
42C2×#13093981—21no—
43C2×#13093981—21no—
44C2×C42×D47C2211yescharacteristic
45#15689531C2218yescomplemented
46#15689516C2218yescomplemented
47#15689490C2218yescomplemented
48#15689484C2218yescomplemented
49#15689380C2218yescomplemented
50#15689378C2218yescomplemented
51#15689372C2218yes—
52#15689370C2218yes—
53C4×#10625337C2218yescomplemented
54C4×#10625325C2218yescomplemented
55C4×#10625336C2218yescomplemented
56C2×#13093957C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C4×#10625324C2218yescomplemented
66C2×#13093934C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C4×C47⋊C8C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic
72C4×Q16×C47C2218yescomplemented
73C2×#107×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188—21no—
80C22×D188C2311yescharacteristic
81C22×C4×D47—21no—
82C22×C4×D47D411yescharacteristic
83C22×C4×D47D411yescharacteristic
84C22×C4×D47C2311yescharacteristic
85C2×#10625337—24no—
86C2×#10625337C2314yes—
87C2×#10625325—24no—
88C2×#10625325C2314yes—
89C2×#10625336—24no—
90C2×#10625336C2314yes—
91C2×#10625324—24no—
92C2×#10625324—24no—
93C2×#10625324C2314yes—
94C2×#10625324C2314yes—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97#13094023—22no—
98#13094023C2314yes—
99#13094022—22no—
100#13094022C2314yes—
101#13094019—28no—
102#13094015—22no—
103#13094015C2314yes—
104#13094014—28no—
105#13094013—22no—
106#13094013C2314yes—
107#13094009—28no—
108#13094004—22no—
109#13094004C2314yes—
110#13094002—28no—
111#13094000—22no—
112#13094000—22no—
113#13094000C2314yes—
114#13094000C2314yes—
115#13093999—22no—
116#13093999C2314yes—
117C4×Dic94—22no—
118C4×Dic94—28no—
119C4×Dic94C2314yes—
120C4×D188—28no—
121C4×D188—22no—
122C4×D188C2314yes—
123#13093981—28no—
124#13093981—28no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
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×C4×Dic47—21no—
144C2×C4×Dic47D411yescharacteristic
145C2×C4×Dic47D411yescharacteristic
146C2×C4×Dic47C2311yescharacteristic
147C42×D47D414yes—
148C42×D47C2314yes—
149#13093957C2314yes—
150#13093956C2314yes—
151#13093955C2314yes—
152#13093949C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093947C2314yes—
156#13093946C2314yes—
157#13093944C2314yes—
158#13093934C2314yes—
159#13093934C2314yes—
160C4×C47⋊C8C2314yes—
161C22×Q8×C47C2311yescharacteristic
162C22×Q8×C47C2311yescharacteristic
163C2×Q16×C47—24no—
164C2×Q16×C47C2314yes—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C4×Q8×C47—22no—
168C4×Q8×C47—22no—
169C4×Q8×C47C2314yes—
170C4×Q8×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C42×C47—21no—
176C2×C42×C47—21no—
177C2×C42×C47C2311yescharacteristic
178#107×C47C2314yes—
179#103×C47C2314yes—
180#103×C47C2314yes—
181C4×C8×C47C2314yes—
182C23×D47—21no—
183C23×D47C2×D411yescharacteristic
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47C2412yes—
191C2×Q8×C47C2412yes—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47C2×D411yescharacteristic
203C22×Dic47C2×D411yescharacteristic
204C22×Dic47C2×D411yescharacteristic
205C2×D188—22no—
206C2×D188—22no—
207C2×D188—24no—
208C2×D188—21no—
209C2×D188—44no—
210C2×D188C2412yes—
211C2×C4×D47—24no—
212C2×C4×D47—22no—
213C2×C4×D47—22no—
214C2×C4×D47—24no—
215C2×C4×D47—42no—
216C2×C4×D47—44no—
217C2×C4×D47C2×D412yes—
218C2×C4×D47C2×D414yes—
219C2×C4×D47C2×D414yes—
220C2×C4×D47C2412yes—
221C2×Dic94—22no—
222C2×Dic94—22no—
223C2×Dic94—21no—
224C2×Dic94—24no—
225C2×Dic94—44no—
226C2×Dic94C2412yes—
227Q16×C47—28no—
228C2×C8×C47—22no—
229C2×C8×C47#4114yes—
230C2×C8×C47C2412yes—
231C2×C8×C47C2412yes—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—24no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C42×C47—24no—
239C42×C47—24no—
240C42×C47C2×D412yes—
241C42×C47C2412yes—
242#10625337—28no—
243#10625336—28no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—24no—
251C4⋊Dic47—21no—
252C4⋊Dic47—21no—
253C4⋊Dic47—24no—
254C4⋊Dic47—24no—
255C4⋊Dic47C2412yes—
256C4⋊Dic47C2412yes—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264C4×Dic47—24no—
265C4×Dic47C2×D412yes—
266C4×Dic47C2×D414yes—
267C4×Dic47C2×D414yes—
268C4×Dic47C2412yes—
269C2×C47⋊C8—22no—
270C2×C47⋊C8#4114yes—
271C2×C47⋊C8C2412yes—
272C2×C47⋊C8C2412yes—
273#10625325—28no—
274#10625324—28no—
275#10625324—28no—
276C23×C47C22×D411yescharacteristic
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47—42no—
282C22×D47—42no—
283C22×D47—42no—
284C22×D47C22×D412yes—
285Q8×C47—22no—
286Q8×C47—22no—
287Q8×C47—22no—
288Q8×C47—22no—
289Q8×C47—42no—
290Q8×C47—42no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47#13714yes—
301C2×C4×C47C22×D412yes—
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47C22×D412yes—
304C2×C4×C47C2×#4112yes—
305C2×C4×C47C2×#4112yes—
306C2×C4×C47C2511yescharacteristic
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47C22×D412yes—
317C2×Dic47C22×D412yes—
318C2×Dic47C22×D412yes—
319D188—22no—
320D188—22no—
321D188—48no—
322D188—42no—
323C4×D47—24no—
324C4×D47—28no—
325C4×D47—22no—
326C4×D47—22no—
327C4×D47—44no—
328C4×D47—48no—
329Dic94—22no—
330Dic94—22no—
331Dic94—48no—
332Dic94—42no—
333C8×C47—22no—
334C8×C47C2×#4114yes—
335C47⋊C8—22no—
336C47⋊C8C2×#4114yes—
337C2×#3172—471nomaximal, Sylow
338C22×C47#53212yes—
339C22×C47C2×#13712yes—
340C22×C47#57512yes—
341C22×C47C23×D411yescharacteristic
342C2×D47—22no—
343C2×D47—22no—
344C2×D47—22no—
345C2×D47—44no—
346C2×D47—42no—
347C2×D47—42no—
348C2×D47—42no—
349C2×D47—84no—
350C4×C47—22no—
351C4×C47—42no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47#53212yes—
356C4×C47C2×#13714yes—
357C4×C47C22×#4111yescharacteristic
358C4×C47C22×#4111yescharacteristic
359Dic47—22no—
360Dic47—22no—
361Dic47—22no—
362Dic47—42no—
363Dic47—42no—
364Dic47—42no—
365C2×#533—471no—
366C2×#529—471no—
367#3172—4716no—
368C2×#501—471no—
369C2×#497—471no—
370C2×#491—471no—
371C2×#489—471no—
372C2×#470—471no—
373C2×#470—471no—
374C2×#468—471no—
375C2×#468—471no—
376C2×C4×Q16—471no—
377C2×C4×Q16D4711yescharacteristic, complemented
378C2×C4×SD16—471no—
379C2×C4×SD16—471no—
380C2×C4×M16—471no—
381C2×C47#317214yescomplemented
382C2×C47C2×#53211yescharacteristic
383C2×C47C22×#13711yescharacteristic
384C2×C47C2×#57511yescharacteristic
385D47—42no—
386D47—82no—
387C22×Q16—471no—
388C22×Q16C2×D4711yescharacteristic
389C22×SD16—471no—
390C22×SD16—471no—
391C22×M16—471no—
392C22×M16—471no—
393#533—478no—
394#533—944no—
395C2×C4⋊Q8—471no—
396C2×C4⋊Q8—471no—
397#529—478no—
398#529—944no—
399C2×#126—941no—
400C2×#125—471no—
401C2×#125—941no—
402C2×#124—471no—
403C2×#123—941no—
404C2×C22⋊Q8—471no—
405C2×C22⋊Q8—471no—
406C2×C22⋊Q8—471no—
407C2×C22⋊Q8—941no—
408C2×#121—471no—
409C2×C4×Q8—471no—
410C2×C4×Q8—941no—
411C2×C4×Q8C2×D4711yescharacteristic
412C2×C4×Q8C2×D4711yescharacteristic
413C2×C4×D4—471no—
414C2×C4×D4—941no—
415C2×#117—941no—
416C2×#117—941no—
417C22×C42—471no—
418#501—478no—
419#497—478no—
420#491—478no—
421#489—478no—
422#470—478no—
423#470—478no—
424#468—478no—
425#468—478no—
426C4×Q16—478no—
427C4×Q16C2×D4718yescomplemented
428C4×SD16—478no—
429C4×SD16—478no—
430C2×#107—471no—
431C2×#107C2×D4711yescharacteristic
432C2×#106—471no—
433C2×#106—471no—
434C2×#103—471no—
435C2×#103—471no—
436C2×#103—471no—
437C2×#103—471no—
438C2×#103C2×D4711yescharacteristic
439C2×#103C2×D4711yescharacteristic
440C2×#102—471no—
441C2×#102—471no—
442C4×M16—478no—
443C2×#97—471no—
444C2×#97—471no—
445C2×C4×C8—471no—
446C2×C4×C8C2×D4711yescharacteristic
447C47C2×#317211yescharacteristic, complemented, Sylow
448C22×Q8—471no—
449C22×Q8—941no—
450C22×Q8C22×D4711yescharacteristic
451C22×Q8C22×D4711yescharacteristic
452C22×D4—471no—
453C22×D4—941no—
454C23×C4—471no—
455C23×C4—471no—
456C23×C4—471no—
457C23×C4—941no—
458C2×Q16—24no—
459C2×Q16—474no—
460C2×Q16—944no—
461C2×Q16C22×D4714yes—
462C2×SD16—474no—
463C2×SD16—474no—
464C2×SD16—944no—
465C2×SD16—944no—
466C2×M16—474no—
467C2×M16—474no—
468C2×M16—944no—
469C2×M16—944no—
470C22×C8—471no—
471C22×C8—471no—
472C22×C8C22×D4711yescharacteristic
473C22×C8C22×D4711yescharacteristic
474C4⋊Q8—474no—
475C4⋊Q8—474no—
476C4⋊Q8—942no—
477C4⋊Q8—942no—
478#126—948no—
479#125—474no—
480#125—942no—
481#125—948no—
482#124—474no—
483#124—942no—
484#123—948no—
485C22⋊Q8—474no—
486C22⋊Q8—474no—
487C22⋊Q8—474no—
488C22⋊Q8—942no—
489C22⋊Q8—948no—
490C22⋊Q8—942no—
491C22⋊Q8—942no—
492#121—474no—
493#121—942no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8—474no—
497C4×Q8—948no—
498C4×Q8—942no—
499C4×Q8C22×D4714yes—
500C4×Q8C22×D4714yes—
501C4×D4—474no—
502C4×D4—948no—
503C4×D4—942no—
504#117—948no—
505#117—948no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4C22×D4711yescharacteristic
520C2×C4⋊C4C22×D4711yescharacteristic
521C2×C22⋊C4—941no—
522C2×C22⋊C4—941no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—471no—
531C2×C42—471no—
532C2×C42—471no—
533C2×C42—474no—
534C2×C42—474no—
535C2×C42—941no—
536C2×C42C22×D4711yescharacteristic
537#107—474no—
538#107C22×D4714yes—
539#106—474no—
540#106—474no—
541#103—474no—
542#103—474no—
543#103—474no—
544#103—474no—
545#103C22×D4714yes—
546#103C22×D4714yes—
547#102—474no—
548#102—474no—
549#97—474no—
550#97—474no—
551C4×C8—474no—
552C4×C8C22×D4714yes—
553C24—471no—
554C24—941no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—472no—
562C2×Q8—944no—
563C2×Q8—941no—
564C2×Q8—942no—
565C2×Q8—942no—
566C2×Q8—1884no—
567C2×Q8C23×D4712yes—
568C2×Q8C23×D4712yes—
569C2×D4—472no—
570C2×D4—944no—
571C2×D4—941no—
572C2×D4—942no—
573C2×D4—942no—
574C2×D4—1884no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—471no—
582C22×C4—474no—
583C22×C4—472no—
584C22×C4—472no—
585C22×C4—474no—
586C22×C4—944no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—944no—
593C22×C4—1882no—
594C22×C4—1884no—
595C22×C4D4×D4711yescharacteristic
596C22×C4D4×D4711yescharacteristic
597C22×C4C23×D4711yescharacteristic
598Q16—28no—
599Q16—948no—
600SD16—948no—
601SD16—948no—
602M16—948no—
603M16—948no—
604C2×C8—22no—
605C2×C8—474no—
606C2×C8—472no—
607C2×C8—472no—
608C2×C8—942no—
609C2×C8#1062535014yes—
610C2×C8C23×D4712yes—
611C2×C8C23×D4712yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—472no—
617C4⋊C4—472no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—944no—
621C4⋊C4—944no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—941no—
628C4⋊C4—941no—
629C4⋊C4C23×D4712yes—
630C4⋊C4C23×D4712yes—
631C22⋊C4—944no—
632C22⋊C4—944no—
633C22⋊C4—944no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C42—24no—
639C42—24no—
640C42—474no—
641C42—472no—
642C42—474no—
643C42—472no—
644C42—944no—
645C42D4×D4712yes—
646C42C23×D4712yes—
647C23—472no—
648C23—942no—
649C23—942no—
650C23—942no—
651C23—942no—
652C23—1882no—
653C23—1882no—
654C23—1882no—
655C23C2×D4×D4711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—942no—
663Q8—942no—
664Q8—1888no—
665Q8—1882no—
666D4—942no—
667D4—942no—
668D4—1888no—
669D4—1882no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—472no—
680C2×C4—472no—
681C2×C4—472no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—948no—
686C2×C4—944no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—1884no—
693C2×C4—1882no—
694C2×C4—1882no—
695C2×C4—1882no—
696C2×C4—1888no—
697C2×C4#1309405614yes—
698C2×C4C2×D4×D4712yes—
699C2×C4C2×D4×D4712yes—
700C2×C4C2×D4×D4711yescharacteristic
701C2×C4#41×D4712yes—
702C2×C4C2×#1062535012yes—
703C2×C4C24×D4711yescharacteristic
704C8—22no—
705C8—474no—
706C8—942no—
707C8C2×#1062535014yes—
708C22—942no—
709C22—942no—
710C22—942no—
711C22—3764no—
712C22—1882no—
713C22—1882no—
714C22—1882no—
715C22—1884no—
716C22#1568967012yes—
717C22C2×#1309405612yes—
718C22#1568992012yes—
719C22C22×D4×D4711yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—942no—
726C4—942no—
727C4—942no—
728C4—1882no—
729C4—1882no—
730C4—1882no—
731C4#1568967012yes—
732C4C2×#1309405614yes—
733C4C2×#41×D4711yescharacteristic
734C4C22×#1062535011yescharacteristic
735C2—3762no—
736C2—1882no—
737C2#2025399214yesdirect product factor
738C2C2×#1568967011yescharacteristic
739C2C22×#1309405611yescharacteristic
740C2C2×#1568992011yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×Q16×C47C2
socleC23×C47C22×D4
prime radicalC2×#13093999C22
hypercenterC2×C4×Q16D47
hypocenterC47C2×#3172
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#15689677C2semidirect
3. #20253992C2direct (N × H)
4. C2×#15689531C2semidirect
5. C2×#15689516C2semidirect
6. C2×#15689490C2semidirect
7. C2×#15689484C2semidirect
8. C2×#15689380C2semidirect
9. C2×#15689378C2semidirect
12. C2×C4×#10625337C2semidirect
13. C2×C4×#10625325C2semidirect
14. C2×C4×#10625336C2semidirect
15. C2×C4×#10625324C2semidirect
16. C2×C4×Q16×C47C2semidirect
23. #15689677C22semidirect
45. #15689531C22semidirect
46. #15689516C22semidirect
47. #15689490C22semidirect
48. #15689484C22semidirect
49. #15689380C22semidirect
50. #15689378C22semidirect
53. C4×#10625337C22semidirect
54. C4×#10625325C22semidirect
55. C4×#10625336C22semidirect
65. C4×#10625324C22semidirect
72. C4×Q16×C47C22semidirect
377. C2×C4×Q16D47semidirect
381. C2×C47#3172semidirect
427. C4×Q16C2×D47semidirect
447. C47C2×#3172semidirect
737. C2#20253992direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896772
C2×#156896602
#202539922
C2×#156895312
C2×#156895162
C2×#156894902
C2×#156894842
C2×#156893802
C2×#156893782
C2×#156893722
C2×#156893702
C2×C4×#106253372
C2×C4×#106253252
C2×C4×#106253362
C2×C4×#106253242
C2×C4×Q16×C472
C2×#317247