Finite Group Databasebeta

← C2×#20254758 #27089131

Subgroups — C2×#20254758 #27089131

Order 12032.

1898 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×#15689652C211yesmaximal, characteristic
3#20254758C2116yesmaximal, direct product factor
4C2×#15689431C211yesmaximal, characteristic, complemented
5C2×#15689430C211yesmaximal, characteristic, complemented
6C2×#15689416C211yesmaximal, characteristic, complemented
7C2×#15689411C211yesmaximal, characteristic, complemented
8C2×#15689380C211yesmaximal, characteristic, complemented
9C2×#15689378C211yesmaximal, characteristic, complemented
10C2×#15689368C211yesmaximal, characteristic
11C2×#15689366C211yesmaximal, characteristic
12C2×#15689342C211yesmaximal, characteristic, complemented
13C2×#15689331C211yesmaximal, characteristic, complemented
14C2×#15689326C211yesmaximal, characteristic, complemented
15C2×#15689145C211yesmaximal, characteristic, complemented
16C2×C47×#464C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625335C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×#10625324C2211yescharacteristic
21#15689677—24no—
22#15689677C2218yescomplemented
23C2×#13094023C2211yescharacteristic
24C2×#13094022C2211yescharacteristic
25#15689652—24no—
26#15689652C2218yes—
27C2×#13094017—21no—
28C2×#13094016C2211yescharacteristic
29C2×#13094014—21no—
30C2×#13094006—21no—
31C2×#13094004C2211yescharacteristic
32C2×#13094002—21no—
33C2×#13094000C2211yescharacteristic
34C2×#13094000C2211yescharacteristic
35C2×#13093995C2211yescharacteristic
36C2×Q8×Dic47C2211yescharacteristic
37C2×C4×Dic94—21no—
38C2×C4×Dic94C2211yescharacteristic
39C2×D4×Dic47C2211yescharacteristic
40C2×(C22⋊D47)⋊C4—21no—
41C2×#13093981—21no—
42C2×#13093980—21no—
43C2×C42×D47C2211yescharacteristic
44#15689431C2218yescomplemented
45#15689430C2218yescomplemented
46#15689416C2218yescomplemented
47#15689411C2218yescomplemented
48#15689380C2218yescomplemented
49#15689378C2218yescomplemented
50#15689368C2218yes—
51#15689366C2218yes—
52#15689342C2218yescomplemented
53#15689331C2218yescomplemented
54#15689326C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59#15689145C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093948C2211yescharacteristic
67C2×#13093948C2211yescharacteristic
68C2×#13093945C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×SD16×C47C2211yescharacteristic
71C2×#124×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic
73C47×#464C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×C22⋊D47—21no—
80C23×Dic47—21no—
81C22×C4×D47D411yescharacteristic
82C22×C4×D47D411yescharacteristic
83C22×C4×D47C2311yescharacteristic
84C2×#10625337—42no—
85C2×#10625337C2314yes—
86C2×#10625335—42no—
87C2×#10625335C2314yes—
88C2×#10625324—42no—
89C2×#10625324—42no—
90C2×#10625324C2314yes—
91C2×#10625324C2314yes—
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94#13094023—22no—
95#13094023C2314yes—
96#13094022—22no—
97#13094022C2314yes—
98#13094017—28no—
99#13094016—22no—
100#13094016C2314yes—
101#13094014—28no—
102#13094006—28no—
103#13094004—22no—
104#13094004C2314yes—
105#13094002—28no—
106#13094000—22no—
107#13094000—22no—
108#13094000C2314yes—
109#13094000C2314yes—
110#13093995—22no—
111#13093995C2314yes—
112Q8×Dic47—22no—
113Q8×Dic47C2314yes—
114C4×Dic94—22no—
115C4×Dic94—28no—
116C4×Dic94C2314yes—
117D4×Dic47—22no—
118D4×Dic47C2314yes—
119(C22⋊D47)⋊C4—28no—
120#13093981—28no—
121#13093980—28no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
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×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47D411yescharacteristic
143C2×C4×Dic47D411yescharacteristic
144C2×C4×Dic47C2311yescharacteristic
145C42×D47D414yes—
146C42×D47C2314yes—
147#13093958C2314yes—
148#13093957C2314yes—
149#13093956C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152Dic47⋊C8C2314yes—
153Dic47⋊C8C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093948C2314yes—
157#13093948C2314yes—
158#13093948C2314yes—
159#13093945C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×Q8×C47C2311yescharacteristic
162C22×D4×C47C2311yescharacteristic
163C2×Q16×C47—42no—
164C2×Q16×C47C2314yes—
165C2×SD16×C47—42no—
166C2×SD16×C47C2314yes—
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169#124×C47—22no—
170#124×C47C2314yes—
171C4×Q8×C47—22no—
172C4×Q8×C47C2314yes—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C42×C47—21no—
178C2×C42×C47C2311yescharacteristic
179C4⋊C8×C47C2314yes—
180#103×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—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—
192C2×D4×C47—21no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47C2412yes—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2411yescharacteristic
202C2×C22⋊D47—24no—
203C2×C22⋊D47—44no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—24no—
209C22×Dic47—44no—
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213C2×C4×D47—22no—
214C2×C4×D47—22no—
215C2×C4×D47—24no—
216C2×C4×D47—42no—
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—44no—
228SD16×C47—44no—
229C2×C8×C47—22no—
230C2×C8×C47—22no—
231C2×C8×C47C2412yes—
232C2×C8×C47C2412yes—
233C4⋊C4×C47—24no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47C2412yes—
236C22⋊C4×C47—24no—
237C22⋊C4×C47—24no—
238C42×C47—24no—
239C42×C47C2×D412yes—
240C42×C47C2412yes—
241C22⋊Dic47—24no—
242C22⋊Dic47—24no—
243#10625337—44no—
244#10625335—44no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248C4⋊Dic47—21no—
249C4⋊Dic47—21no—
250C4⋊Dic47—21no—
251C4⋊Dic47—24no—
252C4⋊Dic47—24no—
253C4⋊Dic47C2412yes—
254C4⋊Dic47C2412yes—
255C4⋊Dic47C2412yes—
256Dic47⋊C4—24no—
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×Dic47—24no—
266C4×Dic47C2×D412yes—
267C4×Dic47C2×D414yes—
268C4×Dic47C2×D414yes—
269C4×Dic47C2412yes—
270C2×C47⋊C8—22no—
271C2×C47⋊C8—22no—
272C2×C47⋊C8C2412yes—
273C2×C47⋊C8C2412yes—
274#10625324—44no—
275#10625324—44no—
276C23×C47—22no—
277C23×C47—42no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47C22×D411yescharacteristic
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47C22×D412yes—
285Q8×C47—22no—
286Q8×C47—22no—
287Q8×C47—22no—
288Q8×C47—22no—
289Q8×C47—42no—
290Q8×C47—42no—
291D4×C47—22no—
292D4×C47—22no—
293D4×C47—42no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47H(5,𝔽2)12yes—
306C2×C4×C472−1+412yes—
307C2×C4×C47C2511yescharacteristic
308C22⋊D47—48no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319C2×Dic47—48no—
320C2×Dic47#13714yes—
321C2×Dic47C22×D412yes—
322C2×Dic47C22×D412yes—
323C2×Dic47C22×D412yes—
324C4×D47—24no—
325C4×D47—22no—
326C4×D47—22no—
327C4×D47—28no—
328C4×D47—44no—
329Dic94—22no—
330Dic94—22no—
331Dic94—48no—
332Dic94—42no—
333C8×C47—22no—
334C8×C47—22no—
335C47⋊C8—22no—
336C47⋊C8—22no—
337C2×#3252—471nomaximal, Sylow
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—84no—
342C22×C47#53712yes—
343C22×C47C2×#13712yes—
344C22×C47#57512yes—
345C22×C47C23×D411yescharacteristic
346C2×D47—22no—
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—44no—
350C4×C47—22no—
351C4×C47—22no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47#53712yes—
356C4×C47C2×H(5,𝔽2)11yescharacteristic
357C4×C47C2×2−1+411yescharacteristic
358Dic47—22no—
359Dic47—22no—
360Dic47—42no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47C2×#13714yes—
365C2×#533—471no—
366C2×#529—471no—
367#3252—4716no—
368C2×#479—471no—
369C2×#479—471no—
370C2×#477—471no—
371C2×#476—471no—
372C2×#470—471no—
373C2×#470—471no—
374C2×#468—471no—
375C2×#468—471no—
376C2×#464—471no—
377C2×#464D4711yescharacteristic, complemented
378C2×#462—471no—
379C2×#461—471no—
380C2×#423—471no—
381C2×C47—82no—
382C2×C47#325214yescomplemented
383C2×C47C2×#53711yescharacteristic
384C2×C47C22×#13711yescharacteristic
385C2×C47C2×#57511yescharacteristic
386D47—42no—
387C22×Q16—471no—
388C22×Q16C2×D4711yescharacteristic
389C22×SD16—471no—
390C22×SD16C2×D4711yescharacteristic
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×#124C2×D4711yescharacteristic
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—471no—
411C2×C4×Q8—941no—
412C2×C4×Q8C2×D4711yescharacteristic
413C2×C4×D4—471no—
414C2×C4×D4—941no—
415C2×#117—941no—
416C2×#117—941no—
417C22×C42—471no—
418#479—478no—
419#479—478no—
420#477—478no—
421#476—478no—
422#470—478no—
423#470—478no—
424#468—478no—
425#468—478no—
426#464—478no—
427#464C2×D4718yescomplemented
428#462—478no—
429#461—478no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#106—471no—
433C2×#106—471no—
434#423—478no—
435C2×C4⋊C8—471no—
436C2×C4⋊C8—471no—
437C2×C4⋊C8—471no—
438C2×C4⋊C8C2×D4711yescharacteristic
439C2×#103—471no—
440C2×#103—471no—
441C2×#103—471no—
442C2×#103—471no—
443C2×#103—471no—
444C2×#103C2×D4711yescharacteristic
445C2×#102—471no—
446C2×#102C2×D4711yescharacteristic
447C47C2×#325211yescharacteristic, complemented, Sylow
448C22×Q8—471no—
449C22×Q8—941no—
450C22×Q8C22×D4711yescharacteristic
451C22×Q8C22×D4711yescharacteristic
452C22×D4—941no—
453C22×D4C22×D4711yescharacteristic
454C23×C4—471no—
455C23×C4—471no—
456C23×C4—471no—
457C23×C4—941no—
458C2×Q16—42no—
459C2×Q16—474no—
460C2×Q16—1882no—
461C2×Q16C22×D4714yes—
462C2×SD16—42no—
463C2×SD16—474no—
464C2×SD16—1882no—
465C2×SD16C22×D4714yes—
466C2×M16—474no—
467C2×M16—474no—
468C2×M16—1882no—
469C2×M16—1882no—
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—948no—
481#125—942no—
482#124—22no—
483#124C22×D4714yes—
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—474no—
496C4×Q8—474no—
497C4×Q8—948no—
498C4×Q8—942no—
499C4×Q8—942no—
500C4×Q8C22×D4714yes—
501C4×D4—474no—
502C4×D4—942no—
503C4×D4—948no—
504#117—948no—
505#117—948no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—471no—
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⋊C4—941no—
520C2×C4⋊C4C22×D4711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
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—471no—
530C2×C42—471no—
531C2×C42—471no—
532C2×C42—474no—
533C2×C42—474no—
534C2×C42—941no—
535C2×C42—941no—
536C2×C42C22×D4711yescharacteristic
537#107—474no—
538#107—474no—
539#106—474no—
540#106—474no—
541C4⋊C8—474no—
542C4⋊C8—474no—
543C4⋊C8—474no—
544C4⋊C8C22×D4714yes—
545#103—474no—
546#103—474no—
547#103—474no—
548#103—474no—
549#103—474no—
550#103C22×D4714yes—
551#102—474no—
552#102C22×D4714yes—
553C24—21no—
554C24—471no—
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—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—944no—
573C2×D4—1884no—
574C2×D4C23×D4712yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—471no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—474no—
582C22×C4—472no—
583C22×C4—472no—
584C22×C4—474no—
585C22×C4—944no—
586C22×C4—944no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—1882no—
594C22×C4—1884no—
595C22×C4D4×D4711yescharacteristic
596C22×C4D4×D4711yescharacteristic
597C22×C4C23×D4711yescharacteristic
598Q16—44no—
599Q16—1884no—
600SD16—44no—
601SD16—1884no—
602M16—1884no—
603M16—1884no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—472no—
607C2×C8—472no—
608C2×C8—942no—
609C2×C8—942no—
610C2×C8C23×D4712yes—
611C2×C8C23×D4712yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—472no—
615C4⋊C4—472no—
616C4⋊C4—472no—
617C4⋊C4—944no—
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⋊C4—941no—
630C4⋊C4C23×D4712yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—944no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C42—24no—
639C42—474no—
640C42—472no—
641C42—474no—
642C42—472no—
643C42—944no—
644C42—944no—
645C42D4×D4712yes—
646C42C23×D4712yes—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—472no—
652C23—942no—
653C23—942no—
654C23—942no—
655C23C2×D4×D4711yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—942no—
663Q8—942no—
664Q8—1888no—
665Q8—1882no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—1888no—
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—474no—
679C2×C4—472no—
680C2×C4—472no—
681C2×C4—472no—
682C2×C4—948no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—944no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—1884no—
693C2×C4—1888no—
694C2×C4—1882no—
695C2×C4—1882no—
696C2×C4—1882no—
697C2×C4—1882no—
698C2×C4C2×D4×D4712yes—
699C2×C4C2×D4×D4712yes—
700C2×C4C2×D4×D4711yescharacteristic
701C2×C4#1309406912yes—
702C2×C4#1309407112yes—
703C2×C4C24×D4711yescharacteristic
704C8—22no—
705C8—22no—
706C8—942no—
707C8—942no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—84no—
712C22—942no—
713C22—942no—
714C22—942no—
715C22—1884no—
716C22#1568970212yes—
717C22#137×D4712yes—
718C22#1568992012yes—
719C22C22×D4×D4711yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—474no—
726C4—942no—
727C4—942no—
728C4—1882no—
729C4—1882no—
730C4—1882no—
731C4—1882no—
732C4#1568970212yes—
733C4C2×#1309406911yescharacteristic
734C4C2×#1309407111yescharacteristic
735C2—82no—
736C2—1882no—
737C2#2025475814yesdirect product factor
738C2C2×#1568970211yescharacteristic
739C2C2×#137×D4711yescharacteristic
740C2C2×#1568992011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#464C2
socleC23×C47C22×D4
prime radicalC2×#13093995C22
hypercenterC2×#464D47
hypocenterC47C2×#3252
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#15689677C2semidirect
3. #20254758C2direct (N × H)
4. C2×#15689431C2semidirect
5. C2×#15689430C2semidirect
6. C2×#15689416C2semidirect
7. C2×#15689411C2semidirect
8. C2×#15689380C2semidirect
9. C2×#15689378C2semidirect
12. C2×#15689342C2semidirect
13. C2×#15689331C2semidirect
14. C2×#15689326C2semidirect
15. C2×#15689145C2semidirect
16. C2×C47×#464C2semidirect
22. #15689677C22semidirect
44. #15689431C22semidirect
45. #15689430C22semidirect
46. #15689416C22semidirect
47. #15689411C22semidirect
48. #15689380C22semidirect
49. #15689378C22semidirect
52. #15689342C22semidirect
53. #15689331C22semidirect
54. #15689326C22semidirect
59. #15689145C22semidirect
73. C47×#464C22semidirect
377. C2×#464D47semidirect
382. C2×C47#3252semidirect
427. #464C2×D47semidirect
447. C47C2×#3252semidirect
737. C2#20254758direct (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×#156896522
#202547582
C2×#156894312
C2×#156894302
C2×#156894162
C2×#156894112
C2×#156893802
C2×#156893782
C2×#156893682
C2×#156893662
C2×#156893422
C2×#156893312
C2×#156893262
C2×#156891452
C2×C47×#4642
C2×#325247