Finite Group Databasebeta

← C2×#20253207 #27083814

Subgroups — C2×#20253207 #27083814

Order 12032.

2142 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D47C211yesmaximal, characteristic, complemented
2C2×C4×#10625354C211yesmaximal, characteristic
3#20253207C2116yesmaximal, direct product factor
4C2×#15689432C211yesmaximal, characteristic, complemented
5C2×#15689430C211yesmaximal, characteristic, complemented
6C2×#15689428C211yesmaximal, characteristic, complemented
7C2×#15689426C211yesmaximal, characteristic, complemented
8C2×#15689424C211yesmaximal, characteristic, complemented
9C2×#15689422C211yesmaximal, characteristic, complemented
10C2×#15689420C211yesmaximal, characteristic, complemented
11C2×#15689164C211yesmaximal, characteristic, complemented
12C2×#15689162C211yesmaximal, characteristic, complemented
13C2×#15689145C211yesmaximal, characteristic, complemented
14C2×#15689123C211yesmaximal, characteristic
15C2×#15689123C211yesmaximal, characteristic
16C2×C47×#479C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C2×#13094016C2211yescharacteristic
21C2×#13094015C2211yescharacteristic
22C2×#13094015C2211yescharacteristic
23C2×#13094014—21no—
24C2×#13094014—21no—
25#125×D47—24no—
26#125×D47C2218yescomplemented
27C4×#10625354—24no—
28C4×#10625354C2218yes—
29C2×Q8×Dic47C2211yescharacteristic
30C2×C4×D188—21no—
31C2×C4×D188C2211yescharacteristic
32C2×#13093986—21no—
33C2×#13093986C2211yescharacteristic
34C2×#13093982—21no—
35C2×#13093982C2211yescharacteristic
36C2×C4⋊C4×D47—21no—
37C2×C4⋊C4×D47—21no—
38C2×C4⋊C4×D47C2211yescharacteristic
39C2×C4⋊C4×D47C2211yescharacteristic
40C2×C42×D47—21no—
41C2×C42×D47C2211yescharacteristic
42#15689432C2218yescomplemented
43#15689430C2218yescomplemented
44#15689428C2218yescomplemented
45#15689426C2218yescomplemented
46#15689424C2218yescomplemented
47#15689422C2218yescomplemented
48#15689420C2218yescomplemented
49#15689164C2218yescomplemented
50#15689162C2218yescomplemented
51C2×#13093958C2211yescharacteristic
52C2×#13093957C2211yescharacteristic
53C2×#13093957C2211yescharacteristic
54C2×#13093956C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×#13093955C2211yescharacteristic
57#15689145C2218yescomplemented
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61#15689123C2218yes—
62#15689123C2218yes—
63C2×#13093948C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093944C2211yescharacteristic
68C2×#13093944C2211yescharacteristic
69C2×#125×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C47×#479C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C2×#10625354—22no—
78C2×#10625354—24no—
79C2×#10625354Q818yes—
80C2×#10625354C2314yes—
81C22×D188—21no—
82C22×D188C2311yescharacteristic
83C22×C4×D47—21no—
84C22×C4×D47—21no—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47D411yescharacteristic
89C22×C4×D47D411yescharacteristic
90C22×C4×D47C2311yescharacteristic
91C2×#10625324—24no—
92C2×#10625324—24no—
93C2×#10625324C2314yes—
94C2×#10625324C2314yes—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97#13094016—22no—
98#13094016C2314yes—
99#13094015—22no—
100#13094015—22no—
101#13094015C2314yes—
102#13094015C2314yes—
103#13094014—28no—
104#13094014—28no—
105Q8×Dic47—22no—
106Q8×Dic47C2314yes—
107C4×D188—28no—
108C4×D188—22no—
109C4×D188C2314yes—
110#13093986—28no—
111#13093986—22no—
112#13093986C2314yes—
113#13093982—22no—
114#13093982—28no—
115#13093982C2314yes—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×Dic47⋊C4—21no—
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C4⋊C4×D47—28no—
129C4⋊C4×D47—28no—
130C4⋊C4×D47—22no—
131C4⋊C4×D47—22no—
132C4⋊C4×D47C2314yes—
133C4⋊C4×D47C2314yes—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×C4×Dic47—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47D411yescharacteristic
140C2×C4×Dic47D411yescharacteristic
141C2×C4×Dic47C2311yescharacteristic
142C42×D47—28no—
143C42×D47D414yes—
144C42×D47C2314yes—
145#13093958C2314yes—
146#13093957C2314yes—
147#13093957C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152Dic47⋊C8C2314yes—
153Dic47⋊C8C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
158#13093944C2314yes—
159#13093944C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×C8×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163#125×C47—22no—
164#125×C47C2314yes—
165C4×Q8×C47—22no—
166C4×Q8×C47C2314yes—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C42×C47—21no—
174C2×C42×C47C2311yescharacteristic
175#107×C47C2314yes—
176#106×C47C2314yes—
177C4⋊C8×C47C2314yes—
178#103×C47C2314yes—
179#103×C47C2314yes—
180C23×D47—21no—
181C23×D47C2×D411yescharacteristic
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47C2×Q814yes—
185C2×Q8×C47C2412yes—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2411yescharacteristic
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47C2×D411yescharacteristic
197C22×Dic47C2×D411yescharacteristic
198C22×Dic47C2×D411yescharacteristic
199#10625354—216no—
200#10625354—28no—
201#10625354C2×Q8116yes—
202C2×D188—28no—
203C2×D188—24no—
204C2×D188—21no—
205C2×D188—22no—
206C2×D188C2×Q814yes—
207C2×D188C2412yes—
208C2×C4×D47—28no—
209C2×C4×D47—24no—
210C2×C4×D47—24no—
211C2×C4×D47—24no—
212C2×C4×D47—24no—
213C2×C4×D47—24no—
214C2×C4×D47—42no—
215C2×C4×D47—42no—
216C2×C4×D47—44no—
217C2×C4×D47—44no—
218C2×C4×D47—44no—
219C2×C4×D47—44no—
220C2×C4×D47C2×D414yes—
221C2×C4×D47C2×D414yes—
222C2×C4×D47C2×D412yes—
223C2×C4×D47C2×Q814yes—
224C2×C4×D47#4114yes—
225C2×C4×D47C2412yes—
226C2×C8×C47—22no—
227C2×C8×C47—22no—
228C2×C8×C47C2412yes—
229C2×C8×C47C2412yes—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C4⋊C4×C47C2412yes—
239C42×C47—24no—
240C42×C47C2×D412yes—
241C42×C47C2412yes—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47—24no—
249C4⋊Dic47—24no—
250C4⋊Dic47—24no—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253C4⋊Dic47C2412yes—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260C4×Dic47—24no—
261C4×Dic47—24no—
262C4×Dic47C2×D414yes—
263C4×Dic47C2×D412yes—
264C4×Dic47C2×D414yes—
265C4×Dic47C2412yes—
266C2×C47⋊C8—22no—
267C2×C47⋊C8—22no—
268C2×C47⋊C8C2412yes—
269C2×C47⋊C8C2412yes—
270#10625324—28no—
271#10625324—28no—
272C23×C47C22×D411yescharacteristic
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—24no—
276C22×D47—22no—
277C22×D47—42no—
278C22×D47—42no—
279C22×D47C22⋊Q814yes—
280C22×D47C22×D412yes—
281Q8×C47—24no—
282Q8×C47—22no—
283Q8×C47C22×Q814yes—
284C2×C4×C47—24no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47C22×D412yes—
295C2×C4×C47C22×D412yes—
296C2×C4×C47C22×D411yescharacteristic
297C2×C4×C47C22×Q812yes—
298C2×C4×C47C2×#4112yes—
299C2×C4×C47C2511yescharacteristic
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47C22⋊Q814yes—
309C2×Dic47C22×D412yes—
310C2×Dic47C22×D412yes—
311C2×Dic47C22×D412yes—
312D188—216no—
313D188—24no—
314D188—22no—
315D188C22×Q814yes—
316C4×D47—216no—
317C4×D47—44no—
318C4×D47—44no—
319C4×D47—48no—
320C4×D47—48no—
321C4×D47—48no—
322C4×D47—48no—
323C4×D47C22⋊Q818yes—
324C4×D47C22×Q814yes—
325C4×D47C2×#4114yes—
326C8×C47—22no—
327C8×C47—22no—
328C47⋊C8—22no—
329C47⋊C8—22no—
330C2×#3080—471nomaximal, Sylow
331C22×C47C2×C22⋊Q812yes—
332C22×C47#57512yes—
333C22×C47#57512yes—
334C22×C47C23×D411yescharacteristic
335C2×D47—28no—
336C2×D47—22no—
337C2×D47—22no—
338C2×D47—24no—
339C2×D47—48no—
340C2×D47—42no—
341C2×D47—42no—
342C2×D47C2×C22⋊Q814yes—
343C4×C47—24no—
344C4×C47—22no—
345C4×C47—22no—
346C4×C47—42no—
347C4×C47—42no—
348C4×C47—42no—
349C4×C47C2×C22⋊Q812yes—
350C4×C47C23×Q811yescharacteristic
351C4×C47C22×#4111yescharacteristic
352Dic47—22no—
353Dic47—22no—
354Dic47—42no—
355Dic47—42no—
356Dic47—42no—
357Dic47C2×C22⋊Q814yes—
358C22×#125—471no—
359C2×C4×#41—471no—
360#3080—4716no—
361C2×#479—471no—
362C2×#479—471no—
363C2×#479—471no—
364C2×#479D4711yescharacteristic, complemented
365C2×#478—471no—
366C2×#478—471no—
367C2×#478—471no—
368C2×#478—471no—
369C2×#428—471no—
370C2×#428—471no—
371C2×#423—471no—
372C2×#417—471no—
373C2×#417—471no—
374C2×C47#308014yescomplemented
375C2×C47C22×C22⋊Q811yescharacteristic
376C2×C47C2×#57511yescharacteristic
377C2×C47C2×#57511yescharacteristic
378D47—24no—
379D47—44no—
380C22×#41—471no—
381C22×M16—471no—
382C22×M16—471no—
383C2×#125—478no—
384C2×#125—471no—
385C2×#125—471no—
386C2×#125—471no—
387C2×#125—941no—
388C2×#125—941no—
389C2×#125—944no—
390C2×#125C2×D4711yescharacteristic
391C4×#41—478no—
392C4×#41—944no—
393C2×C4×Q8—471no—
394C2×C4×Q8C2×D4711yescharacteristic
395C2×C4×D4—471no—
396C2×C4×D4—471no—
397C2×C4×D4—941no—
398C2×C4×D4—941no—
399C2×#117—471no—
400C2×#117—941no—
401C22×C4⋊C4—471no—
402C22×C4⋊C4—471no—
403C22×C4⋊C4—941no—
404C22×C4⋊C4—941no—
405C22×C42—471no—
406C22×C42—941no—
407#479—478no—
408#479—478no—
409#479—478no—
410#479C2×D4718yescomplemented
411#478—478no—
412#478—478no—
413#478—478no—
414#478—478no—
415#428—478no—
416#428—478no—
417C2×#107—471no—
418C2×#107—471no—
419C2×#107—471no—
420C2×#107C2×D4711yescharacteristic
421C2×#106—471no—
422C2×#106—471no—
423C2×#106—471no—
424C2×#106C2×D4711yescharacteristic
425#423—478no—
426C2×C4⋊C8—471no—
427C2×C4⋊C8—471no—
428C2×C4⋊C8—471no—
429C2×C4⋊C8C2×D4711yescharacteristic
430#417—478no—
431#417—478no—
432C2×#103—471no—
433C2×#103—471no—
434C2×#103C2×D4711yescharacteristic
435C2×#103C2×D4711yescharacteristic
436C2×#102—471no—
437C2×#102—471no—
438C2×#102—471no—
439C2×#102—471no—
440C47C2×#308011yescharacteristic, complemented, Sylow
441C2×#41—478no—
442C2×#41—474no—
443C2×#41—942no—
444C2×#41—944no—
445C22×Q8C22×D4711yescharacteristic
446C22×D4—471no—
447C22×D4—941no—
448C23×C4—471no—
449C23×C4—471no—
450C23×C4—471no—
451C23×C4—941no—
452C23×C4—941no—
453C23×C4—941no—
454C23×C4—941no—
455C23×C4—941no—
456C2×M16—474no—
457C2×M16—474no—
458C2×M16—944no—
459C2×M16—944no—
460C22×C8—471no—
461C22×C8—471no—
462C22×C8C22×D4711yescharacteristic
463C22×C8C22×D4711yescharacteristic
464#125—22no—
465#125—474no—
466#125—474no—
467#125—474no—
468#125—948no—
469#125—948no—
470#125—942no—
471#125—942no—
472#125—942no—
473#125C22×D4714yes—
474C4×Q8—22no—
475C4×Q8—474no—
476C4×Q8—942no—
477C4×Q8C22×D4714yes—
478C4×D4—474no—
479C4×D4—474no—
480C4×D4—948no—
481C4×D4—942no—
482C4×D4—948no—
483C4×D4—942no—
484#117—474no—
485#117—948no—
486#117—942no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—471no—
491C2×C4⋊C4—471no—
492C2×C4⋊C4—471no—
493C2×C4⋊C4—474no—
494C2×C4⋊C4—474no—
495C2×C4⋊C4—942no—
496C2×C4⋊C4—942no—
497C2×C4⋊C4—948no—
498C2×C4⋊C4—948no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4C22×D4711yescharacteristic
509C2×C4⋊C4C22×D4711yescharacteristic
510C2×C4⋊C4C22×D4711yescharacteristic
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C42—21no—
515C2×C42—471no—
516C2×C42—471no—
517C2×C42—471no—
518C2×C42—474no—
519C2×C42—474no—
520C2×C42—948no—
521C2×C42—941no—
522C2×C42—941no—
523C2×C42C22×D4711yescharacteristic
524#107—474no—
525#107—474no—
526#107—474no—
527#107C22×D4714yes—
528#106—474no—
529#106—474no—
530#106—474no—
531#106C22×D4714yes—
532C4⋊C8—474no—
533C4⋊C8—474no—
534C4⋊C8—474no—
535C4⋊C8C22×D4714yes—
536#103—474no—
537#103—474no—
538#103C22×D4714yes—
539#103C22×D4714yes—
540#102—474no—
541#102—474no—
542#102—474no—
543#102—474no—
544C24—471no—
545C24—941no—
546#41—4716no—
547#41—9416no—
548#41—948no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8Q8×D4714yes—
552C2×Q8C23×D4712yes—
553C2×D4—474no—
554C2×D4—472no—
555C2×D4—944no—
556C2×D4—948no—
557C2×D4—941no—
558C2×D4—942no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—471no—
564C22×C4—472no—
565C22×C4—474no—
566C22×C4—474no—
567C22×C4—472no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4—474no—
571C22×C4—474no—
572C22×C4—944no—
573C22×C4—948no—
574C22×C4—944no—
575C22×C4—944no—
576C22×C4—944no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—944no—
581C22×C4—1882no—
582C22×C4—1882no—
583C22×C4—1884no—
584C22×C4—1884no—
585C22×C4—1884no—
586C22×C4—1884no—
587C22×C4D4×D4711yescharacteristic
588C22×C4D4×D4711yescharacteristic
589C22×C4C23×D4711yescharacteristic
590M16—948no—
591M16—948no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—472no—
595C2×C8—472no—
596C2×C8—942no—
597C2×C8—942no—
598C2×C8C23×D4712yes—
599C2×C8C23×D4712yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—472no—
607C4⋊C4—472no—
608C4⋊C4—472no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—944no—
616C4⋊C4—944no—
617C4⋊C4—944no—
618C4⋊C4—941no—
619C4⋊C4—941no—
620C4⋊C4—941no—
621C4⋊C4C23×D4712yes—
622C4⋊C4C23×D4712yes—
623C4⋊C4C23×D4712yes—
624C22⋊C4—944no—
625C22⋊C4—944no—
626C22⋊C4—944no—
627C42—24no—
628C42—474no—
629C42—474no—
630C42—472no—
631C42—472no—
632C42—944no—
633C42—944no—
634C42D4×D4712yes—
635C42C23×D4712yes—
636C23—474no—
637C23—472no—
638C23—942no—
639C23—942no—
640C23—944no—
641C23—942no—
642C23—1882no—
643C23—1882no—
644C23C2×D4×D4711yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8C2×Q8×D4714yes—
648D4—474no—
649D4—9416no—
650D4—944no—
651D4—942no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—474no—
663C2×C4—472no—
664C2×C4—478no—
665C2×C4—474no—
666C2×C4—474no—
667C2×C4—472no—
668C2×C4—472no—
669C2×C4—9416no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—1884no—
676C2×C4—1884no—
677C2×C4—1888no—
678C2×C4—1888no—
679C2×C4—1888no—
680C2×C4—1888no—
681C2×C4—1882no—
682C2×C4—1882no—
683C2×C4—1882no—
684C2×C4C2×D4×D4712yes—
685C2×C4C2×D4×D4712yes—
686C2×C4C2×D4×D4711yescharacteristic
687C2×C4C2×Q8×D4712yes—
688C2×C4#41×D4712yes—
689C2×C4C24×D4711yescharacteristic
690C8—22no—
691C8—22no—
692C8—942no—
693C8—942no—
694C22—474no—
695C22—948no—
696C22—942no—
697C22—942no—
698C22—944no—
699C22—1888no—
700C22—1882no—
701C22—1882no—
702C22C22⋊Q8×D4712yes—
703C22#1568992012yes—
704C22#1568992212yes—
705C22C22×D4×D4711yescharacteristic
706C4—22no—
707C4—22no—
708C4—24no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—474no—
713C4—942no—
714C4—942no—
715C4—1882no—
716C4—1882no—
717C4—1882no—
718C4C22⋊Q8×D4712yes—
719C4C22×Q8×D4711yescharacteristic
720C4C2×#41×D4711yescharacteristic
721C2—944no—
722C2—1884no—
723C2#2025320714yesdirect product factor
724C2C2×C22⋊Q8×D4711yescharacteristic
725C2C2×#1568992011yescharacteristic
726C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#479C2
socleC23×C47C22×D4
prime radicalC22×#10625354C22
hypercenterC2×#479D47
hypocenterC47C2×#3080
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#125×D47C2semidirect
3. #20253207C2direct (N × H)
4. C2×#15689432C2semidirect
5. C2×#15689430C2semidirect
6. C2×#15689428C2semidirect
7. C2×#15689426C2semidirect
8. C2×#15689424C2semidirect
9. C2×#15689422C2semidirect
10. C2×#15689420C2semidirect
11. C2×#15689164C2semidirect
12. C2×#15689162C2semidirect
13. C2×#15689145C2semidirect
16. C2×C47×#479C2semidirect
26. #125×D47C22semidirect
42. #15689432C22semidirect
43. #15689430C22semidirect
44. #15689428C22semidirect
45. #15689426C22semidirect
46. #15689424C22semidirect
47. #15689422C22semidirect
48. #15689420C22semidirect
49. #15689164C22semidirect
50. #15689162C22semidirect
57. #15689145C22semidirect
71. C47×#479C22semidirect
364. C2×#479D47semidirect
374. C2×C47#3080semidirect
410. #479C2×D47semidirect
440. C47C2×#3080semidirect
723. C2#20253207direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#125×D472
C2×C4×#106253542
#202532072
C2×#156894322
C2×#156894302
C2×#156894282
C2×#156894262
C2×#156894242
C2×#156894222
C2×#156894202
C2×#156891642
C2×#156891622
C2×#156891452
C2×#156891232
C2×C47×#4792
C2×#308047