Finite Group Databasebeta

← C2×#20254891 #27091252

Subgroups — C2×#20254891 #27091252

Order 12032.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094056C211yesmaximal, characteristic, complemented
2C23×#10625336C211yesmaximal, characteristic, complemented
3C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
4C2×#15689764C211yesmaximal, characteristic
5#20254891C2116yesmaximal, direct product factor
6C2×#15689516C211yesmaximal, characteristic, complemented
7C2×#15689372C211yesmaximal, characteristic, complemented
8C2×#15689362C211yesmaximal, characteristic, complemented
9C2×#15689347C211yesmaximal, characteristic, complemented
10C2×#15689327C211yesmaximal, characteristic, complemented
11C2×#15689284C211yesmaximal, characteristic, complemented
12C2×#15689263C211yesmaximal, characteristic, complemented
13C2×#15689276C211yesmaximal, characteristic, complemented
14C2×#15689226C211yesmaximal, characteristic, complemented
15C2×#15689191C211yesmaximal, characteristic, complemented
16C2×C47×#451C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic, complemented
19C23×D188C2211yescharacteristic
20C2×#13094056—28no—
21C2×#13094056C2218yescomplemented
22C22×#10625337C2211yescharacteristic, complemented
23C22×#10625325C2211yescharacteristic
24C22×#10625325C2211yescharacteristic
25C22×#10625336—28no—
26C22×#10625336C2211yescharacteristic
27C22×#10625336C2211yescharacteristic
28C22×#10625336C2211yescharacteristic
29C22×#10625336C2211yescharacteristic
30C22×#10625336C2218yescomplemented
31C22×#10625324C2211yescharacteristic, complemented
32C23×C47⋊C8C2211yescharacteristic
33Q8×C22⋊D47—24no—
34Q8×C22⋊D47C2218yescomplemented
35#15689764—24no—
36#15689764C2218yes—
37C2×#13094022—21no—
38C2×#13094022C2211yescharacteristic, complemented
39C2×#13094013C2211yescharacteristic
40C2×#13094009—21no—
41C2×#13094003—21no—
42C2×#13094003C2211yescharacteristic
43C2×#13094000—21no—
44C2×#13094000C2211yescharacteristic, complemented
45C2×#13093999—21no—
46C2×#13093999C2211yescharacteristic
47C2×#13093994—21no—
48C2×Q8×Dic47C2211yescharacteristic, complemented
49C2×#13093986C2211yescharacteristic
50C2×C4×C22⋊D47—21no—
51C2×C4×C22⋊D47C2211yescharacteristic
52C2×C22⋊C4×D47—21no—
53#15689516C2218yescomplemented
54#15689372C2218yescomplemented
55#15689362C2218yescomplemented
56#15689347C2218yescomplemented
57#15689327C2218yescomplemented
58#15689284C2218yescomplemented
59#15689276C2218yescomplemented
60#15689263C2218yescomplemented
61#15689226C2218yescomplemented
62#15689191C2218yescomplemented
63C2×#13093957C2211yescharacteristic, complemented
64C2×Dic47⋊C8C2211yescharacteristic, complemented
65C2×#13093948C2211yescharacteristic, complemented
66C2×#13093947C2211yescharacteristic, complemented
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
70C2×#13093934C2211yescharacteristic, complemented
71C23×Q8×C47C2211yescharacteristic
72C22×Q16×C47C2211yescharacteristic, complemented
73C22×Q16×C47C2211yescharacteristic, complemented
74C2×C22⋊Q8×C47C2211yescharacteristic
75C47×#451C2218yescomplemented
76C2×#103×C47C2211yescharacteristic, complemented
77C2×#103×C47C2211yescharacteristic, complemented
78C2×C22⋊C8×C47C2211yescharacteristic
79C24×D47—21no—
80C2×#10625354—22no—
81C2×#10625354—24no—
82C2×#10625354—42no—
83C2×#10625354C2314yes—
84C22×Dic94—21no—
85C22×Dic94C2311yescharacteristic
86C2×Q8×D47—22no—
87C2×Q8×D47—24no—
88C2×Q8×D47—42no—
89C2×Q8×D47C2314yescomplemented
90C22×D188—24no—
91C22×D188—21no—
92C22×D188—22no—
93C22×D188—21no—
94C22×D188—21no—
95C22×D188—42no—
96C22×D188C2311yescharacteristic
97C22×D188C2314yes—
98C22×D188C2311yescharacteristic
99C22×C22⋊D47D411yescharacteristic
100C22×C4×D47—21no—
101C22×C4×D47—21no—
102C22×C4×D47—21no—
103C22×C4×D47C2311yescharacteristic
104#13094056—232no—
105C2×#10625337—24no—
106C2×#10625337C2314yescomplemented
107C2×#10625325—24no—
108C2×#10625325—42no—
109C2×#10625325C2314yes—
110C2×#10625325C2314yes—
111C2×#10625336—24no—
112C2×#10625336—24no—
113C2×#10625336—232no—
114C2×#10625336—24no—
115C2×#10625336D418yescomplemented
116C2×#10625336C2314yes—
117C2×#10625336C2314yes—
118C2×#10625336C2314yes—
119C2×#10625336C2314yes—
120C2×#10625324—24no—
121C2×#10625324C2314yescomplemented
122C22×C47⋊C8—24no—
123C22×C47⋊C8C2311yescharacteristic
124C22×C47⋊C8C2314yes—
125C22×C47⋊C8C2311yescharacteristic
126#13094022—28no—
127#13094022—22no—
128#13094022C2314yescomplemented
129#13094013—22no—
130#13094013C2314yes—
131#13094009—28no—
132#13094003—22no—
133#13094003—28no—
134#13094003C2314yes—
135#13094000—22no—
136#13094000—28no—
137#13094000C2314yescomplemented
138#13093999—22no—
139#13093999—28no—
140#13093999C2314yes—
141#13093994—28no—
142Q8×Dic47—22no—
143Q8×Dic47C2314yescomplemented
144#13093986—22no—
145#13093986C2314yes—
146C4×C22⋊D47—28no—
147C4×C22⋊D47D414yes—
148C4×C22⋊D47C2314yes—
149C2×C4⋊Dic47—21no—
150C2×C4⋊Dic47C2311yescharacteristic
151C2×Dic47⋊C4—21no—
152C2×Dic47⋊C4—21no—
153C2×Dic47⋊C4—21no—
154C2×Dic47⋊C4—21no—
155C2×Dic47⋊C4D411yescharacteristic
156C2×C22⋊Dic47—21no—
157C2×C22⋊Dic47D411yescharacteristic
158C2×(C2×D47)⋊C4—21no—
159C2×(C2×D47)⋊C4—21no—
160C2×(C2×D47)⋊C4—21no—
161C2×(C2×D47)⋊C4—21no—
162C2×(C2×D47)⋊C4—21no—
163C2×(C2×D47)⋊C4D411yescharacteristic
164C22⋊C4×D47—28no—
165C2×C4×Dic47—21no—
166C2×C4×Dic47C2311yescharacteristic
167#13093957C2314yescomplemented
168Dic47⋊C8C2314yescomplemented
169#13093948C2314yescomplemented
170#13093947C2314yescomplemented
171#13093946C2314yes—
172#13093946C2314yes—
173(C2×D47)⋊C8C2314yescomplemented
174#13093934C2314yescomplemented
175C22×Q8×C47—22no—
176C22×Q8×C47—21no—
177C22×Q8×C47—24no—
178C22×Q8×C47—42no—
179C22×Q8×C47C2311yescharacteristic
180C22×Q8×C47C2311yescharacteristic
181C22×Q8×C47C2314yes—
182C22×Q8×C47C2311yescharacteristic
183C23×C4×C47—21no—
184C23×C4×C47C2311yescharacteristic
185C2×Q16×C47—24no—
186C2×Q16×C47—42no—
187C2×Q16×C47C2314yescomplemented
188C2×Q16×C47C2314yescomplemented
189C22×C8×C47C2311yescharacteristic
190C22×C8×C47C2311yescharacteristic
191C22⋊Q8×C47—22no—
192C22⋊Q8×C47C2314yes—
193C2×C4⋊C4×C47—21no—
194C2×C4⋊C4×C47C2311yescharacteristic
195C2×C22⋊C4×C47—21no—
196#103×C47C2314yescomplemented
197#103×C47C2314yescomplemented
198C22⋊C8×C47C2314yes—
199C24×C47C2×D411yescharacteristic
200C23×D47—21no—
201C23×D47—21no—
202C23×D47—24no—
203C23×D47—44no—
204C23×D47—44no—
205C23×D47—82no—
206C23×D47C2×D411yescharacteristic
207C2×Q8×C47—21no—
208C2×Q8×C47—21no—
209C2×Q8×C47—24no—
210C2×Q8×C47—21no—
211C2×Q8×C47—22no—
212C2×Q8×C47—28no—
213C2×Q8×C47—22no—
214C2×Q8×C47—22no—
215C2×Q8×C47—22no—
216C2×Q8×C47—22no—
217C2×Q8×C47—44no—
218C2×Q8×C47—44no—
219C2×Q8×C47—48no—
220C2×Q8×C47C2×D414yes—
221C2×Q8×C47C2412yes—
222C2×Q8×C47C2412yes—
223C2×Q8×C47C2412yes—
224C22×C4×C47—21no—
225C22×C4×C47—22no—
226C22×C4×C47—22no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—24no—
231C22×C4×C47—44no—
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D412yes—
234C22×C4×C47C2412yes—
235C22×C4×C47C2411yescharacteristic
236C2×C22⋊D47—24no—
237C2×C22⋊D47C2×D414yes—
238C22×Dic47—21no—
239C22×Dic47—21no—
240C22×Dic47C2×D411yescharacteristic
241C22×Dic47C2×D411yescharacteristic
242C22×Dic47C2×D411yescharacteristic
243#10625354—28no—
244#10625354—44no—
245#10625354—48no—
246Q8×D47—28no—
247Q8×D47—44no—
248Q8×D47—48no—
249C2×D188—21no—
250C2×D188—22no—
251C2×D188—22no—
252C2×D188—22no—
253C2×D188—28no—
254C2×D188—24no—
255C2×D188—24no—
256C2×D188—21no—
257C2×D188—24no—
258C2×D188—44no—
259C2×D188—48no—
260C2×D188—44no—
261C2×D188—44no—
262C2×D188—82no—
263C2×D188C2×D414yes—
264C2×D188C2412yes—
265C2×D188C2412yes—
266C2×C4×D47—22no—
267C2×C4×D47—22no—
268C2×C4×D47—24no—
269C2×C4×D47—24no—
270C2×C4×D47—24no—
271C2×C4×D47—44no—
272C2×C4×D47—44no—
273C2×C4×D47—82no—
274C2×C4×D47C2×D412yes—
275C2×C4×D47C2412yes—
276C2×Dic94—22no—
277C2×Dic94—22no—
278C2×Dic94—21no—
279C2×Dic94—24no—
280C2×Dic94—44no—
281C2×Dic94C2412yes—
282Q16×C47—28no—
283Q16×C47—44no—
284C2×C8×C47—22no—
285C2×C8×C47—22no—
286C2×C8×C47C2412yes—
287C2×C8×C47C2412yes—
288C4⋊C4×C47—24no—
289C4⋊C4×C47—21no—
290C4⋊C4×C47C2412yes—
291C22⋊C4×C47—24no—
292C22⋊Dic47—24no—
293C22⋊Dic47C2×D414yes—
294#10625337—28no—
295#10625336—28no—
296#10625336—28no—
297#10625336—28no—
298#10625336C2×D4116yescomplemented
299(C2×D47)⋊C4—24no—
300(C2×D47)⋊C4—24no—
301(C2×D47)⋊C4—24no—
302(C2×D47)⋊C4—24no—
303(C2×D47)⋊C4—24no—
304(C2×D47)⋊C4C2×D414yes—
305C4⋊Dic47—21no—
306C4⋊Dic47—24no—
307C4⋊Dic47C2412yes—
308Dic47⋊C4—24no—
309Dic47⋊C4—24no—
310Dic47⋊C4—24no—
311Dic47⋊C4—24no—
312Dic47⋊C4C2×D414yes—
313C4×Dic47—24no—
314C4×Dic47C2×D412yes—
315C4×Dic47C2412yes—
316C2×C47⋊C8—22no—
317C2×C47⋊C8—28no—
318C2×C47⋊C8C2×D414yes—
319C2×C47⋊C8C2412yes—
320C2×C47⋊C8C2412yes—
321#10625325—28no—
322#10625325—44no—
323#10625324—28no—
324C23×C47—22no—
325C23×C47—22no—
326C23×C47#13714yescomplemented
327C23×C47C22×D412yes—
328C23×C47C22×D411yescharacteristic
329C22×D47—22no—
330C22×D47—24no—
331C22×D47—22no—
332C22×D47—22no—
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—48no—
336C22×D47—42no—
337C22×D47—42no—
338C22×D47—42no—
339C22×D47—42no—
340C22×D47—48no—
341C22×D47—42no—
342C22×D47—84no—
343C22×D47—816no—
344C22×D47C22×D412yes—
345Q8×C47—24no—
346Q8×C47—22no—
347Q8×C47—22no—
348Q8×C47—22no—
349Q8×C47—22no—
350Q8×C47—22no—
351Q8×C47—48no—
352Q8×C47—42no—
353Q8×C47—42no—
354Q8×C47C22×D414yes—
355C2×C4×C47—24no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—24no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—48no—
365C2×C4×C47—42no—
366C2×C4×C47—42no—
367C2×C4×C47—42no—
368C2×C4×C47C22×D412yes—
369C2×C4×C47C22×D411yescharacteristic
370C2×C4×C47C22×D412yes—
371C2×C4×C47H(5,𝔽2)12yes—
372C2×C4×C47C2511yescharacteristic
373C22⋊D47—28no—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—42no—
380C2×Dic47—42no—
381C2×Dic47C22×D412yes—
382C2×Dic47C22×D412yes—
383C2×Dic47C22×D412yes—
384D188—24no—
385D188—22no—
386D188—22no—
387D188—22no—
388D188—48no—
389D188—48no—
390D188—42no—
391D188—84no—
392D188C22×D414yes—
393C4×D47—24no—
394C4×D47—22no—
395C4×D47—22no—
396C4×D47—48no—
397C4×D47—48no—
398C4×D47—84no—
399Dic94—22no—
400Dic94—22no—
401Dic94—48no—
402Dic94—42no—
403C8×C47—22no—
404C8×C47—22no—
405C47⋊C8—22no—
406C47⋊C8C22×D414yes—
407C2×#3266—471nomaximal, Sylow
408C22×C47—22no—
409C22×C47—28no—
410C22×C47—22no—
411C22×C47D4212yes—
412C22×C47C2×#13712yes—
413C22×C47C2×#13714yescomplemented
414C22×C47#57712yes—
415C22×C47C23×D411yescharacteristic
416C2×D47—22no—
417C2×D47—24no—
418C2×D47—22no—
419C2×D47—22no—
420C2×D47—44no—
421C2×D47—48no—
422C2×D47—42no—
423C2×D47—42no—
424C2×D47—42no—
425C2×D47—42no—
426C2×D47—42no—
427C2×D47—816no—
428C2×D47—84no—
429C4×C47—24no—
430C4×C47—22no—
431C4×C47—42no—
432C4×C47—42no—
433C4×C47—42no—
434C4×C47D4212yes—
435C4×C47C23×D411yescharacteristic
436C4×C47C2×H(5,𝔽2)11yescharacteristic
437Dic47—22no—
438Dic47—22no—
439Dic47—22no—
440Dic47—42no—
441Dic47—42no—
442C22×#137—471no—
443C23×SD16—471no—
444C2×D4×Q8—471no—
445C2×#546—471no—
446#3266—4716no—
447C2×#497—471no—
448C2×#468—471no—
449C2×#467—471no—
450C2×#464—471no—
451C2×#461—471no—
452C2×#452—471no—
453C2×#451D4711yescharacteristic, complemented
454C2×#448—471no—
455C2×#450—471no—
456C2×#440—471no—
457C2×#435—471no—
458C2×C47—24no—
459C2×C47#326614yescomplemented
460C2×C47C2×D4211yescharacteristic
461C2×C47C22×#13711yescharacteristic
462C2×C47C2×#57711yescharacteristic
463D47—42no—
464D47—44no—
465D47—82no—
466C22×#41—471no—
467C23×Q8—471no—
468C23×Q8C2×D4711yescharacteristic
469C23×D4—471no—
470C2×#137—478no—
471C2×#137—948no—
472C22×Q16—471no—
473C22×Q16C2×D4711yescharacteristic, complemented
474C22×Q16C2×D4711yescharacteristic, complemented
475C22×SD16—471no—
476C22×SD16—471no—
477C22×SD16—471no—
478C22×SD16—471no—
479C22×SD16—478no—
480C22×SD16—471no—
481C22×SD16—471no—
482C22×SD16—948no—
483C22×M16—471no—
484C23×C8—471no—
485D4×Q8—478no—
486D4×Q8—944no—
487#546—478no—
488#546—944no—
489C2×C4⋊Q8—471no—
490C2×C4⋊Q8—941no—
491C2×#124—471no—
492C2×#123—941no—
493C2×C22⋊Q8—471no—
494C2×C22⋊Q8—471no—
495C2×C22⋊Q8—941no—
496C2×C22⋊Q8—941no—
497C2×C22⋊Q8C2×D4711yescharacteristic
498C2×#121—471no—
499C2×#121—941no—
500C2×#120—941no—
501C2×C4×Q8—471no—
502C2×C4×D4—471no—
503C2×C4×D4—471no—
504C2×C4×D4—941no—
505C22×C22⋊C4—941no—
506#497—478no—
507#468—478no—
508#467—478no—
509#464—478no—
510#461—478no—
511#452—478no—
512#451C2×D4718yescomplemented
513#450—478no—
514#448—478no—
515#440—478no—
516#435—478no—
517C2×#107—471no—
518C2×C4⋊C8—471no—
519C2×#103—471no—
520C2×#103—471no—
521C2×#103C2×D4711yescharacteristic, complemented
522C2×#103C2×D4711yescharacteristic, complemented
523C2×#102—471no—
524C2×#102—471no—
525C2×C22⋊C8—471no—
526C2×C22⋊C8C2×D4711yescharacteristic
527C2×#97—471no—
528C47C2×#326611yescharacteristic, complemented, Sylow
529C25—941no—
530C2×#41—474no—
531C2×#41—942no—
532C2×#41—944no—
533C2×#41—1882no—
534C22×Q8—21no—
535C22×Q8—22no—
536C22×Q8—24no—
537C22×Q8—42no—
538C22×Q8—474no—
539C22×Q8—471no—
540C22×Q8—941no—
541C22×Q8—942no—
542C22×Q8—944no—
543C22×Q8—1882no—
544C22×Q8C22×D4711yescharacteristic
545C22×Q8C22×D4711yescharacteristic
546C22×Q8C22×D4714yes—
547C22×Q8C22×D4711yescharacteristic
548C22×D4—471no—
549C22×D4—471no—
550C22×D4—471no—
551C22×D4—474no—
552C22×D4—944no—
553C22×D4—941no—
554C22×D4—941no—
555C22×D4—941no—
556C22×D4—942no—
557C22×D4—1882no—
558C23×C4—21no—
559C23×C4—471no—
560C23×C4—941no—
561C23×C4—941no—
562C23×C4—941no—
563C23×C4C22×D4711yescharacteristic
564#137—9432no—
565C2×Q16—24no—
566C2×Q16—42no—
567C2×Q16—474no—
568C2×Q16—944no—
569C2×Q16C22×D4714yescomplemented
570C2×Q16C22×D4714yescomplemented
571C2×SD16—478no—
572C2×SD16—474no—
573C2×SD16—474no—
574C2×SD16—474no—
575C2×SD16—474no—
576C2×SD16—474no—
577C2×SD16—474no—
578C2×SD16—944no—
579C2×SD16—944no—
580C2×SD16—9432no—
581C2×SD16—944no—
582C2×SD16—944no—
583C2×SD16—1882no—
584C2×M16—474no—
585C2×M16—944no—
586C22×C8—471no—
587C22×C8—471no—
588C22×C8—474no—
589C22×C8—944no—
590C22×C8C22×D4711yescharacteristic
591C22×C8C22×D4711yescharacteristic
592C4⋊Q8—474no—
593C4⋊Q8—942no—
594C4⋊Q8—948no—
595#124—474no—
596#124—942no—
597#123—948no—
598C22⋊Q8—22no—
599C22⋊Q8—474no—
600C22⋊Q8—474no—
601C22⋊Q8—948no—
602C22⋊Q8—948no—
603C22⋊Q8—942no—
604C22⋊Q8—942no—
605C22⋊Q8C22×D4714yes—
606#121—474no—
607#121—948no—
608#121—942no—
609#120—948no—
610C4×Q8—474no—
611C4×Q8—942no—
612C4×D4—474no—
613C4×D4—474no—
614C4×D4—474no—
615C4×D4—942no—
616C4×D4—948no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—471no—
619C2×C4⋊C4—471no—
620C2×C4⋊C4—941no—
621C2×C4⋊C4—941no—
622C2×C4⋊C4—941no—
623C2×C4⋊C4—941no—
624C2×C4⋊C4—941no—
625C2×C4⋊C4C22×D4711yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—471no—
628C2×C22⋊C4—471no—
629C2×C22⋊C4—948no—
630C2×C22⋊C4—941no—
631C2×C22⋊C4—941no—
632C2×C22⋊C4—941no—
633C2×C22⋊C4—941no—
634C2×C22⋊C4—941no—
635C2×C22⋊C4—941no—
636C2×C42—471no—
637C2×C42—941no—
638#107—474no—
639C4⋊C8—474no—
640#103—474no—
641#103—474no—
642#103C22×D4714yescomplemented
643#103C22×D4714yescomplemented
644#102—474no—
645#102—474no—
646C22⋊C8—474no—
647C22⋊C8C22×D4714yes—
648#97—474no—
649C24—471no—
650C24—941no—
651C24—944no—
652C24—941no—
653C24—3762no—
654C24—1884no—
655C24—1884no—
656C24D4×D4711yescharacteristic
657#41—948no—
658#41—1884no—
659#41—1888no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—24no—
663C2×Q8—21no—
664C2×Q8—22no—
665C2×Q8—28no—
666C2×Q8—22no—
667C2×Q8—22no—
668C2×Q8—22no—
669C2×Q8—22no—
670C2×Q8—44no—
671C2×Q8—44no—
672C2×Q8—48no—
673C2×Q8—472no—
674C2×Q8—944no—
675C2×Q8—941no—
676C2×Q8—948no—
677C2×Q8—942no—
678C2×Q8—942no—
679C2×Q8—1884no—
680C2×Q8—1884no—
681C2×Q8—1888no—
682C2×Q8D4×D4714yes—
683C2×Q8C23×D4712yes—
684C2×Q8C23×D4712yes—
685C2×Q8C23×D4712yes—
686C2×D4—474no—
687C2×D4—474no—
688C2×D4—472no—
689C2×D4—472no—
690C2×D4—948no—
691C2×D4—944no—
692C2×D4—944no—
693C2×D4—944no—
694C2×D4—941no—
695C2×D4—942no—
696C2×D4—944no—
697C2×D4—941no—
698C2×D4—942no—
699C2×D4—942no—
700C2×D4—3762no—
701C2×D4—1884no—
702C2×D4—1888no—
703C2×D4—1884no—
704C2×D4—1884no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—44no—
713C22×C4—471no—
714C22×C4—471no—
715C22×C4—471no—
716C22×C4—472no—
717C22×C4—472no—
718C22×C4—944no—
719C22×C4—944no—
720C22×C4—944no—
721C22×C4—942no—
722C22×C4—942no—
723C22×C4—941no—
724C22×C4—941no—
725C22×C4—3762no—
726C22×C4—1884no—
727C22×C4—1884no—
728C22×C4D4×D4712yes—
729C22×C4D4×D4711yescharacteristic
730C22×C4C23×D4712yes—
731C22×C4C23×D4711yescharacteristic
732Q16—28no—
733Q16—44no—
734Q16—948no—
735SD16—4716no—
736SD16—948no—
737SD16—948no—
738SD16—948no—
739SD16—948no—
740SD16—1884no—
741M16—948no—
742C2×C8—22no—
743C2×C8—22no—
744C2×C8—474no—
745C2×C8—472no—
746C2×C8—472no—
747C2×C8—948no—
748C2×C8—942no—
749C2×C8C23×D4712yes—
750C2×C8C23×D4712yes—
751C4⋊C4—24no—
752C4⋊C4—21no—
753C4⋊C4—474no—
754C4⋊C4—472no—
755C4⋊C4—944no—
756C4⋊C4—944no—
757C4⋊C4—944no—
758C4⋊C4—944no—
759C4⋊C4—944no—
760C4⋊C4—941no—
761C4⋊C4C23×D4712yes—
762C22⋊C4—24no—
763C22⋊C4—474no—
764C22⋊C4—474no—
765C22⋊C4—944no—
766C22⋊C4—944no—
767C22⋊C4—944no—
768C22⋊C4—944no—
769C22⋊C4—944no—
770C22⋊C4—944no—
771C42—472no—
772C42—472no—
773C42—944no—
774C23—22no—
775C23—22no—
776C23—472no—
777C23—942no—
778C23—944no—
779C23—942no—
780C23—942no—
781C23—942no—
782C23—942no—
783C23—37616no—
784C23—3764no—
785C23—1888no—
786C23—1882no—
787C23—1882no—
788C23—1888no—
789C23—1882no—
790C23—1882no—
791C23—1882no—
792C23#1309405614yescomplemented
793C23C2×D4×D4712yes—
794C23C2×D4×D4711yescharacteristic
795Q8—24no—
796Q8—22no—
797Q8—22no—
798Q8—22no—
799Q8—22no—
800Q8—22no—
801Q8—48no—
802Q8—42no—
803Q8—42no—
804Q8—942no—
805Q8—942no—
806Q8—1888no—
807Q8—1882no—
808Q8C2×D4×D4714yes—
809D4—474no—
810D4—948no—
811D4—944no—
812D4—942no—
813D4—942no—
814D4—942no—
815D4—3764no—
816D4—1888no—
817D4—1888no—
818D4—1882no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—48no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—472no—
833C2×C4—472no—
834C2×C4—472no—
835C2×C4—942no—
836C2×C4—942no—
837C2×C4—942no—
838C2×C4—944no—
839C2×C4—942no—
840C2×C4—942no—
841C2×C4—942no—
842C2×C4—942no—
843C2×C4—3764no—
844C2×C4—1888no—
845C2×C4—1888no—
846C2×C4—1882no—
847C2×C4—1882no—
848C2×C4C2×D4×D4712yes—
849C2×C4C2×D4×D4711yescharacteristic
850C2×C4C2×D4×D4712yes—
851C2×C4#1309406912yes—
852C2×C4C24×D4711yescharacteristic
853C8—22no—
854C8—22no—
855C8—474no—
856C8—942no—
857C22—22no—
858C22—22no—
859C22—28no—
860C22—942no—
861C22—944no—
862C22—942no—
863C22—942no—
864C22—37616no—
865C22—3764no—
866C22—1882no—
867C22—1882no—
868C22—1882no—
869C22—1882no—
870C22—1882no—
871C22—1884no—
872C22—1888no—
873C22#1568975512yes—
874C22C2×#1309405612yes—
875C22C2×#1309405614yescomplemented
876C22#1568993212yes—
877C22C22×D4×D4711yescharacteristic
878C4—22no—
879C4—24no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—942no—
884C4—942no—
885C4—942no—
886C4—1882no—
887C4—1882no—
888C4#1568975512yes—
889C4C22×D4×D4711yescharacteristic
890C4C2×#1309406911yescharacteristic
891C2—24no—
892C2—3762no—
893C2—1882no—
894C2—1884no—
895C2#2025489114yesdirect product factor
896C2C2×#1568975511yescharacteristic
897C2C22×#1309405611yescharacteristic
898C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#451C2
socleC23×C47C22×D4
prime radicalC2×#15689764C2
hypercenterC2×#451D47
hypocenterC47C2×#3266
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C22×#13094056C2semidirect
2. C23×#10625336C2semidirect
3. C2×Q8×C22⋊D47C2semidirect
5. #20254891C2direct (N × H)
6. C2×#15689516C2semidirect
7. C2×#15689372C2semidirect
8. C2×#15689362C2semidirect
9. C2×#15689347C2semidirect
10. C2×#15689327C2semidirect
11. C2×#15689284C2semidirect
12. C2×#15689263C2semidirect
13. C2×#15689276C2semidirect
14. C2×#15689226C2semidirect
15. C2×#15689191C2semidirect
16. C2×C47×#451C2semidirect
18. C22×Q8×D47C22semidirect
21. C2×#13094056C22semidirect
22. C22×#10625337C22semidirect
30. C22×#10625336C22semidirect
31. C22×#10625324C22semidirect
34. Q8×C22⋊D47C22semidirect
38. C2×#13094022C22semidirect
44. C2×#13094000C22semidirect
48. C2×Q8×Dic47C22semidirect
53. #15689516C22semidirect
54. #15689372C22semidirect
55. #15689362C22semidirect
56. #15689347C22semidirect
57. #15689327C22semidirect
58. #15689284C22semidirect
59. #15689276C22semidirect
60. #15689263C22semidirect
61. #15689226C22semidirect
62. #15689191C22semidirect
63. C2×#13093957C22semidirect
64. C2×Dic47⋊C8C22semidirect
65. C2×#13093948C22semidirect
66. C2×#13093947C22semidirect
69. C2×(C2×D47)⋊C8C22semidirect
70. C2×#13093934C22semidirect
72. C22×Q16×C47C22semidirect
73. C22×Q16×C47C22semidirect
75. C47×#451C22semidirect
76. C2×#103×C47C22semidirect
77. C2×#103×C47C22semidirect
89. C2×Q8×D47C23semidirect
106. C2×#10625337C23semidirect
115. C2×#10625336D4semidirect
121. C2×#10625324C23semidirect
128. #13094022C23semidirect
137. #13094000C23semidirect
143. Q8×Dic47C23semidirect
167. #13093957C23semidirect
168. Dic47⋊C8C23semidirect
169. #13093948C23semidirect
170. #13093947C23semidirect
173. (C2×D47)⋊C8C23semidirect
174. #13093934C23semidirect
187. C2×Q16×C47C23semidirect
188. C2×Q16×C47C23semidirect
196. #103×C47C23semidirect
197. #103×C47C23semidirect
298. #10625336C2×D4semidirect
326. C23×C47#137semidirect
413. C22×C47C2×#137semidirect
453. C2×#451D47semidirect
459. C2×C47#3266semidirect
473. C22×Q16C2×D47semidirect
474. C22×Q16C2×D47semidirect
512. #451C2×D47semidirect
521. C2×#103C2×D47semidirect
522. C2×#103C2×D47semidirect
528. C47C2×#3266semidirect
569. C2×Q16C22×D47semidirect
570. C2×Q16C22×D47semidirect
642. #103C22×D47semidirect
643. #103C22×D47semidirect
792. C23#13094056semidirect
875. C22C2×#13094056semidirect
895. C2#20254891direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940562
C23×#106253362
C2×Q8×C22⋊D472
C2×#156897642
#202548912
C2×#156895162
C2×#156893722
C2×#156893622
C2×#156893472
C2×#156893272
C2×#156892842
C2×#156892632
C2×#156892762
C2×#156892262
C2×#156891912
C2×C47×#4512
C2×#326647