Finite Group Databasebeta

← C2×#20254969 #27091335

Subgroups — C2×#20254969 #27091335

Order 12032.

2826 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094054C211yesmaximal, characteristic, complemented
2C22×#13094044C211yesmaximal, characteristic, complemented
3C2×#15689782C211yesmaximal, characteristic, complemented
4#20254969C2116yesmaximal, direct product factor
5C2×#15689510C211yesmaximal, characteristic, complemented
6C2×#15689374C211yesmaximal, characteristic, complemented
7C2×#15689350C211yesmaximal, characteristic, complemented
8C2×#15689345C211yesmaximal, characteristic, complemented
9C2×#15689320C211yesmaximal, characteristic, complemented
10C2×#15689285C211yesmaximal, characteristic, complemented
11C2×#15689268C211yesmaximal, characteristic, complemented
12C2×#15689266C211yesmaximal, characteristic, complemented
13C2×#15689261C211yesmaximal, characteristic, complemented
14C2×#15689228C211yesmaximal, characteristic, complemented
15C2×#15689195C211yesmaximal, characteristic, complemented
16C2×C47×#550C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×Dic94C2211yescharacteristic
19C2×#13094054—28no—
20C2×#13094054C2218yescomplemented
21C2×#13094044—28no—
22C2×#13094044C2218yescomplemented
23C22×#10625337C2211yescharacteristic
24C22×#10625337C2211yescharacteristic
25C22×#10625335C2211yescharacteristic
26C22×#10625335C2211yescharacteristic
27C22×#10625335C2211yescharacteristic
28C22×#10625335C2211yescharacteristic
29C22×#10625336C2211yescharacteristic
30C22×#10625334C2211yescharacteristic
31C22×#10625334C2211yescharacteristic
32C22×#10625329C2211yescharacteristic
33C23×C47⋊C8C2211yescharacteristic
34#15689782—24no—
35#15689782C2218yescomplemented
36C2×#13094012C2211yescharacteristic
37C2×#13094010—21no—
38C2×#13094003C2211yescharacteristic
39C2×#13094002—21no—
40C2×#13093998C2211yescharacteristic
41C2×#13093996—21no—
42C2×C4×Dic94C2211yescharacteristic
43C2×(C22⋊D47)⋊C4—21no—
44#15689510C2218yescomplemented
45#15689374C2218yescomplemented
46#15689350C2218yescomplemented
47#15689345C2218yescomplemented
48#15689320C2218yescomplemented
49#15689285C2218yescomplemented
50#15689268C2218yescomplemented
51#15689266C2218yescomplemented
52#15689261C2218yescomplemented
53#15689228C2218yescomplemented
54#15689195C2218yescomplemented
55C2×#13093955C2211yescharacteristic
56C2×C4⋊(C47⋊C8)C2211yescharacteristic
57C2×#13093948C2211yescharacteristic
58C2×#13093947C2211yescharacteristic
59C2×#13093947C2211yescharacteristic
60C2×#13093945C2211yescharacteristic
61C2×#13093945C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×C22⋊(C47⋊C8)C2211yescharacteristic
64C2×C22⋊(C47⋊C8)C2211yescharacteristic
65C2×#13093935C2211yescharacteristic
66C22×#41×C47C2211yescharacteristic
67C22×#41×C47C2211yescharacteristic
68C47×#550—24no—
69C47×#550C2218yescomplemented
70C2×#127×C47—21no—
71C2×#127×C47C2211yescharacteristic
72C2×#121×C47—21no—
73C2×#121×C47—21no—
74C2×#121×C47C2211yescharacteristic
75C2×#121×C47C2211yescharacteristic
76C2×C4×Q8×C47C2211yescharacteristic
77C2×C4×D4×C47—21no—
78C2×C4×D4×C47C2211yescharacteristic
79C2×#10625350—22no—
80C2×#10625350—24no—
81C2×#10625350—42no—
82C2×#10625350C2314yes—
83C22×Dic94—24no—
84C22×Dic94—22no—
85C22×Dic94—21no—
86C22×Dic94—42no—
87C22×Dic94C2311yescharacteristic
88C22×Dic94C2314yes—
89C22×Dic94C2311yescharacteristic
90C22×D188C2311yescharacteristic
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C23×Dic47—21no—
94C22×C4×D47—21no—
95#13094054—232no—
96#13094044—232no—
97C2×#10625337—24no—
98C2×#10625337D418yescomplemented
99C2×#10625337C2314yes—
100C2×#10625337C2314yes—
101C2×#10625335—24no—
102C2×#10625335—24no—
103C2×#10625335—24no—
104C2×#10625335—42no—
105C2×#10625335C2314yes—
106C2×#10625335C2314yes—
107C2×#10625335C2314yes—
108C2×#10625335C2314yes—
109C2×#10625336—24no—
110C2×#10625336C2314yes—
111C2×#10625334—24no—
112C2×#10625334—42no—
113C2×#10625334C2314yes—
114C2×#10625334C2314yes—
115C2×#10625329—24no—
116C2×#10625329C2314yes—
117C22×C47⋊C8—24no—
118C22×C47⋊C8C2311yescharacteristic
119C22×C47⋊C8C2311yescharacteristic
120C22×C47⋊C8C2311yescharacteristic
121C22×C47⋊C8C2314yes—
122C22×C47⋊C8C2311yescharacteristic
123#13094012—22no—
124#13094012C2314yes—
125#13094010—28no—
126#13094003—22no—
127#13094003C2314yes—
128#13094002—28no—
129#13093998—22no—
130#13093998C2314yes—
131#13093996—28no—
132C4×Dic94—22no—
133C4×Dic94C2314yes—
134(C22⋊D47)⋊C4—28no—
135C2×C4⋊Dic47C2311yescharacteristic
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×C22⋊Dic47—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×C4×Dic47—21no—
143#13093955C2314yes—
144C4⋊(C47⋊C8)C2314yes—
145#13093948C2314yes—
146#13093947C2314yes—
147#13093947C2314yes—
148#13093945C2314yes—
149#13093945C2314yes—
150#13093944C2314yes—
151C22⋊(C47⋊C8)C2314yes—
152C22⋊(C47⋊C8)C2314yes—
153#13093935C2314yes—
154C2×#41×C47—22no—
155C2×#41×C47—22no—
156C2×#41×C47—24no—
157C2×#41×C47—24no—
158C2×#41×C47—42no—
159C2×#41×C47—42no—
160C2×#41×C47C2314yes—
161C2×#41×C47C2314yes—
162C22×Q8×C47C2311yescharacteristic
163C22×D4×C47—21no—
164C22×D4×C47—21no—
165C22×D4×C47—21no—
166C22×D4×C47—21no—
167C22×D4×C47—21no—
168C22×D4×C47—21no—
169C22×D4×C47D411yescharacteristic
170C22×D4×C47C2311yescharacteristic
171C22×D4×C47C2311yescharacteristic
172C23×C4×C47—21no—
173C23×C4×C47—21no—
174C23×C4×C47C2311yescharacteristic
175C23×C4×C47C2311yescharacteristic
176#127×C47—28no—
177#127×C47—22no—
178#127×C47C2314yes—
179#121×C47—22no—
180#121×C47—22no—
181#121×C47—28no—
182#121×C47—28no—
183#121×C47C2314yes—
184#121×C47C2314yes—
185C4×Q8×C47—22no—
186C4×Q8×C47C2314yes—
187C4×D4×C47—28no—
188C4×D4×C47D414yes—
189C4×D4×C47C2314yes—
190C2×C4⋊C4×C47—21no—
191C2×C4⋊C4×C47D411yescharacteristic
192C2×C4⋊C4×C47C2311yescharacteristic
193C2×C22⋊C4×C47—21no—
194C2×C22⋊C4×C47—21no—
195C2×C22⋊C4×C47D411yescharacteristic
196C2×C22⋊C4×C47D411yescharacteristic
197C2×C42×C47—21no—
198C2×C42×C47C2311yescharacteristic
199C24×C47—21no—
200C24×C47—21no—
201C24×C47C2×D411yescharacteristic
202C24×C47C2×D411yescharacteristic
203C23×D47—21no—
204#41×C47—28no—
205#41×C47—28no—
206#41×C47—44no—
207#41×C47—44no—
208#41×C47—48no—
209#41×C47—48no—
210C2×Q8×C47—21no—
211C2×Q8×C47—22no—
212C2×Q8×C47C2×D414yes—
213C2×Q8×C47C2412yes—
214C2×D4×C47—24no—
215C2×D4×C47—24no—
216C2×D4×C47—24no—
217C2×D4×C47—24no—
218C2×D4×C47—22no—
219C2×D4×C47—22no—
220C2×D4×C47—24no—
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—24no—
224C2×D4×C47—22no—
225C2×D4×C47—22no—
226C2×D4×C47—42no—
227C2×D4×C47—44no—
228C2×D4×C47—44no—
229C2×D4×C47—44no—
230C2×D4×C47—82no—
231C2×D4×C47—82no—
232C2×D4×C47—82no—
233C2×D4×C47C2×D414yes—
234C2×D4×C47C2412yes—
235C2×D4×C47C2412yes—
236C22×C4×C47—21no—
237C22×C4×C47—22no—
238C22×C4×C47—22no—
239C22×C4×C47—22no—
240C22×C4×C47—22no—
241C22×C4×C47—21no—
242C22×C4×C47—24no—
243C22×C4×C47—24no—
244C22×C4×C47—44no—
245C22×C4×C47—44no—
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D412yes—
251C22×C4×C47C2×D412yes—
252C22×C4×C47C2412yes—
253C22×C4×C47C2412yes—
254C22×C4×C47C2411yescharacteristic
255C2×C22⋊D47—24no—
256C2×C22⋊D47—24no—
257C2×C22⋊D47—44no—
258C2×C22⋊D47—44no—
259C22×Dic47—21no—
260C22×Dic47—21no—
261C22×Dic47—21no—
262C22×Dic47—24no—
263C22×Dic47—44no—
264#10625350—28no—
265#10625350—44no—
266#10625350—48no—
267C2×D188—22no—
268C2×D188—22no—
269C2×D188—21no—
270C2×D188C2412yes—
271C2×C4×D47—24no—
272C2×C4×D47—44no—
273C2×Dic94—21no—
274C2×Dic94—22no—
275C2×Dic94—22no—
276C2×Dic94—22no—
277C2×Dic94—28no—
278C2×Dic94—24no—
279C2×Dic94—21no—
280C2×Dic94—44no—
281C2×Dic94—48no—
282C2×Dic94—44no—
283C2×Dic94C2×D414yes—
284C2×Dic94C2412yes—
285C2×Dic94C2412yes—
286C4⋊C4×C47—24no—
287C4⋊C4×C47—21no—
288C4⋊C4×C47C2×D414yes—
289C4⋊C4×C47C2412yes—
290C22⋊C4×C47—24no—
291C22⋊C4×C47—24no—
292C22⋊C4×C47C2×D414yes—
293C22⋊C4×C47C2×D414yes—
294C42×C47—24no—
295C42×C47C2×D412yes—
296C42×C47C2412yes—
297C22⋊Dic47—24no—
298#10625337—28no—
299#10625337C2×D4116yescomplemented
300#10625336—28no—
301#10625335—28no—
302#10625335—28no—
303#10625335—28no—
304#10625335—44no—
305#10625334—28no—
306#10625334—44no—
307(C2×D47)⋊C4—24no—
308(C2×D47)⋊C4—24no—
309(C2×D47)⋊C4—24no—
310C4⋊Dic47—21no—
311C4⋊Dic47C2412yes—
312Dic47⋊C4—24no—
313Dic47⋊C4—24no—
314C4×Dic47—24no—
315#10625329—28no—
316C2×C47⋊C8—22no—
317C2×C47⋊C8—22no—
318C2×C47⋊C8—22no—
319C2×C47⋊C8—28no—
320C2×C47⋊C8C2×D414yes—
321C2×C47⋊C8C2412yes—
322C2×C47⋊C8C2412yes—
323C2×C47⋊C8C2412yes—
324C2×C47⋊C8C2412yes—
325C23×C47—22no—
326C23×C47—22no—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47—22no—
331C23×C47—22no—
332C23×C47—22no—
333C23×C47—42no—
334C23×C47—42no—
335C23×C47—42no—
336C23×C47—42no—
337C23×C47—42no—
338C23×C47—42no—
339C23×C47C22×D412yes—
340C23×C47C22×D412yes—
341C23×C47C22×D411yescharacteristic
342C22×D47—22no—
343C22×D47—42no—
344C22×D47—42no—
345C22×D47—42no—
346Q8×C47—24no—
347Q8×C47—22no—
348Q8×C47C22×D414yes—
349D4×C47—22no—
350D4×C47—22no—
351D4×C47—22no—
352D4×C47—22no—
353D4×C47—44no—
354D4×C47—48no—
355D4×C47—48no—
356D4×C47—48no—
357D4×C47—42no—
358D4×C47—42no—
359D4×C47—84no—
360D4×C47—84no—
361D4×C47—84no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—24no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—24no—
369C2×C4×C47—24no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—48no—
376C2×C4×C47—48no—
377C2×C4×C47—42no—
378C2×C4×C47C22×D412yes—
379C2×C4×C47C22×D412yes—
380C2×C4×C47C22×D412yes—
381C2×C4×C47C22×D412yes—
382C2×C4×C47C22×D412yes—
383C2×C4×C47C22×D411yescharacteristic
384C2×C4×C47H(5,𝔽2)12yes—
385C2×C4×C47C2511yescharacteristic
386C22⋊D47—48no—
387C22⋊D47—48no—
388C2×Dic47—24no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—48no—
393C2×Dic47—42no—
394C2×Dic47—42no—
395D188—22no—
396D188—22no—
397D188—42no—
398C4×D47—48no—
399Dic94—24no—
400Dic94—22no—
401Dic94—22no—
402Dic94—22no—
403Dic94—48no—
404Dic94—42no—
405Dic94C22×D414yes—
406C47⋊C8—22no—
407C47⋊C8—22no—
408C47⋊C8—22no—
409C47⋊C8C22×D414yes—
410C2×#3271—471nomaximal, Sylow
411C22×C47—22no—
412C22×C47—22no—
413C22×C47—22no—
414C22×C47—22no—
415C22×C47—22no—
416C22×C47—22no—
417C22×C47—44no—
418C22×C47—44no—
419C22×C47—42no—
420C22×C47—42no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47—42no—
424C22×C47—42no—
425C22×C47—84no—
426C22×C47—84no—
427C22×C47D4212yes—
428C22×C47#57512yes—
429C22×C47#57712yes—
430C22×C47C23×D411yescharacteristic
431C2×D47—42no—
432C2×D47—42no—
433C2×D47—42no—
434C2×D47—84no—
435C4×C47—22no—
436C4×C47—22no—
437C4×C47—24no—
438C4×C47—22no—
439C4×C47—22no—
440C4×C47—42no—
441C4×C47D4212yes—
442C4×C47C23×D411yescharacteristic
443C4×C47C2×H(5,𝔽2)11yescharacteristic
444Dic47—24no—
445Dic47—42no—
446Dic47—42no—
447C22×#137—471no—
448C22×#135—471no—
449C2×#550D4711yescharacteristic, complemented
450C2×#548—471no—
451#3271—4716no—
452C2×#496—471no—
453C2×#469—471no—
454C2×#465—471no—
455C2×#464—471no—
456C2×#460—471no—
457C2×#452—471no—
458C2×#449—471no—
459C2×#449—471no—
460C2×#448—471no—
461C2×#441—471no—
462C2×#435—471no—
463C2×C47—42no—
464C2×C47—42no—
465C2×C47—82no—
466C2×C47—82no—
467C2×C47#327114yescomplemented
468C2×C47C2×D4211yescharacteristic
469C2×C47C2×#57511yescharacteristic
470C2×C47C2×#57711yescharacteristic
471D47—82no—
472C22×#41—471no—
473C22×#41C2×D4711yescharacteristic
474C22×#41C2×D4711yescharacteristic
475C23×Q8—471no—
476C2×#137—478no—
477C2×#137—948no—
478C2×#135—478no—
479C2×#135—948no—
480C22×Q16—471no—
481C22×Q16—471no—
482C22×SD16—471no—
483C22×SD16—471no—
484C22×SD16—471no—
485C22×SD16—471no—
486C22×SD16—471no—
487C22×D8—471no—
488C22×D8—471no—
489C22×M16—471no—
490C23×C8—471no—
491#550—24no—
492#550C2×D4718yescomplemented
493#548—478no—
494#548—944no—
495C2×#127—21no—
496C2×#127C2×D4711yescharacteristic
497C2×#124—471no—
498C2×#124—941no—
499C2×C22⋊Q8—471no—
500C2×C22⋊Q8—941no—
501C2×#121—21no—
502C2×#121—21no—
503C2×#121—471no—
504C2×#121—941no—
505C2×#121C2×D4711yescharacteristic
506C2×#121C2×D4711yescharacteristic
507C2×C4×Q8—471no—
508C2×C4×Q8C2×D4711yescharacteristic
509C2×C4×D4—21no—
510C2×C4×D4—941no—
511C2×C4×D4C2×D4711yescharacteristic
512#496—478no—
513#469—478no—
514#465—478no—
515#464—478no—
516#460—478no—
517#452—478no—
518#449—478no—
519#449—478no—
520#448—478no—
521#441—478no—
522#435—478no—
523C2×#106—471no—
524C2×C4⋊C8—471no—
525C2×#103—471no—
526C2×#103—471no—
527C2×#103—471no—
528C2×#102—471no—
529C2×#102—471no—
530C2×#102—471no—
531C2×C22⋊C8—471no—
532C2×C22⋊C8—471no—
533C2×#97—471no—
534C47C2×#327111yescharacteristic, complemented, Sylow
535C2×#41—22no—
536C2×#41—22no—
537C2×#41—24no—
538C2×#41—24no—
539C2×#41—42no—
540C2×#41—42no—
541C2×#41—474no—
542C2×#41—944no—
543C2×#41—942no—
544C2×#41—1882no—
545C2×#41C22×D4714yes—
546C2×#41C22×D4714yes—
547C22×Q8—471no—
548C22×Q8—471no—
549C22×Q8—474no—
550C22×Q8—944no—
551C22×Q8—941no—
552C22×Q8—942no—
553C22×Q8—1882no—
554C22×Q8C22×D4711yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—471no—
562C22×D4—941no—
563C22×D4—941no—
564C22×D4C22⋊D4711yescharacteristic
565C22×D4C22×D4711yescharacteristic
566C22×D4C22×D4711yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—941no—
570C23×C4—941no—
571C23×C4C22×D4711yescharacteristic
572C23×C4C22×D4711yescharacteristic
573#137—9432no—
574#135—9432no—
575C2×Q16—478no—
576C2×Q16—474no—
577C2×Q16—474no—
578C2×Q16—944no—
579C2×SD16—474no—
580C2×SD16—474no—
581C2×SD16—474no—
582C2×SD16—474no—
583C2×SD16—474no—
584C2×SD16—944no—
585C2×SD16—944no—
586C2×SD16—944no—
587C2×SD16—944no—
588C2×SD16—1882no—
589C2×D8—474no—
590C2×D8—474no—
591C2×D8—944no—
592C2×D8—1882no—
593C2×M16—474no—
594C2×M16—944no—
595C22×C8—471no—
596C22×C8—471no—
597C22×C8—474no—
598C22×C8—471no—
599C22×C8—471no—
600C22×C8—944no—
601#127—28no—
602#127—22no—
603#127C22×D4714yes—
604#124—474no—
605#124—948no—
606#124—942no—
607C22⋊Q8—474no—
608C22⋊Q8—942no—
609C22⋊Q8—948no—
610#121—22no—
611#121—22no—
612#121—28no—
613#121—28no—
614#121—474no—
615#121—948no—
616#121—942no—
617#121C22×D4714yes—
618#121C22×D4714yes—
619C4×Q8—22no—
620C4×Q8—474no—
621C4×Q8—942no—
622C4×Q8C22×D4714yes—
623C4×D4—28no—
624C4×D4—948no—
625C4×D4C22⋊D4714yes—
626C4×D4C22×D4714yes—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—471no—
629C2×C4⋊C4—941no—
630C2×C4⋊C4—941no—
631C2×C4⋊C4C22⋊D4711yescharacteristic
632C2×C4⋊C4C22×D4711yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—941no—
636C2×C22⋊C4—941no—
637C2×C22⋊C4—941no—
638C2×C22⋊C4—941no—
639C2×C22⋊C4C22⋊D4711yescharacteristic
640C2×C22⋊C4C22⋊D4711yescharacteristic
641C2×C42—21no—
642C2×C42—941no—
643C2×C42C22×D4711yescharacteristic
644#106—474no—
645C4⋊C8—474no—
646#103—474no—
647#103—474no—
648#103—474no—
649#102—474no—
650#102—474no—
651#102—474no—
652C22⋊C8—474no—
653C22⋊C8—474no—
654#97—474no—
655C24—21no—
656C24—21no—
657C24—941no—
658C24C2×C22⋊D4711yescharacteristic
659C24C2×C22⋊D4711yescharacteristic
660#41—28no—
661#41—28no—
662#41—44no—
663#41—44no—
664#41—48no—
665#41—48no—
666#41—948no—
667#41—1884no—
668#41—1888no—
669C2×Q8—21no—
670C2×Q8—22no—
671C2×Q8—474no—
672C2×Q8—472no—
673C2×Q8—472no—
674C2×Q8—948no—
675C2×Q8—941no—
676C2×Q8—944no—
677C2×Q8—941no—
678C2×Q8—942no—
679C2×Q8—942no—
680C2×Q8—942no—
681C2×Q8—1884no—
682C2×Q8—1884no—
683C2×Q8—1888no—
684C2×Q8D4×D4714yes—
685C2×Q8C23×D4712yes—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—24no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—24no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—42no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—82no—
703C2×D4—82no—
704C2×D4—82no—
705C2×D4—472no—
706C2×D4—944no—
707C2×D4—944no—
708C2×D4—942no—
709C2×D4—941no—
710C2×D4—942no—
711C2×D4—1884no—
712C2×D4—1884no—
713C2×D4C2×C22⋊D4714yes—
714C2×D4C23×D4712yes—
715C2×D4C23×D4712yes—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—21no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—941no—
727C22×C4—944no—
728C22×C4—941no—
729C22×C4—941no—
730C22×C4—944no—
731C22×C4—1884no—
732C22×C4—1884no—
733C22×C4C2×C22⋊D4712yes—
734C22×C4C2×C22⋊D4712yes—
735C22×C4C2×C22⋊D4711yescharacteristic
736C22×C4C2×C22⋊D4711yescharacteristic
737C22×C4C2×C22⋊D4711yescharacteristic
738C22×C4C2×C22⋊D4711yescharacteristic
739C22×C4C23×D4712yes—
740C22×C4C23×D4712yes—
741C22×C4C23×D4711yescharacteristic
742Q16—4716no—
743Q16—948no—
744SD16—948no—
745SD16—948no—
746SD16—948no—
747SD16—948no—
748SD16—1884no—
749D8—948no—
750D8—1884no—
751M16—948no—
752C2×C8—474no—
753C2×C8—472no—
754C2×C8—472no—
755C2×C8—472no—
756C2×C8—472no—
757C2×C8—948no—
758C2×C8—942no—
759C2×C8—942no—
760C2×C8—942no—
761C4⋊C4—24no—
762C4⋊C4—21no—
763C4⋊C4—472no—
764C4⋊C4—944no—
765C4⋊C4—944no—
766C4⋊C4—941no—
767C4⋊C4C2×C22⋊D4714yes—
768C4⋊C4C23×D4712yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—944no—
772C22⋊C4—944no—
773C22⋊C4—944no—
774C22⋊C4—944no—
775C22⋊C4C2×C22⋊D4714yes—
776C22⋊C4C2×C22⋊D4714yes—
777C42—24no—
778C42—944no—
779C42C2×C22⋊D4712yes—
780C42C23×D4712yes—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—942no—
796C23—1882no—
797C23—1882no—
798C23—1882no—
799C23C22×C22⋊D4712yes—
800C23C22×C22⋊D4712yes—
801C23C22×C22⋊D4711yescharacteristic
802Q8—24no—
803Q8—22no—
804Q8—474no—
805Q8—944no—
806Q8—942no—
807Q8—942no—
808Q8—942no—
809Q8—1888no—
810Q8—1882no—
811Q8C2×D4×D4714yes—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—44no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—42no—
821D4—42no—
822D4—84no—
823D4—84no—
824D4—84no—
825D4—942no—
826D4—942no—
827D4—1888no—
828D4—1888no—
829D4—1882no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—48no—
844C2×C4—48no—
845C2×C4—42no—
846C2×C4—944no—
847C2×C4—942no—
848C2×C4—942no—
849C2×C4—942no—
850C2×C4—1888no—
851C2×C4—1888no—
852C2×C4—1882no—
853C2×C4—1882no—
854C2×C4C2×D4×D4712yes—
855C2×C4C22×C22⋊D4712yes—
856C2×C4C22×C22⋊D4712yes—
857C2×C4C22×C22⋊D4712yes—
858C2×C4C22×C22⋊D4712yes—
859C2×C4C22×C22⋊D4711yescharacteristic
860C2×C4#1309406912yes—
861C2×C4C24×D4711yescharacteristic
862C8—474no—
863C8—942no—
864C8—942no—
865C8—942no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—44no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—84no—
881C22—84no—
882C22—3764no—
883C22—1882no—
884C22—1882no—
885C22—1882no—
886C22D4×C22⋊D4712yes—
887C22#1568992112yes—
888C22#1568993412yes—
889C22C23×C22⋊D4711yescharacteristic
890C4—22no—
891C4—22no—
892C4—24no—
893C4—22no—
894C4—22no—
895C4—42no—
896C4—944no—
897C4—1882no—
898C4—1882no—
899C4D4×C22⋊D4712yes—
900C4C22×D4×D4711yescharacteristic
901C4C2×#1309406911yescharacteristic
902C2—42no—
903C2—42no—
904C2—82no—
905C2—82no—
906C2—3762no—
907C2#2025496914yesdirect product factor
908C2C2×D4×C22⋊D4711yescharacteristic
909C2C2×#1568992111yescharacteristic
910C2C2×#1568993411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#550C2
socleC23×C47C22×D4
hypercenterC2×#550D47
hypocenterC47C2×#3271
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#13094054C2semidirect
2. C22×#13094044C2semidirect
3. C2×#15689782C2semidirect
4. #20254969C2direct (N × H)
5. C2×#15689510C2semidirect
6. C2×#15689374C2semidirect
7. C2×#15689350C2semidirect
8. C2×#15689345C2semidirect
9. C2×#15689320C2semidirect
10. C2×#15689285C2semidirect
11. C2×#15689268C2semidirect
12. C2×#15689266C2semidirect
13. C2×#15689261C2semidirect
14. C2×#15689228C2semidirect
15. C2×#15689195C2semidirect
16. C2×C47×#550C2semidirect
20. C2×#13094054C22semidirect
22. C2×#13094044C22semidirect
35. #15689782C22semidirect
44. #15689510C22semidirect
45. #15689374C22semidirect
46. #15689350C22semidirect
47. #15689345C22semidirect
48. #15689320C22semidirect
49. #15689285C22semidirect
50. #15689268C22semidirect
51. #15689266C22semidirect
52. #15689261C22semidirect
53. #15689228C22semidirect
54. #15689195C22semidirect
69. C47×#550C22semidirect
98. C2×#10625337D4semidirect
299. #10625337C2×D4semidirect
449. C2×#550D47semidirect
467. C2×C47#3271semidirect
492. #550C2×D47semidirect
534. C47C2×#3271semidirect
907. C2#20254969direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940542
C22×#130940442
C2×#156897822
#202549692
C2×#156895102
C2×#156893742
C2×#156893502
C2×#156893452
C2×#156893202
C2×#156892852
C2×#156892682
C2×#156892662
C2×#156892612
C2×#156892282
C2×#156891952
C2×C47×#5502
C2×#327147