Finite Group Databasebeta

← C2×#20255249 #27092657

Subgroups — C2×#20255249 #27092657

Order 12032.

2374 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
2C2×#15689774C211yesmaximal, characteristic
3#20255249C2116yesmaximal, direct product factor
4C2×#15689472C211yesmaximal, characteristic, complemented
5C2×#15689453C211yesmaximal, characteristic, complemented
6C2×#15689452C211yesmaximal, characteristic, complemented
7C2×#15689406C211yesmaximal, characteristic, complemented
8C2×#15689355C211yesmaximal, characteristic, complemented
9C2×#15689352C211yesmaximal, characteristic, complemented
10C2×#15689327C211yesmaximal, characteristic, complemented
11C2×#15689263C211yesmaximal, characteristic, complemented
12C2×#15689262C211yesmaximal, characteristic, complemented
13C2×#15689208C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
15C2×#103×D47C211yesmaximal, characteristic, complemented
16C22×#103×C47C211yesmaximal, characteristic, complemented
17C22×#10625350—21no—
18C22×Q8×D47C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22C22×C8×D47C2211yescharacteristic
23Q8×C22⋊D47—24no—
24Q8×C22⋊D47C2218yescomplemented
25#15689774—24no—
26#15689774C2218yes—
27C2×#13094023C2211yescharacteristic
28C2×#13094022—21no—
29C2×#13094022C2211yescharacteristic
30C2×#13094009—21no—
31C2×#13094007—21no—
32C2×#13094003—21no—
33C2×#13094003C2211yescharacteristic
34C2×#13094002—21no—
35C2×#13094000—21no—
36C2×#13094000C2211yescharacteristic
37C2×#13093999C2211yescharacteristic
38C2×#13093998C2211yescharacteristic
39C2×Q8×Dic47C2211yescharacteristic
40C2×#13093986C2211yescharacteristic
41C2×C4×C22⋊D47—21no—
42C2×C4×C22⋊D47C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic
44#15689472C2218yescomplemented
45#15689453C2218yescomplemented
46#15689452C2218yescomplemented
47#15689406C2218yescomplemented
48#15689355C2218yescomplemented
49#15689352C2218yescomplemented
50#15689327C2218yescomplemented
51#15689263C2218yescomplemented
52#15689262C2218yescomplemented
53#15689208C2218yescomplemented
54C8×C22⋊D47C2218yescomplemented
55C2×#13093956C2211yescharacteristic
56C2×#13093955C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64#103×D47C2218yescomplemented
65C2×#13093946C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C23×Q8×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C22×C4⋊C4×C47C2211yescharacteristic
72C2×#103×C47C2211yescharacteristic
73C2×#103×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2218yescomplemented
77C2×#10625350—28no—
78C2×#10625350—48no—
79C22×Dic94—21no—
80C22×Dic94—21no—
81C22×Dic94C2311yescharacteristic
82C2×Q8×D47—22no—
83C2×Q8×D47—24no—
84C2×Q8×D47—42no—
85C2×Q8×D47C2314yes—
86C22×D188—21no—
87C22×D188C2311yescharacteristic
88C22×C22⋊D47—21no—
89C22×C22⋊D47D411yescharacteristic
90C22×C4×D47—21no—
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47C2311yescharacteristic
94C2×#10625325—42no—
95C2×#10625325C2314yes—
96C2×#10625336—24no—
97C2×#10625336—42no—
98C2×#10625336C2314yes—
99C2×#10625336C2314yes—
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2311yescharacteristic
102C2×C8×D47—42no—
103C2×C8×D47C2314yes—
104#13094023—22no—
105#13094023C2314yes—
106#13094022—28no—
107#13094022—22no—
108#13094022C2314yes—
109#13094009—28no—
110#13094007—28no—
111#13094003—22no—
112#13094003—28no—
113#13094003C2314yes—
114#13094002—28no—
115#13094000—22no—
116#13094000—28no—
117#13094000C2314yes—
118#13093999—22no—
119#13093999C2314yes—
120#13093998—22no—
121#13093998C2314yes—
122Q8×Dic47—22no—
123Q8×Dic47C2314yes—
124#13093986—22no—
125#13093986C2314yes—
126C4×C22⋊D47—28no—
127C4×C22⋊D47D414yes—
128C4×C22⋊D47C2314yes—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47C2311yescharacteristic
131C2×C4⋊Dic47C2311yescharacteristic
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4D411yescharacteristic
139C4⋊C4×D47—22no—
140C4⋊C4×D47C2314yes—
141C2×C22⋊Dic47—21no—
142C2×C22⋊Dic47D411yescharacteristic
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4D411yescharacteristic
148C2×C4×Dic47—21no—
149C2×C4×Dic47C2311yescharacteristic
150#13093956C2314yes—
151#13093955C2314yes—
152#13093955C2314yes—
153Dic47⋊C8C2314yes—
154#13093949C2314yes—
155#13093948C2314yes—
156#13093948C2314yes—
157#13093947C2314yes—
158#13093947C2314yes—
159#13093946C2314yes—
160C22⋊(C47⋊C8)C2314yes—
161(C2×D47)⋊C8C2314yes—
162C8×Dic47C2314yes—
163C22×Q8×C47—22no—
164C22×Q8×C47—21no—
165C22×Q8×C47—24no—
166C22×Q8×C47—42no—
167C22×Q8×C47C2311yescharacteristic
168C22×Q8×C47C2314yes—
169C22×Q8×C47C2311yescharacteristic
170C23×C4×C47—21no—
171C23×C4×C47—21no—
172C23×C4×C47C2311yescharacteristic
173C22×C8×C47—42no—
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2311yescharacteristic
176C22×C8×C47C2314yes—
177C2×C4⋊C4×C47—22no—
178C2×C4⋊C4×C47—21no—
179C2×C4⋊C4×C47C2314yes—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C4⋊C4×C47C2311yescharacteristic
182#103×C47C2314yes—
183#103×C47C2314yes—
184#103×C47C2314yes—
185#103×C47C2314yes—
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47C2×D411yescharacteristic
189C2×Q8×C47—21no—
190C2×Q8×C47—24no—
191C2×Q8×C47—21no—
192C2×Q8×C47—22no—
193C2×Q8×C47—28no—
194C2×Q8×C47—22no—
195C2×Q8×C47—22no—
196C2×Q8×C47—44no—
197C2×Q8×C47—44no—
198C2×Q8×C47—48no—
199C2×Q8×C47#4114yescomplemented
200C2×Q8×C47C2412yes—
201C2×Q8×C47C2412yes—
202C22×C4×C47—21no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—24no—
208C22×C4×C47—21no—
209C22×C4×C47—24no—
210C22×C4×C47—44no—
211C22×C4×C47—44no—
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D412yes—
214C22×C4×C47C2412yes—
215C22×C4×C47C2411yescharacteristic
216C2×C22⋊D47—24no—
217C2×C22⋊D47—44no—
218C2×C22⋊D47SD1618yescomplemented
219C2×C22⋊D47C2×D414yes—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47C2×D411yescharacteristic
224C22×Dic47C2×D411yescharacteristic
225C22×Dic47C2×D411yescharacteristic
226Q8×D47—28no—
227Q8×D47—44no—
228Q8×D47—48no—
229#10625350—432no—
230C2×D188—22no—
231C2×D188—22no—
232C2×D188—24no—
233C2×D188—21no—
234C2×D188—44no—
235C2×D188C2412yes—
236C2×C4×D47—22no—
237C2×C4×D47—22no—
238C2×C4×D47—24no—
239C2×C4×D47—24no—
240C2×C4×D47—24no—
241C2×C4×D47—44no—
242C2×C4×D47—44no—
243C2×C4×D47—44no—
244C2×C4×D47C2×D412yes—
245C2×C4×D47C2412yes—
246C2×Dic94—22no—
247C2×Dic94—22no—
248C2×Dic94—21no—
249C2×Dic94—24no—
250C2×Dic94—24no—
251C2×Dic94—44no—
252C2×Dic94—44no—
253C2×Dic94C2412yes—
254C2×C8×C47—22no—
255C2×C8×C47—22no—
256C2×C8×C47—44no—
257C2×C8×C47C2412yes—
258C2×C8×C47C2412yes—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47—24no—
262C4⋊C4×C47C2412yes—
263C4⋊C4×C47C2412yes—
264C22⋊Dic47—24no—
265C22⋊Dic47C2×D414yes—
266#10625336—28no—
267#10625336—44no—
268(C2×D47)⋊C4—24no—
269(C2×D47)⋊C4—24no—
270(C2×D47)⋊C4—24no—
271(C2×D47)⋊C4—24no—
272(C2×D47)⋊C4C2×D414yes—
273C4⋊Dic47—21no—
274C4⋊Dic47—21no—
275C4⋊Dic47—24no—
276C4⋊Dic47C2412yes—
277C4⋊Dic47C2412yes—
278Dic47⋊C4—24no—
279Dic47⋊C4—24no—
280Dic47⋊C4—24no—
281Dic47⋊C4—24no—
282Dic47⋊C4—24no—
283Dic47⋊C4—24no—
284Dic47⋊C4C2×D414yes—
285C4×Dic47—24no—
286C4×Dic47C2×D412yes—
287C4×Dic47C2412yes—
288C2×C47⋊C8—22no—
289C2×C47⋊C8—22no—
290C2×C47⋊C8C2412yes—
291C2×C47⋊C8C2412yes—
292#10625325—44no—
293C8×D47—44no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47C2×SD1614yes—
297C23×C47C22×D412yes—
298C23×C47C22×D411yescharacteristic
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—42no—
303C22×D47—42no—
304C22×D47—42no—
305C22×D47C2×SD1614yes—
306C22×D47C22×D412yes—
307Q8×C47—24no—
308Q8×C47—22no—
309Q8×C47—22no—
310Q8×C47—22no—
311Q8×C47—48no—
312Q8×C47—42no—
313Q8×C47C2×#4114yescomplemented
314C2×C4×C47—24no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—24no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—48no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47—42no—
327C2×C4×C47—48no—
328C2×C4×C47C22×D412yes—
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C2×#4112yes—
331C2×C4×C47H(5,𝔽2)12yes—
332C2×C4×C47C2511yescharacteristic
333C22⋊D47—48no—
334C22⋊D47C2×SD16116yescomplemented
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47C2×SD1614yes—
344C2×Dic47C22×D412yes—
345C2×Dic47C22×D412yes—
346C2×Dic47C22×D412yes—
347D188—22no—
348D188—22no—
349D188—48no—
350D188—42no—
351C4×D47—24no—
352C4×D47—22no—
353C4×D47—22no—
354C4×D47—48no—
355C4×D47—48no—
356C4×D47—48no—
357Dic94—22no—
358Dic94—22no—
359Dic94—48no—
360Dic94—42no—
361Dic94—48no—
362C8×C47—22no—
363C8×C47—22no—
364C47⋊C8—22no—
365C47⋊C8—22no—
366C2×#3298—471nomaximal, Sylow
367C22×C47—22no—
368C22×C47—28no—
369C22×C47—22no—
370C22×C47#54612yes—
371C22×C47C22×SD1614yes—
372C22×C47C22×SD1612yes—
373C22×C47#57812yes—
374C22×C47C23×D411yescharacteristic
375C2×D47—22no—
376C2×D47—28no—
377C2×D47—22no—
378C2×D47—42no—
379C2×D47—42no—
380C2×D47—42no—
381C2×D47—84no—
382C2×D47C22×SD1614yes—
383C4×C47—24no—
384C4×C47—22no—
385C4×C47—42no—
386C4×C47—42no—
387C4×C47—42no—
388C4×C47#54612yes—
389C4×C47C22×#4111yescharacteristic
390C4×C47C2×H(5,𝔽2)11yescharacteristic
391Dic47—22no—
392Dic47—22no—
393Dic47—42no—
394Dic47—42no—
395Dic47—42no—
396Dic47C22×SD1614yes—
397C2×D4×Q8—471no—
398C2×#547—471no—
399#3298—4716no—
400C2×#487—471no—
401C2×#483—471no—
402C2×#483—471no—
403C2×#475—471no—
404C2×#465—471no—
405C2×#465—471no—
406C2×#461—471no—
407C2×#448—471no—
408C2×#448—471no—
409C2×C4×SD16—471no—
410C2×C8×D4—471no—
411C22×#103—471no—
412C22×#103D4711yescharacteristic, complemented
413C2×C47—24no—
414C2×C47#329814yescomplemented
415C2×C47C2×#54611yescharacteristic
416C2×C47C23×SD1611yescharacteristic
417C2×C47C2×#57811yescharacteristic
418D47—24no—
419D47—82no—
420C22×#41—941no—
421C23×Q8—471no—
422C23×Q8C2×D4711yescharacteristic
423C22×SD16—471no—
424C22×SD16—471no—
425C22×SD16—471no—
426C23×C8—471no—
427C23×C8C2×D4711yescharacteristic
428D4×Q8—478no—
429D4×Q8—944no—
430#547—478no—
431#547—944no—
432C2×C4⋊Q8—471no—
433C2×C4⋊Q8—471no—
434C2×C4⋊Q8—941no—
435C2×#123—941no—
436C2×#123—941no—
437C2×C22⋊Q8—471no—
438C2×C22⋊Q8—471no—
439C2×C22⋊Q8—941no—
440C2×C22⋊Q8—941no—
441C2×C22⋊Q8—941no—
442C2×#121—471no—
443C2×#121—471no—
444C2×C4×Q8—471no—
445C2×C4×D4—471no—
446C2×C4×D4—471no—
447C2×C4×D4—941no—
448C22×C4⋊C4—471no—
449C22×C4⋊C4C2×D4711yescharacteristic
450#487—478no—
451#483—478no—
452#483—478no—
453#475—478no—
454#465—478no—
455#465—478no—
456#461—478no—
457#448—478no—
458#448—478no—
459C4×SD16—478no—
460C8×D4—478no—
461C2×#106—471no—
462C2×#106—471no—
463C2×#106—471no—
464C2×C4⋊C8—471no—
465C2×#103—471no—
466C2×#103—471no—
467C2×#103—471no—
468C2×#103—471no—
469C2×#103—471no—
470C2×#103—478no—
471C2×#103C2×D4711yescharacteristic
472C2×#103C2×D4711yescharacteristic
473C2×#103C2×D4711yescharacteristic
474C2×#103C2×D4711yescharacteristic
475C2×#103C2×D4718yescomplemented
476C2×#102—471no—
477C2×C22⋊C8—471no—
478C2×C22⋊C8—471no—
479C2×C4×C8—471no—
480C47C2×#329811yescharacteristic, complemented, Sylow
481C2×#41—948no—
482C2×#41—1888no—
483C22×Q8—21no—
484C22×Q8—22no—
485C22×Q8—24no—
486C22×Q8—42no—
487C22×Q8—474no—
488C22×Q8—471no—
489C22×Q8—941no—
490C22×Q8—941no—
491C22×Q8—942no—
492C22×Q8—944no—
493C22×Q8—1882no—
494C22×Q8C22×D4711yescharacteristic
495C22×Q8C22×D4714yes—
496C22×Q8C22×D4711yescharacteristic
497C22×D4—471no—
498C22×D4—471no—
499C22×D4—941no—
500C22×D4—941no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—471no—
504C23×C4—941no—
505C23×C4—941no—
506C23×C4—941no—
507C23×C4C22×D4711yescharacteristic
508C2×SD16—474no—
509C2×SD16—474no—
510C2×SD16—474no—
511C2×SD16—944no—
512C2×SD16—1882no—
513C2×SD16—1882no—
514C22×C8—42no—
515C22×C8—471no—
516C22×C8—471no—
517C22×C8—474no—
518C22×C8—1882no—
519C22×C8C22×D4711yescharacteristic
520C22×C8C22×D4711yescharacteristic
521C22×C8C22×D4714yes—
522C4⋊Q8—474no—
523C4⋊Q8—474no—
524C4⋊Q8—942no—
525C4⋊Q8—942no—
526C4⋊Q8—948no—
527#123—948no—
528#123—948no—
529C22⋊Q8—474no—
530C22⋊Q8—474no—
531C22⋊Q8—948no—
532C22⋊Q8—948no—
533C22⋊Q8—948no—
534C22⋊Q8—942no—
535C22⋊Q8—942no—
536#121—474no—
537#121—474no—
538#121—942no—
539#121—942no—
540C4×Q8—474no—
541C4×Q8—942no—
542C4×D4—474no—
543C4×D4—474no—
544C4×D4—474no—
545C4×D4—942no—
546C4×D4—948no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—471no—
550C2×C4⋊C4—471no—
551C2×C4⋊C4—471no—
552C2×C4⋊C4—474no—
553C2×C4⋊C4—942no—
554C2×C4⋊C4—941no—
555C2×C4⋊C4—941no—
556C2×C4⋊C4—941no—
557C2×C4⋊C4—941no—
558C2×C4⋊C4—941no—
559C2×C4⋊C4—941no—
560C2×C4⋊C4—941no—
561C2×C4⋊C4C22×D4711yescharacteristic
562C2×C4⋊C4C22×D4711yescharacteristic
563C2×C4⋊C4C22×D4714yes—
564C2×C22⋊C4—471no—
565C2×C22⋊C4—471no—
566C2×C22⋊C4—941no—
567C2×C22⋊C4—941no—
568C2×C22⋊C4—941no—
569C2×C22⋊C4—941no—
570C2×C22⋊C4—941no—
571C2×C42—471no—
572C2×C42—941no—
573#106—474no—
574#106—474no—
575#106—474no—
576C4⋊C8—474no—
577#103—474no—
578#103—474no—
579#103—474no—
580#103—474no—
581#103—474no—
582#103C22×D4714yes—
583#103C22×D4714yes—
584#103C22×D4714yes—
585#103C22×D4714yes—
586#102—474no—
587C22⋊C8—474no—
588C22⋊C8—474no—
589C4×C8—474no—
590C24—471no—
591C24—941no—
592C24D4×D4711yescharacteristic
593#41—18832no—
594C2×Q8—21no—
595C2×Q8—24no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—28no—
599C2×Q8—22no—
600C2×Q8—22no—
601C2×Q8—44no—
602C2×Q8—44no—
603C2×Q8—48no—
604C2×Q8—472no—
605C2×Q8—944no—
606C2×Q8—944no—
607C2×Q8—941no—
608C2×Q8—948no—
609C2×Q8—942no—
610C2×Q8—942no—
611C2×Q8—1884no—
612C2×Q8—1884no—
613C2×Q8—1884no—
614C2×Q8—1888no—
615C2×Q8#1062535014yescomplemented
616C2×Q8C23×D4712yes—
617C2×Q8C23×D4712yes—
618C2×D4—478no—
619C2×D4—474no—
620C2×D4—472no—
621C2×D4—944no—
622C2×D4—944no—
623C2×D4—941no—
624C2×D4—942no—
625C2×D4—942no—
626C2×D4—1884no—
627C2×D4—1884no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—471no—
639C22×C4—471no—
640C22×C4—471no—
641C22×C4—472no—
642C22×C4—472no—
643C22×C4—944no—
644C22×C4—944no—
645C22×C4—944no—
646C22×C4—942no—
647C22×C4—942no—
648C22×C4—941no—
649C22×C4—941no—
650C22×C4—941no—
651C22×C4—1884no—
652C22×C4—1884no—
653C22×C4—1884no—
654C22×C4D4×D4712yes—
655C22×C4D4×D4711yescharacteristic
656C22×C4C23×D4712yes—
657C22×C4C23×D4711yescharacteristic
658SD16—948no—
659SD16—1884no—
660SD16—1884no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8—472no—
665C2×C8—472no—
666C2×C8—942no—
667C2×C8—942no—
668C2×C8—1884no—
669C2×C8C23×D4712yes—
670C2×C8C23×D4712yes—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—24no—
674C4⋊C4—474no—
675C4⋊C4—472no—
676C4⋊C4—472no—
677C4⋊C4—944no—
678C4⋊C4—944no—
679C4⋊C4—944no—
680C4⋊C4—944no—
681C4⋊C4—944no—
682C4⋊C4—944no—
683C4⋊C4—944no—
684C4⋊C4—941no—
685C4⋊C4—941no—
686C4⋊C4C23×D4712yes—
687C4⋊C4C23×D4712yes—
688C22⋊C4—474no—
689C22⋊C4—474no—
690C22⋊C4—944no—
691C22⋊C4—944no—
692C22⋊C4—944no—
693C22⋊C4—944no—
694C22⋊C4—944no—
695C42—472no—
696C42—472no—
697C42—944no—
698C23—22no—
699C23—22no—
700C23—474no—
701C23—472no—
702C23—942no—
703C23—942no—
704C23—942no—
705C23—1882no—
706C23—1882no—
707C23—1882no—
708C23SD16×D4714yes—
709C23C2×D4×D4712yes—
710C23C2×D4×D4711yescharacteristic
711Q8—24no—
712Q8—22no—
713Q8—22no—
714Q8—22no—
715Q8—48no—
716Q8—42no—
717Q8—942no—
718Q8—942no—
719Q8—1888no—
720Q8—1888no—
721Q8—1882no—
722Q8C2×#1062535014yescomplemented
723D4—4716no—
724D4—942no—
725D4—942no—
726D4—1888no—
727D4—1888no—
728D4—1882no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—48no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—48no—
743C2×C4—474no—
744C2×C4—472no—
745C2×C4—472no—
746C2×C4—472no—
747C2×C4—942no—
748C2×C4—942no—
749C2×C4—944no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—1888no—
756C2×C4—1888no—
757C2×C4—1888no—
758C2×C4—1882no—
759C2×C4—1882no—
760C2×C4—1882no—
761C2×C4C2×D4×D4712yes—
762C2×C4C2×D4×D4711yescharacteristic
763C2×C4C2×#1062535012yes—
764C2×C4#1309406912yes—
765C2×C4C24×D4711yescharacteristic
766C8—22no—
767C8—22no—
768C8—942no—
769C8—942no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—474no—
774C22—948no—
775C22—942no—
776C22—942no—
777C22—3764no—
778C22—1882no—
779C22—1882no—
780C22—1882no—
781C22#1568976312yes—
782C22C2×SD16×D4714yes—
783C22C2×SD16×D4712yes—
784C22#1568993612yes—
785C22C22×D4×D4711yescharacteristic
786C4—22no—
787C4—24no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—474no—
792C4—942no—
793C4—942no—
794C4—1882no—
795C4—1882no—
796C4—1882no—
797C4#1568976312yes—
798C4C22×#1062535011yescharacteristic
799C4C2×#1309406911yescharacteristic
800C2—24no—
801C2—944no—
802C2—3762no—
803C2#2025524914yesdirect product factor
804C2C2×#1568976311yescharacteristic
805C2C22×SD16×D4711yescharacteristic
806C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC22×#103×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689774C2
hypercenterC22×#103D47
hypocenterC47C2×#3298
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C22⋊D47C2semidirect
3. #20255249C2direct (N × H)
4. C2×#15689472C2semidirect
5. C2×#15689453C2semidirect
6. C2×#15689452C2semidirect
7. C2×#15689406C2semidirect
8. C2×#15689355C2semidirect
9. C2×#15689352C2semidirect
10. C2×#15689327C2semidirect
11. C2×#15689263C2semidirect
12. C2×#15689262C2semidirect
13. C2×#15689208C2semidirect
14. C2×C8×C22⋊D47C2semidirect
15. C2×#103×D47C2semidirect
16. C22×#103×C47C2semidirect
24. Q8×C22⋊D47C22semidirect
44. #15689472C22semidirect
45. #15689453C22semidirect
46. #15689452C22semidirect
47. #15689406C22semidirect
48. #15689355C22semidirect
49. #15689352C22semidirect
50. #15689327C22semidirect
51. #15689263C22semidirect
52. #15689262C22semidirect
53. #15689208C22semidirect
54. C8×C22⋊D47C22semidirect
64. #103×D47C22semidirect
76. C2×#103×C47C22semidirect
199. C2×Q8×C47#41semidirect
218. C2×C22⋊D47SD16semidirect
313. Q8×C47C2×#41semidirect
334. C22⋊D47C2×SD16semidirect
412. C22×#103D47semidirect
414. C2×C47#3298semidirect
475. C2×#103C2×D47semidirect
480. C47C2×#3298semidirect
615. C2×Q8#10625350semidirect
722. Q8C2×#10625350semidirect
803. C2#20255249direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D472
C2×#156897742
#202552492
C2×#156894722
C2×#156894532
C2×#156894522
C2×#156894062
C2×#156893552
C2×#156893522
C2×#156893272
C2×#156892632
C2×#156892622
C2×#156892082
C2×C8×C22⋊D472
C2×#103×D472
C22×#103×C472
C2×#329847