Finite Group Databasebeta

← C2×#20255667 #27093159

Subgroups — C2×#20255667 #27093159

Order 12032.

2082 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689841C211yesmaximal, characteristic
2C2×Q8×C22⋊D47C211yesmaximal, characteristic
3#20255667C2116yesmaximal, direct product factor
4C2×#15689472C211yesmaximal, characteristic, complemented
5C2×#15689464C211yesmaximal, characteristic, complemented
6C2×#15689462C211yesmaximal, characteristic, complemented
7C2×#15689406C211yesmaximal, characteristic, complemented
8C2×#15689381C211yesmaximal, characteristic, complemented
9C2×#15689380C211yesmaximal, characteristic, complemented
10C2×#15689332C211yesmaximal, characteristic, complemented
11C2×#15689280C211yesmaximal, characteristic, complemented
12C2×#15689279C211yesmaximal, characteristic, complemented
13C2×#15689215C211yesmaximal, characteristic, complemented
14C2×#15689199C211yesmaximal, characteristic
15C2×#15689130C211yesmaximal, characteristic, complemented
16C2×C47×#419C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625337C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22#15689841—24no—
23#15689841C2218yes—
24Q8×C22⋊D47—24no—
25Q8×C22⋊D47C2218yes—
26C2×#13094023C2211yescharacteristic
27C2×#13094022—21no—
28C2×#13094022C2211yescharacteristic
29C2×#13094018—21no—
30C2×#13094017—21no—
31C2×#13094010—21no—
32C2×#13094004C2211yescharacteristic
33C2×#13094003—21no—
34C2×#13094003C2211yescharacteristic
35C2×#13094003C2211yescharacteristic
36C2×#13094000—21no—
37C2×#13094000C2211yescharacteristic
38C2×Q8×Dic47C2211yescharacteristic
39C2×C4×Dic94—21no—
40C2×#13093989C2211yescharacteristic
41C2×C4×C22⋊D47—21no—
42C2×C4×C22⋊D47C2211yescharacteristic
43C2×#13093982C2211yescharacteristic
44#15689472C2218yescomplemented
45#15689464C2218yescomplemented
46#15689462C2218yescomplemented
47#15689406C2218yescomplemented
48#15689381C2218yescomplemented
49#15689380C2218yescomplemented
50#15689332C2218yescomplemented
51#15689280C2218yescomplemented
52#15689279C2218yescomplemented
53#15689215C2218yescomplemented
54#15689199C2218yes—
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59#15689130C2218yescomplemented
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093947C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C23×Q8×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×#117×C47C2211yescharacteristic
72C47×#419C2218yescomplemented
73C2×#103×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×Dic94C2311yescharacteristic
80C22×Dic94C2311yescharacteristic
81C2×Q8×D47—22no—
82C2×Q8×D47—24no—
83C2×Q8×D47—42no—
84C2×Q8×D47C2314yes—
85C22×C22⋊D47D411yescharacteristic
86C22×C4×D47—21no—
87C22×C4×D47C2311yescharacteristic
88C2×Dic188—42no—
89C2×Dic188C2314yes—
90C2×#10625337—24no—
91C2×#10625337—42no—
92C2×#10625337C2314yes—
93C2×#10625337C2314yes—
94C2×#10625324—42no—
95C2×#10625324C2314yes—
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2311yescharacteristic
98#13094023—22no—
99#13094023C2314yes—
100#13094022—28no—
101#13094022—22no—
102#13094022C2314yes—
103#13094018—28no—
104#13094017—28no—
105#13094010—28no—
106#13094004—22no—
107#13094004C2314yes—
108#13094003—22no—
109#13094003—22no—
110#13094003—28no—
111#13094003C2314yes—
112#13094003C2314yes—
113#13094000—22no—
114#13094000—28no—
115#13094000C2314yes—
116Q8×Dic47—22no—
117Q8×Dic47C2314yes—
118C4×Dic94—28no—
119#13093989—22no—
120#13093989C2314yes—
121C4×C22⋊D47—28no—
122C4×C22⋊D47D414yes—
123C4×C22⋊D47C2314yes—
124#13093982—22no—
125#13093982C2314yes—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4D411yescharacteristic
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47D411yescharacteristic
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4D411yescharacteristic
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yes—
150#13093956C2314yes—
151#13093955C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093948C2314yes—
156#13093948C2314yes—
157#13093947C2314yes—
158#13093947C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160(C2×D47)⋊C8C2314yes—
161C8×Dic47C2314yes—
162C22×Q8×C47—22no—
163C22×Q8×C47—21no—
164C22×Q8×C47—24no—
165C22×Q8×C47—42no—
166C22×Q8×C47C2311yescharacteristic
167C22×Q8×C47C2314yes—
168C22×Q8×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47C2311yescharacteristic
171C2×M16×C47—42no—
172C2×M16×C47C2314yes—
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2311yescharacteristic
175#117×C47—22no—
176#117×C47C2314yes—
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C22⋊C4×C47—21no—
180C2×C42×C47—21no—
181#103×C47C2314yes—
182#103×C47C2314yes—
183#103×C47C2314yes—
184#103×C47C2314yes—
185C24×C47C2×D411yescharacteristic
186C23×D47C2×D411yescharacteristic
187C2×Q8×C47—21no—
188C2×Q8×C47—24no—
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—28no—
192C2×Q8×C47—22no—
193C2×Q8×C47—22no—
194C2×Q8×C47—44no—
195C2×Q8×C47—44no—
196C2×Q8×C47—48no—
197C2×Q8×C47#4114yes—
198C2×Q8×C47C2412yes—
199C2×Q8×C47C2412yes—
200C22×C4×C47—21no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—24no—
207C22×C4×C47—44no—
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2411yescharacteristic
212C2×C22⋊D47—24no—
213C2×C22⋊D47C2×D414yes—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220C22×Dic47C2×D411yescharacteristic
221Q8×D47—28no—
222Q8×D47—44no—
223Q8×D47—48no—
224C2×C4×D47—22no—
225C2×C4×D47—22no—
226C2×C4×D47—24no—
227C2×C4×D47—44no—
228C2×C4×D47C2×D412yes—
229C2×C4×D47C2412yes—
230C2×Dic94—22no—
231C2×Dic94—22no—
232C2×Dic94—22no—
233C2×Dic94—22no—
234C2×Dic94—21no—
235C2×Dic94—21no—
236C2×Dic94—24no—
237C2×Dic94—24no—
238C2×Dic94—44no—
239C2×Dic94—44no—
240C2×Dic94C2412yes—
241C2×Dic94C2412yes—
242M16×C47—44no—
243C2×C8×C47—22no—
244C2×C8×C47—22no—
245C2×C8×C47C2412yes—
246C2×C8×C47C2412yes—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47C2412yes—
250C4⋊C4×C47C2412yes—
251C22⋊C4×C47—24no—
252C42×C47—24no—
253C22⋊Dic47—24no—
254C22⋊Dic47—24no—
255C22⋊Dic47C2×D414yes—
256#10625337—28no—
257#10625337—44no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4C2×D414yes—
262C4⋊Dic47—21no—
263C4⋊Dic47—21no—
264C4⋊Dic47—24no—
265C4⋊Dic47—24no—
266C4⋊Dic47C2412yes—
267C4⋊Dic47C2412yes—
268Dic47⋊C4—24no—
269Dic47⋊C4—24no—
270Dic47⋊C4—24no—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4C2×D414yes—
276C4×Dic47—24no—
277C4×Dic47—24no—
278C4×Dic47—24no—
279C4×Dic47C2×D412yes—
280C4×Dic47C2412yes—
281C2×C47⋊C8—22no—
282C2×C47⋊C8—22no—
283C2×C47⋊C8C2412yes—
284C2×C47⋊C8C2412yes—
285Dic188—44no—
286#10625324—44no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47C22×D412yes—
291C23×C47C22×D411yescharacteristic
292C22×D47—22no—
293C22×D47—22no—
294C22×D47—22no—
295C22×D47C22×D412yes—
296Q8×C47—24no—
297Q8×C47—22no—
298Q8×C47—22no—
299Q8×C47—22no—
300Q8×C47—48no—
301Q8×C47—42no—
302Q8×C47C2×#4114yes—
303C2×C4×C47—24no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—24no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—48no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C2×#4112yes—
319C2×C4×C47H(5,𝔽2)12yes—
320C2×C4×C47C2511yescharacteristic
321C22⋊D47—28no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47#13714yes—
333C2×Dic47C22×D412yes—
334C2×Dic47C22×D412yes—
335C2×Dic47C22×D412yes—
336C4×D47—24no—
337C4×D47—22no—
338C4×D47—22no—
339C4×D47—48no—
340Dic94—22no—
341Dic94—22no—
342Dic94—22no—
343Dic94—22no—
344Dic94—48no—
345Dic94—42no—
346Dic94—42no—
347Dic94—48no—
348C8×C47—22no—
349C8×C47—22no—
350C47⋊C8—22no—
351C47⋊C8—22no—
352C2×#3328—471nomaximal, Sylow
353C22×C47—22no—
354C22×C47—22no—
355C22×C47—22no—
356C22×C47—44no—
357C22×C47#54612yes—
358C22×C47C2×#13712yes—
359C22×C47#57812yes—
360C22×C47C23×D411yescharacteristic
361C2×D47—22no—
362C2×D47—22no—
363C2×D47—22no—
364C2×D47—44no—
365C4×C47—24no—
366C4×C47—22no—
367C4×C47—42no—
368C4×C47—42no—
369C4×C47—42no—
370C4×C47#54612yes—
371C4×C47C22×#4111yescharacteristic
372C4×C47C2×H(5,𝔽2)11yescharacteristic
373Dic47—22no—
374Dic47—22no—
375Dic47—42no—
376Dic47—42no—
377Dic47—42no—
378Dic47—42no—
379Dic47C2×#13714yes—
380C2×#556—471no—
381C2×D4×Q8—471no—
382#3328—4716no—
383C2×#487—471no—
384C2×#485—471no—
385C2×#485—471no—
386C2×#475—471no—
387C2×#470—471no—
388C2×#470—471no—
389C2×#462—471no—
390C2×#451—471no—
391C2×#451—471no—
392C2×C4×Q16—471no—
393C2×#436—471no—
394C2×#419—471no—
395C2×#419D4711yescharacteristic, complemented
396C2×C47—42no—
397C2×C47#332814yescomplemented
398C2×C47C2×#54611yescharacteristic
399C2×C47C22×#13711yescharacteristic
400C2×C47C2×#57811yescharacteristic
401D47—42no—
402C23×Q8—471no—
403C23×Q8C2×D4711yescharacteristic
404C22×Q16—471no—
405C22×Q16—471no—
406C22×Q16—471no—
407C22×M16—471no—
408C22×M16C2×D4711yescharacteristic
409#556—478no—
410#556—944no—
411D4×Q8—478no—
412D4×Q8—944no—
413C2×C4⋊Q8—471no—
414C2×C4⋊Q8—471no—
415C2×C4⋊Q8—941no—
416C2×#126—941no—
417C2×#126—941no—
418C2×#124—941no—
419C2×C22⋊Q8—471no—
420C2×C22⋊Q8—471no—
421C2×C22⋊Q8—471no—
422C2×C22⋊Q8—471no—
423C2×C22⋊Q8—941no—
424C2×C22⋊Q8—941no—
425C2×C4×Q8—471no—
426C2×C4×Q8—471no—
427C2×C4×Q8—941no—
428C2×C4×D4—471no—
429C2×C4×D4—941no—
430C2×#117—471no—
431C2×#117C2×D4711yescharacteristic
432#487—478no—
433#485—478no—
434#485—478no—
435#475—478no—
436#470—478no—
437#470—478no—
438#462—478no—
439#451—478no—
440#451—478no—
441C4×Q16—478no—
442#436—478no—
443C2×#107—471no—
444C2×#106—471no—
445C2×#106—471no—
446C2×C4⋊C8—471no—
447#419—478no—
448#419C2×D4718yescomplemented
449C2×#103—471no—
450C2×#103—471no—
451C2×#103—471no—
452C2×#103—471no—
453C2×#103—471no—
454C2×#103—471no—
455C2×#103C2×D4711yescharacteristic
456C2×#103C2×D4711yescharacteristic
457C2×#103C2×D4711yescharacteristic
458C2×#103C2×D4711yescharacteristic
459C2×C22⋊C8—471no—
460C2×C22⋊C8—471no—
461C2×C4×C8—471no—
462C47C2×#332811yescharacteristic, complemented, Sylow
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—24no—
466C22×Q8—42no—
467C22×Q8—474no—
468C22×Q8—471no—
469C22×Q8—471no—
470C22×Q8—941no—
471C22×Q8—941no—
472C22×Q8—942no—
473C22×Q8—944no—
474C22×Q8—1882no—
475C22×Q8C22×D4711yescharacteristic
476C22×Q8C22×D4714yes—
477C22×Q8C22×D4711yescharacteristic
478C22×D4—471no—
479C23×C4—21no—
480C23×C4—471no—
481C23×C4—941no—
482C23×C4C22×D4711yescharacteristic
483C2×Q16—474no—
484C2×Q16—474no—
485C2×Q16—474no—
486C2×Q16—944no—
487C2×Q16—1882no—
488C2×Q16—1882no—
489C2×M16—42no—
490C2×M16—474no—
491C2×M16—1882no—
492C2×M16C22×D4714yes—
493C22×C8—471no—
494C22×C8—471no—
495C22×C8C22×D4711yescharacteristic
496C22×C8C22×D4711yescharacteristic
497C4⋊Q8—474no—
498C4⋊Q8—474no—
499C4⋊Q8—942no—
500C4⋊Q8—942no—
501C4⋊Q8—948no—
502#126—948no—
503#126—948no—
504#124—948no—
505C22⋊Q8—474no—
506C22⋊Q8—474no—
507C22⋊Q8—474no—
508C22⋊Q8—474no—
509C22⋊Q8—948no—
510C22⋊Q8—948no—
511C22⋊Q8—942no—
512C22⋊Q8—942no—
513C22⋊Q8—942no—
514C22⋊Q8—942no—
515C4×Q8—474no—
516C4×Q8—474no—
517C4×Q8—948no—
518C4×Q8—942no—
519C4×Q8—942no—
520C4×D4—474no—
521C4×D4—474no—
522C4×D4—948no—
523#117—22no—
524#117—474no—
525#117—942no—
526#117C22×D4714yes—
527C2×C4⋊C4—471no—
528C2×C4⋊C4—471no—
529C2×C4⋊C4—471no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4—941no—
532C2×C4⋊C4—941no—
533C2×C4⋊C4—941no—
534C2×C4⋊C4—941no—
535C2×C4⋊C4—941no—
536C2×C4⋊C4—941no—
537C2×C4⋊C4—941no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4C22×D4711yescharacteristic
540C2×C4⋊C4C22×D4711yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—471no—
543C2×C22⋊C4—471no—
544C2×C22⋊C4—941no—
545C2×C22⋊C4—941no—
546C2×C22⋊C4—941no—
547C2×C22⋊C4—941no—
548C2×C22⋊C4—941no—
549C2×C42—21no—
550C2×C42—471no—
551C2×C42—941no—
552C2×C42—941no—
553C2×C42—941no—
554#107—474no—
555#106—474no—
556#106—474no—
557C4⋊C8—474no—
558#103—474no—
559#103—474no—
560#103—474no—
561#103—474no—
562#103—474no—
563#103—474no—
564#103C22×D4714yes—
565#103C22×D4714yes—
566#103C22×D4714yes—
567#103C22×D4714yes—
568C22⋊C8—474no—
569C22⋊C8—474no—
570C4×C8—474no—
571C24—471no—
572C24D4×D4711yescharacteristic
573C2×Q8—21no—
574C2×Q8—24no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—28no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—48no—
583C2×Q8—472no—
584C2×Q8—472no—
585C2×Q8—944no—
586C2×Q8—944no—
587C2×Q8—941no—
588C2×Q8—941no—
589C2×Q8—948no—
590C2×Q8—942no—
591C2×Q8—942no—
592C2×Q8—942no—
593C2×Q8—942no—
594C2×Q8—1884no—
595C2×Q8—1884no—
596C2×Q8—1884no—
597C2×Q8—1888no—
598C2×Q8#1062535014yes—
599C2×Q8C23×D4712yes—
600C2×Q8C23×D4712yes—
601C2×D4—474no—
602C2×D4—944no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—44no—
611C22×C4—471no—
612C22×C4—471no—
613C22×C4—471no—
614C22×C4—472no—
615C22×C4—472no—
616C22×C4—944no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—1884no—
624C22×C4D4×D4712yes—
625C22×C4D4×D4711yescharacteristic
626C22×C4C23×D4712yes—
627C22×C4C23×D4711yescharacteristic
628Q16—948no—
629Q16—1884no—
630Q16—1884no—
631M16—44no—
632M16—1884no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—472no—
636C2×C8—472no—
637C2×C8—942no—
638C2×C8—942no—
639C2×C8C23×D4712yes—
640C2×C8C23×D4712yes—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—474no—
644C4⋊C4—472no—
645C4⋊C4—472no—
646C4⋊C4—944no—
647C4⋊C4—944no—
648C4⋊C4—944no—
649C4⋊C4—944no—
650C4⋊C4—944no—
651C4⋊C4—944no—
652C4⋊C4—944no—
653C4⋊C4—944no—
654C4⋊C4—944no—
655C4⋊C4—941no—
656C4⋊C4—941no—
657C4⋊C4C23×D4712yes—
658C4⋊C4C23×D4712yes—
659C22⋊C4—24no—
660C22⋊C4—474no—
661C22⋊C4—474no—
662C22⋊C4—944no—
663C22⋊C4—944no—
664C22⋊C4—944no—
665C22⋊C4—944no—
666C22⋊C4—944no—
667C42—24no—
668C42—472no—
669C42—472no—
670C42—944no—
671C42—944no—
672C42—944no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—472no—
677C23—942no—
678C23—942no—
679C23—942no—
680C23C2×D4×D4712yes—
681C23C2×D4×D4711yescharacteristic
682Q8—24no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—48no—
687Q8—42no—
688Q8—942no—
689Q8—942no—
690Q8—942no—
691Q8—942no—
692Q8—1888no—
693Q8—1888no—
694Q8—1882no—
695Q8—1882no—
696Q8C2×#1062535014yes—
697D4—948no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—48no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—474no—
712C2×C4—472no—
713C2×C4—472no—
714C2×C4—472no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—944no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—1888no—
725C2×C4—1882no—
726C2×C4—1882no—
727C2×C4—1882no—
728C2×C4—1882no—
729C2×C4C2×D4×D4712yes—
730C2×C4C2×D4×D4711yescharacteristic
731C2×C4C2×#1062535012yes—
732C2×C4#1309406912yes—
733C2×C4C24×D4711yescharacteristic
734C8—22no—
735C8—22no—
736C8—942no—
737C8—942no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—942no—
743C22—942no—
744C22—942no—
745C22—1884no—
746C22#1568976312yes—
747C22#137×D4712yes—
748C22#1568993912yes—
749C22C22×D4×D4711yescharacteristic
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—474no—
756C4—942no—
757C4—942no—
758C4—1882no—
759C4—1882no—
760C4—1882no—
761C4—1882no—
762C4#1568976312yes—
763C4C22×#1062535011yescharacteristic
764C4C2×#1309406911yescharacteristic
765C2—42no—
766C2—1882no—
767C2#2025566714yesdirect product factor
768C2C2×#1568976311yescharacteristic
769C2C2×#137×D4711yescharacteristic
770C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#419C2
socleC23×C47C22×D4
prime radicalC22×C22⋊D47D4
hypercenterC2×#419D47
hypocenterC47C2×#3328
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. #20255667C2direct (N × H)
4. C2×#15689472C2semidirect
5. C2×#15689464C2semidirect
6. C2×#15689462C2semidirect
7. C2×#15689406C2semidirect
8. C2×#15689381C2semidirect
9. C2×#15689380C2semidirect
10. C2×#15689332C2semidirect
11. C2×#15689280C2semidirect
12. C2×#15689279C2semidirect
13. C2×#15689215C2semidirect
15. C2×#15689130C2semidirect
16. C2×C47×#419C2semidirect
44. #15689472C22semidirect
45. #15689464C22semidirect
46. #15689462C22semidirect
47. #15689406C22semidirect
48. #15689381C22semidirect
49. #15689380C22semidirect
50. #15689332C22semidirect
51. #15689280C22semidirect
52. #15689279C22semidirect
53. #15689215C22semidirect
59. #15689130C22semidirect
72. C47×#419C22semidirect
395. C2×#419D47semidirect
397. C2×C47#3328semidirect
448. #419C2×D47semidirect
462. C47C2×#3328semidirect
767. C2#20255667direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898412
C2×Q8×C22⋊D472
#202556672
C2×#156894722
C2×#156894642
C2×#156894622
C2×#156894062
C2×#156893812
C2×#156893802
C2×#156893322
C2×#156892802
C2×#156892792
C2×#156892152
C2×#156891992
C2×#156891302
C2×C47×#4192
C2×#332847