Finite Group Databasebeta

← C2×#20253642 #27084584

Subgroups — C2×#20253642 #27084584

Order 12032.

2210 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×#15689736C211yesmaximal, characteristic, complemented
2C2×#15689595C211yesmaximal, characteristic
3#20253642C2116yesmaximal, direct product factor
4C2×#15689467C211yesmaximal, characteristic, complemented
5C2×#15689466C211yesmaximal, characteristic, complemented
6C2×#15689420C211yesmaximal, characteristic, complemented
7C2×#15689329C211yesmaximal, characteristic, complemented
8C2×#15689328C211yesmaximal, characteristic, complemented
9C2×#15689275C211yesmaximal, characteristic
10C2×#15689275C211yesmaximal, characteristic
11C2×#15689222C211yesmaximal, characteristic, complemented
12C2×#15689220C211yesmaximal, characteristic, complemented
13C2×#15689214C211yesmaximal, characteristic, complemented
14C2×#15689210C211yesmaximal, characteristic, complemented
15C2×#15689183C211yesmaximal, characteristic, complemented
16C2×C47×#478C211yesmaximal, characteristic, complemented
17C22×D4×D47C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625335C2211yescharacteristic
22#15689736—24no—
23#15689736C2218yescomplemented
24C2×#13094024C2211yescharacteristic, complemented
25C2×#13094019—21no—
26C2×#13094019—21no—
27C2×#13094015—21no—
28C2×#13094015—21no—
29C2×#13094004C2211yescharacteristic
30C2×#13094004C2211yescharacteristic
31#15689595—24no—
32#15689595C2218yes—
33C2×#13093989C2211yescharacteristic, complemented
34C2×#13093989C2211yescharacteristic, complemented
35C2×C4×D188C2211yescharacteristic
36C2×D4×Dic47C2211yescharacteristic
37C2×#13093986C2211yescharacteristic
38C2×C4×C22⋊D47—21no—
39C2×(C22⋊D47)⋊C4—21no—
40C2×#13093982C2211yescharacteristic
41C2×#13093981C2211yescharacteristic
42C22×(C2×D47)⋊C4—21no—
43C2×C22⋊C4×D47—21no—
44#15689467C2218yescomplemented
45#15689466C2218yescomplemented
46#15689420C2218yescomplemented
47#15689329C2218yescomplemented
48#15689328C2218yescomplemented
49#15689275C2218yes—
50#15689275C2218yes—
51#15689222C2218yescomplemented
52#15689220C2218yescomplemented
53#15689214C2218yescomplemented
54#15689210C2218yescomplemented
55#15689183C2218yescomplemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093949C2211yescharacteristic, complemented
61C2×#13093947C2211yescharacteristic, complemented
62C2×#13093947C2211yescharacteristic, complemented
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×#13093934C2211yescharacteristic, complemented
68C2×C8×Dic47C2211yescharacteristic, complemented
69C2×#125×C47C2211yescharacteristic, complemented
70C2×C4×D4×C47C2211yescharacteristic
71C47×#478C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×C4⋊C8×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C24×D47—21no—
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×C22⋊D47—21no—
82C2×D4×D47—24no—
83C2×D4×D47—24no—
84C2×D4×D47—22no—
85C2×D4×D47C2314yes—
86C23×Dic47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47C2311yescharacteristic
90C2×#10625325—24no—
91C2×#10625325—24no—
92C2×#10625325C2314yes—
93C2×#10625325C2314yes—
94C2×#10625335—24no—
95C2×#10625335—24no—
96C2×#10625335C2314yes—
97C2×#10625335C2314yes—
98C22×C47⋊C8C2311yescharacteristic
99C22×C47⋊C8C2311yescharacteristic
100#13094024—22no—
101#13094024C2314yescomplemented
102#13094019—28no—
103#13094019—28no—
104#13094015—28no—
105#13094015—28no—
106#13094004—22no—
107#13094004—22no—
108#13094004C2314yes—
109#13094004C2314yes—
110#13093989—22no—
111#13093989—22no—
112#13093989C2314yescomplemented
113#13093989C2314yescomplemented
114C4×D188—22no—
115C4×D188C2314yes—
116D4×Dic47—22no—
117D4×Dic47C2314yes—
118#13093986—22no—
119#13093986C2314yes—
120C4×C22⋊D47—28no—
121(C22⋊D47)⋊C4—28no—
122#13093982—22no—
123#13093982C2314yes—
124#13093981D414yes—
125#13093981C2314yes—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47C2311yescharacteristic
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4D411yescharacteristic
134C2×Dic47⋊C4D411yescharacteristic
135C2×C22⋊Dic47—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—28no—
142C2×(C2×D47)⋊C4D411yescharacteristic
143C2×(C2×D47)⋊C4D411yescharacteristic
144C22⋊C4×D47—28no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yescomplemented
150#13093955C2314yescomplemented
151C4⋊(C47⋊C8)C2314yescomplemented
152#13093949C2314yescomplemented
153#13093949C2314yescomplemented
154#13093947C2314yescomplemented
155#13093947C2314yescomplemented
156#13093944C2314yes—
157#13093944C2314yes—
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160#13093934C2314yescomplemented
161C8×Dic47C2314yescomplemented
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47—21no—
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166#125×C47—22no—
167#125×C47C2314yescomplemented
168C4×D4×C47—22no—
169C4×D4×C47C2314yes—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C42×C47C2311yescharacteristic
177#107×C47C2314yescomplemented
178#106×C47C2314yescomplemented
179C4⋊C8×C47C2314yescomplemented
180#102×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C23×D47—21no—
184C23×D47—28no—
185C23×D47—24no—
186C23×D47—82no—
187C23×D47—82no—
188C23×D47C2×D411yescharacteristic
189C2×D4×C47—21no—
190C2×D4×C47—22no—
191C2×D4×C47#4114yes—
192C2×D4×C47C2412yes—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—24no—
197C22×C4×C47—82no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C2×C22⋊D47—28no—
202C2×C22⋊D47—24no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—24no—
207C22×Dic47—82no—
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211D4×D47—216no—
212D4×D47—28no—
213D4×D47—28no—
214C2×D188—21no—
215C2×D188—22no—
216C2×D188#4114yes—
217C2×D188C2412yes—
218C2×C4×D47—22no—
219C2×C4×D47—22no—
220C2×C4×D47—24no—
221C2×C4×D47—24no—
222C2×C4×D47—82no—
223C2×C4×D47—82no—
224C2×C4×D47C2×D412yes—
225C2×C4×D47C2412yes—
226C2×Dic94—22no—
227C2×Dic94—22no—
228C2×Dic94—22no—
229C2×Dic94—22no—
230C2×Dic94—21no—
231C2×Dic94—21no—
232C2×Dic94C2412yes—
233C2×Dic94C2412yes—
234C2×C8×C47—22no—
235C2×C8×C47—22no—
236C2×C8×C47C2412yes—
237C2×C8×C47C2412yes—
238C4⋊C4×C47—24no—
239C4⋊C4×C47—24no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47C2412yes—
244C4⋊C4×C47C2412yes—
245C4⋊C4×C47C2412yes—
246C22⋊C4×C47—24no—
247C42×C47C2×D412yes—
248C42×C47C2412yes—
249C22⋊Dic47—24no—
250#10625335—28no—
251#10625335—28no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4C2×D414yes—
258(C2×D47)⋊C4C2×D414yes—
259C4⋊Dic47—24no—
260C4⋊Dic47—24no—
261C4⋊Dic47—21no—
262C4⋊Dic47—24no—
263C4⋊Dic47—24no—
264C4⋊Dic47C2412yes—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4C2×D414yes—
268Dic47⋊C4C2×D414yes—
269C4×Dic47—24no—
270C4×Dic47—24no—
271C4×Dic47—24no—
272C4×Dic47C2×D412yes—
273C4×Dic47C2412yes—
274C2×C47⋊C8—22no—
275C2×C47⋊C8—22no—
276C2×C47⋊C8C2412yes—
277C2×C47⋊C8C2412yes—
278#10625325—28no—
279#10625325—28no—
280C23×C47—24no—
281C23×C47—22no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47C22×D411yescharacteristic
285C22×D47—22no—
286C22×D47—24no—
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—216no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—84no—
294C22×D47—84no—
295C22×D47—816no—
296C22×D47C22×D412yes—
297D4×C47—24no—
298D4×C47—22no—
299D4×C47C2×#4114yes—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—84no—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D412yes—
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C47C2×#4112yes—
313C2×C4×C47C2×#4112yes—
314C2×C4×C47C2511yescharacteristic
315C22⋊D47—216no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—84no—
326C2×Dic47C22×D412yes—
327C2×Dic47C22×D412yes—
328C2×Dic47C22×D412yes—
329D188—24no—
330D188—22no—
331D188C2×#4114yes—
332C4×D47—24no—
333C4×D47—22no—
334C4×D47—22no—
335C4×D47—84no—
336C4×D47—84no—
337Dic94—22no—
338Dic94—22no—
339Dic94—22no—
340Dic94—22no—
341Dic94—42no—
342Dic94—42no—
343C8×C47—22no—
344C8×C47—22no—
345C47⋊C8—22no—
346C47⋊C8—22no—
347C2×#3123—471nomaximal, Sylow
348C22×C47—24no—
349C22×C47—48no—
350C22×C47—42no—
351C22×C47—42no—
352C22×C47#52512yes—
353C22×C47#57712yes—
354C22×C47#57712yes—
355C22×C47C23×D411yescharacteristic
356C2×D47—22no—
357C2×D47—24no—
358C2×D47—22no—
359C2×D47—22no—
360C2×D47—44no—
361C2×D47—48no—
362C2×D47—42no—
363C2×D47—42no—
364C2×D47—816no—
365C4×C47—22no—
366C4×C47—22no—
367C4×C47—42no—
368C4×C47—42no—
369C4×C47—42no—
370C4×C47#52512yes—
371C4×C47C22×#4111yescharacteristic
372C4×C47C22×#4111yescharacteristic
373Dic47—22no—
374Dic47—22no—
375Dic47—22no—
376Dic47—42no—
377Dic47—42no—
378Dic47—42no—
379C2×#541—471no—
380C2×#518—471no—
381#3123—4716no—
382C2×#485—471no—
383C2×#485—471no—
384C2×#478—471no—
385C2×#478D4711yescharacteristic, complemented
386C2×#461—471no—
387C2×#461—471no—
388C2×#450—471no—
389C2×#450—471no—
390C2×#440—471no—
391C2×#440—471no—
392C2×C4×SD16—471no—
393C2×C4×SD16—471no—
394C2×#433—471no—
395C2×C47—44no—
396C2×C47#312314yescomplemented
397C2×C47C2×#52511yescharacteristic
398C2×C47C2×#57711yescharacteristic
399C2×C47C2×#57711yescharacteristic
400D47—42no—
401D47—44no—
402C23×D4—471no—
403C22×SD16—471no—
404C22×SD16—471no—
405C22×SD16—471no—
406C22×SD16—471no—
407#541—478no—
408#541—944no—
409C2×C4⋊Q8—471no—
410C2×#126—941no—
411C2×#126—941no—
412C2×#125—941no—
413C2×#125—941no—
414C2×#125C2×D4711yescharacteristic, complemented
415C2×C22⋊Q8—471no—
416C2×C22⋊Q8—471no—
417#518—478no—
418#518—944no—
419C2×C4×Q8—471no—
420C2×C4×Q8—471no—
421C2×C4×D4—471no—
422C2×C4×D4—471no—
423C2×C4×D4—471no—
424C2×C4×D4—941no—
425C2×C4×D4—941no—
426C2×C4×D4C2×D4711yescharacteristic
427C2×#117—471no—
428C2×#117—471no—
429C22×C22⋊C4—941no—
430C22×C22⋊C4—941no—
431#485—478no—
432#485—478no—
433#478—478no—
434#478C2×D4718yescomplemented
435#461—478no—
436#461—478no—
437#450—478no—
438#450—478no—
439#440—478no—
440#440—478no—
441C4×SD16—478no—
442C4×SD16—478no—
443#433—478no—
444C2×#107—471no—
445C2×#107C2×D4711yescharacteristic, complemented
446C2×#106—471no—
447C2×#106C2×D4711yescharacteristic, complemented
448C2×C4⋊C8—471no—
449C2×C4⋊C8C2×D4711yescharacteristic, complemented
450C2×#103—471no—
451C2×#103—471no—
452C2×#103—471no—
453C2×#103—471no—
454C2×#102—471no—
455C2×#102—471no—
456C2×#102C2×D4711yescharacteristic
457C2×#102C2×D4711yescharacteristic
458C2×C22⋊C8—471no—
459C2×C22⋊C8—471no—
460C2×#97—471no—
461C2×C4×C8—471no—
462C47C2×#312311yescharacteristic, complemented, Sylow
463C25—941no—
464C22×Q8—471no—
465C22×Q8—471no—
466C22×D4—474no—
467C22×D4—471no—
468C22×D4—942no—
469C22×D4—941no—
470C22×D4—944no—
471C22×D4—944no—
472C22×D4C22×D4711yescharacteristic
473C23×C4—21no—
474C23×C4—471no—
475C23×C4—941no—
476C23×C4—941no—
477C23×C4—941no—
478C2×SD16—474no—
479C2×SD16—474no—
480C2×SD16—474no—
481C2×SD16—474no—
482C2×SD16—944no—
483C2×SD16—944no—
484C2×SD16—944no—
485C2×SD16—944no—
486C22×C8—471no—
487C22×C8—471no—
488C22×C8C22×D4711yescharacteristic
489C22×C8C22×D4711yescharacteristic
490C4⋊Q8—474no—
491C4⋊Q8—942no—
492#126—948no—
493#126—948no—
494#125—22no—
495#125—948no—
496#125—948no—
497#125C22×D4714yescomplemented
498C22⋊Q8—474no—
499C22⋊Q8—474no—
500C22⋊Q8—942no—
501C22⋊Q8—942no—
502C4×Q8—474no—
503C4×Q8—474no—
504C4×Q8—942no—
505C4×Q8—942no—
506C4×D4—22no—
507C4×D4—474no—
508C4×D4—474no—
509C4×D4—474no—
510C4×D4—942no—
511C4×D4—942no—
512C4×D4—948no—
513C4×D4—948no—
514C4×D4—942no—
515C4×D4C22×D4714yes—
516#117—474no—
517#117—474no—
518#117—474no—
519#117—942no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—471no—
524C2×C4⋊C4—471no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4—941no—
529C2×C4⋊C4—941no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4C22×D4711yescharacteristic
532C2×C4⋊C4C22×D4711yescharacteristic
533C2×C4⋊C4C22×D4711yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—471no—
536C2×C22⋊C4—471no—
537C2×C22⋊C4—948no—
538C2×C22⋊C4—948no—
539C2×C22⋊C4—941no—
540C2×C22⋊C4—941no—
541C2×C22⋊C4—941no—
542C2×C22⋊C4—941no—
543C2×C22⋊C4—941no—
544C2×C22⋊C4—941no—
545C2×C42—471no—
546C2×C42—941no—
547C2×C42—941no—
548C2×C42—941no—
549C2×C42C22×D4711yescharacteristic
550#107—474no—
551#107C22×D4714yescomplemented
552#106—474no—
553#106C22×D4714yescomplemented
554C4⋊C8—474no—
555C4⋊C8C22×D4714yescomplemented
556#103—474no—
557#103—474no—
558#103—474no—
559#103—474no—
560#102—474no—
561#102—474no—
562#102C22×D4714yes—
563#102C22×D4714yes—
564C22⋊C8—474no—
565C22⋊C8—474no—
566#97—474no—
567C4×C8—474no—
568C24—21no—
569C24—471no—
570C24—944no—
571C24—948no—
572C24—941no—
573C24—3762no—
574C24—3762no—
575C2×Q8—472no—
576C2×Q8—472no—
577C2×Q8—941no—
578C2×Q8—941no—
579C2×Q8—942no—
580C2×Q8—942no—
581C2×Q8—942no—
582C2×Q8—942no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—474no—
586C2×D4—472no—
587C2×D4—944no—
588C2×D4—948no—
589C2×D4—9416no—
590C2×D4—948no—
591C2×D4—948no—
592C2×D4—941no—
593C2×D4—942no—
594C2×D4#1062535414yes—
595C2×D4C23×D4712yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—471no—
602C22×C4—471no—
603C22×C4—471no—
604C22×C4—472no—
605C22×C4—472no—
606C22×C4—944no—
607C22×C4—944no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4—944no—
614C22×C4—3762no—
615C22×C4—3762no—
616C22×C4—3762no—
617C22×C4D4×D4711yescharacteristic
618C22×C4D4×D4711yescharacteristic
619C22×C4C23×D4711yescharacteristic
620SD16—948no—
621SD16—948no—
622SD16—948no—
623SD16—948no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—472no—
627C2×C8—472no—
628C2×C8—942no—
629C2×C8—942no—
630C2×C8C23×D4712yes—
631C2×C8C23×D4712yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—474no—
638C4⋊C4—474no—
639C4⋊C4—472no—
640C4⋊C4—944no—
641C4⋊C4—944no—
642C4⋊C4—944no—
643C4⋊C4—944no—
644C4⋊C4—941no—
645C4⋊C4—944no—
646C4⋊C4—944no—
647C4⋊C4C23×D4712yes—
648C4⋊C4C23×D4712yes—
649C4⋊C4C23×D4712yes—
650C22⋊C4—24no—
651C22⋊C4—474no—
652C22⋊C4—474no—
653C22⋊C4—944no—
654C22⋊C4—944no—
655C22⋊C4—944no—
656C22⋊C4—944no—
657C22⋊C4—944no—
658C22⋊C4—944no—
659C42—472no—
660C42—472no—
661C42—944no—
662C42—944no—
663C42—944no—
664C42D4×D4712yes—
665C42C23×D4712yes—
666C23—24no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—472no—
671C23—9416no—
672C23—942no—
673C23—944no—
674C23—942no—
675C23—942no—
676C23—942no—
677C23—3764no—
678C23—3764no—
679C23—37616no—
680C23—1882no—
681C23—1882no—
682C23C2×D4×D4711yescharacteristic
683Q8—942no—
684Q8—942no—
685Q8—942no—
686Q8—942no—
687Q8—1882no—
688Q8—1882no—
689D4—24no—
690D4—22no—
691D4—474no—
692D4—9416no—
693D4—944no—
694D4—942no—
695D4C2×#1062535414yes—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—472no—
706C2×C4—472no—
707C2×C4—472no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—944no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—3764no—
718C2×C4—3764no—
719C2×C4—3764no—
720C2×C4—1882no—
721C2×C4—1882no—
722C2×C4—1882no—
723C2×C4C2×D4×D4712yes—
724C2×C4C2×D4×D4712yes—
725C2×C4C2×D4×D4711yescharacteristic
726C2×C4#41×D4712yes—
727C2×C4C2×#1062535412yes—
728C2×C4C24×D4711yescharacteristic
729C8—22no—
730C8—22no—
731C8—942no—
732C8—942no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—48no—
737C22—942no—
738C22—942no—
739C22—942no—
740C22—944no—
741C22—37616no—
742C22—1882no—
743C22—1882no—
744C22—1884no—
745C22—1888no—
746C22#1568963612yes—
747C22#1568993012yes—
748C22#1568993312yes—
749C22C22×D4×D4711yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—942no—
756C4—942no—
757C4—942no—
758C4—1882no—
759C4—1882no—
760C4—1882no—
761C4#1568963612yes—
762C4C2×#41×D4711yescharacteristic
763C4C22×#1062535411yescharacteristic
764C2—44no—
765C2—1882no—
766C2—1884no—
767C2#2025364214yesdirect product factor
768C2C2×#1568963611yescharacteristic
769C2C2×#1568993011yescharacteristic
770C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#478C2
socleC23×C47C22×D4
prime radicalC22×D4×D47C22
hypercenterC2×#478D47
hypocenterC47C2×#3123
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#15689736C2semidirect
3. #20253642C2direct (N × H)
4. C2×#15689467C2semidirect
5. C2×#15689466C2semidirect
6. C2×#15689420C2semidirect
7. C2×#15689329C2semidirect
8. C2×#15689328C2semidirect
11. C2×#15689222C2semidirect
12. C2×#15689220C2semidirect
13. C2×#15689214C2semidirect
14. C2×#15689210C2semidirect
15. C2×#15689183C2semidirect
16. C2×C47×#478C2semidirect
23. #15689736C22semidirect
24. C2×#13094024C22semidirect
33. C2×#13093989C22semidirect
34. C2×#13093989C22semidirect
44. #15689467C22semidirect
45. #15689466C22semidirect
46. #15689420C22semidirect
47. #15689329C22semidirect
48. #15689328C22semidirect
51. #15689222C22semidirect
52. #15689220C22semidirect
53. #15689214C22semidirect
54. #15689210C22semidirect
55. #15689183C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093955C22semidirect
58. C2×C4⋊(C47⋊C8)C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093949C22semidirect
61. C2×#13093947C22semidirect
62. C2×#13093947C22semidirect
67. C2×#13093934C22semidirect
68. C2×C8×Dic47C22semidirect
69. C2×#125×C47C22semidirect
71. C47×#478C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×C4⋊C8×C47C22semidirect
101. #13094024C23semidirect
112. #13093989C23semidirect
113. #13093989C23semidirect
149. #13093957C23semidirect
150. #13093955C23semidirect
151. C4⋊(C47⋊C8)C23semidirect
152. #13093949C23semidirect
153. #13093949C23semidirect
154. #13093947C23semidirect
155. #13093947C23semidirect
160. #13093934C23semidirect
161. C8×Dic47C23semidirect
167. #125×C47C23semidirect
177. #107×C47C23semidirect
178. #106×C47C23semidirect
179. C4⋊C8×C47C23semidirect
385. C2×#478D47semidirect
396. C2×C47#3123semidirect
414. C2×#125C2×D47semidirect
434. #478C2×D47semidirect
445. C2×#107C2×D47semidirect
447. C2×#106C2×D47semidirect
449. C2×C4⋊C8C2×D47semidirect
462. C47C2×#3123semidirect
497. #125C22×D47semidirect
551. #107C22×D47semidirect
553. #106C22×D47semidirect
555. C4⋊C8C22×D47semidirect
767. C2#20253642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897362
C2×#156895952
#202536422
C2×#156894672
C2×#156894662
C2×#156894202
C2×#156893292
C2×#156893282
C2×#156892752
C2×#156892222
C2×#156892202
C2×#156892142
C2×#156892102
C2×#156891832
C2×C47×#4782
C2×#312347