Finite Group Databasebeta

← C2×#20253637 #27084579

Subgroups — C2×#20253637 #27084579

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×#15689731C211yesmaximal, characteristic, complemented
2C2×#15689595C211yesmaximal, characteristic
3#20253637C2116yesmaximal, direct product factor
4C2×#15689467C211yesmaximal, characteristic, complemented
5C2×#15689462C211yesmaximal, characteristic, complemented
6C2×#15689425C211yesmaximal, characteristic, complemented
7C2×#15689422C211yesmaximal, characteristic, complemented
8C2×#15689327C211yesmaximal, characteristic, complemented
9C2×#15689326C211yesmaximal, characteristic, complemented
10C2×#15689275C211yesmaximal, characteristic
11C2×#15689272C211yesmaximal, characteristic
12C2×#15689223C211yesmaximal, characteristic, complemented
13C2×#15689221C211yesmaximal, characteristic, complemented
14C2×C4×#10625325C211yesmaximal, characteristic, complemented
15C2×#15689182C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
17C22×D4×D47C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21#15689731—24no—
22#15689731C2218yescomplemented
23C2×#13094022C2211yescharacteristic, complemented
24C2×#13094019—21no—
25C2×#13094018—21no—
26C2×#13094016—21no—
27C2×#13094015C2211yescharacteristic, complemented
28C2×#13094014—21no—
29C2×#13094004C2211yescharacteristic
30C2×#13094000C2211yescharacteristic
31#15689595—24no—
32#15689595C2218yes—
33C2×C4×Dic94C2211yescharacteristic, complemented
34C2×C4×D188C2211yescharacteristic
35C2×D4×Dic47C2211yescharacteristic
36C2×#13093986C2211yescharacteristic
37C2×C4×C22⋊D47—21no—
38C2×(C22⋊D47)⋊C4—21no—
39C2×#13093982C2211yescharacteristic
40C2×#13093981C2211yescharacteristic
41C22×(C2×D47)⋊C4—21no—
42C2×C22⋊C4×D47—21no—
43#15689467C2218yescomplemented
44#15689462C2218yescomplemented
45#15689425C2218yescomplemented
46#15689422C2218yescomplemented
47#15689327C2218yescomplemented
48#15689326C2218yescomplemented
49#15689275C2218yes—
50#15689272C2218yes—
51#15689223C2218yescomplemented
52#15689221C2218yescomplemented
53C4×#10625325C2218yescomplemented
54#15689182C2218yescomplemented
55C2×#13093957C2211yescharacteristic, complemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093956C2211yescharacteristic, complemented
58C2×Dic47⋊C8C2211yescharacteristic, complemented
59C2×Dic47⋊C8C2211yescharacteristic, complemented
60C2×#13093949C2211yescharacteristic, complemented
61C2×#13093948C2211yescharacteristic, complemented
62C2×#13093947C2211yescharacteristic, complemented
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093935C2211yescharacteristic, complemented
69C22×SD16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic, complemented
71C2×C4×D4×C47C2211yescharacteristic
72C4×SD16×C47C2218yescomplemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C2×D4×D47—24no—
82C2×D4×D47—24no—
83C2×D4×D47—22no—
84C2×D4×D47C2314yes—
85C23×Dic47—21no—
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47C2311yescharacteristic
89C2×#10625325—24no—
90C2×#10625325C2314yes—
91C2×#10625335—24no—
92C2×#10625335C2314yes—
93C2×#10625336—24no—
94C2×#10625336C2314yes—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97#13094022—22no—
98#13094022C2314yescomplemented
99#13094019—28no—
100#13094018—28no—
101#13094016—28no—
102#13094015—22no—
103#13094015C2314yescomplemented
104#13094014—28no—
105#13094004—22no—
106#13094004C2314yes—
107#13094000—22no—
108#13094000C2314yes—
109C4×Dic94—22no—
110C4×Dic94C2314yescomplemented
111C4×D188—22no—
112C4×D188C2314yes—
113D4×Dic47—22no—
114D4×Dic47C2314yes—
115#13093986—22no—
116#13093986C2314yes—
117C4×C22⋊D47—28no—
118(C22⋊D47)⋊C4—28no—
119#13093982—22no—
120#13093982C2314yes—
121#13093981D414yes—
122#13093981C2314yes—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4D411yescharacteristic
133C2×Dic47⋊C4D411yescharacteristic
134C2×C22⋊Dic47—21no—
135C2×(C2×D47)⋊C4—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—28no—
141C2×(C2×D47)⋊C4D411yescharacteristic
142C2×(C2×D47)⋊C4D411yescharacteristic
143C22⋊C4×D47—28no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093957C2314yescomplemented
148#13093957C2314yescomplemented
149#13093956C2314yescomplemented
150Dic47⋊C8C2314yescomplemented
151Dic47⋊C8C2314yescomplemented
152#13093949C2314yescomplemented
153#13093948C2314yescomplemented
154#13093947C2314yescomplemented
155#13093946C2314yes—
156#13093945C2314yes—
157#13093944C2314yes—
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160#13093935C2314yescomplemented
161C22×Q8×C47C2311yescharacteristic
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47—21no—
164C2×SD16×C47—24no—
165C2×SD16×C47C2314yes—
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168C4×Q8×C47—22no—
169C4×Q8×C47C2314yescomplemented
170C4×D4×C47—22no—
171C4×D4×C47C2314yes—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C42×C47—21no—
177C2×C42×C47C2311yescharacteristic
178#106×C47C2314yescomplemented
179#103×C47C2314yescomplemented
180#102×C47C2314yes—
181C4×C8×C47C2314yescomplemented
182C24×C47—21no—
183C23×D47—21no—
184C23×D47—28no—
185C23×D47—24no—
186C23×D47—82no—
187C23×D47—82no—
188C23×D47C2×D411yescharacteristic
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47C2412yes—
193C2×D4×C47—21no—
194C2×D4×C47—22no—
195C2×D4×C47#4114yes—
196C2×D4×C47C2412yes—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—24no—
201C22×C4×C47—82no—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2411yescharacteristic
205C2×C22⋊D47—28no—
206C2×C22⋊D47—24no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—24no—
211C22×Dic47—82no—
212C22×Dic47C2×D411yescharacteristic
213C22×Dic47C2×D411yescharacteristic
214C22×Dic47C2×D411yescharacteristic
215D4×D47—216no—
216D4×D47—28no—
217D4×D47—28no—
218C2×D188—21no—
219C2×D188—22no—
220C2×D188#4114yes—
221C2×D188C2412yes—
222C2×C4×D47—22no—
223C2×C4×D47—22no—
224C2×C4×D47—24no—
225C2×C4×D47—24no—
226C2×C4×D47—82no—
227C2×C4×D47—82no—
228C2×C4×D47C2×D412yes—
229C2×C4×D47C2412yes—
230C2×Dic94—22no—
231C2×Dic94—22no—
232C2×Dic94—21no—
233C2×Dic94C2412yes—
234SD16×C47—28no—
235C2×C8×C47—22no—
236C2×C8×C47—22no—
237C2×C8×C47C2412yes—
238C2×C8×C47C2412yes—
239C4⋊C4×C47—24no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47C2412yes—
243C4⋊C4×C47C2412yes—
244C22⋊C4×C47—24no—
245C42×C47—24no—
246C42×C47C2×D412yes—
247C42×C47C2412yes—
248C22⋊Dic47—24no—
249#10625336—28no—
250#10625335—28no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4C2×D414yes—
257(C2×D47)⋊C4C2×D414yes—
258C4⋊Dic47—21no—
259C4⋊Dic47—21no—
260C4⋊Dic47—24no—
261C4⋊Dic47—24no—
262C4⋊Dic47C2412yes—
263C4⋊Dic47C2412yes—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268Dic47⋊C4—24no—
269Dic47⋊C4C2×D414yes—
270Dic47⋊C4C2×D414yes—
271C4×Dic47—24no—
272C4×Dic47—24no—
273C4×Dic47C2×D412yes—
274C4×Dic47C2412yes—
275C2×C47⋊C8—22no—
276C2×C47⋊C8—22no—
277C2×C47⋊C8C2412yes—
278C2×C47⋊C8C2412yes—
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—
297Q8×C47—22no—
298Q8×C47—22no—
299Q8×C47—42no—
300D4×C47—24no—
301D4×C47—22no—
302D4×C47C2×#4114yes—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—84no—
312C2×C4×C47C22×D412yes—
313C2×C4×C47C22×D412yes—
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C2×#4112yes—
316C2×C4×C47C2×#4112yes—
317C2×C4×C47C2511yescharacteristic
318C22⋊D47—216no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—84no—
329C2×Dic47C22×D412yes—
330C2×Dic47C22×D412yes—
331C2×Dic47C22×D412yes—
332D188—24no—
333D188—22no—
334D188C2×#4114yes—
335C4×D47—24no—
336C4×D47—22no—
337C4×D47—22no—
338C4×D47—84no—
339C4×D47—84no—
340Dic94—22no—
341Dic94—22no—
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×#478—471no—
386C2×#461—471no—
387C2×#461—471no—
388C2×#450—471no—
389C2×#450—471no—
390C2×#440—471no—
391C2×#440—471no—
392C2×C4×SD16—471no—
393C2×C4×SD16D4711yescharacteristic, complemented
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×SD16C2×D4711yescharacteristic
407#541—478no—
408#541—944no—
409C2×C4⋊Q8—471no—
410C2×#126—941no—
411C2×#126—941no—
412C2×#125—471no—
413C2×#125—941no—
414C2×#125—941no—
415C2×C22⋊Q8—471no—
416C2×C22⋊Q8—471no—
417#518—478no—
418#518—944no—
419C2×C4×Q8—471no—
420C2×C4×Q8C2×D4711yescharacteristic, complemented
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#478—478no—
435#461—478no—
436#461—478no—
437#450—478no—
438#450—478no—
439#440—478no—
440#440—478no—
441C4×SD16—478no—
442C4×SD16C2×D4718yescomplemented
443#433—478no—
444C2×#107—471no—
445C2×#107—471no—
446C2×#106—471no—
447C2×#106C2×D4711yescharacteristic, complemented
448C2×C4⋊C8—471no—
449C2×C4⋊C8—471no—
450C2×#103—471no—
451C2×#103—471no—
452C2×#103—471no—
453C2×#103C2×D4711yescharacteristic, complemented
454C2×#102—471no—
455C2×#102—471no—
456C2×#102—471no—
457C2×#102C2×D4711yescharacteristic
458C2×C22⋊C8—471no—
459C2×C22⋊C8—471no—
460C2×#97—471no—
461C2×C4×C8C2×D4711yescharacteristic, complemented
462C47C2×#312311yescharacteristic, complemented, Sylow
463C25—941no—
464C22×Q8—471no—
465C22×Q8C22×D4711yescharacteristic
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—24no—
479C2×SD16—474no—
480C2×SD16—474no—
481C2×SD16—474no—
482C2×SD16—944no—
483C2×SD16—944no—
484C2×SD16—944no—
485C2×SD16C22×D4714yes—
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—474no—
495#125—948no—
496#125—942no—
497#125—948no—
498C22⋊Q8—474no—
499C22⋊Q8—474no—
500C22⋊Q8—942no—
501C22⋊Q8—942no—
502C4×Q8—22no—
503C4×Q8—474no—
504C4×Q8—942no—
505C4×Q8C22×D4714yescomplemented
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—471no—
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⋊C4—941no—
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—21no—
546C2×C42—471no—
547C2×C42—941no—
548C2×C42—941no—
549C2×C42C22×D4711yescharacteristic
550#107—474no—
551#107—474no—
552#106—474no—
553#106C22×D4714yescomplemented
554C4⋊C8—474no—
555C4⋊C8—474no—
556#103—474no—
557#103—474no—
558#103—474no—
559#103C22×D4714yescomplemented
560#102—474no—
561#102—474no—
562#102—474no—
563#102C22×D4714yes—
564C22⋊C8—474no—
565C22⋊C8—474no—
566#97—474no—
567C4×C8C22×D4714yescomplemented
568C24—21no—
569C24—471no—
570C24—944no—
571C24—948no—
572C24—941no—
573C24—3762no—
574C24—3762no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—472no—
579C2×Q8—941no—
580C2×Q8—942no—
581C2×Q8—942no—
582C2×Q8C23×D4712yes—
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#1062535014yes—
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—28no—
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—21no—
634C4⋊C4—21no—
635C4⋊C4—474no—
636C4⋊C4—474no—
637C4⋊C4—472no—
638C4⋊C4—472no—
639C4⋊C4—944no—
640C4⋊C4—944no—
641C4⋊C4—944no—
642C4⋊C4—944no—
643C4⋊C4—944no—
644C4⋊C4—944no—
645C4⋊C4—944no—
646C4⋊C4—941no—
647C4⋊C4—941no—
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—24no—
660C42—472no—
661C42—472no—
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—22no—
684Q8—22no—
685Q8—42no—
686Q8—942no—
687Q8—942no—
688Q8—1882no—
689D4—24no—
690D4—22no—
691D4—474no—
692D4—9416no—
693D4—944no—
694D4—942no—
695D4C2×#1062535014yes—
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×#1062535012yes—
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#1568963212yes—
747C22#1568992912yes—
748C22#1568993012yes—
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#1568963212yes—
762C4C2×#41×D4711yescharacteristic
763C4C22×#1062535011yescharacteristic
764C2—44no—
765C2—1882no—
766C2—1884no—
767C2#2025363714yesdirect product factor
768C2C2×#1568963211yescharacteristic
769C2C2×#1568992911yescharacteristic
770C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×SD16×C47C2
socleC23×C47C22×D4
prime radicalC22×D4×D47C22
hypercenterC2×C4×SD16D47
hypocenterC47C2×#3123
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#15689731C2semidirect
3. #20253637C2direct (N × H)
4. C2×#15689467C2semidirect
5. C2×#15689462C2semidirect
6. C2×#15689425C2semidirect
7. C2×#15689422C2semidirect
8. C2×#15689327C2semidirect
9. C2×#15689326C2semidirect
12. C2×#15689223C2semidirect
13. C2×#15689221C2semidirect
14. C2×C4×#10625325C2semidirect
15. C2×#15689182C2semidirect
16. C2×C4×SD16×C47C2semidirect
22. #15689731C22semidirect
23. C2×#13094022C22semidirect
27. C2×#13094015C22semidirect
33. C2×C4×Dic94C22semidirect
43. #15689467C22semidirect
44. #15689462C22semidirect
45. #15689425C22semidirect
46. #15689422C22semidirect
47. #15689327C22semidirect
48. #15689326C22semidirect
51. #15689223C22semidirect
52. #15689221C22semidirect
53. C4×#10625325C22semidirect
54. #15689182C22semidirect
55. C2×#13093957C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093956C22semidirect
58. C2×Dic47⋊C8C22semidirect
59. C2×Dic47⋊C8C22semidirect
60. C2×#13093949C22semidirect
61. C2×#13093948C22semidirect
62. C2×#13093947C22semidirect
68. C2×#13093935C22semidirect
70. C2×C4×Q8×C47C22semidirect
72. C4×SD16×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×#103×C47C22semidirect
76. C2×C4×C8×C47C22semidirect
98. #13094022C23semidirect
103. #13094015C23semidirect
110. C4×Dic94C23semidirect
147. #13093957C23semidirect
148. #13093957C23semidirect
149. #13093956C23semidirect
150. Dic47⋊C8C23semidirect
151. Dic47⋊C8C23semidirect
152. #13093949C23semidirect
153. #13093948C23semidirect
154. #13093947C23semidirect
160. #13093935C23semidirect
169. C4×Q8×C47C23semidirect
178. #106×C47C23semidirect
179. #103×C47C23semidirect
181. C4×C8×C47C23semidirect
393. C2×C4×SD16D47semidirect
396. C2×C47#3123semidirect
420. C2×C4×Q8C2×D47semidirect
442. C4×SD16C2×D47semidirect
447. C2×#106C2×D47semidirect
453. C2×#103C2×D47semidirect
461. C2×C4×C8C2×D47semidirect
462. C47C2×#3123semidirect
505. C4×Q8C22×D47semidirect
553. #106C22×D47semidirect
559. #103C22×D47semidirect
567. C4×C8C22×D47semidirect
767. C2#20253637direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897312
C2×#156895952
#202536372
C2×#156894672
C2×#156894622
C2×#156894252
C2×#156894222
C2×#156893272
C2×#156893262
C2×#156892752
C2×#156892722
C2×#156892232
C2×#156892212
C2×C4×#106253252
C2×#156891822
C2×C4×SD16×C472
C2×#312347