Finite Group Databasebeta

← C2×#20253612 #27084552

Subgroups — C2×#20253612 #27084552

Order 12032.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689740C211yesmaximal, characteristic
2C2×#15689600C211yesmaximal, characteristic, complemented
3#20253612C2116yesmaximal, direct product factor
4C2×#15689464C211yesmaximal, characteristic, complemented
5C2×#15689417C211yesmaximal, characteristic, complemented
6C2×#15689407C211yesmaximal, characteristic, complemented
7C2×#15689344C211yesmaximal, characteristic, complemented
8C2×#15689344C211yesmaximal, characteristic, complemented
9C2×#15689281C211yesmaximal, characteristic, complemented
10C2×#15689261C211yesmaximal, characteristic
11C2×#15689229C211yesmaximal, characteristic, complemented
12C2×#15689220C211yesmaximal, characteristic, complemented
13C2×#15689217C211yesmaximal, characteristic, complemented
14C2×#15689214C211yesmaximal, characteristic, complemented
15C2×#15689181C211yesmaximal, characteristic, complemented
16C2×C47×#482C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×Dic188C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625335C2211yescharacteristic
22#15689740—24no—
23#15689740C2218yes—
24C2×#13094023C2211yescharacteristic
25C2×#13094017—21no—
26C2×#13094011—21no—
27C2×#13094011C2211yescharacteristic
28C2×#13094005—21no—
29C2×#13094003C2211yescharacteristic
30C2×#13094001—21no—
31#15689600—24no—
32#15689600C2218yescomplemented
33C2×C4×Dic94—21no—
34C2×C4×Dic94—21no—
35C2×#13093989C2211yescharacteristic
36C2×#13093989C2211yescharacteristic
37C2×#13093989C2211yescharacteristic
38C2×#13093989C2211yescharacteristic
39C2×#13093989C2211yescharacteristic
40C2×D4×Dic47C2211yescharacteristic
41C2×#13093983C2211yescharacteristic
42C2×#13093980—21no—
43C2×#13093980—21no—
44#15689464C2218yescomplemented
45#15689417C2218yescomplemented
46#15689407C2218yescomplemented
47#15689344C2218yescomplemented
48#15689344C2218yescomplemented
49#15689281C2218yescomplemented
50#15689261C2218yes—
51#15689229C2218yescomplemented
52#15689220C2218yescomplemented
53#15689217C2218yescomplemented
54#15689214C2218yescomplemented
55#15689181C2218yescomplemented
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093947C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×#121×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#482C2218yes—
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—22no—
79C22×Dic94—24no—
80C22×Dic94—24no—
81C22×Dic94—21no—
82C22×Dic94C2314yes—
83C22×Dic94C2311yescharacteristic
84C22×Dic94C2311yescharacteristic
85C22×Dic94C2311yescharacteristic
86C23×Dic47—21no—
87C23×Dic47—21no—
88C2×Dic188—24no—
89C2×Dic188—24no—
90C2×Dic188C2314yes—
91C2×Dic188C2314yes—
92C2×#10625335—24no—
93C2×#10625335—24no—
94C2×#10625335C2314yes—
95C2×#10625335C2314yes—
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2311yescharacteristic
98#13094023—22no—
99#13094023C2314yes—
100#13094017—28no—
101#13094011—28no—
102#13094011—22no—
103#13094011C2314yes—
104#13094005—28no—
105#13094003—22no—
106#13094003C2314yes—
107#13094001—28no—
108C4×Dic94—28no—
109C4×Dic94—28no—
110#13093989—22no—
111#13093989—22no—
112#13093989—22no—
113#13093989—22no—
114#13093989—22no—
115#13093989C2314yes—
116#13093989C2314yes—
117#13093989C2314yes—
118#13093989C2314yes—
119#13093989C2314yes—
120D4×Dic47—22no—
121D4×Dic47C2314yes—
122#13093983D414yes—
123#13093983C2314yes—
124#13093980—28no—
125#13093980—28no—
126C2×C4⋊Dic47D411yescharacteristic
127C2×C4⋊Dic47D411yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×Dic47⋊C4—21no—
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×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47D411yescharacteristic
141C2×C22⋊Dic47D411yescharacteristic
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47C2311yescharacteristic
148C2×C4×Dic47C2311yescharacteristic
149#13093957C2314yes—
150#13093955C2314yes—
151Dic47⋊C8C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093947C2314yes—
156#13093947C2314yes—
157#13093947C2314yes—
158#13093947C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160#13093934C2314yes—
161C8×Dic47C2314yes—
162C22×D4×C47—21no—
163C22×D4×C47C2311yescharacteristic
164C23×C4×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167#121×C47—22no—
168#121×C47C2314yes—
169#117×C47—22no—
170#117×C47C2314yes—
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C42×C47—21no—
177#107×C47C2314yes—
178#106×C47C2314yes—
179#102×C47C2314yes—
180#102×C47C2314yes—
181C22⋊C8×C47C2314yes—
182C24×C47—21no—
183C24×C47C2×D411yescharacteristic
184C2×D4×C47—24no—
185C2×D4×C47—21no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47—82no—
189C2×D4×C47C2412yes—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2411yescharacteristic
199C22×Dic47—28no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—24no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—24no—
206C22×Dic47—82no—
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211C2×Dic94—28no—
212C2×Dic94—216no—
213C2×Dic94—21no—
214C2×Dic94—21no—
215C2×Dic94—24no—
216C2×Dic94—22no—
217C2×Dic94—22no—
218C2×Dic94—28no—
219C2×Dic94—28no—
220C2×Dic94—22no—
221C2×Dic94—22no—
222C2×Dic94—21no—
223C2×Dic94—24no—
224C2×Dic94—82no—
225C2×Dic94#4114yes—
226C2×Dic94#4114yes—
227C2×Dic94C2412yes—
228C2×Dic94C2412yes—
229C2×Dic94C2412yes—
230C2×C8×C47—22no—
231C2×C8×C47—22no—
232C2×C8×C47C2412yes—
233C2×C8×C47C2412yes—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47C2412yes—
238C4⋊C4×C47C2412yes—
239C4⋊C4×C47C2412yes—
240C22⋊C4×C47—24no—
241C22⋊C4×C47—24no—
242C42×C47—24no—
243C22⋊Dic47—24no—
244C22⋊Dic47—24no—
245C22⋊Dic47—24no—
246C22⋊Dic47—24no—
247C22⋊Dic47C2×D414yes—
248C22⋊Dic47C2×D414yes—
249#10625335—28no—
250#10625335—28no—
251C4⋊Dic47—21no—
252C4⋊Dic47C2×D414yes—
253C4⋊Dic47C2×D414yes—
254C4⋊Dic47C2412yes—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262C4×Dic47—24no—
263C4×Dic47—24no—
264C4×Dic47—24no—
265C4×Dic47—24no—
266C4×Dic47—24no—
267C4×Dic47C2×D412yes—
268C4×Dic47C2×D412yes—
269C4×Dic47C2412yes—
270C4×Dic47C2412yes—
271C2×C47⋊C8—22no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8C2412yes—
274C2×C47⋊C8C2412yes—
275Dic188—28no—
276Dic188—28no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47C22×D412yes—
285C23×C47C22×D411yescharacteristic
286D4×C47—22no—
287D4×C47—22no—
288D4×C47—42no—
289D4×C47—84no—
290C2×C4×C47—22no—
291C2×C4×C47—24no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47C22×D412yes—
301C2×C4×C47C22×D411yescharacteristic
302C2×C4×C47C2×#4112yes—
303C2×C4×C47C2×#4112yes—
304C2×C4×C47C2511yescharacteristic
305C2×Dic47—216no—
306C2×Dic47—24no—
307C2×Dic47—24no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—84no—
319C2×Dic47C22×D412yes—
320C2×Dic47C22×D412yes—
321C2×Dic47C22×D412yes—
322C2×Dic47C22×D412yes—
323Dic94—216no—
324Dic94—24no—
325Dic94—24no—
326Dic94—22no—
327Dic94—22no—
328Dic94—22no—
329Dic94—22no—
330Dic94—42no—
331Dic94—84no—
332Dic94C2×#4114yes—
333Dic94C2×#4114yes—
334C8×C47—22no—
335C8×C47—22no—
336C47⋊C8—22no—
337C47⋊C8—22no—
338C2×#3121—471nomaximal, Sylow
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—44no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—84no—
347C22×C47#52512yes—
348C22×C47#57712yes—
349C22×C47#57812yes—
350C22×C47C23×D411yescharacteristic
351C4×C47—22no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47#52512yes—
356C4×C47C22×#4111yescharacteristic
357C4×C47C22×#4111yescharacteristic
358Dic47—24no—
359Dic47—24no—
360Dic47—22no—
361Dic47—22no—
362Dic47—22no—
363Dic47—22no—
364Dic47—42no—
365Dic47—42no—
366C2×#542—471no—
367C2×#519—471no—
368#3121—4716no—
369C2×#485—471no—
370C2×#482D4711yescharacteristic
371C2×#477—471no—
372C2×#475—471no—
373C2×#464—471no—
374C2×#464—471no—
375C2×#451—471no—
376C2×#448—471no—
377C2×#441—471no—
378C2×#440—471no—
379C2×C4×Q16—471no—
380C2×C4×SD16—471no—
381C2×#433—471no—
382C2×C47—42no—
383C2×C47—82no—
384C2×C47#312114yescomplemented
385C2×C47C2×#52511yescharacteristic
386C2×C47C2×#57711yescharacteristic
387C2×C47C2×#57811yescharacteristic
388C23×Q8—471no—
389C22×Q16—471no—
390C22×Q16—471no—
391C22×SD16—471no—
392C22×SD16—471no—
393#542—478no—
394#542—944no—
395C2×C4⋊Q8—471no—
396C2×#126—941no—
397C2×#124—471no—
398C2×#124—941no—
399C2×#123—941no—
400C2×C22⋊Q8—471no—
401C2×C22⋊Q8—941no—
402C2×#121C2×D4711yescharacteristic
403#519—478no—
404#519—944no—
405C2×C4×Q8—471no—
406C2×C4×Q8—471no—
407C2×C4×Q8—471no—
408C2×C4×Q8—471no—
409C2×C4×Q8—471no—
410C2×C4×Q8—941no—
411C2×C4×Q8—941no—
412C2×C4×D4—471no—
413C2×#117—471no—
414C2×#117—941no—
415C2×#117—941no—
416C2×#117C2×D4711yescharacteristic
417#485—478no—
418#482C2×D4718yes—
419#477—478no—
420#475—478no—
421#464—478no—
422#464—478no—
423#451—478no—
424#448—478no—
425#441—478no—
426#440—478no—
427C4×Q16—478no—
428C4×SD16—478no—
429#433—478no—
430C2×#107—471no—
431C2×#107C2×D4711yescharacteristic
432C2×#106—471no—
433C2×#106C2×D4711yescharacteristic
434C2×C4⋊C8—471no—
435C2×C4⋊C8—471no—
436C2×#103—471no—
437C2×#103—471no—
438C2×#103—471no—
439C2×#103—471no—
440C2×#103—471no—
441C2×#103—471no—
442C2×#102C2×D4711yescharacteristic
443C2×#102C2×D4711yescharacteristic
444C2×C22⋊C8—471no—
445C2×C22⋊C8C2×D4711yescharacteristic
446C2×#97—471no—
447C2×C4×C8—471no—
448C47C2×#312111yescharacteristic, complemented, Sylow
449C22×Q8—471no—
450C22×Q8—471no—
451C22×Q8—471no—
452C22×Q8—474no—
453C22×Q8—941no—
454C22×Q8—944no—
455C22×Q8—944no—
456C22×Q8—941no—
457C22×Q8—942no—
458C22×D4—21no—
459C22×D4C22×D4711yescharacteristic
460C23×C4—941no—
461C23×C4—941no—
462C23×C4C22×D4711yescharacteristic
463C2×Q16—474no—
464C2×Q16—474no—
465C2×Q16—944no—
466C2×Q16—944no—
467C2×SD16—474no—
468C2×SD16—474no—
469C2×SD16—944no—
470C2×SD16—944no—
471C22×C8—471no—
472C22×C8—471no—
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475C4⋊Q8—474no—
476C4⋊Q8—942no—
477#126—948no—
478#124—474no—
479#124—942no—
480#124—948no—
481#123—948no—
482C22⋊Q8—474no—
483C22⋊Q8—948no—
484C22⋊Q8—942no—
485#121—22no—
486#121C22×D4714yes—
487C4×Q8—474no—
488C4×Q8—474no—
489C4×Q8—474no—
490C4×Q8—474no—
491C4×Q8—474no—
492C4×Q8—948no—
493C4×Q8—948no—
494C4×Q8—942no—
495C4×Q8—942no—
496C4×Q8—942no—
497C4×Q8—942no—
498C4×Q8—942no—
499C4×D4—474no—
500C4×D4—942no—
501#117—22no—
502#117—474no—
503#117—474no—
504#117—948no—
505#117—948no—
506#117C22×D4714yes—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4C22×D4711yescharacteristic
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C4⋊C4C22×D4711yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—471no—
523C2×C22⋊C4—471no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—21no—
529C2×C42—471no—
530C2×C42—471no—
531C2×C42—941no—
532C2×C42—941no—
533C2×C42—941no—
534C2×C42—941no—
535C2×C42—941no—
536#107—474no—
537#107C22×D4714yes—
538#106—474no—
539#106C22×D4714yes—
540C4⋊C8—474no—
541C4⋊C8—474no—
542#103—474no—
543#103—474no—
544#103—474no—
545#103—474no—
546#103—474no—
547#103—474no—
548#102C22×D4714yes—
549#102C22×D4714yes—
550C22⋊C8—474no—
551C22⋊C8C22×D4714yes—
552#97—474no—
553C4×C8—474no—
554C24—21no—
555C24D4×D4711yescharacteristic
556C2×Q8—474no—
557C2×Q8—474no—
558C2×Q8—472no—
559C2×Q8—472no—
560C2×Q8—472no—
561C2×Q8—944no—
562C2×Q8—948no—
563C2×Q8—948no—
564C2×Q8—948no—
565C2×Q8—9416no—
566C2×Q8—944no—
567C2×Q8—941no—
568C2×Q8—941no—
569C2×Q8—941no—
570C2×Q8—942no—
571C2×Q8—942no—
572C2×Q8—942no—
573C2×Q8—942no—
574C2×Q8—3762no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—82no—
580C2×D4C23×D4712yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—471no—
587C22×C4—471no—
588C22×C4—471no—
589C22×C4—471no—
590C22×C4—944no—
591C22×C4—948no—
592C22×C4—944no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—3762no—
598C22×C4D4×D4712yes—
599C22×C4D4×D4711yescharacteristic
600C22×C4C23×D4712yes—
601C22×C4C23×D4711yescharacteristic
602Q16—948no—
603Q16—948no—
604SD16—948no—
605SD16—948no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—472no—
609C2×C8—472no—
610C2×C8—942no—
611C2×C8—942no—
612C2×C8C23×D4712yes—
613C2×C8C23×D4712yes—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—474no—
618C4⋊C4—474no—
619C4⋊C4—472no—
620C4⋊C4—944no—
621C4⋊C4—944no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—941no—
628C4⋊C4C23×D4712yes—
629C4⋊C4C23×D4712yes—
630C4⋊C4C23×D4712yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—474no—
634C22⋊C4—474no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C22⋊C4—944no—
639C42—24no—
640C42—472no—
641C42—472no—
642C42—472no—
643C42—472no—
644C42—944no—
645C42—944no—
646C42—944no—
647C42—944no—
648C42—944no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C2×D4×D4712yes—
657C23C2×D4×D4711yescharacteristic
658Q8—474no—
659Q8—474no—
660Q8—9416no—
661Q8—944no—
662Q8—944no—
663Q8—942no—
664Q8—942no—
665Q8—942no—
666Q8—942no—
667Q8—3764no—
668Q8—1882no—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—84no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—472no—
684C2×C4—472no—
685C2×C4—472no—
686C2×C4—472no—
687C2×C4—9416no—
688C2×C4—944no—
689C2×C4—944no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—3764no—
699C2×C4—1882no—
700C2×C4—1882no—
701C2×C4C2×D4×D4712yes—
702C2×C4C2×D4×D4711yescharacteristic
703C2×C4#41×D4712yes—
704C2×C4#41×D4712yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—22no—
708C8—942no—
709C8—942no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22#1568963112yes—
719C22#1568993312yes—
720C22#1568993712yes—
721C22C22×D4×D4711yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—942no—
727C4—942no—
728C4—942no—
729C4—942no—
730C4—944no—
731C4—944no—
732C4—1882no—
733C4—1882no—
734C4#1568963112yes—
735C4C2×#41×D4711yescharacteristic
736C4C2×#41×D4711yescharacteristic
737C2—42no—
738C2—82no—
739C2#2025361214yesdirect product factor
740C2C2×#1568963111yescharacteristic
741C2C2×#1568993311yescharacteristic
742C2C2×#1568993711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#482C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
hypercenterC2×#482D47
hypocenterC47C2×#3121
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#15689600C2semidirect
3. #20253612C2direct (N × H)
4. C2×#15689464C2semidirect
5. C2×#15689417C2semidirect
6. C2×#15689407C2semidirect
7. C2×#15689344C2semidirect
8. C2×#15689344C2semidirect
9. C2×#15689281C2semidirect
11. C2×#15689229C2semidirect
12. C2×#15689220C2semidirect
13. C2×#15689217C2semidirect
14. C2×#15689214C2semidirect
15. C2×#15689181C2semidirect
32. #15689600C22semidirect
44. #15689464C22semidirect
45. #15689417C22semidirect
46. #15689407C22semidirect
47. #15689344C22semidirect
48. #15689344C22semidirect
49. #15689281C22semidirect
51. #15689229C22semidirect
52. #15689220C22semidirect
53. #15689217C22semidirect
54. #15689214C22semidirect
55. #15689181C22semidirect
384. C2×C47#3121semidirect
448. C47C2×#3121semidirect
739. C2#20253612direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897402
C2×#156896002
#202536122
C2×#156894642
C2×#156894172
C2×#156894072
C2×#156893442
C2×#156892812
C2×#156892612
C2×#156892292
C2×#156892202
C2×#156892172
C2×#156892142
C2×#156891812
C2×C47×#4822
C2×#312147