Finite Group Databasebeta

← C2×#20254055 #27086145

Subgroups — C2×#20254055 #27086145

Order 12032.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689742C211yesmaximal, characteristic
2C2×#15689736C211yesmaximal, characteristic, complemented
3#20254055C2116yesmaximal, direct product factor
4C2×#15689533C211yesmaximal, characteristic, complemented
5C2×#15689518C211yesmaximal, characteristic, complemented
6C2×#15689474C211yesmaximal, characteristic, complemented
7C2×#15689380C211yesmaximal, characteristic, complemented
8C2×#15689368C211yesmaximal, characteristic
9C2×#15689363C211yesmaximal, characteristic, complemented
10C2×#15689351C211yesmaximal, characteristic
11C2×#15689227C211yesmaximal, characteristic, complemented
12C2×#15689220C211yesmaximal, characteristic, complemented
13C2×#15689215C211yesmaximal, characteristic, complemented
14C2×#15689214C211yesmaximal, characteristic, complemented
15C2×#15689077C211yesmaximal, characteristic, complemented
16C2×C47×#488C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22C22×C8×D47C2211yescharacteristic
23#15689742—24no—
24#15689742C2218yes—
25#15689736—24no—
26#15689736C2218yescomplemented
27C2×#13094024C2211yescharacteristic
28C2×#13094024C2211yescharacteristic
29C2×#13094019—21no—
30C2×#13094019—21no—
31C2×#13094017—21no—
32C2×#13094015—21no—
33C2×#13094015—21no—
34C2×#13094010—21no—
35C2×#13094008—21no—
36C2×#13094004C2211yescharacteristic
37C2×#13094004C2211yescharacteristic
38C2×#13094001—21no—
39C2×#13094000C2211yescharacteristic
40C2×#13093995C2211yescharacteristic
41C2×Q8×Dic47C2211yescharacteristic
42C2×#13093989C2211yescharacteristic
43C2×#13093989C2211yescharacteristic
44C2×D4×Dic47C2211yescharacteristic
45C2×#13093981C2211yescharacteristic
46#15689533C2218yescomplemented
47#15689518C2218yescomplemented
48#15689474C2218yescomplemented
49#15689380C2218yescomplemented
50#15689368C2218yes—
51#15689363C2218yescomplemented
52#15689351C2218yes—
53#15689227C2218yescomplemented
54#15689220C2218yescomplemented
55#15689215C2218yescomplemented
56#15689214C2218yescomplemented
57C2×#13093957C2211yescharacteristic
58C2×#13093957C2211yescharacteristic
59C2×#13093955C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65#15689077C2218yescomplemented
66C2×#13093935C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×#125×C47C2211yescharacteristic
70C2×#124×C47C2211yescharacteristic
71C47×#488C2218yescomplemented
72C2×#103×C47C2211yescharacteristic
73C2×#103×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×C22⋊D47—21no—
81C23×Dic47—21no—
82C22×C4×D47C2311yescharacteristic
83C2×#10625337—24no—
84C2×#10625337—24no—
85C2×#10625337C2314yes—
86C2×#10625337C2314yes—
87C2×#10625335—24no—
88C2×#10625335—24no—
89C2×#10625335C2314yes—
90C2×#10625335C2314yes—
91C2×#10625324—24no—
92C2×#10625324C2314yes—
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95C2×C8×D47—24no—
96C2×C8×D47C2314yes—
97#13094024—22no—
98#13094024—22no—
99#13094024C2314yes—
100#13094024C2314yes—
101#13094019—28no—
102#13094019—28no—
103#13094017—28no—
104#13094015—28no—
105#13094015—28no—
106#13094010—28no—
107#13094008—28no—
108#13094004—22no—
109#13094004—22no—
110#13094004C2314yes—
111#13094004C2314yes—
112#13094001—28no—
113#13094000—22no—
114#13094000C2314yes—
115#13093995—22no—
116#13093995C2314yes—
117Q8×Dic47—22no—
118Q8×Dic47C2314yes—
119#13093989—22no—
120#13093989—22no—
121#13093989C2314yes—
122#13093989C2314yes—
123D4×Dic47—22no—
124D4×Dic47C2314yes—
125#13093981D414yes—
126#13093981C2314yes—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47—21no—
133C2×C4⋊Dic47C2311yescharacteristic
134C2×C4⋊Dic47C2311yescharacteristic
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4D411yescharacteristic
139C2×Dic47⋊C4D411yescharacteristic
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C2×(C2×D47)⋊C4D411yescharacteristic
147C2×C4×Dic47—21no—
148C2×C4×Dic47—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47C2311yescharacteristic
151#13093957C2314yes—
152#13093957C2314yes—
153#13093955C2314yes—
154#13093955C2314yes—
155#13093949C2314yes—
156#13093949C2314yes—
157#13093949C2314yes—
158#13093949C2314yes—
159#13093935C2314yes—
160#13093934C2314yes—
161C8×Dic47C2314yes—
162C22×Q8×C47C2311yescharacteristic
163C22×D4×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166#125×C47—22no—
167#125×C47C2314yes—
168#124×C47—22no—
169#124×C47C2314yes—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C42×C47C2311yescharacteristic
177#103×C47C2314yes—
178#103×C47C2314yes—
179#102×C47C2314yes—
180#102×C47C2314yes—
181C4×C8×C47C2314yes—
182C24×C47—21no—
183C23×D47C2×D411yescharacteristic
184C2×Q8×C47—21no—
185C2×Q8×C47—22no—
186C2×Q8×C47—22no—
187C2×Q8×C47C2412yes—
188C2×D4×C47—21no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47C2412yes—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198C2×C22⋊D47—24no—
199C2×C22⋊D47—82no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—24no—
205C22×Dic47—82no—
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209C2×C4×D47—22no—
210C2×C4×D47—22no—
211C2×C4×D47C2×D412yes—
212C2×C4×D47C2412yes—
213C2×Dic94—22no—
214C2×Dic94—22no—
215C2×Dic94—22no—
216C2×Dic94—22no—
217C2×Dic94—21no—
218C2×Dic94—21no—
219C2×Dic94—24no—
220C2×Dic94—82no—
221C2×Dic94C2412yes—
222C2×Dic94C2412yes—
223C2×C8×C47—22no—
224C2×C8×C47—22no—
225C2×C8×C47C2412yes—
226C2×C8×C47C2412yes—
227C4⋊C4×C47—24no—
228C4⋊C4×C47—24no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47C2412yes—
232C4⋊C4×C47C2412yes—
233C22⋊C4×C47—24no—
234C22⋊C4×C47—24no—
235C42×C47C2×D412yes—
236C42×C47C2412yes—
237C22⋊Dic47—24no—
238C22⋊Dic47—24no—
239#10625337—28no—
240#10625337—28no—
241#10625335—28no—
242#10625335—28no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4C2×D414yes—
247(C2×D47)⋊C4C2×D414yes—
248C4⋊Dic47—24no—
249C4⋊Dic47—24no—
250C4⋊Dic47—24no—
251C4⋊Dic47—21no—
252C4⋊Dic47—21no—
253C4⋊Dic47—24no—
254C4⋊Dic47—24no—
255C4⋊Dic47—24no—
256C4⋊Dic47C2412yes—
257C4⋊Dic47C2412yes—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261Dic47⋊C4C2×D414yes—
262Dic47⋊C4C2×D414yes—
263C4×Dic47—24no—
264C4×Dic47—24no—
265C4×Dic47—24no—
266C4×Dic47C2×D412yes—
267C4×Dic47C2412yes—
268C2×C47⋊C8#4114yes—
269C2×C47⋊C8#4114yes—
270C2×C47⋊C8C2412yes—
271C2×C47⋊C8C2412yes—
272#10625324—28no—
273C8×D47—28no—
274C23×C47—22no—
275C23×C47—42no—
276C23×C47—42no—
277C23×C47—42no—
278C23×C47C22×D411yescharacteristic
279C22×D47—22no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47C22×D412yes—
283Q8×C47—22no—
284Q8×C47—22no—
285Q8×C47—42no—
286D4×C47—22no—
287D4×C47—22no—
288D4×C47—42no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D412yes—
299C2×C4×C47C22×D411yescharacteristic
300C2×C4×C47C2×#4112yes—
301C2×C4×C47C2×#4112yes—
302C2×C4×C47C2511yescharacteristic
303C22⋊D47—84no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—84no—
316C2×Dic47C22×D412yes—
317C2×Dic47C22×D412yes—
318C2×Dic47C22×D412yes—
319C4×D47—24no—
320C4×D47—22no—
321C4×D47—22no—
322Dic94—22no—
323Dic94—22no—
324Dic94—22no—
325Dic94—22no—
326Dic94—42no—
327Dic94—42no—
328Dic94—84no—
329C8×C47—22no—
330C8×C47—22no—
331C47⋊C8C2×#4114yes—
332C47⋊C8C2×#4114yes—
333C2×#3178—471nomaximal, Sylow
334C22×C47—42no—
335C22×C47—42no—
336C22×C47—42no—
337C22×C47—84no—
338C22×C47#53212yes—
339C22×C47#57712yes—
340C22×C47#57812yes—
341C22×C47C23×D411yescharacteristic
342C2×D47—22no—
343C2×D47—22no—
344C2×D47—22no—
345C2×D47—44no—
346C4×C47—22no—
347C4×C47—22no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47—42no—
351C4×C47#53212yes—
352C4×C47C22×#4111yescharacteristic
353C4×C47C22×#4111yescharacteristic
354Dic47—22no—
355Dic47—22no—
356Dic47—22no—
357Dic47—42no—
358Dic47—42no—
359Dic47—42no—
360Dic47—42no—
361C2×#542—471no—
362C2×#541—471no—
363#3178—4716no—
364C2×#501—471no—
365C2×#497—471no—
366C2×#488D4711yescharacteristic, complemented
367C2×#487—471no—
368C2×#470—471no—
369C2×#468—471no—
370C2×#467—471no—
371C2×#465—471no—
372C2×#441—471no—
373C2×#440—471no—
374C2×C4×Q16—471no—
375C2×C4×SD16—471no—
376C2×#405—471no—
377C2×C47—82no—
378C2×C47#317814yescomplemented
379C2×C47C2×#53211yescharacteristic
380C2×C47C2×#57711yescharacteristic
381C2×C47C2×#57811yescharacteristic
382D47—42no—
383C22×Q16—471no—
384C22×Q16—471no—
385C22×SD16—471no—
386C22×SD16—471no—
387C22×M16—471no—
388C23×C8—471no—
389#542—478no—
390#542—944no—
391#541—478no—
392#541—944no—
393C2×C4⋊Q8—471no—
394C2×C4⋊Q8—471no—
395C2×#126—941no—
396C2×#126—941no—
397C2×#126—941no—
398C2×#125—941no—
399C2×#125—941no—
400C2×#125C2×D4711yescharacteristic
401C2×#124—941no—
402C2×#124C2×D4711yescharacteristic
403C2×#123—941no—
404C2×C22⋊Q8—471no—
405C2×C22⋊Q8—471no—
406C2×C22⋊Q8—471no—
407C2×C22⋊Q8—941no—
408C2×#121—471no—
409C2×C4×Q8—471no—
410C2×C4×Q8—471no—
411C2×C4×Q8—471no—
412C2×C4×D4—471no—
413C2×#117—471no—
414#501—478no—
415#497—478no—
416#488C2×D4718yescomplemented
417#487—478no—
418#470—478no—
419#468—478no—
420#467—478no—
421#465—478no—
422#441—478no—
423#440—478no—
424C4×Q16—478no—
425C4×SD16—478no—
426C2×#107—471no—
427C2×#107—471no—
428C2×#106—471no—
429C2×#106—471no—
430C2×#103—471no—
431C2×#103—471no—
432C2×#103—471no—
433C2×#103—471no—
434C2×#103C2×D4711yescharacteristic
435C2×#103C2×D4711yescharacteristic
436C2×#102C2×D4711yescharacteristic
437C2×#102C2×D4711yescharacteristic
438#405—478no—
439C2×#97—471no—
440C2×#97—471no—
441C2×C4×C8—471no—
442C2×C4×C8C2×D4711yescharacteristic
443C47C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—471no—
445C22×Q8—471no—
446C22×Q8—941no—
447C22×Q8C22×D4711yescharacteristic
448C22×D4—941no—
449C22×D4C22×D4711yescharacteristic
450C23×C4—471no—
451C23×C4—941no—
452C2×Q16—474no—
453C2×Q16—474no—
454C2×Q16—944no—
455C2×Q16—944no—
456C2×SD16—474no—
457C2×SD16—474no—
458C2×SD16—944no—
459C2×SD16—944no—
460C2×M16—474no—
461C2×M16—944no—
462C22×C8—471no—
463C22×C8—471no—
464C22×C8—474no—
465C22×C8—944no—
466C22×C8C22×D4711yescharacteristic
467C22×C8C22×D4711yescharacteristic
468C4⋊Q8—474no—
469C4⋊Q8—474no—
470C4⋊Q8—942no—
471C4⋊Q8—942no—
472#126—948no—
473#126—948no—
474#126—948no—
475#125—22no—
476#125—948no—
477#125—948no—
478#125C22×D4714yes—
479#124—22no—
480#124—948no—
481#124C22×D4714yes—
482#123—948no—
483C22⋊Q8—474no—
484C22⋊Q8—474no—
485C22⋊Q8—474no—
486C22⋊Q8—948no—
487C22⋊Q8—942no—
488C22⋊Q8—942no—
489C22⋊Q8—942no—
490#121—474no—
491#121—942no—
492C4×Q8—474no—
493C4×Q8—474no—
494C4×Q8—474no—
495C4×Q8—942no—
496C4×Q8—942no—
497C4×Q8—942no—
498C4×D4—474no—
499C4×D4—942no—
500#117—474no—
501#117—474no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—941no—
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×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—471no—
522C2×C22⋊C4—471no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—471no—
529C2×C42—941no—
530C2×C42—941no—
531C2×C42—941no—
532C2×C42C22×D4711yescharacteristic
533#107—474no—
534#107—474no—
535#106—474no—
536#106—474no—
537#103—474no—
538#103—474no—
539#103—474no—
540#103—474no—
541#103C22×D4714yes—
542#103C22×D4714yes—
543#102C22×D4714yes—
544#102C22×D4714yes—
545#97—474no—
546#97—474no—
547C4×C8—474no—
548C4×C8C22×D4714yes—
549C24—21no—
550C24—471no—
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—472no—
555C2×Q8—472no—
556C2×Q8—944no—
557C2×Q8—941no—
558C2×Q8—941no—
559C2×Q8—942no—
560C2×Q8—942no—
561C2×Q8—942no—
562C2×Q8—942no—
563C2×Q8—3762no—
564C2×Q8C23×D4712yes—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—944no—
569C2×D4—3762no—
570C2×D4C23×D4712yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—471no—
577C22×C4—472no—
578C22×C4—472no—
579C22×C4—944no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—3762no—
587C22×C4D4×D4711yescharacteristic
588C22×C4D4×D4711yescharacteristic
589C22×C4C23×D4711yescharacteristic
590Q16—948no—
591Q16—948no—
592SD16—948no—
593SD16—948no—
594M16—948no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—474no—
598C2×C8—474no—
599C2×C8—472no—
600C2×C8—472no—
601C2×C8—948no—
602C2×C8C23×D4712yes—
603C2×C8C23×D4712yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—474no—
609C4⋊C4—474no—
610C4⋊C4—472no—
611C4⋊C4—472no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—944no—
616C4⋊C4—944no—
617C4⋊C4—944no—
618C4⋊C4—941no—
619C4⋊C4—941no—
620C4⋊C4—944no—
621C4⋊C4—944no—
622C4⋊C4—944no—
623C4⋊C4C23×D4712yes—
624C4⋊C4C23×D4712yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—474no—
628C22⋊C4—474no—
629C22⋊C4—944no—
630C22⋊C4—944no—
631C22⋊C4—944no—
632C22⋊C4—944no—
633C22⋊C4—944no—
634C42—472no—
635C42—472no—
636C42—944no—
637C42—944no—
638C42—944no—
639C42D4×D4712yes—
640C42C23×D4712yes—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—472no—
646C23—942no—
647C23—942no—
648C23—942no—
649C23C2×D4×D4711yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—942no—
654Q8—942no—
655Q8—942no—
656Q8—942no—
657Q8—3764no—
658Q8—1882no—
659Q8—1882no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—3764no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—472no—
673C2×C4—472no—
674C2×C4—472no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—944no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—3764no—
686C2×C4—1882no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4—1882no—
690C2×C4C2×D4×D4712yes—
691C2×C4C2×D4×D4712yes—
692C2×C4C2×D4×D4711yescharacteristic
693C2×C4#41×D4712yes—
694C2×C4#41×D4712yes—
695C2×C4C24×D4711yescharacteristic
696C8—22no—
697C8—22no—
698C8—474no—
699C8—474no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—942no—
705C22—942no—
706C22—942no—
707C22—1884no—
708C22#1568967212yes—
709C22#1568993012yes—
710C22#1568993712yes—
711C22C22×D4×D4711yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—942no—
718C4—942no—
719C4—942no—
720C4—1882no—
721C4—1882no—
722C4—1882no—
723C4—1882no—
724C4#1568967212yes—
725C4C2×#41×D4711yescharacteristic
726C4C2×#41×D4711yescharacteristic
727C2—82no—
728C2—1882no—
729C2#2025405514yesdirect product factor
730C2C2×#1568967211yescharacteristic
731C2C2×#1568993011yescharacteristic
732C2C2×#1568993711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#488C2
socleC23×C47C22×D4
prime radicalC2×#13093995C22
hypercenterC2×#488D47
hypocenterC47C2×#3178
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
2. C2×#15689736C2semidirect
3. #20254055C2direct (N × H)
4. C2×#15689533C2semidirect
5. C2×#15689518C2semidirect
6. C2×#15689474C2semidirect
7. C2×#15689380C2semidirect
9. C2×#15689363C2semidirect
11. C2×#15689227C2semidirect
12. C2×#15689220C2semidirect
13. C2×#15689215C2semidirect
14. C2×#15689214C2semidirect
15. C2×#15689077C2semidirect
16. C2×C47×#488C2semidirect
26. #15689736C22semidirect
46. #15689533C22semidirect
47. #15689518C22semidirect
48. #15689474C22semidirect
49. #15689380C22semidirect
51. #15689363C22semidirect
53. #15689227C22semidirect
54. #15689220C22semidirect
55. #15689215C22semidirect
56. #15689214C22semidirect
65. #15689077C22semidirect
71. C47×#488C22semidirect
366. C2×#488D47semidirect
378. C2×C47#3178semidirect
416. #488C2×D47semidirect
443. C47C2×#3178semidirect
729. C2#20254055direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897422
C2×#156897362
#202540552
C2×#156895332
C2×#156895182
C2×#156894742
C2×#156893802
C2×#156893682
C2×#156893632
C2×#156893512
C2×#156892272
C2×#156892202
C2×#156892152
C2×#156892142
C2×#156890772
C2×C47×#4882
C2×#317847