Finite Group Databasebeta

← C2×#20254807 #27089197

Subgroups — C2×#20254807 #27089197

Order 12032.

1818 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×#15689740C211yesmaximal, characteristic
2C2×#15689733C211yesmaximal, characteristic, complemented
3#20254807C2116yesmaximal, direct product factor
4C2×#15689433C211yesmaximal, characteristic, complemented
5C2×#15689416C211yesmaximal, characteristic, complemented
6C2×#15689407C211yesmaximal, characteristic, complemented
7C2×#15689421C211yesmaximal, characteristic, complemented
8C2×#15689379C211yesmaximal, characteristic, complemented
9C2×#15689367C211yesmaximal, characteristic
10C2×#15689364C211yesmaximal, characteristic, complemented
11C2×#15689344C211yesmaximal, characteristic, complemented
12C2×#15689343C211yesmaximal, characteristic, complemented
13C2×#15689332C211yesmaximal, characteristic, complemented
14C2×#15689326C211yesmaximal, characteristic, complemented
15C2×#15689149C211yesmaximal, characteristic, complemented
16C2×C47×#465C211yesmaximal, characteristic
17C22×Dic188C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625329C2211yescharacteristic
21#15689740—24no—
22#15689740C2218yes—
23#15689733—24no—
24#15689733C2218yescomplemented
25C2×#13094023C2211yescharacteristic
26C2×#13094022C2211yescharacteristic
27C2×#13094017—21no—
28C2×#13094017—21no—
29C2×#13094017—21no—
30C2×#13094015—21no—
31C2×#13094015C2211yescharacteristic
32C2×#13094014—21no—
33C2×#13094011—21no—
34C2×#13094011C2211yescharacteristic
35C2×#13094005—21no—
36C2×#13094003C2211yescharacteristic
37C2×#13094003C2211yescharacteristic
38C2×#13094001—21no—
39C2×Q8×Dic47C2211yescharacteristic
40C2×#13093989C2211yescharacteristic
41C2×#13093989C2211yescharacteristic
42C2×D4×Dic47C2211yescharacteristic
43C2×#13093983C2211yescharacteristic
44#15689433C2218yescomplemented
45#15689421C2218yescomplemented
46#15689416C2218yescomplemented
47#15689407C2218yescomplemented
48#15689379C2218yescomplemented
49#15689367C2218yes—
50#15689364C2218yescomplemented
51#15689344C2218yescomplemented
52#15689343C2218yescomplemented
53#15689332C2218yescomplemented
54#15689326C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58#15689149C2218yescomplemented
59C2×Dic47⋊C8C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093947C2211yescharacteristic
67C2×#13093947C2211yescharacteristic
68C2×#13093945C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#465C2218yes—
74C2×#106×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C23×Dic47—21no—
81C2×Dic188—42no—
82C2×Dic188C2314yes—
83C2×#10625337—42no—
84C2×#10625337C2314yes—
85C2×#10625335—42no—
86C2×#10625335C2314yes—
87C2×#10625329—42no—
88C2×#10625329C2314yes—
89C22×C47⋊C8C2311yescharacteristic
90C22×C47⋊C8C2311yescharacteristic
91#13094023—22no—
92#13094023C2314yes—
93#13094022—22no—
94#13094022C2314yes—
95#13094017—28no—
96#13094017—28no—
97#13094017—28no—
98#13094015—28no—
99#13094015—22no—
100#13094015C2314yes—
101#13094014—28no—
102#13094011—28no—
103#13094011—22no—
104#13094011C2314yes—
105#13094005—28no—
106#13094003—22no—
107#13094003—22no—
108#13094003C2314yes—
109#13094003C2314yes—
110#13094001—28no—
111Q8×Dic47—22no—
112Q8×Dic47C2314yes—
113#13093989—22no—
114#13093989—22no—
115#13093989C2314yes—
116#13093989C2314yes—
117D4×Dic47—22no—
118D4×Dic47C2314yes—
119#13093983D414yes—
120#13093983C2314yes—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47D411yescharacteristic
124C2×C4⋊Dic47D411yescharacteristic
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⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×C22⋊Dic47—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×Dic47C2311yescharacteristic
146C2×C4×Dic47C2311yescharacteristic
147#13093958C2314yes—
148#13093957C2314yes—
149#13093955C2314yes—
150Dic47⋊C8C2314yes—
151Dic47⋊C8C2314yes—
152Dic47⋊C8C2314yes—
153Dic47⋊C8C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093948C2314yes—
157#13093947C2314yes—
158#13093947C2314yes—
159#13093945C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×D4×C47—21no—
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C2×SD16×C47—42no—
165C2×SD16×C47C2314yes—
166C22×C8×C47—42no—
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2314yes—
170C22⋊Q8×C47—22no—
171C22⋊Q8×C47C2314yes—
172#121×C47—22no—
173#121×C47C2314yes—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179#106×C47C2314yes—
180#103×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C24×C47C2×D411yescharacteristic
184C2×Q8×C47—21no—
185C2×Q8×C47—22no—
186C2×Q8×C47—22no—
187C2×Q8×C47C2412yes—
188C2×D4×C47—24no—
189C2×D4×C47—21no—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—82no—
193C2×D4×C47C2412yes—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2411yescharacteristic
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—24no—
208C22×Dic47—82no—
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
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—
223SD16×C47—44no—
224C2×C8×C47—22no—
225C2×C8×C47—22no—
226C2×C8×C47—44no—
227C2×C8×C47C2412yes—
228C2×C8×C47C2412yes—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47C2412yes—
233C4⋊C4×C47C2412yes—
234C22⋊C4×C47—24no—
235C22⋊C4×C47—24no—
236C22⋊Dic47—24no—
237C22⋊Dic47—24no—
238C22⋊Dic47—24no—
239C22⋊Dic47—24no—
240C22⋊Dic47—24no—
241C22⋊Dic47C2×D414yes—
242C22⋊Dic47C2×D414yes—
243#10625337—44no—
244#10625335—44no—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47—24no—
248C4⋊Dic47—24no—
249C4⋊Dic47C2×D414yes—
250C4⋊Dic47C2×D414yes—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260Dic47⋊C4—24no—
261C4×Dic47—24no—
262C4×Dic47—24no—
263C4×Dic47—24no—
264C4×Dic47C2×D412yes—
265C4×Dic47C2×D412yes—
266C4×Dic47C2412yes—
267C4×Dic47C2412yes—
268#10625329—44no—
269C2×C47⋊C8—22no—
270C2×C47⋊C8—22no—
271C2×C47⋊C8C2412yes—
272C2×C47⋊C8C2412yes—
273Dic188—44no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47—42no—
281C23×C47C22×D412yes—
282C23×C47C22×D411yescharacteristic
283Q8×C47—22no—
284Q8×C47—22no—
285Q8×C47—42no—
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×C47H(5,𝔽2)12yes—
303C2×C4×C472−1+412yes—
304C2×C4×C47C2511yescharacteristic
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—84no—
318C2×Dic47C22×D412yes—
319C2×Dic47C22×D412yes—
320C2×Dic47C22×D412yes—
321C2×Dic47C22×D412yes—
322Dic94—22no—
323Dic94—22no—
324Dic94—22no—
325Dic94—22no—
326Dic94—42no—
327Dic94—42no—
328Dic94—84no—
329C8×C47—22no—
330C8×C47—22no—
331C47⋊C8—22no—
332C47⋊C8—22no—
333C2×#3258—471nomaximal, Sylow
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—44no—
338C22×C47—42no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—84no—
342C22×C47#53712yes—
343C22×C47#57712yes—
344C22×C47#57812yes—
345C22×C47C23×D411yescharacteristic
346C4×C47—22no—
347C4×C47—42no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47#53712yes—
351C4×C47C2×H(5,𝔽2)11yescharacteristic
352C4×C47C2×2−1+411yescharacteristic
353Dic47—22no—
354Dic47—22no—
355Dic47—22no—
356Dic47—22no—
357Dic47—42no—
358Dic47—42no—
359Dic47—42no—
360Dic47—42no—
361C2×#542—471no—
362C2×#541—471no—
363#3258—4716no—
364C2×#479—471no—
365C2×#477—471no—
366C2×#475—471no—
367C2×#478—471no—
368C2×#470—471no—
369C2×#468—471no—
370C2×#467—471no—
371C2×#465D4711yescharacteristic
372C2×#464—471no—
373C2×#464—471no—
374C2×#462—471no—
375C2×#461—471no—
376C2×#424—471no—
377C2×C47—42no—
378C2×C47—82no—
379C2×C47#325814yescomplemented
380C2×C47C2×#53711yescharacteristic
381C2×C47C2×#57711yescharacteristic
382C2×C47C2×#57811yescharacteristic
383C22×Q16—471no—
384C22×Q16—471no—
385C22×SD16—471no—
386C22×SD16C2×D4711yescharacteristic
387C22×M16—471no—
388C23×C8C2×D4711yescharacteristic
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—471no—
399C2×#125—941no—
400C2×#125—941no—
401C2×#124—471no—
402C2×#124—941no—
403C2×#123—941no—
404C2×C22⋊Q8—471no—
405C2×C22⋊Q8—471no—
406C2×C22⋊Q8—941no—
407C2×C22⋊Q8C2×D4711yescharacteristic
408C2×#121C2×D4711yescharacteristic
409C2×C4×Q8—471no—
410C2×C4×Q8—471no—
411C2×C4×Q8—471no—
412C2×C4×D4—471no—
413C2×#117—471no—
414#479—478no—
415#478—478no—
416#477—478no—
417#475—478no—
418#470—478no—
419#468—478no—
420#467—478no—
421#465C2×D4718yes—
422#464—478no—
423#464—478no—
424#462—478no—
425#461—478no—
426C2×#107—471no—
427C2×#107—471no—
428C2×#106—471no—
429C2×#106C2×D4711yescharacteristic
430#424—478no—
431C2×C4⋊C8—471no—
432C2×C4⋊C8—471no—
433C2×C4⋊C8—471no—
434C2×C4⋊C8—471no—
435C2×#103—471no—
436C2×#103—471no—
437C2×#103—471no—
438C2×#103—471no—
439C2×#103—471no—
440C2×#103C2×D4711yescharacteristic
441C2×#102—471no—
442C2×#102C2×D4711yescharacteristic
443C47C2×#325811yescharacteristic, complemented, Sylow
444C22×Q8—471no—
445C22×Q8—471no—
446C22×Q8—941no—
447C22×Q8C22×D4711yescharacteristic
448C22×D4—21no—
449C22×D4C22×D4711yescharacteristic
450C23×C4—941no—
451C23×C4C22×D4711yescharacteristic
452C2×Q16—474no—
453C2×Q16—474no—
454C2×Q16—1882no—
455C2×Q16—1882no—
456C2×SD16—42no—
457C2×SD16—474no—
458C2×SD16—1882no—
459C2×SD16C22×D4714yes—
460C2×M16—474no—
461C2×M16—1882no—
462C22×C8—42no—
463C22×C8—471no—
464C22×C8—471no—
465C22×C8C22×D4711yescharacteristic
466C22×C8C22×D4711yescharacteristic
467C22×C8C22×D4714yes—
468C4⋊Q8—474no—
469C4⋊Q8—474no—
470C4⋊Q8—942no—
471C4⋊Q8—942no—
472#126—948no—
473#126—948no—
474#126—948no—
475#125—474no—
476#125—942no—
477#125—948no—
478#125—948no—
479#124—474no—
480#124—942no—
481#124—948no—
482#123—948no—
483C22⋊Q8—22no—
484C22⋊Q8—474no—
485C22⋊Q8—474no—
486C22⋊Q8—948no—
487C22⋊Q8—942no—
488C22⋊Q8—942no—
489C22⋊Q8C22×D4714yes—
490#121—22no—
491#121C22×D4714yes—
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—471no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—941no—
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—471no—
530C2×C42—941no—
531C2×C42—941no—
532C2×C42—941no—
533#107—474no—
534#107—474no—
535#106—474no—
536#106C22×D4714yes—
537C4⋊C8—474no—
538C4⋊C8—474no—
539C4⋊C8—474no—
540C4⋊C8—474no—
541#103—474no—
542#103—474no—
543#103—474no—
544#103—474no—
545#103—474no—
546#103C22×D4714yes—
547#102—474no—
548#102C22×D4714yes—
549C24—21no—
550C24D4×D4711yescharacteristic
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—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—82no—
570C2×D4C23×D4712yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—471no—
577C22×C4—471no—
578C22×C4—471no—
579C22×C4—471no—
580C22×C4—944no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—3762no—
586C22×C4D4×D4712yes—
587C22×C4D4×D4711yescharacteristic
588C22×C4C23×D4712yes—
589C22×C4C23×D4711yescharacteristic
590Q16—1884no—
591Q16—1884no—
592SD16—44no—
593SD16—1884no—
594M16—1884no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—44no—
598C2×C8—472no—
599C2×C8—472no—
600C2×C8—942no—
601C2×C8—942no—
602C2×C8C23×D4712yes—
603C2×C8C23×D4712yes—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—474no—
608C4⋊C4—474no—
609C4⋊C4—472no—
610C4⋊C4—472no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—944no—
616C4⋊C4—944no—
617C4⋊C4—944no—
618C4⋊C4—944no—
619C4⋊C4—944no—
620C4⋊C4—944no—
621C4⋊C4—941no—
622C4⋊C4—941no—
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—472no—
637C42—472no—
638C42—944no—
639C42—944no—
640C42—944no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C2×D4×D4712yes—
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—84no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—472no—
675C2×C4—472no—
676C2×C4—472no—
677C2×C4—472no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—3764no—
687C2×C4—1882no—
688C2×C4—1882no—
689C2×C4—1882no—
690C2×C4—1882no—
691C2×C4C2×D4×D4712yes—
692C2×C4C2×D4×D4711yescharacteristic
693C2×C4#1309406912yes—
694C2×C4#1309407112yes—
695C2×C4C24×D4711yescharacteristic
696C8—22no—
697C8—22no—
698C8—942no—
699C8—942no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#1568970012yes—
709C22#1568992912yes—
710C22#1568993712yes—
711C22C22×D4×D4711yescharacteristic
712C4—22no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—942no—
717C4—942no—
718C4—942no—
719C4—942no—
720C4—1882no—
721C4—1882no—
722C4—1882no—
723C4—1882no—
724C4#1568970012yes—
725C4C2×#1309406911yescharacteristic
726C4C2×#1309407111yescharacteristic
727C2—42no—
728C2—82no—
729C2#2025480714yesdirect product factor
730C2C2×#1568970011yescharacteristic
731C2C2×#1568992911yescharacteristic
732C2C2×#1568993711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#465C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
hypercenterC2×#465D47
hypocenterC47C2×#3258
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. C2×#15689733C2semidirect
3. #20254807C2direct (N × H)
4. C2×#15689433C2semidirect
5. C2×#15689416C2semidirect
6. C2×#15689407C2semidirect
7. C2×#15689421C2semidirect
8. C2×#15689379C2semidirect
10. C2×#15689364C2semidirect
11. C2×#15689344C2semidirect
12. C2×#15689343C2semidirect
13. C2×#15689332C2semidirect
14. C2×#15689326C2semidirect
15. C2×#15689149C2semidirect
24. #15689733C22semidirect
44. #15689433C22semidirect
45. #15689421C22semidirect
46. #15689416C22semidirect
47. #15689407C22semidirect
48. #15689379C22semidirect
50. #15689364C22semidirect
51. #15689344C22semidirect
52. #15689343C22semidirect
53. #15689332C22semidirect
54. #15689326C22semidirect
58. #15689149C22semidirect
379. C2×C47#3258semidirect
443. C47C2×#3258semidirect
729. C2#20254807direct (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×#156897332
#202548072
C2×#156894332
C2×#156894162
C2×#156894072
C2×#156894212
C2×#156893792
C2×#156893672
C2×#156893642
C2×#156893442
C2×#156893432
C2×#156893322
C2×#156893262
C2×#156891492
C2×C47×#4652
C2×#325847