Finite Group Databasebeta

← C2×#20257782 #27124068

Subgroups — C2×#20257782 #27124068

Order 12032.

7810 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257782C2132yesmaximal, direct product factor
2C2×#15689870C214yesmaximal, complemented
3C2×#15689832C212yesmaximal, complemented
4C2×#15689829C212yesmaximal, complemented
5C2×#15689794C212yesmaximal, complemented
6C2×#15689793C212yesmaximal, complemented
7C2×#15689771C214yesmaximal, complemented
8C2×#15689728C211yesmaximal, characteristic, complemented
9C2×#15689726C212yesmaximal, complemented
10C2×#15689702C214yesmaximal, complemented
11C2×#15689700C214yesmaximal, complemented
12C2×#15689676C211yesmaximal, characteristic, complemented
13C2×#15689668C212yesmaximal, complemented
14C2×C47×#540C211yesmaximal, characteristic, complemented
15C22×#10625350C2214yes—
16C22×#10625352C2214yes—
17C22×#10625352C2214yes—
18#15689870C22164yescomplemented
19#15689832C22132yescomplemented
20#15689829C22132yescomplemented
21#15689794C22132yescomplemented
22#15689793C22132yescomplemented
23#15689771C22164yescomplemented
24#15689728C22116yescomplemented
25#15689726C22132yescomplemented
26#15689702C22164yescomplemented
27#15689700C22164yescomplemented
28#15689676C22116yescomplemented
29#15689668C22132yescomplemented
30C2×#13094023C2212yes—
31C2×#13094023C2212yes—
32C2×#13094021C2211yescharacteristic
33C2×#13094020C2212yes—
34C2×#13094020C2212yes—
35C2×#13094016C2211yescharacteristic
36C2×#13094015C2212yes—
37C2×#13094015C2212yes—
38C2×#13094010C2214yes—
39C2×#13094009C2214yes—
40C2×#13094008C2214yes—
41C2×#13094006C2214yes—
42C2×#13094004C2214yes—
43C2×#13094003C2214yes—
44C2×#13094002C2214yes—
45C2×#13094002C2214yes—
46C2×#13094001C2214yes—
47C2×#13094001C2214yes—
48C2×#13094001C2212yes—
49C2×#13094001C2212yes—
50C2×#13093998C2214yes—
51C2×#13093998C2212yes—
52C2×#13093997C2214yes—
53C2×#13093997C2214yes—
54C2×#13093997C2214yes—
55C2×#13093996C2214yes—
56C2×#13093996C2214yes—
57C2×#13093996C2214yes—
58C2×#13093996C2214yes—
59C2×#13093995C2214yes—
60C2×#13093995C2214yes—
61C2×C4×Dic94C2212yes—
62C2×C4×Dic94C2212yes—
63C2×C4×D188C2212yes—
64C2×D4×Dic47C2212yes—
65C2×D4×Dic47C2212yes—
66C2×#13093986C2212yes—
67C2×#13093986C2212yes—
68C2×(C22⋊D47)⋊C4C2214yes—
69C2×#13093983C2211yescharacteristic
70C22×Dic47⋊C4C2214yes—
71C2×C4⋊C4×D47C2214yes—
72C22×C4×Dic47C2211yescharacteristic
73C47×#540C22116yescomplemented
74C2×#127×C47C2211yescharacteristic
75C2×#125×C47C2211yescharacteristic
76C2×#123×C47C2214yes—
77C2×#121×C47C2212yes—
78C2×#121×C47C2214yes—
79C2×C4×D4×C47C2212yes—
80C2×#117×C47C2211yescharacteristic
81C2×#10625350—416no—
82C2×#10625350C23132yes—
83C2×#10625352—416no—
84C2×#10625352—416no—
85C2×#10625352C23132yes—
86C2×#10625352C23132yes—
87C22×Dic94C2312yes—
88C22×Dic94C2312yes—
89C22×Dic94C2314yes—
90C22×D188C2312yes—
91C22×D188C2314yes—
92C22×C22⋊D47C2314yes—
93C22×C22⋊D47C2314yes—
94C22×C22⋊D47C2314yes—
95C22×C22⋊D47C2314yes—
96C22×C22⋊D47C2314yes—
97C23×Dic47C2312yes—
98C23×Dic47C2314yes—
99C23×Dic47C2314yes—
100C22×C4×D47C2314yes—
101C22×C4×D47C2314yes—
102C22×C4×D47C2314yes—
103#13094023C23116yes—
104#13094023C23116yes—
105#13094021C2318yes—
106#13094020C23116yes—
107#13094020C23116yes—
108#13094016C2318yes—
109#13094015C23116yes—
110#13094015C23116yes—
111#13094010C23132yes—
112#13094009C23132yes—
113#13094008C23132yes—
114#13094006C23132yes—
115#13094004C23132yes—
116#13094003C23132yes—
117#13094002C23132yes—
118#13094002C23132yes—
119#13094001C23132yes—
120#13094001C23132yes—
121#13094001C23116yes—
122#13094001C23116yes—
123#13093998C23116yes—
124#13093998C23132yes—
125#13093997C23132yes—
126#13093997C23132yes—
127#13093997C23132yes—
128#13093996C23132yes—
129#13093996C23132yes—
130#13093996C23132yes—
131#13093996C23132yes—
132#13093995C23132yes—
133#13093995C23132yes—
134C4×Dic94C23116yes—
135C4×Dic94C23116yes—
136C4×D188C23116yes—
137D4×Dic47C23116yes—
138D4×Dic47C23116yes—
139#13093986C23116yes—
140#13093986C23116yes—
141(C22⋊D47)⋊C4C23132yes—
142#13093983C2318yes—
143C2×C4⋊Dic47C2314yes—
144C2×C4⋊Dic47C2312yes—
145C2×C4⋊Dic47C2312yes—
146C2×C4⋊Dic47C2312yes—
147C2×C4⋊Dic47C2312yes—
148C2×Dic47⋊C4C23132yes—
149C2×Dic47⋊C4C2312yes—
150C2×Dic47⋊C4C2314yes—
151C2×Dic47⋊C4C2312yes—
152C2×Dic47⋊C4C2314yes—
153C2×Dic47⋊C4C2314yes—
154C2×Dic47⋊C4C2312yes—
155C2×Dic47⋊C4C2312yes—
156C4⋊C4×D47C23132yes—
157C2×C22⋊Dic47C2311yescharacteristic
158C2×C22⋊Dic47C2311yescharacteristic
159C2×C22⋊Dic47C2314yes—
160C2×C22⋊Dic47C2314yes—
161C2×(C2×D47)⋊C4C2314yes—
162C2×(C2×D47)⋊C4C2314yes—
163C2×(C2×D47)⋊C4C2314yes—
164C2×(C2×D47)⋊C4C2314yes—
165C2×C4×Dic47C2311yescharacteristic
166C2×C4×Dic47C2312yes—
167C2×C4×Dic47C2311yescharacteristic
168C2×C4×Dic47C2318yes—
169C2×C4×Dic47C2312yes—
170C22×D4×C47C2312yes—
171C22×D4×C47C2314yes—
172C22×D4×C47C2314yes—
173C23×C4×C47C2311yescharacteristic
174C23×C4×C47C2314yes—
175#127×C47C2318yes—
176#125×C47C2318yes—
177#123×C47C23132yes—
178#121×C47C23116yes—
179#121×C47C23132yes—
180C4×D4×C47C23116yes—
181#117×C47C2318yes—
182C2×C4⋊C4×C47C2312yes—
183C2×C4⋊C4×C47C2312yes—
184C2×C4⋊C4×C47C2314yes—
185C2×C22⋊C4×C47C2312yes—
186C2×C22⋊C4×C47C2314yes—
187C2×C22⋊C4×C47C2314yes—
188C2×C42×C47C2311yescharacteristic
189C2×C42×C47C2311yescharacteristic
190C24×C47C2411yescharacteristic
191C24×C47C2414yes—
192C23×D47C2414yes—
193C2×D4×C47—28no—
194C2×D4×C47—48no—
195C2×D4×C47—48no—
196C2×D4×C47C2418yes—
197C2×D4×C47C24116yes—
198C2×D4×C47C24116yes—
199C22×C4×C47—24no—
200C22×C4×C47—48no—
201C22×C4×C47C2412yes—
202C22×C4×C47C2412yes—
203C22×C4×C47C2411yescharacteristic
204C22×C4×C47C2414yes—
205C22×C4×C47C2414yes—
206C22×C4×C47C24116yes—
207C22×C4×C47C2411yescharacteristic
208C2×C22⋊D47—216no—
209C2×C22⋊D47—48no—
210C2×C22⋊D47—48no—
211C2×C22⋊D47—48no—
212C2×C22⋊D47—48no—
213C2×C22⋊D47C24116yes—
214C2×C22⋊D47C24116yes—
215C2×C22⋊D47C24116yes—
216C2×C22⋊D47C24116yes—
217C2×C22⋊D47C24116yes—
218C22×Dic47—28no—
219C22×Dic47—216no—
220C22×Dic47—48no—
221C22×Dic47C2412yes—
222C22×Dic47C2418yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C22×Dic47C2414yes—
226C22×Dic47C24116yes—
227C22×Dic47C24116yes—
228C22×Dic47C2412yes—
229#10625352—464no—
230#10625352—464no—
231#10625350—464no—
232C2×D188—28no—
233C2×D188—48no—
234C2×D188C2418yes—
235C2×D188C24116yes—
236C2×C4×D47—216no—
237C2×C4×D47—48no—
238C2×C4×D47—48no—
239C2×C4×D47C24116yes—
240C2×C4×D47C24116yes—
241C2×C4×D47C24116yes—
242C2×Dic94—28no—
243C2×Dic94—28no—
244C2×Dic94—48no—
245C2×Dic94C2418yes—
246C2×Dic94C2418yes—
247C2×Dic94C24116yes—
248C4⋊C4×C47C2418yes—
249C4⋊C4×C47C2418yes—
250C4⋊C4×C47C24116yes—
251C22⋊C4×C47C2418yes—
252C22⋊C4×C47C24116yes—
253C22⋊C4×C47C24116yes—
254C42×C47C2414yes—
255C42×C47C2414yes—
256C22⋊Dic47C2414yes—
257C22⋊Dic47C2414yes—
258C22⋊Dic47C24116yes—
259C22⋊Dic47C24116yes—
260(C2×D47)⋊C4C24116yes—
261(C2×D47)⋊C4C24116yes—
262(C2×D47)⋊C4C24116yes—
263(C2×D47)⋊C4C24116yes—
264C4⋊Dic47C24116yes—
265C4⋊Dic47C2418yes—
266C4⋊Dic47C2418yes—
267C4⋊Dic47C2418yes—
268C4⋊Dic47C2418yes—
269Dic47⋊C4C2418yes—
270Dic47⋊C4C24116yes—
271Dic47⋊C4C2418yes—
272Dic47⋊C4C24116yes—
273Dic47⋊C4C24116yes—
274Dic47⋊C4C2418yes—
275Dic47⋊C4C2418yes—
276C4×Dic47C2414yes—
277C4×Dic47C2418yes—
278C4×Dic47C2414yes—
279C4×Dic47C2418yes—
280C23×C47—24no—
281C23×C47—28no—
282C23×C47—28no—
283C23×C47—22no—
284C23×C47—28no—
285C23×C47C2512yes—
286C23×C47C2518yes—
287C23×C47C2511yescharacteristic
288C22×D47—28no—
289C22×D47—28no—
290C22×D47—28no—
291C22×D47C2518yes—
292D4×C47—216no—
293D4×C47—416no—
294D4×C47—416no—
295C2×C4×C47—24no—
296C2×C4×C47—24no—
297C2×C4×C47—28no—
298C2×C4×C47—22no—
299C2×C4×C47—28no—
300C2×C4×C47—416no—
301C2×C4×C472−1+414yes—
302C2×C4×C47C2512yes—
303C2×C4×C47C2514yes—
304C2×C4×C47C2514yes—
305C2×C4×C47C2518yes—
306C2×C4×C47C2512yes—
307C22⋊D47—232no—
308C22⋊D47—416no—
309C22⋊D47—416no—
310C22⋊D47—416no—
311C22⋊D47—416no—
312C2×Dic47—24no—
313C2×Dic47—24no—
314C2×Dic47—24no—
315C2×Dic47—28no—
316C2×Dic47—216no—
317C2×Dic47—232no—
318C2×Dic47—416no—
319C2×Dic47H(5,𝔽2)18yes—
320C2×Dic47C2514yes—
321C2×Dic47C2514yes—
322C2×Dic47C2514yes—
323C2×Dic47C2518yes—
324C2×Dic47C2514yes—
325D188—216no—
326D188—416no—
327C4×D47—232no—
328C4×D47—416no—
329C4×D47—416no—
330Dic94—216no—
331Dic94—216no—
332Dic94—416no—
333C2×#3548—471nomaximal, Sylow
334C22×C47—24no—
335C22×C47—28no—
336C22×C47—28no—
337C22×C47—22no—
338C22×C47—28no—
339C22×C47—44no—
340C22×C47—416no—
341C22×C47C2×H(5,𝔽2)14yes—
342C22×C47C2×2−1+412yes—
343C22×C47C2611yescharacteristic
344C2×D47—28no—
345C2×D47—28no—
346C2×D47—28no—
347C2×D47—416no—
348C4×C47—24no—
349C4×C47—24no—
350C4×C47—28no—
351C4×C47—22no—
352C4×C47C2×2−1+414yes—
353Dic47—24no—
354Dic47—24no—
355Dic47—24no—
356Dic47—28no—
357Dic47C2×H(5,𝔽2)18yes—
358#3548—4732no—
359C2×#562—474no—
360C2×#554—472no—
361C2×#554—472no—
362C2×#550—472no—
363C2×#550—472no—
364C2×#547—474no—
365C2×#540—472no—
366C2×#540—471no—
367C2×#540D4711yescharacteristic, complemented
368C2×#537—474no—
369C2×#537—474no—
370C2×#533—471no—
371C2×#532—472no—
372C2×C47—42no—
373C2×C47—48no—
374C2×C47#354814yescomplemented
375C2×C47C22×H(5,𝔽2)12yes—
376C2×C47C22×2−1+411yescharacteristic
377D47—48no—
378C22×#41—474no—
379C22×#41—474no—
380C22×#41—474no—
381#562—4764no—
382#554—4732no—
383#554—4732no—
384#550—4732no—
385#550—4732no—
386#547—4764no—
387#540—4732no—
388#540—4716no—
389#540C2×D47116yescomplemented
390#537—4764no—
391#537—4764no—
392#533—4716no—
393#532—4732no—
394C2×C4⋊Q8—472no—
395C2×C4⋊Q8—472no—
396C2×#127—472no—
397C2×#127—472no—
398C2×#127—471no—
399C2×#127C2×D4711yescharacteristic
400C2×#125—472no—
401C2×#125—472no—
402C2×#125—471no—
403C2×#125C2×D4711yescharacteristic
404C2×#124—474no—
405C2×#123—474no—
406C2×#123—474no—
407C2×#123—474no—
408C2×#123C2×D4714yes—
409C2×C22⋊Q8—474no—
410C2×C22⋊Q8—474no—
411C2×C22⋊Q8—474no—
412C2×C22⋊Q8—474no—
413C2×C22⋊Q8—472no—
414C2×C22⋊Q8—472no—
415C2×C22⋊Q8—474no—
416C2×C22⋊Q8—474no—
417C2×#121—474no—
418C2×#121—474no—
419C2×#121—474no—
420C2×#121—474no—
421C2×#121—474no—
422C2×#121—474no—
423C2×#121—472no—
424C2×#121—474no—
425C2×#121—474no—
426C2×#121—474no—
427C2×#121—474no—
428C2×#121C2×D4712yes—
429C2×#121C2×D4714yes—
430C2×C4×Q8—472no—
431C2×C4×Q8—472no—
432C2×C4×D4—472no—
433C2×C4×D4—472no—
434C2×C4×D4—472no—
435C2×C4×D4—472no—
436C2×C4×D4—474no—
437C2×C4×D4—472no—
438C2×C4×D4C2×D4712yes—
439C2×#117—471no—
440C2×#117C2×D4711yescharacteristic
441C22×C4⋊C4—474no—
442C22×C4⋊C4—474no—
443C22×C42—471no—
444C47C2×#354811yescharacteristic, complemented, Sylow
445C2×#41—4732no—
446C2×#41—4732no—
447C2×#41—4732no—
448C2×#41—18816no—
449C2×#41—18816no—
450C2×#41—18816no—
451C22×Q8—472no—
452C22×Q8—472no—
453C22×Q8—474no—
454C22×D4—474no—
455C22×D4—474no—
456C22×D4—474no—
457C22×D4—474no—
458C22×D4—474no—
459C22×D4—472no—
460C22×D4—474no—
461C22×D4C22×D4712yes—
462C22×D4C22×D4714yes—
463C22×D4C22×D4714yes—
464C23×C4—474no—
465C23×C4—472no—
466C23×C4—474no—
467C23×C4—474no—
468C23×C4—474no—
469C23×C4—474no—
470C23×C4C22×D4711yescharacteristic
471C23×C4C22×D4714yes—
472C4⋊Q8—4716no—
473C4⋊Q8—4716no—
474#127—4716no—
475#127—4716no—
476#127—478no—
477#127C22×D4718yes—
478#125—4716no—
479#125—4716no—
480#125—478no—
481#125C22×D4718yes—
482#124—4732no—
483#123—4732no—
484#123—4732no—
485#123—4732no—
486#123C22×D47132yes—
487C22⋊Q8—4732no—
488C22⋊Q8—4732no—
489C22⋊Q8—4732no—
490C22⋊Q8—4732no—
491C22⋊Q8—4716no—
492C22⋊Q8—4716no—
493C22⋊Q8—4732no—
494C22⋊Q8—4732no—
495#121—4732no—
496#121—4732no—
497#121—4732no—
498#121—4732no—
499#121—4732no—
500#121—4732no—
501#121—4716no—
502#121—4732no—
503#121—4732no—
504#121—4732no—
505#121—4732no—
506#121C22×D47116yes—
507#121C22×D47132yes—
508C4×Q8—4716no—
509C4×Q8—4716no—
510C4×D4—4716no—
511C4×D4—4716no—
512C4×D4—4716no—
513C4×D4—4716no—
514C4×D4—4732no—
515C4×D4—4716no—
516C4×D4C22×D47116yes—
517#117—478no—
518#117C22×D4718yes—
519C2×C4⋊C4—474no—
520C2×C4⋊C4—472no—
521C2×C4⋊C4—472no—
522C2×C4⋊C4—474no—
523C2×C4⋊C4—474no—
524C2×C4⋊C4—474no—
525C2×C4⋊C4—4732no—
526C2×C4⋊C4—472no—
527C2×C4⋊C4—472no—
528C2×C4⋊C4—472no—
529C2×C4⋊C4—472no—
530C2×C4⋊C4—472no—
531C2×C4⋊C4—472no—
532C2×C4⋊C4—4732no—
533C2×C4⋊C4C22×D4714yes—
534C2×C4⋊C4C22×D4712yes—
535C2×C4⋊C4C22×D4712yes—
536C2×C22⋊C4—471no—
537C2×C22⋊C4—471no—
538C2×C22⋊C4—474no—
539C2×C22⋊C4—474no—
540C2×C22⋊C4—474no—
541C2×C22⋊C4—474no—
542C2×C22⋊C4—474no—
543C2×C22⋊C4—474no—
544C2×C22⋊C4C22×D4712yes—
545C2×C22⋊C4C22×D4714yes—
546C2×C22⋊C4C22×D4714yes—
547C2×C42—472no—
548C2×C42—471no—
549C2×C42—472no—
550C2×C42—471no—
551C2×C42—478no—
552C2×C42C22×D4711yescharacteristic
553C2×C42C22×D4711yescharacteristic
554C24—474no—
555C24C23×D4714yes—
556C24C23×D4711yescharacteristic
557#41—18864no—
558#41—18864no—
559#41—18864no—
560C2×Q8—478no—
561C2×Q8—478no—
562C2×Q8—4716no—
563C2×Q8—948no—
564C2×Q8—948no—
565C2×Q8—1888no—
566C2×D4—28no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—4716no—
570C2×D4—4716no—
571C2×D4—4716no—
572C2×D4—4716no—
573C2×D4—4716no—
574C2×D4—478no—
575C2×D4—4716no—
576C2×D4—9416no—
577C2×D4—948no—
578C2×D4—1888no—
579C2×D4—1888no—
580C2×D4—1888no—
581C2×D4—1888no—
582C2×D4—1888no—
583C2×D4C23×D4718yes—
584C2×D4C23×D47116yes—
585C2×D4C23×D47116yes—
586C22×C4—24no—
587C22×C4—48no—
588C22×C4—472no—
589C22×C4—478no—
590C22×C4—4716no—
591C22×C4—472no—
592C22×C4—472no—
593C22×C4—472no—
594C22×C4—474no—
595C22×C4—4716no—
596C22×C4—4716no—
597C22×C4—4716no—
598C22×C4—4716no—
599C22×C4—9416no—
600C22×C4—9416no—
601C22×C4—948no—
602C22×C4—1888no—
603C22×C4—1888no—
604C22×C4—1888no—
605C22×C4C23×D4714yes—
606C22×C4C23×D4711yescharacteristic
607C22×C4C23×D4712yes—
608C22×C4C23×D4712yes—
609C22×C4C23×D4714yes—
610C22×C4C23×D47116yes—
611C22×C4C23×D4711yescharacteristic
612C4⋊C4—4716no—
613C4⋊C4—478no—
614C4⋊C4—478no—
615C4⋊C4—4716no—
616C4⋊C4—4716no—
617C4⋊C4—478no—
618C4⋊C4—478no—
619C4⋊C4—4716no—
620C4⋊C4—478no—
621C4⋊C4—478no—
622C4⋊C4—478no—
623C4⋊C4—478no—
624C4⋊C4C23×D47116yes—
625C4⋊C4C23×D4718yes—
626C4⋊C4C23×D4718yes—
627C22⋊C4—474no—
628C22⋊C4—474no—
629C22⋊C4—4716no—
630C22⋊C4—4716no—
631C22⋊C4—4716no—
632C22⋊C4—4716no—
633C22⋊C4—4716no—
634C22⋊C4—4716no—
635C22⋊C4C23×D4718yes—
636C22⋊C4C23×D47116yes—
637C22⋊C4C23×D47116yes—
638C42—474no—
639C42—478no—
640C42—474no—
641C42—478no—
642C42C23×D4714yes—
643C42C23×D4714yes—
644C23—28no—
645C23—28no—
646C23—24no—
647C23—22no—
648C23—28no—
649C23—478no—
650C23—948no—
651C23—948no—
652C23—948no—
653C23C24×D4718yes—
654C23C24×D4712yes—
655C23C24×D4711yescharacteristic
656Q8—9416no—
657Q8—9416no—
658Q8—18816no—
659D4—216no—
660D4—416no—
661D4—416no—
662D4—9432no—
663D4—9416no—
664D4—18816no—
665D4—18816no—
666D4—18816no—
667D4—18816no—
668D4—18816no—
669C2×C4—24no—
670C2×C4—28no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—416no—
675C2×C4—478no—
676C2×C4—474no—
677C2×C4—474no—
678C2×C4—474no—
679C2×C4—474no—
680C2×C4—478no—
681C2×C4—9432no—
682C2×C4—9432no—
683C2×C4—9416no—
684C2×C4—948no—
685C2×C4—944no—
686C2×C4—944no—
687C2×C4—944no—
688C2×C4—18816no—
689C2×C4—18816no—
690C2×C4—18816no—
691C2×C4#1309407114yes—
692C2×C4C24×D4712yes—
693C2×C4C24×D4714yes—
694C2×C4C24×D4714yes—
695C2×C4C24×D4718yes—
696C2×C4C24×D4712yes—
697C22—28no—
698C22—28no—
699C22—24no—
700C22—22no—
701C22—28no—
702C22—416no—
703C22—44no—
704C22—948no—
705C22—948no—
706C22—948no—
707C22—18816no—
708C22H(5,𝔽2)×D4714yes—
709C22C2×#1309407112yes—
710C22C25×D4711yescharacteristic
711C4—24no—
712C4—28no—
713C4—24no—
714C4—22no—
715C4—478no—
716C4—948no—
717C4—944no—
718C4—944no—
719C4—944no—
720C4C2×#1309407114yes—
721C2—48no—
722C2—42no—
723C2—1888no—
724C2#2025778214yesdirect product factor
725C2C2×H(5,𝔽2)×D4712yes—
726C2C22×#1309407111yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#540C2
socleC23×C47C25
hypercenterC2×#540D47
hypocenterC47C2×#3548
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #20257782C2direct (N × H)
2. C2×#15689870C2semidirect
3. C2×#15689832C2semidirect
4. C2×#15689829C2semidirect
5. C2×#15689794C2semidirect
6. C2×#15689793C2semidirect
7. C2×#15689771C2semidirect
8. C2×#15689728C2semidirect
9. C2×#15689726C2semidirect
10. C2×#15689702C2semidirect
11. C2×#15689700C2semidirect
12. C2×#15689676C2semidirect
13. C2×#15689668C2semidirect
14. C2×C47×#540C2semidirect
18. #15689870C22semidirect
19. #15689832C22semidirect
20. #15689829C22semidirect
21. #15689794C22semidirect
22. #15689793C22semidirect
23. #15689771C22semidirect
24. #15689728C22semidirect
25. #15689726C22semidirect
26. #15689702C22semidirect
27. #15689700C22semidirect
28. #15689676C22semidirect
29. #15689668C22semidirect
73. C47×#540C22semidirect
367. C2×#540D47semidirect
374. C2×C47#3548semidirect
389. #540C2×D47semidirect
444. C47C2×#3548semidirect
724. C2#20257782direct (N × H)

Maximal subgroups

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

subgroupindex
#202577822
C2×#156898702
C2×#156898322
C2×#156898292
C2×#156897942
C2×#156897932
C2×#156897712
C2×#156897282
C2×#156897262
C2×#156897022
C2×#156897002
C2×#156896762
C2×#156896682
C2×C47×#5402
C2×#354847