Finite Group Databasebeta

← C2×#20253618 #27084558

Subgroups — C2×#20253618 #27084558

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×#15689746C211yesmaximal, characteristic
2C2×#15689601C211yesmaximal, characteristic, complemented
3#20253618C2116yesmaximal, direct product factor
4C2×#15689461C211yesmaximal, characteristic, complemented
5C2×#15689448C211yesmaximal, characteristic
6C2×#15689416C211yesmaximal, characteristic, complemented
7C2×#15689406C211yesmaximal, characteristic, complemented
8C2×#15689347C211yesmaximal, characteristic, complemented
9C2×#15689347C211yesmaximal, characteristic, complemented
10C2×#15689262C211yesmaximal, characteristic
11C2×#15689230C211yesmaximal, characteristic, complemented
12C2×#15689226C211yesmaximal, characteristic, complemented
13C2×Q16×Dic47C211yesmaximal, characteristic, complemented
14C2×#15689208C211yesmaximal, characteristic, complemented
15C2×#15689181C211yesmaximal, characteristic, complemented
16C2×C47×#451C211yesmaximal, characteristic, complemented
17C22×#10625336C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19#15689746—24no—
20#15689746C2218yes—
21C2×#13094023C2211yescharacteristic
22C2×#13094019—21no—
23C2×#13094013C2211yescharacteristic
24C2×#13094010—21no—
25C2×#13094006—21no—
26C2×#13094004—21no—
27C2×#13093998C2211yescharacteristic
28#15689601—24no—
29#15689601C2218yescomplemented
30C2×Q8×Dic47—21no—
31C2×Q8×Dic47—21no—
32C2×Q8×Dic47C2211yescharacteristic
33C2×Q8×Dic47C2211yescharacteristic
34C2×Q8×Dic47C2211yescharacteristic
35C2×Q8×Dic47C2211yescharacteristic
36C2×Q8×Dic47C2211yescharacteristic
37C2×#13093986C2211yescharacteristic
38C2×#13093983—21no—
39C2×#13093983—21no—
40C2×#13093983C2211yescharacteristic
41C2×#13093983C2211yescharacteristic
42#15689461C2218yescomplemented
43#15689448C2218yes—
44#15689416C2218yescomplemented
45#15689406C2218yescomplemented
46#15689347C2218yescomplemented
47#15689347C2218yescomplemented
48#15689262C2218yes—
49#15689230C2218yescomplemented
50#15689226C2218yescomplemented
51Q16×Dic47C2218yescomplemented
52#15689208C2218yescomplemented
53#15689181C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C23×Q8×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C22×Q16×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#451C2218yescomplemented
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×D188C2311yescharacteristic
79C22×C22⋊D47—21no—
80C22×C4×D47—21no—
81C2×#10625336—24no—
82C2×#10625336—24no—
83C2×#10625336C2314yes—
84C2×#10625336C2314yes—
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2311yescharacteristic
87#13094023—22no—
88#13094023C2314yes—
89#13094019—28no—
90#13094013—22no—
91#13094013C2314yes—
92#13094010—28no—
93#13094006—28no—
94#13094004—28no—
95#13093998—22no—
96#13093998C2314yes—
97Q8×Dic47—28no—
98Q8×Dic47—28no—
99Q8×Dic47—22no—
100Q8×Dic47—22no—
101Q8×Dic47—22no—
102Q8×Dic47—22no—
103Q8×Dic47—22no—
104Q8×Dic47C2314yes—
105Q8×Dic47C2314yes—
106Q8×Dic47C2314yes—
107Q8×Dic47C2314yes—
108Q8×Dic47C2314yes—
109#13093986—22no—
110#13093986C2314yes—
111#13093983—22no—
112#13093983—28no—
113#13093983—28no—
114#13093983D414yes—
115#13093983C2314yes—
116#13093983C2314yes—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47D411yescharacteristic
123C2×C4⋊Dic47D411yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×C22⋊Dic47—21no—
129C2×C22⋊Dic47D411yescharacteristic
130C2×C22⋊Dic47D411yescharacteristic
131C2×(C2×D47)⋊C4—21no—
132C2×(C2×D47)⋊C4—21no—
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×C4×Dic47—21no—
136C2×C4×Dic47—21no—
137C2×C4×Dic47—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47C2311yescharacteristic
142C2×C4×Dic47C2311yescharacteristic
143#13093958C2314yes—
144#13093957C2314yes—
145#13093956C2314yes—
146#13093955C2314yes—
147Dic47⋊C8C2314yes—
148Dic47⋊C8C2314yes—
149#13093948C2314yes—
150#13093948C2314yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093946C2314yes—
154#13093946C2314yes—
155C22⋊(C47⋊C8)C2314yes—
156#13093934C2314yes—
157C8×Dic47C2314yes—
158C22×Q8×C47—24no—
159C22×Q8×C47—24no—
160C22×Q8×C47—21no—
161C22×Q8×C47—22no—
162C22×Q8×C47C2314yes—
163C22×Q8×C47C2311yescharacteristic
164C22×Q8×C47C2311yescharacteristic
165C22×Q8×C47C2311yescharacteristic
166C23×C4×C47—21no—
167C23×C4×C47C2311yescharacteristic
168C2×Q16×C47—24no—
169C2×Q16×C47—24no—
170C2×Q16×C47C2314yes—
171C2×Q16×C47C2314yes—
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174C22⋊Q8×C47—22no—
175C22⋊Q8×C47C2314yes—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—21no—
179#103×C47C2314yes—
180#103×C47C2314yes—
181C22⋊C8×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C2×Q8×C47—216no—
185C2×Q8×C47—28no—
186C2×Q8×C47—28no—
187C2×Q8×C47—28no—
188C2×Q8×C47—24no—
189C2×Q8×C47—21no—
190C2×Q8×C47—21no—
191C2×Q8×C47—21no—
192C2×Q8×C47—22no—
193C2×Q8×C47—22no—
194C2×Q8×C47—22no—
195C2×Q8×C47—22no—
196C2×Q8×C47#4114yes—
197C2×Q8×C47#4114yes—
198C2×Q8×C47C2412yes—
199C2×Q8×C47C2412yes—
200C2×Q8×C47C2412yes—
201C22×C4×C47—28no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—24no—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2411yescharacteristic
213C2×C22⋊D47—24no—
214C2×C22⋊D47—82no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47C2×D411yescharacteristic
219C22×Dic47C2×D411yescharacteristic
220C22×Dic47C2×D411yescharacteristic
221C22×Dic47C2×D411yescharacteristic
222C2×D188—22no—
223C2×D188—22no—
224C2×D188—21no—
225C2×D188C2412yes—
226C2×C4×D47—24no—
227C2×C4×D47—82no—
228C2×Dic94—24no—
229C2×Dic94—82no—
230Q16×C47—28no—
231Q16×C47—28no—
232C2×C8×C47—22no—
233C2×C8×C47—22no—
234C2×C8×C47C2412yes—
235C2×C8×C47C2412yes—
236C4⋊C4×C47—24no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47C2412yes—
239C22⋊C4×C47—24no—
240C22⋊Dic47—24no—
241C22⋊Dic47C2×D414yes—
242C22⋊Dic47C2×D414yes—
243#10625336—28no—
244#10625336—28no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249C4⋊Dic47—21no—
250C4⋊Dic47—21no—
251C4⋊Dic47—21no—
252C4⋊Dic47—24no—
253C4⋊Dic47—24no—
254C4⋊Dic47—24no—
255C4⋊Dic47—24no—
256C4⋊Dic47—24no—
257C4⋊Dic47C2×D414yes—
258C4⋊Dic47C2×D414yes—
259C4⋊Dic47C2412yes—
260C4⋊Dic47C2412yes—
261C4⋊Dic47C2412yes—
262Dic47⋊C4—24no—
263C4×Dic47—24no—
264C4×Dic47—24no—
265C4×Dic47—24no—
266C4×Dic47—24no—
267C4×Dic47—24no—
268C4×Dic47—24no—
269C4×Dic47C2×D412yes—
270C4×Dic47C2×D412yes—
271C4×Dic47C2412yes—
272C4×Dic47C2412yes—
273C2×C47⋊C8—22no—
274C2×C47⋊C8—22no—
275C2×C47⋊C8C2412yes—
276C2×C47⋊C8C2412yes—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47C22×D412yes—
281C23×C47C22×D411yescharacteristic
282C22×D47—22no—
283C22×D47—42no—
284C22×D47—42no—
285C22×D47—42no—
286Q8×C47—216no—
287Q8×C47—24no—
288Q8×C47—24no—
289Q8×C47—22no—
290Q8×C47—22no—
291Q8×C47—22no—
292Q8×C47—22no—
293Q8×C47—42no—
294Q8×C47C2×#4114yes—
295Q8×C47C2×#4114yes—
296C2×C4×C47—216no—
297C2×C4×C47—24no—
298C2×C4×C47—24no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—24no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D411yescharacteristic
311C2×C4×C47C2×#4112yes—
312C2×C4×C47C2×#4112yes—
313C2×C4×C47C2511yescharacteristic
314C22⋊D47—84no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47C22×D412yes—
326C2×Dic47C22×D412yes—
327C2×Dic47C22×D412yes—
328C2×Dic47C22×D412yes—
329D188—22no—
330D188—22no—
331D188—42no—
332C4×D47—84no—
333Dic94—84no—
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#52512yes—
344C22×C47#57712yes—
345C22×C47#57812yes—
346C22×C47C23×D411yescharacteristic
347C2×D47—42no—
348C2×D47—42no—
349C2×D47—42no—
350C2×D47—84no—
351C4×C47—24no—
352C4×C47—24no—
353C4×C47—22no—
354C4×C47—42no—
355C4×C47—42no—
356C4×C47#52512yes—
357C4×C47C22×#4111yescharacteristic
358C4×C47C22×#4111yescharacteristic
359Dic47—22no—
360Dic47—22no—
361Dic47—22no—
362Dic47—22no—
363Dic47—42no—
364Dic47—42no—
365Dic47—42no—
366C2×#542—471no—
367C2×#519—471no—
368#3121—4716no—
369C2×#485—471no—
370C2×#482—471no—
371C2×#477—471no—
372C2×#475—471no—
373C2×#464—471no—
374C2×#464—471no—
375C2×#451D4711yescharacteristic, complemented
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#312114yescomplemented
384C2×C47C2×#52511yescharacteristic
385C2×C47C2×#57711yescharacteristic
386C2×C47C2×#57811yescharacteristic
387D47—82no—
388C23×Q8C2×D4711yescharacteristic
389C22×Q16C2×D4711yescharacteristic
390C22×Q16C2×D4711yescharacteristic
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—941no—
401C2×C22⋊Q8C2×D4711yescharacteristic
402C2×#121—471no—
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—471no—
415C2×#117—941no—
416C2×#117—941no—
417#485—478no—
418#482—478no—
419#477—478no—
420#475—478no—
421#464—478no—
422#464—478no—
423#451C2×D4718yescomplemented
424#448—478no—
425#441—478no—
426#440—478no—
427C4×Q16—478no—
428C4×SD16—478no—
429#433—478no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#106—471no—
433C2×#106—471no—
434C2×C4⋊C8—471no—
435C2×C4⋊C8—471no—
436C2×#103—471no—
437C2×#103—471no—
438C2×#103—471no—
439C2×#103—471no—
440C2×#103C2×D4711yescharacteristic
441C2×#103C2×D4711yescharacteristic
442C2×#102—471no—
443C2×#102—471no—
444C2×C22⋊C8—471no—
445C2×C22⋊C8C2×D4711yescharacteristic
446C2×#97—471no—
447C2×C4×C8—471no—
448C47C2×#312111yescharacteristic, complemented, Sylow
449C22×Q8—24no—
450C22×Q8—24no—
451C22×Q8—21no—
452C22×Q8—22no—
453C22×Q8—941no—
454C22×Q8C22×D4711yescharacteristic
455C22×Q8C22×D4714yes—
456C22×Q8C22×D4711yescharacteristic
457C22×Q8C22×D4711yescharacteristic
458C22×D4—471no—
459C22×D4—941no—
460C23×C4—21no—
461C23×C4—941no—
462C23×C4C22×D4711yescharacteristic
463C2×Q16—24no—
464C2×Q16—24no—
465C2×Q16C22×D4714yes—
466C2×Q16C22×D4714yes—
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—22no—
483C22⋊Q8—948no—
484C22⋊Q8C22×D4714yes—
485#121—474no—
486#121—942no—
487C4×Q8—474no—
488C4×Q8—474no—
489C4×Q8—474no—
490C4×Q8—474no—
491C4×Q8—474no—
492C4×Q8—942no—
493C4×Q8—942no—
494C4×Q8—942no—
495C4×Q8—942no—
496C4×Q8—942no—
497C4×Q8—948no—
498C4×Q8—948no—
499C4×D4—474no—
500C4×D4—942no—
501#117—474no—
502#117—474no—
503#117—474no—
504#117—948no—
505#117—948no—
506#117—942no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4C22×D4711yescharacteristic
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—
533C2×C42—941no—
534C2×C42—941no—
535C2×C42—941no—
536#107—474no—
537#107—474no—
538#106—474no—
539#106—474no—
540C4⋊C8—474no—
541C4⋊C8—474no—
542#103—474no—
543#103—474no—
544#103—474no—
545#103—474no—
546#103C22×D4714yes—
547#103C22×D4714yes—
548#102—474no—
549#102—474no—
550C22⋊C8—474no—
551C22⋊C8C22×D4714yes—
552#97—474no—
553C4×C8—474no—
554C24—941no—
555C24D4×D4711yescharacteristic
556C2×Q8—216no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—24no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—944no—
569C2×Q8—3762no—
570C2×Q8#1062535214yes—
571C2×Q8#1062535214yes—
572C2×Q8C23×D4712yes—
573C2×Q8C23×D4712yes—
574C2×Q8C23×D4712yes—
575C2×D4—472no—
576C2×D4—944no—
577C2×D4—941no—
578C2×D4—942no—
579C2×D4—942no—
580C2×D4—3762no—
581C22×C4—28no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—471no—
590C22×C4—471no—
591C22×C4—471no—
592C22×C4—471no—
593C22×C4—944no—
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—28no—
603Q16—28no—
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—24no—
615C4⋊C4—21no—
616C4⋊C4—474no—
617C4⋊C4—474no—
618C4⋊C4—472no—
619C4⋊C4—472no—
620C4⋊C4—472no—
621C4⋊C4—944no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—941no—
628C4⋊C4—941no—
629C4⋊C4—941no—
630C4⋊C4C23×D4712yes—
631C22⋊C4—24no—
632C22⋊C4—474no—
633C22⋊C4—474no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C22⋊C4—944no—
639C42—472no—
640C42—472no—
641C42—472no—
642C42—472no—
643C42—944no—
644C42—944no—
645C42—944no—
646C42—944no—
647C42—944no—
648C42—944no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—942no—
653C23—1882no—
654C23—1882no—
655C23—1882no—
656C23C2×D4×D4712yes—
657C23C2×D4×D4711yescharacteristic
658Q8—216no—
659Q8—24no—
660Q8—24no—
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8—22no—
665Q8—42no—
666Q8—3764no—
667Q8C2×#1062535214yes—
668Q8C2×#1062535214yes—
669D4—942no—
670D4—942no—
671D4—3764no—
672D4—1882no—
673C2×C4—216no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—472no—
687C2×C4—472no—
688C2×C4—472no—
689C2×C4—472no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—3764no—
698C2×C4—1882no—
699C2×C4—1882no—
700C2×C4—1882no—
701C2×C4C2×D4×D4712yes—
702C2×C4C2×D4×D4711yescharacteristic
703C2×C4C2×#1062535212yes—
704C2×C4C2×#1062535212yes—
705C2×C4C24×D4711yescharacteristic
706C8—22no—
707C8—22no—
708C8—942no—
709C8—942no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—3764no—
715C22—1882no—
716C22—1882no—
717C22—1882no—
718C22#1568962912yes—
719C22#1568993212yes—
720C22#1568993612yes—
721C22C22×D4×D4711yescharacteristic
722C4—24no—
723C4—24no—
724C4—22no—
725C4—42no—
726C4—42no—
727C4—942no—
728C4—942no—
729C4—942no—
730C4—942no—
731C4—1882no—
732C4—1882no—
733C4—1882no—
734C4#1568962912yes—
735C4C22×#1062535211yescharacteristic
736C4C22×#1062535211yescharacteristic
737C2—42no—
738C2—3762no—
739C2#2025361814yesdirect product factor
740C2C2×#1568962911yescharacteristic
741C2C2×#1568993211yescharacteristic
742C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#451C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenterC2×#451D47
hypocenterC47C2×#3121
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#15689601C2semidirect
3. #20253618C2direct (N × H)
4. C2×#15689461C2semidirect
6. C2×#15689416C2semidirect
7. C2×#15689406C2semidirect
8. C2×#15689347C2semidirect
9. C2×#15689347C2semidirect
11. C2×#15689230C2semidirect
12. C2×#15689226C2semidirect
13. C2×Q16×Dic47C2semidirect
14. C2×#15689208C2semidirect
15. C2×#15689181C2semidirect
16. C2×C47×#451C2semidirect
29. #15689601C22semidirect
42. #15689461C22semidirect
44. #15689416C22semidirect
45. #15689406C22semidirect
46. #15689347C22semidirect
47. #15689347C22semidirect
49. #15689230C22semidirect
50. #15689226C22semidirect
51. Q16×Dic47C22semidirect
52. #15689208C22semidirect
53. #15689181C22semidirect
73. C47×#451C22semidirect
375. C2×#451D47semidirect
383. C2×C47#3121semidirect
423. #451C2×D47semidirect
448. C47C2×#3121semidirect
739. C2#20253618direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897462
C2×#156896012
#202536182
C2×#156894612
C2×#156894482
C2×#156894162
C2×#156894062
C2×#156893472
C2×#156892622
C2×#156892302
C2×#156892262
C2×Q16×Dic472
C2×#156892082
C2×#156891812
C2×C47×#4512
C2×#312147