Finite Group Databasebeta

← C2×#20255893 #27094878

Subgroups — C2×#20255893 #27094878

Order 12032.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689838C211yesmaximal, characteristic, complemented
2C2×#15689823C211yesmaximal, characteristic, complemented
3#20255893C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689446C211yesmaximal, characteristic, complemented
6C2×#15689446C211yesmaximal, characteristic, complemented
7C2×#15689445C211yesmaximal, characteristic, complemented
8C2×#15689435C211yesmaximal, characteristic, complemented
9C2×#15689423C211yesmaximal, characteristic, complemented
10C2×#15689403C211yesmaximal, characteristic, complemented
11C2×#15689373C211yesmaximal, characteristic, complemented
12C2×#15689356C211yesmaximal, characteristic, complemented
13C2×#15689196C211yesmaximal, characteristic, complemented
14C2×#15689162C211yesmaximal, characteristic, complemented
15C2×#15689158C211yesmaximal, characteristic, complemented
16C2×C47×#442C211yesmaximal, characteristic, complemented
17C22×#10625324C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19#15689838—24no—
20#15689838C2218yescomplemented
21#15689823—24no—
22#15689823C2218yescomplemented
23C2×#13094024C2211yescharacteristic
24C2×#13094017—21no—
25C2×#13094016C2211yescharacteristic
26C2×#13094010—21no—
27C2×#13094010—21no—
28C2×#13094007—21no—
29C2×#13093998—21no—
30C2×#13093997—21no—
31C2×#13093995C2211yescharacteristic
32C2×#13093995C2211yescharacteristic
33C2×#13093995C2211yescharacteristic
34C2×#13093995C2211yescharacteristic
35C2×C4×D188C2211yescharacteristic
36C2×C4×C22⋊D47—21no—
37C2×#13093983—21no—
38C2×#13093982C2211yescharacteristic
39C2×#13093982C2211yescharacteristic
40C2×#13093982C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689532C2218yescomplemented
43#15689446C2218yescomplemented
44#15689446C2218yescomplemented
45#15689445C2218yescomplemented
46#15689435C2218yescomplemented
47#15689423C2218yescomplemented
48#15689403C2218yescomplemented
49#15689373C2218yescomplemented
50#15689356C2218yescomplemented
51#15689196C2218yescomplemented
52#15689162C2218yescomplemented
53#15689158C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093957C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093956C2211yescharacteristic
61C2×#13093955C2211yescharacteristic
62C2×C4⋊(C47⋊C8)C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093945C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C22×D8×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#442C2218yescomplemented
73C2×#106×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×D188D411yescharacteristic
79C22×C22⋊D47—21no—
80C22×C22⋊D47—21no—
81C22×C22⋊D47—21no—
82C22×C22⋊D47—21no—
83C22×C4×D47—21no—
84C22×C4×D47C2311yescharacteristic
85C22×C4×D47C2311yescharacteristic
86C2×#10625324—24no—
87C2×#10625324C2314yes—
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90C2×C8×D47—24no—
91C2×C8×D47C2314yes—
92#13094024—22no—
93#13094024C2314yes—
94#13094017—28no—
95#13094016—22no—
96#13094016C2314yes—
97#13094010—28no—
98#13094010—28no—
99#13094007—28no—
100#13093998—28no—
101#13093997—28no—
102#13093995—22no—
103#13093995—22no—
104#13093995—22no—
105#13093995—22no—
106#13093995C2314yes—
107#13093995C2314yes—
108#13093995C2314yes—
109#13093995C2314yes—
110C4×D188D414yes—
111C4×D188C2314yes—
112C4×C22⋊D47—28no—
113#13093983—28no—
114#13093982—22no—
115#13093982—22no—
116#13093982—22no—
117#13093982C2314yes—
118#13093982C2314yes—
119#13093982C2314yes—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47D411yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×C4⋊Dic47C2311yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C4⋊C4×D47—22no—
130C4⋊C4×D47C2314yes—
131C2×C22⋊Dic47—21no—
132C2×C22⋊Dic47—21no—
133C2×C22⋊Dic47—21no—
134C2×C22⋊Dic47—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4D411yescharacteristic
139C2×(C2×D47)⋊C4D411yescharacteristic
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143#13093958C2314yes—
144#13093958C2314yes—
145#13093957C2314yes—
146#13093957C2314yes—
147#13093957C2314yes—
148#13093956C2314yes—
149#13093956C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152#13093945C2314yes—
153#13093945C2314yes—
154#13093945C2314yes—
155#13093945C2314yes—
156(C2×D47)⋊C8C2314yes—
157(C2×D47)⋊C8C2314yes—
158C22×D4×C47C2311yescharacteristic
159C22×D4×C47C2311yescharacteristic
160C23×C4×C47—21no—
161C23×C4×C47—21no—
162C2×D8×C47—24no—
163C2×D8×C47C2314yes—
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C4×D4×C47—22no—
167C4×D4×C47—22no—
168C4×D4×C47C2314yes—
169C4×D4×C47C2314yes—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47—21no—
174C2×C42×C47C2311yescharacteristic
175#106×C47C2314yes—
176#102×C47C2314yes—
177#102×C47C2314yes—
178#97×C47C2314yes—
179C24×C47—21no—
180C24×C47—21no—
181C23×D47C2×D411yescharacteristic
182C23×D47C2×D411yescharacteristic
183C2×D4×C47—21no—
184C2×D4×C47—21no—
185C2×D4×C47—22no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47—22no—
189C2×D4×C47C2412yes—
190C2×D4×C47C2412yes—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—24no—
194C22×C4×C47—24no—
195C22×C4×C47—44no—
196C22×C4×C47—82no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2411yescharacteristic
200C2×C22⋊D47—24no—
201C2×C22⋊D47—24no—
202C2×C22⋊D47—24no—
203C2×C22⋊D47—24no—
204C2×C22⋊D47—44no—
205C2×C22⋊D47—82no—
206C2×C22⋊D47—82no—
207C2×C22⋊D47—82no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47C2×D411yescharacteristic
213C22×Dic47C2×D411yescharacteristic
214C2×D188—42no—
215C2×D188C2×D414yes—
216C2×C4×D47—22no—
217C2×C4×D47—22no—
218C2×C4×D47—22no—
219C2×C4×D47—22no—
220C2×C4×D47—24no—
221C2×C4×D47—82no—
222C2×C4×D47C2×D412yes—
223C2×C4×D47C2×D412yes—
224C2×C4×D47C2412yes—
225C2×C4×D47C2412yes—
226C2×Dic94—24no—
227C2×Dic94—82no—
228D8×C47—28no—
229C2×C8×C47—22no—
230C2×C8×C47#4114yes—
231C2×C8×C47C2412yes—
232C2×C8×C47C2412yes—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C22⋊C4×C47—24no—
238C22⋊C4×C47—24no—
239C42×C47C2×D412yes—
240C42×C47C2412yes—
241C22⋊Dic47—24no—
242C22⋊Dic47—24no—
243C22⋊Dic47—24no—
244C22⋊Dic47—24no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4C2×D414yes—
249(C2×D47)⋊C4C2×D414yes—
250C4⋊Dic47—21no—
251C4⋊Dic47—24no—
252C4⋊Dic47—21no—
253C4⋊Dic47—21no—
254C4⋊Dic47—21no—
255C4⋊Dic47C2×D414yes—
256C4⋊Dic47C2412yes—
257C4⋊Dic47C2412yes—
258C4⋊Dic47C2412yes—
259C4⋊Dic47C2412yes—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263C4×Dic47—24no—
264C4×Dic47—24no—
265C4×Dic47—24no—
266C2×C47⋊C8—22no—
267C2×C47⋊C8—22no—
268C2×C47⋊C8C2412yes—
269C2×C47⋊C8C2412yes—
270#10625324—28no—
271C8×D47—28no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—42no—
275C23×C47—42no—
276C23×C47—42no—
277C23×C47—42no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47C22×D411yescharacteristic
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—22no—
285C22×D47—22no—
286C22×D47—22no—
287C22×D47C22×D412yes—
288C22×D47C22×D412yes—
289D4×C47—22no—
290D4×C47—22no—
291D4×C47—22no—
292D4×C47—22no—
293D4×C47—42no—
294D4×C47—42no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—48no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—84no—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D412yes—
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C2×#4112yes—
307C2×C4×C472−1+412yes—
308C2×C4×C47C2511yescharacteristic
309C22⋊D47—48no—
310C22⋊D47—84no—
311C22⋊D47—84no—
312C22⋊D47—84no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47C22×D412yes—
324C2×Dic47C22×D412yes—
325D188—44no—
326C4×D47—24no—
327C4×D47—24no—
328C4×D47—22no—
329C4×D47—22no—
330C4×D47—22no—
331C4×D47—22no—
332C4×D47—84no—
333Dic94—84no—
334C8×C47—22no—
335C8×C47C2×#4114yes—
336C47⋊C8—22no—
337C47⋊C8—22no—
338C2×#3347—471nomaximal, Sylow
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—84no—
346C22×C47—84no—
347C22×C47#54712yes—
348C22×C47#57512yes—
349C22×C47#57612yes—
350C22×C47C23×D411yescharacteristic
351C2×D47—22no—
352C2×D47—22no—
353C2×D47—22no—
354C2×D47—22no—
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—44no—
358C2×D47—44no—
359C4×C47—22no—
360C4×C47—22no—
361C4×C47—42no—
362C4×C47—42no—
363C4×C47#54712yes—
364C4×C47C22×#4111yescharacteristic
365C4×C47C2×2−1+411yescharacteristic
366Dic47—22no—
367Dic47—22no—
368Dic47—42no—
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#555—471no—
373C2×#553—471no—
374#3347—4716no—
375C2×#501—471no—
376C2×#482—471no—
377C2×#482—471no—
378C2×#482—471no—
379C2×#480—471no—
380C2×#478—471no—
381C2×#474—471no—
382C2×#469—471no—
383C2×#466—471no—
384C2×#442D4711yescharacteristic, complemented
385C2×#435—471no—
386C2×#428—471no—
387C2×#427—471no—
388C2×C47—82no—
389C2×C47—82no—
390C2×C47#334714yescomplemented
391C2×C47C2×#54711yescharacteristic
392C2×C47C2×#57511yescharacteristic
393C2×C47C2×#57611yescharacteristic
394D47—42no—
395D47—42no—
396C22×D8C2×D4711yescharacteristic
397C22×M16—471no—
398C23×C8—471no—
399#555—478no—
400#555—944no—
401#553—478no—
402#553—944no—
403C2×C4⋊Q8—471no—
404C2×#126—941no—
405C2×#125—471no—
406C2×#124—941no—
407C2×#124—941no—
408C2×#123—941no—
409C2×#121—471no—
410C2×#121—471no—
411C2×#121—471no—
412C2×#121—471no—
413C2×#121—941no—
414C2×#121—941no—
415C2×C4×D4—471no—
416C2×C4×D4—941no—
417C2×C4×D4C2×D4711yescharacteristic
418C2×C4×D4C2×D4711yescharacteristic
419C2×#117—471no—
420C2×#117—471no—
421C2×#117—471no—
422C2×#117—941no—
423C22×C4⋊C4—471no—
424#501—478no—
425#482—478no—
426#482—478no—
427#482—478no—
428#480—478no—
429#478—478no—
430#474—478no—
431#469—478no—
432#466—478no—
433#442C2×D4718yescomplemented
434#435—478no—
435#428—478no—
436#427—478no—
437C2×#107—471no—
438C2×#107—471no—
439C2×#107—471no—
440C2×#107—471no—
441C2×#107—471no—
442C2×#106—471no—
443C2×#106—471no—
444C2×#106—471no—
445C2×#106C2×D4711yescharacteristic
446C2×C4⋊C8—471no—
447C2×#102—471no—
448C2×#102—471no—
449C2×#102—471no—
450C2×#102—471no—
451C2×#102C2×D4711yescharacteristic
452C2×#102C2×D4711yescharacteristic
453C2×C22⋊C8—471no—
454C2×C22⋊C8—471no—
455C2×#97C2×D4711yescharacteristic
456C47C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—941no—
458C22×D4—471no—
459C22×D4—941no—
460C22×D4—941no—
461C22×D4—941no—
462C22×D4—941no—
463C22×D4C22×D4711yescharacteristic
464C22×D4C22×D4711yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4—941no—
470C2×D8—24no—
471C2×D8C22×D4714yes—
472C2×M16—474no—
473C2×M16—944no—
474C22×C8—471no—
475C22×C8—471no—
476C22×C8—474no—
477C22×C8—944no—
478C22×C8C22×D4711yescharacteristic
479C22×C8C22×D4711yescharacteristic
480C4⋊Q8—474no—
481C4⋊Q8—942no—
482#126—948no—
483#125—474no—
484#125—942no—
485#124—948no—
486#124—948no—
487#123—948no—
488#121—474no—
489#121—474no—
490#121—474no—
491#121—474no—
492#121—948no—
493#121—948no—
494#121—942no—
495#121—942no—
496#121—942no—
497#121—942no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—474no—
501C4×D4—474no—
502C4×D4—948no—
503C4×D4C22×D4714yes—
504C4×D4C22×D4714yes—
505#117—474no—
506#117—474no—
507#117—474no—
508#117—942no—
509#117—942no—
510#117—942no—
511#117—948no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—471no—
514C2×C4⋊C4—471no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—471no—
517C2×C4⋊C4—474no—
518C2×C4⋊C4—942no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4C22×D4711yescharacteristic
524C2×C4⋊C4C22×D4711yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—471no—
528C2×C22⋊C4—471no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C42—941no—
537C2×C42—941no—
538C2×C42—941no—
539C2×C42C22×D4711yescharacteristic
540#107—474no—
541#107—474no—
542#107—474no—
543#107—474no—
544#107—474no—
545#106—474no—
546#106—474no—
547#106—474no—
548#106C22×D4714yes—
549C4⋊C8—474no—
550#102—474no—
551#102—474no—
552#102—474no—
553#102—474no—
554#102C22×D4714yes—
555#102C22×D4714yes—
556C22⋊C8—474no—
557C22⋊C8—474no—
558#97C22×D4714yes—
559C24—21no—
560C24—21no—
561C24—471no—
562C24—471no—
563C2×Q8—944no—
564C2×Q8—3762no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—474no—
572C2×D4—944no—
573C2×D4—944no—
574C2×D4—944no—
575C2×D4—944no—
576C2×D4—3762no—
577C2×D4—3762no—
578C2×D4—3762no—
579C2×D4—1882no—
580C2×D4—1884no—
581C2×D4C23×D4712yes—
582C2×D4C23×D4712yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—82no—
589C22×C4—471no—
590C22×C4—471no—
591C22×C4—472no—
592C22×C4—472no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—944no—
596C22×C4—942no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—3762no—
605C22×C4D4×D4711yescharacteristic
606C22×C4D4×D4711yescharacteristic
607C22×C4C23×D4711yescharacteristic
608D8—28no—
609M16—948no—
610C2×C8—22no—
611C2×C8—472no—
612C2×C8—472no—
613C2×C8—942no—
614C2×C8—942no—
615C2×C8—948no—
616C2×C8#1062535014yes—
617C2×C8C23×D4712yes—
618C2×C8C23×D4712yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—474no—
622C4⋊C4—472no—
623C4⋊C4—472no—
624C4⋊C4—472no—
625C4⋊C4—472no—
626C4⋊C4—944no—
627C4⋊C4—944no—
628C4⋊C4—944no—
629C4⋊C4—941no—
630C4⋊C4—941no—
631C4⋊C4—941no—
632C4⋊C4—941no—
633C4⋊C4—944no—
634C4⋊C4C23×D4712yes—
635C4⋊C4C23×D4712yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—474no—
639C22⋊C4—474no—
640C22⋊C4—944no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C42—944no—
648C42—944no—
649C42—944no—
650C42D4×D4712yes—
651C42C23×D4712yes—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—472no—
661C23—472no—
662C23—942no—
663C23—942no—
664C23—942no—
665C23—942no—
666C23—942no—
667C23—942no—
668C23C2×D4×D4711yescharacteristic
669Q8—3764no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—22no—
674D4—42no—
675D4—42no—
676D4—3764no—
677D4—3764no—
678D4—3764no—
679D4—1884no—
680D4—1888no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—48no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—84no—
689C2×C4—472no—
690C2×C4—472no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—944no—
694C2×C4—944no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—3764no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4—1882no—
707C2×C4—1882no—
708C2×C4C2×D4×D4712yes—
709C2×C4C2×D4×D4712yes—
710C2×C4C2×D4×D4711yescharacteristic
711C2×C4C2×#1062535012yes—
712C2×C4#1309407112yes—
713C2×C4C24×D4711yescharacteristic
714C8—22no—
715C8—942no—
716C8—942no—
717C8C2×#1062535014yes—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—84no—
726C22—942no—
727C22—942no—
728C22—942no—
729C22—942no—
730C22—942no—
731C22—942no—
732C22—1884no—
733C22—1884no—
734C22#1568977812yes—
735C22#1568991912yes—
736C22#1568992712yes—
737C22C22×D4×D4711yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—942no—
743C4—942no—
744C4—1882no—
745C4—1882no—
746C4—1882no—
747C4—1882no—
748C4#1568977812yes—
749C4C22×#1062535011yescharacteristic
750C4C2×#1309407111yescharacteristic
751C2—82no—
752C2—82no—
753C2—1882no—
754C2—1882no—
755C2#2025589314yesdirect product factor
756C2C2×#1568977811yescharacteristic
757C2C2×#1568991911yescharacteristic
758C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#442C2
socleC23×C47C22×D4
hypercenterC2×#442D47
hypocenterC47C2×#3347
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#15689838C2semidirect
2. C2×#15689823C2semidirect
3. #20255893C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689446C2semidirect
6. C2×#15689446C2semidirect
7. C2×#15689445C2semidirect
8. C2×#15689435C2semidirect
9. C2×#15689423C2semidirect
10. C2×#15689403C2semidirect
11. C2×#15689373C2semidirect
12. C2×#15689356C2semidirect
13. C2×#15689196C2semidirect
14. C2×#15689162C2semidirect
15. C2×#15689158C2semidirect
16. C2×C47×#442C2semidirect
20. #15689838C22semidirect
22. #15689823C22semidirect
42. #15689532C22semidirect
43. #15689446C22semidirect
44. #15689446C22semidirect
45. #15689445C22semidirect
46. #15689435C22semidirect
47. #15689423C22semidirect
48. #15689403C22semidirect
49. #15689373C22semidirect
50. #15689356C22semidirect
51. #15689196C22semidirect
52. #15689162C22semidirect
53. #15689158C22semidirect
72. C47×#442C22semidirect
384. C2×#442D47semidirect
390. C2×C47#3347semidirect
433. #442C2×D47semidirect
456. C47C2×#3347semidirect
755. C2#20255893direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898382
C2×#156898232
#202558932
C2×#156895322
C2×#156894462
C2×#156894452
C2×#156894352
C2×#156894232
C2×#156894032
C2×#156893732
C2×#156893562
C2×#156891962
C2×#156891622
C2×#156891582
C2×C47×#4422
C2×#334747