Finite Group Databasebeta

← C2×#20255890 #27094875

Subgroups — C2×#20255890 #27094875

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×#15689819C211yesmaximal, characteristic, complemented
3#20255890C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689448C211yesmaximal, characteristic, complemented
6C2×#15689448C211yesmaximal, characteristic, complemented
7C2×#15689448C211yesmaximal, characteristic, complemented
8C2×#15689437C211yesmaximal, characteristic, complemented
9C2×#15689424C211yesmaximal, characteristic, complemented
10C2×#15689404C211yesmaximal, characteristic, complemented
11C2×#15689376C211yesmaximal, characteristic, complemented
12C2×#15689359C211yesmaximal, characteristic, complemented
13C2×#15689236C211yesmaximal, characteristic, complemented
14C2×#15689165C211yesmaximal, characteristic, complemented
15C2×#15689161C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic, complemented
17C22×D376C2211yescharacteristic
18#15689838—24no—
19#15689838C2218yescomplemented
20#15689819—24no—
21#15689819C2218yescomplemented
22C2×#13094024C2211yescharacteristic
23C2×#13094019—21no—
24C2×#13094016C2211yescharacteristic
25C2×#13094010—21no—
26C2×#13094010—21no—
27C2×#13094006—21no—
28C2×#13093998C2211yescharacteristic
29C2×#13093998C2211yescharacteristic
30C2×#13093998C2211yescharacteristic
31C2×#13093998C2211yescharacteristic
32C2×#13093996—21no—
33C2×#13093995—21no—
34C2×C4×D188C2211yescharacteristic
35C2×C4×D188C2211yescharacteristic
36C2×(C22⋊D47)⋊C4—21no—
37C2×#13093983C2211yescharacteristic
38C2×#13093983C2211yescharacteristic
39C2×#13093983C2211yescharacteristic
40C2×#13093982—21no—
41C22×C4⋊Dic47C2211yescharacteristic
42#15689532C2218yescomplemented
43#15689448C2218yescomplemented
44#15689448C2218yescomplemented
45#15689448C2218yescomplemented
46#15689437C2218yescomplemented
47#15689424C2218yescomplemented
48#15689404C2218yescomplemented
49#15689376C2218yescomplemented
50#15689359C2218yescomplemented
51#15689236C2218yescomplemented
52#15689165C2218yescomplemented
53#15689161C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093958C2211yescharacteristic
56C2×#13093958C2211yescharacteristic
57C2×#13093958C2211yescharacteristic
58C2×#13093958C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093956C2211yescharacteristic
61C2×#13093956C2211yescharacteristic
62C2×#13093956C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C22×M16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#435C2218yescomplemented
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×D188C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C22⋊D47—21no—
82C22×C22⋊D47—21no—
83C22×C22⋊D47—21no—
84C23×Dic47—21no—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C2×D376—24no—
88C2×D376C2314yes—
89#13094024—22no—
90#13094024C2314yes—
91#13094019—28no—
92#13094016—22no—
93#13094016C2314yes—
94#13094010—28no—
95#13094010—28no—
96#13094006—28no—
97#13093998—22no—
98#13093998—22no—
99#13093998—22no—
100#13093998—22no—
101#13093998C2314yes—
102#13093998C2314yes—
103#13093998C2314yes—
104#13093998C2314yes—
105#13093996—28no—
106#13093995—28no—
107C4×D188—22no—
108C4×D188—22no—
109C4×D188C2314yes—
110C4×D188C2314yes—
111(C22⋊D47)⋊C4—28no—
112#13093983—22no—
113#13093983—22no—
114#13093983—22no—
115#13093983C2314yes—
116#13093983C2314yes—
117#13093983C2314yes—
118#13093982—28no—
119C2×C4⋊Dic47—22no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47C2314yes—
123C2×C4⋊Dic47C2311yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×C22⋊Dic47—21no—
132C2×C22⋊Dic47—21no—
133C2×C22⋊Dic47—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143#13093958C2314yes—
144#13093958C2314yes—
145#13093958C2314yes—
146#13093958C2314yes—
147#13093958C2314yes—
148#13093956C2314yes—
149#13093956C2314yes—
150#13093956C2314yes—
151#13093956C2314yes—
152#13093946C2314yes—
153#13093946C2314yes—
154#13093946C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
158C22×D4×C47D411yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C2×M16×C47—24no—
162C2×M16×C47C2314yes—
163C22×C8×C47—24no—
164C22×C8×C47C2314yes—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C4×D4×C47D414yes—
170C4×D4×C47C2314yes—
171C2×C4⋊C4×C47D411yescharacteristic
172C2×C22⋊C4×C47D411yescharacteristic
173C2×C22⋊C4×C47D411yescharacteristic
174C2×C42×C47C2311yescharacteristic
175C4⋊C8×C47C2314yes—
176C22⋊C8×C47C2314yes—
177C22⋊C8×C47C2314yes—
178#97×C47C2314yes—
179C24×C47C2×D411yescharacteristic
180C24×C47C2×D411yescharacteristic
181C23×D47—21no—
182C23×D47—21no—
183C2×D4×C47—42no—
184C2×D4×C47C2×D414yes—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D412yes—
194C22×C4×C47C2×D412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2411yescharacteristic
198C2×C22⋊D47—24no—
199C2×C22⋊D47—24no—
200C2×C22⋊D47—24no—
201C2×C22⋊D47—24no—
202C2×C22⋊D47—44no—
203C2×C22⋊D47—82no—
204C2×C22⋊D47—82no—
205C2×C22⋊D47—82no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—24no—
213C22×Dic47—82no—
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188—21no—
219C2×D188—21no—
220C2×D188C2412yes—
221C2×D188C2412yes—
222C2×C4×D47—24no—
223C2×C4×D47—24no—
224C2×C4×D47—44no—
225C2×C4×D47—82no—
226C2×Dic94—24no—
227C2×Dic94—82no—
228M16×C47—28no—
229C2×C8×C47—22no—
230C2×C8×C47—22no—
231C2×C8×C47—22no—
232C2×C8×C47—28no—
233C2×C8×C47#4114yes—
234C2×C8×C47C2412yes—
235C2×C8×C47C2412yes—
236C2×C8×C47C2412yes—
237C2×C8×C47C2412yes—
238C4⋊C4×C47C2×D414yes—
239C22⋊C4×C47C2×D414yes—
240C22⋊C4×C47C2×D414yes—
241C42×C47C2×D412yes—
242C42×C47C2412yes—
243C22⋊Dic47—24no—
244C22⋊Dic47—24no—
245C22⋊Dic47—24no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4—24no—
252C4⋊Dic47—21no—
253C4⋊Dic47—21no—
254C4⋊Dic47—24no—
255C4⋊Dic47—24no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47—21no—
259C4⋊Dic47—21no—
260C4⋊Dic47C2412yes—
261C4⋊Dic47C2412yes—
262C4⋊Dic47C2412yes—
263C4⋊Dic47C2412yes—
264C4⋊Dic47C2412yes—
265C4⋊Dic47C2412yes—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268C4×Dic47—24no—
269C4×Dic47—24no—
270C4×Dic47—24no—
271D376—28no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47C22×D412yes—
279C23×C47C22×D412yes—
280C23×C47C22×D411yescharacteristic
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—42no—
284C22×D47—42no—
285C22×D47—42no—
286C22×D47—42no—
287C22×D47—42no—
288C22×D47—42no—
289D4×C47—44no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—24no—
295C2×C4×C47—24no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47C22×D412yes—
301C2×C4×C47C22×D412yes—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C2×#4112yes—
306C2×C4×C472−1+412yes—
307C2×C4×C47C2511yescharacteristic
308C22⋊D47—48no—
309C22⋊D47—84no—
310C22⋊D47—84no—
311C22⋊D47—84no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—84no—
325D188—22no—
326D188—22no—
327D188—22no—
328D188—22no—
329D188—42no—
330D188—42no—
331C4×D47—48no—
332C4×D47—84no—
333Dic94—84no—
334C8×C47—22no—
335C8×C47—22no—
336C8×C47—22no—
337C8×C47C2×#4114yes—
338C2×#3347—471nomaximal, Sylow
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—44no—
346C22×C47—44no—
347C22×C47#54712yes—
348C22×C47#57512yes—
349C22×C47#57612yes—
350C22×C47C23×D411yescharacteristic
351C2×D47—42no—
352C2×D47—42no—
353C2×D47—42no—
354C2×D47—42no—
355C2×D47—42no—
356C2×D47—42no—
357C2×D47—84no—
358C2×D47—84no—
359C4×C47—22no—
360C4×C47—22no—
361C4×C47—22no—
362C4×C47—22no—
363C4×C47#54712yes—
364C4×C47C22×#4111yescharacteristic
365C4×C47C2×2−1+411yescharacteristic
366Dic47—42no—
367Dic47—42no—
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×#442—471no—
385C2×#435D4711yescharacteristic, complemented
386C2×#428—471no—
387C2×#427—471no—
388C2×C47—42no—
389C2×C47—42no—
390C2×C47#334714yescomplemented
391C2×C47C2×#54711yescharacteristic
392C2×C47C2×#57511yescharacteristic
393C2×C47C2×#57611yescharacteristic
394D47—82no—
395D47—82no—
396C22×D8—471no—
397C22×M16C2×D4711yescharacteristic
398C23×C8C2×D4711yescharacteristic
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—471no—
417C2×C4×D4—941no—
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#442—478no—
434#435C2×D4718yescomplemented
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×#106—471no—
446C2×C4⋊C8C2×D4711yescharacteristic
447C2×#102—471no—
448C2×#102—471no—
449C2×#102—471no—
450C2×#102—471no—
451C2×#102—471no—
452C2×#102—471no—
453C2×C22⋊C8C2×D4711yescharacteristic
454C2×C22⋊C8C2×D4711yescharacteristic
455C2×#97C2×D4711yescharacteristic
456C47C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—941no—
458C22×D4—471no—
459C22×D4—471no—
460C22×D4—941no—
461C22×D4—941no—
462C22×D4—941no—
463C22×D4—941no—
464C22×D4D18811yescharacteristic
465C23×C4—941no—
466C23×C4—941no—
467C23×C4—941no—
468C23×C4C22×D4711yescharacteristic
469C23×C4C22×D4711yescharacteristic
470C2×D8—474no—
471C2×D8—944no—
472C2×M16—24no—
473C2×M16C22×D4714yes—
474C22×C8—24no—
475C22×C8C22×D4711yescharacteristic
476C22×C8C22×D4714yes—
477C22×C8C22×D4711yescharacteristic
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—474no—
499C4×D4—474no—
500C4×D4—948no—
501C4×D4—942no—
502C4×D4—942no—
503C4×D4D18814yes—
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—474no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—471no—
517C2×C4⋊C4—471no—
518C2×C4⋊C4—471no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—942no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4D18811yescharacteristic
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4—941no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4D18811yescharacteristic
535C2×C22⋊C4D18811yescharacteristic
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#106—474no—
549C4⋊C8C22×D4714yes—
550#102—474no—
551#102—474no—
552#102—474no—
553#102—474no—
554#102—474no—
555#102—474no—
556C22⋊C8C22×D4714yes—
557C22⋊C8C22×D4714yes—
558#97C22×D4714yes—
559C24—941no—
560C24—941no—
561C24C2×D18811yescharacteristic
562C24C2×D18811yescharacteristic
563C2×Q8—944no—
564C2×Q8—3762no—
565C2×D4—42no—
566C2×D4—472no—
567C2×D4—472no—
568C2×D4—944no—
569C2×D4—944no—
570C2×D4—944no—
571C2×D4—944no—
572C2×D4—941no—
573C2×D4—941no—
574C2×D4—942no—
575C2×D4—942no—
576C2×D4—942no—
577C2×D4—942no—
578C2×D4—3762no—
579C2×D4—3762no—
580C2×D4—3762no—
581C2×D4—1884no—
582C2×D4C2×D18814yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—944no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—944no—
595C22×C4—944no—
596C22×C4—3762no—
597C22×C4—3762no—
598C22×C4—1884no—
599C22×C4C2×D18812yes—
600C22×C4C2×D18812yes—
601C22×C4C2×D18811yescharacteristic
602C22×C4C2×D18811yescharacteristic
603C22×C4C2×D18811yescharacteristic
604C22×C4C2×D18811yescharacteristic
605C22×C4C23×D4712yes—
606C22×C4C23×D4712yes—
607C22×C4C23×D4711yescharacteristic
608D8—948no—
609M16—28no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—28no—
614C2×C8#1062535214yes—
615C2×C8C23×D4712yes—
616C2×C8C23×D4712yes—
617C2×C8C23×D4712yes—
618C2×C8C23×D4712yes—
619C4⋊C4—472no—
620C4⋊C4—472no—
621C4⋊C4—472no—
622C4⋊C4—472no—
623C4⋊C4—472no—
624C4⋊C4—472no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—941no—
628C4⋊C4—941no—
629C4⋊C4—944no—
630C4⋊C4—941no—
631C4⋊C4—941no—
632C4⋊C4—941no—
633C4⋊C4—941no—
634C4⋊C4—944no—
635C4⋊C4C2×D18814yes—
636C22⋊C4—944no—
637C22⋊C4—944no—
638C22⋊C4—944no—
639C22⋊C4—944no—
640C22⋊C4—944no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4C2×D18814yes—
646C22⋊C4C2×D18814yes—
647C42—944no—
648C42—944no—
649C42—944no—
650C42C2×D18812yes—
651C42C23×D4712yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—942no—
659C23—942no—
660C23—1882no—
661C23—1882no—
662C23—1882no—
663C23—1882no—
664C23—1882no—
665C23—1882no—
666C23C22×D18812yes—
667C23C22×D18812yes—
668C23C22×D18811yescharacteristic
669Q8—3764no—
670D4—44no—
671D4—942no—
672D4—942no—
673D4—942no—
674D4—942no—
675D4—3764no—
676D4—3764no—
677D4—3764no—
678D4—1888no—
679D4—1882no—
680D4—1882no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—3764no—
698C2×C4—3764no—
699C2×C4—1888no—
700C2×C4—1882no—
701C2×C4—1882no—
702C2×C4—1882no—
703C2×C4—1882no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4C22×D18812yes—
707C2×C4C22×D18812yes—
708C2×C4C22×D18812yes—
709C2×C4C22×D18812yes—
710C2×C4C22×D18811yescharacteristic
711C2×C4C2×#1062535212yes—
712C2×C4#1309407112yes—
713C2×C4C24×D4711yescharacteristic
714C8—22no—
715C8—22no—
716C8—22no—
717C8C2×#1062535214yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—3764no—
727C22—3764no—
728C22—1882no—
729C22—1882no—
730C22—1882no—
731C22—1882no—
732C22—1882no—
733C22—1882no—
734C22#1568977712yes—
735C22#1568992312yes—
736C22#1568992812yes—
737C22C23×D18811yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—1882no—
743C4—1882no—
744C4—1882no—
745C4—1882no—
746C4—1882no—
747C4—1882no—
748C4#1568977712yes—
749C4C22×#1062535211yescharacteristic
750C4C2×#1309407111yescharacteristic
751C2—42no—
752C2—42no—
753C2—3762no—
754C2—3762no—
755C2#2025589014yesdirect product factor
756C2C2×#1568977711yescharacteristic
757C2C2×#1568992311yescharacteristic
758C2C2×#1568992811yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C22×D4
hypercenterC2×#435D47
hypocenterC47C2×#3347
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#15689838C2semidirect
2. C2×#15689819C2semidirect
3. #20255890C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689448C2semidirect
6. C2×#15689448C2semidirect
7. C2×#15689448C2semidirect
8. C2×#15689437C2semidirect
9. C2×#15689424C2semidirect
10. C2×#15689404C2semidirect
11. C2×#15689376C2semidirect
12. C2×#15689359C2semidirect
13. C2×#15689236C2semidirect
14. C2×#15689165C2semidirect
15. C2×#15689161C2semidirect
16. C2×C47×#435C2semidirect
19. #15689838C22semidirect
21. #15689819C22semidirect
42. #15689532C22semidirect
43. #15689448C22semidirect
44. #15689448C22semidirect
45. #15689448C22semidirect
46. #15689437C22semidirect
47. #15689424C22semidirect
48. #15689404C22semidirect
49. #15689376C22semidirect
50. #15689359C22semidirect
51. #15689236C22semidirect
52. #15689165C22semidirect
53. #15689161C22semidirect
72. C47×#435C22semidirect
385. C2×#435D47semidirect
390. C2×C47#3347semidirect
434. #435C2×D47semidirect
456. C47C2×#3347semidirect
755. C2#20255890direct (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×#156898192
#202558902
C2×#156895322
C2×#156894482
C2×#156894372
C2×#156894242
C2×#156894042
C2×#156893762
C2×#156893592
C2×#156892362
C2×#156891652
C2×#156891612
C2×C47×#4352
C2×#334747