Finite Group Databasebeta

← C2×#20255953 #27094961

Subgroups — C2×#20255953 #27094961

Order 12032.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689823C211yesmaximal, characteristic
2C2×#15689814C211yesmaximal, characteristic, complemented
3#20255953C2116yesmaximal, direct product factor
4C2×#15689525C211yesmaximal, characteristic, complemented
5C2×#15689440C211yesmaximal, characteristic, complemented
6C2×#15689462C211yesmaximal, characteristic, complemented
7C2×#15689446C211yesmaximal, characteristic, complemented
8C2×#15689452C211yesmaximal, characteristic, complemented
9C2×#15689430C211yesmaximal, characteristic, complemented
10C2×#15689423C211yesmaximal, characteristic, complemented
11C2×#15689366C211yesmaximal, characteristic, complemented
12C2×#15689366C211yesmaximal, characteristic, complemented
13C2×#15689202C211yesmaximal, characteristic, complemented
14C2×#15689162C211yesmaximal, characteristic, complemented
15C2×#15689162C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
17C22×#10625324C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19#15689823—24no—
20#15689823C2218yes—
21#15689814—24no—
22#15689814C2218yescomplemented
23C2×#13094018—21no—
24C2×#13094017—21no—
25C2×#13094016C2211yescharacteristic
26C2×#13094016C2211yescharacteristic
27C2×#13094014—21no—
28C2×#13094009—21no—
29C2×#13094007—21no—
30C2×#13094000C2211yescharacteristic
31C2×#13094000C2211yescharacteristic
32C2×#13093997—21no—
33C2×#13093995C2211yescharacteristic
34C2×#13093995C2211yescharacteristic
35C2×C4×D188C2211yescharacteristic
36C2×C4×C22⋊D47—21no—
37C2×#13093982C2211yescharacteristic
38C2×#13093982C2211yescharacteristic
39C2×#13093981—21no—
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689525C2218yescomplemented
43#15689462C2218yescomplemented
44#15689452C2218yescomplemented
45#15689446C2218yescomplemented
46#15689440C2218yescomplemented
47#15689430C2218yescomplemented
48#15689423C2218yescomplemented
49#15689366C2218yescomplemented
50#15689366C2218yescomplemented
51#15689202C2218yescomplemented
52#15689162C2218yescomplemented
53#15689162C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61C2×#13093955C2211yescharacteristic
62C2×C4⋊(C47⋊C8)C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093945C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C4×SD16×C47C2218yescomplemented
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×D188D411yescharacteristic
78C22×C22⋊D47—21no—
79C22×C22⋊D47—21no—
80C22×C4×D47—21no—
81C22×C4×D47—21no—
82C22×C4×D47C2311yescharacteristic
83C22×C4×D47C2311yescharacteristic
84C2×#10625324—24no—
85C2×#10625324—24no—
86C2×#10625324C2314yes—
87C2×#10625324C2314yes—
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90#13094018—28no—
91#13094017—28no—
92#13094016—22no—
93#13094016—22no—
94#13094016C2314yes—
95#13094016C2314yes—
96#13094014—28no—
97#13094009—28no—
98#13094007—28no—
99#13094000—22no—
100#13094000—22no—
101#13094000C2314yes—
102#13094000C2314yes—
103#13093997—28no—
104#13093995—22no—
105#13093995—22no—
106#13093995C2314yes—
107#13093995C2314yes—
108C4×D188D414yes—
109C4×D188C2314yes—
110C4×C22⋊D47—28no—
111#13093982—22no—
112#13093982—22no—
113#13093982C2314yes—
114#13093982C2314yes—
115#13093981—28no—
116C2×C4⋊Dic47D411yescharacteristic
117C2×C4⋊Dic47C2311yescharacteristic
118C2×C4⋊Dic47C2311yescharacteristic
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×Dic47⋊C4—21no—
122C2×Dic47⋊C4—21no—
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C4⋊C4×D47—22no—
130C4⋊C4×D47—22no—
131C4⋊C4×D47C2314yes—
132C4⋊C4×D47C2314yes—
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)⋊C4—21no—
139C2×(C2×D47)⋊C4D411yescharacteristic
140C2×(C2×D47)⋊C4D411yescharacteristic
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143#13093958C2314yes—
144#13093958C2314yes—
145#13093957C2314yes—
146#13093957C2314yes—
147#13093956C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152#13093948C2314yes—
153#13093948C2314yes—
154#13093945C2314yes—
155#13093945C2314yes—
156(C2×D47)⋊C8C2314yes—
157(C2×D47)⋊C8C2314yes—
158C22×Q8×C47C2311yescharacteristic
159C22×D4×C47C2311yescharacteristic
160C23×C4×C47—21no—
161C2×SD16×C47—24no—
162C2×SD16×C47C2314yes—
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C4×Q8×C47—22no—
166C4×Q8×C47C2314yes—
167C4×D4×C47—22no—
168C4×D4×C47C2314yes—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C22⋊C4×C47—21no—
173C2×C42×C47—21no—
174C2×C42×C47C2311yescharacteristic
175#106×C47C2314yes—
176#103×C47C2314yes—
177#102×C47C2314yes—
178C4×C8×C47C2314yes—
179C24×C47—21no—
180C23×D47C2×D411yescharacteristic
181C23×D47C2×D411yescharacteristic
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47—22no—
185C2×Q8×C47C2412yes—
186C2×D4×C47—21no—
187C2×D4×C47—22no—
188C2×D4×C47—22no—
189C2×D4×C47C2412yes—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—24no—
194C22×C4×C47—82no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198C2×C22⋊D47—24no—
199C2×C22⋊D47—24no—
200C2×C22⋊D47—44no—
201C2×C22⋊D47—82no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C2×D188—42no—
209C2×D188C2×D414yes—
210C2×C4×D47—22no—
211C2×C4×D47—22no—
212C2×C4×D47—22no—
213C2×C4×D47—22no—
214C2×C4×D47—24no—
215C2×C4×D47—24no—
216C2×C4×D47—44no—
217C2×C4×D47—82no—
218C2×C4×D47C2×D412yes—
219C2×C4×D47C2×D412yes—
220C2×C4×D47C2412yes—
221C2×C4×D47C2412yes—
222SD16×C47—28no—
223C2×C8×C47—22no—
224C2×C8×C47#4114yes—
225C2×C8×C47C2412yes—
226C2×C8×C47C2412yes—
227C4⋊C4×C47—24no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47C2412yes—
231C4⋊C4×C47C2412yes—
232C22⋊C4×C47—24no—
233C42×C47—24no—
234C42×C47C2×D412yes—
235C42×C47C2412yes—
236C22⋊Dic47—24no—
237C22⋊Dic47—24no—
238(C2×D47)⋊C4—24no—
239(C2×D47)⋊C4—24no—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4C2×D414yes—
243(C2×D47)⋊C4C2×D414yes—
244C4⋊Dic47—21no—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47C2×D414yes—
249C4⋊Dic47C2412yes—
250C4⋊Dic47C2412yes—
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—
263C2×C47⋊C8—22no—
264C2×C47⋊C8—22no—
265C2×C47⋊C8C2412yes—
266C2×C47⋊C8C2412yes—
267#10625324—28no—
268#10625324—28no—
269C23×C47—22no—
270C23×C47—42no—
271C23×C47—42no—
272C23×C47—42no—
273C23×C47C22×D411yescharacteristic
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47C22×D412yes—
281C22×D47C22×D412yes—
282Q8×C47—22no—
283Q8×C47—22no—
284Q8×C47—42no—
285D4×C47—22no—
286D4×C47—22no—
287D4×C47—42no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—84no—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D412yes—
299C2×C4×C47C22×D411yescharacteristic
300C2×C4×C47C2×#4112yes—
301C2×C4×C472−1+412yes—
302C2×C4×C47C2511yescharacteristic
303C22⋊D47—48no—
304C22⋊D47—84no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47C22×D412yes—
316C2×Dic47C22×D412yes—
317D188—44no—
318C4×D47—24no—
319C4×D47—24no—
320C4×D47—22no—
321C4×D47—22no—
322C4×D47—22no—
323C4×D47—22no—
324C4×D47—48no—
325C4×D47—84no—
326C8×C47—22no—
327C8×C47C2×#4114yes—
328C47⋊C8—22no—
329C47⋊C8—22no—
330C2×#3351—471nomaximal, Sylow
331C22×C47—42no—
332C22×C47—42no—
333C22×C47—42no—
334C22×C47—84no—
335C22×C47#54712yes—
336C22×C47#57512yes—
337C22×C47#57712yes—
338C22×C47C23×D411yescharacteristic
339C2×D47—22no—
340C2×D47—22no—
341C2×D47—22no—
342C2×D47—22no—
343C2×D47—22no—
344C2×D47—22no—
345C2×D47—44no—
346C2×D47—44no—
347C4×C47—22no—
348C4×C47—22no—
349C4×C47—42no—
350C4×C47—42no—
351C4×C47—42no—
352C4×C47#54712yes—
353C4×C47C22×#4111yescharacteristic
354C4×C47C2×2−1+411yescharacteristic
355Dic47—22no—
356Dic47—22no—
357Dic47—42no—
358Dic47—42no—
359Dic47—42no—
360Dic47—42no—
361C2×#553—471no—
362C2×#552—471no—
363#3351—4716no—
364C2×#499—471no—
365C2×#481—471no—
366C2×#485—471no—
367C2×#482—471no—
368C2×#483—471no—
369C2×#479—471no—
370C2×#478—471no—
371C2×#468—471no—
372C2×#468—471no—
373C2×C4×SD16D4711yescharacteristic, complemented
374C2×#436—471no—
375C2×#428—471no—
376C2×#428—471no—
377C2×C47—82no—
378C2×C47#335114yescomplemented
379C2×C47C2×#54711yescharacteristic
380C2×C47C2×#57511yescharacteristic
381C2×C47C2×#57711yescharacteristic
382D47—42no—
383D47—42no—
384C22×SD16C2×D4711yescharacteristic
385C22×M16—471no—
386C22×M16—471no—
387#553—478no—
388#553—944no—
389#552—478no—
390#552—944no—
391C2×#126—941no—
392C2×#126—941no—
393C2×#125—471no—
394C2×#125—471no—
395C2×#125—941no—
396C2×#123—941no—
397C2×#123—941no—
398C2×C22⋊Q8—471no—
399C2×C22⋊Q8—471no—
400C2×#121—471no—
401C2×#121—471no—
402C2×#121—941no—
403C2×C4×Q8C2×D4711yescharacteristic
404C2×C4×D4—471no—
405C2×C4×D4—941no—
406C2×C4×D4C2×D4711yescharacteristic
407C2×#117—471no—
408C2×#117—471no—
409C2×#117—941no—
410C22×C4⋊C4—471no—
411C22×C4⋊C4—471no—
412#499—478no—
413#485—478no—
414#483—478no—
415#482—478no—
416#481—478no—
417#479—478no—
418#478—478no—
419#468—478no—
420#468—478no—
421C4×SD16C2×D4718yescomplemented
422#436—478no—
423#428—478no—
424#428—478no—
425C2×#107—471no—
426C2×#107—471no—
427C2×#107—471no—
428C2×#107—471no—
429C2×#106—471no—
430C2×#106—471no—
431C2×#106—471no—
432C2×#106—471no—
433C2×#106C2×D4711yescharacteristic
434C2×C4⋊C8—471no—
435C2×#103—471no—
436C2×#103—471no—
437C2×#103C2×D4711yescharacteristic
438C2×#102—471no—
439C2×#102—471no—
440C2×#102C2×D4711yescharacteristic
441C2×C22⋊C8—471no—
442C2×C22⋊C8—471no—
443C2×C4×C8C2×D4711yescharacteristic
444C47C2×#335111yescharacteristic, complemented, Sylow
445C22×Q8C22×D4711yescharacteristic
446C22×D4—471no—
447C22×D4—941no—
448C22×D4—941no—
449C22×D4C22×D4711yescharacteristic
450C23×C4—21no—
451C23×C4—471no—
452C23×C4—471no—
453C23×C4—941no—
454C23×C4—941no—
455C2×SD16—24no—
456C2×SD16C22×D4714yes—
457C2×M16—474no—
458C2×M16—474no—
459C2×M16—944no—
460C2×M16—944no—
461C22×C8—471no—
462C22×C8—471no—
463C22×C8C22×D4711yescharacteristic
464C22×C8C22×D4711yescharacteristic
465#126—948no—
466#126—948no—
467#125—474no—
468#125—474no—
469#125—948no—
470#125—942no—
471#125—942no—
472#123—948no—
473#123—948no—
474C22⋊Q8—474no—
475C22⋊Q8—474no—
476C22⋊Q8—942no—
477C22⋊Q8—942no—
478#121—474no—
479#121—474no—
480#121—948no—
481#121—942no—
482#121—942no—
483C4×Q8—22no—
484C4×Q8C22×D4714yes—
485C4×D4—22no—
486C4×D4—474no—
487C4×D4—474no—
488C4×D4—948no—
489C4×D4C22×D4714yes—
490#117—474no—
491#117—474no—
492#117—948no—
493#117—942no—
494#117—942no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—474no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—942no—
504C2×C4⋊C4—942no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
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⋊C4C22×D4711yescharacteristic
514C2×C4⋊C4C22×D4711yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—471no—
517C2×C22⋊C4—471no—
518C2×C22⋊C4—941no—
519C2×C22⋊C4—941no—
520C2×C22⋊C4—941no—
521C2×C22⋊C4—941no—
522C2×C22⋊C4—941no—
523C2×C22⋊C4—941no—
524C2×C42—21no—
525C2×C42—941no—
526C2×C42—941no—
527C2×C42C22×D4711yescharacteristic
528#107—474no—
529#107—474no—
530#107—474no—
531#107—474no—
532#106—474no—
533#106—474no—
534#106—474no—
535#106—474no—
536#106C22×D4714yes—
537C4⋊C8—474no—
538#103—474no—
539#103—474no—
540#103C22×D4714yes—
541#102—474no—
542#102—474no—
543#102C22×D4714yes—
544C22⋊C8—474no—
545C22⋊C8—474no—
546C4×C8C22×D4714yes—
547C24—21no—
548C24—471no—
549C24—471no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8C23×D4712yes—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—474no—
558C2×D4—944no—
559C2×D4—944no—
560C2×D4—3762no—
561C2×D4—1882no—
562C2×D4—1884no—
563C2×D4C23×D4712yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—471no—
570C22×C4—471no—
571C22×C4—472no—
572C22×C4—472no—
573C22×C4—472no—
574C22×C4—472no—
575C22×C4—944no—
576C22×C4—944no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—3762no—
586C22×C4—1884no—
587C22×C4D4×D4711yescharacteristic
588C22×C4D4×D4711yescharacteristic
589C22×C4C23×D4711yescharacteristic
590SD16—28no—
591M16—948no—
592M16—948no—
593C2×C8—22no—
594C2×C8—472no—
595C2×C8—472no—
596C2×C8—942no—
597C2×C8—942no—
598C2×C8#1062535014yes—
599C2×C8C23×D4712yes—
600C2×C8C23×D4712yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—474no—
605C4⋊C4—472no—
606C4⋊C4—472no—
607C4⋊C4—472no—
608C4⋊C4—472no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—944no—
612C4⋊C4—944no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—944no—
616C4⋊C4—944no—
617C4⋊C4—941no—
618C4⋊C4—941no—
619C4⋊C4—941no—
620C4⋊C4—941no—
621C4⋊C4C23×D4712yes—
622C4⋊C4C23×D4712yes—
623C22⋊C4—24no—
624C22⋊C4—474no—
625C22⋊C4—474no—
626C22⋊C4—944no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C22⋊C4—944no—
630C22⋊C4—944no—
631C22⋊C4—944no—
632C42—24no—
633C42—944no—
634C42—944no—
635C42D4×D4712yes—
636C42C23×D4712yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—472no—
642C23—472no—
643C23—942no—
644C23—942no—
645C23—942no—
646C23—942no—
647C23—942no—
648C23—942no—
649C23C2×D4×D4711yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—22no—
654D4—22no—
655D4—42no—
656D4—3764no—
657D4—1884no—
658D4—1888no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—84no—
668C2×C4—472no—
669C2×C4—472no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—944no—
673C2×C4—944no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—3764no—
683C2×C4—1888no—
684C2×C4—1882no—
685C2×C4—1882no—
686C2×C4—1882no—
687C2×C4—1882no—
688C2×C4C2×D4×D4712yes—
689C2×C4C2×D4×D4712yes—
690C2×C4C2×D4×D4711yescharacteristic
691C2×C4C2×#1062535012yes—
692C2×C4#1309407112yes—
693C2×C4C24×D4711yescharacteristic
694C8—22no—
695C8—942no—
696C8—942no—
697C8C2×#1062535014yes—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—84no—
702C22—942no—
703C22—942no—
704C22—942no—
705C22—942no—
706C22—942no—
707C22—942no—
708C22—1884no—
709C22—1884no—
710C22#1568977812yes—
711C22#1568992012yes—
712C22#1568992912yes—
713C22C22×D4×D4711yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—942no—
720C4—942no—
721C4—1882no—
722C4—1882no—
723C4—1882no—
724C4—1882no—
725C4#1568977812yes—
726C4C22×#1062535011yescharacteristic
727C4C2×#1309407111yescharacteristic
728C2—82no—
729C2—1882no—
730C2—1882no—
731C2#2025595314yesdirect product factor
732C2C2×#1568977811yescharacteristic
733C2C2×#1568992011yescharacteristic
734C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×SD16×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689823C2
hypercenterC2×C4×SD16D47
hypocenterC47C2×#3351
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#15689814C2semidirect
3. #20255953C2direct (N × H)
4. C2×#15689525C2semidirect
5. C2×#15689440C2semidirect
6. C2×#15689462C2semidirect
7. C2×#15689446C2semidirect
8. C2×#15689452C2semidirect
9. C2×#15689430C2semidirect
10. C2×#15689423C2semidirect
11. C2×#15689366C2semidirect
12. C2×#15689366C2semidirect
13. C2×#15689202C2semidirect
14. C2×#15689162C2semidirect
15. C2×#15689162C2semidirect
16. C2×C4×SD16×C47C2semidirect
22. #15689814C22semidirect
42. #15689525C22semidirect
43. #15689462C22semidirect
44. #15689452C22semidirect
45. #15689446C22semidirect
46. #15689440C22semidirect
47. #15689430C22semidirect
48. #15689423C22semidirect
49. #15689366C22semidirect
50. #15689366C22semidirect
51. #15689202C22semidirect
52. #15689162C22semidirect
53. #15689162C22semidirect
72. C4×SD16×C47C22semidirect
373. C2×C4×SD16D47semidirect
378. C2×C47#3351semidirect
421. C4×SD16C2×D47semidirect
444. C47C2×#3351semidirect
731. C2#20255953direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898232
C2×#156898142
#202559532
C2×#156895252
C2×#156894402
C2×#156894622
C2×#156894462
C2×#156894522
C2×#156894302
C2×#156894232
C2×#156893662
C2×#156892022
C2×#156891622
C2×C4×SD16×C472
C2×#335147