Finite Group Databasebeta

← C2×#20255697 #27093192

Subgroups — C2×#20255697 #27093192

Order 12032.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689831C211yesmaximal, characteristic, complemented
2C2×#15689772C211yesmaximal, characteristic
3#20255697C2116yesmaximal, direct product factor
4C2×#15689472C211yesmaximal, characteristic, complemented
5C2×#15689454C211yesmaximal, characteristic, complemented
6C2×#15689452C211yesmaximal, characteristic, complemented
7C2×#15689411C211yesmaximal, characteristic, complemented
8C2×#15689379C211yesmaximal, characteristic, complemented
9C2×#15689378C211yesmaximal, characteristic, complemented
10C2×#15689331C211yesmaximal, characteristic, complemented
11C2×#15689282C211yesmaximal, characteristic, complemented
12C2×SD16×Dic47C211yesmaximal, characteristic, complemented
13C2×#15689198C211yesmaximal, characteristic, complemented
14C2×#15689124C211yesmaximal, characteristic, complemented
15C2×#15689121C211yesmaximal, characteristic, complemented
16C2×C47×#452C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625329C2211yescharacteristic
20C22×#10625324C2211yescharacteristic
21#15689831—24no—
22#15689831C2218yescomplemented
23#15689772—24no—
24#15689772C2218yes—
25C2×#13094023C2211yescharacteristic
26C2×#13094022C2211yescharacteristic
27C2×#13094014—21no—
28C2×#13094007—21no—
29C2×#13094005—21no—
30C2×#13094004—21no—
31C2×#13094003C2211yescharacteristic
32C2×#13094001—21no—
33C2×#13094000C2211yescharacteristic
34C2×#13094000C2211yescharacteristic
35C2×#13093996—21no—
36C2×Q8×Dic47C2211yescharacteristic
37C2×D4×Dic47C2211yescharacteristic
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×(C22⋊D47)⋊C4—21no—
40C22×C4⋊Dic47C2211yescharacteristic
41C22×Dic47⋊C4—21no—
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689472C2218yescomplemented
44#15689454C2218yescomplemented
45#15689452C2218yescomplemented
46#15689411C2218yescomplemented
47#15689379C2218yescomplemented
48#15689378C2218yescomplemented
49#15689331C2218yescomplemented
50#15689282C2218yescomplemented
51SD16×Dic47C2218yescomplemented
52#15689198C2218yescomplemented
53C2×#13093956C2211yescharacteristic
54C2×#13093956C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×Dic47⋊C8C2211yescharacteristic
57#15689124C2218yescomplemented
58#15689121C2218yescomplemented
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093945C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×#41×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C22×SD16×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#452C2218yescomplemented
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625352—24no—
78C2×#10625352—22no—
79C2×#10625352—42no—
80C2×#10625352C2314yes—
81C22×Dic94—21no—
82C22×Dic94C2311yescharacteristic
83C22×C22⋊D47—21no—
84C22×C22⋊D47D411yescharacteristic
85C23×Dic47—21no—
86C23×Dic47—21no—
87C23×Dic47—21no—
88C22×C4×D47—21no—
89C22×C4×D47C2311yescharacteristic
90C2×#10625337—42no—
91C2×#10625337C2314yes—
92C2×#10625329—42no—
93C2×#10625329C2314yes—
94C2×#10625324—42no—
95C2×#10625324C2314yes—
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2311yescharacteristic
98#13094023—22no—
99#13094023C2314yes—
100#13094022—22no—
101#13094022C2314yes—
102#13094014—28no—
103#13094007—28no—
104#13094005—28no—
105#13094004—28no—
106#13094003—22no—
107#13094003C2314yes—
108#13094001—28no—
109#13094000—22no—
110#13094000—22no—
111#13094000C2314yes—
112#13094000C2314yes—
113#13093996—28no—
114Q8×Dic47—22no—
115Q8×Dic47C2314yes—
116D4×Dic47—22no—
117D4×Dic47C2314yes—
118C4×C22⋊D47D414yes—
119C4×C22⋊D47C2314yes—
120(C22⋊D47)⋊C4—28no—
121C2×C4⋊Dic47—22no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2314yes—
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—28no—
136C2×Dic47⋊C4D411yescharacteristic
137C4⋊C4×D47—22no—
138C4⋊C4×D47C2314yes—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47D411yescharacteristic
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4D411yescharacteristic
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093956C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150Dic47⋊C8C2314yes—
151#13093949C2314yes—
152#13093949C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093947C2314yes—
157#13093945C2314yes—
158#13093945C2314yes—
159(C2×D47)⋊C8C2314yes—
160C8×Dic47C2314yes—
161C2×#41×C47—22no—
162C2×#41×C47—24no—
163C2×#41×C47—42no—
164C2×#41×C47C2314yes—
165C22×Q8×C47C2311yescharacteristic
166C22×Q8×C47C2311yescharacteristic
167C22×D4×C47—21no—
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47C2311yescharacteristic
171C2×Q16×C47—42no—
172C2×Q16×C47C2314yes—
173C2×SD16×C47—24no—
174C2×SD16×C47C2314yes—
175C22×C8×C47C2311yescharacteristic
176C22×C8×C47C2311yescharacteristic
177C22⋊Q8×C47—22no—
178C22⋊Q8×C47C2314yes—
179C2×C4⋊C4×C47—21no—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—21no—
182#103×C47C2314yes—
183#102×C47C2314yes—
184C22⋊C8×C47C2314yes—
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47C2×D411yescharacteristic
188#41×C47—28no—
189#41×C47—44no—
190#41×C47—48no—
191C2×Q8×C47—21no—
192C2×Q8×C47—21no—
193C2×Q8×C47—22no—
194C2×Q8×C47—22no—
195C2×Q8×C47—22no—
196C2×Q8×C47—22no—
197C2×Q8×C47C2412yes—
198C2×Q8×C47C2412yes—
199C2×D4×C47—24no—
200C2×D4×C47—21no—
201C2×D4×C47—22no—
202C2×D4×C47—44no—
203C2×D4×C47#4114yes—
204C2×D4×C47C2412yes—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—24no—
211C22×C4×C47—44no—
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D412yes—
214C22×C4×C47C2412yes—
215C22×C4×C47C2411yescharacteristic
216C2×C22⋊D47—24no—
217C2×C22⋊D47—24no—
218C2×C22⋊D47—44no—
219C2×C22⋊D47C2×D414yes—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—24no—
225C22×Dic47—24no—
226C22×Dic47—24no—
227C22×Dic47—44no—
228C22×Dic47—44no—
229C22×Dic47—82no—
230C22×Dic47C2×D411yescharacteristic
231C22×Dic47C2×D411yescharacteristic
232C22×Dic47C2×D411yescharacteristic
233#10625352—28no—
234#10625352—44no—
235#10625352—48no—
236C2×C4×D47—22no—
237C2×C4×D47—22no—
238C2×C4×D47—24no—
239C2×C4×D47—82no—
240C2×C4×D47C2×D412yes—
241C2×C4×D47C2412yes—
242C2×Dic94—22no—
243C2×Dic94—22no—
244C2×Dic94—21no—
245C2×Dic94—24no—
246C2×Dic94—82no—
247C2×Dic94C2412yes—
248Q16×C47—44no—
249SD16×C47—28no—
250C2×C8×C47—22no—
251C2×C8×C47—22no—
252C2×C8×C47C2412yes—
253C2×C8×C47C2412yes—
254C4⋊C4×C47—24no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47C2412yes—
257C22⋊C4×C47—24no—
258C22⋊Dic47—24no—
259C22⋊Dic47—24no—
260C22⋊Dic47C2×D414yes—
261#10625337—44no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4C2×D414yes—
265C4⋊Dic47—21no—
266C4⋊Dic47—21no—
267C4⋊Dic47—24no—
268C4⋊Dic47—21no—
269C4⋊Dic47—24no—
270C4⋊Dic47C2412yes—
271C4⋊Dic47C2412yes—
272C4⋊Dic47C2412yes—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4—24no—
280Dic47⋊C4C2×D414yes—
281C4×Dic47—24no—
282C4×Dic47C2×D412yes—
283C4×Dic47C2412yes—
284#10625329—44no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8C2412yes—
288C2×C47⋊C8C2412yes—
289#10625324—44no—
290C23×C47—24no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—42no—
296C23×C47—42no—
297C23×C47C22×D412yes—
298C23×C47C22×D411yescharacteristic
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47C22×D412yes—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47—22no—
306Q8×C47—22no—
307Q8×C47—42no—
308Q8×C47—42no—
309D4×C47—24no—
310D4×C47—22no—
311D4×C47—48no—
312D4×C47C2×#4114yes—
313C2×C4×C47—22no—
314C2×C4×C47—24no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—48no—
321C2×C4×C47—42no—
322C2×C4×C47—42no—
323C2×C4×C47—42no—
324C2×C4×C47C22×D412yes—
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C2×#4112yes—
327C2×C4×C47H(5,𝔽2)12yes—
328C2×C4×C47C2511yescharacteristic
329C22⋊D47—28no—
330C22⋊D47—48no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—48no—
338C2×Dic47—42no—
339C2×Dic47—42no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—48no—
343C2×Dic47—84no—
344C2×Dic47#13714yes—
345C2×Dic47C22×D412yes—
346C2×Dic47C22×D412yes—
347C2×Dic47C22×D412yes—
348C4×D47—24no—
349C4×D47—22no—
350C4×D47—22no—
351C4×D47—84no—
352Dic94—22no—
353Dic94—22no—
354Dic94—42no—
355Dic94—84no—
356C8×C47—22no—
357C8×C47—22no—
358C47⋊C8—22no—
359C47⋊C8—22no—
360C2×#3331—471nomaximal, Sylow
361C22×C47—24no—
362C22×C47—22no—
363C22×C47—22no—
364C22×C47—22no—
365C22×C47—44no—
366C22×C47—48no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47#54612yes—
370C22×C47C2×#13712yes—
371C22×C47#57712yes—
372C22×C47C23×D411yescharacteristic
373C2×D47—22no—
374C2×D47—22no—
375C2×D47—22no—
376C2×D47—44no—
377C4×C47—22no—
378C4×C47—42no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47#54612yes—
382C4×C47C22×#4111yescharacteristic
383C4×C47C2×H(5,𝔽2)11yescharacteristic
384Dic47—22no—
385Dic47—22no—
386Dic47—42no—
387Dic47—42no—
388Dic47—42no—
389Dic47—42no—
390Dic47C2×#13714yes—
391C2×#554—471no—
392C2×#547—471no—
393#3331—4716no—
394C2×#487—471no—
395C2×#483—471no—
396C2×#483—471no—
397C2×#476—471no—
398C2×#470—471no—
399C2×#470—471no—
400C2×#462—471no—
401C2×#452—471no—
402C2×#452D4711yescharacteristic, complemented
403C2×C4×SD16—471no—
404C2×#436—471no—
405C2×#417—471no—
406C2×#417—471no—
407C2×C47—42no—
408C2×C47—44no—
409C2×C47#333114yescomplemented
410C2×C47C2×#54611yescharacteristic
411C2×C47C22×#13711yescharacteristic
412C2×C47C2×#57711yescharacteristic
413D47—42no—
414C22×#41—471no—
415C22×#41C2×D4711yescharacteristic
416C22×Q16—471no—
417C22×Q16C2×D4711yescharacteristic
418C22×SD16C2×D4711yescharacteristic
419C22×M16—471no—
420C22×M16—471no—
421#554—478no—
422#554—944no—
423#547—478no—
424#547—944no—
425C2×C4⋊Q8—471no—
426C2×C4⋊Q8—471no—
427C2×#125—941no—
428C2×#123—941no—
429C2×#123—941no—
430C2×C22⋊Q8—471no—
431C2×C22⋊Q8—471no—
432C2×C22⋊Q8—471no—
433C2×C22⋊Q8—941no—
434C2×C22⋊Q8—941no—
435C2×C22⋊Q8C2×D4711yescharacteristic
436C2×#121—941no—
437C2×C4×Q8—471no—
438C2×C4×D4—471no—
439C2×C4×D4—471no—
440C2×C4×D4—941no—
441C22×C4⋊C4—471no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4—941no—
444#487—478no—
445#483—478no—
446#483—478no—
447#476—478no—
448#470—478no—
449#470—478no—
450#462—478no—
451#452—478no—
452#452C2×D4718yescomplemented
453C4×SD16—478no—
454#436—478no—
455C2×#106—471no—
456C2×#106—471no—
457C2×#106—471no—
458C2×C4⋊C8—471no—
459#417—478no—
460#417—478no—
461C2×#103—471no—
462C2×#103—471no—
463C2×#103—471no—
464C2×#103—471no—
465C2×#103—471no—
466C2×#103—471no—
467C2×#103C2×D4711yescharacteristic
468C2×#102—471no—
469C2×#102—471no—
470C2×#102C2×D4711yescharacteristic
471C2×C22⋊C8—471no—
472C2×C22⋊C8C2×D4711yescharacteristic
473C2×C4×C8—471no—
474C47C2×#333111yescharacteristic, complemented, Sylow
475C2×#41—22no—
476C2×#41—24no—
477C2×#41—42no—
478C2×#41—474no—
479C2×#41—942no—
480C2×#41—944no—
481C2×#41—1882no—
482C2×#41C22×D4714yes—
483C22×Q8—471no—
484C22×Q8—941no—
485C22×Q8C22×D4711yescharacteristic
486C22×Q8C22×D4711yescharacteristic
487C22×D4—21no—
488C22×D4—471no—
489C22×D4—941no—
490C22×D4C22×D4711yescharacteristic
491C23×C4—21no—
492C23×C4—471no—
493C23×C4—941no—
494C23×C4—941no—
495C23×C4—941no—
496C23×C4—941no—
497C23×C4C22×D4711yescharacteristic
498C2×Q16—42no—
499C2×Q16—474no—
500C2×Q16—1882no—
501C2×Q16C22×D4714yes—
502C2×SD16—24no—
503C2×SD16C22×D4714yes—
504C2×M16—474no—
505C2×M16—474no—
506C2×M16—1882no—
507C2×M16—1882no—
508C22×C8—471no—
509C22×C8—471no—
510C22×C8C22×D4711yescharacteristic
511C22×C8C22×D4711yescharacteristic
512C4⋊Q8—474no—
513C4⋊Q8—474no—
514C4⋊Q8—942no—
515C4⋊Q8—942no—
516#125—948no—
517#123—948no—
518#123—948no—
519C22⋊Q8—22no—
520C22⋊Q8—474no—
521C22⋊Q8—474no—
522C22⋊Q8—474no—
523C22⋊Q8—948no—
524C22⋊Q8—948no—
525C22⋊Q8—942no—
526C22⋊Q8—942no—
527C22⋊Q8—942no—
528C22⋊Q8C22×D4714yes—
529#121—948no—
530C4×Q8—474no—
531C4×Q8—942no—
532C4×D4—474no—
533C4×D4—474no—
534C4×D4—474no—
535C4×D4—942no—
536C4×D4—948no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—471no—
540C2×C4⋊C4—471no—
541C2×C4⋊C4—474no—
542C2×C4⋊C4—471no—
543C2×C4⋊C4—474no—
544C2×C4⋊C4—942no—
545C2×C4⋊C4—948no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4—941no—
548C2×C4⋊C4—941no—
549C2×C4⋊C4—941no—
550C2×C4⋊C4—941no—
551C2×C4⋊C4—941no—
552C2×C4⋊C4—941no—
553C2×C4⋊C4—941no—
554C2×C4⋊C4—942no—
555C2×C4⋊C4—941no—
556C2×C4⋊C4C22×D4711yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—471no—
559C2×C22⋊C4—471no—
560C2×C22⋊C4—941no—
561C2×C22⋊C4—941no—
562C2×C22⋊C4—941no—
563C2×C22⋊C4—941no—
564C2×C42—471no—
565C2×C42—941no—
566#106—474no—
567#106—474no—
568#106—474no—
569C4⋊C8—474no—
570#103—474no—
571#103—474no—
572#103—474no—
573#103—474no—
574#103—474no—
575#103—474no—
576#103C22×D4714yes—
577#102—474no—
578#102—474no—
579#102C22×D4714yes—
580C22⋊C8—474no—
581C22⋊C8C22×D4714yes—
582C4×C8—474no—
583C24—21no—
584C24—471no—
585C24D4×D4711yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589#41—948no—
590#41—1884no—
591#41—1888no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—22no—
598C2×Q8—472no—
599C2×Q8—944no—
600C2×Q8—941no—
601C2×Q8—942no—
602C2×Q8—942no—
603C2×Q8—3762no—
604C2×Q8C23×D4712yes—
605C2×Q8C23×D4712yes—
606C2×D4—24no—
607C2×D4—21no—
608C2×D4—22no—
609C2×D4—44no—
610C2×D4—474no—
611C2×D4—944no—
612C2×D4—944no—
613C2×D4—1884no—
614C2×D4#1062535214yes—
615C2×D4C23×D4712yes—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—44no—
623C22×C4—471no—
624C22×C4—471no—
625C22×C4—471no—
626C22×C4—472no—
627C22×C4—472no—
628C22×C4—944no—
629C22×C4—944no—
630C22×C4—944no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—944no—
634C22×C4—941no—
635C22×C4—941no—
636C22×C4—941no—
637C22×C4—941no—
638C22×C4—3762no—
639C22×C4—3762no—
640C22×C4—1884no—
641C22×C4—1884no—
642C22×C4D4×D4712yes—
643C22×C4D4×D4711yescharacteristic
644C22×C4C23×D4712yes—
645C22×C4C23×D4711yescharacteristic
646Q16—44no—
647Q16—1884no—
648SD16—28no—
649M16—1884no—
650M16—1884no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—472no—
654C2×C8—472no—
655C2×C8—942no—
656C2×C8—942no—
657C2×C8C23×D4712yes—
658C2×C8C23×D4712yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—474no—
662C4⋊C4—472no—
663C4⋊C4—472no—
664C4⋊C4—472no—
665C4⋊C4—944no—
666C4⋊C4—944no—
667C4⋊C4—944no—
668C4⋊C4—944no—
669C4⋊C4—944no—
670C4⋊C4—944no—
671C4⋊C4—944no—
672C4⋊C4—944no—
673C4⋊C4—941no—
674C4⋊C4—944no—
675C4⋊C4—941no—
676C4⋊C4—941no—
677C4⋊C4C23×D4712yes—
678C22⋊C4—24no—
679C22⋊C4—474no—
680C22⋊C4—474no—
681C22⋊C4—944no—
682C22⋊C4—944no—
683C22⋊C4—944no—
684C22⋊C4—944no—
685C42—472no—
686C42—472no—
687C42—944no—
688C23—22no—
689C23—24no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—472no—
696C23—942no—
697C23—942no—
698C23—942no—
699C23C2×D4×D4712yes—
700C23C2×D4×D4711yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—42no—
706Q8—42no—
707Q8—942no—
708Q8—942no—
709Q8—3764no—
710Q8—1882no—
711D4—24no—
712D4—22no—
713D4—48no—
714D4—948no—
715D4—1888no—
716D4C2×#1062535214yes—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—48no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—474no—
729C2×C4—472no—
730C2×C4—472no—
731C2×C4—472no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—944no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—3764no—
742C2×C4—3764no—
743C2×C4—1888no—
744C2×C4—1888no—
745C2×C4—1882no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4C2×D4×D4712yes—
750C2×C4C2×D4×D4711yescharacteristic
751C2×C4C2×#1062535212yes—
752C2×C4#1309406912yes—
753C2×C4C24×D4711yescharacteristic
754C8—22no—
755C8—22no—
756C8—942no—
757C8—942no—
758C22—22no—
759C22—24no—
760C22—22no—
761C22—22no—
762C22—42no—
763C22—42no—
764C22—44no—
765C22—48no—
766C22—942no—
767C22—942no—
768C22—942no—
769C22—1884no—
770C22#1568976012yes—
771C22#137×D4712yes—
772C22#1568993012yes—
773C22C22×D4×D4711yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—474no—
779C4—942no—
780C4—942no—
781C4—1882no—
782C4—1882no—
783C4—1882no—
784C4—1882no—
785C4#1568976012yes—
786C4C22×#1062535211yescharacteristic
787C4C2×#1309406911yescharacteristic
788C2—42no—
789C2—44no—
790C2—1882no—
791C2#2025569714yesdirect product factor
792C2C2×#1568976011yescharacteristic
793C2C2×#137×D4711yescharacteristic
794C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#452C2
socleC23×C47C22×D4
prime radicalC2×#15689772C2
hypercenterC2×#452D47
hypocenterC47C2×#3331
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#15689831C2semidirect
3. #20255697C2direct (N × H)
4. C2×#15689472C2semidirect
5. C2×#15689454C2semidirect
6. C2×#15689452C2semidirect
7. C2×#15689411C2semidirect
8. C2×#15689379C2semidirect
9. C2×#15689378C2semidirect
10. C2×#15689331C2semidirect
11. C2×#15689282C2semidirect
12. C2×SD16×Dic47C2semidirect
13. C2×#15689198C2semidirect
14. C2×#15689124C2semidirect
15. C2×#15689121C2semidirect
16. C2×C47×#452C2semidirect
22. #15689831C22semidirect
43. #15689472C22semidirect
44. #15689454C22semidirect
45. #15689452C22semidirect
46. #15689411C22semidirect
47. #15689379C22semidirect
48. #15689378C22semidirect
49. #15689331C22semidirect
50. #15689282C22semidirect
51. SD16×Dic47C22semidirect
52. #15689198C22semidirect
57. #15689124C22semidirect
58. #15689121C22semidirect
73. C47×#452C22semidirect
402. C2×#452D47semidirect
409. C2×C47#3331semidirect
452. #452C2×D47semidirect
474. C47C2×#3331semidirect
791. C2#20255697direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898312
C2×#156897722
#202556972
C2×#156894722
C2×#156894542
C2×#156894522
C2×#156894112
C2×#156893792
C2×#156893782
C2×#156893312
C2×#156892822
C2×SD16×Dic472
C2×#156891982
C2×#156891242
C2×#156891212
C2×C47×#4522
C2×#333147