Finite Group Databasebeta

← C2×#20255678 #27093171

Subgroups — C2×#20255678 #27093171

Order 12032.

2146 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×#15689836C211yesmaximal, characteristic
2C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
3#20255678C2116yesmaximal, direct product factor
4C2×#15689472C211yesmaximal, characteristic, complemented
5C2×#15689464C211yesmaximal, characteristic, complemented
6C2×#15689463C211yesmaximal, characteristic, complemented
7C2×#15689416C211yesmaximal, characteristic, complemented
8C2×#15689372C211yesmaximal, characteristic, complemented
9C2×#15689369C211yesmaximal, characteristic, complemented
10C2×#15689327C211yesmaximal, characteristic, complemented
11C2×#15689263C211yesmaximal, characteristic, complemented
12C2×#15689262C211yesmaximal, characteristic, complemented
13C2×#15689208C211yesmaximal, characteristic, complemented
14C2×#15689199C211yesmaximal, characteristic, complemented
15C2×#15689130C211yesmaximal, characteristic, complemented
16C2×C47×#419C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22#15689836—24no—
23#15689836C2218yes—
24Q8×C22⋊D47—24no—
25Q8×C22⋊D47C2218yescomplemented
26C2×#13094023C2211yescharacteristic
27C2×#13094022—21no—
28C2×#13094022C2211yescharacteristic
29C2×#13094012—21no—
30C2×#13094010—21no—
31C2×#13094003—21no—
32C2×#13094003C2211yescharacteristic
33C2×#13094000—21no—
34C2×#13094000C2211yescharacteristic
35C2×#13093999C2211yescharacteristic
36C2×#13093998C2211yescharacteristic
37C2×#13093997—21no—
38C2×Q8×Dic47C2211yescharacteristic
39C2×#13093986C2211yescharacteristic
40C2×C4×C22⋊D47—21no—
41C2×C4×C22⋊D47C2211yescharacteristic
42C2×#13093982C2211yescharacteristic
43C2×#13093981—21no—
44#15689472C2218yescomplemented
45#15689464C2218yescomplemented
46#15689463C2218yescomplemented
47#15689416C2218yescomplemented
48#15689372C2218yescomplemented
49#15689369C2218yescomplemented
50#15689327C2218yescomplemented
51#15689263C2218yescomplemented
52#15689262C2218yescomplemented
53#15689208C2218yescomplemented
54#15689199C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59#15689130C2218yescomplemented
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C23×Q8×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×#117×C47C2211yescharacteristic
72C47×#419C2218yescomplemented
73C2×#103×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×Dic94C2311yescharacteristic
80C2×Q8×D47—22no—
81C2×Q8×D47—24no—
82C2×Q8×D47—42no—
83C2×Q8×D47C2314yes—
84C22×D188—21no—
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C22×C22⋊D47D411yescharacteristic
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47C2311yescharacteristic
91C2×#10625325—42no—
92C2×#10625325C2314yes—
93C2×#10625336—24no—
94C2×#10625336—42no—
95C2×#10625336C2314yes—
96C2×#10625336C2314yes—
97C2×#10625324—42no—
98C2×#10625324C2314yes—
99C22×C47⋊C8C2311yescharacteristic
100C22×C47⋊C8C2311yescharacteristic
101#13094023—22no—
102#13094023C2314yes—
103#13094022—28no—
104#13094022—22no—
105#13094022C2314yes—
106#13094012—28no—
107#13094010—28no—
108#13094003—22no—
109#13094003—28no—
110#13094003C2314yes—
111#13094000—22no—
112#13094000—28no—
113#13094000C2314yes—
114#13093999—22no—
115#13093999C2314yes—
116#13093998—22no—
117#13093998C2314yes—
118#13093997—28no—
119Q8×Dic47—22no—
120Q8×Dic47C2314yes—
121#13093986—22no—
122#13093986C2314yes—
123C4×C22⋊D47—28no—
124C4×C22⋊D47D414yes—
125C4×C22⋊D47C2314yes—
126#13093982—22no—
127#13093982C2314yes—
128#13093981—28no—
129C2×C4⋊Dic47—21no—
130C2×C4⋊Dic47C2311yescharacteristic
131C2×C4⋊Dic47C2311yescharacteristic
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4D411yescharacteristic
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47D411yescharacteristic
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093958C2314yes—
150#13093957C2314yes—
151#13093955C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093947C2314yes—
157#13093947C2314yes—
158#13093946C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160(C2×D47)⋊C8C2314yes—
161C8×Dic47C2314yes—
162C22×Q8×C47—22no—
163C22×Q8×C47—21no—
164C22×Q8×C47—24no—
165C22×Q8×C47—42no—
166C22×Q8×C47C2311yescharacteristic
167C22×Q8×C47C2314yes—
168C22×Q8×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47C2311yescharacteristic
171C2×M16×C47—42no—
172C2×M16×C47C2314yes—
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2311yescharacteristic
175#117×C47—22no—
176#117×C47C2314yes—
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C22⋊C4×C47—21no—
180C2×C42×C47—21no—
181#103×C47C2314yes—
182#103×C47C2314yes—
183#103×C47C2314yes—
184#103×C47C2314yes—
185C24×C47C2×D411yescharacteristic
186C23×D47—21no—
187C23×D47C2×D411yescharacteristic
188C2×Q8×C47—21no—
189C2×Q8×C47—24no—
190C2×Q8×C47—21no—
191C2×Q8×C47—22no—
192C2×Q8×C47—28no—
193C2×Q8×C47—22no—
194C2×Q8×C47—22no—
195C2×Q8×C47—44no—
196C2×Q8×C47—44no—
197C2×Q8×C47—48no—
198C2×Q8×C47#4114yes—
199C2×Q8×C47C2412yes—
200C2×Q8×C47C2412yes—
201C22×C4×C47—21no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—24no—
208C22×C4×C47—44no—
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2411yescharacteristic
213C2×C22⋊D47—24no—
214C2×C22⋊D47—24no—
215C2×C22⋊D47—82no—
216C2×C22⋊D47C2×D414yes—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47C2×D411yescharacteristic
221C22×Dic47C2×D411yescharacteristic
222C22×Dic47C2×D411yescharacteristic
223Q8×D47—28no—
224Q8×D47—44no—
225Q8×D47—48no—
226C2×D188—22no—
227C2×D188—22no—
228C2×D188—21no—
229C2×D188—24no—
230C2×D188—82no—
231C2×D188C2412yes—
232C2×C4×D47—22no—
233C2×C4×D47—22no—
234C2×C4×D47—24no—
235C2×C4×D47—24no—
236C2×C4×D47—44no—
237C2×C4×D47—44no—
238C2×C4×D47C2×D412yes—
239C2×C4×D47C2412yes—
240C2×Dic94—22no—
241C2×Dic94—22no—
242C2×Dic94—21no—
243C2×Dic94—24no—
244C2×Dic94—24no—
245C2×Dic94—44no—
246C2×Dic94—82no—
247C2×Dic94C2412yes—
248M16×C47—44no—
249C2×C8×C47—22no—
250C2×C8×C47—22no—
251C2×C8×C47C2412yes—
252C2×C8×C47C2412yes—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47C2412yes—
256C4⋊C4×C47C2412yes—
257C22⋊C4×C47—24no—
258C42×C47—24no—
259C22⋊Dic47—24no—
260C22⋊Dic47C2×D414yes—
261#10625336—28no—
262#10625336—44no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4C2×D414yes—
269C4⋊Dic47—21no—
270C4⋊Dic47—21no—
271C4⋊Dic47—24no—
272C4⋊Dic47C2412yes—
273C4⋊Dic47C2412yes—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4C2×D414yes—
280C4×Dic47—24no—
281C4×Dic47—24no—
282C4×Dic47C2×D412yes—
283C4×Dic47C2412yes—
284C2×C47⋊C8—22no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8C2412yes—
287C2×C47⋊C8C2412yes—
288#10625325—44no—
289#10625324—44no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47C22×D412yes—
294C23×C47C22×D411yescharacteristic
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—42no—
300C22×D47—42no—
301C22×D47—42no—
302C22×D47C22×D412yes—
303Q8×C47—24no—
304Q8×C47—22no—
305Q8×C47—22no—
306Q8×C47—22no—
307Q8×C47—48no—
308Q8×C47—42no—
309Q8×C47C2×#4114yes—
310C2×C4×C47—24no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—24no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—48no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47—42no—
323C2×C4×C47C22×D412yes—
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C2×#4112yes—
326C2×C4×C47H(5,𝔽2)12yes—
327C2×C4×C47C2511yescharacteristic
328C22⋊D47—28no—
329C22⋊D47—84no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47#13714yes—
339C2×Dic47C22×D412yes—
340C2×Dic47C22×D412yes—
341C2×Dic47C22×D412yes—
342D188—22no—
343D188—22no—
344D188—42no—
345D188—84no—
346C4×D47—24no—
347C4×D47—22no—
348C4×D47—22no—
349C4×D47—48no—
350C4×D47—48no—
351Dic94—22no—
352Dic94—22no—
353Dic94—48no—
354Dic94—42no—
355Dic94—84no—
356C8×C47—22no—
357C8×C47—22no—
358C47⋊C8—22no—
359C47⋊C8—22no—
360C2×#3329—471nomaximal, Sylow
361C22×C47—22no—
362C22×C47—22no—
363C22×C47—22no—
364C22×C47—44no—
365C22×C47#54612yes—
366C22×C47C2×#13712yes—
367C22×C47#57712yes—
368C22×C47C23×D411yescharacteristic
369C2×D47—22no—
370C2×D47—22no—
371C2×D47—22no—
372C2×D47—44no—
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—84no—
377C4×C47—24no—
378C4×C47—22no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47—42no—
382C4×C47#54612yes—
383C4×C47C22×#4111yescharacteristic
384C4×C47C2×H(5,𝔽2)11yescharacteristic
385Dic47—22no—
386Dic47—22no—
387Dic47—42no—
388Dic47—42no—
389Dic47—42no—
390Dic47C2×#13714yes—
391C2×#555—471no—
392C2×D4×Q8—471no—
393#3329—4716no—
394C2×#487—471no—
395C2×#485—471no—
396C2×#485—471no—
397C2×#477—471no—
398C2×#468—471no—
399C2×#468—471no—
400C2×#461—471no—
401C2×#448—471no—
402C2×#448—471no—
403C2×C4×SD16—471no—
404C2×#436—471no—
405C2×#419—471no—
406C2×#419D4711yescharacteristic, complemented
407C2×C47—42no—
408C2×C47#332914yescomplemented
409C2×C47C2×#54611yescharacteristic
410C2×C47C22×#13711yescharacteristic
411C2×C47C2×#57711yescharacteristic
412D47—42no—
413D47—82no—
414C23×Q8—471no—
415C23×Q8C2×D4711yescharacteristic
416C22×SD16—471no—
417C22×SD16—471no—
418C22×SD16—471no—
419C22×M16—471no—
420C22×M16C2×D4711yescharacteristic
421#555—478no—
422#555—944no—
423D4×Q8—478no—
424D4×Q8—944no—
425C2×C4⋊Q8—471no—
426C2×C4⋊Q8—471no—
427C2×C4⋊Q8—941no—
428C2×#124—941no—
429C2×#124—941no—
430C2×C22⋊Q8—471no—
431C2×C22⋊Q8—471no—
432C2×C22⋊Q8—941no—
433C2×C22⋊Q8—941no—
434C2×#121—471no—
435C2×#121—471no—
436C2×#121—941no—
437C2×C4×Q8—471no—
438C2×C4×D4—471no—
439C2×C4×D4—471no—
440C2×C4×D4—941no—
441C2×#117—471no—
442C2×#117—941no—
443C2×#117C2×D4711yescharacteristic
444#487—478no—
445#485—478no—
446#485—478no—
447#477—478no—
448#468—478no—
449#468—478no—
450#461—478no—
451#448—478no—
452#448—478no—
453C4×SD16—478no—
454#436—478no—
455C2×#107—471no—
456C2×#107—471no—
457C2×#106—471no—
458C2×C4⋊C8—471no—
459#419—478no—
460#419C2×D4718yescomplemented
461C2×#103—471no—
462C2×#103—471no—
463C2×#103—471no—
464C2×#103—471no—
465C2×#103—471no—
466C2×#103C2×D4711yescharacteristic
467C2×#103C2×D4711yescharacteristic
468C2×#103C2×D4711yescharacteristic
469C2×#103C2×D4711yescharacteristic
470C2×#102—471no—
471C2×C22⋊C8—471no—
472C2×C22⋊C8—471no—
473C2×C4×C8—471no—
474C47C2×#332911yescharacteristic, complemented, Sylow
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—24no—
478C22×Q8—42no—
479C22×Q8—474no—
480C22×Q8—471no—
481C22×Q8—941no—
482C22×Q8—941no—
483C22×Q8—942no—
484C22×Q8—944no—
485C22×Q8—1882no—
486C22×Q8C22×D4711yescharacteristic
487C22×Q8C22×D4714yes—
488C22×Q8C22×D4711yescharacteristic
489C22×D4—471no—
490C22×D4—471no—
491C22×D4—941no—
492C22×D4—941no—
493C23×C4—21no—
494C23×C4—471no—
495C23×C4—941no—
496C23×C4—941no—
497C23×C4C22×D4711yescharacteristic
498C2×SD16—474no—
499C2×SD16—474no—
500C2×SD16—474no—
501C2×SD16—944no—
502C2×SD16—1882no—
503C2×SD16—1882no—
504C2×M16—42no—
505C2×M16—474no—
506C2×M16—1882no—
507C2×M16C22×D4714yes—
508C22×C8—471no—
509C22×C8—471no—
510C22×C8C22×D4711yescharacteristic
511C22×C8C22×D4711yescharacteristic
512C4⋊Q8—474no—
513C4⋊Q8—474no—
514C4⋊Q8—942no—
515C4⋊Q8—942no—
516C4⋊Q8—948no—
517#124—948no—
518#124—948no—
519C22⋊Q8—474no—
520C22⋊Q8—474no—
521C22⋊Q8—948no—
522C22⋊Q8—948no—
523C22⋊Q8—942no—
524C22⋊Q8—942no—
525#121—474no—
526#121—474no—
527#121—948no—
528#121—942no—
529#121—942no—
530C4×Q8—474no—
531C4×Q8—942no—
532C4×D4—474no—
533C4×D4—474no—
534C4×D4—474no—
535C4×D4—942no—
536C4×D4—948no—
537#117—22no—
538#117—474no—
539#117—948no—
540#117—942no—
541#117C22×D4714yes—
542C2×C4⋊C4—471no—
543C2×C4⋊C4—471no—
544C2×C4⋊C4—471no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4—941no—
548C2×C4⋊C4—941no—
549C2×C4⋊C4—941no—
550C2×C4⋊C4—941no—
551C2×C4⋊C4C22×D4711yescharacteristic
552C2×C4⋊C4C22×D4711yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—471no—
555C2×C22⋊C4—471no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4—941no—
558C2×C22⋊C4—941no—
559C2×C22⋊C4—941no—
560C2×C22⋊C4—941no—
561C2×C22⋊C4—941no—
562C2×C42—21no—
563C2×C42—471no—
564C2×C42—941no—
565C2×C42—941no—
566#107—474no—
567#107—474no—
568#106—474no—
569C4⋊C8—474no—
570#103—474no—
571#103—474no—
572#103—474no—
573#103—474no—
574#103—474no—
575#103C22×D4714yes—
576#103C22×D4714yes—
577#103C22×D4714yes—
578#103C22×D4714yes—
579#102—474no—
580C22⋊C8—474no—
581C22⋊C8—474no—
582C4×C8—474no—
583C24—471no—
584C24—941no—
585C24D4×D4711yescharacteristic
586C2×Q8—21no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—28no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—44no—
594C2×Q8—44no—
595C2×Q8—48no—
596C2×Q8—472no—
597C2×Q8—944no—
598C2×Q8—944no—
599C2×Q8—941no—
600C2×Q8—948no—
601C2×Q8—942no—
602C2×Q8—942no—
603C2×Q8—3762no—
604C2×Q8—1884no—
605C2×Q8—1884no—
606C2×Q8—1888no—
607C2×Q8#1062535014yes—
608C2×Q8C23×D4712yes—
609C2×Q8C23×D4712yes—
610C2×D4—474no—
611C2×D4—472no—
612C2×D4—944no—
613C2×D4—944no—
614C2×D4—944no—
615C2×D4—941no—
616C2×D4—942no—
617C2×D4—942no—
618C2×D4—3762no—
619C2×D4—3762no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—44no—
628C22×C4—471no—
629C22×C4—471no—
630C22×C4—471no—
631C22×C4—472no—
632C22×C4—472no—
633C22×C4—944no—
634C22×C4—944no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—941no—
638C22×C4—941no—
639C22×C4—941no—
640C22×C4—1884no—
641C22×C4—1884no—
642C22×C4D4×D4712yes—
643C22×C4D4×D4711yescharacteristic
644C22×C4C23×D4712yes—
645C22×C4C23×D4711yescharacteristic
646SD16—948no—
647SD16—1884no—
648SD16—1884no—
649M16—44no—
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—21no—
660C4⋊C4—21no—
661C4⋊C4—474no—
662C4⋊C4—472no—
663C4⋊C4—472no—
664C4⋊C4—944no—
665C4⋊C4—944no—
666C4⋊C4—944no—
667C4⋊C4—944no—
668C4⋊C4—944no—
669C4⋊C4—944no—
670C4⋊C4—941no—
671C4⋊C4—941no—
672C4⋊C4C23×D4712yes—
673C4⋊C4C23×D4712yes—
674C22⋊C4—24no—
675C22⋊C4—474no—
676C22⋊C4—474no—
677C22⋊C4—944no—
678C22⋊C4—944no—
679C22⋊C4—944no—
680C22⋊C4—944no—
681C22⋊C4—944no—
682C22⋊C4—944no—
683C42—24no—
684C42—472no—
685C42—472no—
686C42—944no—
687C42—944no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—472no—
692C23—942no—
693C23—942no—
694C23—942no—
695C23—942no—
696C23—1882no—
697C23—1882no—
698C23—1882no—
699C23C2×D4×D4712yes—
700C23C2×D4×D4711yescharacteristic
701Q8—24no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—48no—
706Q8—42no—
707Q8—942no—
708Q8—942no—
709Q8—3764no—
710Q8—1888no—
711Q8—1882no—
712Q8C2×#1062535014yes—
713D4—948no—
714D4—942no—
715D4—942no—
716D4—3764no—
717D4—3764no—
718D4—1882no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—48no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—474no—
733C2×C4—472no—
734C2×C4—472no—
735C2×C4—472no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—944no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—1888no—
745C2×C4—1888no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4C2×D4×D4712yes—
750C2×C4C2×D4×D4711yescharacteristic
751C2×C4C2×#1062535012yes—
752C2×C4#1309406912yes—
753C2×C4C24×D4711yescharacteristic
754C8—22no—
755C8—22no—
756C8—942no—
757C8—942no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—942no—
763C22—942no—
764C22—942no—
765C22—3764no—
766C22—1882no—
767C22—1882no—
768C22—1882no—
769C22—1884no—
770C22#1568976312yes—
771C22#137×D4712yes—
772C22#1568993212yes—
773C22C22×D4×D4711yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—474no—
780C4—942no—
781C4—942no—
782C4—1882no—
783C4—1882no—
784C4—1882no—
785C4#1568976312yes—
786C4C22×#1062535011yescharacteristic
787C4C2×#1309406911yescharacteristic
788C2—42no—
789C2—3762no—
790C2—1882no—
791C2#2025567814yesdirect product factor
792C2C2×#1568976311yescharacteristic
793C2C2×#137×D4711yescharacteristic
794C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#419C2
socleC23×C47C22×D4
prime radicalC2×#15689836C2
hypercenterC2×#419D47
hypocenterC47C2×#3329
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C22⋊D47C2semidirect
3. #20255678C2direct (N × H)
4. C2×#15689472C2semidirect
5. C2×#15689464C2semidirect
6. C2×#15689463C2semidirect
7. C2×#15689416C2semidirect
8. C2×#15689372C2semidirect
9. C2×#15689369C2semidirect
10. C2×#15689327C2semidirect
11. C2×#15689263C2semidirect
12. C2×#15689262C2semidirect
13. C2×#15689208C2semidirect
14. C2×#15689199C2semidirect
15. C2×#15689130C2semidirect
16. C2×C47×#419C2semidirect
25. Q8×C22⋊D47C22semidirect
44. #15689472C22semidirect
45. #15689464C22semidirect
46. #15689463C22semidirect
47. #15689416C22semidirect
48. #15689372C22semidirect
49. #15689369C22semidirect
50. #15689327C22semidirect
51. #15689263C22semidirect
52. #15689262C22semidirect
53. #15689208C22semidirect
54. #15689199C22semidirect
59. #15689130C22semidirect
72. C47×#419C22semidirect
406. C2×#419D47semidirect
408. C2×C47#3329semidirect
460. #419C2×D47semidirect
474. C47C2×#3329semidirect
791. C2#20255678direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898362
C2×Q8×C22⋊D472
#202556782
C2×#156894722
C2×#156894642
C2×#156894632
C2×#156894162
C2×#156893722
C2×#156893692
C2×#156893272
C2×#156892632
C2×#156892622
C2×#156892082
C2×#156891992
C2×#156891302
C2×C47×#4192
C2×#332947