Finite Group Databasebeta

← C2×#20255028 #27091418

Subgroups — C2×#20255028 #27091418

Order 12032.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094053C211yesmaximal, characteristic, complemented
2C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
3C2×#15689772C211yesmaximal, characteristic
4#20255028C2116yesmaximal, direct product factor
5C2×#15689501C211yesmaximal, characteristic, complemented
6C2×#15689381C211yesmaximal, characteristic, complemented
7C2×#15689378C211yesmaximal, characteristic, complemented
8C2×#15689331C211yesmaximal, characteristic, complemented
9C2×#15689326C211yesmaximal, characteristic, complemented
10C2×#15689285C211yesmaximal, characteristic, complemented
11C2×#15689282C211yesmaximal, characteristic, complemented
12C2×#15689279C211yesmaximal, characteristic, complemented
13C2×#15689277C211yesmaximal, characteristic, complemented
14C2×SD16×Dic47C211yesmaximal, characteristic, complemented
15C2×#15689199C211yesmaximal, characteristic, complemented
16C22×#137×C47C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C2×#13094053—28no—
20C2×#13094053C2218yescomplemented
21C22×Dic188C2211yescharacteristic
22C22×#10625337C2211yescharacteristic
23C22×#10625337C2211yescharacteristic
24C22×#10625337C2211yescharacteristic
25C22×#10625335C2211yescharacteristic
26C22×#10625324C2211yescharacteristic
27Q8×C22⋊D47—24no—
28Q8×C22⋊D47C2218yescomplemented
29#15689772—24no—
30#15689772C2218yes—
31C2×#13094022—21no—
32C2×#13094022C2211yescharacteristic
33C2×#13094022C2211yescharacteristic
34C2×#13094007—21no—
35C2×#13094005—21no—
36C2×#13094003—21no—
37C2×#13094003C2211yescharacteristic
38C2×#13094003C2211yescharacteristic
39C2×#13094000—21no—
40C2×#13094000C2211yescharacteristic
41C2×#13094000C2211yescharacteristic
42C2×#13093996—21no—
43C2×Q8×Dic47C2211yescharacteristic
44C2×D4×Dic47C2211yescharacteristic
45C2×C4×C22⋊D47—21no—
46C2×C4×C22⋊D47C2211yescharacteristic
47C22×Dic47⋊C4—21no—
48#15689501C2218yescomplemented
49#15689381C2218yescomplemented
50#15689378C2218yescomplemented
51#15689331C2218yescomplemented
52#15689326C2218yescomplemented
53#15689285C2218yescomplemented
54#15689282C2218yescomplemented
55#15689279C2218yescomplemented
56#15689277C2218yescomplemented
57SD16×Dic47C2218yescomplemented
58#15689199C2218yescomplemented
59C2×#13093956C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093945C2211yescharacteristic
67C2×C22⋊(C47⋊C8)C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C2×C8×Dic47C2211yescharacteristic
70C22×#41×C47C2211yescharacteristic
71C23×Q8×C47C2211yescharacteristic
72C2×#137×C47—28no—
73C2×#137×C47C2218yescomplemented
74C22×Q16×C47C2211yescharacteristic
75C22×Q16×C47C2211yescharacteristic
76C22×SD16×C47C2211yescharacteristic
77C22×SD16×C47C2211yescharacteristic
78C22×M16×C47C2211yescharacteristic
79C2×#10625352—24no—
80C2×#10625352—22no—
81C2×#10625352—42no—
82C2×#10625352C2314yes—
83C22×Dic94—21no—
84C22×Dic94C2311yescharacteristic
85C22×Dic94C2311yescharacteristic
86C2×Q8×D47—22no—
87C2×Q8×D47—24no—
88C2×Q8×D47—42no—
89C2×Q8×D47C2314yes—
90C22×C22⋊D47—21no—
91C22×C22⋊D47D411yescharacteristic
92C23×Dic47—21no—
93C23×Dic47—21no—
94C22×C4×D47—21no—
95C22×C4×D47C2311yescharacteristic
96#13094053—232no—
97C2×Dic188—24no—
98C2×Dic188C2314yes—
99C2×#10625337—24no—
100C2×#10625337—42no—
101C2×#10625337—42no—
102C2×#10625337C2314yes—
103C2×#10625337C2314yes—
104C2×#10625337C2314yes—
105C2×#10625335—24no—
106C2×#10625335C2314yes—
107C2×#10625324—24no—
108C2×#10625324C2314yes—
109C22×C47⋊C8C2311yescharacteristic
110C22×C47⋊C8C2311yescharacteristic
111#13094022—28no—
112#13094022—22no—
113#13094022—22no—
114#13094022C2314yes—
115#13094022C2314yes—
116#13094007—28no—
117#13094005—28no—
118#13094003—22no—
119#13094003—22no—
120#13094003—28no—
121#13094003C2314yes—
122#13094003C2314yes—
123#13094000—22no—
124#13094000—22no—
125#13094000—28no—
126#13094000C2314yes—
127#13094000C2314yes—
128#13093996—28no—
129Q8×Dic47—22no—
130Q8×Dic47C2314yes—
131D4×Dic47—22no—
132D4×Dic47C2314yes—
133C4×C22⋊D47—28no—
134C4×C22⋊D47D414yes—
135C4×C22⋊D47C2314yes—
136C2×C4⋊Dic47—21no—
137C2×C4⋊Dic47C2311yescharacteristic
138C2×C4⋊Dic47C2311yescharacteristic
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4—21no—
143C2×Dic47⋊C4—21no—
144C2×Dic47⋊C4—21no—
145C2×Dic47⋊C4—21no—
146C2×Dic47⋊C4—21no—
147C2×Dic47⋊C4—28no—
148C2×Dic47⋊C4D411yescharacteristic
149C2×C22⋊Dic47—21no—
150C2×C22⋊Dic47—21no—
151C2×C22⋊Dic47—21no—
152C2×C22⋊Dic47D411yescharacteristic
153C2×(C2×D47)⋊C4—21no—
154C2×(C2×D47)⋊C4—21no—
155C2×(C2×D47)⋊C4D411yescharacteristic
156C2×C4×Dic47—21no—
157C2×C4×Dic47C2311yescharacteristic
158#13093956C2314yes—
159Dic47⋊C8C2314yes—
160#13093949C2314yes—
161#13093949C2314yes—
162#13093948C2314yes—
163#13093948C2314yes—
164#13093948C2314yes—
165#13093945C2314yes—
166C22⋊(C47⋊C8)C2314yes—
167(C2×D47)⋊C8C2314yes—
168C8×Dic47C2314yes—
169C2×#41×C47—22no—
170C2×#41×C47—24no—
171C2×#41×C47—42no—
172C2×#41×C47C2314yes—
173C22×Q8×C47—22no—
174C22×Q8×C47—21no—
175C22×Q8×C47—24no—
176C22×Q8×C47—42no—
177C22×Q8×C47C2311yescharacteristic
178C22×Q8×C47C2311yescharacteristic
179C22×Q8×C47C2314yes—
180C22×Q8×C47C2311yescharacteristic
181C22×D4×C47—21no—
182C22×D4×C47C2311yescharacteristic
183C23×C4×C47—21no—
184C23×C4×C47—21no—
185C23×C4×C47C2311yescharacteristic
186#137×C47—232no—
187C2×Q16×C47—24no—
188C2×Q16×C47—24no—
189C2×Q16×C47C2314yes—
190C2×Q16×C47C2314yes—
191C2×SD16×C47—24no—
192C2×SD16×C47D418yescomplemented
193C2×SD16×C47C2314yes—
194C2×SD16×C47C2314yes—
195C2×M16×C47—24no—
196C2×M16×C47C2314yes—
197C22×C8×C47C2311yescharacteristic
198C22×C8×C47C2311yescharacteristic
199C24×C47—21no—
200C24×C47C2×D411yescharacteristic
201C23×D47C2×D411yescharacteristic
202#41×C47—28no—
203#41×C47—44no—
204#41×C47—48no—
205C2×Q8×C47—21no—
206C2×Q8×C47—24no—
207C2×Q8×C47—21no—
208C2×Q8×C47—21no—
209C2×Q8×C47—22no—
210C2×Q8×C47—28no—
211C2×Q8×C47—22no—
212C2×Q8×C47—22no—
213C2×Q8×C47—22no—
214C2×Q8×C47—22no—
215C2×Q8×C47—44no—
216C2×Q8×C47—44no—
217C2×Q8×C47—48no—
218C2×Q8×C47C2×D414yes—
219C2×Q8×C47C2412yes—
220C2×Q8×C47C2412yes—
221C2×Q8×C47C2412yes—
222C2×D4×C47—24no—
223C2×D4×C47—21no—
224C2×D4×C47—22no—
225C2×D4×C47—44no—
226C2×D4×C47C2×D414yes—
227C2×D4×C47C2412yes—
228C22×C4×C47—21no—
229C22×C4×C47—22no—
230C22×C4×C47—22no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—24no—
234C22×C4×C47—24no—
235C22×C4×C47—44no—
236C22×C4×C47—44no—
237C22×C4×C47C2×D411yescharacteristic
238C22×C4×C47C2×D412yes—
239C22×C4×C47C2412yes—
240C22×C4×C47C2411yescharacteristic
241C2×C22⋊D47—24no—
242C2×C22⋊D47—24no—
243C2×C22⋊D47—44no—
244C2×C22⋊D47C2×D414yes—
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—21no—
249C22×Dic47—24no—
250C22×Dic47—24no—
251C22×Dic47—44no—
252C22×Dic47—44no—
253C22×Dic47C2×D411yescharacteristic
254C22×Dic47C2×D411yescharacteristic
255C22×Dic47C2×D411yescharacteristic
256Q8×D47—28no—
257Q8×D47—44no—
258Q8×D47—48no—
259#10625352—28no—
260#10625352—44no—
261#10625352—48no—
262C2×C4×D47—22no—
263C2×C4×D47—22no—
264C2×C4×D47—24no—
265C2×C4×D47—44no—
266C2×C4×D47C2×D412yes—
267C2×C4×D47C2412yes—
268C2×Dic94—22no—
269C2×Dic94—22no—
270C2×Dic94—22no—
271C2×Dic94—22no—
272C2×Dic94—21no—
273C2×Dic94—21no—
274C2×Dic94—24no—
275C2×Dic94—44no—
276C2×Dic94C2412yes—
277C2×Dic94C2412yes—
278Q16×C47—28no—
279Q16×C47—28no—
280SD16×C47—28no—
281SD16×C47C2×D4116yescomplemented
282M16×C47—28no—
283C2×C8×C47—22no—
284C2×C8×C47C2×D414yes—
285C2×C8×C47C2412yes—
286C2×C8×C47C2412yes—
287C22⋊Dic47—24no—
288C22⋊Dic47—24no—
289C22⋊Dic47—24no—
290C22⋊Dic47C2×D414yes—
291#10625337—28no—
292#10625337—44no—
293#10625337—44no—
294#10625335—28no—
295(C2×D47)⋊C4—24no—
296(C2×D47)⋊C4—24no—
297(C2×D47)⋊C4C2×D414yes—
298C4⋊Dic47—21no—
299C4⋊Dic47—21no—
300C4⋊Dic47—24no—
301C4⋊Dic47C2412yes—
302C4⋊Dic47C2412yes—
303Dic47⋊C4—24no—
304Dic47⋊C4—24no—
305Dic47⋊C4—24no—
306Dic47⋊C4—24no—
307Dic47⋊C4—24no—
308Dic47⋊C4—24no—
309Dic47⋊C4—24no—
310Dic47⋊C4—24no—
311Dic47⋊C4C2×D414yes—
312C4×Dic47—24no—
313C4×Dic47C2×D412yes—
314C4×Dic47C2412yes—
315C2×C47⋊C8—22no—
316C2×C47⋊C8—22no—
317C2×C47⋊C8C2412yes—
318C2×C47⋊C8C2412yes—
319Dic188—28no—
320#10625324—28no—
321C23×C47—24no—
322C23×C47—22no—
323C23×C47—22no—
324C23×C47—22no—
325C23×C47—22no—
326C23×C47—42no—
327C23×C47—42no—
328C23×C47C22×D412yes—
329C23×C47C22×D411yescharacteristic
330C22×D47—22no—
331C22×D47—22no—
332C22×D47—22no—
333C22×D47C22×D412yes—
334Q8×C47—24no—
335Q8×C47—22no—
336Q8×C47—22no—
337Q8×C47—22no—
338Q8×C47—22no—
339Q8×C47—22no—
340Q8×C47—48no—
341Q8×C47—42no—
342Q8×C47—42no—
343Q8×C47C22×D414yes—
344D4×C47—24no—
345D4×C47—22no—
346D4×C47—48no—
347D4×C47C22×D414yes—
348C2×C4×C47—24no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—24no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—48no—
357C2×C4×C47—48no—
358C2×C4×C47—42no—
359C2×C4×C47—42no—
360C2×C4×C47C22×D412yes—
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47C22×D412yes—
363C2×C4×C47H(5,𝔽2)12yes—
364C2×C4×C47C2511yescharacteristic
365C22⋊D47—28no—
366C22⋊D47—48no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—48no—
374C2×Dic47—42no—
375C2×Dic47—42no—
376C2×Dic47—42no—
377C2×Dic47—42no—
378C2×Dic47—48no—
379C2×Dic47#13714yescomplemented
380C2×Dic47C22×D412yes—
381C2×Dic47C22×D412yes—
382C2×Dic47C22×D412yes—
383C4×D47—24no—
384C4×D47—22no—
385C4×D47—22no—
386C4×D47—48no—
387Dic94—22no—
388Dic94—22no—
389Dic94—22no—
390Dic94—22no—
391Dic94—48no—
392Dic94—42no—
393Dic94—42no—
394C8×C47—22no—
395C8×C47C22×D414yes—
396C47⋊C8—22no—
397C47⋊C8—22no—
398C2×#3276—471nomaximal, Sylow
399C22×C47—24no—
400C22×C47—22no—
401C22×C47—22no—
402C22×C47—22no—
403C22×C47—44no—
404C22×C47—48no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47D4212yes—
408C22×C47C2×#13712yes—
409C22×C47#57812yes—
410C22×C47C23×D411yescharacteristic
411C2×D47—22no—
412C2×D47—22no—
413C2×D47—22no—
414C2×D47—44no—
415C4×C47—24no—
416C4×C47—22no—
417C4×C47—42no—
418C4×C47—42no—
419C4×C47D4212yes—
420C4×C47C23×D411yescharacteristic
421C4×C47C2×H(5,𝔽2)11yescharacteristic
422Dic47—22no—
423Dic47—22no—
424Dic47—42no—
425Dic47—42no—
426Dic47—42no—
427Dic47—42no—
428Dic47C2×#13714yescomplemented
429C22×#137—471no—
430C22×#137D4711yescharacteristic, complemented
431C2×D4×Q8—471no—
432C2×#547—471no—
433#3276—4716no—
434C2×#494—471no—
435C2×#470—471no—
436C2×#470—471no—
437C2×#462—471no—
438C2×#461—471no—
439C2×#452—471no—
440C2×#452—471no—
441C2×#451—471no—
442C2×#451—471no—
443C2×C4×SD16—471no—
444C2×#436—471no—
445C2×C47—42no—
446C2×C47—44no—
447C2×C47#327614yescomplemented
448C2×C47C2×D4211yescharacteristic
449C2×C47C22×#13711yescharacteristic
450C2×C47C2×#57811yescharacteristic
451D47—42no—
452C22×#41—471no—
453C22×#41C2×D4711yescharacteristic
454C23×Q8—471no—
455C23×Q8C2×D4711yescharacteristic
456C2×#137—28no—
457C2×#137—478no—
458C2×#137—948no—
459C2×#137C2×D4718yescomplemented
460C22×Q16—471no—
461C22×Q16—471no—
462C22×Q16—471no—
463C22×Q16—471no—
464C22×Q16C2×D4711yescharacteristic
465C22×Q16C2×D4711yescharacteristic
466C22×SD16—471no—
467C22×SD16C2×D4711yescharacteristic
468C22×SD16C2×D4711yescharacteristic
469C22×M16—471no—
470C22×M16C2×D4711yescharacteristic
471D4×Q8—478no—
472D4×Q8—944no—
473#547—478no—
474#547—944no—
475C2×C4⋊Q8—471no—
476C2×C4⋊Q8—471no—
477C2×C4⋊Q8—941no—
478C2×#123—941no—
479C2×#123—941no—
480C2×C22⋊Q8—471no—
481C2×C22⋊Q8—471no—
482C2×C22⋊Q8—471no—
483C2×C22⋊Q8—471no—
484C2×C22⋊Q8—941no—
485C2×C22⋊Q8—941no—
486C2×#121—941no—
487C2×C4×Q8—471no—
488C2×C4×D4—471no—
489C2×C4×D4—471no—
490C2×C4×D4—941no—
491C22×C4⋊C4—941no—
492#494—478no—
493#470—478no—
494#470—478no—
495#462—478no—
496#461—478no—
497#452—478no—
498#452—478no—
499#451—478no—
500#451—478no—
501C4×SD16—478no—
502#436—478no—
503C2×#106—471no—
504C2×C4⋊C8—471no—
505C2×#103—471no—
506C2×#103—471no—
507C2×#103—471no—
508C2×#103—471no—
509C2×#103—471no—
510C2×#102—471no—
511C2×C22⋊C8—471no—
512C2×C22⋊C8—471no—
513C2×C4×C8—471no—
514C47C2×#327611yescharacteristic, complemented, Sylow
515C2×#41—22no—
516C2×#41—24no—
517C2×#41—42no—
518C2×#41—474no—
519C2×#41—942no—
520C2×#41—944no—
521C2×#41—1882no—
522C2×#41C22×D4714yes—
523C22×Q8—21no—
524C22×Q8—22no—
525C22×Q8—24no—
526C22×Q8—42no—
527C22×Q8—474no—
528C22×Q8—471no—
529C22×Q8—471no—
530C22×Q8—941no—
531C22×Q8—942no—
532C22×Q8—944no—
533C22×Q8—1882no—
534C22×Q8C22×D4711yescharacteristic
535C22×Q8C22×D4711yescharacteristic
536C22×Q8C22×D4714yes—
537C22×Q8C22×D4711yescharacteristic
538C22×D4—21no—
539C22×D4—471no—
540C22×D4—941no—
541C22×D4C22×D4711yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—471no—
545C23×C4—941no—
546C23×C4—941no—
547C23×C4—941no—
548C23×C4C22×D4711yescharacteristic
549#137—232no—
550#137—9432no—
551C2×Q16—24no—
552C2×Q16—24no—
553C2×Q16—474no—
554C2×Q16—474no—
555C2×Q16—474no—
556C2×Q16—474no—
557C2×Q16—944no—
558C2×Q16—944no—
559C2×Q16—1882no—
560C2×Q16—1882no—
561C2×Q16C22×D4714yes—
562C2×Q16C22×D4714yes—
563C2×SD16—24no—
564C2×SD16—474no—
565C2×SD16—944no—
566C2×SD16C22⋊D4718yescomplemented
567C2×SD16C22×D4714yes—
568C2×SD16C22×D4714yes—
569C2×M16—24no—
570C2×M16—474no—
571C2×M16—944no—
572C2×M16C22×D4714yes—
573C22×C8—471no—
574C22×C8—471no—
575C22×C8C22×D4711yescharacteristic
576C22×C8C22×D4711yescharacteristic
577C4⋊Q8—474no—
578C4⋊Q8—474no—
579C4⋊Q8—942no—
580C4⋊Q8—942no—
581C4⋊Q8—948no—
582#123—948no—
583#123—948no—
584C22⋊Q8—474no—
585C22⋊Q8—474no—
586C22⋊Q8—474no—
587C22⋊Q8—474no—
588C22⋊Q8—948no—
589C22⋊Q8—948no—
590C22⋊Q8—942no—
591C22⋊Q8—942no—
592C22⋊Q8—942no—
593C22⋊Q8—942no—
594#121—948no—
595C4×Q8—474no—
596C4×Q8—942no—
597C4×D4—474no—
598C4×D4—474no—
599C4×D4—474no—
600C4×D4—942no—
601C4×D4—948no—
602C2×C4⋊C4—471no—
603C2×C4⋊C4—471no—
604C2×C4⋊C4—471no—
605C2×C4⋊C4—948no—
606C2×C4⋊C4—941no—
607C2×C4⋊C4—941no—
608C2×C4⋊C4—941no—
609C2×C4⋊C4—941no—
610C2×C4⋊C4—941no—
611C2×C4⋊C4—941no—
612C2×C4⋊C4—941no—
613C2×C4⋊C4—941no—
614C2×C4⋊C4—941no—
615C2×C22⋊C4—471no—
616C2×C22⋊C4—471no—
617C2×C22⋊C4—941no—
618C2×C22⋊C4—941no—
619C2×C22⋊C4—941no—
620C2×C22⋊C4—941no—
621C2×C22⋊C4—941no—
622C2×C42—471no—
623C2×C42—941no—
624#106—474no—
625C4⋊C8—474no—
626#103—474no—
627#103—474no—
628#103—474no—
629#103—474no—
630#103—474no—
631#102—474no—
632C22⋊C8—474no—
633C22⋊C8—474no—
634C4×C8—474no—
635C24—21no—
636C24—471no—
637C24D4×D4711yescharacteristic
638#41—28no—
639#41—44no—
640#41—48no—
641#41—948no—
642#41—1884no—
643#41—1888no—
644C2×Q8—21no—
645C2×Q8—24no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—22no—
649C2×Q8—28no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—22no—
654C2×Q8—44no—
655C2×Q8—44no—
656C2×Q8—48no—
657C2×Q8—472no—
658C2×Q8—472no—
659C2×Q8—944no—
660C2×Q8—941no—
661C2×Q8—941no—
662C2×Q8—948no—
663C2×Q8—942no—
664C2×Q8—942no—
665C2×Q8—942no—
666C2×Q8—942no—
667C2×Q8—1884no—
668C2×Q8—1884no—
669C2×Q8—1888no—
670C2×Q8C2×C22⋊D4714yes—
671C2×Q8C23×D4712yes—
672C2×Q8C23×D4712yes—
673C2×Q8C23×D4712yes—
674C2×D4—24no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—44no—
678C2×D4—474no—
679C2×D4—944no—
680C2×D4—944no—
681C2×D4—1884no—
682C2×D4C2×C22⋊D4714yes—
683C2×D4C23×D4712yes—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—24no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—471no—
694C22×C4—471no—
695C22×C4—471no—
696C22×C4—472no—
697C22×C4—472no—
698C22×C4—944no—
699C22×C4—944no—
700C22×C4—944no—
701C22×C4—942no—
702C22×C4—942no—
703C22×C4—941no—
704C22×C4—941no—
705C22×C4—941no—
706C22×C4—941no—
707C22×C4—1884no—
708C22×C4—1884no—
709C22×C4—1884no—
710C22×C4D4×D4712yes—
711C22×C4D4×D4711yescharacteristic
712C22×C4C23×D4712yes—
713C22×C4C23×D4711yescharacteristic
714Q16—28no—
715Q16—28no—
716Q16—948no—
717Q16—948no—
718Q16—1884no—
719Q16—1884no—
720SD16—28no—
721SD16—948no—
722SD16C2×C22⋊D47116yescomplemented
723M16—28no—
724M16—948no—
725C2×C8—22no—
726C2×C8—472no—
727C2×C8—472no—
728C2×C8—942no—
729C2×C8—942no—
730C2×C8C2×C22⋊D4714yes—
731C2×C8C23×D4712yes—
732C2×C8C23×D4712yes—
733C4⋊C4—474no—
734C4⋊C4—472no—
735C4⋊C4—472no—
736C4⋊C4—944no—
737C4⋊C4—944no—
738C4⋊C4—944no—
739C4⋊C4—944no—
740C4⋊C4—944no—
741C4⋊C4—944no—
742C4⋊C4—944no—
743C4⋊C4—944no—
744C4⋊C4—944no—
745C4⋊C4—941no—
746C4⋊C4—941no—
747C22⋊C4—474no—
748C22⋊C4—474no—
749C22⋊C4—944no—
750C22⋊C4—944no—
751C22⋊C4—944no—
752C22⋊C4—944no—
753C22⋊C4—944no—
754C42—472no—
755C42—472no—
756C42—944no—
757C23—22no—
758C23—24no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—42no—
763C23—42no—
764C23—472no—
765C23—942no—
766C23—942no—
767C23—942no—
768C23C2×D4×D4712yes—
769C23C2×D4×D4711yescharacteristic
770Q8—24no—
771Q8—22no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—22no—
776Q8—48no—
777Q8—42no—
778Q8—42no—
779Q8—942no—
780Q8—942no—
781Q8—942no—
782Q8—942no—
783Q8—1888no—
784Q8—1882no—
785Q8—1882no—
786Q8C22×C22⋊D4714yes—
787D4—24no—
788D4—22no—
789D4—48no—
790D4—948no—
791D4—1888no—
792D4C22×C22⋊D4714yes—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—48no—
802C2×C4—48no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—474no—
806C2×C4—472no—
807C2×C4—472no—
808C2×C4—472no—
809C2×C4—942no—
810C2×C4—942no—
811C2×C4—944no—
812C2×C4—942no—
813C2×C4—942no—
814C2×C4—942no—
815C2×C4—942no—
816C2×C4—942no—
817C2×C4—942no—
818C2×C4—1888no—
819C2×C4—1888no—
820C2×C4—1888no—
821C2×C4—1882no—
822C2×C4—1882no—
823C2×C4—1882no—
824C2×C4—1882no—
825C2×C4C2×D4×D4712yes—
826C2×C4C2×D4×D4711yescharacteristic
827C2×C4C22×C22⋊D4712yes—
828C2×C4#1309406912yes—
829C2×C4C24×D4711yescharacteristic
830C8—22no—
831C8—942no—
832C8—942no—
833C8C22×C22⋊D4714yes—
834C22—22no—
835C22—24no—
836C22—22no—
837C22—22no—
838C22—44no—
839C22—48no—
840C22—42no—
841C22—42no—
842C22—942no—
843C22—942no—
844C22—942no—
845C22—1884no—
846C22D4×C22⋊D4712yes—
847C22#137×D4712yes—
848C22#1568993912yes—
849C22C22×D4×D4711yescharacteristic
850C4—22no—
851C4—24no—
852C4—42no—
853C4—42no—
854C4—474no—
855C4—942no—
856C4—942no—
857C4—1882no—
858C4—1882no—
859C4—1882no—
860C4—1882no—
861C4D4×C22⋊D4712yes—
862C4C23×C22⋊D4711yescharacteristic
863C4C2×#1309406911yescharacteristic
864C2—42no—
865C2—44no—
866C2—1882no—
867C2#2025502814yesdirect product factor
868C2C2×D4×C22⋊D4711yescharacteristic
869C2C2×#137×D4711yescharacteristic
870C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC22×#137×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689772C2
hypercenterC22×#137D47
hypocenterC47C2×#3276
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×#13094053C2semidirect
2. C2×Q8×C22⋊D47C2semidirect
4. #20255028C2direct (N × H)
5. C2×#15689501C2semidirect
6. C2×#15689381C2semidirect
7. C2×#15689378C2semidirect
8. C2×#15689331C2semidirect
9. C2×#15689326C2semidirect
10. C2×#15689285C2semidirect
11. C2×#15689282C2semidirect
12. C2×#15689279C2semidirect
13. C2×#15689277C2semidirect
14. C2×SD16×Dic47C2semidirect
15. C2×#15689199C2semidirect
16. C22×#137×C47C2semidirect
20. C2×#13094053C22semidirect
28. Q8×C22⋊D47C22semidirect
48. #15689501C22semidirect
49. #15689381C22semidirect
50. #15689378C22semidirect
51. #15689331C22semidirect
52. #15689326C22semidirect
53. #15689285C22semidirect
54. #15689282C22semidirect
55. #15689279C22semidirect
56. #15689277C22semidirect
57. SD16×Dic47C22semidirect
58. #15689199C22semidirect
73. C2×#137×C47C22semidirect
192. C2×SD16×C47D4semidirect
281. SD16×C47C2×D4semidirect
379. C2×Dic47#137semidirect
428. Dic47C2×#137semidirect
430. C22×#137D47semidirect
447. C2×C47#3276semidirect
459. C2×#137C2×D47semidirect
514. C47C2×#3276semidirect
566. C2×SD16C22⋊D47semidirect
722. SD16C2×C22⋊D47semidirect
867. C2#20255028direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940532
C2×Q8×C22⋊D472
C2×#156897722
#202550282
C2×#156895012
C2×#156893812
C2×#156893782
C2×#156893312
C2×#156893262
C2×#156892852
C2×#156892822
C2×#156892792
C2×#156892772
C2×SD16×Dic472
C2×#156891992
C22×#137×C472
C2×#327647