Finite Group Databasebeta

← C2×#20254958 #27091323

Subgroups — C2×#20254958 #27091323

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×#13094056C211yesmaximal, characteristic, complemented
2C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
3C2×#15689784C211yesmaximal, characteristic
4#20254958C2116yesmaximal, direct product factor
5C2×#15689516C211yesmaximal, characteristic, complemented
6C2×#15689378C211yesmaximal, characteristic, complemented
7C2×#15689352C211yesmaximal, characteristic, complemented
8C2×#15689347C211yesmaximal, characteristic, complemented
9C2×#15689331C211yesmaximal, characteristic, complemented
10C2×#15689284C211yesmaximal, characteristic, complemented
11C2×#15689279C211yesmaximal, characteristic, complemented
12C2×#15689277C211yesmaximal, characteristic, complemented
13C2×#15689262C211yesmaximal, characteristic, complemented
14C2×#15689230C211yesmaximal, characteristic, complemented
15C2×#15689194C211yesmaximal, characteristic, complemented
16C23×Q16×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C2×#13094056—28no—
20C2×#13094056C2218yescomplemented
21C22×#10625337C2211yescharacteristic
22C22×#10625337C2211yescharacteristic
23C22×#10625325C2211yescharacteristic
24C22×#10625336C2211yescharacteristic
25C22×#10625336C2211yescharacteristic
26C22×#10625324C2211yescharacteristic
27Q8×C22⋊D47—24no—
28Q8×C22⋊D47C2218yescomplemented
29#15689784—24no—
30#15689784C2218yes—
31C2×#13094022—21no—
32C2×#13094022C2211yescharacteristic
33C2×#13094013—21no—
34C2×#13094013C2211yescharacteristic
35C2×#13094003—21no—
36C2×#13094003C2211yescharacteristic
37C2×#13094000—21no—
38C2×#13094000—21no—
39C2×#13094000C2211yescharacteristic
40C2×#13094000C2211yescharacteristic
41C2×#13093998—21no—
42C2×#13093998C2211yescharacteristic
43C2×Q8×Dic47C2211yescharacteristic
44C2×Q8×Dic47C2211yescharacteristic
45C2×C4×C22⋊D47—21no—
46C2×C4×C22⋊D47—21no—
47C2×C4×C22⋊D47C2211yescharacteristic
48#15689516C2218yescomplemented
49#15689378C2218yescomplemented
50#15689352C2218yescomplemented
51#15689347C2218yescomplemented
52#15689331C2218yescomplemented
53#15689284C2218yescomplemented
54#15689279C2218yescomplemented
55#15689277C2218yescomplemented
56#15689262C2218yescomplemented
57#15689230C2218yescomplemented
58#15689194C2218yescomplemented
59C2×#13093956C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×C22⋊(C47⋊C8)C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C2×#13093934C2211yescharacteristic
70C23×Q8×C47C2211yescharacteristic
71C23×Q8×C47C2211yescharacteristic
72C22×Q16×C47—28no—
73C22×Q16×C47C2211yescharacteristic
74C22×Q16×C47C2211yescharacteristic
75C22×Q16×C47C2211yescharacteristic
76C22×Q16×C47C2211yescharacteristic
77C22×Q16×C47C2218yescomplemented
78C23×C8×C47C2211yescharacteristic
79C2×#10625354—22no—
80C2×#10625354—24no—
81C2×#10625354—42no—
82C2×#10625354C2314yes—
83C22×Dic94—21no—
84C22×Dic94C2311yescharacteristic
85C2×Q8×D47—22no—
86C2×Q8×D47—24no—
87C2×Q8×D47—42no—
88C2×Q8×D47C2314yes—
89C22×D188—21no—
90C22×D188C2311yescharacteristic
91C22×C22⋊D47—21no—
92C22×C22⋊D47D411yescharacteristic
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47C2311yescharacteristic
96#13094056—232no—
97C2×#10625337—24no—
98C2×#10625337—42no—
99C2×#10625337C2314yes—
100C2×#10625337C2314yes—
101C2×#10625325—24no—
102C2×#10625325C2314yes—
103C2×#10625336—24no—
104C2×#10625336—42no—
105C2×#10625336C2314yes—
106C2×#10625336C2314yes—
107C2×#10625324—24no—
108C2×#10625324C2314yes—
109C22×C47⋊C8C2311yescharacteristic
110C22×C47⋊C8C2311yescharacteristic
111#13094022—28no—
112#13094022—22no—
113#13094022C2314yes—
114#13094013—28no—
115#13094013—22no—
116#13094013C2314yes—
117#13094003—22no—
118#13094003—28no—
119#13094003C2314yes—
120#13094000—22no—
121#13094000—22no—
122#13094000—28no—
123#13094000—28no—
124#13094000C2314yes—
125#13094000C2314yes—
126#13093998—22no—
127#13093998—28no—
128#13093998C2314yes—
129Q8×Dic47—22no—
130Q8×Dic47—22no—
131Q8×Dic47C2314yes—
132Q8×Dic47C2314yes—
133C4×C22⋊D47—28no—
134C4×C22⋊D47—28no—
135C4×C22⋊D47D414yes—
136C4×C22⋊D47C2314yes—
137C2×C4⋊Dic47—21no—
138C2×C4⋊Dic47—21no—
139C2×C4⋊Dic47C2311yescharacteristic
140C2×C4⋊Dic47C2311yescharacteristic
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4—21no—
143C2×Dic47⋊C4—21no—
144C2×Dic47⋊C4—21no—
145C2×Dic47⋊C4—21no—
146C2×Dic47⋊C4D411yescharacteristic
147C2×C22⋊Dic47—21no—
148C2×C22⋊Dic47D411yescharacteristic
149C2×(C2×D47)⋊C4—21no—
150C2×(C2×D47)⋊C4—21no—
151C2×(C2×D47)⋊C4—21no—
152C2×(C2×D47)⋊C4—21no—
153C2×(C2×D47)⋊C4—21no—
154C2×(C2×D47)⋊C4D411yescharacteristic
155C2×C4×Dic47—21no—
156C2×C4×Dic47—21no—
157C2×C4×Dic47C2311yescharacteristic
158#13093956C2314yes—
159Dic47⋊C8C2314yes—
160#13093949C2314yes—
161#13093948C2314yes—
162#13093948C2314yes—
163#13093948C2314yes—
164#13093948C2314yes—
165#13093946C2314yes—
166C22⋊(C47⋊C8)C2314yes—
167(C2×D47)⋊C8C2314yes—
168#13093934C2314yes—
169C22×Q8×C47—22no—
170C22×Q8×C47—22no—
171C22×Q8×C47—21no—
172C22×Q8×C47—21no—
173C22×Q8×C47—24no—
174C22×Q8×C47—24no—
175C22×Q8×C47—42no—
176C22×Q8×C47—42no—
177C22×Q8×C47C2311yescharacteristic
178C22×Q8×C47C2311yescharacteristic
179C22×Q8×C47C2314yes—
180C22×Q8×C47C2314yes—
181C22×Q8×C47C2311yescharacteristic
182C22×Q8×C47C2311yescharacteristic
183C23×C4×C47—21no—
184C23×C4×C47—21no—
185C23×C4×C47C2311yescharacteristic
186C2×Q16×C47—24no—
187C2×Q16×C47—24no—
188C2×Q16×C47—232no—
189C2×Q16×C47—24no—
190C2×Q16×C47D418yescomplemented
191C2×Q16×C47C2314yes—
192C2×Q16×C47C2314yes—
193C2×Q16×C47C2314yes—
194C2×Q16×C47C2314yes—
195C22×C8×C47—24no—
196C22×C8×C47C2311yescharacteristic
197C22×C8×C47C2314yes—
198C22×C8×C47C2311yescharacteristic
199C24×C47C2×D411yescharacteristic
200C23×D47—21no—
201C23×D47C2×D411yescharacteristic
202C2×Q8×C47—21no—
203C2×Q8×C47—21no—
204C2×Q8×C47—24no—
205C2×Q8×C47—21no—
206C2×Q8×C47—24no—
207C2×Q8×C47—21no—
208C2×Q8×C47—22no—
209C2×Q8×C47—22no—
210C2×Q8×C47—28no—
211C2×Q8×C47—28no—
212C2×Q8×C47—22no—
213C2×Q8×C47—22no—
214C2×Q8×C47—22no—
215C2×Q8×C47—22no—
216C2×Q8×C47—44no—
217C2×Q8×C47—44no—
218C2×Q8×C47—44no—
219C2×Q8×C47—44no—
220C2×Q8×C47—48no—
221C2×Q8×C47—48no—
222C2×Q8×C47C2×D414yes—
223C2×Q8×C47C2×D414yes—
224C2×Q8×C47C2412yes—
225C2×Q8×C47C2412yes—
226C2×Q8×C47C2412yes—
227C2×Q8×C47C2412yes—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—24no—
235C22×C4×C47—24no—
236C22×C4×C47—44no—
237C22×C4×C47—44no—
238C22×C4×C47C2×D411yescharacteristic
239C22×C4×C47C2×D412yes—
240C22×C4×C47C2412yes—
241C22×C4×C47C2411yescharacteristic
242C2×C22⋊D47—24no—
243C2×C22⋊D47—24no—
244C2×C22⋊D47—44no—
245C2×C22⋊D47C2×D414yes—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47—21no—
249C22×Dic47C2×D411yescharacteristic
250C22×Dic47C2×D411yescharacteristic
251C22×Dic47C2×D411yescharacteristic
252#10625354—28no—
253#10625354—44no—
254#10625354—48no—
255Q8×D47—28no—
256Q8×D47—44no—
257Q8×D47—48no—
258C2×D188—22no—
259C2×D188—22no—
260C2×D188—24no—
261C2×D188—21no—
262C2×D188—44no—
263C2×D188C2412yes—
264C2×C4×D47—22no—
265C2×C4×D47—22no—
266C2×C4×D47—24no—
267C2×C4×D47—24no—
268C2×C4×D47—44no—
269C2×C4×D47—44no—
270C2×C4×D47C2×D412yes—
271C2×C4×D47C2412yes—
272C2×Dic94—22no—
273C2×Dic94—22no—
274C2×Dic94—21no—
275C2×Dic94—24no—
276C2×Dic94—44no—
277C2×Dic94C2412yes—
278Q16×C47—28no—
279Q16×C47—28no—
280Q16×C47—28no—
281Q16×C47C2×D4116yescomplemented
282C2×C8×C47—22no—
283C2×C8×C47—28no—
284C2×C8×C47C2×D414yes—
285C2×C8×C47C2412yes—
286C2×C8×C47C2412yes—
287C22⋊Dic47—24no—
288C22⋊Dic47C2×D414yes—
289#10625337—28no—
290#10625337—44no—
291#10625336—28no—
292#10625336—44no—
293(C2×D47)⋊C4—24no—
294(C2×D47)⋊C4—24no—
295(C2×D47)⋊C4—24no—
296(C2×D47)⋊C4—24no—
297(C2×D47)⋊C4—24no—
298(C2×D47)⋊C4C2×D414yes—
299C4⋊Dic47—21no—
300C4⋊Dic47—21no—
301C4⋊Dic47—24no—
302C4⋊Dic47—24no—
303C4⋊Dic47C2412yes—
304C4⋊Dic47C2412yes—
305Dic47⋊C4—24no—
306Dic47⋊C4—24no—
307Dic47⋊C4—24no—
308Dic47⋊C4—24no—
309Dic47⋊C4—24no—
310Dic47⋊C4C2×D414yes—
311C4×Dic47—24no—
312C4×Dic47—24no—
313C4×Dic47C2×D412yes—
314C4×Dic47C2412yes—
315C2×C47⋊C8—22no—
316C2×C47⋊C8—22no—
317C2×C47⋊C8C2412yes—
318C2×C47⋊C8C2412yes—
319#10625325—28no—
320#10625324—28no—
321C23×C47—22no—
322C23×C47—22no—
323C23×C47#13714yescomplemented
324C23×C47C22×D412yes—
325C23×C47C22×D411yescharacteristic
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—42no—
331C22×D47—42no—
332C22×D47—42no—
333C22×D47C22×D412yes—
334Q8×C47—24no—
335Q8×C47—24no—
336Q8×C47—22no—
337Q8×C47—22no—
338Q8×C47—22no—
339Q8×C47—22no—
340Q8×C47—22no—
341Q8×C47—22no—
342Q8×C47—48no—
343Q8×C47—48no—
344Q8×C47—42no—
345Q8×C47—42no—
346Q8×C47C22×D414yes—
347Q8×C47C22×D414yes—
348C2×C4×C47—24no—
349C2×C4×C47—24no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—24no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—48no—
359C2×C4×C47—48no—
360C2×C4×C47—42no—
361C2×C4×C47—42no—
362C2×C4×C47C22×D412yes—
363C2×C4×C47C22×D411yescharacteristic
364C2×C4×C47C22×D412yes—
365C2×C4×C47H(5,𝔽2)12yes—
366C2×C4×C47C2511yescharacteristic
367C22⋊D47—28no—
368C22⋊D47—48no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—22no—
374C2×Dic47—22no—
375C2×Dic47—42no—
376C2×Dic47—42no—
377C2×Dic47—42no—
378C2×Dic47C22×D412yes—
379C2×Dic47C22×D412yes—
380C2×Dic47C22×D412yes—
381D188—22no—
382D188—22no—
383D188—48no—
384D188—42no—
385C4×D47—24no—
386C4×D47—22no—
387C4×D47—22no—
388C4×D47—48no—
389C4×D47—48no—
390Dic94—22no—
391Dic94—22no—
392Dic94—48no—
393Dic94—42no—
394C8×C47—22no—
395C8×C47C22×D414yes—
396C47⋊C8—22no—
397C47⋊C8—22no—
398C2×#3270—471nomaximal, Sylow
399C22×C47—22no—
400C22×C47—28no—
401C22×C47—22no—
402C22×C47D4212yes—
403C22×C47C2×#13712yes—
404C22×C47C2×#13714yescomplemented
405C22×C47#57812yes—
406C22×C47C23×D411yescharacteristic
407C2×D47—22no—
408C2×D47—22no—
409C2×D47—22no—
410C2×D47—44no—
411C2×D47—42no—
412C2×D47—42no—
413C2×D47—42no—
414C2×D47—84no—
415C4×C47—24no—
416C4×C47—24no—
417C4×C47—22no—
418C4×C47—42no—
419C4×C47—42no—
420C4×C47D4212yes—
421C4×C47C23×D411yescharacteristic
422C4×C47C2×H(5,𝔽2)11yescharacteristic
423Dic47—22no—
424Dic47—22no—
425Dic47—22no—
426Dic47—42no—
427Dic47—42no—
428Dic47—42no—
429C22×#137—471no—
430C23×Q16D4711yescharacteristic, complemented
431C2×D4×Q8—471no—
432C2×#548—471no—
433#3270—4716no—
434C2×#497—471no—
435C2×#470—471no—
436C2×#465—471no—
437C2×#464—471no—
438C2×#462—471no—
439C2×#452—471no—
440C2×#451—471no—
441C2×#451—471no—
442C2×#448—471no—
443C2×#441—471no—
444C2×#435—471no—
445C2×C47—24no—
446C2×C47#327014yescomplemented
447C2×C47C2×D4211yescharacteristic
448C2×C47C22×#13711yescharacteristic
449C2×C47C2×#57811yescharacteristic
450D47—42no—
451D47—82no—
452C22×#41—471no—
453C23×Q8—471no—
454C23×Q8C2×D4711yescharacteristic
455C23×Q8C2×D4711yescharacteristic
456C2×#137—478no—
457C2×#137—948no—
458C22×Q16—28no—
459C22×Q16—471no—
460C22×Q16—471no—
461C22×Q16C2×D4711yescharacteristic
462C22×Q16C2×D4711yescharacteristic
463C22×Q16C2×D4711yescharacteristic
464C22×Q16C2×D4711yescharacteristic
465C22×Q16C2×D4718yescomplemented
466C22×SD16—471no—
467C22×SD16—471no—
468C22×SD16—471no—
469C22×M16—471no—
470C23×C8C2×D4711yescharacteristic
471D4×Q8—478no—
472D4×Q8—944no—
473#548—478no—
474#548—944no—
475C2×C4⋊Q8—471no—
476C2×C4⋊Q8—941no—
477C2×#124—471no—
478C2×#124—941no—
479C2×C22⋊Q8—471no—
480C2×C22⋊Q8—471no—
481C2×C22⋊Q8—471no—
482C2×C22⋊Q8—941no—
483C2×C22⋊Q8—941no—
484C2×C22⋊Q8—941no—
485C2×#121—471no—
486C2×#121—941no—
487C2×C4×Q8—471no—
488C2×C4×Q8—471no—
489C2×C4×D4—471no—
490C2×C4×D4—941no—
491C2×C4×D4—941no—
492#497—478no—
493#470—478no—
494#465—478no—
495#464—478no—
496#462—478no—
497#452—478no—
498#451—478no—
499#451—478no—
500#448—478no—
501#441—478no—
502#435—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×#97—471no—
514C47C2×#327011yescharacteristic, complemented, Sylow
515C2×#41—474no—
516C2×#41—942no—
517C2×#41—944no—
518C2×#41—1882no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—22no—
522C22×Q8—22no—
523C22×Q8—24no—
524C22×Q8—24no—
525C22×Q8—42no—
526C22×Q8—42no—
527C22×Q8—474no—
528C22×Q8—471no—
529C22×Q8—941no—
530C22×Q8—942no—
531C22×Q8—944no—
532C22×Q8—1882no—
533C22×Q8C22×D4711yescharacteristic
534C22×Q8C22×D4711yescharacteristic
535C22×Q8C22×D4714yes—
536C22×Q8C22×D4714yes—
537C22×Q8C22×D4711yescharacteristic
538C22×Q8C22×D4711yescharacteristic
539C22×D4—471no—
540C22×D4—471no—
541C22×D4—941no—
542C22×D4—941no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—471no—
546C23×C4—941no—
547C23×C4—941no—
548C23×C4C22×D4711yescharacteristic
549#137—9432no—
550C2×Q16—24no—
551C2×Q16—24no—
552C2×Q16—232no—
553C2×Q16—24no—
554C2×Q16—474no—
555C2×Q16—474no—
556C2×Q16—944no—
557C2×Q16—1882no—
558C2×Q16C22⋊D4718yescomplemented
559C2×Q16C22×D4714yes—
560C2×Q16C22×D4714yes—
561C2×Q16C22×D4714yes—
562C2×Q16C22×D4714yes—
563C2×SD16—474no—
564C2×SD16—474no—
565C2×SD16—474no—
566C2×SD16—944no—
567C2×SD16—944no—
568C2×SD16—1882no—
569C2×M16—474no—
570C2×M16—944no—
571C22×C8—24no—
572C22×C8—471no—
573C22×C8—471no—
574C22×C8C22×D4711yescharacteristic
575C22×C8C22×D4714yes—
576C22×C8C22×D4711yescharacteristic
577C4⋊Q8—474no—
578C4⋊Q8—942no—
579C4⋊Q8—948no—
580#124—474no—
581#124—942no—
582#124—948no—
583C22⋊Q8—474no—
584C22⋊Q8—474no—
585C22⋊Q8—474no—
586C22⋊Q8—948no—
587C22⋊Q8—948no—
588C22⋊Q8—948no—
589C22⋊Q8—942no—
590C22⋊Q8—942no—
591C22⋊Q8—942no—
592#121—474no—
593#121—948no—
594#121—942no—
595C4×Q8—474no—
596C4×Q8—474no—
597C4×Q8—942no—
598C4×Q8—942no—
599C4×D4—474no—
600C4×D4—474no—
601C4×D4—948no—
602C4×D4—948no—
603C2×C4⋊C4—471no—
604C2×C4⋊C4—471no—
605C2×C4⋊C4—471no—
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×C22⋊C4—471no—
614C2×C22⋊C4—471no—
615C2×C22⋊C4—941no—
616C2×C22⋊C4—941no—
617C2×C22⋊C4—941no—
618C2×C22⋊C4—941no—
619C2×C22⋊C4—941no—
620C2×C22⋊C4—941no—
621C2×C42—471no—
622C2×C42—941no—
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—
634#97—474no—
635C24—471no—
636C24—941no—
637C24D4×D4711yescharacteristic
638#41—948no—
639#41—1884no—
640#41—1888no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—24no—
644C2×Q8—21no—
645C2×Q8—24no—
646C2×Q8—21no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—28no—
650C2×Q8—28no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—22no—
654C2×Q8—22no—
655C2×Q8—44no—
656C2×Q8—44no—
657C2×Q8—44no—
658C2×Q8—44no—
659C2×Q8—48no—
660C2×Q8—48no—
661C2×Q8—472no—
662C2×Q8—944no—
663C2×Q8—941no—
664C2×Q8—948no—
665C2×Q8—942no—
666C2×Q8—942no—
667C2×Q8—1884no—
668C2×Q8—1884no—
669C2×Q8—1888no—
670C2×Q8C2×C22⋊D4714yes—
671C2×Q8C2×C22⋊D4714yes—
672C2×Q8C23×D4712yes—
673C2×Q8C23×D4712yes—
674C2×Q8C23×D4712yes—
675C2×Q8C23×D4712yes—
676C2×D4—474no—
677C2×D4—472no—
678C2×D4—944no—
679C2×D4—944no—
680C2×D4—944no—
681C2×D4—941no—
682C2×D4—942no—
683C2×D4—942no—
684C2×D4—1884no—
685C2×D4—1884no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—471no—
697C22×C4—471no—
698C22×C4—471no—
699C22×C4—472no—
700C22×C4—472no—
701C22×C4—944no—
702C22×C4—944no—
703C22×C4—942no—
704C22×C4—942no—
705C22×C4—941no—
706C22×C4—941no—
707C22×C4—941no—
708C22×C4—1884no—
709C22×C4—1884no—
710C22×C4D4×D4712yes—
711C22×C4D4×D4711yescharacteristic
712C22×C4C23×D4712yes—
713C22×C4C23×D4711yescharacteristic
714Q16—28no—
715Q16—28no—
716Q16—28no—
717Q16—948no—
718Q16—1884no—
719Q16C2×C22⋊D47116yescomplemented
720SD16—948no—
721SD16—948no—
722SD16—1884no—
723M16—948no—
724C2×C8—22no—
725C2×C8—28no—
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—941no—
744C4⋊C4—941no—
745C22⋊C4—474no—
746C22⋊C4—474no—
747C22⋊C4—944no—
748C22⋊C4—944no—
749C22⋊C4—944no—
750C22⋊C4—944no—
751C22⋊C4—944no—
752C22⋊C4—944no—
753C42—472no—
754C42—472no—
755C42—944no—
756C42—944no—
757C23—22no—
758C23—22no—
759C23—472no—
760C23—942no—
761C23—942no—
762C23—942no—
763C23—942no—
764C23—1882no—
765C23—1882no—
766C23—1882no—
767C23#1309405614yescomplemented
768C23C2×D4×D4712yes—
769C23C2×D4×D4711yescharacteristic
770Q8—24no—
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—22no—
776Q8—22no—
777Q8—22no—
778Q8—48no—
779Q8—48no—
780Q8—42no—
781Q8—42no—
782Q8—942no—
783Q8—942no—
784Q8—1888no—
785Q8—1882no—
786Q8C22×C22⋊D4714yes—
787Q8C22×C22⋊D4714yes—
788D4—948no—
789D4—942no—
790D4—942no—
791D4—1888no—
792D4—1888no—
793D4—1882no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—48no—
805C2×C4—48no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—472no—
809C2×C4—472no—
810C2×C4—472no—
811C2×C4—942no—
812C2×C4—942no—
813C2×C4—942no—
814C2×C4—944no—
815C2×C4—942no—
816C2×C4—942no—
817C2×C4—942no—
818C2×C4—942no—
819C2×C4—942no—
820C2×C4—1888no—
821C2×C4—1888no—
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—22no—
836C22—28no—
837C22—942no—
838C22—942no—
839C22—942no—
840C22—3764no—
841C22—1882no—
842C22—1882no—
843C22—1882no—
844C22—1884no—
845C22D4×C22⋊D4712yes—
846C22C2×#1309405612yes—
847C22C2×#1309405614yescomplemented
848C22#1568993612yes—
849C22C22×D4×D4711yescharacteristic
850C4—22no—
851C4—24no—
852C4—24no—
853C4—42no—
854C4—42no—
855C4—942no—
856C4—942no—
857C4—942no—
858C4—1882no—
859C4—1882no—
860C4—1882no—
861C4D4×C22⋊D4712yes—
862C4C23×C22⋊D4711yescharacteristic
863C4C2×#1309406911yescharacteristic
864C2—24no—
865C2—3762no—
866C2—1882no—
867C2#2025495814yesdirect product factor
868C2C2×D4×C22⋊D4711yescharacteristic
869C2C22×#1309405611yescharacteristic
870C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC23×Q16×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689784C2
hypercenterC23×Q16D47
hypocenterC47C2×#3270
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

Complements

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

NH ≅ G/Ntype
1. C22×#13094056C2semidirect
2. C2×Q8×C22⋊D47C2semidirect
4. #20254958C2direct (N × H)
5. C2×#15689516C2semidirect
6. C2×#15689378C2semidirect
7. C2×#15689352C2semidirect
8. C2×#15689347C2semidirect
9. C2×#15689331C2semidirect
10. C2×#15689284C2semidirect
11. C2×#15689279C2semidirect
12. C2×#15689277C2semidirect
13. C2×#15689262C2semidirect
14. C2×#15689230C2semidirect
15. C2×#15689194C2semidirect
16. C23×Q16×C47C2semidirect
20. C2×#13094056C22semidirect
28. Q8×C22⋊D47C22semidirect
48. #15689516C22semidirect
49. #15689378C22semidirect
50. #15689352C22semidirect
51. #15689347C22semidirect
52. #15689331C22semidirect
53. #15689284C22semidirect
54. #15689279C22semidirect
55. #15689277C22semidirect
56. #15689262C22semidirect
57. #15689230C22semidirect
58. #15689194C22semidirect
77. C22×Q16×C47C22semidirect
190. C2×Q16×C47D4semidirect
281. Q16×C47C2×D4semidirect
323. C23×C47#137semidirect
404. C22×C47C2×#137semidirect
430. C23×Q16D47semidirect
446. C2×C47#3270semidirect
465. C22×Q16C2×D47semidirect
514. C47C2×#3270semidirect
558. C2×Q16C22⋊D47semidirect
719. Q16C2×C22⋊D47semidirect
767. C23#13094056semidirect
847. C22C2×#13094056semidirect
867. C2#20254958direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940562
C2×Q8×C22⋊D472
C2×#156897842
#202549582
C2×#156895162
C2×#156893782
C2×#156893522
C2×#156893472
C2×#156893312
C2×#156892842
C2×#156892792
C2×#156892772
C2×#156892622
C2×#156892302
C2×#156891942
C23×Q16×C472
C2×#327047