Finite Group Databasebeta

← C2×#20255605 #27093092

Subgroups — C2×#20255605 #27093092

Order 12032.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689808C211yesmaximal, characteristic, complemented
2C2×#15689761C211yesmaximal, characteristic
3#20255605C2116yesmaximal, direct product factor
4C2×#15689479C211yesmaximal, characteristic, complemented
5C2×#15689441C211yesmaximal, characteristic, complemented
6C2×#15689463C211yesmaximal, characteristic, complemented
7C2×#15689421C211yesmaximal, characteristic, complemented
8C2×#15689380C211yesmaximal, characteristic, complemented
9C2×#15689369C211yesmaximal, characteristic, complemented
10C2×#15689348C211yesmaximal, characteristic, complemented
11C2×#15689285C211yesmaximal, characteristic, complemented
12C2×#15689275C211yesmaximal, characteristic, complemented
13C2×#15689214C211yesmaximal, characteristic, complemented
14C2×#15689199C211yesmaximal, characteristic, complemented
15C2×#15689126C211yesmaximal, characteristic, complemented
16C2×C47×#417C211yesmaximal, characteristic, complemented
17C22×D4×D47C2211yescharacteristic
18C22×#10625337C2211yescharacteristic, complemented
19C22×#10625325C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22#15689808—24no—
23#15689808C2218yescomplemented
24#15689761—24no—
25#15689761C2218yes—
26C2×#13094019—21no—
27C2×#13094015C2211yescharacteristic, complemented
28C2×#13094014—21no—
29C2×#13094013C2211yescharacteristic
30C2×#13094007—21no—
31C2×#13094007—21no—
32C2×#13094004C2211yescharacteristic
33C2×#13094003C2211yescharacteristic, complemented
34C2×#13094000C2211yescharacteristic
35C2×#13093998C2211yescharacteristic
36C2×#13093996—21no—
37C2×#13093992—21no—
38C2×#13093989C2211yescharacteristic, complemented
39C2×D4×Dic47C2211yescharacteristic
40C2×C4×C22⋊D47C2211yescharacteristic
41C2×#13093983—21no—
42C2×#13093982C2211yescharacteristic
43C22×(C2×D47)⋊C4—21no—
44#15689479C2218yescomplemented
45#15689463C2218yescomplemented
46#15689441C2218yescomplemented
47#15689421C2218yescomplemented
48#15689380C2218yescomplemented
49#15689369C2218yescomplemented
50#15689348C2218yescomplemented
51#15689285C2218yescomplemented
52#15689275C2218yescomplemented
53#15689214C2218yescomplemented
54#15689199C2218yescomplemented
55C2×#13093958C2211yescharacteristic, complemented
56C2×#13093955C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×Dic47⋊C8C2211yescharacteristic, complemented
59#15689126C2218yescomplemented
60C2×#13093949C2211yescharacteristic, complemented
61C2×#13093948C2211yescharacteristic, complemented
62C2×#13093946C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic, complemented
69C22×#41×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic, complemented
71C22×C4⋊C4×C47C2211yescharacteristic, complemented
72C47×#417C2218yescomplemented
73C2×#103×C47C2211yescharacteristic, complemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C24×D47—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C22⋊D47—21no—
82C22×C22⋊D47D411yescharacteristic
83C2×D4×D47—24no—
84C2×D4×D47—22no—
85C2×D4×D47—42no—
86C2×D4×D47C2314yes—
87C23×Dic47—21no—
88C22×C4×D47C2311yescharacteristic
89C2×#10625337—42no—
90C2×#10625337C2314yescomplemented
91C2×#10625325—42no—
92C2×#10625325C2314yes—
93C2×#10625335—24no—
94C2×#10625335C2314yes—
95C2×#10625324—42no—
96C2×#10625324C2314yes—
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99#13094019—28no—
100#13094015—22no—
101#13094015C2314yescomplemented
102#13094014—28no—
103#13094013—22no—
104#13094013C2314yes—
105#13094007—28no—
106#13094007—28no—
107#13094004—22no—
108#13094004C2314yes—
109#13094003—22no—
110#13094003C2314yescomplemented
111#13094000—22no—
112#13094000C2314yes—
113#13093998—22no—
114#13093998C2314yes—
115#13093996—28no—
116#13093992—28no—
117#13093989—22no—
118#13093989C2314yescomplemented
119D4×Dic47—22no—
120D4×Dic47C2314yes—
121C4×C22⋊D47D414yes—
122C4×C22⋊D47C2314yes—
123#13093983—28no—
124#13093982—22no—
125#13093982C2314yes—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4D411yescharacteristic
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47D411yescharacteristic
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—28no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093958C2314yescomplemented
150#13093955C2314yescomplemented
151#13093955C2314yescomplemented
152Dic47⋊C8C2314yescomplemented
153#13093949C2314yescomplemented
154#13093948C2314yescomplemented
155#13093946C2314yes—
156#13093945C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159C22⋊(C47⋊C8)C2314yescomplemented
160(C2×D47)⋊C8C2314yes—
161C8×Dic47C2314yescomplemented
162C2×#41×C47—22no—
163C2×#41×C47—24no—
164C2×#41×C47—42no—
165C2×#41×C47C2314yes—
166C22×Q8×C47C2311yescharacteristic
167C22×D4×C47—21no—
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47—21no—
171C23×C4×C47C2311yescharacteristic
172C2×M16×C47—42no—
173C2×M16×C47C2314yescomplemented
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2311yescharacteristic
176C2×C4⋊C4×C47—22no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C4⋊C4×C47C2314yescomplemented
181#103×C47C2314yescomplemented
182#103×C47C2314yescomplemented
183#102×C47C2314yes—
184#102×C47C2314yes—
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47—24no—
189C23×D47—44no—
190C23×D47—44no—
191C23×D47—82no—
192C23×D47C2×D411yescharacteristic
193#41×C47—28no—
194#41×C47—44no—
195#41×C47—48no—
196C2×Q8×C47—21no—
197C2×Q8×C47—22no—
198C2×Q8×C47—22no—
199C2×Q8×C47C2412yes—
200C2×D4×C47—24no—
201C2×D4×C47—21no—
202C2×D4×C47—22no—
203C2×D4×C47—44no—
204C2×D4×C47#4114yes—
205C2×D4×C47C2412yes—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—24no—
211C22×C4×C47—21no—
212C22×C4×C47—24no—
213C22×C4×C47—44no—
214C22×C4×C47—44no—
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D412yes—
217C22×C4×C47C2412yes—
218C22×C4×C47C2411yescharacteristic
219C2×C22⋊D47—24no—
220C2×C22⋊D47—24no—
221C2×C22⋊D47—42no—
222C2×C22⋊D47—44no—
223C2×C22⋊D47—82no—
224C2×C22⋊D47C2×D414yes—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—24no—
229C22×Dic47—82no—
230C22×Dic47C2×D411yescharacteristic
231C22×Dic47C2×D411yescharacteristic
232C22×Dic47C2×D411yescharacteristic
233D4×D47—28no—
234D4×D47—44no—
235D4×D47—48no—
236C2×D188—22no—
237C2×D188—22no—
238C2×D188—21no—
239C2×D188C2412yes—
240C2×C4×D47—22no—
241C2×C4×D47—22no—
242C2×C4×D47C2×D412yes—
243C2×C4×D47C2412yes—
244C2×Dic94—22no—
245C2×Dic94—22no—
246C2×Dic94—21no—
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×C47—24no—
256C4⋊C4×C47C2412yes—
257C4⋊C4×C47C2412yes—
258C22⋊Dic47—24no—
259C22⋊Dic47—24no—
260C22⋊Dic47C2×D414yes—
261#10625337—44no—
262#10625335—28no—
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)⋊C4—24no—
269(C2×D47)⋊C4C2×D414yes—
270C4⋊Dic47—21no—
271C4⋊Dic47—21no—
272C4⋊Dic47—24no—
273C4⋊Dic47—24no—
274C4⋊Dic47C2412yes—
275C4⋊Dic47C2412yes—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4—24no—
280Dic47⋊C4C2×D414yes—
281C4×Dic47—24no—
282C4×Dic47—24no—
283C4×Dic47C2×D412yes—
284C4×Dic47C2412yes—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8C2412yes—
288C2×C47⋊C8C2412yes—
289#10625325—44no—
290#10625324—44no—
291C23×C47—24no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—42no—
297C23×C47—42no—
298C23×C47C22×D412yes—
299C23×C47C22×D411yescharacteristic
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—48no—
305C22×D47—48no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—42no—
309C22×D47—84no—
310C22×D47—816no—
311C22×D47C22×D412yes—
312Q8×C47—22no—
313Q8×C47—22no—
314Q8×C47—42no—
315D4×C47—24no—
316D4×C47—22no—
317D4×C47—48no—
318D4×C47C2×#4114yes—
319C2×C4×C47—22no—
320C2×C4×C47—24no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—48no—
327C2×C4×C47—48no—
328C2×C4×C47—42no—
329C2×C4×C47—42no—
330C2×C4×C47—42no—
331C2×C4×C47C22×D412yes—
332C2×C4×C47C22×D411yescharacteristic
333C2×C4×C47C2×#4112yes—
334C2×C4×C47H(5,𝔽2)12yes—
335C2×C4×C47C2511yescharacteristic
336C22⋊D47—44no—
337C22⋊D47—48no—
338C22⋊D47—84no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47—84no—
349C2×Dic47C22×D412yes—
350C2×Dic47C22×D412yes—
351C2×Dic47C22×D412yes—
352D188—22no—
353D188—22no—
354D188—42no—
355C4×D47—24no—
356C4×D47—22no—
357C4×D47—22no—
358Dic94—22no—
359Dic94—22no—
360Dic94—42no—
361C8×C47—22no—
362C8×C47—22no—
363C47⋊C8—22no—
364C47⋊C8—22no—
365C2×#3323—471nomaximal, Sylow
366C22×C47—24no—
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—48no—
371C22×C47—44no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47#54612yes—
375C22×C47#57512yes—
376C22×C47#57712yes—
377C22×C47C23×D411yescharacteristic
378C2×D47—22no—
379C2×D47—22no—
380C2×D47—22no—
381C2×D47—44no—
382C2×D47—42no—
383C2×D47—42no—
384C2×D47—42no—
385C2×D47—816no—
386C2×D47—84no—
387C4×C47—22no—
388C4×C47—42no—
389C4×C47—42no—
390C4×C47—42no—
391C4×C47#54612yes—
392C4×C47C22×#4111yescharacteristic
393C4×C47C2×H(5,𝔽2)11yescharacteristic
394Dic47—22no—
395Dic47—22no—
396Dic47—22no—
397Dic47—42no—
398Dic47—42no—
399Dic47—42no—
400C2×#552—471no—
401C2×#546—471no—
402#3323—4716no—
403C2×#488—471no—
404C2×#481—471no—
405C2×#485—471no—
406C2×#478—471no—
407C2×#470—471no—
408C2×#468—471no—
409C2×#464—471no—
410C2×#452—471no—
411C2×#450—471no—
412C2×C4×SD16—471no—
413C2×#436—471no—
414C2×#417D4711yescharacteristic, complemented
415C2×#418—471no—
416C2×C47—44no—
417C2×C47—42no—
418C2×C47#332314yescomplemented
419C2×C47C2×#54611yescharacteristic
420C2×C47C2×#57511yescharacteristic
421C2×C47C2×#57711yescharacteristic
422D47—42no—
423D47—82no—
424C22×#41C2×D4711yescharacteristic
425C23×D4—471no—
426C22×Q16—471no—
427C22×SD16—471no—
428C22×SD16—471no—
429C22×M16—471no—
430C22×M16C2×D4711yescharacteristic, complemented
431#552—478no—
432#552—944no—
433#546—478no—
434#546—944no—
435C2×#126—941no—
436C2×#125—471no—
437C2×#125—941no—
438C2×#124—471no—
439C2×#123—941no—
440C2×#123—941no—
441C2×C22⋊Q8—471no—
442C2×C22⋊Q8—471no—
443C2×C22⋊Q8—471no—
444C2×#121—471no—
445C2×#121—941no—
446C2×#120—941no—
447C2×C4×Q8—471no—
448C2×C4×D4—471no—
449C2×C4×D4—471no—
450C2×#117—471no—
451C2×#117—941no—
452C22×C4⋊C4C2×D4711yescharacteristic, complemented
453C22×C22⋊C4—941no—
454#488—478no—
455#485—478no—
456#481—478no—
457#478—478no—
458#470—478no—
459#468—478no—
460#464—478no—
461#452—478no—
462#450—478no—
463C4×SD16—478no—
464#436—478no—
465C2×#107—471no—
466C2×#106—471no—
467C2×#106—471no—
468C2×C4⋊C8—471no—
469#418—478no—
470#417C2×D4718yescomplemented
471C2×#103—471no—
472C2×#103—471no—
473C2×#103C2×D4711yescharacteristic, complemented
474C2×#103C2×D4711yescharacteristic, complemented
475C2×#102—471no—
476C2×#102—471no—
477C2×#102—471no—
478C2×#102—471no—
479C2×#102C2×D4711yescharacteristic
480C2×#102C2×D4711yescharacteristic
481C2×C22⋊C8—471no—
482C2×C22⋊C8—471no—
483C2×C4×C8—471no—
484C47C2×#332311yescharacteristic, complemented, Sylow
485C25—941no—
486C2×#41—22no—
487C2×#41—24no—
488C2×#41—42no—
489C2×#41C22×D4714yes—
490C22×Q8—471no—
491C22×Q8C22×D4711yescharacteristic
492C22×D4—21no—
493C22×D4—471no—
494C22×D4—474no—
495C22×D4—471no—
496C22×D4—942no—
497C22×D4—941no—
498C22×D4—944no—
499C22×D4—941no—
500C22×D4—1882no—
501C22×D4C22×D4711yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—471no—
505C23×C4—941no—
506C23×C4C22×D4711yescharacteristic
507C2×Q16—474no—
508C2×Q16—1882no—
509C2×SD16—474no—
510C2×SD16—474no—
511C2×SD16—944no—
512C2×SD16—1882no—
513C2×M16—42no—
514C2×M16—474no—
515C2×M16—1882no—
516C2×M16C22×D4714yescomplemented
517C22×C8—471no—
518C22×C8—471no—
519C22×C8C22×D4711yescharacteristic
520C22×C8C22×D4711yescharacteristic
521#126—948no—
522#125—474no—
523#125—942no—
524#125—948no—
525#124—474no—
526#124—942no—
527#123—948no—
528#123—948no—
529C22⋊Q8—474no—
530C22⋊Q8—474no—
531C22⋊Q8—474no—
532C22⋊Q8—942no—
533C22⋊Q8—942no—
534C22⋊Q8—942no—
535#121—474no—
536#121—948no—
537#121—942no—
538#120—948no—
539C4×Q8—474no—
540C4×Q8—942no—
541C4×D4—474no—
542C4×D4—474no—
543C4×D4—474no—
544C4×D4—942no—
545#117—474no—
546#117—948no—
547#117—942no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—471no—
551C2×C4⋊C4—471no—
552C2×C4⋊C4—471no—
553C2×C4⋊C4—941no—
554C2×C4⋊C4—941no—
555C2×C4⋊C4—941no—
556C2×C4⋊C4—941no—
557C2×C4⋊C4—941no—
558C2×C4⋊C4—941no—
559C2×C4⋊C4C22×D4711yescharacteristic
560C2×C4⋊C4C22×D4711yescharacteristic
561C2×C4⋊C4C22×D4714yescomplemented
562C2×C22⋊C4—471no—
563C2×C22⋊C4—471no—
564C2×C22⋊C4—948no—
565C2×C22⋊C4—941no—
566C2×C22⋊C4—941no—
567C2×C22⋊C4—941no—
568C2×C22⋊C4—941no—
569C2×C22⋊C4—941no—
570C2×C22⋊C4—941no—
571C2×C22⋊C4—941no—
572C2×C22⋊C4—941no—
573C2×C42—471no—
574C2×C42—941no—
575C2×C42—941no—
576#107—474no—
577#106—474no—
578#106—474no—
579C4⋊C8—474no—
580#103—474no—
581#103—474no—
582#103C22×D4714yescomplemented
583#103C22×D4714yescomplemented
584#102—474no—
585#102—474no—
586#102—474no—
587#102—474no—
588#102C22×D4714yes—
589#102C22×D4714yes—
590C22⋊C8—474no—
591C22⋊C8—474no—
592C4×C8—474no—
593C24—21no—
594C24—471no—
595C24—944no—
596C24—941no—
597C24—3762no—
598C24—1884no—
599C24—1884no—
600C24D4×D4711yescharacteristic
601#41—28no—
602#41—44no—
603#41—48no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—472no—
608C2×Q8—941no—
609C2×Q8—942no—
610C2×Q8—942no—
611C2×Q8C23×D4712yes—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—44no—
616C2×D4—474no—
617C2×D4—472no—
618C2×D4—944no—
619C2×D4—948no—
620C2×D4—944no—
621C2×D4—941no—
622C2×D4—942no—
623C2×D4—942no—
624C2×D4—3762no—
625C2×D4—1884no—
626C2×D4—1888no—
627C2×D4—1882no—
628C2×D4—1884no—
629C2×D4#1062535014yes—
630C2×D4C23×D4712yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—471no—
641C22×C4—471no—
642C22×C4—471no—
643C22×C4—472no—
644C22×C4—472no—
645C22×C4—944no—
646C22×C4—942no—
647C22×C4—942no—
648C22×C4—941no—
649C22×C4—941no—
650C22×C4—941no—
651C22×C4—3762no—
652C22×C4D4×D4712yes—
653C22×C4D4×D4711yescharacteristic
654C22×C4C23×D4712yes—
655C22×C4C23×D4711yescharacteristic
656Q16—1884no—
657SD16—948no—
658SD16—1884no—
659M16—44no—
660M16—1884no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—472no—
664C2×C8—472no—
665C2×C8—942no—
666C2×C8—942no—
667C2×C8C23×D4712yes—
668C2×C8C23×D4712yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—474no—
673C4⋊C4—472no—
674C4⋊C4—472no—
675C4⋊C4—944no—
676C4⋊C4—944no—
677C4⋊C4—944no—
678C4⋊C4—944no—
679C4⋊C4—944no—
680C4⋊C4—944no—
681C4⋊C4—941no—
682C4⋊C4—941no—
683C4⋊C4C23×D4712yes—
684C4⋊C4C23×D4712yes—
685C22⋊C4—474no—
686C22⋊C4—474no—
687C22⋊C4—944no—
688C22⋊C4—944no—
689C22⋊C4—944no—
690C22⋊C4—944no—
691C22⋊C4—944no—
692C22⋊C4—944no—
693C22⋊C4—944no—
694C22⋊C4—944no—
695C42—472no—
696C42—472no—
697C42—944no—
698C42—944no—
699C23—22no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—472no—
707C23—942no—
708C23—942no—
709C23—942no—
710C23—942no—
711C23—3764no—
712C23—37616no—
713C23—1888no—
714C23—1888no—
715C23—1882no—
716C23—1882no—
717C23—1882no—
718C23C2×D4×D4712yes—
719C23C2×D4×D4711yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—942no—
724Q8—942no—
725Q8—1882no—
726D4—24no—
727D4—22no—
728D4—48no—
729D4—942no—
730D4—942no—
731D4—3764no—
732D4—1884no—
733D4—1888no—
734D4—1882no—
735D4C2×#1062535014yes—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—48no—
744C2×C4—48no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—472no—
749C2×C4—472no—
750C2×C4—472no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—944no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—3764no—
761C2×C4—1882no—
762C2×C4—1882no—
763C2×C4—1882no—
764C2×C4C2×D4×D4712yes—
765C2×C4C2×D4×D4711yescharacteristic
766C2×C4C2×#1062535012yes—
767C2×C4#1309406912yes—
768C2×C4C24×D4711yescharacteristic
769C8—22no—
770C8—22no—
771C8—942no—
772C8—942no—
773C22—22no—
774C22—24no—
775C22—22no—
776C22—22no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—48no—
781C22—942no—
782C22—942no—
783C22—942no—
784C22—37616no—
785C22—3764no—
786C22—1882no—
787C22—1882no—
788C22—1882no—
789C22—1884no—
790C22#1568976312yes—
791C22#1568991912yes—
792C22#1568993212yes—
793C22C22×D4×D4711yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—942no—
799C4—942no—
800C4—942no—
801C4—1882no—
802C4—1882no—
803C4—1882no—
804C4#1568976312yes—
805C4C22×#1062535011yescharacteristic
806C4C2×#1309406911yescharacteristic
807C2—42no—
808C2—44no—
809C2—3762no—
810C2—1882no—
811C2#2025560514yesdirect product factor
812C2C2×#1568976311yescharacteristic
813C2C2×#1568991911yescharacteristic
814C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#417C2
socleC23×C47C22×D4
prime radicalC2×#15689761C2
hypercenterC2×#417D47
hypocenterC47C2×#3323
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#15689808C2semidirect
3. #20255605C2direct (N × H)
4. C2×#15689479C2semidirect
5. C2×#15689441C2semidirect
6. C2×#15689463C2semidirect
7. C2×#15689421C2semidirect
8. C2×#15689380C2semidirect
9. C2×#15689369C2semidirect
10. C2×#15689348C2semidirect
11. C2×#15689285C2semidirect
12. C2×#15689275C2semidirect
13. C2×#15689214C2semidirect
14. C2×#15689199C2semidirect
15. C2×#15689126C2semidirect
16. C2×C47×#417C2semidirect
18. C22×#10625337C22semidirect
23. #15689808C22semidirect
27. C2×#13094015C22semidirect
33. C2×#13094003C22semidirect
38. C2×#13093989C22semidirect
44. #15689479C22semidirect
45. #15689463C22semidirect
46. #15689441C22semidirect
47. #15689421C22semidirect
48. #15689380C22semidirect
49. #15689369C22semidirect
50. #15689348C22semidirect
51. #15689285C22semidirect
52. #15689275C22semidirect
53. #15689214C22semidirect
54. #15689199C22semidirect
55. C2×#13093958C22semidirect
56. C2×#13093955C22semidirect
57. C2×#13093955C22semidirect
58. C2×Dic47⋊C8C22semidirect
59. #15689126C22semidirect
60. C2×#13093949C22semidirect
61. C2×#13093948C22semidirect
66. C2×C22⋊(C47⋊C8)C22semidirect
68. C2×C8×Dic47C22semidirect
70. C22×M16×C47C22semidirect
71. C22×C4⋊C4×C47C22semidirect
72. C47×#417C22semidirect
73. C2×#103×C47C22semidirect
74. C2×#103×C47C22semidirect
90. C2×#10625337C23semidirect
101. #13094015C23semidirect
110. #13094003C23semidirect
118. #13093989C23semidirect
149. #13093958C23semidirect
150. #13093955C23semidirect
151. #13093955C23semidirect
152. Dic47⋊C8C23semidirect
153. #13093949C23semidirect
154. #13093948C23semidirect
159. C22⋊(C47⋊C8)C23semidirect
161. C8×Dic47C23semidirect
173. C2×M16×C47C23semidirect
180. C2×C4⋊C4×C47C23semidirect
181. #103×C47C23semidirect
182. #103×C47C23semidirect
414. C2×#417D47semidirect
418. C2×C47#3323semidirect
430. C22×M16C2×D47semidirect
452. C22×C4⋊C4C2×D47semidirect
470. #417C2×D47semidirect
473. C2×#103C2×D47semidirect
474. C2×#103C2×D47semidirect
484. C47C2×#3323semidirect
516. C2×M16C22×D47semidirect
561. C2×C4⋊C4C22×D47semidirect
582. #103C22×D47semidirect
583. #103C22×D47semidirect
811. C2#20255605direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898082
C2×#156897612
#202556052
C2×#156894792
C2×#156894412
C2×#156894632
C2×#156894212
C2×#156893802
C2×#156893692
C2×#156893482
C2×#156892852
C2×#156892752
C2×#156892142
C2×#156891992
C2×#156891262
C2×C47×#4172
C2×#332347