Finite Group Databasebeta

← C2×#20254458 #27087619

Subgroups — C2×#20254458 #27087619

Order 12032.

2214 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689733C211yesmaximal, characteristic, complemented
2C2×#15689687C211yesmaximal, characteristic
3#20254458C2116yesmaximal, direct product factor
4C2×#15689516C211yesmaximal, characteristic, complemented
5C2×#15689494C211yesmaximal, characteristic, complemented
6C2×#15689486C211yesmaximal, characteristic, complemented
7C2×#15689479C211yesmaximal, characteristic, complemented
8C2×#15689348C211yesmaximal, characteristic, complemented
9C2×#15689347C211yesmaximal, characteristic, complemented
10C2×#15689322C211yesmaximal, characteristic, complemented
11C2×#15689321C211yesmaximal, characteristic, complemented
12C2×#15689285C211yesmaximal, characteristic, complemented
13C2×#15689276C211yesmaximal, characteristic, complemented
14C2×#15689273C211yesmaximal, characteristic, complemented
15C2×#15689181C211yesmaximal, characteristic, complemented
16C2×C47×#452C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C22×#10625337C2211yescharacteristic, complemented
19C22×#10625325C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625335C2211yescharacteristic, complemented
22C22×#10625336C2211yescharacteristic
23C22×#10625336C2211yescharacteristic
24#15689733—24no—
25#15689733C2218yescomplemented
26#15689687—24no—
27#15689687C2218yes—
28C2×#13094022C2211yescharacteristic, complemented
29C2×#13094020C2211yescharacteristic
30C2×#13094020C2211yescharacteristic
31C2×#13094017—21no—
32C2×#13094017—21no—
33C2×#13094015—21no—
34C2×#13094015C2211yescharacteristic, complemented
35C2×#13094014—21no—
36C2×#13094013C2211yescharacteristic
37C2×#13094013C2211yescharacteristic
38C2×#13094003C2211yescharacteristic
39C2×#13093998—21no—
40C2×#13093998—21no—
41C2×#13093992—21no—
42C2×#13093992—21no—
43C2×Q8×Dic47C2211yescharacteristic, complemented
44C2×#13093989C2211yescharacteristic, complemented
45C2×#13093983C2211yescharacteristic
46#15689516C2218yescomplemented
47#15689494C2218yescomplemented
48#15689486C2218yescomplemented
49#15689479C2218yescomplemented
50#15689348C2218yescomplemented
51#15689347C2218yescomplemented
52#15689322C2218yescomplemented
53#15689321C2218yescomplemented
54#15689285C2218yescomplemented
55#15689276C2218yescomplemented
56#15689273C2218yescomplemented
57#15689181C2218yescomplemented
58C2×Dic47⋊C8C2211yescharacteristic, complemented
59C2×Dic47⋊C8C2211yescharacteristic, complemented
60C2×#13093948C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093945C2211yescharacteristic, complemented
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×#13093934C2211yescharacteristic, complemented
68C2×C8×Dic47C2211yescharacteristic, complemented
69C22×#41×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic, complemented
71C22×SD16×C47C2211yescharacteristic, complemented
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#452C2218yescomplemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic
77C24×D47—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188—21no—
80C22×D188—22no—
81C22×D188—42no—
82C22×D188—42no—
83C22×D188C2311yescharacteristic
84C22×D188C2311yescharacteristic
85C22×D188C2314yes—
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C22⋊D47—21no—
90C2×#10625337—42no—
91C2×#10625337C2314yescomplemented
92C2×#10625325—42no—
93C2×#10625325—42no—
94C2×#10625325C2314yes—
95C2×#10625325C2314yes—
96C2×#10625335—42no—
97C2×#10625335C2314yescomplemented
98C2×#10625336—42no—
99C2×#10625336—42no—
100C2×#10625336C2314yes—
101C2×#10625336C2314yes—
102C22×C47⋊C8C2311yescharacteristic
103C22×C47⋊C8C2311yescharacteristic
104#13094022—22no—
105#13094022C2314yescomplemented
106#13094020—22no—
107#13094020—22no—
108#13094020C2314yes—
109#13094020C2314yes—
110#13094017—28no—
111#13094017—28no—
112#13094015—28no—
113#13094015—22no—
114#13094015C2314yescomplemented
115#13094014—28no—
116#13094013—22no—
117#13094013—22no—
118#13094013C2314yes—
119#13094013C2314yes—
120#13094003—22no—
121#13094003C2314yes—
122#13093998—28no—
123#13093998—28no—
124#13093992—28no—
125#13093992—28no—
126Q8×Dic47—22no—
127Q8×Dic47C2314yescomplemented
128#13093989—22no—
129#13093989C2314yescomplemented
130#13093983D414yes—
131#13093983C2314yes—
132C2×C4⋊Dic47—21no—
133C2×C4⋊Dic47—21no—
134C2×C4⋊Dic47D411yescharacteristic
135C2×C4⋊Dic47D411yescharacteristic
136C2×C4⋊Dic47C2311yescharacteristic
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4—21no—
142C2×C22⋊Dic47—21no—
143C2×C22⋊Dic47D411yescharacteristic
144C2×C22⋊Dic47D411yescharacteristic
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151C2×C4×Dic47C2311yescharacteristic
152C2×C4×Dic47C2311yescharacteristic
153Dic47⋊C8C2314yescomplemented
154Dic47⋊C8C2314yescomplemented
155#13093948C2314yescomplemented
156#13093946C2314yes—
157#13093946C2314yes—
158#13093945C2314yescomplemented
159#13093944C2314yes—
160#13093944C2314yes—
161C22⋊(C47⋊C8)C2314yes—
162#13093934C2314yescomplemented
163C8×Dic47C2314yescomplemented
164C2×#41×C47—22no—
165C2×#41×C47—42no—
166C2×#41×C47—42no—
167C2×#41×C47C2314yes—
168C22×Q8×C47C2311yescharacteristic
169C22×Q8×C47C2311yescharacteristic
170C22×D4×C47—21no—
171C22×D4×C47C2311yescharacteristic
172C23×C4×C47—21no—
173C23×C4×C47C2311yescharacteristic
174C2×Q16×C47—42no—
175C2×Q16×C47C2314yescomplemented
176C2×SD16×C47—42no—
177C2×SD16×C47C2314yescomplemented
178C22×C8×C47C2311yescharacteristic
179C22×C8×C47C2311yescharacteristic
180C22⋊Q8×C47—22no—
181C22⋊Q8×C47C2314yes—
182C2×C4⋊C4×C47—21no—
183C2×C4⋊C4×C47C2311yescharacteristic
184C2×C22⋊C4×C47—21no—
185#103×C47C2314yescomplemented
186#102×C47C2314yescomplemented
187C22⋊C8×C47C2314yes—
188C24×C47—21no—
189C24×C47C2×D411yescharacteristic
190C23×D47—21no—
191C23×D47—21no—
192C23×D47—24no—
193C23×D47—44no—
194C23×D47—82no—
195C23×D47—82no—
196#41×C47—44no—
197#41×C47—44no—
198#41×C47—48no—
199C2×Q8×C47—21no—
200C2×Q8×C47—21no—
201C2×Q8×C47—22no—
202C2×Q8×C47—22no—
203C2×Q8×C47—22no—
204C2×Q8×C47—22no—
205C2×Q8×C47C2412yes—
206C2×Q8×C47C2412yes—
207C2×D4×C47—24no—
208C2×D4×C47—21no—
209C2×D4×C47—22no—
210C2×D4×C47—22no—
211C2×D4×C47—44no—
212C2×D4×C47C2412yes—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—24no—
219C22×C4×C47—44no—
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D412yes—
222C22×C4×C47C2412yes—
223C22×C4×C47C2411yescharacteristic
224C2×C22⋊D47—24no—
225C2×C22⋊D47—24no—
226C2×C22⋊D47—24no—
227C2×C22⋊D47—24no—
228C2×C22⋊D47—82no—
229C2×C22⋊D47—82no—
230C2×C22⋊D47—82no—
231C2×C22⋊D47—82no—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47C2×D411yescharacteristic
235C22×Dic47C2×D411yescharacteristic
236C22×Dic47C2×D411yescharacteristic
237C22×Dic47C2×D411yescharacteristic
238C2×D188—22no—
239C2×D188—22no—
240C2×D188—22no—
241C2×D188—22no—
242C2×D188—24no—
243C2×D188—21no—
244C2×D188—21no—
245C2×D188—44no—
246C2×D188—44no—
247C2×D188—44no—
248C2×D188—48no—
249C2×D188C2412yes—
250C2×D188C2412yes—
251C2×Dic94—22no—
252C2×Dic94—22no—
253C2×Dic94—21no—
254C2×Dic94C2412yes—
255Q16×C47—44no—
256SD16×C47—44no—
257C2×C8×C47—22no—
258C2×C8×C47—22no—
259C2×C8×C47C2412yes—
260C2×C8×C47C2412yes—
261C4⋊C4×C47—24no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47C2412yes—
264C22⋊C4×C47—24no—
265C22⋊Dic47—24no—
266C22⋊Dic47C2×D414yes—
267C22⋊Dic47C2×D414yes—
268#10625337—44no—
269#10625336—44no—
270#10625336—44no—
271#10625335—44no—
272(C2×D47)⋊C4—24no—
273(C2×D47)⋊C4—24no—
274(C2×D47)⋊C4—24no—
275(C2×D47)⋊C4—24no—
276C4⋊Dic47—21no—
277C4⋊Dic47—24no—
278C4⋊Dic47—24no—
279C4⋊Dic47C2×D414yes—
280C4⋊Dic47C2×D414yes—
281C4⋊Dic47C2412yes—
282Dic47⋊C4—24no—
283Dic47⋊C4—24no—
284Dic47⋊C4—24no—
285Dic47⋊C4—24no—
286Dic47⋊C4—24no—
287C4×Dic47—24no—
288C4×Dic47—24no—
289C4×Dic47C2×D412yes—
290C4×Dic47C2×D412yes—
291C4×Dic47C2412yes—
292C4×Dic47C2412yes—
293C2×C47⋊C8—22no—
294C2×C47⋊C8—22no—
295C2×C47⋊C8C2412yes—
296C2×C47⋊C8C2412yes—
297#10625325—44no—
298#10625325—44no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—42no—
304C23×C47—42no—
305C23×C47—42no—
306C23×C47C22×D412yes—
307C23×C47C22×D411yescharacteristic
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—48no—
311C22×D47—42no—
312C22×D47—42no—
313C22×D47—42no—
314C22×D47—42no—
315C22×D47—42no—
316C22×D47—42no—
317C22×D47—84no—
318C22×D47—84no—
319C22×D47—816no—
320Q8×C47—22no—
321Q8×C47—22no—
322Q8×C47—22no—
323Q8×C47—22no—
324Q8×C47—42no—
325Q8×C47—42no—
326D4×C47—22no—
327D4×C47—22no—
328D4×C47—48no—
329D4×C47—42no—
330C2×C4×C47—22no—
331C2×C4×C47—24no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—48no—
338C2×C4×C47—42no—
339C2×C4×C47—42no—
340C2×C4×C47—42no—
341C2×C4×C47C22×D412yes—
342C2×C4×C47C22×D411yescharacteristic
343C2×C4×C47H(5,𝔽2)12yes—
344C2×C4×C47H(5,𝔽2)12yes—
345C2×C4×C47C2511yescharacteristic
346C22⋊D47—84no—
347C22⋊D47—84no—
348C22⋊D47—84no—
349C22⋊D47—84no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—22no—
353C2×Dic47—22no—
354C2×Dic47—22no—
355C2×Dic47—22no—
356C2×Dic47—42no—
357C2×Dic47—42no—
358C2×Dic47C22×D412yes—
359C2×Dic47C22×D412yes—
360C2×Dic47C22×D412yes—
361C2×Dic47C22×D412yes—
362D188—22no—
363D188—22no—
364D188—22no—
365D188—22no—
366D188—48no—
367D188—42no—
368D188—42no—
369Dic94—22no—
370Dic94—22no—
371Dic94—42no—
372C8×C47—22no—
373C8×C47—22no—
374C47⋊C8—22no—
375C47⋊C8—22no—
376C2×#3222—471nomaximal, Sylow
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—22no—
380C22×C47—44no—
381C22×C47—42no—
382C22×C47—42no—
383C22×C47—42no—
384C22×C47—84no—
385C22×C47#53512yes—
386C22×C47#57712yes—
387C22×C47#57712yes—
388C22×C47C23×D411yescharacteristic
389C2×D47—42no—
390C2×D47—42no—
391C2×D47—42no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—42no—
395C2×D47—816no—
396C2×D47—84no—
397C2×D47—84no—
398C4×C47—22no—
399C4×C47—42no—
400C4×C47—42no—
401C4×C47—42no—
402C4×C47#53512yes—
403C4×C47C2×H(5,𝔽2)11yescharacteristic
404C4×C47C2×H(5,𝔽2)11yescharacteristic
405Dic47—22no—
406Dic47—22no—
407Dic47—22no—
408Dic47—22no—
409Dic47—42no—
410Dic47—42no—
411C2×#541—471no—
412C2×#535—471no—
413#3222—4716no—
414C2×#497—471no—
415C2×#492—471no—
416C2×#490—471no—
417C2×#488—471no—
418C2×#464—471no—
419C2×#464—471no—
420C2×#460—471no—
421C2×#460—471no—
422C2×#452—471no—
423C2×#452D4711yescharacteristic, complemented
424C2×#450—471no—
425C2×#450—471no—
426C2×#433—471no—
427C2×C47—42no—
428C2×C47—82no—
429C2×C47#322214yescomplemented
430C2×C47C2×#53511yescharacteristic
431C2×C47C2×#57711yescharacteristic
432C2×C47C2×#57711yescharacteristic
433D47—82no—
434D47—82no—
435C22×#41C2×D4711yescharacteristic
436C23×D4—471no—
437C22×Q16—471no—
438C22×Q16C2×D4711yescharacteristic, complemented
439C22×SD16—471no—
440C22×SD16—471no—
441C22×SD16—471no—
442C22×SD16—471no—
443C22×SD16—471no—
444C22×SD16C2×D4711yescharacteristic, complemented
445#541—478no—
446#541—944no—
447#535—478no—
448#535—944no—
449C2×C4⋊Q8—471no—
450C2×#127—471no—
451C2×#127—471no—
452C2×#126—941no—
453C2×#126—941no—
454C2×#125—471no—
455C2×#125—941no—
456C2×#125—941no—
457C2×#124—471no—
458C2×#124—471no—
459C2×C22⋊Q8—471no—
460C2×C22⋊Q8C2×D4711yescharacteristic
461C2×#121—941no—
462C2×#121—941no—
463C2×#120—941no—
464C2×#120—941no—
465C2×C4×Q8—471no—
466C2×C4×Q8—471no—
467C2×#117—471no—
468#497—478no—
469#492—478no—
470#490—478no—
471#488—478no—
472#464—478no—
473#464—478no—
474#460—478no—
475#460—478no—
476#452—478no—
477#452C2×D4718yescomplemented
478#450—478no—
479#450—478no—
480#433—478no—
481C2×C4⋊C8—471no—
482C2×C4⋊C8—471no—
483C2×#103—471no—
484C2×#103C2×D4711yescharacteristic, complemented
485C2×#102—471no—
486C2×#102—471no—
487C2×#102—471no—
488C2×#102—471no—
489C2×#102—471no—
490C2×#102C2×D4711yescharacteristic, complemented
491C2×C22⋊C8—471no—
492C2×C22⋊C8C2×D4711yescharacteristic
493C2×#97—471no—
494C2×C4×C8—471no—
495C47C2×#322211yescharacteristic, complemented, Sylow
496C25—941no—
497C2×#41—22no—
498C2×#41—42no—
499C2×#41—42no—
500C2×#41C22×D4714yes—
501C22×Q8—471no—
502C22×Q8C22×D4711yescharacteristic
503C22×Q8C22×D4711yescharacteristic
504C22×D4—21no—
505C22×D4—471no—
506C22×D4—471no—
507C22×D4—474no—
508C22×D4—941no—
509C22×D4—941no—
510C22×D4—941no—
511C22×D4—941no—
512C22×D4—941no—
513C22×D4—942no—
514C22×D4—1882no—
515C22×D4—1882no—
516C22×D4C22×D4711yescharacteristic
517C23×C4—21no—
518C23×C4C22×D4711yescharacteristic
519C2×Q16—42no—
520C2×Q16—474no—
521C2×Q16—1882no—
522C2×Q16C22×D4714yescomplemented
523C2×SD16—42no—
524C2×SD16—474no—
525C2×SD16—474no—
526C2×SD16—474no—
527C2×SD16—474no—
528C2×SD16—474no—
529C2×SD16—1882no—
530C2×SD16—1882no—
531C2×SD16—1882no—
532C2×SD16—1882no—
533C2×SD16—1882no—
534C2×SD16C22×D4714yescomplemented
535C22×C8—471no—
536C22×C8—471no—
537C22×C8C22×D4711yescharacteristic
538C22×C8C22×D4711yescharacteristic
539C4⋊Q8—474no—
540C4⋊Q8—942no—
541#127—474no—
542#127—474no—
543#127—942no—
544#127—942no—
545#126—948no—
546#126—948no—
547#125—474no—
548#125—942no—
549#125—948no—
550#125—948no—
551#124—474no—
552#124—474no—
553#124—942no—
554#124—942no—
555C22⋊Q8—22no—
556C22⋊Q8—474no—
557C22⋊Q8—942no—
558C22⋊Q8C22×D4714yes—
559#121—948no—
560#121—948no—
561#120—948no—
562#120—948no—
563C4×Q8—474no—
564C4×Q8—474no—
565C4×Q8—942no—
566C4×Q8—942no—
567#117—474no—
568#117—474no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—471no—
571C2×C4⋊C4—471no—
572C2×C4⋊C4—471no—
573C2×C4⋊C4—941no—
574C2×C4⋊C4—941no—
575C2×C4⋊C4—941no—
576C2×C4⋊C4—941no—
577C2×C4⋊C4—941no—
578C2×C4⋊C4—941no—
579C2×C4⋊C4—941no—
580C2×C4⋊C4C22×D4711yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—471no—
583C2×C22⋊C4—471no—
584C2×C22⋊C4—941no—
585C2×C22⋊C4—941no—
586C2×C22⋊C4—941no—
587C2×C22⋊C4—941no—
588C2×C22⋊C4—941no—
589C2×C42—471no—
590C2×C42—471no—
591C2×C42—941no—
592C2×C42—941no—
593C4⋊C8—474no—
594C4⋊C8—474no—
595#103—474no—
596#103C22×D4714yescomplemented
597#102—474no—
598#102—474no—
599#102—474no—
600#102—474no—
601#102—474no—
602#102C22×D4714yescomplemented
603C22⋊C8—474no—
604C22⋊C8C22×D4714yes—
605#97—474no—
606C4×C8—474no—
607C24—21no—
608C24—944no—
609C24—941no—
610C24—941no—
611C24—3762no—
612C24—3762no—
613C24—1884no—
614C24D4×D4711yescharacteristic
615#41—44no—
616#41—44no—
617#41—48no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—22no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—472no—
625C2×Q8—941no—
626C2×Q8—942no—
627C2×Q8—942no—
628C2×Q8C23×D4712yes—
629C2×Q8C23×D4712yes—
630C2×D4—24no—
631C2×D4—21no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—44no—
635C2×D4—472no—
636C2×D4—472no—
637C2×D4—944no—
638C2×D4—944no—
639C2×D4—944no—
640C2×D4—944no—
641C2×D4—944no—
642C2×D4—941no—
643C2×D4—941no—
644C2×D4—942no—
645C2×D4—942no—
646C2×D4—942no—
647C2×D4—942no—
648C2×D4—3762no—
649C2×D4—3762no—
650C2×D4—3762no—
651C2×D4—3762no—
652C2×D4—1884no—
653C2×D4—1884no—
654C2×D4—1884no—
655C2×D4—1888no—
656C2×D4C23×D4712yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—44no—
664C22×C4—471no—
665C22×C4—471no—
666C22×C4—471no—
667C22×C4—471no—
668C22×C4—941no—
669C22×C4—941no—
670C22×C4D4×D4712yes—
671C22×C4D4×D4711yescharacteristic
672C22×C4C23×D4712yes—
673C22×C4C23×D4711yescharacteristic
674Q16—44no—
675Q16—1884no—
676SD16—44no—
677SD16—1884no—
678SD16—1884no—
679SD16—1884no—
680SD16—1884no—
681SD16—1884no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—472no—
685C2×C8—472no—
686C2×C8—942no—
687C2×C8—942no—
688C2×C8C23×D4712yes—
689C2×C8C23×D4712yes—
690C4⋊C4—24no—
691C4⋊C4—21no—
692C4⋊C4—474no—
693C4⋊C4—474no—
694C4⋊C4—472no—
695C4⋊C4—944no—
696C4⋊C4—944no—
697C4⋊C4—944no—
698C4⋊C4—944no—
699C4⋊C4—944no—
700C4⋊C4—944no—
701C4⋊C4—944no—
702C4⋊C4—941no—
703C4⋊C4C23×D4712yes—
704C22⋊C4—24no—
705C22⋊C4—474no—
706C22⋊C4—474no—
707C22⋊C4—944no—
708C22⋊C4—944no—
709C22⋊C4—944no—
710C22⋊C4—944no—
711C22⋊C4—944no—
712C42—472no—
713C42—472no—
714C42—472no—
715C42—472no—
716C42—944no—
717C42—944no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—942no—
726C23—942no—
727C23—3764no—
728C23—3764no—
729C23—37616no—
730C23—1888no—
731C23—1882no—
732C23—1882no—
733C23—1882no—
734C23—1882no—
735C23—1882no—
736C23—1882no—
737C23C2×D4×D4712yes—
738C23C2×D4×D4711yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—42no—
744Q8—42no—
745Q8—942no—
746Q8—942no—
747Q8—1882no—
748D4—22no—
749D4—22no—
750D4—48no—
751D4—42no—
752D4—942no—
753D4—942no—
754D4—942no—
755D4—942no—
756D4—3764no—
757D4—3764no—
758D4—3764no—
759D4—3764no—
760D4—1888no—
761D4—1882no—
762D4—1882no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—48no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—472no—
775C2×C4—472no—
776C2×C4—472no—
777C2×C4—472no—
778C2×C4—942no—
779C2×C4—942no—
780C2×C4—942no—
781C2×C4—942no—
782C2×C4—942no—
783C2×C4—942no—
784C2×C4—1882no—
785C2×C4—1882no—
786C2×C4C2×D4×D4712yes—
787C2×C4C2×D4×D4711yescharacteristic
788C2×C4#1309406912yes—
789C2×C4#1309406912yes—
790C2×C4C24×D4711yescharacteristic
791C8—22no—
792C8—22no—
793C8—942no—
794C8—942no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—84no—
803C22—37616no—
804C22—3764no—
805C22—3764no—
806C22—1882no—
807C22—1882no—
808C22—1882no—
809C22—1882no—
810C22—1882no—
811C22—1882no—
812C22#1568968812yes—
813C22#1568993012yes—
814C22#1568993212yes—
815C22C22×D4×D4711yescharacteristic
816C4—22no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—942no—
821C4—942no—
822C4—942no—
823C4—942no—
824C4—1882no—
825C4—1882no—
826C4#1568968812yes—
827C4C2×#1309406911yescharacteristic
828C4C2×#1309406911yescharacteristic
829C2—42no—
830C2—82no—
831C2—3762no—
832C2—3762no—
833C2#2025445814yesdirect product factor
834C2C2×#1568968811yescharacteristic
835C2C2×#1568993011yescharacteristic
836C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#452C2
socleC23×C47C22×D4
prime radicalC2×#15689687C2
hypercenterC2×#452D47
hypocenterC47C2×#3222
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×#15689733C2semidirect
3. #20254458C2direct (N × H)
4. C2×#15689516C2semidirect
5. C2×#15689494C2semidirect
6. C2×#15689486C2semidirect
7. C2×#15689479C2semidirect
8. C2×#15689348C2semidirect
9. C2×#15689347C2semidirect
10. C2×#15689322C2semidirect
11. C2×#15689321C2semidirect
12. C2×#15689285C2semidirect
13. C2×#15689276C2semidirect
14. C2×#15689273C2semidirect
15. C2×#15689181C2semidirect
16. C2×C47×#452C2semidirect
18. C22×#10625337C22semidirect
21. C22×#10625335C22semidirect
25. #15689733C22semidirect
28. C2×#13094022C22semidirect
34. C2×#13094015C22semidirect
43. C2×Q8×Dic47C22semidirect
44. C2×#13093989C22semidirect
46. #15689516C22semidirect
47. #15689494C22semidirect
48. #15689486C22semidirect
49. #15689479C22semidirect
50. #15689348C22semidirect
51. #15689347C22semidirect
52. #15689322C22semidirect
53. #15689321C22semidirect
54. #15689285C22semidirect
55. #15689276C22semidirect
56. #15689273C22semidirect
57. #15689181C22semidirect
58. C2×Dic47⋊C8C22semidirect
59. C2×Dic47⋊C8C22semidirect
60. C2×#13093948C22semidirect
63. C2×#13093945C22semidirect
67. C2×#13093934C22semidirect
68. C2×C8×Dic47C22semidirect
70. C22×Q16×C47C22semidirect
71. C22×SD16×C47C22semidirect
73. C47×#452C22semidirect
74. C2×#103×C47C22semidirect
75. C2×#102×C47C22semidirect
91. C2×#10625337C23semidirect
97. C2×#10625335C23semidirect
105. #13094022C23semidirect
114. #13094015C23semidirect
127. Q8×Dic47C23semidirect
129. #13093989C23semidirect
153. Dic47⋊C8C23semidirect
154. Dic47⋊C8C23semidirect
155. #13093948C23semidirect
158. #13093945C23semidirect
162. #13093934C23semidirect
163. C8×Dic47C23semidirect
175. C2×Q16×C47C23semidirect
177. C2×SD16×C47C23semidirect
185. #103×C47C23semidirect
186. #102×C47C23semidirect
423. C2×#452D47semidirect
429. C2×C47#3222semidirect
438. C22×Q16C2×D47semidirect
444. C22×SD16C2×D47semidirect
477. #452C2×D47semidirect
484. C2×#103C2×D47semidirect
490. C2×#102C2×D47semidirect
495. C47C2×#3222semidirect
522. C2×Q16C22×D47semidirect
534. C2×SD16C22×D47semidirect
596. #103C22×D47semidirect
602. #102C22×D47semidirect
833. C2#20254458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897332
C2×#156896872
#202544582
C2×#156895162
C2×#156894942
C2×#156894862
C2×#156894792
C2×#156893482
C2×#156893472
C2×#156893222
C2×#156893212
C2×#156892852
C2×#156892762
C2×#156892732
C2×#156891812
C2×C47×#4522
C2×#322247