Finite Group Databasebeta

← C2×#19145665 #25967938

Subgroups — C2×#19145665 #25967938

Order 11008.

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×#14583509C211yesmaximal, characteristic, complemented
2C2×#14583463C211yesmaximal, characteristic
3#19145665C2116yesmaximal, direct product factor
4C2×#14583292C211yesmaximal, characteristic, complemented
5C2×#14583270C211yesmaximal, characteristic, complemented
6C2×#14583262C211yesmaximal, characteristic, complemented
7C2×#14583255C211yesmaximal, characteristic, complemented
8C2×#14583124C211yesmaximal, characteristic, complemented
9C2×#14583123C211yesmaximal, characteristic, complemented
10C2×#14583098C211yesmaximal, characteristic, complemented
11C2×#14583097C211yesmaximal, characteristic, complemented
12C2×#14583061C211yesmaximal, characteristic, complemented
13C2×#14583052C211yesmaximal, characteristic, complemented
14C2×#14583049C211yesmaximal, characteristic, complemented
15C2×#14582957C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C22×#10621885C2211yescharacteristic, complemented
19C22×#10621873C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621883C2211yescharacteristic, complemented
22C22×#10621884C2211yescharacteristic
23C22×#10621884C2211yescharacteristic
24#14583509—24no—
25#14583509C2218yescomplemented
26#14583463—24no—
27#14583463C2218yes—
28C2×#13063323C2211yescharacteristic, complemented
29C2×#13063321C2211yescharacteristic
30C2×#13063321C2211yescharacteristic
31C2×#13063318—21no—
32C2×#13063318—21no—
33C2×#13063316—21no—
34C2×#13063316C2211yescharacteristic, complemented
35C2×#13063315—21no—
36C2×#13063314C2211yescharacteristic
37C2×#13063314C2211yescharacteristic
38C2×#13063304C2211yescharacteristic
39C2×#13063299—21no—
40C2×#13063299—21no—
41C2×#13063293—21no—
42C2×#13063293—21no—
43C2×Q8×Dic43C2211yescharacteristic, complemented
44C2×#13063290C2211yescharacteristic, complemented
45C2×#13063284C2211yescharacteristic
46#14583292C2218yescomplemented
47#14583270C2218yescomplemented
48#14583262C2218yescomplemented
49#14583255C2218yescomplemented
50#14583124C2218yescomplemented
51#14583123C2218yescomplemented
52#14583098C2218yescomplemented
53#14583097C2218yescomplemented
54#14583061C2218yescomplemented
55#14583052C2218yescomplemented
56#14583049C2218yescomplemented
57#14582957C2218yescomplemented
58C2×Dic43⋊C8C2211yescharacteristic, complemented
59C2×Dic43⋊C8C2211yescharacteristic, complemented
60C2×#13063249C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic, complemented
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×#13063235C2211yescharacteristic, complemented
68C2×C8×Dic43C2211yescharacteristic, complemented
69C22×#41×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic, complemented
71C22×SD16×C43C2211yescharacteristic, complemented
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#452C2218yescomplemented
74C2×#103×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic, complemented
76C2×C22⋊C8×C43C2211yescharacteristic
77C24×D43—21no—
78C22×Dic86C2311yescharacteristic
79C22×D172—21no—
80C22×D172—22no—
81C22×D172—42no—
82C22×D172—42no—
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×D172C2314yes—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C2×#10621885—42no—
91C2×#10621885C2314yescomplemented
92C2×#10621873—42no—
93C2×#10621873—42no—
94C2×#10621873C2314yes—
95C2×#10621873C2314yes—
96C2×#10621883—42no—
97C2×#10621883C2314yescomplemented
98C2×#10621884—42no—
99C2×#10621884—42no—
100C2×#10621884C2314yes—
101C2×#10621884C2314yes—
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104#13063323—22no—
105#13063323C2314yescomplemented
106#13063321—22no—
107#13063321—22no—
108#13063321C2314yes—
109#13063321C2314yes—
110#13063318—28no—
111#13063318—28no—
112#13063316—28no—
113#13063316—22no—
114#13063316C2314yescomplemented
115#13063315—28no—
116#13063314—22no—
117#13063314—22no—
118#13063314C2314yes—
119#13063314C2314yes—
120#13063304—22no—
121#13063304C2314yes—
122#13063299—28no—
123#13063299—28no—
124#13063293—28no—
125#13063293—28no—
126Q8×Dic43—22no—
127Q8×Dic43C2314yescomplemented
128#13063290—22no—
129#13063290C2314yescomplemented
130#13063284D414yes—
131#13063284C2314yes—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43D411yescharacteristic
135C2×C4⋊Dic43D411yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×C22⋊Dic43—21no—
143C2×C22⋊Dic43D411yescharacteristic
144C2×C22⋊Dic43D411yescharacteristic
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151C2×C4×Dic43C2311yescharacteristic
152C2×C4×Dic43C2311yescharacteristic
153Dic43⋊C8C2314yescomplemented
154Dic43⋊C8C2314yescomplemented
155#13063249C2314yescomplemented
156#13063247C2314yes—
157#13063247C2314yes—
158#13063246C2314yescomplemented
159#13063245C2314yes—
160#13063245C2314yes—
161C22⋊(C43⋊C8)C2314yes—
162#13063235C2314yescomplemented
163C8×Dic43C2314yescomplemented
164C2×#41×C43—22no—
165C2×#41×C43—42no—
166C2×#41×C43—42no—
167C2×#41×C43C2314yes—
168C22×Q8×C43C2311yescharacteristic
169C22×Q8×C43C2311yescharacteristic
170C22×D4×C43—21no—
171C22×D4×C43C2311yescharacteristic
172C23×C4×C43—21no—
173C23×C4×C43C2311yescharacteristic
174C2×Q16×C43—42no—
175C2×Q16×C43C2314yescomplemented
176C2×SD16×C43—42no—
177C2×SD16×C43C2314yescomplemented
178C22×C8×C43C2311yescharacteristic
179C22×C8×C43C2311yescharacteristic
180C22⋊Q8×C43—22no—
181C22⋊Q8×C43C2314yes—
182C2×C4⋊C4×C43—21no—
183C2×C4⋊C4×C43C2311yescharacteristic
184C2×C22⋊C4×C43—21no—
185#103×C43C2314yescomplemented
186#102×C43C2314yescomplemented
187C22⋊C8×C43C2314yes—
188C24×C43—21no—
189C24×C43C2×D411yescharacteristic
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—24no—
193C23×D43—44no—
194C23×D43—82no—
195C23×D43—82no—
196#41×C43—44no—
197#41×C43—44no—
198#41×C43—48no—
199C2×Q8×C43—21no—
200C2×Q8×C43—21no—
201C2×Q8×C43—22no—
202C2×Q8×C43—22no—
203C2×Q8×C43—22no—
204C2×Q8×C43—22no—
205C2×Q8×C43C2412yes—
206C2×Q8×C43C2412yes—
207C2×D4×C43—21no—
208C2×D4×C43—24no—
209C2×D4×C43—22no—
210C2×D4×C43—22no—
211C2×D4×C43—44no—
212C2×D4×C43C2412yes—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43—24no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—44no—
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2412yes—
223C22×C4×C43C2411yescharacteristic
224C2×C22⋊D43—24no—
225C2×C22⋊D43—24no—
226C2×C22⋊D43—24no—
227C2×C22⋊D43—24no—
228C2×C22⋊D43—82no—
229C2×C22⋊D43—82no—
230C2×C22⋊D43—82no—
231C2×C22⋊D43—82no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43C2×D411yescharacteristic
235C22×Dic43C2×D411yescharacteristic
236C22×Dic43C2×D411yescharacteristic
237C22×Dic43C2×D411yescharacteristic
238C2×D172—24no—
239C2×D172—21no—
240C2×D172—21no—
241C2×D172—22no—
242C2×D172—22no—
243C2×D172—22no—
244C2×D172—22no—
245C2×D172—44no—
246C2×D172—44no—
247C2×D172—48no—
248C2×D172—44no—
249C2×D172C2412yes—
250C2×D172C2412yes—
251C2×Dic86—22no—
252C2×Dic86—22no—
253C2×Dic86—21no—
254C2×Dic86C2412yes—
255Q16×C43—44no—
256SD16×C43—44no—
257C2×C8×C43—22no—
258C2×C8×C43—22no—
259C2×C8×C43C2412yes—
260C2×C8×C43C2412yes—
261C4⋊C4×C43—24no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43C2412yes—
264C22⋊C4×C43—24no—
265C22⋊Dic43—24no—
266C22⋊Dic43C2×D414yes—
267C22⋊Dic43C2×D414yes—
268#10621885—44no—
269#10621884—44no—
270#10621884—44no—
271#10621883—44no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276C4⋊Dic43—21no—
277C4⋊Dic43—24no—
278C4⋊Dic43—24no—
279C4⋊Dic43C2×D414yes—
280C4⋊Dic43C2×D414yes—
281C4⋊Dic43C2412yes—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287C4×Dic43—24no—
288C4×Dic43—24no—
289C4×Dic43C2×D412yes—
290C4×Dic43C2×D412yes—
291C4×Dic43C2412yes—
292C4×Dic43C2412yes—
293C2×C43⋊C8—22no—
294C2×C43⋊C8—22no—
295C2×C43⋊C8C2412yes—
296C2×C43⋊C8C2412yes—
297#10621873—44no—
298#10621873—44no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43—42no—
304C23×C43—42no—
305C23×C43—42no—
306C23×C43C22×D412yes—
307C23×C43C22×D411yescharacteristic
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—48no—
311C22×D43—42no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43—42no—
315C22×D43—42no—
316C22×D43—42no—
317C22×D43—84no—
318C22×D43—84no—
319C22×D43—816no—
320Q8×C43—22no—
321Q8×C43—22no—
322Q8×C43—22no—
323Q8×C43—22no—
324Q8×C43—42no—
325Q8×C43—42no—
326D4×C43—22no—
327D4×C43—22no—
328D4×C43—48no—
329D4×C43—42no—
330C2×C4×C43—22no—
331C2×C4×C43—24no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—48no—
338C2×C4×C43—42no—
339C2×C4×C43—42no—
340C2×C4×C43—42no—
341C2×C4×C43C22×D412yes—
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43H(5,𝔽2)12yes—
344C2×C4×C43H(5,𝔽2)12yes—
345C2×C4×C43C2511yescharacteristic
346C22⋊D43—84no—
347C22⋊D43—84no—
348C22⋊D43—84no—
349C22⋊D43—84no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—42no—
357C2×Dic43—42no—
358C2×Dic43C22×D412yes—
359C2×Dic43C22×D412yes—
360C2×Dic43C22×D412yes—
361C2×Dic43C22×D412yes—
362D172—22no—
363D172—22no—
364D172—22no—
365D172—22no—
366D172—48no—
367D172—42no—
368D172—42no—
369Dic86—22no—
370Dic86—22no—
371Dic86—42no—
372C8×C43—22no—
373C8×C43—22no—
374C43⋊C8—22no—
375C43⋊C8—22no—
376C2×#3222—431nomaximal, Sylow
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—44no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—84no—
385C22×C43#53512yes—
386C22×C43#57712yes—
387C22×C43#57712yes—
388C22×C43C23×D411yescharacteristic
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—816no—
396C2×D43—84no—
397C2×D43—84no—
398C4×C43—22no—
399C4×C43—42no—
400C4×C43—42no—
401C4×C43—42no—
402C4×C43#53512yes—
403C4×C43C2×H(5,𝔽2)11yescharacteristic
404C4×C43C2×H(5,𝔽2)11yescharacteristic
405Dic43—22no—
406Dic43—22no—
407Dic43—22no—
408Dic43—22no—
409Dic43—42no—
410Dic43—42no—
411C2×#541—431no—
412C2×#535—431no—
413#3222—4316no—
414C2×#497—431no—
415C2×#492—431no—
416C2×#490—431no—
417C2×#488—431no—
418C2×#464—431no—
419C2×#464—431no—
420C2×#460—431no—
421C2×#460—431no—
422C2×#452—431no—
423C2×#452D4311yescharacteristic, complemented
424C2×#450—431no—
425C2×#450—431no—
426C2×#433—431no—
427C2×C43—42no—
428C2×C43—82no—
429C2×C43#322214yescomplemented
430C2×C43C2×#53511yescharacteristic
431C2×C43C2×#57711yescharacteristic
432C2×C43C2×#57711yescharacteristic
433D43—82no—
434D43—82no—
435C22×#41C2×D4311yescharacteristic
436C23×D4—431no—
437C22×Q16—431no—
438C22×Q16C2×D4311yescharacteristic, complemented
439C22×SD16—431no—
440C22×SD16—431no—
441C22×SD16—431no—
442C22×SD16—431no—
443C22×SD16—431no—
444C22×SD16C2×D4311yescharacteristic, complemented
445#541—438no—
446#541—864no—
447#535—438no—
448#535—864no—
449C2×C4⋊Q8—431no—
450C2×#127—431no—
451C2×#127—431no—
452C2×#126—861no—
453C2×#126—861no—
454C2×#125—431no—
455C2×#125—861no—
456C2×#125—861no—
457C2×#124—431no—
458C2×#124—431no—
459C2×C22⋊Q8—431no—
460C2×C22⋊Q8C2×D4311yescharacteristic
461C2×#121—861no—
462C2×#121—861no—
463C2×#120—861no—
464C2×#120—861no—
465C2×C4×Q8—431no—
466C2×C4×Q8—431no—
467C2×#117—431no—
468#497—438no—
469#492—438no—
470#490—438no—
471#488—438no—
472#464—438no—
473#464—438no—
474#460—438no—
475#460—438no—
476#452—438no—
477#452C2×D4318yescomplemented
478#450—438no—
479#450—438no—
480#433—438no—
481C2×C4⋊C8—431no—
482C2×C4⋊C8—431no—
483C2×#103—431no—
484C2×#103C2×D4311yescharacteristic, complemented
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102C2×D4311yescharacteristic, complemented
491C2×C22⋊C8—431no—
492C2×C22⋊C8C2×D4311yescharacteristic
493C2×#97—431no—
494C2×C4×C8—431no—
495C43C2×#322211yescharacteristic, complemented, Sylow
496C25—861no—
497C2×#41—22no—
498C2×#41—42no—
499C2×#41—42no—
500C2×#41C22×D4314yes—
501C22×Q8—431no—
502C22×Q8C22×D4311yescharacteristic
503C22×Q8C22×D4311yescharacteristic
504C22×D4—21no—
505C22×D4—431no—
506C22×D4—431no—
507C22×D4—434no—
508C22×D4—861no—
509C22×D4—861no—
510C22×D4—861no—
511C22×D4—861no—
512C22×D4—861no—
513C22×D4—862no—
514C22×D4—1722no—
515C22×D4—1722no—
516C22×D4C22×D4311yescharacteristic
517C23×C4—21no—
518C23×C4C22×D4311yescharacteristic
519C2×Q16—42no—
520C2×Q16—434no—
521C2×Q16—1722no—
522C2×Q16C22×D4314yescomplemented
523C2×SD16—42no—
524C2×SD16—434no—
525C2×SD16—434no—
526C2×SD16—434no—
527C2×SD16—434no—
528C2×SD16—434no—
529C2×SD16—1722no—
530C2×SD16—1722no—
531C2×SD16—1722no—
532C2×SD16—1722no—
533C2×SD16—1722no—
534C2×SD16C22×D4314yescomplemented
535C22×C8—431no—
536C22×C8—431no—
537C22×C8C22×D4311yescharacteristic
538C22×C8C22×D4311yescharacteristic
539C4⋊Q8—434no—
540C4⋊Q8—862no—
541#127—434no—
542#127—434no—
543#127—862no—
544#127—862no—
545#126—868no—
546#126—868no—
547#125—434no—
548#125—862no—
549#125—868no—
550#125—868no—
551#124—434no—
552#124—434no—
553#124—862no—
554#124—862no—
555C22⋊Q8—22no—
556C22⋊Q8—434no—
557C22⋊Q8—862no—
558C22⋊Q8C22×D4314yes—
559#121—868no—
560#121—868no—
561#120—868no—
562#120—868no—
563C4×Q8—434no—
564C4×Q8—434no—
565C4×Q8—862no—
566C4×Q8—862no—
567#117—434no—
568#117—434no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—431no—
571C2×C4⋊C4—431no—
572C2×C4⋊C4—431no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4—861no—
577C2×C4⋊C4—861no—
578C2×C4⋊C4—861no—
579C2×C4⋊C4—861no—
580C2×C4⋊C4C22×D4311yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—431no—
583C2×C22⋊C4—431no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C42—431no—
590C2×C42—431no—
591C2×C42—861no—
592C2×C42—861no—
593C4⋊C8—434no—
594C4⋊C8—434no—
595#103—434no—
596#103C22×D4314yescomplemented
597#102—434no—
598#102—434no—
599#102—434no—
600#102—434no—
601#102—434no—
602#102C22×D4314yescomplemented
603C22⋊C8—434no—
604C22⋊C8C22×D4314yes—
605#97—434no—
606C4×C8—434no—
607C24—21no—
608C24—864no—
609C24—861no—
610C24—861no—
611C24—3442no—
612C24—3442no—
613C24—1724no—
614C24D4×D4311yescharacteristic
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—432no—
625C2×Q8—861no—
626C2×Q8—862no—
627C2×Q8—862no—
628C2×Q8C23×D4312yes—
629C2×Q8C23×D4312yes—
630C2×D4—24no—
631C2×D4—21no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—44no—
635C2×D4—432no—
636C2×D4—432no—
637C2×D4—864no—
638C2×D4—864no—
639C2×D4—864no—
640C2×D4—864no—
641C2×D4—864no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—862no—
645C2×D4—862no—
646C2×D4—862no—
647C2×D4—862no—
648C2×D4—3442no—
649C2×D4—3442no—
650C2×D4—3442no—
651C2×D4—3442no—
652C2×D4—1724no—
653C2×D4—1724no—
654C2×D4—1724no—
655C2×D4—1728no—
656C2×D4C23×D4312yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—44no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—431no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4D4×D4312yes—
671C22×C4D4×D4311yescharacteristic
672C22×C4C23×D4312yes—
673C22×C4C23×D4311yescharacteristic
674Q16—44no—
675Q16—1724no—
676SD16—44no—
677SD16—1724no—
678SD16—1724no—
679SD16—1724no—
680SD16—1724no—
681SD16—1724no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—432no—
685C2×C8—432no—
686C2×C8—862no—
687C2×C8—862no—
688C2×C8C23×D4312yes—
689C2×C8C23×D4312yes—
690C4⋊C4—24no—
691C4⋊C4—21no—
692C4⋊C4—434no—
693C4⋊C4—434no—
694C4⋊C4—432no—
695C4⋊C4—864no—
696C4⋊C4—864no—
697C4⋊C4—864no—
698C4⋊C4—864no—
699C4⋊C4—864no—
700C4⋊C4—864no—
701C4⋊C4—861no—
702C4⋊C4—864no—
703C4⋊C4C23×D4312yes—
704C22⋊C4—24no—
705C22⋊C4—434no—
706C22⋊C4—434no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C22⋊C4—864no—
710C22⋊C4—864no—
711C22⋊C4—864no—
712C42—432no—
713C42—432no—
714C42—432no—
715C42—432no—
716C42—864no—
717C42—864no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—862no—
726C23—862no—
727C23—3444no—
728C23—3444no—
729C23—34416no—
730C23—1728no—
731C23—1722no—
732C23—1722no—
733C23—1722no—
734C23—1722no—
735C23—1722no—
736C23—1722no—
737C23C2×D4×D4312yes—
738C23C2×D4×D4311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—42no—
744Q8—42no—
745Q8—862no—
746Q8—862no—
747Q8—1722no—
748D4—22no—
749D4—22no—
750D4—48no—
751D4—42no—
752D4—862no—
753D4—862no—
754D4—862no—
755D4—862no—
756D4—3444no—
757D4—3444no—
758D4—3444no—
759D4—3444no—
760D4—1728no—
761D4—1722no—
762D4—1722no—
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—432no—
775C2×C4—432no—
776C2×C4—432no—
777C2×C4—432no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—1722no—
785C2×C4—1722no—
786C2×C4C2×D4×D4312yes—
787C2×C4C2×D4×D4311yescharacteristic
788C2×C4#1306337012yes—
789C2×C4#1306337012yes—
790C2×C4C24×D4311yescharacteristic
791C8—22no—
792C8—22no—
793C8—862no—
794C8—862no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—84no—
803C22—34416no—
804C22—3444no—
805C22—3444no—
806C22—1722no—
807C22—1722no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22#1458346412yes—
813C22#1458370612yes—
814C22#1458370812yes—
815C22C22×D4×D4311yescharacteristic
816C4—22no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—862no—
821C4—862no—
822C4—862no—
823C4—862no—
824C4—1722no—
825C4—1722no—
826C4#1458346412yes—
827C4C2×#1306337011yescharacteristic
828C4C2×#1306337011yescharacteristic
829C2—42no—
830C2—82no—
831C2—3442no—
832C2—3442no—
833C2#1914566514yesdirect product factor
834C2C2×#1458346411yescharacteristic
835C2C2×#1458370611yescharacteristic
836C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC2×#14583463C2
hypercenterC2×#452D43
hypocenterC43C2×#3222
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#14583509C2semidirect
3. #19145665C2direct (N × H)
4. C2×#14583292C2semidirect
5. C2×#14583270C2semidirect
6. C2×#14583262C2semidirect
7. C2×#14583255C2semidirect
8. C2×#14583124C2semidirect
9. C2×#14583123C2semidirect
10. C2×#14583098C2semidirect
11. C2×#14583097C2semidirect
12. C2×#14583061C2semidirect
13. C2×#14583052C2semidirect
14. C2×#14583049C2semidirect
15. C2×#14582957C2semidirect
16. C2×C43×#452C2semidirect
18. C22×#10621885C22semidirect
21. C22×#10621883C22semidirect
25. #14583509C22semidirect
28. C2×#13063323C22semidirect
34. C2×#13063316C22semidirect
43. C2×Q8×Dic43C22semidirect
44. C2×#13063290C22semidirect
46. #14583292C22semidirect
47. #14583270C22semidirect
48. #14583262C22semidirect
49. #14583255C22semidirect
50. #14583124C22semidirect
51. #14583123C22semidirect
52. #14583098C22semidirect
53. #14583097C22semidirect
54. #14583061C22semidirect
55. #14583052C22semidirect
56. #14583049C22semidirect
57. #14582957C22semidirect
58. C2×Dic43⋊C8C22semidirect
59. C2×Dic43⋊C8C22semidirect
60. C2×#13063249C22semidirect
63. C2×#13063246C22semidirect
67. C2×#13063235C22semidirect
68. C2×C8×Dic43C22semidirect
70. C22×Q16×C43C22semidirect
71. C22×SD16×C43C22semidirect
73. C43×#452C22semidirect
74. C2×#103×C43C22semidirect
75. C2×#102×C43C22semidirect
91. C2×#10621885C23semidirect
97. C2×#10621883C23semidirect
105. #13063323C23semidirect
114. #13063316C23semidirect
127. Q8×Dic43C23semidirect
129. #13063290C23semidirect
153. Dic43⋊C8C23semidirect
154. Dic43⋊C8C23semidirect
155. #13063249C23semidirect
158. #13063246C23semidirect
162. #13063235C23semidirect
163. C8×Dic43C23semidirect
175. C2×Q16×C43C23semidirect
177. C2×SD16×C43C23semidirect
185. #103×C43C23semidirect
186. #102×C43C23semidirect
423. C2×#452D43semidirect
429. C2×C43#3222semidirect
438. C22×Q16C2×D43semidirect
444. C22×SD16C2×D43semidirect
477. #452C2×D43semidirect
484. C2×#103C2×D43semidirect
490. C2×#102C2×D43semidirect
495. C43C2×#3222semidirect
522. C2×Q16C22×D43semidirect
534. C2×SD16C22×D43semidirect
596. #103C22×D43semidirect
602. #102C22×D43semidirect
833. C2#19145665direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835092
C2×#145834632
#191456652
C2×#145832922
C2×#145832702
C2×#145832622
C2×#145832552
C2×#145831242
C2×#145831232
C2×#145830982
C2×#145830972
C2×#145830612
C2×#145830522
C2×#145830492
C2×#145829572
C2×C43×#4522
C2×#322243