Finite Group Databasebeta

← C2×#19145561 #25967770

Subgroups — C2×#19145561 #25967770

Order 11008.

2294 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×#14583434C211yesmaximal, characteristic, complemented
2C2×#124×D43C211yesmaximal, characteristic, complemented
3#19145561C2116yesmaximal, direct product factor
4C2×#14583283C211yesmaximal, characteristic, complemented
5C2×#14583281C211yesmaximal, characteristic, complemented
6C2×#14583256C211yesmaximal, characteristic, complemented
7C2×#14583124C211yesmaximal, characteristic, complemented
8C2×#14583120C211yesmaximal, characteristic, complemented
9C2×#14583117C211yesmaximal, characteristic, complemented
10C2×#14583113C211yesmaximal, characteristic, complemented
11C2×#14583056C211yesmaximal, characteristic, complemented
12C2×#14583039C211yesmaximal, characteristic, complemented
13C2×#14583051C211yesmaximal, characteristic, complemented
14C2×#14583034C211yesmaximal, characteristic
15C2×#14582950C211yesmaximal, characteristic, complemented
16C2×C43×#488C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×Dic172C2211yescharacteristic, complemented
20C22×#10621885C2211yescharacteristic, complemented
21C22×#10621873C2211yescharacteristic
22C22×#10621873C2211yescharacteristic, complemented
23C22×#10621883C2211yescharacteristic
24C22×#10621884C2211yescharacteristic, complemented
25C22×D344C2211yescharacteristic
26C22×#10621882C2211yescharacteristic
27#14583434—24no—
28#14583434C2218yescomplemented
29C2×#13063320—21no—
30C2×#13063314C2211yescharacteristic
31C2×#13063313C2211yescharacteristic
32C2×#13063313C2211yescharacteristic, complemented
33C2×#13063312C2211yescharacteristic
34C2×#13063311—21no—
35C2×#13063311—21no—
36#124×D43—24no—
37#124×D43C2218yescomplemented
38C2×#13063310—21no—
39C2×#13063305C2211yescharacteristic
40C2×#13063300C2211yescharacteristic
41C2×#13063290C2211yescharacteristic, complemented
42C2×#13063287—21no—
43C2×#13063287C2211yescharacteristic, complemented
44C2×#13063283—21no—
45C2×C22⋊C4×D43—21no—
46C2×C22⋊C4×D43—21no—
47C2×C42×D43C2211yescharacteristic
48#14583283C2218yescomplemented
49#14583281C2218yescomplemented
50#14583256C2218yescomplemented
51#14583124C2218yescomplemented
52#14583120C2218yescomplemented
53#14583117C2218yescomplemented
54#14583113C2218yescomplemented
55#14583056C2218yescomplemented
56#14583051C2218yescomplemented
57#14583039C2218yescomplemented
58#14583034C2218yes—
59#14582950C2218yescomplemented
60C2×Dic43⋊C8C2211yescharacteristic, complemented
61C2×Dic43⋊C8C2211yescharacteristic, complemented
62C2×#13063248C2211yescharacteristic, complemented
63C2×#13063248C2211yescharacteristic, complemented
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic, complemented
69C2×#125×C43C2211yescharacteristic, complemented
70C2×#124×C43C2211yescharacteristic
71C43×#488C2218yescomplemented
72C2×#103×C43C2211yescharacteristic, complemented
73C2×#103×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C22×Dic86—21no—
79C22×Dic86C2311yescharacteristic
80C22×Dic86C2311yescharacteristic
81C2×Q8×D43—22no—
82C2×Q8×D43—42no—
83C2×Q8×D43—42no—
84C2×Q8×D43C2314yes—
85C22×D172—21no—
86C22×D172C2311yescharacteristic
87C22×D172C2311yescharacteristic
88C22×C22⋊D43—21no—
89C2×D4×D43—22no—
90C2×D4×D43—42no—
91C2×D4×D43—42no—
92C2×D4×D43C2314yes—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43D411yescharacteristic
96C22×C4×D43D411yescharacteristic
97C22×C4×D43C2311yescharacteristic
98C2×Dic172—42no—
99C2×Dic172C2314yescomplemented
100C2×#10621885—42no—
101C2×#10621885C2314yescomplemented
102C2×#10621873—42no—
103C2×#10621873—42no—
104C2×#10621873C2314yes—
105C2×#10621873C2314yescomplemented
106C2×#10621883—42no—
107C2×#10621883C2314yes—
108C2×#10621884—42no—
109C2×#10621884C2314yescomplemented
110C2×D344—42no—
111C2×D344C2314yes—
112C2×#10621882—42no—
113C2×#10621882C2314yes—
114C22×C43⋊C8C2311yescharacteristic
115C22×C43⋊C8C2311yescharacteristic
116#13063320—28no—
117#13063314—22no—
118#13063314C2314yes—
119#13063313—22no—
120#13063313—22no—
121#13063313C2314yes—
122#13063313C2314yescomplemented
123#13063312—22no—
124#13063312C2314yes—
125#13063311—28no—
126#13063311—28no—
127#13063310—28no—
128#13063305—22no—
129#13063305C2314yes—
130#13063300—22no—
131#13063300C2314yes—
132#13063290—22no—
133#13063290C2314yescomplemented
134#13063287—28no—
135#13063287—22no—
136#13063287C2314yescomplemented
137#13063283—28no—
138C2×C4⋊Dic43—21no—
139C2×Dic43⋊C4—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C22⋊C4×D43—28no—
152C22⋊C4×D43—28no—
153C2×C4×Dic43—21no—
154C2×C4×Dic43D411yescharacteristic
155C2×C4×Dic43D411yescharacteristic
156C2×C4×Dic43C2311yescharacteristic
157C42×D43D414yes—
158C42×D43C2314yes—
159Dic43⋊C8C2314yescomplemented
160Dic43⋊C8C2314yescomplemented
161#13063248C2314yescomplemented
162#13063248C2314yescomplemented
163#13063245C2314yes—
164#13063245C2314yes—
165(C2×D43)⋊C8C2314yes—
166(C2×D43)⋊C8C2314yes—
167C4×C43⋊C8C2314yescomplemented
168C22×Q8×C43C2311yescharacteristic
169C22×D4×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172#125×C43—22no—
173#125×C43C2314yescomplemented
174#124×C43—22no—
175#124×C43C2314yes—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182C2×C42×C43C2311yescharacteristic
183#103×C43C2314yescomplemented
184#103×C43C2314yescomplemented
185#102×C43C2314yes—
186#102×C43C2314yes—
187C4×C8×C43C2314yescomplemented
188C24×C43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—24no—
192C23×D43—44no—
193C23×D43—44no—
194C23×D43—44no—
195C23×D43C2×D411yescharacteristic
196C2×Q8×C43—21no—
197C2×Q8×C43—22no—
198C2×Q8×C43—22no—
199C2×Q8×C43C2412yes—
200C2×D4×C43—21no—
201C2×D4×C43—22no—
202C2×D4×C43—22no—
203C2×D4×C43C2412yes—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2411yescharacteristic
210C2×C22⋊D43—24no—
211C2×C22⋊D43—44no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217Q8×D43—44no—
218Q8×D43—44no—
219Q8×D43—48no—
220D4×D43—44no—
221D4×D43—44no—
222D4×D43—48no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—24no—
226C2×D172—22no—
227C2×D172—22no—
228C2×D172—22no—
229C2×D172—22no—
230C2×D172—44no—
231C2×D172C2412yes—
232C2×D172C2412yes—
233C2×C4×D43—22no—
234C2×C4×D43—22no—
235C2×C4×D43—24no—
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—42no—
239C2×C4×D43—44no—
240C2×C4×D43—44no—
241C2×C4×D43C2×D412yes—
242C2×C4×D43C2×D414yes—
243C2×C4×D43C2×D414yes—
244C2×C4×D43C2412yes—
245C2×Dic86—22no—
246C2×Dic86—22no—
247C2×Dic86—22no—
248C2×Dic86—22no—
249C2×Dic86—21no—
250C2×Dic86—21no—
251C2×Dic86—24no—
252C2×Dic86—44no—
253C2×Dic86C2412yes—
254C2×Dic86C2412yes—
255C2×C8×C43—22no—
256C2×C8×C43—22no—
257C2×C8×C43C2412yes—
258C2×C8×C43C2412yes—
259C4⋊C4×C43—24no—
260C4⋊C4×C43—24no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43C2412yes—
264C4⋊C4×C43C2412yes—
265C22⋊C4×C43—24no—
266C22⋊C4×C43—24no—
267C42×C43C2×D412yes—
268C42×C43C2412yes—
269C22⋊Dic43—24no—
270C22⋊Dic43—24no—
271#10621885—44no—
272#10621884—44no—
273#10621883—44no—
274#10621882—44no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4—24no—
280(C2×D43)⋊C4—24no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284C4⋊Dic43—24no—
285Dic43⋊C4—24no—
286C4×Dic43—24no—
287C4×Dic43C2×D412yes—
288C4×Dic43C2×D414yes—
289C4×Dic43C2×D414yes—
290C4×Dic43C2412yes—
291C2×C43⋊C8—22no—
292C2×C43⋊C8—22no—
293C2×C43⋊C8C2412yes—
294C2×C43⋊C8C2412yes—
295Dic172—44no—
296D344—44no—
297#10621873—44no—
298#10621873—44no—
299C23×C43—22no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43—42no—
303C23×C43C22×D411yescharacteristic
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—48no—
309C22×D43—48no—
310C22×D43—42no—
311C22×D43—42no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43—42no—
315C22×D43—42no—
316C22×D43—48no—
317C22×D43—816no—
318C22×D43#13514yes—
319C22×D43C22×D412yes—
320Q8×C43—22no—
321Q8×C43—22no—
322Q8×C43—42no—
323D4×C43—22no—
324D4×C43—22no—
325D4×C43—42no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—42no—
332C2×C4×C43—42no—
333C2×C4×C43—42no—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D412yes—
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43H(5,𝔽2)12yes—
338C2×C4×C43H(5,𝔽2)12yes—
339C2×C4×C43C2511yescharacteristic
340C22⋊D43—48no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350C2×Dic43C22×D412yes—
351D172—22no—
352D172—22no—
353D172—22no—
354D172—22no—
355D172—48no—
356D172—42no—
357D172—42no—
358C4×D43—28no—
359C4×D43—24no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—44no—
363C4×D43—48no—
364C4×D43—48no—
365Dic86—22no—
366Dic86—22no—
367Dic86—22no—
368Dic86—22no—
369Dic86—48no—
370Dic86—42no—
371Dic86—42no—
372C8×C43—22no—
373C8×C43—22no—
374C43⋊C8—22no—
375C43⋊C8—22no—
376C2×#3211—431nomaximal, Sylow
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—84no—
381C22×C43#53512yes—
382C22×C43C2×#13512yes—
383C22×C43#57512yes—
384C22×C43C23×D411yescharacteristic
385C2×D43—22no—
386C2×D43—28no—
387C2×D43—22no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—816no—
395C2×D43—84no—
396C2×D43—84no—
397C2×D43C2×#13514yes—
398C4×C43—22no—
399C4×C43—22no—
400C4×C43—42no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43#53512yes—
404C4×C43C2×H(5,𝔽2)11yescharacteristic
405C4×C43C2×H(5,𝔽2)11yescharacteristic
406Dic43—22no—
407Dic43—22no—
408Dic43—22no—
409Dic43—42no—
410Dic43—42no—
411C2×#529—431no—
412C22×#124—431no—
413#3211—4316no—
414C2×#495—431no—
415C2×#495—431no—
416C2×#488—431no—
417C2×#488D4311yescharacteristic, complemented
418C2×#464—431no—
419C2×#464—431no—
420C2×#463—431no—
421C2×#463—431no—
422C2×#451—431no—
423C2×#448—431no—
424C2×#450—431no—
425C2×#447—431no—
426C2×#431—431no—
427C2×C43—82no—
428C2×C43#321114yescomplemented
429C2×C43C2×#53511yescharacteristic
430C2×C43C22×#13511yescharacteristic
431C2×C43C2×#57511yescharacteristic
432D43—24no—
433D43—82no—
434D43—82no—
435C23×Q8—431no—
436C23×D4—431no—
437C22×Q16—431no—
438C22×Q16—431no—
439C22×SD16—431no—
440C22×SD16—431no—
441C22×SD16—431no—
442C22×SD16—431no—
443C22×D8—431no—
444C22×D8—431no—
445#529—438no—
446#529—864no—
447C2×#126—861no—
448C2×#125C2×D4311yescharacteristic, complemented
449C2×#124—431no—
450C2×#124—431no—
451C2×#124—438no—
452C2×#124—431no—
453C2×#124—431no—
454C2×#124—861no—
455C2×#124—861no—
456C2×#124—864no—
457C2×#124C2×D4311yescharacteristic
458C2×#123—861no—
459C2×C22⋊Q8—431no—
460C2×#121—431no—
461C2×C4×Q8—431no—
462C2×C4×D4—431no—
463C2×C4×D4—861no—
464C2×#117—861no—
465C22×C22⋊C4—861no—
466C22×C22⋊C4—861no—
467C22×C42—431no—
468#495—438no—
469#495—438no—
470#488—438no—
471#488C2×D4318yescomplemented
472#464—438no—
473#464—438no—
474#463—438no—
475#463—438no—
476#451—438no—
477#450—438no—
478#448—438no—
479#447—438no—
480#431—438no—
481C2×C4⋊C8—431no—
482C2×C4⋊C8—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#103C2×D4311yescharacteristic, complemented
486C2×#103C2×D4311yescharacteristic, complemented
487C2×#102—431no—
488C2×#102—431no—
489C2×#102C2×D4311yescharacteristic
490C2×#102C2×D4311yescharacteristic
491C2×C22⋊C8—431no—
492C2×C22⋊C8—431no—
493C2×C4×C8—431no—
494C2×C4×C8C2×D4311yescharacteristic, complemented
495C43C2×#321111yescharacteristic, complemented, Sylow
496C25—861no—
497C22×Q8—434no—
498C22×Q8—431no—
499C22×Q8—431no—
500C22×Q8—861no—
501C22×Q8—862no—
502C22×Q8—1722no—
503C22×Q8—1722no—
504C22×Q8C22×D4311yescharacteristic
505C22×D4—434no—
506C22×D4—431no—
507C22×D4—431no—
508C22×D4—861no—
509C22×D4—862no—
510C22×D4—861no—
511C22×D4—1722no—
512C22×D4—1722no—
513C22×D4C22×D4311yescharacteristic
514C23×C4—431no—
515C23×C4—431no—
516C23×C4—431no—
517C23×C4—861no—
518C23×C4—861no—
519C2×Q16—434no—
520C2×Q16—434no—
521C2×Q16—1722no—
522C2×Q16—1722no—
523C2×SD16—434no—
524C2×SD16—434no—
525C2×SD16—434no—
526C2×SD16—434no—
527C2×SD16—1722no—
528C2×SD16—1722no—
529C2×SD16—1722no—
530C2×SD16—1722no—
531C2×D8—434no—
532C2×D8—434no—
533C2×D8—1722no—
534C2×D8—1722no—
535C22×C8—431no—
536C22×C8—431no—
537C22×C8C22×D4311yescharacteristic
538C22×C8C22×D4311yescharacteristic
539#126—868no—
540#125—22no—
541#125C22×D4314yescomplemented
542#124—22no—
543#124—434no—
544#124—434no—
545#124—434no—
546#124—434no—
547#124—868no—
548#124—868no—
549#124—862no—
550#124—862no—
551#124—862no—
552#124—862no—
553#124C22×D4314yes—
554#123—868no—
555C22⋊Q8—434no—
556C22⋊Q8—862no—
557#121—434no—
558#121—862no—
559C4×Q8—434no—
560C4×Q8—862no—
561C4×D4—434no—
562C4×D4—862no—
563C4×D4—868no—
564#117—868no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4—861no—
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C4⋊C4C22×D4311yescharacteristic
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—868no—
574C2×C22⋊C4—868no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C22⋊C4—861no—
582C2×C22⋊C4—861no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C42—431no—
587C2×C42—431no—
588C2×C42—431no—
589C2×C42—434no—
590C2×C42—434no—
591C2×C42—861no—
592C2×C42C22×D4311yescharacteristic
593C4⋊C8—434no—
594C4⋊C8—434no—
595#103—434no—
596#103—434no—
597#103C22×D4314yescomplemented
598#103C22×D4314yescomplemented
599#102—434no—
600#102—434no—
601#102C22×D4314yes—
602#102C22×D4314yes—
603C22⋊C8—434no—
604C22⋊C8—434no—
605C4×C8—434no—
606C4×C8C22×D4314yescomplemented
607C24—21no—
608C24—431no—
609C24—864no—
610C24—861no—
611C24—861no—
612C24—1724no—
613C24—1724no—
614C24—1724no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—432no—
619C2×Q8—432no—
620C2×Q8—864no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—862no—
624C2×Q8—862no—
625C2×Q8—862no—
626C2×Q8—862no—
627C2×Q8—1724no—
628C2×Q8—1724no—
629C2×Q8—1724no—
630C2×Q8—1728no—
631C2×Q8C23×D4312yes—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—432no—
636C2×D4—432no—
637C2×D4—864no—
638C2×D4—864no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—862no—
642C2×D4—862no—
643C2×D4—862no—
644C2×D4—862no—
645C2×D4—1724no—
646C2×D4—1724no—
647C2×D4—1724no—
648C2×D4—1728no—
649C2×D4—1724no—
650C2×D4C23×D4312yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—434no—
658C22×C4—432no—
659C22×C4—432no—
660C22×C4—434no—
661C22×C4—864no—
662C22×C4—864no—
663C22×C4—864no—
664C22×C4—862no—
665C22×C4—862no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—1722no—
669C22×C4—1724no—
670C22×C4—1724no—
671C22×C4D4×D4311yescharacteristic
672C22×C4D4×D4311yescharacteristic
673C22×C4C23×D4311yescharacteristic
674Q16—1724no—
675Q16—1724no—
676SD16—1724no—
677SD16—1724no—
678SD16—1724no—
679SD16—1724no—
680D8—1724no—
681D8—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—24no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—864no—
695C4⋊C4—864no—
696C4⋊C4C23×D4312yes—
697C4⋊C4C23×D4312yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C22⋊C4—864no—
710C22⋊C4—864no—
711C42—434no—
712C42—432no—
713C42—434no—
714C42—432no—
715C42—864no—
716C42D4×D4312yes—
717C42C23×D4312yes—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—434no—
723C23—432no—
724C23—862no—
725C23—862no—
726C23—862no—
727C23—862no—
728C23—34416no—
729C23—1728no—
730C23—1728no—
731C23—1728no—
732C23—1722no—
733C23—1722no—
734C23—1722no—
735C23—1722no—
736C23—1722no—
737C23—1722no—
738C23C2×D4×D4311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742Q8—862no—
743Q8—862no—
744Q8—862no—
745Q8—862no—
746Q8—1728no—
747Q8—1722no—
748Q8—1722no—
749D4—22no—
750D4—22no—
751D4—42no—
752D4—862no—
753D4—862no—
754D4—862no—
755D4—862no—
756D4—1728no—
757D4—1728no—
758D4—1722no—
759D4—1722no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—432no—
769C2×C4—432no—
770C2×C4—432no—
771C2×C4—868no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—864no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—1724no—
781C2×C4—1728no—
782C2×C4—1728no—
783C2×C4—1722no—
784C2×C4—1722no—
785C2×C4C2×D4×D4312yes—
786C2×C4C2×D4×D4312yes—
787C2×C4C2×D4×D4311yescharacteristic
788C2×C4#1306337112yes—
789C2×C4#1306337112yes—
790C2×C4C24×D4311yescharacteristic
791C8—22no—
792C8—22no—
793C8—862no—
794C8—862no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—84no—
799C22—434no—
800C22—862no—
801C22—868no—
802C22—862no—
803C22—34416no—
804C22—3444no—
805C22—3444no—
806C22—1722no—
807C22—1722no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22#1458346712yes—
813C22#135×D4312yes—
814C22#1458369612yes—
815C22C22×D4×D4311yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—862no—
822C4—862no—
823C4—862no—
824C4—1722no—
825C4—1722no—
826C4#1458346712yes—
827C4C2×#1306337111yescharacteristic
828C4C2×#1306337111yescharacteristic
829C2—82no—
830C2—864no—
831C2—3442no—
832C2—3442no—
833C2#1914556114yesdirect product factor
834C2C2×#1458346711yescharacteristic
835C2C2×#135×D4311yescharacteristic
836C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#488C2
socleC23×C43C22×D4
prime radicalC2×#14583034C2
hypercenterC2×#488D43
hypocenterC43C2×#3211
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#14583434C2semidirect
2. C2×#124×D43C2semidirect
3. #19145561C2direct (N × H)
4. C2×#14583283C2semidirect
5. C2×#14583281C2semidirect
6. C2×#14583256C2semidirect
7. C2×#14583124C2semidirect
8. C2×#14583120C2semidirect
9. C2×#14583117C2semidirect
10. C2×#14583113C2semidirect
11. C2×#14583056C2semidirect
12. C2×#14583039C2semidirect
13. C2×#14583051C2semidirect
15. C2×#14582950C2semidirect
16. C2×C43×#488C2semidirect
19. C22×Dic172C22semidirect
20. C22×#10621885C22semidirect
22. C22×#10621873C22semidirect
24. C22×#10621884C22semidirect
28. #14583434C22semidirect
32. C2×#13063313C22semidirect
37. #124×D43C22semidirect
41. C2×#13063290C22semidirect
43. C2×#13063287C22semidirect
48. #14583283C22semidirect
49. #14583281C22semidirect
50. #14583256C22semidirect
51. #14583124C22semidirect
52. #14583120C22semidirect
53. #14583117C22semidirect
54. #14583113C22semidirect
55. #14583056C22semidirect
56. #14583051C22semidirect
57. #14583039C22semidirect
59. #14582950C22semidirect
60. C2×Dic43⋊C8C22semidirect
61. C2×Dic43⋊C8C22semidirect
62. C2×#13063248C22semidirect
63. C2×#13063248C22semidirect
68. C2×C4×C43⋊C8C22semidirect
69. C2×#125×C43C22semidirect
71. C43×#488C22semidirect
72. C2×#103×C43C22semidirect
73. C2×#103×C43C22semidirect
76. C2×C4×C8×C43C22semidirect
99. C2×Dic172C23semidirect
101. C2×#10621885C23semidirect
105. C2×#10621873C23semidirect
109. C2×#10621884C23semidirect
122. #13063313C23semidirect
133. #13063290C23semidirect
136. #13063287C23semidirect
159. Dic43⋊C8C23semidirect
160. Dic43⋊C8C23semidirect
161. #13063248C23semidirect
162. #13063248C23semidirect
167. C4×C43⋊C8C23semidirect
173. #125×C43C23semidirect
183. #103×C43C23semidirect
184. #103×C43C23semidirect
187. C4×C8×C43C23semidirect
417. C2×#488D43semidirect
428. C2×C43#3211semidirect
448. C2×#125C2×D43semidirect
471. #488C2×D43semidirect
485. C2×#103C2×D43semidirect
486. C2×#103C2×D43semidirect
494. C2×C4×C8C2×D43semidirect
495. C43C2×#3211semidirect
541. #125C22×D43semidirect
597. #103C22×D43semidirect
598. #103C22×D43semidirect
606. C4×C8C22×D43semidirect
833. C2#19145561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834342
C2×#124×D432
#191455612
C2×#145832832
C2×#145832812
C2×#145832562
C2×#145831242
C2×#145831202
C2×#145831172
C2×#145831132
C2×#145830562
C2×#145830392
C2×#145830512
C2×#145830342
C2×#145829502
C2×C43×#4882
C2×#321143