Finite Group Databasebeta

← C2×#19146669 #25973116

Subgroups — C2×#19146669 #25973116

Order 11008.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic, complemented
2C2×#14583537C211yesmaximal, characteristic
3#19146669C2116yesmaximal, direct product factor
4C2×#14583260C211yesmaximal, characteristic, complemented
5C2×#14583233C211yesmaximal, characteristic, complemented
6C2×#14583213C211yesmaximal, characteristic, complemented
7C2×#14583177C211yesmaximal, characteristic, complemented
8C2×#14583147C211yesmaximal, characteristic, complemented
9C2×#14583137C211yesmaximal, characteristic, complemented
10C2×#14583123C211yesmaximal, characteristic, complemented
11C2×#14583048C211yesmaximal, characteristic, complemented
12C2×#14583000C211yesmaximal, characteristic, complemented
13C2×#14582973C211yesmaximal, characteristic, complemented
14C2×#14582900C211yesmaximal, characteristic, complemented
15C2×#102×D43C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic, complemented
17C22×D4×D43C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621877C2211yescharacteristic, complemented
20C22×C8×D43C2211yescharacteristic
21#14583607—24no—
22#14583607C2218yescomplemented
23#14583537—24no—
24#14583537C2218yes—
25C2×#13063324C2211yescharacteristic, complemented
26C2×#13063315—21no—
27C2×#13063314C2211yescharacteristic
28C2×#13063308—21no—
29C2×#13063305—21no—
30C2×#13063302—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063301C2211yescharacteristic
33C2×#13063299C2211yescharacteristic
34C2×#13063297—21no—
35C2×#13063293—21no—
36C2×Q8×Dic43C2211yescharacteristic, complemented
37C2×D4×Dic43C2211yescharacteristic
38C2×C4×C22⋊D43C2211yescharacteristic
39C2×(C22⋊D43)⋊C4—21no—
40C22×C4⋊Dic43C2211yescharacteristic, complemented
41C2×C4⋊C4×D43C2211yescharacteristic
42C22×(C2×D43)⋊C4—21no—
43#14583260C2218yescomplemented
44#14583233C2218yescomplemented
45#14583213C2218yescomplemented
46#14583177C2218yescomplemented
47#14583147C2218yescomplemented
48#14583137C2218yescomplemented
49#14583123C2218yescomplemented
50#14583048C2218yescomplemented
51#14583000C2218yescomplemented
52#14582973C2218yescomplemented
53C2×#13063259C2211yescharacteristic, complemented
54C2×#13063259C2211yescharacteristic, complemented
55C2×#13063258C2211yescharacteristic, complemented
56C2×Dic43⋊C8C2211yescharacteristic, complemented
57#14582900C2218yescomplemented
58C2×#13063249C2211yescharacteristic, complemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063249C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66#102×D43C2218yescomplemented
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic, complemented
69C22×#41×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic, complemented
71C22×SD16×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic, complemented
73C43×#452C2218yescomplemented
74C2×#103×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C22×Dic86—21no—
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C22×C22⋊D43D411yescharacteristic
83C2×D4×D43—24no—
84C2×D4×D43—22no—
85C2×D4×D43—42no—
86C2×D4×D43C2314yes—
87C23×Dic43—21no—
88C23×Dic43—21no—
89C22×C4×D43—21no—
90C22×C4×D43C2311yescharacteristic
91C2×#10621884—42no—
92C2×#10621884C2314yes—
93C2×#10621877—42no—
94C2×#10621877C2314yescomplemented
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97C2×C8×D43—42no—
98C2×C8×D43C2314yes—
99#13063324—22no—
100#13063324C2314yescomplemented
101#13063315—28no—
102#13063314—22no—
103#13063314C2314yes—
104#13063308—28no—
105#13063305—28no—
106#13063302—28no—
107#13063301—22no—
108#13063301—22no—
109#13063301C2314yes—
110#13063301C2314yes—
111#13063299—22no—
112#13063299C2314yes—
113#13063297—28no—
114#13063293—28no—
115Q8×Dic43—22no—
116Q8×Dic43C2314yescomplemented
117D4×Dic43—22no—
118D4×Dic43C2314yes—
119C4×C22⋊D43D414yes—
120C4×C22⋊D43C2314yes—
121(C22⋊D43)⋊C4—28no—
122C2×C4⋊Dic43—22no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2314yescomplemented
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4D411yescharacteristic
134C4⋊C4×D43—22no—
135C4⋊C4×D43C2314yes—
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43D411yescharacteristic
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—28no—
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063259C2314yescomplemented
148#13063259C2314yescomplemented
149#13063258C2314yescomplemented
150Dic43⋊C8C2314yescomplemented
151#13063249C2314yescomplemented
152#13063249C2314yescomplemented
153#13063249C2314yescomplemented
154#13063247C2314yes—
155#13063247C2314yes—
156#13063246C2314yes—
157#13063246C2314yes—
158#13063245C2314yes—
159(C2×D43)⋊C8C2314yes—
160#13063235C2314yescomplemented
161C2×#41×C43—22no—
162C2×#41×C43—24no—
163C2×#41×C43—42no—
164C2×#41×C43C2314yes—
165C22×Q8×C43C2311yescharacteristic
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43—21no—
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C23×C4×C43C2311yescharacteristic
171C2×Q16×C43—42no—
172C2×Q16×C43C2314yescomplemented
173C2×SD16×C43—24no—
174C2×SD16×C43C2314yes—
175C22×C8×C43C2311yescharacteristic
176C22×C8×C43C2311yescharacteristic
177C22⋊Q8×C43—22no—
178C22⋊Q8×C43C2314yescomplemented
179C2×C4⋊C4×C43—21no—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182#103×C43C2314yescomplemented
183#102×C43C2314yes—
184C22⋊C8×C43C2314yescomplemented
185C24×C43—21no—
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C23×D43—24no—
189C23×D43—44no—
190C23×D43—44no—
191C23×D43—82no—
192C23×D43C2×D411yescharacteristic
193#41×C43—28no—
194#41×C43—44no—
195#41×C43—48no—
196C2×Q8×C43—21no—
197C2×Q8×C43—21no—
198C2×Q8×C43—22no—
199C2×Q8×C43—22no—
200C2×Q8×C43—22no—
201C2×Q8×C43—22no—
202C2×Q8×C43C2412yes—
203C2×Q8×C43C2412yes—
204C2×D4×C43—21no—
205C2×D4×C43—22no—
206C2×D4×C43—24no—
207C2×D4×C43—44no—
208C2×D4×C43#4114yes—
209C2×D4×C43C2412yes—
210C22×C4×C43—22no—
211C22×C4×C43—22no—
212C22×C4×C43—24no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—44no—
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D412yes—
219C22×C4×C43C2412yes—
220C22×C4×C43C2411yescharacteristic
221C2×C22⋊D43—24no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—24no—
224C2×C22⋊D43—44no—
225C2×C22⋊D43—82no—
226C2×C22⋊D43C2×D414yes—
227C22×Dic43—24no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—24no—
232C22×Dic43—82no—
233C22×Dic43—82no—
234C22×Dic43C2×D411yescharacteristic
235C22×Dic43C2×D411yescharacteristic
236C22×Dic43C2×D411yescharacteristic
237D4×D43—28no—
238D4×D43—44no—
239D4×D43—48no—
240C2×D172—21no—
241C2×D172—22no—
242C2×D172—22no—
243C2×D172C2412yes—
244C2×C4×D43—22no—
245C2×C4×D43—22no—
246C2×C4×D43—24no—
247C2×C4×D43—82no—
248C2×C4×D43C2×D412yes—
249C2×C4×D43C2412yes—
250C2×Dic86—24no—
251C2×Dic86—82no—
252Q16×C43—44no—
253SD16×C43—28no—
254C2×C8×C43—22no—
255C2×C8×C43—22no—
256C2×C8×C43C2412yes—
257C2×C8×C43C2412yes—
258C4⋊C4×C43—24no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43C2412yes—
261C22⋊C4×C43—24no—
262C22⋊Dic43—24no—
263C22⋊Dic43C2×D414yes—
264#10621884—44no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4C2×D414yes—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—24no—
274C4⋊Dic43—21no—
275C4⋊Dic43—24no—
276C4⋊Dic43C2412yes—
277C4⋊Dic43C2412yes—
278C4⋊Dic43C2412yes—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283Dic43⋊C4C2×D414yes—
284C4×Dic43—24no—
285C4×Dic43C2×D412yes—
286C4×Dic43C2412yes—
287#10621877—44no—
288C2×C43⋊C8—22no—
289C2×C43⋊C8—22no—
290C2×C43⋊C8C2412yes—
291C2×C43⋊C8C2412yes—
292C8×D43—44no—
293C23×C43—24no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43C22×D412yes—
301C23×C43C22×D411yescharacteristic
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—48no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—48no—
310C22×D43—84no—
311C22×D43—816no—
312C22×D43#13714yes—
313C22×D43C22×D412yes—
314Q8×C43—22no—
315Q8×C43—22no—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43—42no—
319Q8×C43—42no—
320D4×C43—24no—
321D4×C43—22no—
322D4×C43—48no—
323D4×C43C2×#4114yes—
324C2×C4×C43—22no—
325C2×C4×C43—24no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—48no—
332C2×C4×C43—42no—
333C2×C4×C43—42no—
334C2×C4×C43—42no—
335C2×C4×C43C22×D412yes—
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C2×#4112yes—
338C2×C4×C43H(5,𝔽2)12yes—
339C2×C4×C43C2511yescharacteristic
340C22⋊D43—28no—
341C22⋊D43—48no—
342C22⋊D43—84no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43—42no—
352C2×Dic43—84no—
353C2×Dic43—84no—
354C2×Dic43C22×D412yes—
355C2×Dic43C22×D412yes—
356C2×Dic43C22×D412yes—
357D172—22no—
358D172—22no—
359D172—42no—
360C4×D43—24no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—84no—
364Dic86—84no—
365C8×C43—22no—
366C8×C43—22no—
367C43⋊C8—22no—
368C43⋊C8—22no—
369C2×#3314—431nomaximal, Sylow
370C22×C43—24no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—48no—
375C22×C43—44no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43#54612yes—
379C22×C43C2×#13712yes—
380C22×C43#57612yes—
381C22×C43C23×D411yescharacteristic
382C2×D43—22no—
383C2×D43—28no—
384C2×D43—22no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—816no—
389C2×D43—84no—
390C2×D43C2×#13714yes—
391C4×C43—22no—
392C4×C43—42no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43#54612yes—
396C4×C43C22×#4111yescharacteristic
397C4×C43C2×H(5,𝔽2)11yescharacteristic
398Dic43—22no—
399Dic43—22no—
400Dic43—22no—
401Dic43—42no—
402Dic43—42no—
403Dic43—42no—
404C2×#554—431no—
405C2×#546—431no—
406#3314—4316no—
407C2×#489—431no—
408C2×#484—431no—
409C2×#480—431no—
410C2×#474—431no—
411C2×#468—431no—
412C2×#467—431no—
413C2×#464—431no—
414C2×#452D4311yescharacteristic, complemented
415C2×#450—431no—
416C2×#440—431no—
417C2×#435—431no—
418C2×#417—431no—
419C22×#102—431no—
420C2×C43—44no—
421C2×C43—42no—
422C2×C43#331414yescomplemented
423C2×C43C2×#54611yescharacteristic
424C2×C43C22×#13711yescharacteristic
425C2×C43C2×#57611yescharacteristic
426D43—24no—
427D43—82no—
428C22×#41C2×D4311yescharacteristic
429C23×D4—431no—
430C22×Q16C2×D4311yescharacteristic, complemented
431C22×SD16—431no—
432C22×SD16C2×D4311yescharacteristic
433C22×M16—431no—
434C23×C8—431no—
435#554—438no—
436#554—864no—
437#546—438no—
438#546—864no—
439C2×C4⋊Q8—431no—
440C2×#125—861no—
441C2×#124—431no—
442C2×#123—861no—
443C2×C22⋊Q8—431no—
444C2×C22⋊Q8—431no—
445C2×C22⋊Q8—861no—
446C2×C22⋊Q8—861no—
447C2×C22⋊Q8C2×D4311yescharacteristic, complemented
448C2×#121—431no—
449C2×#121—861no—
450C2×#120—861no—
451C2×C4×Q8—431no—
452C2×C4×D4—431no—
453C2×C4×D4—431no—
454C2×C4×D4—861no—
455C22×C4⋊C4—431no—
456C22×C4⋊C4—431no—
457C22×C22⋊C4—861no—
458#489—438no—
459#484—438no—
460#480—438no—
461#474—438no—
462#468—438no—
463#467—438no—
464#464—438no—
465#452C2×D4318yescomplemented
466#450—438no—
467#440—438no—
468#435—438no—
469C2×#107—431no—
470C2×#107—431no—
471C2×#107—431no—
472C2×C4⋊C8—431no—
473#417—438no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103—431no—
477C2×#103C2×D4311yescharacteristic, complemented
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—438no—
484C2×#102C2×D4311yescharacteristic
485C2×C22⋊C8—431no—
486C2×C22⋊C8C2×D4311yescharacteristic, complemented
487C2×#97—431no—
488C43C2×#331411yescharacteristic, complemented, Sylow
489C25—861no—
490C2×#41—22no—
491C2×#41—24no—
492C2×#41—42no—
493C2×#41C22×D4314yes—
494C22×Q8—861no—
495C22×Q8C22×D4311yescharacteristic
496C22×Q8C22×D4311yescharacteristic
497C22×D4—21no—
498C22×D4—431no—
499C22×D4—434no—
500C22×D4—431no—
501C22×D4—862no—
502C22×D4—861no—
503C22×D4—864no—
504C22×D4—861no—
505C22×D4—1722no—
506C22×D4C22×D4311yescharacteristic
507C23×C4—21no—
508C23×C4—431no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4—861no—
512C23×C4C22×D4311yescharacteristic
513C2×Q16—42no—
514C2×Q16C22×D4314yescomplemented
515C2×SD16—24no—
516C2×SD16—434no—
517C2×SD16—1722no—
518C2×SD16C22×D4314yes—
519C2×M16—434no—
520C2×M16—1722no—
521C22×C8—431no—
522C22×C8—431no—
523C22×C8—434no—
524C22×C8—1722no—
525C22×C8C22×D4311yescharacteristic
526C22×C8C22×D4311yescharacteristic
527C4⋊Q8—434no—
528C4⋊Q8—862no—
529#125—868no—
530#124—434no—
531#124—862no—
532#123—868no—
533C22⋊Q8—22no—
534C22⋊Q8—434no—
535C22⋊Q8—434no—
536C22⋊Q8—868no—
537C22⋊Q8—868no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540C22⋊Q8C22×D4314yescomplemented
541#121—434no—
542#121—868no—
543#121—862no—
544#120—868no—
545C4×Q8—434no—
546C4×Q8—862no—
547C4×D4—434no—
548C4×D4—434no—
549C4×D4—434no—
550C4×D4—862no—
551C4×D4—868no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—434no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—434no—
559C2×C4⋊C4—862no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—862no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—431no—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—868no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C42—431no—
579C2×C42—861no—
580#107—434no—
581#107—434no—
582#107—434no—
583C4⋊C8—434no—
584#103—434no—
585#103—434no—
586#103—434no—
587#103C22×D4314yescomplemented
588#102—434no—
589#102—434no—
590#102—434no—
591#102—434no—
592#102—434no—
593#102C22×D4314yes—
594C22⋊C8—434no—
595C22⋊C8C22×D4314yescomplemented
596#97—434no—
597C24—21no—
598C24—431no—
599C24—864no—
600C24—861no—
601C24—3442no—
602C24—1724no—
603C24—1724no—
604C24D4×D4311yescharacteristic
605#41—28no—
606#41—44no—
607#41—48no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—864no—
615C2×Q8—3442no—
616C2×Q8C23×D4312yes—
617C2×Q8C23×D4312yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—434no—
623C2×D4—432no—
624C2×D4—864no—
625C2×D4—864no—
626C2×D4—868no—
627C2×D4—864no—
628C2×D4—861no—
629C2×D4—862no—
630C2×D4—862no—
631C2×D4—3442no—
632C2×D4—1724no—
633C2×D4—1728no—
634C2×D4—1724no—
635C2×D4#1062190014yes—
636C2×D4C23×D4312yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—431no—
645C22×C4—431no—
646C22×C4—431no—
647C22×C4—432no—
648C22×C4—432no—
649C22×C4—864no—
650C22×C4—864no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—864no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—3442no—
658C22×C4—3442no—
659C22×C4—3442no—
660C22×C4D4×D4312yes—
661C22×C4D4×D4311yescharacteristic
662C22×C4C23×D4312yes—
663C22×C4C23×D4311yescharacteristic
664Q16—44no—
665SD16—28no—
666SD16—1724no—
667M16—1724no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—432no—
671C2×C8—432no—
672C2×C8—862no—
673C2×C8—862no—
674C2×C8—1724no—
675C2×C8C23×D4312yes—
676C2×C8C23×D4312yes—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—434no—
680C4⋊C4—432no—
681C4⋊C4—432no—
682C4⋊C4—432no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—864no—
687C4⋊C4—864no—
688C4⋊C4—861no—
689C4⋊C4—864no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4C23×D4312yes—
693C22⋊C4—24no—
694C22⋊C4—434no—
695C22⋊C4—434no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C42—432no—
703C42—432no—
704C42—864no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—24no—
710C23—42no—
711C23—42no—
712C23—434no—
713C23—432no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—34416no—
718C23—3444no—
719C23—1728no—
720C23—1728no—
721C23—1722no—
722C23—1722no—
723C23—1722no—
724C23C2×D4×D4312yes—
725C23C2×D4×D4311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—3444no—
733D4—22no—
734D4—24no—
735D4—48no—
736D4—868no—
737D4—862no—
738D4—862no—
739D4—3444no—
740D4—1728no—
741D4—1722no—
742D4C2×#1062190014yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—432no—
755C2×C4—432no—
756C2×C4—432no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—864no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—3444no—
767C2×C4—3444no—
768C2×C4—3444no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—1722no—
772C2×C4C2×D4×D4312yes—
773C2×C4C2×D4×D4311yescharacteristic
774C2×C4C2×#1062190012yes—
775C2×C4#1306337012yes—
776C2×C4C24×D4311yescharacteristic
777C8—22no—
778C8—22no—
779C8—862no—
780C8—862no—
781C22—22no—
782C22—24no—
783C22—22no—
784C22—22no—
785C22—42no—
786C22—42no—
787C22—44no—
788C22—48no—
789C22—434no—
790C22—862no—
791C22—862no—
792C22—868no—
793C22—34416no—
794C22—3444no—
795C22—1722no—
796C22—1722no—
797C22—1722no—
798C22#1458353612yes—
799C22#137×D4312yes—
800C22#1458370112yes—
801C22C22×D4×D4311yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—862no—
807C4—862no—
808C4—862no—
809C4—1722no—
810C4—1722no—
811C4—1722no—
812C4#1458353612yes—
813C4C22×#1062190011yescharacteristic
814C4C2×#1306337011yescharacteristic
815C2—42no—
816C2—44no—
817C2—864no—
818C2—3442no—
819C2#1914666914yesdirect product factor
820C2C2×#1458353611yescharacteristic
821C2C2×#137×D4311yescharacteristic
822C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC2×#14583537C2
hypercenterC2×#452D43
hypocenterC43C2×#3314
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×#14583607C2semidirect
3. #19146669C2direct (N × H)
4. C2×#14583260C2semidirect
5. C2×#14583233C2semidirect
6. C2×#14583213C2semidirect
7. C2×#14583177C2semidirect
8. C2×#14583147C2semidirect
9. C2×#14583137C2semidirect
10. C2×#14583123C2semidirect
11. C2×#14583048C2semidirect
12. C2×#14583000C2semidirect
13. C2×#14582973C2semidirect
14. C2×#14582900C2semidirect
15. C2×#102×D43C2semidirect
16. C2×C43×#452C2semidirect
19. C22×#10621877C22semidirect
22. #14583607C22semidirect
25. C2×#13063324C22semidirect
36. C2×Q8×Dic43C22semidirect
40. C22×C4⋊Dic43C22semidirect
43. #14583260C22semidirect
44. #14583233C22semidirect
45. #14583213C22semidirect
46. #14583177C22semidirect
47. #14583147C22semidirect
48. #14583137C22semidirect
49. #14583123C22semidirect
50. #14583048C22semidirect
51. #14583000C22semidirect
52. #14582973C22semidirect
53. C2×#13063259C22semidirect
54. C2×#13063259C22semidirect
55. C2×#13063258C22semidirect
56. C2×Dic43⋊C8C22semidirect
57. #14582900C22semidirect
58. C2×#13063249C22semidirect
59. C2×#13063249C22semidirect
60. C2×#13063249C22semidirect
66. #102×D43C22semidirect
68. C2×#13063235C22semidirect
70. C22×Q16×C43C22semidirect
72. C2×C22⋊Q8×C43C22semidirect
73. C43×#452C22semidirect
74. C2×#103×C43C22semidirect
76. C2×C22⋊C8×C43C22semidirect
94. C2×#10621877C23semidirect
100. #13063324C23semidirect
116. Q8×Dic43C23semidirect
128. C2×C4⋊Dic43C23semidirect
147. #13063259C23semidirect
148. #13063259C23semidirect
149. #13063258C23semidirect
150. Dic43⋊C8C23semidirect
151. #13063249C23semidirect
152. #13063249C23semidirect
153. #13063249C23semidirect
160. #13063235C23semidirect
172. C2×Q16×C43C23semidirect
178. C22⋊Q8×C43C23semidirect
182. #103×C43C23semidirect
184. C22⋊C8×C43C23semidirect
414. C2×#452D43semidirect
422. C2×C43#3314semidirect
430. C22×Q16C2×D43semidirect
447. C2×C22⋊Q8C2×D43semidirect
465. #452C2×D43semidirect
477. C2×#103C2×D43semidirect
486. C2×C22⋊C8C2×D43semidirect
488. C43C2×#3314semidirect
514. C2×Q16C22×D43semidirect
540. C22⋊Q8C22×D43semidirect
587. #103C22×D43semidirect
595. C22⋊C8C22×D43semidirect
819. C2#19146669direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836072
C2×#145835372
#191466692
C2×#145832602
C2×#145832332
C2×#145832132
C2×#145831772
C2×#145831472
C2×#145831372
C2×#145831232
C2×#145830482
C2×#145830002
C2×#145829732
C2×#145829002
C2×#102×D432
C2×C43×#4522
C2×#331443