Finite Group Databasebeta

← C2×#19146675 #25973122

Subgroups — C2×#19146675 #25973122

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×#14583610C211yesmaximal, characteristic, complemented
2C2×#14583542C211yesmaximal, characteristic
3#19146675C2116yesmaximal, direct product factor
4C2×#14583233C211yesmaximal, characteristic, complemented
5C2×#14583211C211yesmaximal, characteristic, complemented
6C2×#14583176C211yesmaximal, characteristic, complemented
7C2×#14583144C211yesmaximal, characteristic, complemented
8C2×#14583139C211yesmaximal, characteristic, complemented
9C2×#14583118C211yesmaximal, characteristic, complemented
10C2×#14583064C211yesmaximal, characteristic, complemented
11C2×#14583051C211yesmaximal, characteristic, complemented
12C2×#14583001C211yesmaximal, characteristic, complemented
13C2×#14582972C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C2×#102×D43C211yesmaximal, characteristic, complemented
16C2×C43×#489C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621885C2211yescharacteristic, complemented
20C22×#10621873C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621872C2211yescharacteristic, complemented
23C22×C8×D43C2211yescharacteristic
24#14583610—24no—
25#14583610C2218yescomplemented
26#14583542—24no—
27#14583542C2218yes—
28C2×#13063316—21no—
29C2×#13063307—21no—
30C2×#13063305C2211yescharacteristic
31C2×#13063305C2211yescharacteristic, complemented
32C2×#13063301—21no—
33C2×#13063301—21no—
34C2×#13063301C2211yescharacteristic
35C2×#13063298—21no—
36C2×#13063296C2211yescharacteristic
37C2×#13063295—21no—
38C2×C4×Dic86C2211yescharacteristic, complemented
39C2×C4×D172C2211yescharacteristic
40C2×C4×D172C2211yescharacteristic
41C2×#13063287—21no—
42C2×C4⋊C4×D43C2211yescharacteristic
43C2×C4⋊C4×D43C2211yescharacteristic, complemented
44C2×C22⋊C4×D43—21no—
45#14583233C2218yescomplemented
46#14583211C2218yescomplemented
47#14583176C2218yescomplemented
48#14583144C2218yescomplemented
49#14583139C2218yescomplemented
50#14583118C2218yescomplemented
51#14583064C2218yescomplemented
52#14583051C2218yescomplemented
53#14583001C2218yescomplemented
54#14582972C2218yescomplemented
55C2×#13063259C2211yescharacteristic, complemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063258C2211yescharacteristic, complemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
59#14582899C2218yescomplemented
60C2×#13063250C2211yescharacteristic, complemented
61C2×#13063249C2211yescharacteristic, complemented
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66#102×D43C2218yescomplemented
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C2×C4⋊Q8×C43C2211yescharacteristic, complemented
70C2×#124×C43C2211yescharacteristic
71C43×#489C2218yescomplemented
72C2×#103×C43C2211yescharacteristic, complemented
73C2×#103×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621902—22no—
79C2×#10621902—24no—
80C2×#10621902—42no—
81C2×#10621902C2314yes—
82C22×Dic86C2311yescharacteristic
83C22×D172—21no—
84C22×D172D411yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C2×D4×D43—24no—
89C2×D4×D43—22no—
90C2×D4×D43—42no—
91C2×D4×D43C2314yes—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2311yescharacteristic
98C2×#10621885—42no—
99C2×#10621885C2314yescomplemented
100C2×#10621873—24no—
101C2×#10621873C2314yes—
102C2×#10621883—42no—
103C2×#10621883C2314yes—
104C2×#10621872—42no—
105C2×#10621872C2314yescomplemented
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
108C2×C8×D43—42no—
109C2×C8×D43C2314yes—
110#13063316—28no—
111#13063307—28no—
112#13063305—22no—
113#13063305—22no—
114#13063305C2314yes—
115#13063305C2314yescomplemented
116#13063301—22no—
117#13063301—28no—
118#13063301—28no—
119#13063301C2314yes—
120#13063298—28no—
121#13063296—22no—
122#13063296C2314yes—
123#13063295—28no—
124C4×Dic86—22no—
125C4×Dic86C2314yescomplemented
126C4×D172—22no—
127C4×D172D414yes—
128C4×D172C2314yes—
129C4×D172C2314yes—
130#13063287—28no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43D411yescharacteristic
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C4⋊C4×D43—22no—
141C4⋊C4×D43—22no—
142C4⋊C4×D43C2314yes—
143C4⋊C4×D43C2314yescomplemented
144C2×C22⋊Dic43—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×(C2×D43)⋊C4D411yescharacteristic
151C22⋊C4×D43—28no—
152C2×C4×Dic43—21no—
153#13063259C2314yescomplemented
154#13063258C2314yescomplemented
155#13063258C2314yescomplemented
156C4⋊(C43⋊C8)C2314yescomplemented
157#13063250C2314yescomplemented
158#13063249C2314yescomplemented
159#13063247C2314yes—
160#13063246C2314yes—
161#13063245C2314yes—
162#13063245C2314yes—
163(C2×D43)⋊C8C2314yes—
164(C2×D43)⋊C8C2314yescomplemented
165C22×Q8×C43—21no—
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C4⋊Q8×C43—22no—
171C4⋊Q8×C43C2314yescomplemented
172#124×C43—22no—
173#124×C43C2314yes—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C42×C43C2311yescharacteristic
180#103×C43C2314yescomplemented
181#103×C43C2314yescomplemented
182#102×C43C2314yes—
183#102×C43C2314yes—
184#97×C43C2314yescomplemented
185C24×C43—21no—
186C23×D43—21no—
187C23×D43—24no—
188C23×D43—44no—
189C23×D43—44no—
190C23×D43—82no—
191C23×D43C2×D411yescharacteristic
192C23×D43C2×D411yescharacteristic
193C2×Q8×C43—21no—
194C2×Q8×C43—24no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43—82no—
198C2×Q8×C43C2412yes—
199C2×D4×C43—21no—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43C2412yes—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2411yescharacteristic
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—44no—
212C2×C22⋊D43—82no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218#10621902—28no—
219#10621902—44no—
220#10621902—48no—
221D4×D43—28no—
222D4×D43—44no—
223D4×D43—48no—
224C2×D172—21no—
225C2×D172—22no—
226C2×D172—24no—
227C2×D172—24no—
228C2×D172—44no—
229C2×D172C2×D414yes—
230C2×D172#4114yes—
231C2×D172C2412yes—
232C2×C4×D43—22no—
233C2×C4×D43—22no—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—44no—
241C2×C4×D43—82no—
242C2×C4×D43—82no—
243C2×C4×D43—82no—
244C2×C4×D43C2×D412yes—
245C2×C4×D43C2×D412yes—
246C2×C4×D43C2412yes—
247C2×C4×D43C2412yes—
248C2×Dic86—22no—
249C2×Dic86—22no—
250C2×Dic86—21no—
251C2×Dic86C2412yes—
252C2×C8×C43—22no—
253C2×C8×C43—22no—
254C2×C8×C43C2412yes—
255C2×C8×C43C2412yes—
256C4⋊C4×C43—24no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43C2412yes—
260C4⋊C4×C43C2412yes—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—24no—
263C42×C43C2×D412yes—
264C42×C43C2412yes—
265C22⋊Dic43—24no—
266#10621885—44no—
267#10621883—44no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4C2×D414yes—
273(C2×D43)⋊C4C2×D414yes—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—24no—
277C4⋊Dic43—24no—
278C4⋊Dic43C2×D414yes—
279C4⋊Dic43C2412yes—
280C4⋊Dic43C2412yes—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285C4×Dic43—24no—
286C2×C43⋊C8—22no—
287C2×C43⋊C8—22no—
288C2×C43⋊C8C2412yes—
289C2×C43⋊C8C2412yes—
290#10621873—28no—
291#10621872—44no—
292C8×D43—44no—
293C23×C43—22no—
294C23×C43—42no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43C22×D411yescharacteristic
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—24no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—48no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—48no—
309C22×D43—84no—
310C22×D43—816no—
311C22×D43#13714yes—
312C22×D43C22×D412yes—
313C22×D43C22×D412yes—
314Q8×C43—22no—
315Q8×C43—22no—
316Q8×C43—42no—
317Q8×C43—84no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—42no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—42no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43C22×D412yes—
330C2×C4×C43C22×D412yes—
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4112yes—
333C2×C4×C43H(5,𝔽2)12yes—
334C2×C4×C43C2511yescharacteristic
335C22⋊D43—48no—
336C22⋊D43—84no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43C22×D412yes—
346C2×Dic43C22×D412yes—
347D172—28no—
348D172—24no—
349D172—22no—
350D172—48no—
351D172C2×#4114yes—
352C4×D43—24no—
353C4×D43—24no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—48no—
359C4×D43—84no—
360C4×D43—84no—
361C4×D43—84no—
362Dic86—22no—
363Dic86—22no—
364Dic86—42no—
365C8×C43—22no—
366C8×C43—22no—
367C43⋊C8—22no—
368C43⋊C8—22no—
369C2×#3314—431nomaximal, Sylow
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—84no—
374C22×C43#54612yes—
375C22×C43C2×#13712yes—
376C22×C43#57612yes—
377C22×C43C23×D411yescharacteristic
378C2×D43—22no—
379C2×D43—28no—
380C2×D43—22no—
381C2×D43—24no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—44no—
386C2×D43—48no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—816no—
390C2×D43C2×#13714yes—
391C4×C43—22no—
392C4×C43—22no—
393C4×C43—42no—
394C4×C43—42no—
395C4×C43—42no—
396C4×C43#54612yes—
397C4×C43C22×#4111yescharacteristic
398C4×C43C2×H(5,𝔽2)11yescharacteristic
399Dic43—22no—
400Dic43—22no—
401Dic43—42no—
402Dic43—42no—
403Dic43—42no—
404C2×#554—431no—
405C2×#546—431no—
406#3314—4316no—
407C2×#489D4311yescharacteristic, complemented
408C2×#484—431no—
409C2×#480—431no—
410C2×#474—431no—
411C2×#468—431no—
412C2×#467—431no—
413C2×#464—431no—
414C2×#452—431no—
415C2×#450—431no—
416C2×#440—431no—
417C2×#435—431no—
418C2×#417—431no—
419C22×#102—431no—
420C2×C43—82no—
421C2×C43#331414yescomplemented
422C2×C43C2×#54611yescharacteristic
423C2×C43C22×#13711yescharacteristic
424C2×C43C2×#57611yescharacteristic
425D43—24no—
426D43—42no—
427D43—44no—
428C22×#41—431no—
429C23×D4—431no—
430C22×Q16—431no—
431C22×SD16—431no—
432C22×SD16—431no—
433C22×M16—431no—
434C23×C8—431no—
435#554—438no—
436#554—864no—
437#546—438no—
438#546—864no—
439C2×C4⋊Q8C2×D4311yescharacteristic, complemented
440C2×#125—861no—
441C2×#124C2×D4311yescharacteristic
442C2×#123—861no—
443C2×C22⋊Q8—431no—
444C2×C22⋊Q8—431no—
445C2×C22⋊Q8—431no—
446C2×C22⋊Q8—861no—
447C2×C22⋊Q8—861no—
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#489C2×D4318yescomplemented
459#484—438no—
460#480—438no—
461#474—438no—
462#468—438no—
463#467—438no—
464#464—438no—
465#452—438no—
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×#103C2×D4311yescharacteristic, complemented
477C2×#103C2×D4311yescharacteristic, complemented
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—438no—
483C2×#102C2×D4311yescharacteristic
484C2×#102C2×D4311yescharacteristic
485C2×C22⋊C8—431no—
486C2×C22⋊C8—431no—
487C2×#97C2×D4311yescharacteristic, complemented
488C43C2×#331411yescharacteristic, complemented, Sylow
489C25—861no—
490C2×#41—434no—
491C2×#41—862no—
492C2×#41—864no—
493C2×#41—1722no—
494C22×Q8—21no—
495C22×Q8—431no—
496C22×Q8C22×D4311yescharacteristic
497C22×D4—434no—
498C22×D4—431no—
499C22×D4—431no—
500C22×D4—861no—
501C22×D4—862no—
502C22×D4—861no—
503C22×D4—864no—
504C22×D4—861no—
505C22×D4—1722no—
506C22×D4C22×D4311yescharacteristic
507C23×C4—431no—
508C23×C4—431no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4—861no—
512C23×C4—861no—
513C2×Q16—434no—
514C2×Q16—1722no—
515C2×SD16—434no—
516C2×SD16—434no—
517C2×SD16—864no—
518C2×SD16—1722no—
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—22no—
528C4⋊Q8C22×D4314yescomplemented
529#125—868no—
530#124—22no—
531#124C22×D4314yes—
532#123—868no—
533C22⋊Q8—434no—
534C22⋊Q8—434no—
535C22⋊Q8—434no—
536C22⋊Q8—868no—
537C22⋊Q8—868no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540C22⋊Q8—862no—
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—868no—
551C4×D4—862no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—434no—
557C2×C4⋊C4—434no—
558C2×C4⋊C4—862no—
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⋊C4C22×D4311yescharacteristic
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—868no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C42—861no—
579C2×C42C22×D4311yescharacteristic
580#107—434no—
581#107—434no—
582#107—434no—
583C4⋊C8—434no—
584#103—434no—
585#103—434no—
586#103C22×D4314yescomplemented
587#103C22×D4314yescomplemented
588#102—434no—
589#102—434no—
590#102—434no—
591#102—434no—
592#102C22×D4314yes—
593#102C22×D4314yes—
594C22⋊C8—434no—
595C22⋊C8—434no—
596#97C22×D4314yescomplemented
597C24—21no—
598C24—431no—
599C24—431no—
600C24—864no—
601C24—861no—
602C24—3442no—
603C24—1724no—
604C24—1724no—
605#41—868no—
606#41—1724no—
607#41—1728no—
608C2×Q8—21no—
609C2×Q8—24no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—82no—
613C2×Q8—432no—
614C2×Q8—861no—
615C2×Q8—862no—
616C2×Q8—862no—
617C2×Q8C23×D4312yes—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—434no—
622C2×D4—434no—
623C2×D4—432no—
624C2×D4—864no—
625C2×D4—864no—
626C2×D4—864no—
627C2×D4—868no—
628C2×D4—864no—
629C2×D4—861no—
630C2×D4—862no—
631C2×D4—3442no—
632C2×D4—1724no—
633C2×D4—1724no—
634C2×D4—1728no—
635C2×D4—1724no—
636C2×D4C23×D4312yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—432no—
643C22×C4—432no—
644C22×C4—432no—
645C22×C4—432no—
646C22×C4—864no—
647C22×C4—864no—
648C22×C4—864no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—864no—
657C22×C4—3442no—
658C22×C4—3442no—
659C22×C4—3442no—
660C22×C4—1724no—
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663C22×C4C23×D4311yescharacteristic
664Q16—1724no—
665SD16—868no—
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—21no—
680C4⋊C4—434no—
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—861no—
690C4⋊C4—864no—
691C4⋊C4C23×D4312yes—
692C4⋊C4C23×D4312yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—434no—
696C22⋊C4—434no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C42—864no—
703C42D4×D4312yes—
704C42C23×D4312yes—
705C23—22no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—434no—
710C23—432no—
711C23—432no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23—864no—
719C23—3444no—
720C23—34416no—
721C23—1728no—
722C23—1728no—
723C23—1722no—
724C23—1722no—
725C23C2×D4×D4311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—84no—
730Q8—862no—
731Q8—862no—
732Q8—1722no—
733D4—22no—
734D4—22no—
735D4—42no—
736D4—434no—
737D4—868no—
738D4—862no—
739D4—864no—
740D4—3444no—
741D4—1728no—
742D4—1728no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—432no—
752C2×C4—432no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—864no—
760C2×C4—864no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—3444no—
765C2×C4—3444no—
766C2×C4—3444no—
767C2×C4—1728no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4C2×D4×D4312yes—
772C2×C4C2×D4×D4312yes—
773C2×C4C2×D4×D4311yescharacteristic
774C2×C4#41×D4312yes—
775C2×C4#1306337112yes—
776C2×C4C24×D4311yescharacteristic
777C8—22no—
778C8—22no—
779C8—862no—
780C8—862no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—84no—
785C22—434no—
786C22—862no—
787C22—862no—
788C22—868no—
789C22—862no—
790C22—864no—
791C22—862no—
792C22—862no—
793C22—34416no—
794C22—1722no—
795C22—1722no—
796C22—1724no—
797C22—1728no—
798C22#1458354212yes—
799C22#137×D4312yes—
800C22#1458370312yes—
801C22C22×D4×D4311yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—862no—
808C4—862no—
809C4—1722no—
810C4—1722no—
811C4—1722no—
812C4#1458354212yes—
813C4C2×#41×D4311yescharacteristic
814C4C2×#1306337111yescharacteristic
815C2—82no—
816C2—864no—
817C2—1722no—
818C2—1724no—
819C2#1914667514yesdirect product factor
820C2C2×#1458354211yescharacteristic
821C2C2×#137×D4311yescharacteristic
822C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#489C2
socleC23×C43C22×D4
prime radicalC2×#14583542C2
hypercenterC2×#489D43
hypocenterC43C2×#3314
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#14583610C2semidirect
3. #19146675C2direct (N × H)
4. C2×#14583233C2semidirect
5. C2×#14583211C2semidirect
6. C2×#14583176C2semidirect
7. C2×#14583144C2semidirect
8. C2×#14583139C2semidirect
9. C2×#14583118C2semidirect
10. C2×#14583064C2semidirect
11. C2×#14583051C2semidirect
12. C2×#14583001C2semidirect
13. C2×#14582972C2semidirect
14. C2×#14582899C2semidirect
15. C2×#102×D43C2semidirect
16. C2×C43×#489C2semidirect
19. C22×#10621885C22semidirect
22. C22×#10621872C22semidirect
25. #14583610C22semidirect
31. C2×#13063305C22semidirect
38. C2×C4×Dic86C22semidirect
43. C2×C4⋊C4×D43C22semidirect
45. #14583233C22semidirect
46. #14583211C22semidirect
47. #14583176C22semidirect
48. #14583144C22semidirect
49. #14583139C22semidirect
50. #14583118C22semidirect
51. #14583064C22semidirect
52. #14583051C22semidirect
53. #14583001C22semidirect
54. #14582972C22semidirect
55. C2×#13063259C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063258C22semidirect
58. C2×C4⋊(C43⋊C8)C22semidirect
59. #14582899C22semidirect
60. C2×#13063250C22semidirect
61. C2×#13063249C22semidirect
66. #102×D43C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
69. C2×C4⋊Q8×C43C22semidirect
71. C43×#489C22semidirect
72. C2×#103×C43C22semidirect
73. C2×#103×C43C22semidirect
76. C2×#97×C43C22semidirect
99. C2×#10621885C23semidirect
105. C2×#10621872C23semidirect
115. #13063305C23semidirect
125. C4×Dic86C23semidirect
143. C4⋊C4×D43C23semidirect
153. #13063259C23semidirect
154. #13063258C23semidirect
155. #13063258C23semidirect
156. C4⋊(C43⋊C8)C23semidirect
157. #13063250C23semidirect
158. #13063249C23semidirect
164. (C2×D43)⋊C8C23semidirect
171. C4⋊Q8×C43C23semidirect
180. #103×C43C23semidirect
181. #103×C43C23semidirect
184. #97×C43C23semidirect
407. C2×#489D43semidirect
421. C2×C43#3314semidirect
439. C2×C4⋊Q8C2×D43semidirect
458. #489C2×D43semidirect
476. C2×#103C2×D43semidirect
477. C2×#103C2×D43semidirect
487. C2×#97C2×D43semidirect
488. C43C2×#3314semidirect
528. C4⋊Q8C22×D43semidirect
586. #103C22×D43semidirect
587. #103C22×D43semidirect
596. #97C22×D43semidirect
819. C2#19146675direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836102
C2×#145835422
#191466752
C2×#145832332
C2×#145832112
C2×#145831762
C2×#145831442
C2×#145831392
C2×#145831182
C2×#145830642
C2×#145830512
C2×#145830012
C2×#145829722
C2×#145828992
C2×#102×D432
C2×C43×#4892
C2×#331443