Finite Group Databasebeta

← C2×#19146681 #25973128

Subgroups — C2×#19146681 #25973128

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×#14583609C211yesmaximal, characteristic, complemented
2C2×#14583544C211yesmaximal, characteristic
3#19146681C2116yesmaximal, direct product factor
4C2×#14583259C211yesmaximal, characteristic, complemented
5C2×#14583236C211yesmaximal, characteristic, complemented
6C2×#14583214C211yesmaximal, characteristic, complemented
7C2×#14583179C211yesmaximal, characteristic, complemented
8C2×#14583148C211yesmaximal, characteristic, complemented
9C2×#14583139C211yesmaximal, characteristic, complemented
10C2×#14583121C211yesmaximal, characteristic, complemented
11C2×#14583058C211yesmaximal, characteristic, complemented
12C2×#14583048C211yesmaximal, characteristic, complemented
13C2×#14582972C211yesmaximal, characteristic, complemented
14C2×#14582897C211yesmaximal, characteristic, complemented
15C2×#102×D43C211yesmaximal, characteristic, complemented
16C2×C43×#440C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621885C2211yescharacteristic, complemented
20C22×#10621884C2211yescharacteristic
21C22×#10621872C2211yescharacteristic, complemented
22C22×C8×D43C2211yescharacteristic
23#14583609—24no—
24#14583609C2218yescomplemented
25#14583544—24no—
26#14583544C2218yes—
27C2×#13063325C2211yescharacteristic, complemented
28C2×#13063317—21no—
29C2×#13063313C2211yescharacteristic
30C2×#13063309—21no—
31C2×#13063305C2211yescharacteristic
32C2×#13063303—21no—
33C2×#13063303—21no—
34C2×#13063301C2211yescharacteristic
35C2×#13063301C2211yescharacteristic, complemented
36C2×#13063300C2211yescharacteristic
37C2×#13063299—21no—
38C2×#13063295—21no—
39C2×C4×D172—21no—
40C2×C4×D172C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic, complemented
43C22×(C2×D43)⋊C4—21no—
44#14583259C2218yescomplemented
45#14583236C2218yescomplemented
46#14583214C2218yescomplemented
47#14583179C2218yescomplemented
48#14583148C2218yescomplemented
49#14583139C2218yescomplemented
50#14583121C2218yescomplemented
51#14583058C2218yescomplemented
52#14583048C2218yescomplemented
53#14582972C2218yescomplemented
54C2×#13063258C2211yescharacteristic, complemented
55C2×#13063258C2211yescharacteristic, complemented
56C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
57#14582897C2218yescomplemented
58C2×#13063250C2211yescharacteristic, complemented
59C2×#13063250C2211yescharacteristic, complemented
60C2×#13063248C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66#102×D43C2218yescomplemented
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic, complemented
71C2×C4×D4×C43C2211yescharacteristic
72C43×#440C2218yescomplemented
73C2×#107×C43C2211yescharacteristic, complemented
74C2×#103×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621900—24no—
79C2×#10621900—22no—
80C2×#10621900—42no—
81C2×#10621900C2314yes—
82C22×Dic86—21no—
83C22×Dic86C2311yescharacteristic
84C22×D172—21no—
85C22×D172D411yescharacteristic
86C22×D172C2311yescharacteristic
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C2×D4×D43—24no—
90C2×D4×D43—22no—
91C2×D4×D43—42no—
92C2×D4×D43C2314yes—
93C23×Dic43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2311yescharacteristic
98C2×#10621885—42no—
99C2×#10621885C2314yescomplemented
100C2×#10621884—42no—
101C2×#10621884C2314yes—
102C2×#10621872—42no—
103C2×#10621872C2314yescomplemented
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106C2×C8×D43—42no—
107C2×C8×D43C2314yes—
108#13063325—22no—
109#13063325C2314yescomplemented
110#13063317—28no—
111#13063313—22no—
112#13063313C2314yes—
113#13063309—28no—
114#13063305—22no—
115#13063305C2314yes—
116#13063303—28no—
117#13063303—28no—
118#13063301—22no—
119#13063301—22no—
120#13063301C2314yes—
121#13063301C2314yescomplemented
122#13063300—22no—
123#13063300C2314yes—
124#13063299—28no—
125#13063295—28no—
126C4×D172—28no—
127C4×D172D414yes—
128C4×D172C2314yes—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43D411yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C4⋊C4×D43—22no—
139C4⋊C4×D43—22no—
140C4⋊C4×D43C2314yes—
141C4⋊C4×D43C2314yescomplemented
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—28no—
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×(C2×D43)⋊C4D411yescharacteristic
151#13063258C2314yescomplemented
152#13063258C2314yescomplemented
153C4⋊(C43⋊C8)C2314yescomplemented
154#13063250C2314yescomplemented
155#13063250C2314yescomplemented
156#13063248C2314yescomplemented
157#13063247C2314yes—
158#13063247C2314yes—
159#13063246C2314yes—
160#13063246C2314yes—
161#13063245C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yescomplemented
164C22×Q8×C43C2311yescharacteristic
165C22×D4×C43C2311yescharacteristic
166C23×C4×C43—21no—
167C2×SD16×C43—24no—
168C2×SD16×C43C2314yes—
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C4×Q8×C43—22no—
172C4×Q8×C43C2314yescomplemented
173C4×D4×C43—22no—
174C4×D4×C43C2314yes—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C42×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#107×C43C2314yescomplemented
182#103×C43C2314yescomplemented
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—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43C2412yes—
197C2×D4×C43—21no—
198C2×D4×C43—22no—
199C2×D4×C43#4114yes—
200C2×D4×C43C2412yes—
201C22×C4×C43—24no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—82no—
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—44no—
213C22×Dic43—24no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—44no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220#10621900—28no—
221#10621900—44no—
222#10621900—48no—
223D4×D43—28no—
224D4×D43—44no—
225D4×D43—48no—
226C2×D172—21no—
227C2×D172—24no—
228C2×D172—24no—
229C2×D172—22no—
230C2×D172—22no—
231C2×D172—82no—
232C2×D172C2×D414yes—
233C2×D172C2412yes—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—82no—
241C2×C4×D43—82no—
242C2×C4×D43C2×D412yes—
243C2×C4×D43C2×D412yes—
244C2×C4×D43C2412yes—
245C2×C4×D43C2412yes—
246C2×Dic86—22no—
247C2×Dic86—22no—
248C2×Dic86—21no—
249C2×Dic86—24no—
250C2×Dic86—82no—
251C2×Dic86C2412yes—
252SD16×C43—28no—
253C2×C8×C43—22no—
254C2×C8×C43—22no—
255C2×C8×C43C2412yes—
256C2×C8×C43C2412yes—
257C4⋊C4×C43—24no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43C2412yes—
261C4⋊C4×C43C2412yes—
262C22⋊C4×C43—24no—
263C42×C43—24no—
264C42×C43C2×D412yes—
265C42×C43C2412yes—
266#10621885—44no—
267#10621884—44no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4C2×D414yes—
275(C2×D43)⋊C4C2×D414yes—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—24no—
279C4⋊Dic43—24no—
280C4⋊Dic43C2×D414yes—
281C4⋊Dic43C2412yes—
282C4⋊Dic43C2412yes—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286Dic43⋊C4—24no—
287C2×C43⋊C8—22no—
288C2×C43⋊C8—22no—
289C2×C43⋊C8C2412yes—
290C2×C43⋊C8C2412yes—
291#10621872—44no—
292C8×D43—44no—
293C23×C43—24no—
294C23×C43—22no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43C22×D411yescharacteristic
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—48no—
305C22×D43—42no—
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—
317D4×C43—24no—
318D4×C43—22no—
319D4×C43C2×#4114yes—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—42no—
326C2×C4×C43—42no—
327C2×C4×C43—42no—
328C2×C4×C43—84no—
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—48no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—48no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43C22×D412yes—
347C2×Dic43C22×D412yes—
348D172—28no—
349D172—22no—
350D172—22no—
351D172—42no—
352D172—84no—
353C4×D43—24no—
354C4×D43—24no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—84no—
360C4×D43—84no—
361Dic86—22no—
362Dic86—22no—
363Dic86—42no—
364Dic86—84no—
365C8×C43—22no—
366C8×C43—22no—
367C43⋊C8—22no—
368C43⋊C8—22no—
369C2×#3314—431nomaximal, Sylow
370C22×C43—24no—
371C22×C43—48no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43#54612yes—
375C22×C43C2×#13712yes—
376C22×C43#57612yes—
377C22×C43C23×D411yescharacteristic
378C2×D43—22no—
379C2×D43—28no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—44no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—816no—
389C2×D43—84no—
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×#489—431no—
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×#440D4311yescharacteristic, complemented
417C2×#435—431no—
418C2×#417—431no—
419C22×#102—431no—
420C2×C43—44no—
421C2×C43#331414yescomplemented
422C2×C43C2×#54611yescharacteristic
423C2×C43C22×#13711yescharacteristic
424C2×C43C2×#57611yescharacteristic
425D43—24no—
426D43—42no—
427D43—82no—
428C22×#41—431no—
429C23×D4—431no—
430C22×Q16—431no—
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—431no—
446C2×C22⋊Q8—861no—
447C2×C22⋊Q8—861no—
448C2×#121—431no—
449C2×#121—861no—
450C2×#120—861no—
451C2×C4×Q8C2×D4311yescharacteristic, complemented
452C2×C4×D4—431no—
453C2×C4×D4—861no—
454C2×C4×D4C2×D4311yescharacteristic
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#452—438no—
466#450—438no—
467#440C2×D4318yescomplemented
468#435—438no—
469C2×#107—431no—
470C2×#107—431no—
471C2×#107C2×D4311yescharacteristic, complemented
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⋊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—431no—
495C22×Q8—861no—
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—21no—
508C23×C4—431no—
509C23×C4—431no—
510C23×C4—861no—
511C23×C4—861no—
512C23×C4—861no—
513C2×Q16—434no—
514C2×Q16—1722no—
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—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—22no—
546C4×Q8C22×D4314yescomplemented
547C4×D4—22no—
548C4×D4—434no—
549C4×D4—434no—
550C4×D4—868no—
551C4×D4C22×D4314yes—
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—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—21no—
579C2×C42C22×D4311yescharacteristic
580#107—434no—
581#107—434no—
582#107C22×D4314yescomplemented
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⋊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—22no—
610C2×Q8—22no—
611C2×Q8—432no—
612C2×Q8—864no—
613C2×Q8—861no—
614C2×Q8—862no—
615C2×Q8—862no—
616C2×Q8—3442no—
617C2×Q8C23×D4312yes—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—434no—
621C2×D4—432no—
622C2×D4—864no—
623C2×D4—864no—
624C2×D4—864no—
625C2×D4—868no—
626C2×D4—864no—
627C2×D4—861no—
628C2×D4—862no—
629C2×D4—862no—
630C2×D4—3442no—
631C2×D4—1724no—
632C2×D4—1728no—
633C2×D4—1724no—
634C2×D4—1724no—
635C2×D4#1062189814yes—
636C2×D4C23×D4312yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—82no—
642C22×C4—431no—
643C22×C4—431no—
644C22×C4—432no—
645C22×C4—432no—
646C22×C4—432no—
647C22×C4—432no—
648C22×C4—864no—
649C22×C4—864no—
650C22×C4—864no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—3442no—
659C22×C4—3442no—
660C22×C4—1724no—
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663C22×C4C23×D4311yescharacteristic
664Q16—1724no—
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—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—434no—
695C22⋊C4—434no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C42—24no—
703C42D4×D4312yes—
704C42C23×D4312yes—
705C23—22no—
706C23—24no—
707C23—42no—
708C23—42no—
709C23—434no—
710C23—432no—
711C23—432no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23—34416no—
719C23—3444no—
720C23—1728no—
721C23—1728no—
722C23—1722no—
723C23—1722no—
724C23—1722no—
725C23C2×D4×D4311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—862no—
730Q8—862no—
731Q8—3444no—
732Q8—1722no—
733D4—22no—
734D4—24no—
735D4—868no—
736D4—862no—
737D4—862no—
738D4—3444no—
739D4—1728no—
740D4—1728no—
741D4—1722no—
742D4C2×#1062189814yes—
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—84no—
752C2×C4—432no—
753C2×C4—432no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—864no—
761C2×C4—864no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
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×C4C2×#1062189812yes—
775C2×C4#1306337112yes—
776C2×C4C24×D4311yescharacteristic
777C8—22no—
778C8—22no—
779C8—862no—
780C8—862no—
781C22—24no—
782C22—42no—
783C22—42no—
784C22—48no—
785C22—434no—
786C22—862no—
787C22—862no—
788C22—868no—
789C22—862no—
790C22—862no—
791C22—862no—
792C22—34416no—
793C22—3444no—
794C22—1722no—
795C22—1722no—
796C22—1722no—
797C22—1724no—
798C22#1458354512yes—
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#1458354512yes—
813C4C22×#1062189811yescharacteristic
814C4C2×#1306337111yescharacteristic
815C2—44no—
816C2—864no—
817C2—3442no—
818C2—1722no—
819C2#1914668114yesdirect product factor
820C2C2×#1458354511yescharacteristic
821C2C2×#137×D4311yescharacteristic
822C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC2×#14583544C2
hypercenterC2×#440D43
hypocenterC43C2×#3314
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#14583609C2semidirect
3. #19146681C2direct (N × H)
4. C2×#14583259C2semidirect
5. C2×#14583236C2semidirect
6. C2×#14583214C2semidirect
7. C2×#14583179C2semidirect
8. C2×#14583148C2semidirect
9. C2×#14583139C2semidirect
10. C2×#14583121C2semidirect
11. C2×#14583058C2semidirect
12. C2×#14583048C2semidirect
13. C2×#14582972C2semidirect
14. C2×#14582897C2semidirect
15. C2×#102×D43C2semidirect
16. C2×C43×#440C2semidirect
19. C22×#10621885C22semidirect
21. C22×#10621872C22semidirect
24. #14583609C22semidirect
27. C2×#13063325C22semidirect
35. C2×#13063301C22semidirect
42. C2×C4⋊C4×D43C22semidirect
44. #14583259C22semidirect
45. #14583236C22semidirect
46. #14583214C22semidirect
47. #14583179C22semidirect
48. #14583148C22semidirect
49. #14583139C22semidirect
50. #14583121C22semidirect
51. #14583058C22semidirect
52. #14583048C22semidirect
53. #14582972C22semidirect
54. C2×#13063258C22semidirect
55. C2×#13063258C22semidirect
56. C2×C4⋊(C43⋊C8)C22semidirect
57. #14582897C22semidirect
58. C2×#13063250C22semidirect
59. C2×#13063250C22semidirect
60. C2×#13063248C22semidirect
66. #102×D43C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
70. C2×C4×Q8×C43C22semidirect
72. C43×#440C22semidirect
73. C2×#107×C43C22semidirect
74. C2×#103×C43C22semidirect
76. C2×#97×C43C22semidirect
99. C2×#10621885C23semidirect
103. C2×#10621872C23semidirect
109. #13063325C23semidirect
121. #13063301C23semidirect
141. C4⋊C4×D43C23semidirect
151. #13063258C23semidirect
152. #13063258C23semidirect
153. C4⋊(C43⋊C8)C23semidirect
154. #13063250C23semidirect
155. #13063250C23semidirect
156. #13063248C23semidirect
163. (C2×D43)⋊C8C23semidirect
172. C4×Q8×C43C23semidirect
181. #107×C43C23semidirect
182. #103×C43C23semidirect
184. #97×C43C23semidirect
416. C2×#440D43semidirect
421. C2×C43#3314semidirect
451. C2×C4×Q8C2×D43semidirect
467. #440C2×D43semidirect
471. C2×#107C2×D43semidirect
477. C2×#103C2×D43semidirect
487. C2×#97C2×D43semidirect
488. C43C2×#3314semidirect
546. C4×Q8C22×D43semidirect
582. #107C22×D43semidirect
587. #103C22×D43semidirect
596. #97C22×D43semidirect
819. C2#19146681direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836092
C2×#145835442
#191466812
C2×#145832592
C2×#145832362
C2×#145832142
C2×#145831792
C2×#145831482
C2×#145831392
C2×#145831212
C2×#145830582
C2×#145830482
C2×#145829722
C2×#145828972
C2×#102×D432
C2×C43×#4402
C2×#331443