Finite Group Databasebeta

← C2×#19146679 #25973126

Subgroups — C2×#19146679 #25973126

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×#14583604C211yesmaximal, characteristic, complemented
2C2×#14583546C211yesmaximal, characteristic
3#19146679C2116yesmaximal, direct product factor
4C2×#14583257C211yesmaximal, characteristic, complemented
5C2×#14583236C211yesmaximal, characteristic, complemented
6C2×#14583178C211yesmaximal, characteristic, complemented
7C2×#14583143C211yesmaximal, characteristic, complemented
8C2×#14583141C211yesmaximal, characteristic, complemented
9C2×#14583120C211yesmaximal, characteristic, complemented
10C2×#14583063C211yesmaximal, characteristic, complemented
11C2×#14583051C211yesmaximal, characteristic, complemented
12C2×#14582998C211yesmaximal, characteristic, complemented
13C2×#14582973C211yesmaximal, characteristic, complemented
14C2×#14582898C211yesmaximal, characteristic, complemented
15C2×#102×D43C211yesmaximal, characteristic, complemented
16C2×C43×#480C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×Dic172C2211yescharacteristic, complemented
20C22×#10621873C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621877C2211yescharacteristic, complemented
23C22×C8×D43C2211yescharacteristic
24#14583604—24no—
25#14583604C2218yescomplemented
26#14583546—24no—
27#14583546C2218yes—
28C2×#13063324C2211yescharacteristic, complemented
29C2×#13063315—21no—
30C2×#13063312C2211yescharacteristic
31C2×#13063307—21no—
32C2×#13063305C2211yescharacteristic
33C2×#13063305C2211yescharacteristic
34C2×#13063304—21no—
35C2×#13063304C2211yescharacteristic, complemented
36C2×#13063303—21no—
37C2×#13063296—21no—
38C2×#13063293—21no—
39C2×#13063290C2211yescharacteristic, complemented
40C2×#13063287C2211yescharacteristic
41C2×C4×C22⋊D43—21no—
42C2×C4×C22⋊D43C2211yescharacteristic
43C2×C4⋊C4×D43C2211yescharacteristic
44C2×C22⋊C4×D43—21no—
45#14583257C2218yescomplemented
46#14583236C2218yescomplemented
47#14583178C2218yescomplemented
48#14583143C2218yescomplemented
49#14583141C2218yescomplemented
50#14583120C2218yescomplemented
51#14583063C2218yescomplemented
52#14583051C2218yescomplemented
53#14582998C2218yescomplemented
54#14582973C2218yescomplemented
55C2×#13063258C2211yescharacteristic, complemented
56C2×Dic43⋊C8C2211yescharacteristic, complemented
57#14582898C2218yescomplemented
58C2×#13063250C2211yescharacteristic, complemented
59C2×#13063248C2211yescharacteristic, complemented
60C2×#13063248C2211yescharacteristic, complemented
61C2×#13063248C2211yescharacteristic, complemented
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66#102×D43C2218yescomplemented
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic, complemented
69C2×#121×C43C2211yescharacteristic
70C22×C4⋊C4×C43C2211yescharacteristic, complemented
71C43×#480C2218yescomplemented
72C2×#107×C43C2211yescharacteristic, complemented
73C2×#107×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621898—22no—
79C2×#10621898—24no—
80C2×#10621898—42no—
81C2×#10621898C2314yes—
82C22×Dic86—21no—
83C22×Dic86C2311yescharacteristic
84C22×Dic86C2311yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43D411yescharacteristic
89C2×D4×D43—24no—
90C2×D4×D43—22no—
91C2×D4×D43—42no—
92C2×D4×D43C2314yes—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43C2311yescharacteristic
97C2×Dic172—42no—
98C2×Dic172C2314yescomplemented
99C2×#10621873—24no—
100C2×#10621873C2314yes—
101C2×#10621883—42no—
102C2×#10621883C2314yes—
103C2×#10621877—42no—
104C2×#10621877C2314yescomplemented
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107C2×C8×D43—42no—
108C2×C8×D43C2314yes—
109#13063324—22no—
110#13063324C2314yescomplemented
111#13063315—28no—
112#13063312—22no—
113#13063312C2314yes—
114#13063307—28no—
115#13063305—22no—
116#13063305—22no—
117#13063305C2314yes—
118#13063305C2314yes—
119#13063304—22no—
120#13063304—28no—
121#13063304C2314yescomplemented
122#13063303—28no—
123#13063296—28no—
124#13063293—28no—
125#13063290—22no—
126#13063290C2314yescomplemented
127#13063287—22no—
128#13063287C2314yes—
129C4×C22⋊D43—28no—
130C4×C22⋊D43D414yes—
131C4×C22⋊D43C2314yes—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43C2311yescharacteristic
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4D411yescharacteristic
140C4⋊C4×D43—22no—
141C4⋊C4×D43C2314yes—
142C2×C22⋊Dic43—21no—
143C2×C22⋊Dic43—21no—
144C2×C22⋊Dic43—21no—
145C2×C22⋊Dic43D411yescharacteristic
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4D411yescharacteristic
150C22⋊C4×D43—28no—
151C2×C4×Dic43—21no—
152C2×C4×Dic43C2311yescharacteristic
153#13063258C2314yescomplemented
154Dic43⋊C8C2314yescomplemented
155#13063250C2314yescomplemented
156#13063248C2314yescomplemented
157#13063248C2314yescomplemented
158#13063248C2314yescomplemented
159#13063247C2314yes—
160#13063246C2314yes—
161#13063245C2314yes—
162#13063245C2314yes—
163(C2×D43)⋊C8C2314yes—
164#13063235C2314yescomplemented
165C22×D4×C43—21no—
166C22×D4×C43C2311yescharacteristic
167C23×C4×C43—21no—
168C23×C4×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171#121×C43—22no—
172#121×C43C2314yes—
173C2×C4⋊C4×C43—22no—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2314yescomplemented
179C2×C22⋊C4×C43—21no—
180#107×C43C2314yescomplemented
181#107×C43C2314yescomplemented
182#102×C43C2314yes—
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
193C2×D4×C43—21no—
194C2×D4×C43—24no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—82no—
198C2×D4×C43C2412yes—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—24no—
205C22×C4×C43—82no—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D412yes—
208C22×C4×C43C2412yes—
209C22×C4×C43C2411yescharacteristic
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—24no—
213C2×C22⋊D43—44no—
214C2×C22⋊D43—44no—
215C2×C22⋊D43C2×D414yes—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222D4×D43—28no—
223D4×D43—44no—
224D4×D43—48no—
225#10621898—28no—
226#10621898—44no—
227#10621898—48no—
228C2×D172—21no—
229C2×D172—22no—
230C2×D172#4114yes—
231C2×D172C2412yes—
232C2×C4×D43—22no—
233C2×C4×D43—22no—
234C2×C4×D43—24no—
235C2×C4×D43—24no—
236C2×C4×D43—24no—
237C2×C4×D43—44no—
238C2×C4×D43—82no—
239C2×C4×D43—82no—
240C2×C4×D43C2×D412yes—
241C2×C4×D43C2412yes—
242C2×Dic86—22no—
243C2×Dic86—22no—
244C2×Dic86—22no—
245C2×Dic86—22no—
246C2×Dic86—21no—
247C2×Dic86—21no—
248C2×Dic86—24no—
249C2×Dic86—82no—
250C2×Dic86C2412yes—
251C2×Dic86C2412yes—
252C2×C8×C43—22no—
253C2×C8×C43—22no—
254C2×C8×C43C2412yes—
255C2×C8×C43C2412yes—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—24no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43C2412yes—
261C4⋊C4×C43C2412yes—
262C4⋊C4×C43C2412yes—
263C22⋊C4×C43—24no—
264C22⋊Dic43—24no—
265C22⋊Dic43—24no—
266C22⋊Dic43—24no—
267C22⋊Dic43C2×D414yes—
268#10621883—44no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4C2×D414yes—
273C4⋊Dic43—21no—
274C4⋊Dic43—24no—
275C4⋊Dic43—24no—
276C4⋊Dic43C2412yes—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4C2×D414yes—
282C4×Dic43—24no—
283C4×Dic43C2×D412yes—
284C4×Dic43C2412yes—
285#10621877—44no—
286C2×C43⋊C8—22no—
287C2×C43⋊C8—22no—
288C2×C43⋊C8C2412yes—
289C2×C43⋊C8C2412yes—
290Dic172—44no—
291#10621873—28no—
292C8×D43—44no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43C22×D412yes—
301C23×C43C22×D411yescharacteristic
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—24no—
305C22×D43—22no—
306C22×D43—48no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—48no—
310C22×D43—84no—
311C22×D43—816no—
312C22×D43#13714yes—
313C22×D43C22×D412yes—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—42no—
317D4×C43—84no—
318C2×C4×C43—22no—
319C2×C4×C43—24no—
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×D411yescharacteristic
331C2×C4×C43C2×#4112yes—
332C2×C4×C43H(5,𝔽2)12yes—
333C2×C4×C43C2511yescharacteristic
334C22⋊D43—28no—
335C22⋊D43—48no—
336C22⋊D43—48no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43C22×D412yes—
347C2×Dic43C22×D412yes—
348C2×Dic43C22×D412yes—
349D172—24no—
350D172—22no—
351D172C2×#4114yes—
352C4×D43—24no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—48no—
356C4×D43—84no—
357C4×D43—84no—
358Dic86—22no—
359Dic86—22no—
360Dic86—22no—
361Dic86—22no—
362Dic86—42no—
363Dic86—42no—
364Dic86—84no—
365C8×C43—22no—
366C8×C43—22no—
367C43⋊C8—22no—
368C43⋊C8—22no—
369C2×#3314—431nomaximal, Sylow
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—44no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—84no—
378C22×C43#54612yes—
379C22×C43C2×#13712yes—
380C22×C43#57612yes—
381C22×C43C23×D411yescharacteristic
382C2×D43—22no—
383C2×D43—28no—
384C2×D43—22no—
385C2×D43—24no—
386C2×D43—48no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—816no—
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×#480D4311yescharacteristic, complemented
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—42no—
421C2×C43—82no—
422C2×C43#331414yescomplemented
423C2×C43C2×#54611yescharacteristic
424C2×C43C22×#13711yescharacteristic
425C2×C43C2×#57611yescharacteristic
426D43—24no—
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⋊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—861no—
449C2×#121C2×D4311yescharacteristic
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⋊C4C2×D4311yescharacteristic, complemented
457C22×C22⋊C4—861no—
458#489—438no—
459#484—438no—
460#480C2×D4318yescomplemented
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×#107C2×D4311yescharacteristic, complemented
471C2×#107C2×D4311yescharacteristic, complemented
472C2×C4⋊C8—431no—
473#417—438no—
474C2×#103—431no—
475C2×#103—431no—
476C2×#103—431no—
477C2×#103—431no—
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⋊C8C2×D4311yescharacteristic, complemented
487C2×#97—431no—
488C43C2×#331411yescharacteristic, complemented, Sylow
489C25—861no—
490C2×#41—434no—
491C2×#41—864no—
492C2×#41—862no—
493C2×#41—1722no—
494C22×Q8—431no—
495C22×Q8—431no—
496C22×Q8—861no—
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—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—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—22no—
542#121—868no—
543#121C22×D4314yes—
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—22no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—434no—
557C2×C4⋊C4—862no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4—861no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4C22×D4311yescharacteristic
565C2×C4⋊C4C22×D4311yescharacteristic
566C2×C4⋊C4C22×D4311yescharacteristic
567C2×C4⋊C4C22×D4314yescomplemented
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#107C22×D4314yescomplemented
582#107C22×D4314yescomplemented
583C4⋊C8—434no—
584#103—434no—
585#103—434no—
586#103—434no—
587#103—434no—
588#102—434no—
589#102—434no—
590#102—434no—
591#102—434no—
592#102C22×D4314yes—
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—868no—
606#41—1724no—
607#41—1728no—
608C2×Q8—432no—
609C2×Q8—432no—
610C2×Q8—864no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×Q8—862no—
614C2×Q8—862no—
615C2×Q8—862no—
616C2×Q8—862no—
617C2×Q8—3442no—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—82no—
623C2×D4—434no—
624C2×D4—434no—
625C2×D4—432no—
626C2×D4—864no—
627C2×D4—868no—
628C2×D4—864no—
629C2×D4—864no—
630C2×D4—861no—
631C2×D4—862no—
632C2×D4—1724no—
633C2×D4—1728no—
634C2×D4—1724no—
635C2×D4—1724no—
636C2×D4C23×D4312yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—82no—
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—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—864no—
657C22×C4—3442no—
658C22×C4—3442no—
659C22×C4—1724no—
660C22×C4D4×D4312yes—
661C22×C4D4×D4311yescharacteristic
662C22×C4C23×D4312yes—
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—21no—
678C4⋊C4—21no—
679C4⋊C4—24no—
680C4⋊C4—21no—
681C4⋊C4—434no—
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⋊C4C23×D4312yes—
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—432no—
703C42—432no—
704C42—864no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—434no—
713C23—432no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—864no—
718C23—3444no—
719C23—34416no—
720C23—1728no—
721C23—1728no—
722C23—1722no—
723C23—1722no—
724C23C2×D4×D4312yes—
725C23C2×D4×D4311yescharacteristic
726Q8—862no—
727Q8—862no—
728Q8—862no—
729Q8—862no—
730Q8—3444no—
731Q8—1722no—
732Q8—1722no—
733D4—22no—
734D4—22no—
735D4—42no—
736D4—84no—
737D4—434no—
738D4—868no—
739D4—862no—
740D4—864no—
741D4—1728no—
742D4—1728no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—84no—
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—1728no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—1722no—
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—22no—
782C22—22no—
783C22—22no—
784C22—44no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22—434no—
790C22—862no—
791C22—862no—
792C22—868no—
793C22—864no—
794C22—34416no—
795C22—1722no—
796C22—1722no—
797C22—1728no—
798C22#1458354112yes—
799C22#137×D4312yes—
800C22#1458370012yes—
801C22C22×D4×D4311yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—862no—
807C4—862no—
808C4—862no—
809C4—1722no—
810C4—1722no—
811C4—1722no—
812C4#1458354112yes—
813C4C2×#41×D4311yescharacteristic
814C4C2×#1306337111yescharacteristic
815C2—42no—
816C2—82no—
817C2—864no—
818C2—1724no—
819C2#1914667914yesdirect product factor
820C2C2×#1458354111yescharacteristic
821C2C2×#137×D4311yescharacteristic
822C2C2×#1458370011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#480C2
socleC23×C43C22×D4
prime radicalC2×#14583546C2
hypercenterC2×#480D43
hypocenterC43C2×#3314
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#14583604C2semidirect
3. #19146679C2direct (N × H)
4. C2×#14583257C2semidirect
5. C2×#14583236C2semidirect
6. C2×#14583178C2semidirect
7. C2×#14583143C2semidirect
8. C2×#14583141C2semidirect
9. C2×#14583120C2semidirect
10. C2×#14583063C2semidirect
11. C2×#14583051C2semidirect
12. C2×#14582998C2semidirect
13. C2×#14582973C2semidirect
14. C2×#14582898C2semidirect
15. C2×#102×D43C2semidirect
16. C2×C43×#480C2semidirect
19. C22×Dic172C22semidirect
22. C22×#10621877C22semidirect
25. #14583604C22semidirect
28. C2×#13063324C22semidirect
35. C2×#13063304C22semidirect
39. C2×#13063290C22semidirect
45. #14583257C22semidirect
46. #14583236C22semidirect
47. #14583178C22semidirect
48. #14583143C22semidirect
49. #14583141C22semidirect
50. #14583120C22semidirect
51. #14583063C22semidirect
52. #14583051C22semidirect
53. #14582998C22semidirect
54. #14582973C22semidirect
55. C2×#13063258C22semidirect
56. C2×Dic43⋊C8C22semidirect
57. #14582898C22semidirect
58. C2×#13063250C22semidirect
59. C2×#13063248C22semidirect
60. C2×#13063248C22semidirect
61. C2×#13063248C22semidirect
66. #102×D43C22semidirect
68. C2×#13063235C22semidirect
70. C22×C4⋊C4×C43C22semidirect
71. C43×#480C22semidirect
72. C2×#107×C43C22semidirect
73. C2×#107×C43C22semidirect
76. C2×C22⋊C8×C43C22semidirect
98. C2×Dic172C23semidirect
104. C2×#10621877C23semidirect
110. #13063324C23semidirect
121. #13063304C23semidirect
126. #13063290C23semidirect
153. #13063258C23semidirect
154. Dic43⋊C8C23semidirect
155. #13063250C23semidirect
156. #13063248C23semidirect
157. #13063248C23semidirect
158. #13063248C23semidirect
164. #13063235C23semidirect
178. C2×C4⋊C4×C43C23semidirect
180. #107×C43C23semidirect
181. #107×C43C23semidirect
184. C22⋊C8×C43C23semidirect
409. C2×#480D43semidirect
422. C2×C43#3314semidirect
456. C22×C4⋊C4C2×D43semidirect
460. #480C2×D43semidirect
470. C2×#107C2×D43semidirect
471. C2×#107C2×D43semidirect
486. C2×C22⋊C8C2×D43semidirect
488. C43C2×#3314semidirect
567. C2×C4⋊C4C22×D43semidirect
581. #107C22×D43semidirect
582. #107C22×D43semidirect
595. C22⋊C8C22×D43semidirect
819. C2#19146679direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836042
C2×#145835462
#191466792
C2×#145832572
C2×#145832362
C2×#145831782
C2×#145831432
C2×#145831412
C2×#145831202
C2×#145830632
C2×#145830512
C2×#145829982
C2×#145829732
C2×#145828982
C2×#102×D432
C2×C43×#4802
C2×#331443