Finite Group Databasebeta

← C2×#19146632 #25973268

Subgroups — C2×#19146632 #25973268

Order 11008.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583617C211yesmaximal, characteristic, complemented
2C2×#14583543C211yesmaximal, characteristic
3#19146632C2116yesmaximal, direct product factor
4C2×#14583257C211yesmaximal, characteristic, complemented
5C2×#14583240C211yesmaximal, characteristic, complemented
6C2×#14583222C211yesmaximal, characteristic, complemented
7C2×#14583187C211yesmaximal, characteristic, complemented
8C2×#14583157C211yesmaximal, characteristic, complemented
9C2×#14583127C211yesmaximal, characteristic, complemented
10C2×#14583120C211yesmaximal, characteristic, complemented
11C2×#14583062C211yesmaximal, characteristic, complemented
12C2×#14583050C211yesmaximal, characteristic, complemented
13C2×#14582996C211yesmaximal, characteristic, complemented
14C2×#14582968C211yesmaximal, characteristic, complemented
15C2×#14582892C211yesmaximal, characteristic, complemented
16C2×C43×#418C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×Dic172C2211yescharacteristic, complemented
19C22×#10621883C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic, complemented
22#14583617—24no—
23#14583617C2218yescomplemented
24#14583543—24no—
25#14583543C2218yes—
26C2×#13063324C2211yescharacteristic, complemented
27C2×#13063319—21no—
28C2×#13063318—21no—
29C2×#13063312C2211yescharacteristic
30C2×#13063311—21no—
31C2×#13063306—21no—
32C2×#13063305C2211yescharacteristic, complemented
33C2×#13063304C2211yescharacteristic
34C2×#13063304C2211yescharacteristic
35C2×#13063297—21no—
36C2×#13063296C2211yescharacteristic
37C2×#13063294—21no—
38C2×C4×Dic86—21no—
39C2×#13063290C2211yescharacteristic, complemented
40C2×D4×Dic43C2211yescharacteristic
41C2×C4×C22⋊D43C2211yescharacteristic
42C2×#13063283C2211yescharacteristic, complemented
43C22×C22⋊Dic43—21no—
44#14583257C2218yescomplemented
45#14583240C2218yescomplemented
46#14583222C2218yescomplemented
47#14583187C2218yescomplemented
48#14583157C2218yescomplemented
49#14583127C2218yescomplemented
50#14583120C2218yescomplemented
51#14583062C2218yescomplemented
52#14583050C2218yescomplemented
53#14582996C2218yescomplemented
54#14582968C2218yescomplemented
55C2×#13063258C2211yescharacteristic, complemented
56C2×#13063257C2211yescharacteristic, complemented
57C2×#13063256C2211yescharacteristic, complemented
58C2×Dic43⋊C8C2211yescharacteristic, complemented
59#14582892C2218yescomplemented
60C2×#13063250C2211yescharacteristic, complemented
61C2×#13063250C2211yescharacteristic, complemented
62C2×#13063248C2211yescharacteristic, complemented
63C2×#13063248C2211yescharacteristic, complemented
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×#13063235C2211yescharacteristic, complemented
69C23×D4×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic
71C2×#117×C43C2211yescharacteristic
72C43×#418C2218yescomplemented
73C2×#102×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621900—24no—
78C2×#10621900—22no—
79C2×#10621900—42no—
80C2×#10621900C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C22×Dic86C2311yescharacteristic
84C22×C22⋊D43—21no—
85C22×C22⋊D43—21no—
86C22×C22⋊D43D411yescharacteristic
87C23×Dic43—21no—
88C23×Dic43—21no—
89C22×C4×D43C2311yescharacteristic
90C2×Dic172—42no—
91C2×Dic172C2314yescomplemented
92C2×#10621883—24no—
93C2×#10621883—42no—
94C2×#10621883C2314yes—
95C2×#10621883C2314yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C2×C8×D43—42no—
99C2×C8×D43C2314yescomplemented
100#13063324—22no—
101#13063324C2314yescomplemented
102#13063319—28no—
103#13063318—28no—
104#13063312—22no—
105#13063312C2314yes—
106#13063311—28no—
107#13063306—28no—
108#13063305—22no—
109#13063305C2314yescomplemented
110#13063304—22no—
111#13063304—22no—
112#13063304C2314yes—
113#13063304C2314yes—
114#13063297—28no—
115#13063296—22no—
116#13063296C2314yes—
117#13063294—28no—
118C4×Dic86—28no—
119#13063290—22no—
120#13063290C2314yescomplemented
121D4×Dic43—22no—
122D4×Dic43C2314yes—
123C4×C22⋊D43D414yes—
124C4×C22⋊D43C2314yes—
125#13063283—22no—
126#13063283C2314yescomplemented
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4D411yescharacteristic
135C2×C22⋊Dic43—21no—
136C2×C22⋊Dic43—21no—
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—28no—
142C2×C22⋊Dic43D411yescharacteristic
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4D411yescharacteristic
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yescomplemented
150#13063257C2314yescomplemented
151#13063256C2314yescomplemented
152Dic43⋊C8C2314yescomplemented
153#13063250C2314yescomplemented
154#13063250C2314yescomplemented
155#13063248C2314yescomplemented
156#13063248C2314yescomplemented
157#13063246C2314yes—
158#13063246C2314yes—
159C22⋊(C43⋊C8)C2314yes—
160(C2×D43)⋊C8C2314yescomplemented
161#13063235C2314yescomplemented
162C25×C43—21no—
163C22×D4×C43—24no—
164C22×D4×C43—21no—
165C22×D4×C43—22no—
166C22×D4×C43—42no—
167C22×D4×C43C2311yescharacteristic
168C22×D4×C43C2314yes—
169C22×D4×C43C2311yescharacteristic
170C23×C4×C43C2311yescharacteristic
171C2×M16×C43—42no—
172C2×M16×C43C2314yes—
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2311yescharacteristic
175#117×C43—22no—
176#117×C43C2314yes—
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C22⋊C4×C43—21no—
180C2×C42×C43—21no—
181#102×C43C2314yes—
182#102×C43C2314yes—
183#102×C43C2314yes—
184#102×C43C2314yes—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43—24no—
188C24×C43—44no—
189C24×C43—44no—
190C24×C43—82no—
191C24×C43C2×D411yescharacteristic
192C23×D43C2×D411yescharacteristic
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—24no—
196C2×D4×C43—22no—
197C2×D4×C43—28no—
198C2×D4×C43—22no—
199C2×D4×C43—22no—
200C2×D4×C43—44no—
201C2×D4×C43—44no—
202C2×D4×C43—48no—
203C2×D4×C43#4114yes—
204C2×D4×C43C2412yes—
205C2×D4×C43C2412yes—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D412yes—
212C22×C4×C43C2412yes—
213C22×C4×C43C2411yescharacteristic
214C2×C22⋊D43—24no—
215C2×C22⋊D43—24no—
216C2×C22⋊D43—42no—
217C2×C22⋊D43—44no—
218C2×C22⋊D43—82no—
219C2×C22⋊D43C2×D414yes—
220C22×Dic43—24no—
221C22×Dic43—24no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—44no—
227C22×Dic43—82no—
228C22×Dic43C2×D411yescharacteristic
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231#10621900—28no—
232#10621900—44no—
233#10621900—48no—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43C2×D412yes—
237C2×C4×D43C2412yes—
238C2×Dic86—22no—
239C2×Dic86—22no—
240C2×Dic86—22no—
241C2×Dic86—22no—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—24no—
245C2×Dic86—44no—
246C2×Dic86C2412yes—
247C2×Dic86C2412yes—
248M16×C43—44no—
249C2×C8×C43—22no—
250C2×C8×C43—22no—
251C2×C8×C43C2412yes—
252C2×C8×C43C2412yes—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43C2412yes—
256C4⋊C4×C43C2412yes—
257C22⋊C4×C43—24no—
258C42×C43—24no—
259C22⋊Dic43—24no—
260C22⋊Dic43—24no—
261C22⋊Dic43—24no—
262C22⋊Dic43—24no—
263C22⋊Dic43—24no—
264C22⋊Dic43—24no—
265C22⋊Dic43C2×D414yes—
266#10621883—28no—
267#10621883—44no—
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⋊Dic43C2412yes—
275C4⋊Dic43C2412yes—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4C2×D414yes—
281C4×Dic43—24no—
282C4×Dic43—24no—
283C4×Dic43C2×D412yes—
284C4×Dic43C2412yes—
285C2×C43⋊C8—22no—
286C2×C43⋊C8—22no—
287C2×C43⋊C8C2412yes—
288C2×C43⋊C8C2412yes—
289Dic172—44no—
290C8×D43—44no—
291C23×C43—24no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—48no—
298C23×C43—48no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43—42no—
303C23×C43—42no—
304C23×C43—84no—
305C23×C43—816no—
306C23×C43C22×D412yes—
307C23×C43C22×D411yescharacteristic
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43C22×D412yes—
312D4×C43—24no—
313D4×C43—22no—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—48no—
317D4×C43—42no—
318D4×C43C2×#4114yes—
319C2×C4×C43—22no—
320C2×C4×C43—24no—
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×C43C22×D412yes—
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4112yes—
330C2×C4×C43H(5,𝔽2)12yes—
331C2×C4×C43C2511yescharacteristic
332C22⋊D43—44no—
333C22⋊D43—48no—
334C22⋊D43—84no—
335C2×Dic43—22no—
336C2×Dic43—22no—
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×Dic43—42no—
347C2×Dic43—84no—
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350C2×Dic43C22×D412yes—
351C4×D43—24no—
352C4×D43—22no—
353C4×D43—22no—
354Dic86—22no—
355Dic86—22no—
356Dic86—22no—
357Dic86—22no—
358Dic86—48no—
359Dic86—42no—
360Dic86—42no—
361C8×C43—22no—
362C8×C43—22no—
363C43⋊C8—22no—
364C43⋊C8—22no—
365C2×#3311—431nomaximal, Sylow
366C22×C43—24no—
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—44no—
371C22×C43—48no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—816no—
378C22×C43—84no—
379C22×C43#54612yes—
380C22×C43#57512yes—
381C22×C43#57712yes—
382C22×C43C23×D411yescharacteristic
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—22no—
386C2×D43—44no—
387C4×C43—22no—
388C4×C43—42no—
389C4×C43—42no—
390C4×C43#54612yes—
391C4×C43C22×#4111yescharacteristic
392C4×C43C2×H(5,𝔽2)11yescharacteristic
393Dic43—22no—
394Dic43—22no—
395Dic43—22no—
396Dic43—42no—
397Dic43—42no—
398Dic43—42no—
399Dic43—42no—
400C2×#556—431no—
401C2×#546—431no—
402#3311—4316no—
403C2×#489—431no—
404C2×#485—431no—
405C2×#482—431no—
406C2×#476—431no—
407C2×#470—431no—
408C2×#465—431no—
409C2×#464—431no—
410C2×#452—431no—
411C2×#450—431no—
412C2×#440—431no—
413C2×#435—431no—
414C2×#418D4311yescharacteristic, complemented
415C2×#416—431no—
416C2×C43—42no—
417C2×C43—44no—
418C2×C43—82no—
419C2×C43#331114yescomplemented
420C2×C43C2×#54611yescharacteristic
421C2×C43C2×#57511yescharacteristic
422C2×C43C2×#57711yescharacteristic
423D43—42no—
424C22×#41—431no—
425C23×D4C2×D4311yescharacteristic
426C22×Q16—431no—
427C22×SD16—431no—
428C22×SD16—431no—
429C22×M16C2×D4311yescharacteristic
430C23×C8—431no—
431#556—438no—
432#556—864no—
433#546—438no—
434#546—864no—
435C2×C4⋊Q8—431no—
436C2×#126—861no—
437C2×#126—861no—
438C2×#124—431no—
439C2×#124—861no—
440C2×#123—861no—
441C2×C22⋊Q8—431no—
442C2×C22⋊Q8—431no—
443C2×C22⋊Q8—431no—
444C2×#121—431no—
445C2×#121—861no—
446C2×#120—861no—
447C2×C4×Q8—431no—
448C2×C4×Q8—861no—
449C2×C4×D4—431no—
450C2×C4×D4—431no—
451C2×#117—431no—
452C2×#117C2×D4311yescharacteristic
453C22×C22⋊C4—861no—
454#489—438no—
455#485—438no—
456#482—438no—
457#476—438no—
458#470—438no—
459#465—438no—
460#464—438no—
461#452—438no—
462#450—438no—
463#440—438no—
464#435—438no—
465C2×#107—431no—
466C2×#106—431no—
467C2×#106—431no—
468C2×C4⋊C8—431no—
469#418C2×D4318yescomplemented
470#416—438no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102C2×D4311yescharacteristic
478C2×#102C2×D4311yescharacteristic
479C2×#102C2×D4311yescharacteristic
480C2×#102C2×D4311yescharacteristic
481C2×C22⋊C8—431no—
482C2×C22⋊C8—431no—
483C2×#97—431no—
484C43C2×#331111yescharacteristic, complemented, Sylow
485C25—21no—
486C2×#41—434no—
487C2×#41—862no—
488C2×#41—864no—
489C2×#41—1722no—
490C22×Q8—431no—
491C22×Q8—431no—
492C22×Q8—861no—
493C22×D4—24no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—42no—
497C22×D4—431no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4C22×D4311yescharacteristic
501C22×D4C22×D4314yes—
502C22×D4C22×D4311yescharacteristic
503C23×C4—431no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4C22×D4311yescharacteristic
507C2×Q16—434no—
508C2×Q16—1722no—
509C2×SD16—434no—
510C2×SD16—434no—
511C2×SD16—864no—
512C2×SD16—1722no—
513C2×M16—42no—
514C2×M16C22×D4314yes—
515C22×C8—431no—
516C22×C8—431no—
517C22×C8—434no—
518C22×C8—1722no—
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4311yescharacteristic
521C4⋊Q8—434no—
522C4⋊Q8—862no—
523#126—868no—
524#126—868no—
525#124—434no—
526#124—862no—
527#124—868no—
528#123—868no—
529C22⋊Q8—434no—
530C22⋊Q8—434no—
531C22⋊Q8—434no—
532C22⋊Q8—862no—
533C22⋊Q8—862no—
534C22⋊Q8—862no—
535#121—434no—
536#121—868no—
537#121—862no—
538#120—868no—
539C4×Q8—434no—
540C4×Q8—868no—
541C4×Q8—862no—
542C4×D4—434no—
543C4×D4—434no—
544C4×D4—434no—
545C4×D4—862no—
546#117—22no—
547#117—434no—
548#117—862no—
549#117C22×D4314yes—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—861no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4C22×D4311yescharacteristic
559C2×C4⋊C4C22×D4311yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—431no—
562C2×C22⋊C4—431no—
563C2×C22⋊C4—868no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C42—21no—
573C2×C42—431no—
574C2×C42—861no—
575C2×C42—861no—
576#107—434no—
577#106—434no—
578#106—434no—
579C4⋊C8—434no—
580#103—434no—
581#103—434no—
582#103—434no—
583#103—434no—
584#102—434no—
585#102—434no—
586#102C22×D4314yes—
587#102C22×D4314yes—
588#102C22×D4314yes—
589#102C22×D4314yes—
590C22⋊C8—434no—
591C22⋊C8—434no—
592#97—434no—
593C24—21no—
594C24—21no—
595C24—24no—
596C24—44no—
597C24—44no—
598C24—82no—
599C24—431no—
600C24D4×D4311yescharacteristic
601#41—868no—
602#41—1724no—
603#41—1728no—
604C2×Q8—432no—
605C2×Q8—432no—
606C2×Q8—864no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8—862no—
610C2×Q8—862no—
611C2×Q8—862no—
612C2×Q8—862no—
613C2×Q8—1724no—
614C2×D4—28no—
615C2×D4—21no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—48no—
623C2×D4—44no—
624C2×D4—434no—
625C2×D4—864no—
626C2×D4—864no—
627C2×D4—3442no—
628C2×D4—1722no—
629C2×D4—1724no—
630C2×D4#1062189814yes—
631C2×D4C23×D4312yes—
632C2×D4C23×D4312yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—432no—
641C22×C4—432no—
642C22×C4—864no—
643C22×C4—864no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—3442no—
651C22×C4—1724no—
652C22×C4D4×D4312yes—
653C22×C4D4×D4311yescharacteristic
654C22×C4C23×D4312yes—
655C22×C4C23×D4311yescharacteristic
656Q16—1724no—
657SD16—868no—
658SD16—1724no—
659M16—44no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—432no—
663C2×C8—432no—
664C2×C8—862no—
665C2×C8—862no—
666C2×C8—1724no—
667C2×C8C23×D4312yes—
668C2×C8C23×D4312yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—434no—
672C4⋊C4—432no—
673C4⋊C4—432no—
674C4⋊C4—864no—
675C4⋊C4—864no—
676C4⋊C4—864no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4—864no—
680C4⋊C4—864no—
681C4⋊C4C23×D4312yes—
682C4⋊C4C23×D4312yes—
683C22⋊C4—24no—
684C22⋊C4—434no—
685C22⋊C4—434no—
686C22⋊C4—864no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4—864no—
693C22⋊C4—864no—
694C42—24no—
695C42—432no—
696C42—432no—
697C42—864no—
698C42—864no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—22no—
705C23—48no—
706C23—48no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—84no—
713C23—816no—
714C23—432no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23C2×D4×D4312yes—
719C23C2×D4×D4311yescharacteristic
720Q8—862no—
721Q8—862no—
722Q8—862no—
723Q8—862no—
724Q8—1728no—
725Q8—1722no—
726Q8—1722no—
727D4—22no—
728D4—22no—
729D4—22no—
730D4—24no—
731D4—48no—
732D4—42no—
733D4—3444no—
734D4—1724no—
735D4—1728no—
736D4C2×#1062189814yes—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—432no—
746C2×C4—432no—
747C2×C4—432no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—864no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—3444no—
759C2×C4—1728no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4C2×D4×D4312yes—
765C2×C4C2×D4×D4311yescharacteristic
766C2×C4C2×#1062189812yes—
767C2×C4#1306337012yes—
768C2×C4C24×D4311yescharacteristic
769C8—22no—
770C8—22no—
771C8—862no—
772C8—862no—
773C22—22no—
774C22—24no—
775C22—22no—
776C22—22no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—48no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—816no—
785C22—84no—
786C22—862no—
787C22—862no—
788C22—862no—
789C22—1724no—
790C22#1458353912yes—
791C22#1458369512yes—
792C22#1458370912yes—
793C22C22×D4×D4311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—862no—
798C4—862no—
799C4—862no—
800C4—1722no—
801C4—1722no—
802C4—1722no—
803C4—1722no—
804C4#1458353912yes—
805C4C22×#1062189811yescharacteristic
806C4C2×#1306337011yescharacteristic
807C2—42no—
808C2—44no—
809C2—82no—
810C2—1722no—
811C2#1914663214yesdirect product factor
812C2C2×#1458353911yescharacteristic
813C2C2×#1458369511yescharacteristic
814C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#418C2
socleC23×C43C22×D4
prime radicalC2×#14583543C2
hypercenterC2×#418D43
hypocenterC43C2×#3311
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. C2×#14583617C2semidirect
3. #19146632C2direct (N × H)
4. C2×#14583257C2semidirect
5. C2×#14583240C2semidirect
6. C2×#14583222C2semidirect
7. C2×#14583187C2semidirect
8. C2×#14583157C2semidirect
9. C2×#14583127C2semidirect
10. C2×#14583120C2semidirect
11. C2×#14583062C2semidirect
12. C2×#14583050C2semidirect
13. C2×#14582996C2semidirect
14. C2×#14582968C2semidirect
15. C2×#14582892C2semidirect
16. C2×C43×#418C2semidirect
18. C22×Dic172C22semidirect
21. C22×C8×D43C22semidirect
23. #14583617C22semidirect
26. C2×#13063324C22semidirect
32. C2×#13063305C22semidirect
39. C2×#13063290C22semidirect
42. C2×#13063283C22semidirect
44. #14583257C22semidirect
45. #14583240C22semidirect
46. #14583222C22semidirect
47. #14583187C22semidirect
48. #14583157C22semidirect
49. #14583127C22semidirect
50. #14583120C22semidirect
51. #14583062C22semidirect
52. #14583050C22semidirect
53. #14582996C22semidirect
54. #14582968C22semidirect
55. C2×#13063258C22semidirect
56. C2×#13063257C22semidirect
57. C2×#13063256C22semidirect
58. C2×Dic43⋊C8C22semidirect
59. #14582892C22semidirect
60. C2×#13063250C22semidirect
61. C2×#13063250C22semidirect
62. C2×#13063248C22semidirect
63. C2×#13063248C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×#13063235C22semidirect
72. C43×#418C22semidirect
91. C2×Dic172C23semidirect
99. C2×C8×D43C23semidirect
101. #13063324C23semidirect
109. #13063305C23semidirect
120. #13063290C23semidirect
126. #13063283C23semidirect
149. #13063258C23semidirect
150. #13063257C23semidirect
151. #13063256C23semidirect
152. Dic43⋊C8C23semidirect
153. #13063250C23semidirect
154. #13063250C23semidirect
155. #13063248C23semidirect
156. #13063248C23semidirect
160. (C2×D43)⋊C8C23semidirect
161. #13063235C23semidirect
414. C2×#418D43semidirect
419. C2×C43#3311semidirect
469. #418C2×D43semidirect
484. C43C2×#3311semidirect
811. C2#19146632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836172
C2×#145835432
#191466322
C2×#145832572
C2×#145832402
C2×#145832222
C2×#145831872
C2×#145831572
C2×#145831272
C2×#145831202
C2×#145830622
C2×#145830502
C2×#145829962
C2×#145829682
C2×#145828922
C2×C43×#4182
C2×#331143