Finite Group Databasebeta

← C2×#19146627 #25973263

Subgroups — C2×#19146627 #25973263

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×#14583537C211yesmaximal, characteristic
3#19146627C2116yesmaximal, direct product factor
4C2×#14583260C211yesmaximal, characteristic, complemented
5C2×#14583238C211yesmaximal, characteristic, complemented
6C2×#14583223C211yesmaximal, characteristic, complemented
7C2×#14583187C211yesmaximal, characteristic, complemented
8C2×#14583156C211yesmaximal, characteristic, complemented
9C2×#14583128C211yesmaximal, characteristic, complemented
10C2×#14583124C211yesmaximal, characteristic, complemented
11C2×#14583061C211yesmaximal, characteristic, complemented
12C2×#14583051C211yesmaximal, characteristic, complemented
13C2×#14582996C211yesmaximal, characteristic, complemented
14C2×#14582970C211yesmaximal, characteristic, complemented
15C2×#14582902C211yesmaximal, characteristic, complemented
16C2×C43×#416C211yesmaximal, characteristic, complemented
17C22×D4×D43C2211yescharacteristic
18C22×#10621885C2211yescharacteristic, complemented
19C22×#10621873C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22#14583617—24no—
23#14583617C2218yescomplemented
24#14583537—24no—
25#14583537C2218yes—
26C2×#13063324C2211yescharacteristic, complemented
27C2×#13063319—21no—
28C2×#13063318—21no—
29C2×#13063314C2211yescharacteristic
30C2×#13063311—21no—
31C2×#13063308—21no—
32C2×#13063305C2211yescharacteristic
33C2×#13063304C2211yescharacteristic, complemented
34C2×#13063301C2211yescharacteristic
35C2×#13063299C2211yescharacteristic
36C2×#13063297—21no—
37C2×#13063293—21no—
38C2×C4×Dic86—21no—
39C2×#13063290C2211yescharacteristic, complemented
40C2×D4×Dic43C2211yescharacteristic
41C2×C4×C22⋊D43C2211yescharacteristic
42C2×#13063283C2211yescharacteristic
43C22×(C2×D43)⋊C4—21no—
44#14583260C2218yescomplemented
45#14583238C2218yescomplemented
46#14583223C2218yescomplemented
47#14583187C2218yescomplemented
48#14583156C2218yescomplemented
49#14583128C2218yescomplemented
50#14583124C2218yescomplemented
51#14583061C2218yescomplemented
52#14583051C2218yescomplemented
53#14582996C2218yescomplemented
54#14582970C2218yescomplemented
55C2×#13063258C2211yescharacteristic, complemented
56C2×#13063257C2211yescharacteristic, complemented
57C2×#13063256C2211yescharacteristic, complemented
58C2×Dic43⋊C8C2211yescharacteristic, complemented
59#14582902C2218yescomplemented
60C2×#13063250C2211yescharacteristic, complemented
61C2×#13063249C2211yescharacteristic, complemented
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic, complemented
69C22×#41×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic, complemented
71C2×#117×C43C2211yescharacteristic, complemented
72C43×#416C2218yescomplemented
73C2×#103×C43C2211yescharacteristic, complemented
74C2×#103×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C24×D43—21no—
78C22×Dic86—21no—
79C22×Dic86C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C22⋊D43D411yescharacteristic
84C2×D4×D43—24no—
85C2×D4×D43—22no—
86C2×D4×D43—42no—
87C2×D4×D43C2314yes—
88C23×Dic43—21no—
89C22×C4×D43C2311yescharacteristic
90C2×#10621885—42no—
91C2×#10621885C2314yescomplemented
92C2×#10621873—42no—
93C2×#10621873C2314yes—
94C2×#10621883—24no—
95C2×#10621883C2314yes—
96C2×#10621872—42no—
97C2×#10621872C2314yes—
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100#13063324—22no—
101#13063324C2314yescomplemented
102#13063319—28no—
103#13063318—28no—
104#13063314—22no—
105#13063314C2314yes—
106#13063311—28no—
107#13063308—28no—
108#13063305—22no—
109#13063305C2314yes—
110#13063304—22no—
111#13063304C2314yescomplemented
112#13063301—22no—
113#13063301C2314yes—
114#13063299—22no—
115#13063299C2314yes—
116#13063297—28no—
117#13063293—28no—
118C4×Dic86—28no—
119#13063290—22no—
120#13063290C2314yescomplemented
121D4×Dic43—22no—
122D4×Dic43C2314yes—
123C4×C22⋊D43D414yes—
124C4×C22⋊D43C2314yes—
125#13063283—22no—
126#13063283C2314yes—
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⋊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—21no—
144C2×(C2×D43)⋊C4—28no—
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#13063249C2314yescomplemented
155#13063247C2314yes—
156#13063246C2314yes—
157#13063245C2314yes—
158#13063245C2314yes—
159C22⋊(C43⋊C8)C2314yescomplemented
160(C2×D43)⋊C8C2314yes—
161#13063235C2314yescomplemented
162C2×#41×C43—22no—
163C2×#41×C43—24no—
164C2×#41×C43—42no—
165C2×#41×C43C2314yes—
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43—21no—
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C23×C4×C43C2311yescharacteristic
171C22×C8×C43—42no—
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2314yescomplemented
175#117×C43—22no—
176#117×C43C2314yescomplemented
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C22⋊C4×C43—21no—
180C2×C42×C43—21no—
181#103×C43C2314yescomplemented
182#103×C43C2314yescomplemented
183#102×C43C2314yes—
184#102×C43C2314yes—
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—22no—
198C2×Q8×C43—22no—
199C2×Q8×C43C2412yes—
200C2×D4×C43—21no—
201C2×D4×C43—22no—
202C2×D4×C43—24no—
203C2×D4×C43—44no—
204C2×D4×C43#4114yes—
205C2×D4×C43C2412yes—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—24no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—44no—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—42no—
220C2×C22⋊D43—44no—
221C2×C22⋊D43—82no—
222C2×C22⋊D43C2×D414yes—
223C22×Dic43—24no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—82no—
228C22×Dic43C2×D411yescharacteristic
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231D4×D43—28no—
232D4×D43—44no—
233D4×D43—48no—
234C2×D172—21no—
235C2×D172—22no—
236C2×D172—22no—
237C2×D172C2412yes—
238C2×C4×D43—22no—
239C2×C4×D43—22no—
240C2×C4×D43C2×D412yes—
241C2×C4×D43C2412yes—
242C2×Dic86—22no—
243C2×Dic86—22no—
244C2×Dic86—21no—
245C2×Dic86—24no—
246C2×Dic86—44no—
247C2×Dic86C2412yes—
248C2×C8×C43—22no—
249C2×C8×C43—22no—
250C2×C8×C43—44no—
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⋊Dic43C2×D414yes—
262#10621885—44no—
263#10621883—28no—
264(C2×D43)⋊C4—24no—
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⋊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—
289#10621873—44no—
290#10621872—44no—
291C23×C43—24no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—42no—
297C23×C43—42no—
298C23×C43C22×D412yes—
299C23×C43C22×D411yescharacteristic
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—48no—
305C22×D43—48no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—84no—
310C22×D43—816no—
311C22×D43C22×D412yes—
312Q8×C43—22no—
313Q8×C43—22no—
314Q8×C43—42no—
315D4×C43—24no—
316D4×C43—22no—
317D4×C43—48no—
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—22no—
326C2×C4×C43—48no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43C22×D412yes—
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4112yes—
333C2×C4×C43H(5,𝔽2)12yes—
334C2×C4×C43C2511yescharacteristic
335C22⋊D43—44no—
336C22⋊D43—48no—
337C22⋊D43—84no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—84no—
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350C2×Dic43C22×D412yes—
351D172—22no—
352D172—22no—
353D172—42no—
354C4×D43—24no—
355C4×D43—22no—
356C4×D43—22no—
357Dic86—22no—
358Dic86—22no—
359Dic86—48no—
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—48no—
371C22×C43—44no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43#54612yes—
375C22×C43#57512yes—
376C22×C43#57712yes—
377C22×C43C23×D411yescharacteristic
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—44no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—816no—
386C2×D43—84no—
387C4×C43—22no—
388C4×C43—42no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43#54612yes—
392C4×C43C22×#4111yescharacteristic
393C4×C43C2×H(5,𝔽2)11yescharacteristic
394Dic43—22no—
395Dic43—22no—
396Dic43—22no—
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×#418—431no—
415C2×#416D4311yescharacteristic, complemented
416C2×C43—44no—
417C2×C43—42no—
418C2×C43#331114yescomplemented
419C2×C43C2×#54611yescharacteristic
420C2×C43C2×#57511yescharacteristic
421C2×C43C2×#57711yescharacteristic
422D43—42no—
423D43—82no—
424C22×#41C2×D4311yescharacteristic
425C23×D4—431no—
426C22×Q16—431no—
427C22×SD16—431no—
428C22×SD16—431no—
429C22×M16—431no—
430C23×C8C2×D4311yescharacteristic, complemented
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, complemented
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#418—438no—
470#416C2×D4318yescomplemented
471C2×#103—431no—
472C2×#103—431no—
473C2×#103C2×D4311yescharacteristic, complemented
474C2×#103C2×D4311yescharacteristic, complemented
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×#102C2×D4311yescharacteristic
480C2×#102C2×D4311yescharacteristic
481C2×C22⋊C8—431no—
482C2×C22⋊C8—431no—
483C2×#97—431no—
484C43C2×#331111yescharacteristic, complemented, Sylow
485C25—861no—
486C2×#41—22no—
487C2×#41—24no—
488C2×#41—42no—
489C2×#41C22×D4314yes—
490C22×Q8—431no—
491C22×Q8—861no—
492C22×Q8C22×D4311yescharacteristic
493C22×D4—21no—
494C22×D4—431no—
495C22×D4—434no—
496C22×D4—431no—
497C22×D4—862no—
498C22×D4—861no—
499C22×D4—864no—
500C22×D4—861no—
501C22×D4—1722no—
502C22×D4C22×D4311yescharacteristic
503C23×C4—21no—
504C23×C4—431no—
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—434no—
514C2×M16—1722no—
515C22×C8—42no—
516C22×C8—431no—
517C22×C8—431no—
518C22×C8C22×D4311yescharacteristic
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4314yescomplemented
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×D4314yescomplemented
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#103C22×D4314yescomplemented
583#103C22×D4314yescomplemented
584#102—434no—
585#102—434no—
586#102—434no—
587#102—434no—
588#102C22×D4314yes—
589#102C22×D4314yes—
590C22⋊C8—434no—
591C22⋊C8—434no—
592#97—434no—
593C24—21no—
594C24—431no—
595C24—864no—
596C24—861no—
597C24—3442no—
598C24—1724no—
599C24—1724no—
600C24D4×D4311yescharacteristic
601#41—28no—
602#41—44no—
603#41—48no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—432no—
608C2×Q8—864no—
609C2×Q8—861no—
610C2×Q8—862no—
611C2×Q8—862no—
612C2×Q8—1724no—
613C2×Q8C23×D4312yes—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—434no—
619C2×D4—432no—
620C2×D4—864no—
621C2×D4—868no—
622C2×D4—864no—
623C2×D4—861no—
624C2×D4—862no—
625C2×D4—862no—
626C2×D4—3442no—
627C2×D4—1724no—
628C2×D4—1728no—
629C2×D4—1722no—
630C2×D4—1724no—
631C2×D4#1062189814yes—
632C2×D4C23×D4312yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—44no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—432no—
644C22×C4—432no—
645C22×C4—864no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—3442no—
652C22×C4D4×D4312yes—
653C22×C4D4×D4311yescharacteristic
654C22×C4C23×D4312yes—
655C22×C4C23×D4311yescharacteristic
656Q16—1724no—
657SD16—868no—
658SD16—1724no—
659M16—1724no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—44no—
663C2×C8—432no—
664C2×C8—432no—
665C2×C8—862no—
666C2×C8—862no—
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—864no—
678C4⋊C4—861no—
679C4⋊C4—861no—
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—42no—
705C23—42no—
706C23—432no—
707C23—862no—
708C23—862no—
709C23—862no—
710C23—862no—
711C23—3444no—
712C23—34416no—
713C23—1728no—
714C23—1728no—
715C23—1722no—
716C23—1722no—
717C23—1722no—
718C23C2×D4×D4312yes—
719C23C2×D4×D4311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—862no—
724Q8—862no—
725Q8—1728no—
726Q8—1722no—
727D4—22no—
728D4—24no—
729D4—48no—
730D4—862no—
731D4—862no—
732D4—3444no—
733D4—1724no—
734D4—1728no—
735D4—1722no—
736D4C2×#1062189814yes—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—48no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—432no—
749C2×C4—432no—
750C2×C4—432no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—864no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—3444no—
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—862no—
782C22—862no—
783C22—862no—
784C22—34416no—
785C22—3444no—
786C22—1722no—
787C22—1722no—
788C22—1722no—
789C22—1724no—
790C22#1458353912yes—
791C22#1458369612yes—
792C22#1458370612yes—
793C22C22×D4×D4311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—862no—
799C4—862no—
800C4—862no—
801C4—1722no—
802C4—1722no—
803C4—1722no—
804C4#1458353912yes—
805C4C22×#1062189811yescharacteristic
806C4C2×#1306337011yescharacteristic
807C2—42no—
808C2—44no—
809C2—3442no—
810C2—1722no—
811C2#1914662714yesdirect product factor
812C2C2×#1458353911yescharacteristic
813C2C2×#1458369611yescharacteristic
814C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#416C2
socleC23×C43C22×D4
prime radicalC2×#14583537C2
hypercenterC2×#416D43
hypocenterC43C2×#3311
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#14583617C2semidirect
3. #19146627C2direct (N × H)
4. C2×#14583260C2semidirect
5. C2×#14583238C2semidirect
6. C2×#14583223C2semidirect
7. C2×#14583187C2semidirect
8. C2×#14583156C2semidirect
9. C2×#14583128C2semidirect
10. C2×#14583124C2semidirect
11. C2×#14583061C2semidirect
12. C2×#14583051C2semidirect
13. C2×#14582996C2semidirect
14. C2×#14582970C2semidirect
15. C2×#14582902C2semidirect
16. C2×C43×#416C2semidirect
18. C22×#10621885C22semidirect
23. #14583617C22semidirect
26. C2×#13063324C22semidirect
33. C2×#13063304C22semidirect
39. C2×#13063290C22semidirect
44. #14583260C22semidirect
45. #14583238C22semidirect
46. #14583223C22semidirect
47. #14583187C22semidirect
48. #14583156C22semidirect
49. #14583128C22semidirect
50. #14583124C22semidirect
51. #14583061C22semidirect
52. #14583051C22semidirect
53. #14582996C22semidirect
54. #14582970C22semidirect
55. C2×#13063258C22semidirect
56. C2×#13063257C22semidirect
57. C2×#13063256C22semidirect
58. C2×Dic43⋊C8C22semidirect
59. #14582902C22semidirect
60. C2×#13063250C22semidirect
61. C2×#13063249C22semidirect
66. C2×C22⋊(C43⋊C8)C22semidirect
68. C2×#13063235C22semidirect
70. C23×C8×C43C22semidirect
71. C2×#117×C43C22semidirect
72. C43×#416C22semidirect
73. C2×#103×C43C22semidirect
74. C2×#103×C43C22semidirect
91. C2×#10621885C23semidirect
101. #13063324C23semidirect
111. #13063304C23semidirect
120. #13063290C23semidirect
149. #13063258C23semidirect
150. #13063257C23semidirect
151. #13063256C23semidirect
152. Dic43⋊C8C23semidirect
153. #13063250C23semidirect
154. #13063249C23semidirect
159. C22⋊(C43⋊C8)C23semidirect
161. #13063235C23semidirect
174. C22×C8×C43C23semidirect
176. #117×C43C23semidirect
181. #103×C43C23semidirect
182. #103×C43C23semidirect
415. C2×#416D43semidirect
418. C2×C43#3311semidirect
430. C23×C8C2×D43semidirect
452. C2×#117C2×D43semidirect
470. #416C2×D43semidirect
473. C2×#103C2×D43semidirect
474. C2×#103C2×D43semidirect
484. C43C2×#3311semidirect
520. C22×C8C22×D43semidirect
549. #117C22×D43semidirect
582. #103C22×D43semidirect
583. #103C22×D43semidirect
811. C2#19146627direct (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×#145835372
#191466272
C2×#145832602
C2×#145832382
C2×#145832232
C2×#145831872
C2×#145831562
C2×#145831282
C2×#145831242
C2×#145830612
C2×#145830512
C2×#145829962
C2×#145829702
C2×#145829022
C2×C43×#4162
C2×#331143