Finite Group Databasebeta

← C2×#19134382 #25094242

Subgroups — C2×#19134382 #25094242

Order 11008.

2242 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C22×#13063239C212yesmaximal
3C2×C22⋊C4×Dic43C212yesmaximal, complemented
4#19134382C218yesmaximal, direct product factor
5C2×#14582666C211yesmaximal, characteristic, complemented
6C2×C43×#342C211yesmaximal, characteristic, complemented
7C23×C22⋊D43C2211yescharacteristic
8C24×Dic43C2211yescharacteristic
9C23×C4×D43C411yescharacteristic, complemented
10C2×(C22⋊D43)⋊C4—22no—
11C2×(C22⋊D43)⋊C4—22no—
12C2×(C22⋊D43)⋊C4—24no—
13C2×(C22⋊D43)⋊C4C414yescomplemented
14C2×(C22⋊D43)⋊C4C2214yes—
15C22×Dic43⋊C4C411yescharacteristic, complemented
16C22×C22⋊Dic43C2212yes—
17C22×(C2×D43)⋊C4C411yescharacteristic, complemented
18C22×C4×Dic43—22no—
19C22×C4×Dic43C411yescharacteristic, complemented
20C2×#13063239C4116yescomplemented
21C2×#13063239C2218yes—
22C22⋊C4×Dic43—24no—
23C22⋊C4×Dic43C2218yescomplemented
24C2×C43⋊#95—22no—
25#14582666C2214yescomplemented
26C22×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊C4×C43C2212yes—
28C43×#342C2214yescomplemented
29C24×D43C2×C411yescharacteristic
30C22×C22⋊D43—22no—
31C22×C22⋊D43—22no—
32C22×C22⋊D43—22no—
33C22×C22⋊D43—22no—
34C22×C22⋊D43C2×C418yes—
35C22×C22⋊D43C2×C412yes—
36C22×C22⋊D43C2312yes—
37C23×Dic43—22no—
38C23×Dic43—44no—
39C23×Dic43C2×C411yescharacteristic
40C23×Dic43C2×C411yescharacteristic
41C23×Dic43C2×C411yescharacteristic
42C23×Dic43C2×C412yes—
43C23×Dic43D412yes—
44C23×Dic43D412yes—
45C23×Dic43D414yes—
46C23×Dic43C2312yes—
47C22×C4×D43—22no—
48C22×C4×D43—21no—
49C22×C4×D43—21no—
50C22×C4×D43—44no—
51C22×C4×D43C2×C414yescomplemented
52(C22⋊D43)⋊C4—28no—
53(C22⋊D43)⋊C4—28no—
54(C22⋊D43)⋊C4—28no—
55(C22⋊D43)⋊C4—28no—
56C2×Dic43⋊C4—22no—
57C2×Dic43⋊C4—22no—
58C2×Dic43⋊C4C2×C414yescomplemented
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—24no—
61C2×C22⋊Dic43C2×C418yescomplemented
62C2×C22⋊Dic43C2314yes—
63C2×(C2×D43)⋊C4—22no—
64C2×(C2×D43)⋊C4—22no—
65C2×(C2×D43)⋊C4C2×C414yescomplemented
66C2×C4×Dic43—22no—
67C2×C4×Dic43—21no—
68C2×C4×Dic43—21no—
69C2×C4×Dic43—28no—
70C2×C4×Dic43—48no—
71C2×C4×Dic43C2×C414yescomplemented
72#13063239C2×C4132yescomplemented
73C43⋊#95—28no—
74C25×C43C2311yescharacteristic
75C23×C4×C43—22no—
76C23×C4×C43C2×C411yescharacteristic
77C23×C4×C43C2×C411yescharacteristic
78C2×C22⋊C4×C43—22no—
79C2×C22⋊C4×C43—22no—
80C2×C22⋊C4×C43—22no—
81C2×C22⋊C4×C43—24no—
82C2×C22⋊C4×C43C2×C412yes—
83C2×C22⋊C4×C43C2×C418yescomplemented
84C2×C22⋊C4×C43C2312yes—
85C2×C22⋊C4×C43C2314yes—
86C24×C43—42no—
87C24×C43—42no—
88C24×C43C22×C411yescharacteristic
89C24×C43C22×C411yescharacteristic
90C24×C43C22×C414yes—
91C24×C43C2×D412yes—
92C24×C43C2×D412yes—
93C24×C43#4112yes—
94C24×C43#4112yes—
95C24×C43C2411yescharacteristic
96C23×D43—21no—
97C23×D43—21no—
98C23×D43—22no—
99C23×D43—42no—
100C23×D43—42no—
101C23×D43C4214yescomplemented
102C23×D43C22×C412yes—
103C22×C4×C43—21no—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—28no—
108C22×C4×C43—24no—
109C22×C4×C43—42no—
110C22×C4×C43—42no—
111C22×C4×C43—44no—
112C22×C4×C43—44no—
113C22×C4×C43C22×C412yes—
114C22×C4×C43C22×C412yes—
115C2×C22⋊D43—24no—
116C2×C22⋊D43—24no—
117C2×C22⋊D43—28no—
118C2×C22⋊D43—28no—
119C2×C22⋊D43—28no—
120C2×C22⋊D43—28no—
121C2×C22⋊D43—24no—
122C2×C22⋊D43—22no—
123C2×C22⋊D43—22no—
124C2×C22⋊D43C4218yescomplemented
125C2×C22⋊D43C22×C418yes—
126C22×Dic43—28no—
127C22×Dic43—24no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—22no—
131C22×Dic43—28no—
132C22×Dic43—24no—
133C22×Dic43—42no—
134C22×Dic43—44no—
135C22×Dic43—44no—
136C22×Dic43—44no—
137C22×Dic43—44no—
138C22×Dic43—48no—
139C22×Dic43—44no—
140C22×Dic43C4214yescomplemented
141C22×Dic43C22⋊C412yes—
142C22×Dic43C22⋊C411yescharacteristic
143C22×Dic43C22⋊C412yes—
144C22×Dic43C22⋊C414yes—
145C22×Dic43C22⋊C412yes—
146C22×Dic43C22⋊C414yes—
147C22×Dic43C22⋊C411yescharacteristic
148C22×Dic43C22×C412yes—
149C22×Dic43C22×C412yes—
150C22×Dic43C22×C412yes—
151C22×Dic43C2×D414yes—
152C22×Dic43C2×D414yes—
153C2×C4×D43—24no—
154C2×C4×D43—24no—
155C2×C4×D43—48no—
156C2×C4×D43—44no—
157C2×C4×D43—44no—
158C2×C4×D43—48no—
159C22⋊C4×C43—24no—
160C22⋊C4×C43—28no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—24no—
163C22⋊C4×C43C22×C418yescomplemented
164C22⋊Dic43—28no—
165C22⋊Dic43—24no—
166C22⋊Dic43C22×C418yescomplemented
167(C2×D43)⋊C4—28no—
168Dic43⋊C4—28no—
169C4×Dic43—24no—
170C4×Dic43—24no—
171C4×Dic43—416no—
172C23×C43—24no—
173C23×C43—22no—
174C23×C43—24no—
175C23×C43—22no—
176C23×C43—41no—
177C23×C43—42no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—48no—
181C23×C43—42no—
182C23×C43—44no—
183C23×C43—44no—
184C23×C43—41no—
185C23×C43C2×C4212yes—
186C23×C43C2×C4212yes—
187C23×C43C2×C22⋊C412yes—
188C23×C43C2×C22⋊C411yescharacteristic
189C23×C43C2×C22⋊C411yescharacteristic
190C23×C43#11712yes—
191C23×C43#11712yes—
192C23×C43C4×D414yes—
193C23×C43C4×D414yes—
194C23×C43C4×D414yes—
195C23×C43C4×D414yes—
196C23×C43C23×C411yescharacteristic
197C23×C43C23×C412yes—
198C23×C43C22×D412yes—
199C23×C43C2×#4111yescharacteristic
200C23×C43C2×#4111yescharacteristic
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—24no—
204C22×D43—24no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—48no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—48no—
212C22×D43—42no—
213C22×D43C2×C4214yescomplemented
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—28no—
217C2×C4×C43—44no—
218C2×C4×C43—42no—
219C2×C4×C43—44no—
220C2×C4×C43—416no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C22⋊D43—28no—
227C22⋊D43—28no—
228C22⋊D43—216no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—24no—
232C2×Dic43—24no—
233C2×Dic43—22no—
234C2×Dic43—24no—
235C2×Dic43—28no—
236C2×Dic43—24no—
237C2×Dic43—24no—
238C2×Dic43—28no—
239C2×Dic43—28no—
240C2×Dic43—44no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—44no—
244C2×Dic43—44no—
245C2×Dic43—44no—
246C2×Dic43—416no—
247C2×Dic43#9914yescomplemented
248C2×Dic43C2×C4214yescomplemented
249C2×Dic43C2×C22⋊C412yes—
250C2×Dic43C2×C22⋊C414yes—
251C2×Dic43C2×C22⋊C412yes—
252C4×D43—48no—
253C4×D43—48no—
254C2×C4×#99—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—22no—
262C22×C43—22no—
263C22×C43—24no—
264C22×C43—24no—
265C22×C43—28no—
266C22×C43—28no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—44no—
270C22×C43—44no—
271C22×C43—42no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43C4×C22⋊C412yes—
275C22×C43C4×C22⋊C414yes—
276C22×C43C4×C22⋊C412yes—
277C22×C43C2×#9912yes—
278C22×C43#41012yes—
279C22×C43C22×C4211yescharacteristic
280C22×C43C22×C22⋊C411yescharacteristic
281C22×C43C2×#11711yescharacteristic
282C22×C43C2×C4×D412yes—
283C22×C43C2×C4×D412yes—
284C2×D43—24no—
285C2×D43—44no—
286C2×D43—48no—
287C2×D43—42no—
288C2×D43—42no—
289C2×D43—48no—
290C2×D43—44no—
291C4×C43—48no—
292C4×C43—42no—
293C4×C43—42no—
294Dic43—22no—
295Dic43—24no—
296Dic43—24no—
297Dic43—48no—
298Dic43C2×#9914yescomplemented
299C22×C4×D4—431no—
300C22×#99—432no—
301C2×C4×C22⋊C4—432no—
302C4×#99—438no—
303C2×#342—431no—
304C2×#342D4311yescharacteristic, complemented
305C2×C43—22no—
306C2×C43—22no—
307C2×C43—21no—
308C2×C43—22no—
309C2×C43—21no—
310C2×C43—24no—
311C2×C43C4×#9914yescomplemented
312C2×C43C2×C4×C22⋊C411yescharacteristic
313C2×C43C22×#9911yescharacteristic
314C2×C43C2×#41011yescharacteristic
315D43—44no—
316C23×D4—431no—
317C24×C4—431no—
318C24×C4—431no—
319C2×C4×D4—434no—
320C2×C4×D4—434no—
321C2×C4×D4—862no—
322C2×C4×D4—862no—
323C2×C4×D4—864no—
324C22×C4⋊C4—431no—
325C22×C22⋊C4—432no—
326C22×C22⋊C4—431no—
327C22×C22⋊C4C2×D4311yescharacteristic
328C22×C22⋊C4C2×D4312yes—
329C22×C42—431no—
330C22×C42—862no—
331C2×#99—438no—
332C2×#99—4316no—
333C4×C22⋊C4—438no—
334C4×C22⋊C4—864no—
335C2×#95—862no—
336#342—434no—
337#342C2×D4314yescomplemented
338C43C2×C4×#9911yescharacteristic, complemented, Sylow
339C25—431no—
340C25C22×D4311yescharacteristic
341C22×D4—432no—
342C22×D4—438no—
343C22×D4—432no—
344C22×D4—862no—
345C22×D4—862no—
346C22×D4—862no—
347C22×D4—862no—
348C23×C4—22no—
349C23×C4—431no—
350C23×C4—431no—
351C23×C4—432no—
352C23×C4—431no—
353C23×C4—432no—
354C23×C4—432no—
355C23×C4—434no—
356C23×C4—432no—
357C23×C4—434no—
358C23×C4—862no—
359C23×C4—861no—
360C23×C4—861no—
361C23×C4—862no—
362C23×C4—1724no—
363C23×C4—1724no—
364C23×C4C4×D4311yescharacteristic
365C23×C4C4×D4311yescharacteristic
366C4×D4—868no—
367C4×D4—868no—
368C4×D4—868no—
369C4×D4—868no—
370C2×C4⋊C4—434no—
371C2×C4⋊C4—862no—
372C2×C4⋊C4—862no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—438no—
378C2×C22⋊C4—434no—
379C2×C22⋊C4—434no—
380C2×C22⋊C4—862no—
381C2×C22⋊C4—862no—
382C2×C22⋊C4—862no—
383C2×C22⋊C4—864no—
384C2×C22⋊C4C4×D4312yes—
385C2×C22⋊C4C4×D4318yescomplemented
386C2×C22⋊C4C22×D4312yes—
387C2×C22⋊C4C22×D4314yes—
388C2×C42—434no—
389C2×C42—862no—
390C2×C42—861no—
391C2×C42—861no—
392C2×C42—868no—
393C2×C42—1728no—
394#99—4332no—
395#95—868no—
396C24—42no—
397C24—42no—
398C24—434no—
399C24—432no—
400C24—861no—
401C24—861no—
402C24—862no—
403C24—1722no—
404C24—1722no—
405C24C2×C4×D4311yescharacteristic
406C24C2×C4×D4311yescharacteristic
407C24C2×C4×D4314yes—
408C24D4×D4312yes—
409C24D4×D4312yes—
410C24#1062190012yes—
411C24#1062190212yes—
412C24C23×D4311yescharacteristic
413C2×D4—438no—
414C2×D4—438no—
415C2×D4—864no—
416C2×D4—864no—
417C2×D4—868no—
418C2×D4—868no—
419C2×D4—868no—
420C2×D4—868no—
421C2×D4—864no—
422C2×D4—862no—
423C2×D4—862no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—28no—
429C22×C4—24no—
430C22×C4—44no—
431C22×C4—44no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—431no—
435C22×C4—434no—
436C22×C4—432no—
437C22×C4—434no—
438C22×C4—431no—
439C22×C4—432no—
440C22×C4—432no—
441C22×C4—432no—
442C22×C4—434no—
443C22×C4—432no—
444C22×C4—434no—
445C22×C4—432no—
446C22×C4—434no—
447C22×C4—864no—
448C22×C4—864no—
449C22×C4—868no—
450C22×C4—864no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—862no—
454C22×C4—868no—
455C22×C4—864no—
456C22×C4—1724no—
457C22×C4—1728no—
458C22×C4—1724no—
459C22×C4—1728no—
460C22×C4—1724no—
461C22×C4—1728no—
462C22×C4—1724no—
463C22×C4—1724no—
464C22×C4—1722no—
465C22×C4—1724no—
466C22×C4—1724no—
467C22×C4C2×C4×D4312yes—
468C22×C4C2×C4×D4312yes—
469C4⋊C4—868no—
470C22⋊C4—24no—
471C22⋊C4—28no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—438no—
475C22⋊C4—868no—
476C22⋊C4—868no—
477C22⋊C4—864no—
478C22⋊C4C2×C4×D4318yescomplemented
479C42—864no—
480C42—864no—
481C42—17216no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—41no—
487C23—42no—
488C23—41no—
489C23—41no—
490C23—48no—
491C23—42no—
492C23—44no—
493C23—44no—
494C23—41no—
495C23—434no—
496C23—862no—
497C23—862no—
498C23—864no—
499C23—864no—
500C23—1722no—
501C23—1722no—
502C23—1728no—
503C23—1722no—
504C23—1722no—
505C23—1728no—
506C23—1722no—
507C23—1722no—
508C23C42×D4312yes—
509C23C42×D4312yes—
510C23C22⋊C4×D4312yes—
511C23C22⋊C4×D4311yescharacteristic
512C23C22⋊C4×D4311yescharacteristic
513C23#1306328312yes—
514C23#1306328312yes—
515C23(C22⋊D43)⋊C414yes—
516C23(C22⋊D43)⋊C414yes—
517C23#1306328714yes—
518C23#1306328714yes—
519C23C22×C4×D4311yescharacteristic
520C23C22×C4×D4312yes—
521C23C2×D4×D4312yes—
522C23C2×#1062190011yescharacteristic
523C23C2×#1062190211yescharacteristic
524D4—868no—
525D4—868no—
526D4—8616no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—28no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—416no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—432no—
540C2×C4—434no—
541C2×C4—434no—
542C2×C4—432no—
543C2×C4—434no—
544C2×C4—868no—
545C2×C4—864no—
546C2×C4—864no—
547C2×C4—868no—
548C2×C4—862no—
549C2×C4—862no—
550C2×C4—862no—
551C2×C4—864no—
552C2×C4—864no—
553C2×C4—864no—
554C2×C4—868no—
555C2×C4—1728no—
556C2×C4—1728no—
557C2×C4—1724no—
558C2×C4—1724no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1724no—
562C2×C4—1724no—
563C2×C4—17216no—
564C22—22no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—28no—
573C22—28no—
574C22—24no—
575C22—24no—
576C22—42no—
577C22—42no—
578C22—44no—
579C22—44no—
580C22—42no—
581C22—41no—
582C22—41no—
583C22—864no—
584C22—1724no—
585C22—1724no—
586C22—1728no—
587C22—1722no—
588C22—1722no—
589C22—1728no—
590C22#1458274612yes—
591C22#1458274614yes—
592C22#1458274612yes—
593C22#99×D4312yes—
594C22#1458287112yes—
595C22C2×C42×D4311yescharacteristic
596C22C2×C22⋊C4×D4311yescharacteristic
597C22C2×#1306328311yescharacteristic
598C22C2×(C22⋊D43)⋊C412yes—
599C22C2×#1306328712yes—
600C4—48no—
601C4—42no—
602C4—42no—
603C4—434no—
604C4—862no—
605C4—864no—
606C4—864no—
607C4—1728no—
608C2—22no—
609C2—22no—
610C2—21no—
611C2—21no—
612C2—22no—
613C2—24no—
614C2—1724no—
615C2#1913438214yesdirect product factor
616C2C2×#1458274611yescharacteristic
617C2C2×#99×D4311yescharacteristic
618C2C2×#1458287111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C43C22×C42
FrattiniC24C23×D43
FittingC2×C43×#342C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C22
cosocleC24×C43C24
hypercenterC2×#342D43
hypocenterC43C2×C4×#99
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic43C2semidirect
4. #19134382C2direct (N × H)
5. C2×#14582666C2semidirect
6. C2×C43×#342C2semidirect
9. C23×C4×D43C4semidirect
13. C2×(C22⋊D43)⋊C4C4semidirect
15. C22×Dic43⋊C4C4semidirect
17. C22×(C2×D43)⋊C4C4semidirect
19. C22×C4×Dic43C4semidirect
20. C2×#13063239C4semidirect
23. C22⋊C4×Dic43C22semidirect
25. #14582666C22semidirect
28. C43×#342C22semidirect
51. C22×C4×D43C2×C4semidirect
58. C2×Dic43⋊C4C2×C4semidirect
61. C2×C22⋊Dic43C2×C4semidirect
65. C2×(C2×D43)⋊C4C2×C4semidirect
71. C2×C4×Dic43C2×C4semidirect
72. #13063239C2×C4semidirect
83. C2×C22⋊C4×C43C2×C4semidirect
101. C23×D43C42semidirect
124. C2×C22⋊D43C42semidirect
140. C22×Dic43C42semidirect
163. C22⋊C4×C43C22×C4semidirect
166. C22⋊Dic43C22×C4semidirect
213. C22×D43C2×C42semidirect
247. C2×Dic43#99semidirect
248. C2×Dic43C2×C42semidirect
298. Dic43C2×#99semidirect
304. C2×#342D43semidirect
311. C2×C43C4×#99semidirect
337. #342C2×D43semidirect
338. C43C2×C4×#99semidirect
385. C2×C22⋊C4C4×D43semidirect
478. C22⋊C4C2×C4×D43semidirect
615. C2#19134382direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C22×#130632392
C2×C22⋊C4×Dic432
#191343822
C2×#145826662
C2×C43×#3422
C2×C4×#9943