Finite Group Databasebeta

← C2×#19133113 #25063716

Subgroups — C2×#19133113 #25063716

Order 11008.

1554 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D43C211yesmaximal, characteristic
2C2×#14582861C211yesmaximal, characteristic
3C2×#14582746C211yesmaximal, characteristic
4#19133113C218yesmaximal, direct product factor
5C2×#14582637C211yesmaximal, characteristic, complemented
6C2×#14582636C211yesmaximal, characteristic, complemented
7C2×#14582635C211yesmaximal, characteristic, complemented
8C2×C43×#328C211yesmaximal, characteristic, complemented
9C22×Q8×D43C411yescharacteristic, complemented
10C23×C4×D43C2211yescharacteristic
11C22×#10621872—21no—
12C2×#13063305C411yescharacteristic, complemented
13C2×#13063304C2211yescharacteristic
14C2×#13063303—21no—
15C2×#13063302—21no—
16C2×#13063301C411yescharacteristic, complemented
17C22⋊Q8×D43—22no—
18C22⋊Q8×D43—22no—
19C22⋊Q8×D43C414yescomplemented
20C22⋊Q8×D43C2214yes—
21C2×C4⋊C4×D43—21no—
22C2×C4⋊C4×D43C411yescharacteristic, complemented
23C22×(C2×D43)⋊C4—21no—
24C2×C22⋊C4×D43—21no—
25C22×C4×Dic43—21no—
26#14582861—22no—
27#14582861C2214yes—
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×(C2×D43)⋊C8—21no—
30#14582746—22no—
31#14582746C2214yes—
32C2×C43⋊#95C2211yescharacteristic
33#14582637C2214yescomplemented
34#14582636C2214yescomplemented
35#14582635C2214yescomplemented
36C2×C22⋊Q8×C43C2211yescharacteristic
37C2×C22⋊C8×C43C2211yescharacteristic
38C2×#95×C43C2211yescharacteristic
39C43×#328C2214yescomplemented
40C24×D43D411yescharacteristic
41C22×Dic86—21no—
42C22×Dic86C2×C411yescharacteristic
43C2×Q8×D43—22no—
44C2×Q8×D43—44no—
45C2×Q8×D43C2×C414yescomplemented
46C23×Dic43—21no—
47C23×Dic43D411yescharacteristic
48C22×C4×D43—21no—
49C22×C4×D43—21no—
50C22×C4×D43—44no—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43C2×C412yes—
53C22×C4×D43C2×C411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C22×C4×D43D412yes—
56C22×C4×D43D411yescharacteristic
57C22×C4×D43D412yes—
58C22×C4×D43C2312yes—
59C2×#10621872—24no—
60C2×#10621872—44no—
61C22×C43⋊C8—21no—
62#13063305—22no—
63#13063305C2×C414yescomplemented
64#13063304—21no—
65#13063304—21no—
66#13063304C2×C412yes—
67#13063304C2312yes—
68#13063303—24no—
69#13063303—24no—
70#13063302—24no—
71#13063302—24no—
72#13063301—22no—
73#13063301C2×C414yescomplemented
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2×C411yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C4⋊C4×D43—24no—
80C4⋊C4×D43—22no—
81C4⋊C4×D43—24no—
82C4⋊C4×D43C2×C414yescomplemented
83C2×C22⋊Dic43—21no—
84C2×(C2×D43)⋊C4—28no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—24no—
88C22⋊C4×D43—24no—
89C22⋊C4×D43—24no—
90C2×C4×Dic43—24no—
91C2×C4×Dic43—44no—
92C22⋊(C43⋊C8)—21no—
93C22⋊(C43⋊C8)C2312yes—
94(C2×D43)⋊C8—24no—
95C43⋊#95—21no—
96C43⋊#95C2312yes—
97C22×Q8×C43C2×C411yescharacteristic
98C23×C4×C43—21no—
99C23×C4×C43C2311yescharacteristic
100C22×C8×C43—21no—
101C22⋊Q8×C43—21no—
102C22⋊Q8×C43—21no—
103C22⋊Q8×C43C2×C412yes—
104C22⋊Q8×C43C2312yes—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2×C411yescharacteristic
107C2×C22⋊C4×C43—21no—
108C22⋊C8×C43—21no—
109C22⋊C8×C43C2312yes—
110#95×C43—21no—
111#95×C43C2312yes—
112C24×C43C2×D411yescharacteristic
113C23×D43—22no—
114C23×D43—22no—
115C23×D43—24no—
116C23×D43—42no—
117C23×D43C22⋊C411yescharacteristic
118C23×D43C22⋊C412yes—
119C23×D43C22⋊C411yescharacteristic
120C23×D43C2×D412yes—
121C2×Q8×C43—21no—
122C2×Q8×C43—42no—
123C2×Q8×C43C22×C412yes—
124C22×C4×C43—24no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—22no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43C22×C411yescharacteristic
132C22×C4×C43C22×C411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—24no—
138C22×Dic43—24no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C22×Dic43C22⋊C411yescharacteristic
145C22×Dic43C22⋊C412yes—
146C22×Dic43C22⋊C411yescharacteristic
147C22×Dic43C2×D412yes—
148Q8×D43—48no—
149Q8×D43—48no—
150C2×C4×D43—24no—
151C2×C4×D43—24no—
152C2×C4×D43—24no—
153C2×C4×D43—24no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—44no—
157C2×C4×D43—44no—
158C2×C4×D43—44no—
159C2×C4×D43—44no—
160C2×C4×D43—44no—
161C2×C4×D43—44no—
162C2×C4×D43C22⋊C412yes—
163C2×C4×D43C22⋊C412yes—
164C2×C4×D43C22⋊C412yes—
165C2×C4×D43C22⋊C412yes—
166C2×C4×D43C22×C412yes—
167C2×C4×D43C22×C412yes—
168C2×C4×D43C2×D412yes—
169C2×C4×D43C2×D412yes—
170C2×Dic86—21no—
171C2×Dic86—24no—
172C2×Dic86—44no—
173C2×Dic86—42no—
174C2×Dic86C22×C412yes—
175C2×C8×C43—22no—
176C2×C8×C43—42no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43C22×C412yes—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—22no—
183C22⋊Dic43—22no—
184C22⋊Dic43—22no—
185(C2×D43)⋊C4—216no—
186(C2×D43)⋊C4—24no—
187(C2×D43)⋊C4—24no—
188C4⋊Dic43—21no—
189C4⋊Dic43—24no—
190C4⋊Dic43C22×C412yes—
191Dic43⋊C4—22no—
192Dic43⋊C4—22no—
193Dic43⋊C4—24no—
194Dic43⋊C4—24no—
195C4×Dic43—48no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—42no—
198#10621872—48no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43C2×C22⋊C411yescharacteristic
202C23×C43C2×C22⋊C411yescharacteristic
203C23×C43#13712yes—
204C23×C43#13712yes—
205C23×C43C22×D411yescharacteristic
206C22×D43—22no—
207C22×D43—22no—
208C22×D43—22no—
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—24no—
212C22×D43—22no—
213C22×D43—22no—
214C22×D43—24no—
215C22×D43—24no—
216C22×D43—42no—
217C22×D43—42no—
218C22×D43—48no—
219C22×D43—48no—
220C22×D43#10414yes—
221C22×D43C2×C22⋊C412yes—
222C22×D43C2×C22⋊C412yes—
223Q8×C43—42no—
224Q8×C43—42no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—24no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—42no—
235C2×C4×C43—48no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C23×C411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×Dic43—22no—
244C2×Dic43—24no—
245C2×Dic43—24no—
246C2×Dic43—24no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—42no—
250C2×Dic43—48no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43#9914yes—
255C2×Dic43C2×C22⋊C412yes—
256C2×Dic43C2×C22⋊C412yes—
257C4×D43—24no—
258C4×D43—24no—
259C4×D43—24no—
260C4×D43—24no—
261C4×D43—42no—
262C4×D43—42no—
263C4×D43—42no—
264C4×D43—42no—
265C4×D43—48no—
266C4×D43—48no—
267Dic86—42no—
268Dic86—48no—
269Dic86—42no—
270C8×C43—42no—
271C43⋊C8—42no—
272C2×#1508—431nomaximal, Sylow
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—24no—
278C22×C43—24no—
279C22×C43C2×#9912yes—
280C22×C43#41912yes—
281C22×C43#41912yes—
282C22×C43C2×#10412yes—
283C22×C43C22×C22⋊C411yescharacteristic
284C22×C43C2×#13711yescharacteristic
285C22×C43C2×#13711yescharacteristic
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—28no—
289C2×D43—22no—
290C2×D43—22no—
291C2×D43—22no—
292C2×D43—44no—
293C2×D43—44no—
294C2×D43—48no—
295C2×D43—44no—
296C2×D43C2×#10414yes—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—44no—
302C4×C43—42no—
303C4×C43—42no—
304Dic43—22no—
305Dic43—44no—
306Dic43—42no—
307Dic43—42no—
308Dic43C2×#9914yes—
309C22×C22⋊Q8—431no—
310C2×#407—431no—
311C2×C4×C22⋊C4—431no—
312#1508—438no—
313C2×#328—431no—
314C2×#328—431no—
315C2×#328—431no—
316C2×#328D4311yescharacteristic, complemented
317C2×C43—21no—
318C2×C43—21no—
319C2×C43—22no—
320C2×C43#150814yescomplemented
321C2×C43C22×#9911yescharacteristic
322C2×C43C2×#41911yescharacteristic
323C2×C43C22×#10411yescharacteristic
324D43—24no—
325D43—42no—
326C23×Q8—431no—
327C24×C4—431no—
328C22×M16—861no—
329C2×C22⋊Q8—431no—
330C2×C22⋊Q8—431no—
331C2×C22⋊Q8—434no—
332C2×C22⋊Q8—434no—
333C2×C22⋊Q8—431no—
334C2×C22⋊Q8—861no—
335C2×C22⋊Q8—861no—
336C2×C22⋊Q8—862no—
337C2×C22⋊Q8—862no—
338C2×C22⋊Q8C2×D4311yescharacteristic
339C22×C4⋊C4—431no—
340C22×C4⋊C4—861no—
341C22×C22⋊C4—861no—
342C22×C22⋊C4—861no—
343C22×C42—861no—
344#407—434no—
345#407—862no—
346C2×C22⋊C8—431no—
347C2×C22⋊C8—861no—
348C2×C22⋊C8C2×D4311yescharacteristic
349C4×C22⋊C4—434no—
350C4×C22⋊C4—862no—
351C2×#95—431no—
352C2×#95C2×D4311yescharacteristic
353#328—434no—
354#328—434no—
355#328—434no—
356#328C2×D4314yescomplemented
357C43C2×#150811yescharacteristic, complemented, Sylow
358C25—431no—
359C22×Q8—434no—
360C22×Q8—431no—
361C22×Q8—861no—
362C22×Q8—862no—
363C22×Q8—1724no—
364C22×Q8C4×D4311yescharacteristic
365C23×C4—21no—
366C23×C4—431no—
367C23×C4—431no—
368C23×C4—431no—
369C23×C4—432no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4—432no—
373C23×C4—432no—
374C23×C4—432no—
375C23×C4—861no—
376C23×C4—861no—
377C23×C4—861no—
378C23×C4—1724no—
379C23×C4C22×D4311yescharacteristic
380C2×M16—864no—
381C2×M16—1724no—
382C22×C8—21no—
383C22×C8—861no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—434no—
387C22⋊Q8—432no—
388C22⋊Q8—432no—
389C22⋊Q8—434no—
390C22⋊Q8—864no—
391C22⋊Q8—864no—
392C22⋊Q8—864no—
393C22⋊Q8—864no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C22⋊Q8—861no—
397C22⋊Q8—861no—
398C22⋊Q8C4×D4312yes—
399C22⋊Q8C22×D4312yes—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—434no—
403C2×C4⋊C4—862no—
404C2×C4⋊C4—864no—
405C2×C4⋊C4—864no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4C4×D4311yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—864no—
413C2×C22⋊C4—864no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—864no—
417C2×C22⋊C4—868no—
418C2×C22⋊C4—861no—
419C2×C42—864no—
420C2×C42—1724no—
421C22⋊C8—21no—
422C22⋊C8—432no—
423C22⋊C8—864no—
424C22⋊C8—861no—
425C22⋊C8C22×D4312yes—
426#95—21no—
427#95—432no—
428#95—861no—
429#95C22×D4312yes—
430C24—431no—
431C24—431no—
432C24—432no—
433C24—432no—
434C24—864no—
435C24—862no—
436C24—862no—
437C24—1722no—
438C24D4×D4311yescharacteristic
439C2×Q8—21no—
440C2×Q8—42no—
441C2×Q8—432no—
442C2×Q8—864no—
443C2×Q8—861no—
444C2×Q8—1722no—
445C2×Q8—1724no—
446C2×Q8—1728no—
447C2×Q8—1728no—
448C2×Q8C2×C4×D4312yes—
449C22×C4—24no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—431no—
457C22×C4—432no—
458C22×C4—431no—
459C22×C4—432no—
460C22×C4—432no—
461C22×C4—432no—
462C22×C4—432no—
463C22×C4—432no—
464C22×C4—432no—
465C22×C4—432no—
466C22×C4—432no—
467C22×C4—432no—
468C22×C4—864no—
469C22×C4—864no—
470C22×C4—864no—
471C22×C4—864no—
472C22×C4—864no—
473C22×C4—864no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—862no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4—1724no—
480C22×C4—1724no—
481C22×C4—1724no—
482C22×C4—1724no—
483C22×C4—1724no—
484C22×C4—1724no—
485C22×C4—1722no—
486C22×C4—1722no—
487C22×C4C2×C4×D4311yescharacteristic
488C22×C4C2×C4×D4311yescharacteristic
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493M16—1728no—
494C2×C8—22no—
495C2×C8—42no—
496C2×C8—862no—
497C2×C8—1722no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—432no—
502C4⋊C4—864no—
503C4⋊C4—864no—
504C4⋊C4—864no—
505C4⋊C4—861no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4C2×C4×D4312yes—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—864no—
512C22⋊C4—864no—
513C22⋊C4—8616no—
514C22⋊C4—862no—
515C22⋊C4—862no—
516C42—1728no—
517C23—22no—
518C23—22no—
519C23—432no—
520C23—434no—
521C23—432no—
522C23—864no—
523C23—864no—
524C23—862no—
525C23—862no—
526C23—862no—
527C23—864no—
528C23—862no—
529C23—862no—
530C23—862no—
531C23—862no—
532C23—1722no—
533C23—1722no—
534C23—1728no—
535C23—1728no—
536C23C22⋊C4×D4311yescharacteristic
537C23C22⋊C4×D4311yescharacteristic
538C23#1306335412yes—
539C23#1306335712yes—
540C23C2×D4×D4311yescharacteristic
541Q8—42no—
542Q8—42no—
543Q8—1722no—
544Q8—1722no—
545Q8—1728no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—48no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—432no—
561C2×C4—434no—
562C2×C4—432no—
563C2×C4—864no—
564C2×C4—864no—
565C2×C4—864no—
566C2×C4—864no—
567C2×C4—864no—
568C2×C4—864no—
569C2×C4—862no—
570C2×C4—864no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1728no—
578C2×C4—1728no—
579C2×C4—1722no—
580C2×C4—1728no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4C22⋊C4×D4311yescharacteristic
585C2×C4C22⋊C4×D4311yescharacteristic
586C2×C4C22×C4×D4311yescharacteristic
587C2×C4C2×D4×D4311yescharacteristic
588C8—42no—
589C8—1722no—
590C22—21no—
591C22—21no—
592C22—24no—
593C22—24no—
594C22—21no—
595C22—21no—
596C22—434no—
597C22—862no—
598C22—868no—
599C22—862no—
600C22—862no—
601C22—862no—
602C22—862no—
603C22—1724no—
604C22—1724no—
605C22—1728no—
606C22—1724no—
607C22#99×D4312yes—
608C22#1458290612yes—
609C22#1458290612yes—
610C22#104×D4312yes—
611C22C2×C22⋊C4×D4311yescharacteristic
612C22C2×#1306335411yescharacteristic
613C22C2×#1306335711yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—44no—
619C4—42no—
620C4—42no—
621C4—434no—
622C4—862no—
623C4—1724no—
624C4—1722no—
625C4—1722no—
626C2—21no—
627C2—21no—
628C2—22no—
629C2—864no—
630C2—1722no—
631C2#1913311314yesdirect product factor
632C2C2×#99×D4311yescharacteristic
633C2C2×#1458290611yescharacteristic
634C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#328C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenterC2×#328D43
hypocenterC43C2×#1508
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
4. #19133113C2direct (N × H)
5. C2×#14582637C2semidirect
6. C2×#14582636C2semidirect
7. C2×#14582635C2semidirect
8. C2×C43×#328C2semidirect
9. C22×Q8×D43C4semidirect
12. C2×#13063305C4semidirect
16. C2×#13063301C4semidirect
19. C22⋊Q8×D43C4semidirect
22. C2×C4⋊C4×D43C4semidirect
33. #14582637C22semidirect
34. #14582636C22semidirect
35. #14582635C22semidirect
39. C43×#328C22semidirect
45. C2×Q8×D43C2×C4semidirect
63. #13063305C2×C4semidirect
73. #13063301C2×C4semidirect
82. C4⋊C4×D43C2×C4semidirect
316. C2×#328D43semidirect
320. C2×C43#1508semidirect
356. #328C2×D43semidirect
357. C43C2×#1508semidirect
631. C2#19133113direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D432
C2×#145828612
C2×#145827462
#191331132
C2×#145826372
C2×#145826362
C2×#145826352
C2×C43×#3282
C2×#150843