Finite Group Databasebeta

← C2×#19132719 #25011563

Subgroups — C2×#19132719 #25011563

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063240C211yesmaximal, characteristic
2C2×#14582802C211yesmaximal, characteristic
3#19132719C214yesmaximal, direct product factor
4C22×#99×C43C211yesmaximal, characteristic
5C22×C4⋊Dic43C411yescharacteristic, complemented
6C22×C22⋊Dic43—21no—
7C22×C22⋊Dic43—21no—
8C22×C22⋊Dic43—21no—
9C22×C4×Dic43C411yescharacteristic, complemented
10C2×#13063240—21no—
11C2×#13063240—22no—
12C2×#13063240C414yescomplemented
13C2×#13063240C2212yes—
14#14582802—21no—
15#14582802—21no—
16#14582802C412yescomplemented
17#14582802C2212yes—
18C23×D4×C43C2211yescharacteristic
19C22×C22⋊C4×C43—21no—
20C2×#99×C43—21no—
21C2×#99×C43—22no—
22C2×#99×C43C414yescomplemented
23C2×#99×C43C2212yes—
24C23×Dic43—21no—
25C23×Dic43—21no—
26C23×Dic43—41no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—41no—
29C2×C4⋊Dic43—41no—
30C2×C4⋊Dic43C2×C412yescomplemented
31C2×C22⋊Dic43—24no—
32C2×C22⋊Dic43—22no—
33C2×C22⋊Dic43—22no—
34C2×C22⋊Dic43—22no—
35C2×C22⋊Dic43—22no—
36C2×C22⋊Dic43—22no—
37C2×C22⋊Dic43—44no—
38C2×C22⋊Dic43—44no—
39C2×C22⋊Dic43—41no—
40C2×C22⋊Dic43—42no—
41C2×C4×Dic43—21no—
42C2×C4×Dic43—42no—
43C2×C4×Dic43C2×C412yescomplemented
44#13063240—24no—
45#13063240—22no—
46#13063240C2×C414yescomplemented
47C25×C43D411yescharacteristic
48C25×C43D411yescharacteristic
49C22×D4×C43—42no—
50C22×D4×C43—41no—
51C22×D4×C43—41no—
52C22×D4×C43C2×C412yes—
53C22×D4×C43C2×C411yescharacteristic
54C22×D4×C43C2×C412yes—
55C22×D4×C43D411yescharacteristic
56C22×D4×C43D411yescharacteristic
57C22×D4×C43D412yes—
58C22×D4×C43Q812yes—
59C22×D4×C43C2311yescharacteristic
60C23×C4×C43—41no—
61C23×C4×C43C2×C411yescharacteristic
62C2×C22⋊C4×C43—24no—
63C2×C22⋊C4×C43—22no—
64C2×C22⋊C4×C43—41no—
65C2×C22⋊C4×C43—42no—
66#99×C43—24no—
67#99×C43—22no—
68#99×C43C2×C414yescomplemented
69C24×C43—21no—
70C24×C43—21no—
71C24×C43—22no—
72C24×C43—21no—
73C24×C43—22no—
74C24×C43—21no—
75C24×C43—42no—
76C24×C43—42no—
77C24×C43—42no—
78C24×C43—42no—
79C24×C43C22⋊C411yescharacteristic
80C24×C43C22⋊C412yes—
81C24×C43C22⋊C411yescharacteristic
82C24×C43C22⋊C411yescharacteristic
83C24×C43C22⋊C412yes—
84C24×C43C4⋊C412yes—
85C24×C43C4⋊C412yes—
86C24×C43C2×D411yescharacteristic
87C24×C43C2×D411yescharacteristic
88C2×D4×C43—42no—
89C2×D4×C43—42no—
90C2×D4×C43—41no—
91C2×D4×C43—42no—
92C2×D4×C43—42no—
93C2×D4×C43—41no—
94C2×D4×C43—42no—
95C2×D4×C43—41no—
96C2×D4×C43—41no—
97C2×D4×C43—42no—
98C2×D4×C43—41no—
99C2×D4×C43—41no—
100C2×D4×C43—42no—
101C2×D4×C43—42no—
102C2×D4×C43—41no—
103C2×D4×C43—41no—
104C2×D4×C43C4212yes—
105C2×D4×C43C22⋊C412yes—
106C2×D4×C43C22⋊C412yes—
107C2×D4×C43C4⋊C412yes—
108C2×D4×C43C4⋊C412yes—
109C2×D4×C43C4⋊C412yes—
110C2×D4×C43C22×C411yescharacteristic
111C2×D4×C43C22×C411yescharacteristic
112C2×D4×C43C2×D411yescharacteristic
113C2×D4×C43C2×Q811yescharacteristic
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—44no—
118C22×C4×C43—42no—
119C22×C4×C43—82no—
120C22×C4×C43—82no—
121C22×C4×C43C4212yes—
122C22×C4×C43C22⋊C411yescharacteristic
123C22×C4×C43C4⋊C412yes—
124C22×C4×C43C22×C411yescharacteristic
125C22×Dic43—24no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—42no—
129C22×Dic43—44no—
130C22×Dic43—42no—
131C22×Dic43—42no—
132C22×Dic43—42no—
133C22×Dic43—42no—
134C22×Dic43—41no—
135C22×Dic43—41no—
136C22×Dic43—82no—
137C22×Dic43—82no—
138C22⋊C4×C43—24no—
139C22⋊C4×C43—44no—
140C22⋊C4×C43—42no—
141C22⋊Dic43—24no—
142C22⋊Dic43—44no—
143C22⋊Dic43—42no—
144C22⋊Dic43—44no—
145C22⋊Dic43—44no—
146C22⋊Dic43—44no—
147C22⋊Dic43—44no—
148C4⋊Dic43—42no—
149C4⋊Dic43—42no—
150C4×Dic43—42no—
151C4×Dic43—42no—
152C23×C43—22no—
153C23×C43—22no—
154C23×C43—22no—
155C23×C43—22no—
156C23×C43—22no—
157C23×C43—22no—
158C23×C43—21no—
159C23×C43—21no—
160C23×C43—21no—
161C23×C43—21no—
162C23×C43—22no—
163C23×C43—22no—
164C23×C43—22no—
165C23×C43—22no—
166C23×C43—21no—
167C23×C43—21no—
168C23×C43—21no—
169C23×C43—21no—
170C23×C43—41no—
171C23×C43—41no—
172C23×C43—41no—
173C23×C43—41no—
174C23×C43—41no—
175C23×C43—41no—
176C23×C43—44no—
177C23×C43—44no—
178C23×C43—44no—
179C23×C43—44no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—81no—
187C23×C43—81no—
188C23×C43—81no—
189C23×C43—81no—
190C23×C43—84no—
191C23×C43—84no—
192C23×C43#9512yes—
193C23×C43#9512yes—
194C23×C43#9512yes—
195C23×C43#9911yescharacteristic
196C23×C43#9912yes—
197C23×C43#9911yescharacteristic
198C23×C43C2×C22⋊C411yescharacteristic
199C23×C43C2×C22⋊C411yescharacteristic
200C23×C43C2×C22⋊C411yescharacteristic
201C23×C43C2×C4⋊C411yescharacteristic
202C23×C43C2×C4⋊C411yescharacteristic
203D4×C43—42no—
204D4×C43—42no—
205D4×C43—42no—
206D4×C43—42no—
207D4×C43—42no—
208D4×C43—42no—
209D4×C43—41no—
210D4×C43—41no—
211D4×C43—41no—
212D4×C43—41no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—44no—
222C2×C4×C43—82no—
223C2×C4×C43—82no—
224C2×C4×C43—88no—
225C2×C4×C43#9512yes—
226C2×C4×C43C2×C4211yescharacteristic
227C2×C4×C43C2×C4⋊C411yescharacteristic
228C2×Dic43—24no—
229C2×Dic43—42no—
230C2×Dic43—48no—
231C2×Dic43—42no—
232C2×Dic43—44no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—82no—
237C2×Dic43—82no—
238C2×Dic43—82no—
239C2×Dic43—88no—
240C2×Dic43—82no—
241C2×#1393—431nomaximal, Sylow
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—21no—
245C22×C43—21no—
246C22×C43—24no—
247C22×C43—24no—
248C22×C43—22no—
249C22×C43—22no—
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—42no—
255C22×C43—42no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—44no—
269C22×C43—44no—
270C22×C43—44no—
271C22×C43—44no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—82no—
277C22×C43—82no—
278C22×C43—82no—
279C22×C43—82no—
280C22×C43#34212yes—
281C22×C43#34212yes—
282C22×C43#35312yes—
283C22×C43#35412yes—
284C22×C43C2×#9511yescharacteristic
285C22×C43C2×#9911yescharacteristic
286C22×C43C2×#9911yescharacteristic
287C4×C43—22no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—84no—
291Dic43—44no—
292Dic43—84no—
293Dic43—82no—
294C22×#99—431no—
295C22×#99D4311yescharacteristic
296C2×#390—431no—
297#1393—434no—
298C2×C43—21no—
299C2×C43—21no—
300C2×C43—22no—
301C2×C43—41no—
302C2×C43—41no—
303C2×C43—42no—
304C2×C43—42no—
305C2×C43—41no—
306C2×C43—41no—
307C2×C43#139314yescomplemented
308C2×C43C2×#34211yescharacteristic
309C2×C43C2×#35311yescharacteristic
310C2×C43C2×#35411yescharacteristic
311C23×D4C2×D4311yescharacteristic
312C22×C4⋊C4—431no—
313C22×C22⋊C4—21no—
314C22×C22⋊C4—861no—
315C22×C22⋊C4—861no—
316C22×C22⋊C4—861no—
317C22×C42—431no—
318C2×#99—21no—
319C2×#99—22no—
320C2×#99—432no—
321C2×#99—434no—
322C2×#99—861no—
323C2×#99—862no—
324C2×#99Dic4314yescomplemented
325C2×#99C2×D4312yes—
326#390—432no—
327#390—432no—
328#390—861no—
329#390—861no—
330C43C2×#139311yescharacteristic, complemented, Sylow
331C25D17211yescharacteristic
332C25C22⋊D4311yescharacteristic
333C22×D4—42no—
334C22×D4—41no—
335C22×D4—41no—
336C22×D4Dic8612yes—
337C22×D4C4×D4312yes—
338C22×D4C4×D4311yescharacteristic
339C22×D4D17211yescharacteristic
340C22×D4C2×Dic4312yes—
341C22×D4C22⋊D4312yes—
342C22×D4C22⋊D4311yescharacteristic
343C22×D4C22×D4311yescharacteristic
344C23×C4—41no—
345C23×C4—861no—
346C23×C4—861no—
347C23×C4—1721no—
348C23×C4C4×D4311yescharacteristic
349C2×C4⋊C4—432no—
350C2×C4⋊C4—861no—
351C2×C4⋊C4—1721no—
352C2×C4⋊C4—1721no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—864no—
358C2×C22⋊C4—862no—
359C2×C22⋊C4—862no—
360C2×C22⋊C4—862no—
361C2×C22⋊C4—862no—
362C2×C22⋊C4—862no—
363C2×C22⋊C4—1724no—
364C2×C22⋊C4—1724no—
365C2×C22⋊C4—1722no—
366C2×C22⋊C4—1721no—
367C2×C42—432no—
368C2×C42—861no—
369C2×C42—1722no—
370#99—24no—
371#99—22no—
372#99—434no—
373#99—864no—
374#99—862no—
375#99C2×Dic4314yescomplemented
376C24—21no—
377C24—21no—
378C24—21no—
379C24—22no—
380C24—21no—
381C24—22no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24—42no—
386C24Dic43⋊C412yes—
387C24C4⋊Dic4312yes—
388C24(C2×D43)⋊C411yescharacteristic
389C24(C2×D43)⋊C411yescharacteristic
390C24(C2×D43)⋊C412yes—
391C24(C2×D43)⋊C411yescharacteristic
392C24C22⋊Dic4312yes—
393C24C2×D17211yescharacteristic
394C24C2×C22⋊D4311yescharacteristic
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4C4×Dic4312yes—
412C2×D4Dic43⋊C412yes—
413C2×D4Dic43⋊C412yes—
414C2×D4C4⋊Dic4312yes—
415C2×D4(C2×D43)⋊C412yes—
416C2×D4C22⋊Dic4312yes—
417C2×D4C2×Dic8611yescharacteristic
418C2×D4C2×C4×D4311yescharacteristic
419C2×D4C22×Dic4311yescharacteristic
420C2×D4C2×C22⋊D4311yescharacteristic
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—42no—
425C22×C4—44no—
426C22×C4—82no—
427C22×C4—82no—
428C22×C4—864no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—3442no—
432C22×C4—3442no—
433C22×C4—1722no—
434C22×C4—1724no—
435C22×C4—1722no—
436C22×C4—1722no—
437C22×C4—1721no—
438C22×C4—1721no—
439C22×C4—1722no—
440C22×C4—1722no—
441C22×C4C4×Dic4312yes—
442C22×C4Dic43⋊C412yes—
443C22×C4(C2×D43)⋊C411yescharacteristic
444C22×C4C2×C4×D4311yescharacteristic
445C4⋊C4—1722no—
446C4⋊C4—1722no—
447C22⋊C4—24no—
448C22⋊C4—42no—
449C22⋊C4—44no—
450C22⋊C4—864no—
451C22⋊C4—1724no—
452C22⋊C4—1724no—
453C22⋊C4—1724no—
454C22⋊C4—1724no—
455C22⋊C4—1722no—
456C22⋊C4—1724no—
457C42—1722no—
458C42—1722no—
459C23—22no—
460C23—22no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23—41no—
485C23—41no—
486C23—44no—
487C23—41no—
488C23—41no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—84no—
494C23—84no—
495C23—81no—
496C23—81no—
497C23—81no—
498C23—81no—
499C23C43⋊#9512yes—
500C23C43⋊#9512yes—
501C23C43⋊#9512yes—
502C23#1306323912yes—
503C23#1306323911yescharacteristic
504C23#1306323911yescharacteristic
505C23C2×(C2×D43)⋊C411yescharacteristic
506C23C2×(C2×D43)⋊C411yescharacteristic
507C23C2×C22⋊Dic4311yescharacteristic
508C23C2×Dic43⋊C411yescharacteristic
509C23C2×C4⋊Dic4311yescharacteristic
510D4—42no—
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—44no—
529C2×C4—88no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4—864no—
533C2×C4—3442no—
534C2×C4—3448no—
535C2×C4—3442no—
536C2×C4—3442no—
537C2×C4—3442no—
538C2×C4—1724no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4—1728no—
543C2×C4—1722no—
544C2×C4—1722no—
545C2×C4C43⋊#9512yes—
546C2×C4C2×C4×Dic4311yescharacteristic
547C2×C4C2×Dic43⋊C411yescharacteristic
548C22—24no—
549C22—24no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—21no—
559C22—21no—
560C22—42no—
561C22—42no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—44no—
567C22—44no—
568C22—44no—
569C22—44no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22#1458266512yes—
587C22#1458266512yes—
588C22#1458269112yes—
589C22#1458269312yes—
590C22C2×C43⋊#9511yescharacteristic
591C22C2×#1306323911yescharacteristic
592C22C2×#1306323911yescharacteristic
593C4—22no—
594C4—21no—
595C4—21no—
596C4—84no—
597C4—3444no—
598C4—3442no—
599C4—1724no—
600C2—21no—
601C2—21no—
602C2—22no—
603C2—41no—
604C2—41no—
605C2—42no—
606C2—42no—
607C2—41no—
608C2—41no—
609C2#1913271914yesdirect product factor
610C2C2×#1458266511yescharacteristic
611C2C2×#1458269111yescharacteristic
612C2C2×#1458269311yescharacteristic
subgroupG/H
centerC23#13063239
commutatorC2×C4×C43C2×C42
FrattiniC22×D4C22×D43
FittingC22×#99×C43C2
socleC23×C43#99
prime radicalC23×D4×C43C22
cosocleC22×D4×C43C23
hypercenterC22×#99D43
hypocenterC43C2×#1393
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24 ◁ C23×D4 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
3. #19132719C2direct (N × H)
5. C22×C4⋊Dic43C4semidirect
9. C22×C4×Dic43C4semidirect
12. C2×#13063240C4semidirect
16. #14582802C4semidirect
22. C2×#99×C43C4semidirect
30. C2×C4⋊Dic43C2×C4semidirect
43. C2×C4×Dic43C2×C4semidirect
46. #13063240C2×C4semidirect
68. #99×C43C2×C4semidirect
307. C2×C43#1393semidirect
324. C2×#99Dic43semidirect
330. C43C2×#1393semidirect
375. #99C2×Dic43semidirect
609. C2#19132719direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632402
C2×#145828022
#191327192
C22×#99×C432
C2×#139343