Finite Group Databasebeta

← C2×#19136247 #25249332

Subgroups — C2×#19136247 #25249332

Order 11008.

1214 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583471C211yesmaximal, characteristic
2C2×#14582880C211yesmaximal, characteristic
3C2×#14582871C211yesmaximal, characteristic
4#19136247C218yesmaximal, direct product factor
5C2×#14582690C211yesmaximal, characteristic, complemented
6C2×#14582689C211yesmaximal, characteristic, complemented
7C2×#14582688C211yesmaximal, characteristic, complemented
8C2×C43×#352C211yesmaximal, characteristic, complemented
9C22×#10621900C2211yescharacteristic
10C23×Dic86C411yescharacteristic, complemented
11C2×M16×D43—21no—
12#14583471—22no—
13#14583471—22no—
14#14583471C414yescomplemented
15#14583471C2214yes—
16C2×#13063324—21no—
17C2×#13063311—21no—
18C2×#13063309C411yescharacteristic, complemented
19C2×#13063308C411yescharacteristic, complemented
20C2×#13063306C2211yescharacteristic
21C2×#13063303—21no—
22C2×#13063302—21no—
23C2×#13063281—21no—
24C2×#13063281C411yescharacteristic, complemented
25#14582880—22no—
26#14582880C2214yes—
27C2×#13063243—21no—
28C2×#13063242C2211yescharacteristic
29#14582871—22no—
30#14582871C2214yes—
31C2×#13063240C2211yescharacteristic
32C2×#13063239—21no—
33#14582690C2214yescomplemented
34#14582689C2214yescomplemented
35#14582688C2214yescomplemented
36C2×#123×C43C2211yescharacteristic
37C2×#100×C43C2211yescharacteristic
38C2×#99×C43C2211yescharacteristic
39C43×#352C2214yescomplemented
40C2×#10621900—41no—
41C2×#10621900—42no—
42C2×#10621900—41no—
43C2×#10621900C2×C412yes—
44C2×#10621900D412yes—
45C2×#10621900D412yes—
46C2×#10621900C2312yes—
47C22×Dic86—21no—
48C22×Dic86—21no—
49C22×Dic86—22no—
50C22×Dic86—42no—
51C22×Dic86—41no—
52C22×Dic86—41no—
53C22×Dic86C2×C414yescomplemented
54C22×Dic86D411yescharacteristic
55C22×C22⋊D43C2×C411yescharacteristic
56C22×C22⋊D43D411yescharacteristic
57C23×Dic43C2×C411yescharacteristic
58C23×Dic43C2×C411yescharacteristic
59C23×Dic43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C2×#10621877—21no—
62C2×#10621872—41no—
63M16×D43—24no—
64M16×D43—42no—
65C2×C8×D43—41no—
66#13063324—24no—
67#13063324—24no—
68#13063311—24no—
69#13063311—24no—
70#13063309—22no—
71#13063309C2×C414yescomplemented
72#13063308—22no—
73#13063308C2×C414yescomplemented
74#13063306—21no—
75#13063306—21no—
76#13063306C2×C412yes—
77#13063306C2312yes—
78#13063303—24no—
79#13063303—24no—
80#13063302—24no—
81#13063302—24no—
82#13063281—22no—
83#13063281—24no—
84#13063281—42no—
85#13063281C2×C414yescomplemented
86C2×C4⋊Dic43—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—41no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43C2×C411yescharacteristic
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—41no—
98#13063243—24no—
99#13063242—21no—
100#13063242C2312yes—
101#13063240—21no—
102#13063240C2312yes—
103#13063239—24no—
104C22×D4×C43C2311yescharacteristic
105C23×C4×C43C2×C411yescharacteristic
106C2×M16×C43—21no—
107#123×C43—21no—
108#123×C43—21no—
109#123×C43C2×C412yes—
110#123×C43C2312yes—
111C2×C4⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43C2×C411yescharacteristic
115#100×C43—21no—
116#100×C43C2312yes—
117#99×C43—21no—
118#99×C43C2312yes—
119C24×C43C22×C411yescharacteristic
120C24×C43C2×D411yescharacteristic
121C23×D43C22⋊C411yescharacteristic
122C2×D4×C43—41no—
123C2×D4×C43—41no—
124C2×D4×C43C22×C411yescharacteristic
125C2×D4×C43C2×D411yescharacteristic
126C2×D4×C43C2×D411yescharacteristic
127C2×D4×C43C2411yescharacteristic
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—41no—
132C22×C4×C43—41no—
133C22×C4×C43—41no—
134C22×C4×C43C22×C412yes—
135C22×C4×C43C2×D411yescharacteristic
136C2×C22⋊D43—41no—
137C2×C22⋊D43—41no—
138C2×C22⋊D43—41no—
139C2×C22⋊D43—41no—
140C2×C22⋊D43C22⋊C412yes—
141C2×C22⋊D43C22⋊C412yes—
142C2×C22⋊D43C22×C412yes—
143C2×C22⋊D43C2×D412yes—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—41no—
154C22×Dic43—41no—
155C22×Dic43—41no—
156C22×Dic43C22⋊C411yescharacteristic
157C22×Dic43C22⋊C411yescharacteristic
158C22×Dic43C22⋊C412yes—
159C22×Dic43C22⋊C412yes—
160C22×Dic43C22⋊C411yescharacteristic
161C22×Dic43C22×C412yes—
162C22×Dic43C22×C412yes—
163C22×Dic43C2×D412yes—
164#10621900—42no—
165#10621900—42no—
166#10621900—42no—
167#10621900—42no—
168#10621900—42no—
169#10621900—42no—
170#10621900—42no—
171#10621900—42no—
172C2×C4×D43—21no—
173C2×C4×D43—22no—
174C2×C4×D43—21no—
175C2×C4×D43C22⋊C412yes—
176C2×C4×D43C2×D412yes—
177C2×Dic86—24no—
178C2×Dic86—24no—
179C2×Dic86—41no—
180C2×Dic86—41no—
181C2×Dic86—42no—
182C2×Dic86—42no—
183C2×Dic86—44no—
184C2×Dic86—44no—
185C2×Dic86—42no—
186C2×Dic86—41no—
187C2×Dic86—41no—
188C2×Dic86—44no—
189C2×Dic86—44no—
190C2×Dic86C22⋊C412yes—
191C2×Dic86C2×D412yes—
192M16×C43—22no—
193M16×C43—41no—
194C2×C8×C43—41no—
195C4⋊C4×C43—22no—
196C4⋊C4×C43—22no—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—21no—
199C22⋊C4×C43—22no—
200C22⋊C4×C43—22no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43C22×C412yes—
203C22⋊Dic43—22no—
204C22⋊Dic43—21no—
205C22⋊Dic43—22no—
206C22⋊Dic43—22no—
207C22⋊Dic43—41no—
208C22⋊Dic43C22×C412yes—
209(C2×D43)⋊C4—24no—
210(C2×D43)⋊C4—24no—
211C4⋊Dic43—24no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—24no—
215Dic43⋊C4—24no—
216Dic43⋊C4—44no—
217C4×Dic43—24no—
218C4×Dic43—44no—
219#10621877—22no—
220#10621877—41no—
221C2×C43⋊C8—41no—
222#10621872—44no—
223C8×D43—44no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—42no—
229C23×C43—42no—
230C23×C43C2×C22⋊C411yescharacteristic
231C23×C43C2×C22⋊C411yescharacteristic
232C23×C43C2×C22⋊C411yescharacteristic
233C23×C43C23×C411yescharacteristic
234C23×C43C22×D411yescharacteristic
235C22×D43—21no—
236C22×D43—21no—
237C22×D43—42no—
238C22×D43C2×C22⋊C412yes—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—82no—
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C22⋊D43—42no—
257C22⋊D43—42no—
258C22⋊D43—42no—
259C22⋊D43—42no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—82no—
281C2×Dic43#9912yes—
282C2×Dic43#9911yescharacteristic
283C2×Dic43#9911yescharacteristic
284C2×Dic43C2×C22⋊C412yes—
285C2×Dic43C2×C22⋊C412yes—
286C2×Dic43C2×C22⋊C412yes—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291Dic86—42no—
292Dic86—42no—
293Dic86—48no—
294Dic86—44no—
295Dic86—44no—
296C8×C43—42no—
297C43⋊C8—42no—
298C2×#2123—431nomaximal, Sylow
299C22×C43—22no—
300C22×C43—21no—
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—21no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—42no—
309C22×C43—42no—
310C22×C43—42no—
311C22×C43—81no—
312C22×C43C2×#9911yescharacteristic
313C22×C43C2×#9911yescharacteristic
314C22×C43C22×C22⋊C411yescharacteristic
315C2×D43—22no—
316C2×D43—42no—
317C2×D43—42no—
318C2×D43—81no—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43—42no—
322C4×C43—42no—
323C4×C43—82no—
324Dic43—22no—
325Dic43—22no—
326Dic43—42no—
327Dic43—42no—
328Dic43—82no—
329Dic43C2×#9912yes—
330Dic43C2×#9912yes—
331C2×#536—431no—
332C2×#413—431no—
333C2×#410—431no—
334#2123—438no—
335C2×#352—431no—
336C2×#352—431no—
337C2×#352—431no—
338C2×#352D4311yescharacteristic, complemented
339C2×C43—21no—
340C2×C43—21no—
341C2×C43—41no—
342C2×C43—41no—
343C2×C43—41no—
344C2×C43—41no—
345C2×C43#212312yescomplemented
346C2×C43C22×#9911yescharacteristic
347D43—42no—
348C22×#41—431no—
349C23×Q8—431no—
350C22×M16—861no—
351#536—434no—
352#536—434no—
353#536—862no—
354#536—862no—
355C2×C4⋊Q8—861no—
356C2×#124—861no—
357C2×#123—431no—
358C2×#123—431no—
359C2×#123—431no—
360C2×#123C2×D4311yescharacteristic
361C2×C22⋊Q8—861no—
362C2×C22⋊Q8—861no—
363C2×#117—431no—
364C2×#117—861no—
365#413—434no—
366#413—862no—
367C2×#101—861no—
368C2×#100—431no—
369C2×#100C2×D4311yescharacteristic
370#410—434no—
371#410—862no—
372C2×#99—431no—
373C2×#99—861no—
374C2×#99C2×D4311yescharacteristic
375#352—434no—
376#352—434no—
377#352—434no—
378#352C2×D4314yescomplemented
379C43C2×#212311yescharacteristic, complemented, Sylow
380C2×#41—432no—
381C2×#41—432no—
382C2×#41—432no—
383C2×#41—432no—
384C2×#41—1721no—
385C2×#41—1721no—
386C2×#41—1722no—
387C22×Q8—434no—
388C22×Q8—431no—
389C22×Q8—861no—
390C22×Q8—861no—
391C22×Q8—862no—
392C22×Q8—1722no—
393C22×Q8—1721no—
394C22×Q8—1721no—
395C22×D4—431no—
396C22×D4—431no—
397C22×D4C22×D4311yescharacteristic
398C23×C4—431no—
399C23×C4—431no—
400C23×C4—431no—
401C23×C4—431no—
402C23×C4C4×D4311yescharacteristic
403C2×M16—21no—
404C2×M16—864no—
405C2×M16—861no—
406C2×M16—1721no—
407C2×M16—1722no—
408C22×C8—1721no—
409C4⋊Q8—864no—
410C4⋊Q8—864no—
411#124—864no—
412#124—864no—
413#123—21no—
414#123—21no—
415#123—432no—
416#123—432no—
417#123—434no—
418#123—434no—
419#123—862no—
420#123—862no—
421#123—861no—
422#123—861no—
423#123C4×D4312yes—
424#123C22×D4312yes—
425C22⋊Q8—864no—
426C22⋊Q8—864no—
427C22⋊Q8—864no—
428C22⋊Q8—864no—
429#117—434no—
430#117—862no—
431#117—864no—
432#117—1722no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—1721no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—431no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4C4×D4311yescharacteristic
447C2×C42—861no—
448C2×C42—1721no—
449#101—864no—
450#100—21no—
451#100—432no—
452#100—861no—
453#100C22×D4312yes—
454#99—21no—
455#99—432no—
456#99—864no—
457#99—861no—
458#99C22×D4312yes—
459C24—431no—
460C24C2×C4×D4311yescharacteristic
461C24D4×D4311yescharacteristic
462#41—1722no—
463#41—1722no—
464#41—1722no—
465#41—1722no—
466#41—1722no—
467#41—1722no—
468#41—1722no—
469#41—1722no—
470C2×Q8—432no—
471C2×Q8—432no—
472C2×Q8—864no—
473C2×Q8—864no—
474C2×Q8—1721no—
475C2×Q8—1721no—
476C2×Q8—1722no—
477C2×Q8—1721no—
478C2×Q8—1721no—
479C2×Q8—1724no—
480C2×Q8—1724no—
481C2×Q8—1724no—
482C2×Q8—1724no—
483C2×Q8—1722no—
484C2×Q8—1722no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—432no—
488C2×D4—432no—
489C2×D4—432no—
490C2×D4—432no—
491C2×D4—1721no—
492C2×D4—1721no—
493C2×D4—1721no—
494C2×D4—1721no—
495C2×D4C2×C4×D4311yescharacteristic
496C2×D4D4×D4311yescharacteristic
497C2×D4D4×D4311yescharacteristic
498C2×D4C23×D4311yescharacteristic
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—431no—
506C22×C4—432no—
507C22×C4—432no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—432no—
511C22×C4—432no—
512C22×C4—432no—
513C22×C4—432no—
514C22×C4—432no—
515C22×C4—861no—
516C22×C4—862no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—862no—
521C22×C4—862no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—1721no—
528C22×C4—1721no—
529C22×C4—1721no—
530C22×C4C2×C4×D4312yes—
531C22×C4D4×D4311yescharacteristic
532M16—22no—
533M16—41no—
534M16—862no—
535M16—1724no—
536M16—1721no—
537C2×C8—41no—
538C2×C8—1724no—
539C2×C8—1721no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—864no—
543C4⋊C4—864no—
544C4⋊C4—864no—
545C4⋊C4—862no—
546C4⋊C4—862no—
547C4⋊C4—1724no—
548C22⋊C4—22no—
549C22⋊C4—21no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—41no—
553C22⋊C4—432no—
554C22⋊C4—864no—
555C22⋊C4—864no—
556C22⋊C4—861no—
557C22⋊C4—862no—
558C22⋊C4—862no—
559C22⋊C4—862no—
560C22⋊C4—1721no—
561C22⋊C4C2×C4×D4312yes—
562C42—864no—
563C42—1724no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—42no—
569C23—42no—
570C23—432no—
571C23—861no—
572C23—861no—
573C23—1722no—
574C23C22⋊C4×D4311yescharacteristic
575C23C22⋊C4×D4311yescharacteristic
576C23C22⋊C4×D4311yescharacteristic
577C23C22×C4×D4311yescharacteristic
578C23C2×D4×D4311yescharacteristic
579Q8—1722no—
580Q8—1722no—
581Q8—1724no—
582Q8—1724no—
583Q8—1728no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—1722no—
589D4—1722no—
590D4—1722no—
591D4—1722no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—82no—
603C2×C4—432no—
604C2×C4—432no—
605C2×C4—431no—
606C2×C4—431no—
607C2×C4—432no—
608C2×C4—432no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—3442no—
628C2×C4—1722no—
629C2×C4—1722no—
630C2×C4—1722no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1722no—
634C2×C4C22⋊C4×D4311yescharacteristic
635C2×C4C2×D4×D4311yescharacteristic
636C8—42no—
637C8—1722no—
638C22—22no—
639C22—21no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—81no—
651C22—862no—
652C22—3441no—
653C22—1722no—
654C22—1722no—
655C22#99×D4311yescharacteristic
656C22#99×D4311yescharacteristic
657C22C2×C22⋊C4×D4311yescharacteristic
658C4—21no—
659C4—21no—
660C4—42no—
661C4—42no—
662C4—82no—
663C4—432no—
664C4—432no—
665C4—862no—
666C4—862no—
667C4—3442no—
668C4—1722no—
669C4—1722no—
670C2—21no—
671C2—21no—
672C2—41no—
673C2—41no—
674C2—41no—
675C2—41no—
676C2—1722no—
677C2#1913624712yesdirect product factor
678C2C2×#99×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC23×C43C23×C4
FrattiniC2×D4C23×D43
FittingC2×C43×#352C2
socleC22×C43C2×#99
prime radicalC22×#10621900C22
cosocleC2×D4×C43C24
hypercenterC2×#352D43
hypocenterC43C2×#2123
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
4. #19136247C2direct (N × H)
5. C2×#14582690C2semidirect
6. C2×#14582689C2semidirect
7. C2×#14582688C2semidirect
8. C2×C43×#352C2semidirect
10. C23×Dic86C4semidirect
14. #14583471C4semidirect
18. C2×#13063309C4semidirect
19. C2×#13063308C4semidirect
24. C2×#13063281C4semidirect
33. #14582690C22semidirect
34. #14582689C22semidirect
35. #14582688C22semidirect
39. C43×#352C22semidirect
53. C22×Dic86C2×C4semidirect
71. #13063309C2×C4semidirect
73. #13063308C2×C4semidirect
85. #13063281C2×C4semidirect
338. C2×#352D43semidirect
345. C2×C43#2123semidirect
378. #352C2×D43semidirect
379. C43C2×#2123semidirect
677. C2#19136247direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834712
C2×#145828802
C2×#145828712
#191362472
C2×#145826902
C2×#145826892
C2×#145826882
C2×C43×#3522
C2×#212343