Finite Group Databasebeta

← C2×#19135765 #25124019

Subgroups — C2×#19135765 #25124019

Order 11008.

1234 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583452C211yesmaximal, characteristic, complemented
2C22×#13063252C211yesmaximal, characteristic
3C2×#14582873C211yesmaximal, characteristic
4#19135765C218yesmaximal, direct product factor
5C2×#14582670C211yesmaximal, characteristic, complemented
6C2×#14582660C211yesmaximal, characteristic, complemented
7C2×#14582655C211yesmaximal, characteristic, complemented
8C2×C43×#421C211yesmaximal, characteristic
9C22×#10621877C2211yescharacteristic
10#14583452—22no—
11#14583452—22no—
12#14583452—22no—
13#14583452C2214yescomplemented
14C2×#13063324—21no—
15C2×#13063316—21no—
16C2×#13063302—22no—
17C2×C4×Dic86—22no—
18C2×#13063284C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C22×C4×Dic43C2211yescharacteristic
21C2×#13063252—21no—
22C2×#13063252—21no—
23C2×#13063252—22no—
24C2×#13063252C2214yes—
25#14582873—22no—
26#14582873C2214yes—
27C2×#13063240—22no—
28#14582670C2214yescomplemented
29#14582660C2214yescomplemented
30#14582655C2214yescomplemented
31C22×#41×C43C2211yescharacteristic
32C22×M16×C43C2211yescharacteristic
33C2×#117×C43C2211yescharacteristic
34C43×#421—22no—
35C43×#421C2214yes—
36C2×#104×C43—22no—
37C22×Dic86—22no—
38C23×Dic43—21no—
39C2×#10621877—21no—
40C2×#10621877—21no—
41C2×#10621877—21no—
42C2×#10621877—21no—
43C2×#10621877—21no—
44C2×#10621877C2312yes—
45C22×C43⋊C8—21no—
46#13063324—24no—
47#13063324—24no—
48#13063316—24no—
49#13063316—24no—
50#13063302—28no—
51#13063302—28no—
52C4×Dic86—28no—
53C4×Dic86—28no—
54#13063284—21no—
55#13063284—21no—
56#13063284—21no—
57#13063284—21no—
58#13063284—21no—
59#13063284D412yes—
60#13063284C2312yes—
61#13063284C2312yes—
62C2×C4⋊Dic43—22no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×Dic43⋊C4—22no—
66C2×Dic43⋊C4—22no—
67C2×C22⋊Dic43—21no—
68C2×C22⋊Dic43D412yes—
69C2×C4×Dic43—21no—
70C2×C4×Dic43—21no—
71C2×C4×Dic43—21no—
72C2×C4×Dic43—21no—
73C2×C4×Dic43—21no—
74C2×C4×Dic43D411yescharacteristic
75C2×C4×Dic43D411yescharacteristic
76C2×C4×Dic43D412yes—
77C2×C4×Dic43C2312yes—
78#13063252—24no—
79#13063252—24no—
80#13063240—28no—
81C2×#41×C43—21no—
82C2×#41×C43—21no—
83C2×#41×C43—21no—
84C2×#41×C43—21no—
85C2×#41×C43—21no—
86C2×#41×C43—21no—
87C2×#41×C43—21no—
88C2×#41×C43—21no—
89C2×#41×C43—21no—
90C2×#41×C43—21no—
91C2×#41×C43Q812yescomplemented
92C2×#41×C43C2312yes—
93C22×Q8×C43Q811yescharacteristic, complemented
94C22×D4×C43—21no—
95C22×D4×C43Q811yescharacteristic, complemented
96C23×C4×C43—21no—
97C23×C4×C43C2311yescharacteristic
98C2×M16×C43—21no—
99C2×M16×C43—21no—
100C2×M16×C43—21no—
101C2×M16×C43—21no—
102C2×M16×C43—21no—
103C2×M16×C43C2312yes—
104C22×C8×C43—21no—
105#117×C43—21no—
106#117×C43—21no—
107#117×C43D412yes—
108#117×C43C2312yes—
109C2×C4⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C42×C43D412yes—
112#104×C43—28no—
113C24×C43—21no—
114C24×C43C2×D411yescharacteristic
115#41×C43—22no—
116#41×C43—22no—
117#41×C43—22no—
118#41×C43—22no—
119#41×C43—22no—
120#41×C43—22no—
121#41×C43—22no—
122#41×C43—22no—
123#41×C43—41no—
124#41×C43—41no—
125#41×C43—41no—
126#41×C43—41no—
127#41×C43—41no—
128#41×C43—41no—
129#41×C43—41no—
130#41×C43—41no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43C2×Q812yescomplemented
137C2×D4×C43—21no—
138C2×D4×C43—22no—
139C2×D4×C43—22no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—41no—
145C2×D4×C43—41no—
146C2×D4×C43—41no—
147C2×D4×C43—41no—
148C2×D4×C43C2×Q812yescomplemented
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—21no—
153C22×C4×C43—41no—
154C22×C4×C43—41no—
155C22×C4×C43—41no—
156C22×C4×C43—41no—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×Q811yescharacteristic
163C22×C4×C43C2×Q811yescharacteristic
164C22×C4×C43#4111yescharacteristic
165C22×C4×C43#4111yescharacteristic
166C22×C4×C43#4111yescharacteristic
167C22×C4×C43#4111yescharacteristic
168C22×C4×C43#4111yescharacteristic
169C22×C4×C43#4111yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—44no—
177C22×Dic43—41no—
178C2×Dic86—28no—
179C2×Dic86—48no—
180M16×C43—22no—
181M16×C43—22no—
182M16×C43—41no—
183M16×C43—41no—
184C2×C8×C43—22no—
185C2×C8×C43—41no—
186C2×C8×C43—41no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43—22no—
189C22⋊C4×C43—22no—
190C22⋊C4×C43—22no—
191C42×C43—22no—
192C42×C43C2×D414yes—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—41no—
196C22⋊Dic43C2×D414yes—
197C4⋊Dic43—28no—
198C4⋊Dic43—22no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43—41no—
202Dic43⋊C4—28no—
203Dic43⋊C4—28no—
204C4×Dic43—22no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—22no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43—41no—
212C4×Dic43C2×D412yes—
213C4×Dic43C2×D412yes—
214#10621877—22no—
215#10621877—22no—
216#10621877—41no—
217#10621877—41no—
218C2×C43⋊C8—22no—
219C2×C43⋊C8—41no—
220C2×C43⋊C8—41no—
221C23×C43—22no—
222C23×C43—42no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—82no—
226C23×C43#12011yescharacteristic
227C23×C43#12011yescharacteristic
228C23×C43C22⋊Q811yescharacteristic
229C23×C43C22⋊Q811yescharacteristic
230C23×C43#12411yescharacteristic
231C23×C43#12411yescharacteristic
232C23×C43C22×D411yescharacteristic
233Q8×C43—22no—
234Q8×C43—22no—
235Q8×C43—41no—
236Q8×C43—41no—
237D4×C43—22no—
238D4×C43—22no—
239D4×C43—42no—
240D4×C43—42no—
241D4×C43—42no—
242D4×C43—42no—
243D4×C43—41no—
244D4×C43—41no—
245C2×C4×C43—24no—
246C2×C4×C43—22no—
247C2×C4×C43—44no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43#12011yescharacteristic
255C2×C4×C43#12011yescharacteristic
256C2×C4×C43C22⋊Q811yescharacteristic
257C2×C4×C43C22⋊Q811yescharacteristic
258C2×C4×C43C22⋊Q811yescharacteristic
259C2×C4×C43C22⋊Q811yescharacteristic
260C2×C4×C43C22⋊Q811yescharacteristic
261C2×C4×C43C22⋊Q811yescharacteristic
262C2×C4×C43C22⋊Q811yescharacteristic
263C2×C4×C43C22⋊Q811yescharacteristic
264C2×C4×C43C22⋊Q811yescharacteristic
265C2×C4×C43C22⋊Q811yescharacteristic
266C2×C4×C43#12411yescharacteristic
267C2×C4×C43#12411yescharacteristic
268C2×C4×C43#12411yescharacteristic
269C2×C4×C43#12411yescharacteristic
270C2×C4×C43#12411yescharacteristic
271C2×C4×C43#12411yescharacteristic
272C2×C4×C43#12411yescharacteristic
273C2×C4×C43#12411yescharacteristic
274C2×C4×C43#12411yescharacteristic
275C2×C4×C43#12411yescharacteristic
276C2×C4×C43C22×D411yescharacteristic
277C2×C4×C43C22×D411yescharacteristic
278C2×C4×C43C22×Q811yescharacteristic
279C2×C4×C43C2×#4111yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×Dic43—24no—
283C2×Dic43—22no—
284C2×Dic43—22no—
285C2×Dic43—24no—
286C2×Dic43—44no—
287C2×Dic43—44no—
288C2×Dic43—44no—
289C2×Dic43—42no—
290C2×Dic43—42no—
291C2×Dic43—82no—
292Dic86—416no—
293C8×C43—42no—
294C43⋊C8—42no—
295C2×#2031—431nomaximal, Sylow
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—22no—
299C22×C43—41no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43—42no—
304C22×C43—82no—
305C22×C43—82no—
306C22×C43—82no—
307C22×C43#39311yescharacteristic
308C22×C43#39311yescharacteristic
309C22×C43#39311yescharacteristic
310C22×C43#39311yescharacteristic
311C22×C43C2×#12011yescharacteristic
312C22×C43C2×C22⋊Q811yescharacteristic
313C22×C43C2×#12411yescharacteristic
314C4×C43—44no—
315C4×C43—42no—
316C4×C43#39311yescharacteristic
317C4×C43#39311yescharacteristic
318C4×C43#39311yescharacteristic
319C4×C43#39311yescharacteristic
320C4×C43C2×C22⋊Q811yescharacteristic
321C4×C43C2×C22⋊Q811yescharacteristic
322C4×C43C2×#12411yescharacteristic
323C4×C43C2×#12411yescharacteristic
324Dic43—24no—
325Dic43—44no—
326Dic43—42no—
327Dic43—82no—
328C2×#533—431no—
329C2×#421D4311yescharacteristic
330C22×#104—431no—
331C2×#410—431no—
332#2031—438no—
333C2×#344—431no—
334C2×#339—431no—
335C2×H(3,ℤ/4)—431no—
336C2×C43—21no—
337C2×C43—21no—
338C2×C43—21no—
339C2×C43—21no—
340C2×C43—21no—
341C2×C43—21no—
342C2×C43—82no—
343C2×C43#203112yescomplemented
344C2×C43C2×#39311yescharacteristic
345C22×#41C2×D4311yescharacteristic
346C22×M16—431no—
347C22×M16C2×D4311yescharacteristic
348#533—434no—
349#533—862no—
350#533—862no—
351#533—862no—
352C2×C4⋊Q8—861no—
353C2×#125—861no—
354C2×C22⋊Q8—862no—
355C2×C4×Q8—862no—
356C2×#117—431no—
357C2×#117—431no—
358C2×#117C2×D4311yescharacteristic
359C22×C42—431no—
360#421—22no—
361#421C2×D4314yes—
362C2×#104—22no—
363C2×#104—434no—
364C2×#104—861no—
365C2×#104—861no—
366C2×#104—862no—
367#410—434no—
368#410—862no—
369C2×#99—862no—
370#344—434no—
371#339—434no—
372H(3,ℤ/4)—434no—
373C43C2×#203111yescharacteristic, complemented, Sylow
374C2×#41—21no—
375C2×#41—21no—
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379C2×#41—21no—
380C2×#41—21no—
381C2×#41—21no—
382C2×#41—21no—
383C2×#41—21no—
384C2×#41Dic8612yescomplemented
385C2×#41C22×D4312yes—
386C22×Q8—862no—
387C22×Q8Dic8611yescharacteristic, complemented
388C22×D4—21no—
389C22×D4Dic8611yescharacteristic, complemented
390C23×C4—21no—
391C23×C4—861no—
392C23×C4C22×D4311yescharacteristic
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—21no—
396C2×M16—21no—
397C2×M16—21no—
398C2×M16—432no—
399C2×M16—861no—
400C2×M16—861no—
401C2×M16—861no—
402C2×M16—861no—
403C2×M16—861no—
404C2×M16C22×D4312yes—
405C22×C8—21no—
406C22×C8—861no—
407C4⋊Q8—864no—
408C4⋊Q8—864no—
409#125—864no—
410#125—864no—
411C22⋊Q8—868no—
412C22⋊Q8—868no—
413C4×Q8—868no—
414C4×Q8—868no—
415#117—21no—
416#117—21no—
417#117—432no—
418#117—432no—
419#117—432no—
420#117—861no—
421#117—861no—
422#117—861no—
423#117—861no—
424#117—861no—
425#117C22⋊D4312yes—
426#117C22×D4312yes—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—862no—
429C2×C4⋊C4—862no—
430C2×C4⋊C4—862no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—432no—
435C2×C22⋊C4—861no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—432no—
439C2×C42—432no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42—861no—
443C2×C42—861no—
444C2×C42—861no—
445C2×C42C22⋊D4312yes—
446#104—28no—
447#104—864no—
448#104—864no—
449#99—868no—
450C24—21no—
451C24D4×D4311yescharacteristic
452#41—22no—
453#41—22no—
454#41—22no—
455#41—22no—
456#41—22no—
457#41—22no—
458#41—22no—
459#41—22no—
460#41—41no—
461#41—41no—
462#41—41no—
463#41—41no—
464#41—41no—
465#41—41no—
466#41—41no—
467#41—41no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—868no—
474C2×Q8—1728no—
475C2×Q8C2×Dic8612yescomplemented
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4C2×Dic8612yescomplemented
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—1724no—
502C22×C4—1721no—
503C22×C4C2×Dic8611yescharacteristic
504C22×C4C2×Dic8611yescharacteristic
505C22×C4#1062189811yescharacteristic
506C22×C4#1062189811yescharacteristic
507C22×C4D4×D4311yescharacteristic
508C22×C4D4×D4311yescharacteristic
509C22×C4D4×D4311yescharacteristic
510C22×C4#1062190011yescharacteristic
511C22×C4#1062190011yescharacteristic
512C22×C4#1062190011yescharacteristic
513C22×C4#1062190011yescharacteristic
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C23×D4311yescharacteristic
517M16—22no—
518M16—22no—
519M16—41no—
520M16—41no—
521M16—862no—
522M16—862no—
523M16—1721no—
524M16—1721no—
525C2×C8—22no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—862no—
529C2×C8—1721no—
530C2×C8—1721no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—868no—
534C4⋊C4—868no—
535C4⋊C4—868no—
536C4⋊C4—862no—
537C4⋊C4—862no—
538C4⋊C4—862no—
539C4⋊C4—1721no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—434no—
543C22⋊C4—862no—
544C22⋊C4—862no—
545C22⋊C4—1721no—
546C42—22no—
547C42—432no—
548C42—432no—
549C42—862no—
550C42—861no—
551C42—861no—
552C42—862no—
553C42—862no—
554C42—862no—
555C42—862no—
556C42—1721no—
557C42C2×C22⋊D4314yes—
558C23—22no—
559C23—42no—
560C23—41no—
561C23—41no—
562C23—82no—
563C23#1306329311yescharacteristic
564C23#1306329311yescharacteristic
565C23#1306330211yescharacteristic
566C23#1306330211yescharacteristic
567C23#1306331111yescharacteristic
568C23#1306331111yescharacteristic
569C23C2×D4×D4311yescharacteristic
570Q8—22no—
571Q8—22no—
572Q8—41no—
573Q8—41no—
574Q8—17216no—
575D4—22no—
576D4—22no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—42no—
581D4—41no—
582D4—41no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—44no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—864no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—864no—
596C2×C4—3442no—
597C2×C4—1724no—
598C2×C4—1724no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1724no—
602C2×C4#1306329311yescharacteristic
603C2×C4#1306329311yescharacteristic
604C2×C4#1306330211yescharacteristic
605C2×C4#1306330211yescharacteristic
606C2×C4#1306330211yescharacteristic
607C2×C4#1306330211yescharacteristic
608C2×C4#1306330211yescharacteristic
609C2×C4#1306330211yescharacteristic
610C2×C4#1306330411yescharacteristic
611C2×C4#1306330411yescharacteristic
612C2×C4#1306330411yescharacteristic
613C2×C4#1306330411yescharacteristic
614C2×C4#1306331111yescharacteristic
615C2×C4#1306331111yescharacteristic
616C2×C4#1306331111yescharacteristic
617C2×C4#1306331111yescharacteristic
618C2×C4#1306331111yescharacteristic
619C2×C4#1306331111yescharacteristic
620C2×C4#1306331211yescharacteristic
621C2×C4#1306331211yescharacteristic
622C2×C4#1306331211yescharacteristic
623C2×C4#1306331211yescharacteristic
624C2×C4C2×D4×D4311yescharacteristic
625C2×C4C22×C22⋊D4311yescharacteristic
626C2×C4C22×Dic8611yescharacteristic
627C2×C4C2×#1062190011yescharacteristic
628C2×C4C2×#1062190011yescharacteristic
629C2×C4C2×#1062189811yescharacteristic
630C8—42no—
631C8—1722no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—42no—
640C22—82no—
641C22—82no—
642C22—82no—
643C22#1458281111yescharacteristic
644C22#1458281111yescharacteristic
645C22#1458281111yescharacteristic
646C22#1458281111yescharacteristic
647C22C2×#1306329311yescharacteristic
648C22C2×#1306330211yescharacteristic
649C22C2×#1306331111yescharacteristic
650C4—44no—
651C4—42no—
652C4—864no—
653C4—3442no—
654C4—1722no—
655C4—1724no—
656C4#1458281111yescharacteristic
657C4#1458281111yescharacteristic
658C4#1458281111yescharacteristic
659C4#1458281111yescharacteristic
660C4C2×#1306330211yescharacteristic
661C4C2×#1306330411yescharacteristic
662C4C2×#1306331111yescharacteristic
663C4C2×#1306331211yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—82no—
671C2#1913576512yesdirect product factor
672C2C2×#1458281111yescharacteristic
subgroupG/H
centerC2×C4#13063312
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#421C2
socleC22×C43#393
prime radicalC22×#41×C43C22
hypercenterC2×#421D43
hypocenterC43C2×#2031
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#14583452C2semidirect
4. #19135765C2direct (N × H)
5. C2×#14582670C2semidirect
6. C2×#14582660C2semidirect
7. C2×#14582655C2semidirect
13. #14583452C22semidirect
28. #14582670C22semidirect
29. #14582660C22semidirect
30. #14582655C22semidirect
91. C2×#41×C43Q8semidirect
93. C22×Q8×C43Q8semidirect
95. C22×D4×C43Q8semidirect
136. C2×Q8×C43C2×Q8semidirect
148. C2×D4×C43C2×Q8semidirect
343. C2×C43#2031semidirect
373. C43C2×#2031semidirect
384. C2×#41Dic86semidirect
387. C22×Q8Dic86semidirect
389. C22×D4Dic86semidirect
475. C2×Q8C2×Dic86semidirect
487. C2×D4C2×Dic86semidirect
671. C2#19135765direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834522
C22×#130632522
C2×#145828732
#191357652
C2×#145826702
C2×#145826602
C2×#145826552
C2×C43×#4212
C2×#203143