Finite Group Databasebeta

← C2×#19138908 #25265766

Subgroups — C2×#19138908 #25265766

Order 11008.

3374 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C211yesmaximal, characteristic
2C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#19138908C2116yesmaximal, direct product factor
4C2×#14582840C212yesmaximal, complemented
5C2×#14582835C212yesmaximal, complemented
6C2×#14582798C211yesmaximal, characteristic, complemented
7C2×#14582795C211yesmaximal, characteristic, complemented
8C2×#14582775C212yesmaximal
9C2×#14582773C212yesmaximal, complemented
10C2×#14582759C211yesmaximal, characteristic, complemented
11C2×#14582756C211yesmaximal, characteristic, complemented
12C2×C43×#380C211yesmaximal, characteristic, complemented
13C23×C22⋊D43C2211yescharacteristic
14C23×C4×D43C2211yescharacteristic
15C23×C4×D43C2212yes—
16C2×C4×C22⋊D43—28no—
17C2×C4×C22⋊D43C2218yes—
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2212yes—
21C22×Dic43⋊C4C2212yes—
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2212yes—
24C2×C4⋊C4×D43—28no—
25C2×C4⋊C4×D43C2218yescomplemented
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2212yes—
28C22×(C2×D43)⋊C4C2212yes—
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31#14582840C22116yescomplemented
32#14582835C22116yescomplemented
33#14582798C2218yescomplemented
34#14582795C2218yescomplemented
35#14582775C22116yes—
36#14582773C22116yescomplemented
37#14582759C2218yescomplemented
38#14582756C2218yescomplemented
39C2×C43⋊#95C2212yes—
40C2×C43⋊#95C2212yes—
41C2×C43⋊#95C2212yes—
42C2×C43⋊#95C2212yes—
43C24×C4×C43C2211yescharacteristic
44C22×C4⋊C4×C43C2211yescharacteristic
45C22×C4⋊C4×C43C2211yescharacteristic
46C22×C22⋊C4×C43C2212yes—
47C43×#380C2218yescomplemented
48C2×#95×C43C2212yes—
49C24×D43C2311yescharacteristic
50C22×C22⋊D43—24no—
51C22×C22⋊D43—24no—
52C22×C22⋊D43Q818yes—
53C22×C22⋊D43C2314yes—
54C23×Dic43C2311yescharacteristic
55C23×Dic43C2312yes—
56C23×Dic43C2312yes—
57C23×Dic43C2311yescharacteristic
58C23×Dic43C2311yescharacteristic
59C22×C4×D43—24no—
60C22×C4×D43—24no—
61C22×C4×D43—28no—
62C22×C4×D43—44no—
63C22×C4×D43—44no—
64C22×C4×D43D418yes—
65C22×C4×D43C2314yes—
66C22×C4×D43C2318yes—
67C4×C22⋊D43—232no—
68C2×C4⋊Dic43—24no—
69C2×C4⋊Dic43—24no—
70C2×C4⋊Dic43—44no—
71C2×C4⋊Dic43C2314yes—
72C2×C4⋊Dic43C2314yes—
73C2×C4⋊Dic43C2318yes—
74C2×Dic43⋊C4—28no—
75C2×Dic43⋊C4—24no—
76C2×Dic43⋊C4—44no—
77C2×Dic43⋊C4C2318yes—
78C2×Dic43⋊C4C2314yes—
79C2×Dic43⋊C4C2318yes—
80C4⋊C4×D43—232no—
81C2×C22⋊Dic43—24no—
82C2×C22⋊Dic43—44no—
83C2×C22⋊Dic43C2314yes—
84C2×C22⋊Dic43C2318yes—
85C2×(C2×D43)⋊C4—24no—
86C2×(C2×D43)⋊C4—28no—
87C2×(C2×D43)⋊C4C2314yes—
88C2×(C2×D43)⋊C4C2318yes—
89C2×C4×Dic43—24no—
90C2×C4×Dic43C2314yes—
91C43⋊#95C2318yes—
92C43⋊#95C2318yes—
93C43⋊#95C2318yes—
94C43⋊#95C2318yes—
95C25×C43C2311yescharacteristic
96C23×C4×C43—24no—
97C23×C4×C43—24no—
98C23×C4×C43—24no—
99C23×C4×C43C2312yes—
100C23×C4×C43C2312yes—
101C23×C4×C43C2311yescharacteristic
102C23×C4×C43C2314yes—
103C23×C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43—24no—
105C2×C4⋊C4×C43—24no—
106C2×C4⋊C4×C43C2314yes—
107C2×C4⋊C4×C43C2314yes—
108C2×C22⋊C4×C43—44no—
109C2×C22⋊C4×C43C2318yes—
110#95×C43C2318yes—
111C24×C43—22no—
112C24×C43—22no—
113C24×C43—22no—
114C24×C43—22no—
115C24×C43—22no—
116C24×C43—22no—
117C24×C43C2×Q814yes—
118C24×C43C2412yes—
119C24×C43C2411yescharacteristic
120C23×D43—22no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—22no—
124C23×D43C2×D414yes—
125C23×D43C2×Q814yes—
126C23×D43#4114yes—
127C23×D43C2412yes—
128C22×C4×C43—28no—
129C22×C4×C43—28no—
130C22×C4×C43—28no—
131C22×C4×C43—24no—
132C22×C4×C43—22no—
133C22×C4×C43—24no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—24no—
137C22×C4×C43—24no—
138C22×C4×C43—24no—
139C22×C4×C43—24no—
140C22×C4×C43—416no—
141C22×C4×C43C2×D414yes—
142C22×C4×C43#4114yes—
143C22×C4×C43#4114yes—
144C22×C4×C43C2412yes—
145C22×C4×C43C2414yes—
146C22×C4×C43C2414yes—
147C22×C4×C43C2412yes—
148C2×C22⋊D43—232no—
149C2×C22⋊D43—28no—
150C2×C22⋊D43—28no—
151C2×C22⋊D43C2×Q8116yes—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—24no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—24no—
159C22×Dic43—24no—
160C22×Dic43—24no—
161C22×Dic43—24no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—24no—
165C22×Dic43C2×D414yes—
166C22×Dic43C2×Q814yes—
167C22×Dic43C2414yes—
168C22×Dic43C2414yes—
169C22×Dic43C2412yes—
170C22×Dic43C2412yes—
171C22×Dic43C2412yes—
172C2×C4×D43—232no—
173C2×C4×D43—28no—
174C2×C4×D43—28no—
175C2×C4×D43—216no—
176C2×C4×D43—48no—
177C2×C4×D43—48no—
178C2×C4×D43—432no—
179C2×C4×D43C2×D4116yes—
180C4⋊C4×C43—28no—
181C4⋊C4×C43—28no—
182C22⋊C4×C43—48no—
183C22⋊Dic43—28no—
184C22⋊Dic43—48no—
185(C2×D43)⋊C4—28no—
186(C2×D43)⋊C4—216no—
187C4⋊Dic43—28no—
188C4⋊Dic43—28no—
189C4⋊Dic43—48no—
190Dic43⋊C4—216no—
191Dic43⋊C4—28no—
192Dic43⋊C4—48no—
193C4×Dic43—28no—
194C23×C43—28no—
195C23×C43—28no—
196C23×C43—28no—
197C23×C43—22no—
198C23×C43—22no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43—22no—
203C23×C43—44no—
204C23×C43—44no—
205C23×C43—44no—
206C23×C43—44no—
207C23×C43C22×D412yes—
208C23×C43C22×Q814yes—
209C23×C43C22×Q812yes—
210C23×C43C2×#4112yes—
211C23×C43C2×#4112yes—
212C23×C43C2×#4112yes—
213C23×C43H(5,𝔽2)12yes—
214C23×C43H(5,𝔽2)12yes—
215C23×C43C2511yescharacteristic
216C22×D43—28no—
217C22×D43—28no—
218C22×D43—28no—
219C22×D43—28no—
220C22×D43—28no—
221C22×D43—28no—
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43C22⋊Q8116yes—
227C22×D43C22×D414yes—
228C22×D43C22×Q814yes—
229C22×D43C2×#4114yes—
230C2×C4×C43—22no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—24no—
237C2×C4×C43—24no—
238C2×C4×C43—24no—
239C2×C4×C43—44no—
240C2×C4×C43—48no—
241C2×C4×C43—48no—
242C2×C4×C43—416no—
243C2×C4×C43#123116yes—
244C2×C4×C43C22×D414yes—
245C2×C4×C43C2×#4114yes—
246C2×C4×C43C2×#4114yes—
247C22⋊D43—232no—
248C2×Dic43—28no—
249C2×Dic43—28no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—24no—
258C2×Dic43—22no—
259C2×Dic43—24no—
260C2×Dic43—22no—
261C2×Dic43—24no—
262C2×Dic43—24no—
263C2×Dic43—48no—
264C2×Dic43—44no—
265C2×Dic43—48no—
266C2×Dic43C22×D414yes—
267C2×Dic43C22×Q814yes—
268C4×D43—232no—
269C4×D43—432no—
270C2×#2487—431nomaximal, Sylow
271C22×C43—24no—
272C22×C43—24no—
273C22×C43—24no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—416no—
279C22×C43C2×C22⋊Q814yes—
280C22×C43C2×#12314yes—
281C22×C43#53514yes—
282C22×C43#55314yes—
283C22×C43#55314yes—
284C22×C43#55414yes—
285C22×C43#55414yes—
286C22×C43C23×D411yescharacteristic
287C22×C43C23×Q811yescharacteristic
288C22×C43C22×#4111yescharacteristic
289C22×C43C22×#4111yescharacteristic
290C22×C43C22×#4111yescharacteristic
291C22×C43C2×H(5,𝔽2)11yescharacteristic
292C22×C43C2×H(5,𝔽2)11yescharacteristic
293C2×D43—24no—
294C2×D43—24no—
295C2×D43—24no—
296C2×D43—24no—
297C2×D43—24no—
298C2×D43—24no—
299C2×D43—232no—
300C2×D43C2×C22⋊Q818yes—
301C4×C43—42no—
302C4×C43—44no—
303C4×C43—44no—
304C4×C43C2×#12318yes—
305Dic43—24no—
306Dic43—24no—
307Dic43—44no—
308Dic43—42no—
309Dic43—44no—
310C22×C4×D4—431no—
311C23×C4⋊C4—431no—
312#2487—4316no—
313C2×#400—432no—
314C2×#399—432no—
315C2×#389—431no—
316C2×#389—431no—
317C2×#386—432no—
318C2×#385—432no—
319C2×#380—431no—
320C2×#380—431no—
321C2×#380D4311yescharacteristic, complemented
322C2×C43—44no—
323C2×C43#248718yescomplemented
324C2×C43C22×C22⋊Q811yescharacteristic
325C2×C43C22×#12311yescharacteristic
326C2×C43C2×#53511yescharacteristic
327C2×C43C2×#55311yescharacteristic
328C2×C43C2×#55311yescharacteristic
329C2×C43C2×#55411yescharacteristic
330C2×C43C2×#55411yescharacteristic
331D43—28no—
332C23×D4—431no—
333C24×C4—431no—
334C24×C4—432no—
335C24×C4C2×D4311yescharacteristic
336C2×C4×D4—438no—
337C2×C4×D4—868no—
338C22×C4⋊C4—432no—
339C22×C4⋊C4—431no—
340C22×C4⋊C4—431no—
341C22×C4⋊C4—431no—
342C22×C4⋊C4—432no—
343C22×C4⋊C4—432no—
344C22×C4⋊C4—438no—
345C22×C4⋊C4—868no—
346C22×C4⋊C4C2×D4311yescharacteristic
347C22×C4⋊C4C2×D4311yescharacteristic
348C22×C22⋊C4—431no—
349C22×C22⋊C4—431no—
350C22×C22⋊C4—432no—
351C22×C22⋊C4—432no—
352C22×C22⋊C4C2×D4312yes—
353C22×C42—431no—
354#400—4316no—
355#399—4316no—
356#389—438no—
357#389—438no—
358#386—4316no—
359#385—4316no—
360#380—438no—
361#380—438no—
362#380C2×D4318yescomplemented
363C2×#95—432no—
364C2×#95—432no—
365C2×#95—432no—
366C2×#95—432no—
367C2×#95C2×D4312yes—
368C43C2×#248711yescharacteristic, complemented, Sylow
369C25—431no—
370C25C22×D4311yescharacteristic
371C22×D4—438no—
372C22×D4—434no—
373C22×D4—864no—
374C22×D4—864no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—431no—
379C23×C4—431no—
380C23×C4—438no—
381C23×C4—434no—
382C23×C4—431no—
383C23×C4—432no—
384C23×C4—432no—
385C23×C4—438no—
386C23×C4—868no—
387C23×C4—864no—
388C23×C4—864no—
389C23×C4—1724no—
390C23×C4—1724no—
391C23×C4C22×D4314yes—
392C23×C4C22×D4312yes—
393C23×C4C22×D4311yescharacteristic
394C23×C4C22×D4312yes—
395C23×C4C22×D4311yescharacteristic
396C4×D4—8632no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—438no—
400C2×C4⋊C4—434no—
401C2×C4⋊C4—434no—
402C2×C4⋊C4—434no—
403C2×C4⋊C4—438no—
404C2×C4⋊C4—438no—
405C2×C4⋊C4—8632no—
406C2×C4⋊C4—868no—
407C2×C4⋊C4—864no—
408C2×C4⋊C4—864no—
409C2×C4⋊C4—864no—
410C2×C4⋊C4—1724no—
411C2×C4⋊C4—1724no—
412C2×C4⋊C4C22×D4314yes—
413C2×C4⋊C4C22×D4314yes—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—434no—
416C2×C22⋊C4—434no—
417C2×C22⋊C4—438no—
418C2×C22⋊C4—438no—
419C2×C22⋊C4—864no—
420C2×C22⋊C4—868no—
421C2×C22⋊C4—864no—
422C2×C22⋊C4—1724no—
423C2×C22⋊C4C22×D4318yes—
424C2×C42—434no—
425C2×C42—864no—
426#95—438no—
427#95—438no—
428#95—438no—
429#95—438no—
430#95C22×D4318yes—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—434no—
438C24—434no—
439C24—434no—
440C24—432no—
441C24—862no—
442C24—862no—
443C24—862no—
444C24—862no—
445C24Q8×D4314yes—
446C24C23×D4312yes—
447C24C23×D4311yescharacteristic
448C2×D4—4316no—
449C2×D4—868no—
450C2×D4—8632no—
451C2×D4—868no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—416no—
465C22×C4—434no—
466C22×C4—434no—
467C22×C4—432no—
468C22×C4—432no—
469C22×C4—4316no—
470C22×C4—434no—
471C22×C4—434no—
472C22×C4—432no—
473C22×C4—8616no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—8632no—
479C22×C4—868no—
480C22×C4—868no—
481C22×C4—862no—
482C22×C4—864no—
483C22×C4—864no—
484C22×C4—864no—
485C22×C4—862no—
486C22×C4—864no—
487C22×C4—864no—
488C22×C4—864no—
489C22×C4—862no—
490C22×C4—1728no—
491C22×C4—1728no—
492C22×C4—17232no—
493C22×C4#1062189814yes—
494C22×C4D4×D4314yes—
495C22×C4#1062190014yes—
496C22×C4C23×D4312yes—
497C22×C4C23×D4314yes—
498C22×C4C23×D4314yes—
499C22×C4C23×D4312yes—
500C4⋊C4—28no—
501C4⋊C4—28no—
502C4⋊C4—8616no—
503C4⋊C4—868no—
504C4⋊C4—868no—
505C4⋊C4—868no—
506C4⋊C4—1728no—
507C4⋊C4—1728no—
508C22⋊C4—48no—
509C22⋊C4—868no—
510C22⋊C4—8616no—
511C22⋊C4—868no—
512C22⋊C4—1728no—
513C42—868no—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—4316no—
528C23—434no—
529C23—434no—
530C23—434no—
531C23—868no—
532C23—868no—
533C23—868no—
534C23—868no—
535C23—868no—
536C23—868no—
537C23—862no—
538C23—862no—
539C23—862no—
540C23—862no—
541C23C2×D4×D4312yes—
542C23C2×Q8×D4314yes—
543C23C2×Q8×D4312yes—
544C23#41×D4312yes—
545C23C2×#1062190012yes—
546C23C2×#1062189812yes—
547C23#1306337012yes—
548C23#1306337112yes—
549C23C24×D4311yescharacteristic
550D4—8632no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—48no—
561C2×C4—44no—
562C2×C4—48no—
563C2×C4—416no—
564C2×C4—434no—
565C2×C4—434no—
566C2×C4—868no—
567C2×C4—868no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—8632no—
573C2×C4—862no—
574C2×C4—864no—
575C2×C4—864no—
576C2×C4—864no—
577C2×C4—862no—
578C2×C4—864no—
579C2×C4—864no—
580C2×C4—864no—
581C2×C4—862no—
582C2×C4—17232no—
583C2×C4—1728no—
584C2×C4—1728no—
585C2×C4—1724no—
586C2×C4#13063307116yes—
587C2×C4C2×D4×D4314yes—
588C2×C4C2×#1062190014yes—
589C2×C4C2×#1062189814yes—
590C22—24no—
591C22—24no—
592C22—24no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—416no—
597C22—42no—
598C22—438no—
599C22—864no—
600C22—864no—
601C22—864no—
602C22—8632no—
603C22—864no—
604C22—864no—
605C22—864no—
606C22C22⋊Q8×D4314yes—
607C22C2×#1306330714yes—
608C22#1458346514yes—
609C22#1458359314yes—
610C22#1458359614yes—
611C22#1458360414yes—
612C22#1458360714yes—
613C22C22×D4×D4311yescharacteristic
614C22C22×Q8×D4311yescharacteristic
615C22C2×#41×D4311yescharacteristic
616C22C22×#1062190011yescharacteristic
617C22C22×#1062189811yescharacteristic
618C22C2×#1306337011yescharacteristic
619C22C2×#1306337111yescharacteristic
620C4—42no—
621C4—44no—
622C4—44no—
623C4—864no—
624C4—864no—
625C4—1724no—
626C4—1724no—
627C4—1722no—
628C4C2×#1306330718yes—
629C2—44no—
630C2—868no—
631C2#1913890818yesdirect product factor
632C2C2×C22⋊Q8×D4311yescharacteristic
633C2C22×#1306330711yescharacteristic
634C2C2×#1458346511yescharacteristic
635C2C2×#1458359311yescharacteristic
636C2C2×#1458359611yescharacteristic
637C2C2×#1458360411yescharacteristic
638C2C2×#1458360711yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#380C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#380D43
hypocenterC43C2×#2487
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D43C2semidirect
3. #19138908C2direct (N × H)
4. C2×#14582840C2semidirect
5. C2×#14582835C2semidirect
6. C2×#14582798C2semidirect
7. C2×#14582795C2semidirect
9. C2×#14582773C2semidirect
10. C2×#14582759C2semidirect
11. C2×#14582756C2semidirect
12. C2×C43×#380C2semidirect
25. C2×C4⋊C4×D43C22semidirect
31. #14582840C22semidirect
32. #14582835C22semidirect
33. #14582798C22semidirect
34. #14582795C22semidirect
36. #14582773C22semidirect
37. #14582759C22semidirect
38. #14582756C22semidirect
47. C43×#380C22semidirect
321. C2×#380D43semidirect
323. C2×C43#2487semidirect
362. #380C2×D43semidirect
368. C43C2×#2487semidirect
631. C2#19138908direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C22×C4⋊C4×D432
#191389082
C2×#145828402
C2×#145828352
C2×#145827982
C2×#145827952
C2×#145827752
C2×#145827732
C2×#145827592
C2×#145827562
C2×C43×#3802
C2×#248743