Finite Group Databasebeta

← C2×#19133567 #25068779

Subgroups — C2×#19133567 #25068779

Order 11008.

1200 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583528C211yesmaximal, characteristic
2C2×#14583055C211yesmaximal, characteristic
3C2×#14582818C211yesmaximal, characteristic
4#19133567C218yesmaximal, direct product factor
5C2×#14582637C211yesmaximal, characteristic
6C2×#14582636C211yesmaximal, characteristic
7C2×#14582624C211yesmaximal, characteristic
8C2×C43×#451C211yesmaximal, characteristic
9C22×#10621885—21no—
10#14583528—22no—
11#14583528—22no—
12#14583528—22no—
13#14583528C2214yes—
14C2×#13063324—21no—
15C2×#13063323—21no—
16C2×#13063315—21no—
17C2×#13063315—21no—
18C2×#13063304C2211yescharacteristic
19C2×#13063302—21no—
20C2×#13063281—21no—
21C22×Dic43⋊C4—21no—
22C22×Dic43⋊C4C2211yescharacteristic
23#14583055—22no—
24#14583055C2214yes—
25C2×#13063249—21no—
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27#14582818—22no—
28#14582818C2214yes—
29C2×C43⋊#95—21no—
30C2×C43⋊#95C2211yescharacteristic
31#14582637C2214yes—
32#14582636C2214yes—
33#14582624C2214yes—
34C23×Q8×C43C2211yescharacteristic
35C22×Q16×C43—21no—
36C2×C22⋊Q8×C43C2211yescharacteristic
37C43×#451—22no—
38C43×#451C2214yes—
39C2×#103×C43—21no—
40C2×C22⋊C8×C43C2211yescharacteristic
41C22×Dic86—21no—
42C22×Dic86D411yescharacteristic
43C23×Dic43—21no—
44C23×Dic43D411yescharacteristic
45C23×Dic43D411yescharacteristic
46C2×#10621885—24no—
47C2×#10621885—44no—
48C22×C43⋊C8—21no—
49#13063324—24no—
50#13063324—24no—
51#13063323—24no—
52#13063323—24no—
53#13063315—24no—
54#13063315—24no—
55#13063315—24no—
56#13063315—24no—
57#13063304—21no—
58#13063304—21no—
59#13063304D412yes—
60#13063304C2312yes—
61#13063302—24no—
62#13063302—24no—
63#13063281—24no—
64#13063281—24no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43D411yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—24no—
77C2×Dic43⋊C4—44no—
78C2×Dic43⋊C4D412yes—
79C2×Dic43⋊C4C2312yes—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83#13063249—24no—
84C22⋊(C43⋊C8)—21no—
85C22⋊(C43⋊C8)C2312yes—
86C43⋊#95—21no—
87C43⋊#95—24no—
88C43⋊#95C2312yes—
89C22×Q8×C43—21no—
90C22×Q8×C43—21no—
91C22×Q8×C43—21no—
92C22×Q8×C43—21no—
93C22×Q8×C43—21no—
94C22×Q8×C43—44no—
95C22×Q8×C43D411yescharacteristic
96C22×Q8×C43C2312yes—
97C23×C4×C43—21no—
98C23×C4×C43C2311yescharacteristic
99C2×Q16×C43—24no—
100C2×Q16×C43—44no—
101C22×C8×C43—21no—
102C22⋊Q8×C43—21no—
103C22⋊Q8×C43—21no—
104C22⋊Q8×C43D412yes—
105C22⋊Q8×C43C2312yes—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43D411yescharacteristic
108C2×C22⋊C4×C43—21no—
109#103×C43—24no—
110C22⋊C8×C43—21no—
111C22⋊C8×C43C2312yes—
112C24×C43C2×D411yescharacteristic
113C2×Q8×C43—21no—
114C2×Q8×C43—24no—
115C2×Q8×C43—24no—
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C2×Q8×C43—44no—
119C2×Q8×C43—42no—
120C2×Q8×C43—42no—
121C2×Q8×C43—44no—
122C2×Q8×C43—42no—
123C2×Q8×C43—44no—
124C2×Q8×C43—44no—
125C2×Q8×C43—41no—
126C2×Q8×C43—41no—
127C2×Q8×C43C2×D412yes—
128C22×C4×C43—24no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—22no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43—41no—
135C22×C4×C43—41no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—24no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—42no—
154C22×Dic43Q1614yescomplemented
155C22×Dic43C2×D412yes—
156C22×Dic43C2×D412yes—
157C2×Dic86—24no—
158C2×Dic86—21no—
159C2×Dic86—42no—
160C2×Dic86—82no—
161C2×Dic86C2×D412yes—
162Q16×C43—48no—
163C2×C8×C43—22no—
164C2×C8×C43—42no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43C2×D412yes—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊Dic43—22no—
172C22⋊Dic43—22no—
173#10621885—48no—
174C4⋊Dic43—24no—
175C4⋊Dic43—21no—
176C4⋊Dic43C2×D412yes—
177Dic43⋊C4—24no—
178Dic43⋊C4—24no—
179Dic43⋊C4—24no—
180Dic43⋊C4—24no—
181Dic43⋊C4—22no—
182Dic43⋊C4—22no—
183Dic43⋊C4—22no—
184Dic43⋊C4—22no—
185Dic43⋊C4—22no—
186Dic43⋊C4—22no—
187Dic43⋊C4—48no—
188C4×Dic43—24no—
189C4×Dic43—24no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—42no—
192C23×C43—22no—
193C23×C43—22no—
194C23×C43#12011yescharacteristic
195C23×C43#12011yescharacteristic
196C23×C43C2×Q1612yes—
197C23×C43#13712yes—
198C23×C43C22×D411yescharacteristic
199Q8×C43—24no—
200Q8×C43—24no—
201Q8×C43—42no—
202Q8×C43—42no—
203Q8×C43—42no—
204Q8×C43—44no—
205Q8×C43—44no—
206Q8×C43—81no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—24no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—44no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—44no—
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#12011yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×Dic43—22no—
227C2×Dic43—22no—
228C2×Dic43—24no—
229C2×Dic43—24no—
230C2×Dic43—24no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—42no—
235C2×Dic43—48no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—81no—
242C2×Dic43C2×Q1614yescomplemented
243Dic86—42no—
244Dic86—81no—
245Dic86—84no—
246C8×C43—42no—
247C43⋊C8—42no—
248C2×#1605—431nomaximal, Sylow
249C22×C43—24no—
250C22×C43—24no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43#45112yes—
256C22×C43#45112yes—
257C22×C43#45612yes—
258C22×C43B(4,𝔽2)12yes—
259C22×C43C2×#12011yescharacteristic
260C22×C43C22×Q1611yescharacteristic
261C22×C43C2×#13711yescharacteristic
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—42no—
267C4×C43—42no—
268C4×C43—44no—
269Dic43—24no—
270Dic43—44no—
271Dic43—42no—
272Dic43—42no—
273Dic43—42no—
274C2×#544—431no—
275C2×#451—431no—
276C2×#451D4311yescharacteristic
277C2×#395—431no—
278#1605—438no—
279C2×#328—431no—
280C2×#328—431no—
281C2×#324—431no—
282C2×C43—21no—
283C2×C43—21no—
284C2×C43—22no—
285C2×C43#160514yescomplemented
286C2×C43C2×#45111yescharacteristic
287C2×C43C2×#45611yescharacteristic
288C2×C43C2×B(4,𝔽2)11yescharacteristic
289C23×Q8C2×D4311yescharacteristic
290C22×Q16—21no—
291C22×Q16—861no—
292#544—434no—
293#544—862no—
294#544—862no—
295#544—862no—
296C2×C4⋊Q8—861no—
297C2×C4⋊Q8—861no—
298C2×#125—861no—
299C2×#125—861no—
300C2×C22⋊Q8—431no—
301C2×C22⋊Q8—861no—
302C2×C22⋊Q8C2×D4311yescharacteristic
303C2×#117—861no—
304C22×C4⋊C4—431no—
305C22×C4⋊C4—861no—
306#451—22no—
307#451—434no—
308#451—862no—
309#451C2×D4314yes—
310C2×#103—21no—
311C2×#103—861no—
312C2×C22⋊C8—431no—
313C2×C22⋊C8C2×D4311yescharacteristic
314#395—434no—
315#395—862no—
316C2×#95—431no—
317C2×#95—861no—
318#328—434no—
319#328—434no—
320#324—434no—
321C43C2×#160511yescharacteristic, complemented, Sylow
322C22×Q8—21no—
323C22×Q8—21no—
324C22×Q8—21no—
325C22×Q8—21no—
326C22×Q8—21no—
327C22×Q8—44no—
328C22×Q8—431no—
329C22×Q8—861no—
330C22×Q8C22⋊D4311yescharacteristic
331C22×Q8C22×D4312yes—
332C23×C4—21no—
333C23×C4—431no—
334C23×C4—431no—
335C23×C4—861no—
336C23×C4C22×D4311yescharacteristic
337C2×Q16—24no—
338C2×Q16—44no—
339C2×Q16—864no—
340C2×Q16—1724no—
341C22×C8—21no—
342C22×C8—861no—
343C4⋊Q8—864no—
344C4⋊Q8—864no—
345C4⋊Q8—864no—
346C4⋊Q8—864no—
347#125—864no—
348#125—864no—
349#125—864no—
350#125—864no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—432no—
354C22⋊Q8—432no—
355C22⋊Q8—864no—
356C22⋊Q8—864no—
357C22⋊Q8—861no—
358C22⋊Q8—861no—
359C22⋊Q8C22⋊D4312yes—
360C22⋊Q8C22×D4312yes—
361#117—864no—
362#117—864no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—432no—
366C2×C4⋊C4—432no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—864no—
378C2×C4⋊C4—1724no—
379C2×C4⋊C4C22⋊D4311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—861no—
382C2×C42—861no—
383C2×C42—861no—
384#103—24no—
385#103—864no—
386C22⋊C8—21no—
387C22⋊C8—432no—
388C22⋊C8—861no—
389C22⋊C8C22×D4312yes—
390#95—432no—
391#95—864no—
392#95—861no—
393C24D4×D4311yescharacteristic
394C2×Q8—21no—
395C2×Q8—24no—
396C2×Q8—24no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—44no—
400C2×Q8—42no—
401C2×Q8—42no—
402C2×Q8—44no—
403C2×Q8—42no—
404C2×Q8—44no—
405C2×Q8—44no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—432no—
409C2×Q8—864no—
410C2×Q8—861no—
411C2×Q8—3442no—
412C2×Q8—1722no—
413C2×Q8C2×C22⋊D4312yes—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—434no—
423C22×C4—432no—
424C22×C4—432no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—862no—
428C22×C4—861no—
429C22×C4—864no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—862no—
434C22×C4—1722no—
435C22×C4—1722no—
436C22×C4—1722no—
437C22×C4D4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439C22×C4D4×D4311yescharacteristic
440C22×C4C2×C22⋊D4311yescharacteristic
441C22×C4C2×C22⋊D4311yescharacteristic
442C22×C4C23×D4311yescharacteristic
443Q16—48no—
444Q16—1728no—
445C2×C8—22no—
446C2×C8—42no—
447C2×C8—862no—
448C2×C8—1722no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—432no—
453C4⋊C4—864no—
454C4⋊C4—864no—
455C4⋊C4—864no—
456C4⋊C4—864no—
457C4⋊C4—864no—
458C4⋊C4—862no—
459C4⋊C4—862no—
460C4⋊C4—861no—
461C4⋊C4—862no—
462C4⋊C4—862no—
463C4⋊C4—862no—
464C4⋊C4—862no—
465C4⋊C4—1728no—
466C4⋊C4C2×C22⋊D4312yes—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—862no—
470C22⋊C4—862no—
471C42—864no—
472C42—864no—
473C23—22no—
474C23—22no—
475C23#1306329311yescharacteristic
476C23#1306329311yescharacteristic
477C23Q16×D4312yes—
478C23#1306335712yes—
479C23C2×D4×D4311yescharacteristic
480Q8—24no—
481Q8—24no—
482Q8—42no—
483Q8—42no—
484Q8—42no—
485Q8—44no—
486Q8—44no—
487Q8—81no—
488Q8—3441no—
489Q8—3444no—
490Q8—1722no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—434no—
507C2×C4—864no—
508C2×C4—864no—
509C2×C4—862no—
510C2×C4—862no—
511C2×C4—864no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—862no—
515C2×C4—3441no—
516C2×C4—1722no—
517C2×C4—1728no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4—1722no—
522C2×C4—1722no—
523C2×C4#1306329311yescharacteristic
524C2×C4#1306329311yescharacteristic
525C2×C4C2×D4×D4311yescharacteristic
526C2×C4C22×C22⋊D4311yescharacteristic
527C8—42no—
528C8—1722no—
529C22—21no—
530C22—21no—
531C22—24no—
532C22—24no—
533C22—21no—
534C22—21no—
535C22#1458305312yes—
536C22#1458305312yes—
537C22#1458308012yes—
538C22#1458308512yes—
539C22C2×#1306329311yescharacteristic
540C22C2×Q16×D4311yescharacteristic
541C22C2×#1306335711yescharacteristic
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—44no—
547C4—42no—
548C4—42no—
549C4—864no—
550C4—1724no—
551C4—1722no—
552C4—1722no—
553C4—1722no—
554C2—21no—
555C2—22no—
556C2—21no—
557C2#1913356714yesdirect product factor
558C2C2×#1458305311yescharacteristic
559C2C2×#1458308011yescharacteristic
560C2C2×#1458308511yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#451C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenterC2×#451D43
hypocenterC43C2×#1605
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
4. #19133567C2direct (N × H)
154. C22×Dic43Q16semidirect
242. C2×Dic43C2×Q16semidirect
285. C2×C43#1605semidirect
321. C43C2×#1605semidirect
557. C2#19133567direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835282
C2×#145830552
C2×#145828182
#191335672
C2×#145826372
C2×#145826362
C2×#145826242
C2×C43×#4512
C2×#160543