Finite Group Databasebeta

← C2×#19133601 #25068824

Subgroups — C2×#19133601 #25068824

Order 11008.

1028 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583528C211yesmaximal, characteristic
2C2×#14583229C211yesmaximal, characteristic
3C2×#14582830C211yesmaximal, characteristic
4#19133601C218yesmaximal, direct product factor
5C2×#14582637C211yesmaximal, characteristic
6C2×#14582636C211yesmaximal, characteristic
7C2×#14582624C211yesmaximal, characteristic
8C2×C43×#483C211yesmaximal, characteristic
9#14583528—22no—
10#14583528—22no—
11#14583528—22no—
12#14583528C2214yes—
13C2×#13063324—21no—
14C2×#13063323—21no—
15C2×#13063315—21no—
16C2×#13063315—21no—
17C2×#13063304C2211yescharacteristic
18C2×#13063302—21no—
19C2×#13063281—21no—
20C22×Dic43⋊C4—21no—
21C22×Dic43⋊C4C2211yescharacteristic
22#14583229—22no—
23#14583229C2214yes—
24C2×#13063256—21no—
25C2×#13063248—21no—
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27#14582830—22no—
28#14582830C2214yes—
29C2×C43⋊#95—21no—
30C2×C43⋊#95C2211yescharacteristic
31#14582637C2214yes—
32#14582636C2214yes—
33#14582624C2214yes—
34C2×C22⋊Q8×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C43×#483—22no—
37C43×#483C2214yes—
38C2×#106×C43—21no—
39C2×#103×C43—21no—
40C2×C22⋊C8×C43C2211yescharacteristic
41C22×Dic86—21no—
42C22×Dic86D411yescharacteristic
43C23×Dic43—21no—
44C23×Dic43D411yescharacteristic
45C23×Dic43D411yescharacteristic
46C22×C43⋊C8—21no—
47#13063324—24no—
48#13063324—24no—
49#13063323—24no—
50#13063323—24no—
51#13063315—24no—
52#13063315—24no—
53#13063315—24no—
54#13063315—24no—
55#13063304—21no—
56#13063304—21no—
57#13063304D412yes—
58#13063304C2312yes—
59#13063302—24no—
60#13063302—24no—
61#13063281—24no—
62#13063281—24no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43D411yescharacteristic
65C2×Dic43⋊C4—21no—
66C2×Dic43⋊C4—21no—
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—24no—
75C2×Dic43⋊C4—44no—
76C2×Dic43⋊C4D412yes—
77C2×Dic43⋊C4C2312yes—
78C2×C22⋊Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81#13063256—24no—
82#13063248—24no—
83C22⋊(C43⋊C8)—21no—
84C22⋊(C43⋊C8)C2312yes—
85C43⋊#95—21no—
86C43⋊#95—24no—
87C43⋊#95C2312yes—
88C22×Q8×C43D411yescharacteristic
89C23×C4×C43—21no—
90C23×C4×C43C2311yescharacteristic
91C22×C8×C43—21no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43D412yes—
95C22⋊Q8×C43C2312yes—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C4⋊C4×C43C2312yes—
104C2×C22⋊C4×C43—21no—
105#106×C43—24no—
106#103×C43—24no—
107C22⋊C8×C43—21no—
108C22⋊C8×C43C2312yes—
109C24×C43C2×D411yescharacteristic
110C2×Q8×C43—21no—
111C2×Q8×C43—42no—
112C2×Q8×C43C2×D412yes—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—42no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43—42no—
120C22×C4×C43—42no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C22×Dic43—24no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—42no—
137C22×Dic43—42no—
138C22×Dic43—42no—
139C22×Dic43SD1614yes—
140C22×Dic43C2×D412yes—
141C22×Dic43C2×D412yes—
142C2×Dic86—24no—
143C2×Dic86—21no—
144C2×Dic86—42no—
145C2×Dic86—82no—
146C2×Dic86C2×D412yes—
147C2×C8×C43—22no—
148C2×C8×C43—42no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—41no—
155C4⋊C4×C43—41no—
156C4⋊C4×C43C2×D412yes—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159C22⋊Dic43—22no—
160C22⋊Dic43—22no—
161C4⋊Dic43—24no—
162C4⋊Dic43—21no—
163C4⋊Dic43C2×D412yes—
164Dic43⋊C4—24no—
165Dic43⋊C4—24no—
166Dic43⋊C4—24no—
167Dic43⋊C4—24no—
168Dic43⋊C4—22no—
169Dic43⋊C4—22no—
170Dic43⋊C4—22no—
171Dic43⋊C4—22no—
172Dic43⋊C4—22no—
173Dic43⋊C4—22no—
174Dic43⋊C4—48no—
175C4×Dic43—24no—
176C4×Dic43—24no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—42no—
179C23×C43—22no—
180C23×C43—22no—
181C23×C43#12011yescharacteristic
182C23×C43#12011yescharacteristic
183C23×C43C2×SD1612yes—
184C23×C43#13712yes—
185C23×C43C22×D411yescharacteristic
186Q8×C43—42no—
187Q8×C43—81no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—82no—
202C2×C4×C43—82no—
203C2×C4×C43#12011yescharacteristic
204C2×C4×C43#12011yescharacteristic
205C2×C4×C43C22×D411yescharacteristic
206C2×C4×C43C22×D411yescharacteristic
207C2×Dic43—22no—
208C2×Dic43—22no—
209C2×Dic43—24no—
210C2×Dic43—24no—
211C2×Dic43—24no—
212C2×Dic43—22no—
213C2×Dic43—22no—
214C2×Dic43—22no—
215C2×Dic43—48no—
216C2×Dic43—42no—
217C2×Dic43—42no—
218C2×Dic43—42no—
219C2×Dic43—42no—
220C2×Dic43—42no—
221C2×Dic43—42no—
222C2×Dic43—81no—
223C2×Dic43C2×SD1614yes—
224Dic86—42no—
225Dic86—81no—
226Dic86—84no—
227C8×C43—42no—
228C43⋊C8—42no—
229C2×#1611—431nomaximal, Sylow
230C22×C43—24no—
231C22×C43—24no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43#44812yes—
237C22×C43#44812yes—
238C22×C43#45612yes—
239C22×C43#45812yes—
240C22×C43C2×#12011yescharacteristic
241C22×C43C22×SD1611yescharacteristic
242C22×C43C2×#13711yescharacteristic
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—42no—
248C4×C43—42no—
249C4×C43—82no—
250Dic43—24no—
251Dic43—44no—
252Dic43—42no—
253Dic43—42no—
254Dic43—42no—
255C2×#544—431no—
256C2×#483—431no—
257C2×#483D4311yescharacteristic
258C2×#398—431no—
259#1611—438no—
260C2×#328—431no—
261C2×#328—431no—
262C2×#324—431no—
263C2×C43—21no—
264C2×C43—21no—
265C2×C43—22no—
266C2×C43#161114yescomplemented
267C2×C43C2×#44811yescharacteristic
268C2×C43C2×#45611yescharacteristic
269C2×C43C2×#45811yescharacteristic
270#544—434no—
271#544—862no—
272#544—862no—
273#544—862no—
274C2×C4⋊Q8—861no—
275C2×C4⋊Q8—861no—
276C2×#125—861no—
277C2×#125—861no—
278C2×C22⋊Q8—431no—
279C2×C22⋊Q8—861no—
280C2×C22⋊Q8C2×D4311yescharacteristic
281C2×#117—861no—
282C22×C4⋊C4—431no—
283C22×C4⋊C4—861no—
284C22×C4⋊C4C2×D4311yescharacteristic
285#483—22no—
286#483—434no—
287#483—862no—
288#483C2×D4314yes—
289C2×#106—21no—
290C2×#106—861no—
291C2×#103—21no—
292C2×#103—861no—
293C2×C22⋊C8—431no—
294C2×C22⋊C8C2×D4311yescharacteristic
295#398—434no—
296#398—862no—
297C2×#95—431no—
298C2×#95—861no—
299#328—434no—
300#328—434no—
301#324—434no—
302C43C2×#161111yescharacteristic, complemented, Sylow
303C22×Q8—431no—
304C22×Q8—861no—
305C22×Q8C22⋊D4311yescharacteristic
306C23×C4—21no—
307C23×C4—431no—
308C23×C4—431no—
309C23×C4—861no—
310C23×C4C22×D4311yescharacteristic
311C22×C8—21no—
312C22×C8—861no—
313C4⋊Q8—864no—
314C4⋊Q8—864no—
315C4⋊Q8—864no—
316C4⋊Q8—864no—
317#125—864no—
318#125—864no—
319#125—864no—
320#125—864no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—432no—
324C22⋊Q8—432no—
325C22⋊Q8—864no—
326C22⋊Q8—864no—
327C22⋊Q8—861no—
328C22⋊Q8—861no—
329C22⋊Q8C22⋊D4312yes—
330C22⋊Q8C22×D4312yes—
331#117—864no—
332#117—864no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—431no—
340C2×C4⋊C4—432no—
341C2×C4⋊C4—432no—
342C2×C4⋊C4—861no—
343C2×C4⋊C4—861no—
344C2×C4⋊C4—861no—
345C2×C4⋊C4—861no—
346C2×C4⋊C4—861no—
347C2×C4⋊C4—861no—
348C2×C4⋊C4—861no—
349C2×C4⋊C4—861no—
350C2×C4⋊C4—861no—
351C2×C4⋊C4—861no—
352C2×C4⋊C4—864no—
353C2×C4⋊C4—1724no—
354C2×C4⋊C4C22⋊D4311yescharacteristic
355C2×C4⋊C4C22×D4312yes—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—861no—
358C2×C42—861no—
359C2×C42—861no—
360#106—24no—
361#106—864no—
362#103—24no—
363#103—864no—
364C22⋊C8—21no—
365C22⋊C8—432no—
366C22⋊C8—861no—
367C22⋊C8C22×D4312yes—
368#95—432no—
369#95—864no—
370#95—861no—
371C24D4×D4311yescharacteristic
372C2×Q8—21no—
373C2×Q8—42no—
374C2×Q8—432no—
375C2×Q8—864no—
376C2×Q8—861no—
377C2×Q8—3442no—
378C2×Q8—1722no—
379C2×Q8C2×C22⋊D4312yes—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—42no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—434no—
389C22×C4—432no—
390C22×C4—432no—
391C22×C4—861no—
392C22×C4—861no—
393C22×C4—862no—
394C22×C4—861no—
395C22×C4—864no—
396C22×C4—861no—
397C22×C4—861no—
398C22×C4—861no—
399C22×C4—862no—
400C22×C4—1722no—
401C22×C4—1722no—
402C22×C4—1722no—
403C22×C4D4×D4311yescharacteristic
404C22×C4D4×D4311yescharacteristic
405C22×C4D4×D4311yescharacteristic
406C22×C4C2×C22⋊D4311yescharacteristic
407C22×C4C2×C22⋊D4311yescharacteristic
408C22×C4C23×D4311yescharacteristic
409C2×C8—22no—
410C2×C8—42no—
411C2×C8—862no—
412C2×C8—1722no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—432no—
421C4⋊C4—864no—
422C4⋊C4—864no—
423C4⋊C4—864no—
424C4⋊C4—864no—
425C4⋊C4—864no—
426C4⋊C4—862no—
427C4⋊C4—862no—
428C4⋊C4—861no—
429C4⋊C4—862no—
430C4⋊C4—862no—
431C4⋊C4—862no—
432C4⋊C4—862no—
433C4⋊C4—1728no—
434C4⋊C4C2×C22⋊D4312yes—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—862no—
438C22⋊C4—862no—
439C42—864no—
440C42—864no—
441C23—22no—
442C23—22no—
443C23#1306329311yescharacteristic
444C23#1306329311yescharacteristic
445C23SD16×D4312yes—
446C23#1306335412yes—
447C23C2×D4×D4311yescharacteristic
448Q8—42no—
449Q8—81no—
450Q8—3441no—
451Q8—3444no—
452Q8—1722no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4—434no—
469C2×C4—862no—
470C2×C4—862no—
471C2×C4—864no—
472C2×C4—864no—
473C2×C4—864no—
474C2×C4—862no—
475C2×C4—862no—
476C2×C4—862no—
477C2×C4—3441no—
478C2×C4—1722no—
479C2×C4—1728no—
480C2×C4—1722no—
481C2×C4—1722no—
482C2×C4—1722no—
483C2×C4—1722no—
484C2×C4—1722no—
485C2×C4#1306329311yescharacteristic
486C2×C4#1306329311yescharacteristic
487C2×C4C2×D4×D4311yescharacteristic
488C2×C4C22×C22⋊D4311yescharacteristic
489C8—42no—
490C8—1722no—
491C22—21no—
492C22—21no—
493C22—24no—
494C22—24no—
495C22—21no—
496C22—21no—
497C22#1458303612yes—
498C22#1458303612yes—
499C22#1458308012yes—
500C22#1458308812yes—
501C22C2×#1306329311yescharacteristic
502C22C2×SD16×D4311yescharacteristic
503C22C2×#1306335411yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—42no—
509C4—42no—
510C4—82no—
511C4—864no—
512C4—1724no—
513C4—1722no—
514C4—1722no—
515C4—1722no—
516C2—21no—
517C2—21no—
518C2—22no—
519C2#1913360114yesdirect product factor
520C2C2×#1458303611yescharacteristic
521C2C2×#1458308011yescharacteristic
522C2C2×#1458308811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#483C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenterC2×#483D43
hypocenterC43C2×#1611
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
4. #19133601C2direct (N × H)
266. C2×C43#1611semidirect
302. C43C2×#1611semidirect
519. C2#19133601direct (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×#145832292
C2×#145828302
#191336012
C2×#145826372
C2×#145826362
C2×#145826242
C2×C43×#4832
C2×#161143