Finite Group Databasebeta

← C2×#19133604 #25068827

Subgroups — C2×#19133604 #25068827

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×#14583230C211yesmaximal, characteristic
3C2×#14583227C211yesmaximal, characteristic
4C2×#14582831C211yesmaximal, characteristic
5#19133604C218yesmaximal, direct product factor
6C2×#14582635C211yesmaximal, characteristic
7C2×#14582624C211yesmaximal, characteristic
8C2×C43×#328C211yesmaximal, 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×C4⋊Dic43—21no—
21C22×C4⋊Dic43C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23#14583230—22no—
24#14583230C2214yes—
25#14583227—22no—
26#14583227C2214yes—
27C2×#13063257—21no—
28C2×#13063256—21no—
29C2×#13063250—21no—
30C2×#13063249—21no—
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32#14582831—22no—
33#14582831C2214yes—
34C2×C43⋊#95—21no—
35#14582635C2214yes—
36#14582624C2214yes—
37C2×C22⋊Q8×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C43×#328C2214yes—
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⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—24no—
70C2×C4⋊Dic43—44no—
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43C2312yes—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4D412yes—
83C2×Dic43⋊C4C2312yes—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87#13063257—24no—
88#13063256—24no—
89#13063250—24no—
90#13063249—24no—
91C22⋊(C43⋊C8)—21no—
92C22⋊(C43⋊C8)C2312yes—
93C43⋊#95—24no—
94C22×Q8×C43D411yescharacteristic
95C23×C4×C43—21no—
96C23×C4×C43C2311yescharacteristic
97C22×C8×C43—21no—
98C22⋊Q8×C43—21no—
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43D412yes—
101C22⋊Q8×C43C2312yes—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C22⋊C4×C43—21no—
105C22⋊C8×C43—21no—
106C22⋊C8×C43C2312yes—
107#95×C43—21no—
108#95×C43C2312yes—
109C24×C43C2×D411yescharacteristic
110C2×Q8×C43—21no—
111C2×Q8×C43—42no—
112C2×Q8×C43C2×D412yes—
113C22×C4×C43—24no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—42no—
118C22×C4×C43—42no—
119C22×C4×C43—42no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2411yescharacteristic
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—42no—
135C22×Dic43—41no—
136C22×Dic43—41no—
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×C43C2×D412yes—
153C22⋊C4×C43—22no—
154C22⋊C4×C43—22no—
155C22⋊Dic43—22no—
156C22⋊Dic43—22no—
157C4⋊Dic43—24no—
158C4⋊Dic43—21no—
159C4⋊Dic43—22no—
160C4⋊Dic43—22no—
161C4⋊Dic43—41no—
162C4⋊Dic43—41no—
163C4⋊Dic43—48no—
164C4⋊Dic43C2×D412yes—
165Dic43⋊C4—24no—
166Dic43⋊C4—24no—
167Dic43⋊C4—24no—
168Dic43⋊C4—24no—
169Dic43⋊C4—22no—
170Dic43⋊C4—22no—
171Dic43⋊C4—22no—
172Dic43⋊C4—22no—
173Dic43⋊C4—22no—
174Dic43⋊C4—22no—
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—24no—
191C2×C4×C43—22no—
192C2×C4×C43—22no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—48no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43#12011yescharacteristic
203C2×C4×C43#12011yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C2×C4×C43C22×D411yescharacteristic
206C2×Dic43—22no—
207C2×Dic43—22no—
208C2×Dic43—24no—
209C2×Dic43—24no—
210C2×Dic43—22no—
211C2×Dic43—22no—
212C2×Dic43—22no—
213C2×Dic43—42no—
214C2×Dic43—42no—
215C2×Dic43—42no—
216C2×Dic43—42no—
217C2×Dic43—42no—
218C2×Dic43—42no—
219C2×Dic43—42no—
220C2×Dic43—81no—
221C2×Dic43—82no—
222C2×Dic43—82no—
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—44no—
248C4×C43—42no—
249C4×C43—42no—
250Dic43—24no—
251Dic43—42no—
252Dic43—42no—
253Dic43—42no—
254Dic43—82no—
255C2×#544—431no—
256C2×#483—431no—
257C2×#483—431no—
258C2×#398—431no—
259#1611—438no—
260C2×#328—431no—
261C2×#328D4311yescharacteristic
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—431no—
284C22×C4⋊C4—861no—
285#483—434no—
286#483—434no—
287#483—862no—
288#483—862no—
289C2×#106—861no—
290C2×#106—861no—
291C2×#103—861no—
292C2×#103—861no—
293C2×C22⋊C8—431no—
294C2×C22⋊C8C2×D4311yescharacteristic
295#398—434no—
296#398—862no—
297C2×#95—861no—
298C2×#95C2×D4311yescharacteristic
299#328—434no—
300#328C2×D4314yes—
301#324—434no—
302C43C2×#161111yescharacteristic, complemented, Sylow
303C22×Q8—431no—
304C22×Q8—861no—
305C22×Q8D17211yescharacteristic
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⋊Q8D17212yes—
330C22⋊Q8C22×D4312yes—
331#117—864no—
332#117—864no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—431no—
335C2×C4⋊C4—432no—
336C2×C4⋊C4—432no—
337C2×C4⋊C4—432no—
338C2×C4⋊C4—861no—
339C2×C4⋊C4—861no—
340C2×C4⋊C4—861no—
341C2×C4⋊C4—861no—
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—861no—
354C2×C4⋊C4—1724no—
355C2×C4⋊C4D17211yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—861no—
358C2×C42—861no—
359C2×C42—861no—
360#106—864no—
361#106—864no—
362#103—864no—
363#103—864no—
364C22⋊C8—21no—
365C22⋊C8—432no—
366C22⋊C8—861no—
367C22⋊C8C22×D4312yes—
368#95—21no—
369#95—864no—
370#95C22×D4312yes—
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×D17212yes—
380C22×C4—24no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—434no—
388C22×C4—432no—
389C22×C4—432no—
390C22×C4—861no—
391C22×C4—861no—
392C22×C4—862no—
393C22×C4—861no—
394C22×C4—861no—
395C22×C4—861no—
396C22×C4—861no—
397C22×C4—862no—
398C22×C4—1721no—
399C22×C4—1721no—
400C22×C4—1722no—
401C22×C4—1722no—
402C22×C4—1722no—
403C22×C4C2×D17211yescharacteristic
404C22×C4C2×D17211yescharacteristic
405C22×C4D4×D4311yescharacteristic
406C22×C4D4×D4311yescharacteristic
407C22×C4D4×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—432no—
417C4⋊C4—864no—
418C4⋊C4—864no—
419C4⋊C4—864no—
420C4⋊C4—864no—
421C4⋊C4—864no—
422C4⋊C4—862no—
423C4⋊C4—862no—
424C4⋊C4—861no—
425C4⋊C4—862no—
426C4⋊C4—862no—
427C4⋊C4—862no—
428C4⋊C4—862no—
429C4⋊C4—862no—
430C4⋊C4—862no—
431C4⋊C4—1728no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C4⋊C4C2×D17212yes—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—862no—
438C22⋊C4—862no—
439C42—864no—
440C42—864no—
441C23—22no—
442C23—22no—
443C23#1306329511yescharacteristic
444C23#1306329511yescharacteristic
445C23SD16×D4312yes—
446C23#1306335712yes—
447C23C2×D4×D4311yescharacteristic
448Q8—42no—
449Q8—81no—
450Q8—3441no—
451Q8—3444no—
452Q8—1722no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—48no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—434no—
468C2×C4—862no—
469C2×C4—862no—
470C2×C4—864no—
471C2×C4—864no—
472C2×C4—862no—
473C2×C4—862no—
474C2×C4—862no—
475C2×C4—3442no—
476C2×C4—3442no—
477C2×C4—3441no—
478C2×C4—1722no—
479C2×C4—1722no—
480C2×C4—1722no—
481C2×C4—1722no—
482C2×C4—1722no—
483C2×C4—1722no—
484C2×C4—1722no—
485C2×C4#1306329511yescharacteristic
486C2×C4#1306329511yescharacteristic
487C2×C4C2×D4×D4311yescharacteristic
488C2×C4C22×D17211yescharacteristic
489C8—42no—
490C8—1722no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—24no—
496C22—24no—
497C22#1458303912yes—
498C22#1458303912yes—
499C22#1458308312yes—
500C22#1458309012yes—
501C22C2×#1306329511yescharacteristic
502C22C2×SD16×D4311yescharacteristic
503C22C2×#1306335711yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—44no—
509C4—42no—
510C4—42no—
511C4—864no—
512C4—3442no—
513C4—1722no—
514C4—1722no—
515C4—1722no—
516C2—21no—
517C2—21no—
518C2—22no—
519C2#1913360414yesdirect product factor
520C2C2×#1458303911yescharacteristic
521C2C2×#1458308311yescharacteristic
522C2C2×#1458309011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#328C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenterC2×#328D43
hypocenterC43C2×#1611
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
5. #19133604C2direct (N × H)
266. C2×C43#1611semidirect
302. C43C2×#1611semidirect
519. C2#19133604direct (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×#145832302
C2×#145832272
C2×#145828312
#191336042
C2×#145826352
C2×#145826242
C2×C43×#3282
C2×#161143