Finite Group Databasebeta

← C2×#19145116 #25966210

Subgroups — C2×#19145116 #25966210

Order 11008.

1902 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583455C211yesmaximal, characteristic
2C2×#14583454C211yesmaximal, characteristic
3#19145116C2116yesmaximal, direct product factor
4C2×#14583309C211yesmaximal, characteristic, complemented
5C2×#14583308C211yesmaximal, characteristic, complemented
6C2×#14583307C212yesmaximal, complemented
7C2×#14583306C212yesmaximal, complemented
8C2×#14583305C211yesmaximal, characteristic, complemented
9C2×#14582936C212yesmaximal
10C2×#14582934C212yesmaximal
11C2×#97×D43C211yesmaximal, characteristic
12C2×C43×#501C211yesmaximal, characteristic, complemented
13C22×C8×D43C2212yes—
14#14583455—24no—
15#14583455C2218yes—
16#14583454—24no—
17#14583454C2218yes—
18C2×#13063325C2211yescharacteristic
19C2×#13063324C2211yescharacteristic
20C2×#13063324C2211yescharacteristic
21C2×#13063317C2211yescharacteristic
22C2×#13063316C2212yes—
23C2×#13063305—21no—
24C2×#13063303—21no—
25C2×#13063303—21no—
26C2×#13063301—21no—
27C2×Q8×Dic43—21no—
28C2×#13063290—21no—
29C2×#13063290—21no—
30C2×#13063290—21no—
31C2×#13063283C2211yescharacteristic
32C2×#13063283C2212yes—
33C2×#13063283C2211yescharacteristic
34C2×C42×D43C2211yescharacteristic
35#14583309C2218yescomplemented
36#14583308C2218yescomplemented
37#14583307C22116yescomplemented
38#14583306C22116yescomplemented
39#14583305C2218yescomplemented
40#14582936C22116yes—
41#14582934C22116yes—
42C2×#13063259C2212yes—
43C2×#13063258C2212yes—
44C2×#13063258C2212yes—
45C2×#13063257C2212yes—
46C2×#13063256C2212yes—
47C2×#13063256C2212yes—
48C2×#13063236C2211yescharacteristic
49C2×#13063235C2212yes—
50#97×D43C2218yes—
51C2×C4⋊Q8×C43C2211yescharacteristic
52C2×#125×C43C2211yescharacteristic
53C43×#501C2218yescomplemented
54C2×#107×C43C2212yes—
55C2×#106×C43C2212yes—
56C2×#97×C43C2211yescharacteristic
57C22×Dic86—21no—
58C22×Dic86—21no—
59C22×Dic86—21no—
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2312yes—
64C2×C8×D43Q8116yescomplemented
65C2×C8×D43C2318yes—
66#13063325—22no—
67#13063325C2314yes—
68#13063324—22no—
69#13063324—22no—
70#13063324C2314yes—
71#13063324C2314yes—
72#13063317—22no—
73#13063317C2314yes—
74#13063316—24no—
75#13063316C2318yes—
76#13063305—28no—
77#13063303—28no—
78#13063303—28no—
79#13063301—28no—
80Q8×Dic43—28no—
81#13063290—28no—
82#13063290—28no—
83#13063290—28no—
84#13063283—24no—
85#13063283—22no—
86#13063283—22no—
87#13063283C2314yes—
88#13063283C2318yes—
89#13063283C2314yes—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43C2312yes—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109C42×D43D414yes—
110C42×D43C2314yes—
111#13063259C2318yes—
112#13063258C2318yes—
113#13063258C2318yes—
114#13063257C2318yes—
115#13063256C2318yes—
116#13063256C2318yes—
117#13063236C2314yes—
118#13063235C2318yes—
119C22×Q8×C43—21no—
120C22×C8×C43C2312yes—
121C4⋊Q8×C43—22no—
122C4⋊Q8×C43C2314yes—
123#125×C43—22no—
124#125×C43C2314yes—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2312yes—
131C2×C42×C43C2311yescharacteristic
132#107×C43C2318yes—
133#106×C43C2318yes—
134#97×C43C2314yes—
135C23×D43C2×D411yescharacteristic
136C2×Q8×C43—24no—
137C2×Q8×C43—44no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—22no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C4×D43C2×D414yes—
153C2×C4×D43C2×D414yes—
154C2×C4×D43C2×D412yes—
155C2×C4×D43C2×Q818yes—
156C2×C4×D43C2412yes—
157C2×Dic86—24no—
158C2×Dic86—24no—
159C2×Dic86—24no—
160C2×Dic86—44no—
161C2×Dic86—44no—
162C2×Dic86—44no—
163C2×C8×C43C2×Q818yes—
164C2×C8×C43C2414yes—
165C4⋊C4×C43—24no—
166C4⋊C4×C43—24no—
167C4⋊C4×C43—24no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43C2412yes—
172C4⋊C4×C43C2414yes—
173C4⋊C4×C43C2412yes—
174C42×C43C2×D412yes—
175C42×C43C2412yes—
176(C2×D43)⋊C4—28no—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—24no—
179C4⋊Dic43—24no—
180C4⋊Dic43—22no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—28no—
184C4⋊Dic43C2412yes—
185C4⋊Dic43C2414yes—
186C4⋊Dic43C2412yes—
187Dic43⋊C4—24no—
188Dic43⋊C4—24no—
189Dic43⋊C4—28no—
190Dic43⋊C4—24no—
191Dic43⋊C4—24no—
192C4×Dic43—24no—
193C4×Dic43—24no—
194C4×Dic43—28no—
195C4×Dic43C2×D412yes—
196C4×Dic43C2×D414yes—
197C4×Dic43C2×D414yes—
198C4×Dic43C2412yes—
199C2×C43⋊C8C2×Q818yes—
200C2×C43⋊C8C2414yes—
201C8×D43C2×Q8132yescomplemented
202C23×C43C22×D411yescharacteristic
203C22×D43—22no—
204C22×D43—22no—
205C22×D43C4⋊Q814yes—
206C22×D43C22×D412yes—
207Q8×C43—48no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—24no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—44no—
216C2×C4×C43C22×D412yes—
217C2×C4×C43C22×D412yes—
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×Q814yes—
220C2×C4×C43C2511yescharacteristic
221C2×Dic43—22no—
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—24no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—44no—
229C2×Dic43C4⋊Q814yes—
230C2×Dic43C22×D412yes—
231C2×Dic43C22×D412yes—
232C2×Dic43C22×D412yes—
233C4×D43—44no—
234C4×D43—44no—
235C4×D43C4⋊Q818yes—
236C4×D43C22×Q818yes—
237Dic86—48no—
238Dic86—48no—
239Dic86—48no—
240C8×C43C22×Q818yes—
241C43⋊C8C22×Q818yes—
242C2×#3162—431nomaximal, Sylow
243C22×C43C2×C4⋊Q812yes—
244C22×C43#57512yes—
245C22×C43#57512yes—
246C22×C43C23×D411yescharacteristic
247C2×D43—28no—
248C2×D43—22no—
249C2×D43—22no—
250C2×D43C2×C4⋊Q814yes—
251C4×C43—22no—
252C4×C43—22no—
253C4×C43—42no—
254C4×C43—42no—
255C4×C43—44no—
256C4×C43C2×C4⋊Q812yes—
257C4×C43C23×Q812yes—
258Dic43—22no—
259Dic43—22no—
260Dic43—42no—
261Dic43—42no—
262Dic43—44no—
263Dic43C2×C4⋊Q814yes—
264C2×#533—431no—
265C2×#533—431no—
266#3162—4316no—
267C2×#501—432no—
268C2×#501—432no—
269C2×#501—431no—
270C2×#501—431no—
271C2×#501—431no—
272C2×#501D4311yescharacteristic, complemented
273C2×#427—432no—
274C2×#427—432no—
275C22×#97—431no—
276C2×C43#316214yescomplemented
277C2×C43C22×C4⋊Q811yescharacteristic
278C2×C43C2×#57511yescharacteristic
279C2×C43C2×#57511yescharacteristic
280D43—24no—
281C23×C8—432no—
282#533—438no—
283#533—438no—
284#533—864no—
285#533—864no—
286C2×C4⋊Q8—431no—
287C2×C4⋊Q8—431no—
288C2×C4⋊Q8—431no—
289C2×C4⋊Q8C2×D4311yescharacteristic
290C2×#125—432no—
291C2×#125—431no—
292C2×#125C2×D4311yescharacteristic
293C2×C22⋊Q8—861no—
294C2×C22⋊Q8—861no—
295C2×C22⋊Q8—861no—
296C2×C22⋊Q8—861no—
297C2×C4×Q8—861no—
298C2×C4×Q8—861no—
299C2×C4×Q8—861no—
300C2×C4×Q8—861no—
301C2×#117—432no—
302C2×#117—431no—
303C2×#117—431no—
304C22×C42—431no—
305#501—438no—
306#501—438no—
307#501—4316no—
308#501—4316no—
309#501—438no—
310#501C2×D4318yescomplemented
311#427—4316no—
312#427—4316no—
313C2×#107—432no—
314C2×#107—432no—
315C2×#107—432no—
316C2×#107C2×D4312yes—
317C2×#106—432no—
318C2×#106—432no—
319C2×#106—432no—
320C2×#106C2×D4312yes—
321C2×#97—432no—
322C2×#97—431no—
323C2×#97—438no—
324C2×#97C2×D4311yescharacteristic
325C43C2×#316211yescharacteristic, complemented, Sylow
326C22×Q8—21no—
327C22×Q8—861no—
328C22×Q8—861no—
329C22×Q8—861no—
330C23×C4—431no—
331C23×C4—431no—
332C23×C4—431no—
333C22×C8—432no—
334C22×C8—4316no—
335C22×C8—438no—
336C22×C8C22×D4312yes—
337C4⋊Q8—22no—
338C4⋊Q8—434no—
339C4⋊Q8—434no—
340C4⋊Q8—434no—
341C4⋊Q8—862no—
342C4⋊Q8—862no—
343C4⋊Q8—862no—
344C4⋊Q8C22×D4314yes—
345#125—22no—
346#125—438no—
347#125—434no—
348#125—864no—
349#125—862no—
350#125C22×D4314yes—
351C22⋊Q8—868no—
352C22⋊Q8—868no—
353C22⋊Q8—868no—
354C22⋊Q8—868no—
355C4×Q8—868no—
356C4×Q8—868no—
357C4×Q8—868no—
358C4×Q8—868no—
359#117—434no—
360#117—438no—
361#117—434no—
362#117—862no—
363#117—862no—
364#117—864no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—432no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—862no—
372C2×C4⋊C4—862no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4C22×D4312yes—
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—862no—
384C2×C42—431no—
385C2×C42—431no—
386C2×C42—431no—
387C2×C42—434no—
388C2×C42—434no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42—862no—
392C2×C42C22×D4311yescharacteristic
393#107—438no—
394#107—438no—
395#107—438no—
396#107C22×D4318yes—
397#106—438no—
398#106—438no—
399#106—438no—
400#106C22×D4318yes—
401#97—438no—
402#97—434no—
403#97C22×D4314yes—
404C24—431no—
405C2×Q8—24no—
406C2×Q8—44no—
407C2×Q8—864no—
408C2×Q8—864no—
409C2×Q8—864no—
410C2×Q8—1724no—
411C2×Q8—1724no—
412C2×Q8—1724no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—431no—
417C22×C4—432no—
418C22×C4—438no—
419C22×C4—432no—
420C22×C4—431no—
421C22×C4—431no—
422C22×C4—434no—
423C22×C4—434no—
424C22×C4—861no—
425C22×C4—862no—
426C22×C4—861no—
427C22×C4—1722no—
428C22×C4—1722no—
429C22×C4D4×D4311yescharacteristic
430C22×C4D4×D4311yescharacteristic
431C22×C4C23×D4311yescharacteristic
432C2×C8—438no—
433C2×C8—434no—
434C2×C8—4332no—
435C2×C8Q8×D4318yes—
436C2×C8C23×D4314yes—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—432no—
444C4⋊C4—434no—
445C4⋊C4—432no—
446C4⋊C4—868no—
447C4⋊C4—868no—
448C4⋊C4—864no—
449C4⋊C4—864no—
450C4⋊C4—862no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—864no—
454C4⋊C4—864no—
455C4⋊C4—864no—
456C4⋊C4C23×D4312yes—
457C4⋊C4C23×D4314yes—
458C4⋊C4C23×D4312yes—
459C22⋊C4—864no—
460C22⋊C4—864no—
461C22⋊C4—868no—
462C42—434no—
463C42—434no—
464C42—432no—
465C42—432no—
466C42—864no—
467C42—864no—
468C42—868no—
469C42D4×D4312yes—
470C42C23×D4312yes—
471C23—434no—
472C23—432no—
473C23—862no—
474C23—862no—
475C23C2×D4×D4311yescharacteristic
476Q8—48no—
477Q8—1728no—
478Q8—1728no—
479Q8—1728no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—44no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—434no—
489C2×C4—432no—
490C2×C4—438no—
491C2×C4—438no—
492C2×C4—432no—
493C2×C4—432no—
494C2×C4—862no—
495C2×C4—862no—
496C2×C4—862no—
497C2×C4—864no—
498C2×C4—862no—
499C2×C4—1724no—
500C2×C4—1724no—
501C2×C4—1722no—
502C2×C4—1724no—
503C2×C4—1722no—
504C2×C4C2×D4×D4312yes—
505C2×C4C2×D4×D4312yes—
506C2×C4C2×D4×D4311yescharacteristic
507C2×C4C2×Q8×D4314yes—
508C2×C4C24×D4311yescharacteristic
509C8—438no—
510C8C2×Q8×D4318yes—
511C22—434no—
512C22—862no—
513C22—862no—
514C22—868no—
515C22C4⋊Q8×D4312yes—
516C22#1458369512yes—
517C22#1458369812yes—
518C22C22×D4×D4311yescharacteristic
519C4—22no—
520C4—22no—
521C4—44no—
522C4—42no—
523C4—42no—
524C4—434no—
525C4—862no—
526C4—862no—
527C4—1722no—
528C4—1724no—
529C4—1722no—
530C4C4⋊Q8×D4312yes—
531C4C22×Q8×D4312yes—
532C2—864no—
533C2#1914511614yesdirect product factor
534C2C2×C4⋊Q8×D4311yescharacteristic
535C2C2×#1458369511yescharacteristic
536C2C2×#1458369811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#501C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenterC2×#501D43
hypocenterC43C2×#3162
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #19145116C2direct (N × H)
4. C2×#14583309C2semidirect
5. C2×#14583308C2semidirect
6. C2×#14583307C2semidirect
7. C2×#14583306C2semidirect
8. C2×#14583305C2semidirect
12. C2×C43×#501C2semidirect
35. #14583309C22semidirect
36. #14583308C22semidirect
37. #14583307C22semidirect
38. #14583306C22semidirect
39. #14583305C22semidirect
53. C43×#501C22semidirect
64. C2×C8×D43Q8semidirect
201. C8×D43C2×Q8semidirect
272. C2×#501D43semidirect
276. C2×C43#3162semidirect
310. #501C2×D43semidirect
325. C43C2×#3162semidirect
533. C2#19145116direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834552
C2×#145834542
#191451162
C2×#145833092
C2×#145833082
C2×#145833072
C2×#145833062
C2×#145833052
C2×#145829362
C2×#145829342
C2×#97×D432
C2×C43×#5012
C2×#316243