Finite Group Databasebeta

← C2×#11749447 #14429331

Subgroups — C2×#11749447 #14429331

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91840C211yesmaximal, characteristic, complemented
2C2×C5×#949C211yesmaximal, characteristic
3C2×C3×#4094C211yesmaximal, characteristic, complemented
4C22×#6659C211yesmaximal, characteristic, complemented
5#11749447C218yesmaximal, direct product factor
6C2×#90991C211yesmaximal, characteristic, complemented
7C2×#90963C211yesmaximal, characteristic, complemented
8C2×#90959C211yesmaximal, characteristic, complemented
9C2×#65489—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C22×Dic30C2211yescharacteristic
12C22×C5×D12C2211yescharacteristic
13#91840—22no—
14#91840C2214yescomplemented
15C2×#6718—21no—
16C2×#6716—21no—
17C2×#6710C2211yescharacteristic
18C5×#949—22no—
19C5×#949C2214yes—
20C2×C5×#215—21no—
21C2×C5×#213—21no—
22C2×C5×#208C2211yescharacteristic
23C3×#4094—22no—
24C3×#4094C2214yescomplemented
25C2×C3×#681—21no—
26C2×C3×#681C2211yescharacteristic
27C22×C3×#168—21no—
28C22×C3×#168C2211yescharacteristic
29C2×#6659—22no—
30C2×#6659—21no—
31C2×#6659—21no—
32C2×#6659C2214yescomplemented
33#90991C2214yescomplemented
34#90963C2214yescomplemented
35#90959C2214yescomplemented
36C2×#5141—51nomaximal, Hall
37C2×C5×AGL(1,ℤ/8)—31no—
38C2×#4097—31no—
39C2×#4094D311yescharacteristic, complemented
40C22×#687—31no—
41C2×#3965—31no—
42#65489—38no—
43C2×#3956—31no—
44C2×#3954—31no—
45C23×C5×D3—21no—
46C3×C5×#41—21no—
47C3×C5×#41—21no—
48C3×C5×#41D412yes—
49C3×C5×#41C2312yes—
50C2×C3×C5×Q8D411yescharacteristic
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4D411yescharacteristic
53C22×C3×C4×C5—21no—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15—21no—
56C2×Dic30—21no—
57C2×Dic30—21no—
58C2×Dic30—21no—
59C2×Dic30—21no—
60C2×Dic30—21no—
61C2×Dic30C2312yes—
62C2×C5×D12—21no—
63C2×C5×D12—21no—
64C2×C5×D12—21no—
65C2×C5×D12—21no—
66C2×C5×D12—21no—
67C2×C5×D12C2312yes—
68#6718—24no—
69#6716—24no—
70#6710—21no—
71#6710C2312yes—
72C2×C3⋊#168—21no—
73C5×#215—24no—
74C5×#213—24no—
75C5×#208—21no—
76C5×#208C2312yes—
77C2×C5×C3⋊C8—21no—
78C3×#681—21no—
79C3×#681—24no—
80C3×#681C2312yes—
81C2×C3×#168—21no—
82C2×C3×#168—24no—
83C2×C3×#168D412yes—
84C2×C3×#168D411yescharacteristic
85C2×C3×#168D411yescharacteristic
86C2×C3×#168C2312yes—
87#6659—24no—
88#6659—24no—
89C2×C3×#131—51no—
90C2×#951—51no—
91C2×#949D511yescharacteristic
92C22×#204—51no—
93#5141—58no—
94C2×#824—51no—
95C2×#823—51no—
96C2×#819—51no—
97C2×C5×#41C2×D311yescharacteristic
98C22×C5×D4—31no—
99C22×Dic10—31no—
100C5×AGL(1,ℤ/8)—34no—
101C5×AGL(1,ℤ/8)—62no—
102C2×C5×SD16—61no—
103C2×C5×D8—61no—
104C2×C5×M16—31no—
105#4097—34no—
106#4097—62no—
107#4094—22no—
108#4094C2×D314yescomplemented
109C2×#689—61no—
110C2×#687—34no—
111C2×#687—61no—
112C2×#687—61no—
113C2×#687—61no—
114C2×#687—62no—
115C2×#681—21no—
116C2×#681—31no—
117C2×#681C2×D311yescharacteristic
118C22×#168—21no—
119C22×#168C2×D311yescharacteristic
120#3965—34no—
121#3956—34no—
122#3954—34no—
123C2×#471—151noSylow
124C23×C3×C5—21no—
125C23×C3×C5#4111yescharacteristic
126C22×C5×D3—22no—
127C22×C5×D3—41no—
128C22×C5×D3—41no—
129C22×C5×D3—82no—
130C3×C5×Q8—21no—
131C3×C5×Q8C2×D412yes—
132C3×C5×D4—22no—
133C3×C5×D4—22no—
134C3×C5×D4—21no—
135C3×C5×D4C2×D412yes—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5#4111yescharacteristic
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—22no—
146C2×Dic15—41no—
147C2×Dic15—41no—
148Dic30—22no—
149Dic30—22no—
150Dic30—41no—
151Dic30—41no—
152C5×D12—22no—
153C5×D12—22no—
154C5×D12—41no—
155C5×D12—41no—
156C3⋊#168—22no—
157C3×#168—22no—
158C3×#168C2×D412yes—
159C3×#168C2×D412yes—
160C5×C3⋊C8—22no—
161C2×C3×#41C2×D511yescharacteristic
162C22×D12C2×D511yescharacteristic
163C22×Dic6—51no—
164C3×#131—54no—
165C3×#131—102no—
166C2×C3×M16—51no—
167C2×C3×M16—101no—
168C22×C3×C8—51no—
169C22×C3×C8—101no—
170#951—54no—
171#951—102no—
172#949—22no—
173#949C2×D514yes—
174C2×#216—101no—
175C2×#215—21no—
176C2×#214—101no—
177C2×#213—21no—
178C2×#208—51no—
179C2×#208C2×D511yescharacteristic
180C2×#204—54no—
181C2×#204—101no—
182C2×#204—101no—
183C2×#204—102no—
184#824—54no—
185#823—54no—
186#819—54no—
187C24×C5—61no—
188C5×#41—21no—
189C5×#41—21no—
190C5×#41D1212yes—
191C5×#41C22×D312yes—
192C2×C5×Q8D1211yescharacteristic
193C2×C5×D4—21no—
194C2×C5×D4—32no—
195C2×C5×D4—61no—
196C2×C5×D4—61no—
197C2×C5×D4—61no—
198C2×C5×D4—61no—
199C2×C5×D4—61no—
200C2×C5×D4D1211yescharacteristic
201C22×C4×C5—21no—
202C22×C4×C5C22×D311yescharacteristic
203C22×Dic5—61no—
204C2×Dic10—32no—
205C2×Dic10—61no—
206C2×Dic10—61no—
207C2×Dic10—61no—
208C2×Dic10—61no—
209C2×Dic10—61no—
210C5×SD16—64no—
211C5×D8—64no—
212C5×M16—32no—
213C5×M16—61no—
214C2×C5×C8—61no—
215#689—64no—
216#687—64no—
217#687—64no—
218#687—64no—
219#681—21no—
220#681—24no—
221#681—32no—
222#681—61no—
223#681C22×D312yes—
224C2×#168—21no—
225C2×#168—24no—
226C2×#168—61no—
227C2×#168#6711yescharacteristic
228C2×#168#6711yescharacteristic
229C2×#168#6712yes—
230C2×#168C22×D312yes—
231C2×#137—151no—
232C2×AGL(1,ℤ/8)—31no—
233C22×SD16—151no—
234C2×#131—51no—
235#471—158no—
236C2×#108—151no—
237C2×#101—151no—
238C2×#100—151no—
239C22×C3×C5—22no—
240C22×C3×C5—22no—
241C22×C3×C5—42no—
242C22×C3×C5#12111yescharacteristic
243C22×C3×C5#12111yescharacteristic
244C22×C3×C5C2×#4111yescharacteristic
245C2×C5×D3—42no—
246C2×C5×D3—82no—
247C2×C5×D3—82no—
248C2×C5×D3—82no—
249C3×C4×C5—22no—
250C3×C4×C5#12111yescharacteristic
251C3×C4×C5#12111yescharacteristic
252C3×C4×C5C22×D411yescharacteristic
253C3×C4×C5C22×D411yescharacteristic
254Dic15—42no—
255C23×D3—21no—
256C3×#41—21no—
257C3×#41—21no—
258C3×#41C22⋊D512yes—
259C3×#41C22×D512yes—
260C2×C3×Q8C22⋊D511yescharacteristic
261C2×C3×D4—21no—
262C2×C3×D4C22⋊D511yescharacteristic
263C22×C3×C4—21no—
264C22×C3×C4C22×D511yescharacteristic
265C22×Dic3—101no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12C22×D512yes—
272C2×Dic6—52no—
273C2×Dic6—101no—
274C2×Dic6—101no—
275C2×Dic6—101no—
276C2×Dic6—101no—
277C2×Dic6—101no—
278C3×M16—52no—
279C3×M16—104no—
280C3×M16—101no—
281C2×C3×C8—51no—
282C2×C3×C8—51no—
283C2×C3×C8—52no—
284C2×C3×C8—52no—
285C2×C3×C8—104no—
286C2×C3×C8—101no—
287#216—104no—
288#215—24no—
289#214—104no—
290#213—24no—
291#208—21no—
292#208—52no—
293#208—101no—
294#208C22×D512yes—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—101no—
297#204—104no—
298#204—104no—
299C23×C5—21no—
300C23×C5—62no—
301C23×C5—121no—
302C23×C5—121no—
303C23×C5—242no—
304C23×C5#23511yescharacteristic
305C5×Q8—21no—
306C5×Q8C2×D1212yes—
307C5×D4—22no—
308C5×D4—22no—
309C5×D4—21no—
310C5×D4—62no—
311C5×D4—62no—
312C5×D4—121no—
313C5×D4—121no—
314C5×D4C2×D1212yes—
315C2×C4×C5—21no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5C2×D1211yescharacteristic
319C2×C4×C5C2×D1211yescharacteristic
320C2×C4×C5#23511yescharacteristic
321C2×C4×C5C2×#6711yescharacteristic
322C2×C4×C5C2×#6711yescharacteristic
323C2×C4×C5C23×D311yescharacteristic
324C2×Dic5—62no—
325C2×Dic5—121no—
326C2×Dic5—121no—
327Dic10—62no—
328Dic10—62no—
329Dic10—121no—
330Dic10—121no—
331C5×C8—62no—
332#168—22no—
333#168—62no—
334#168C2×#6712yes—
335#168C2×#6712yes—
336C2×#41D3×D511yescharacteristic
337C22×Q8—151no—
338C22×D4—31no—
339#137—154no—
340#137—302no—
341AGL(1,ℤ/8)—34no—
342AGL(1,ℤ/8)—62no—
343C2×Q16—301no—
344C2×SD16—61no—
345C2×SD16—154no—
346C2×SD16—301no—
347C2×SD16—301no—
348C2×SD16—302no—
349C2×SD16—301no—
350C2×D8—61no—
351#131—54no—
352#131—102no—
353C2×M16—31no—
354C2×M16—51no—
355C2×M16—101no—
356C2×M16—151no—
357C22×C8—51no—
358C22×C8—101no—
359#108—154no—
360#101—154no—
361#100—154no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5—42no—
365C2×C3×C5#47112yescomplemented
366C2×C3×C5C2×#12111yescharacteristic
367C5×D3—82no—
368C23×C3—21no—
369C23×C3#71111yescharacteristic
370C22×D3—22no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3—82no—
374C3×Q8—21no—
375C3×Q8C2×C22⋊D512yes—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—21no—
379C3×D4C2×C22⋊D512yes—
380C2×C3×C4—21no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4D4×D511yescharacteristic
384C2×C3×C4D4×D511yescharacteristic
385C2×C3×C4#71111yescharacteristic
386C2×C3×C4C2×C22⋊D511yescharacteristic
387C2×C3×C4C2×C22⋊D511yescharacteristic
388C2×C3×C4C23×D511yescharacteristic
389C2×Dic3—102no—
390C2×Dic3—201no—
391C2×Dic3—201no—
392D12—22no—
393D12—22no—
394D12—41no—
395D12—41no—
396Dic6—102no—
397Dic6—102no—
398Dic6—201no—
399Dic6—201no—
400C3×C8—52no—
401C3×C8—52no—
402C3×C8—102no—
403C3⋊C8—22no—
404C3⋊C8—102no—
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—42no—
408C22×C5—122no—
409C22×C5—242no—
410C22×C5—242no—
411C22×C5—242no—
412C22×C5#93011yescharacteristic
413C22×C5#93011yescharacteristic
414C22×C5C2×#23511yescharacteristic
415C4×C5—22no—
416C4×C5#93011yescharacteristic
417C4×C5#93011yescharacteristic
418C4×C5C22×D1211yescharacteristic
419C4×C5C22×#6711yescharacteristic
420Dic5—122no—
421C24—61no—
422#41—21no—
423#41—21no—
424#41#120312yes—
425#41C2×D3×D512yes—
426C2×Q8—152no—
427C2×Q8—301no—
428C2×Q8—301no—
429C2×Q8—301no—
430C2×Q8—301no—
431C2×Q8—301no—
432C2×Q8#120311yescharacteristic
433C2×D4—21no—
434C2×D4—32no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4—61no—
439C2×D4—61no—
440C2×D4#120311yescharacteristic
441C22×C4—21no—
442C22×C4—301no—
443C22×C4C2×D3×D511yescharacteristic
444Q16—304no—
445SD16—64no—
446SD16—304no—
447SD16—304no—
448SD16—304no—
449D8—64no—
450M16—32no—
451M16—52no—
452M16—61no—
453M16—104no—
454M16—101no—
455M16—152no—
456M16—301no—
457C2×C8—51no—
458C2×C8—51no—
459C2×C8—52no—
460C2×C8—52no—
461C2×C8—61no—
462C2×C8—104no—
463C2×C8—101no—
464C2×C8—301no—
465C3×C5C2×#47111yescharacteristic, complemented, Hall
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—42no—
469C22×C3#408511yescharacteristic
470C22×C3#408511yescharacteristic
471C22×C3C2×#71111yescharacteristic
472C2×D3—42no—
473C2×D3—82no—
474C2×D3—82no—
475C2×D3—82no—
476C3×C4—22no—
477C3×C4#408511yescharacteristic
478C3×C4#408511yescharacteristic
479C3×C4C2×D4×D511yescharacteristic
480C3×C4C22×C22⋊D511yescharacteristic
481Dic3—202no—
482C2×C5—21no—
483C2×C5—21no—
484C2×C5—42no—
485C2×C5—242no—
486C2×C5#514112yescomplemented
487C2×C5C2×#93011yescharacteristic
488C23—21no—
489C23—62no—
490C23—121no—
491C23—121no—
492C23—242no—
493C23#678211yescharacteristic
494Q8—21no—
495Q8—302no—
496Q8—302no—
497Q8—601no—
498Q8—601no—
499Q8C2×#120312yes—
500D4—22no—
501D4—22no—
502D4—21no—
503D4—62no—
504D4—62no—
505D4—121no—
506D4—121no—
507D4C2×#120312yes—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—302no—
512C2×C4—601no—
513C2×C4—601no—
514C2×C4#678211yescharacteristic
515C2×C4C2×#120311yescharacteristic
516C2×C4C2×#120311yescharacteristic
517C2×C4D5×#6711yescharacteristic
518C2×C4D5×#6711yescharacteristic
519C2×C4C22×D3×D511yescharacteristic
520C8—52no—
521C8—52no—
522C8—62no—
523C8—102no—
524C8—302no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—42no—
528C2×C3#6548912yescomplemented
529C2×C3C2×#408511yescharacteristic
530D3—82no—
531C5C2×#514111yescharacteristic, complemented, Sylow
532C22—22no—
533C22—22no—
534C22—42no—
535C22—122no—
536C22—242no—
537C22—242no—
538C22—242no—
539C22#9156611yescharacteristic
540C22#9156611yescharacteristic
541C22C2×#678211yescharacteristic
542C4—22no—
543C4—602no—
544C4#9156611yescharacteristic
545C4#9156611yescharacteristic
546C4C22×#120311yescharacteristic
547C4C2×D5×#6711yescharacteristic
548C3C2×#6548911yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—42no—
552C2—242no—
553C2#1174944712yesdirect product factor
554C2C2×#9156611yescharacteristic
subgroupG/H
centerC22#91566
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5#121
prime radicalC2×C5×#949C2
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#91840C2semidirect
3. C2×C3×#4094C2semidirect
4. C22×#6659C2semidirect
5. #11749447C2direct (N × H)
6. C2×#90991C2semidirect
7. C2×#90963C2semidirect
8. C2×#90959C2semidirect
14. #91840C22semidirect
24. C3×#4094C22semidirect
32. C2×#6659C22semidirect
33. #90991C22semidirect
34. #90963C22semidirect
35. #90959C22semidirect
39. C2×#4094D3semidirect
108. #4094C2×D3semidirect
365. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
486. C2×C5#5141semidirect
528. C2×C3#65489semidirect
531. C5C2×#5141semidirect
548. C3C2×#65489semidirect
553. C2#11749447direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918402
C2×C5×#9492
C2×C3×#40942
C22×#66592
#117494472
C2×#909912
C2×#909632
C2×#909592
C2×#654893
C2×#51415