Finite Group Databasebeta

← C2×#11749376 #14429337

Subgroups — C2×#11749376 #14429337

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
1C22×C5×#215C211yesmaximal, characteristic, complemented
2C2×C3×#4088C211yesmaximal, characteristic, complemented
3C2×#91299C211yesmaximal, characteristic
4C2×#91283C211yesmaximal, characteristic, complemented
5C2×#91120C211yesmaximal, characteristic, complemented
6#11749376C218yesmaximal, direct product factor
7C2×#90993C211yesmaximal, characteristic, complemented
8C2×#90959C211yesmaximal, characteristic, complemented
9C2×#65466—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C5×D12C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C2×C5×#215—21no—
16C2×C5×#215—22no—
17C2×C5×#215—21no—
18C2×C5×#215C2214yescomplemented
19C22×C5×C3⋊C8C2211yescharacteristic
20C2×C3×#689—21no—
21C3×#4088—22no—
22C3×#4088C2214yescomplemented
23C2×C3×#688—21no—
24C2×C3×#681C2211yescharacteristic
25C2×#6656—21no—
26#91299—22no—
27#91299C2214yes—
28C2×#6652—21no—
29C2×#6649—21no—
30#91283—22no—
31#91283C2214yescomplemented
32C2×D5×C3⋊C8—21no—
33#91120C2214yescomplemented
34#90993C2214yescomplemented
35#90959C2214yescomplemented
36C2×#5203—51nomaximal, Hall
37C22×C5×SD16—31no—
38C2×#4088D311yescharacteristic, complemented
39C2×#4078—31no—
40C2×#4047—31no—
41C2×#3968—31no—
42C2×#3965—31no—
43#65466—38no—
44C2×#3951—31no—
45C23×C5×D3—21no—
46C2×C3×C5×Q8—21no—
47C2×C3×C5×Q8—21no—
48C2×C3×C5×Q8—21no—
49C2×C3×C5×Q8—21no—
50C2×C3×C5×Q8—21no—
51C2×C3×C5×Q8C2312yes—
52C22×C3×C4×C5—21no—
53C22×C3×C4×C5C2311yescharacteristic
54C2×C5×D12—21no—
55C2×C5×D12—21no—
56C2×C5×D12—21no—
57C2×C5×D12—21no—
58C2×C5×D12—21no—
59C2×C5×D12C2312yes—
60C2×C3×C22⋊D5—21no—
61C3×#709—21no—
62C3×#709—21no—
63C3×#709D412yes—
64C3×#709C2312yes—
65C2×C3×D20D411yescharacteristic
66C2×C3×C4×D5—21no—
67C2×C3×Dic10D411yescharacteristic
68#6710—21no—
69#6710—21no—
70#6710C2312yes—
71#6710C2312yes—
72C2×C3⋊#168—21no—
73C2×C3⋊#168—21no—
74C5×#215—24no—
75C5×#215—24no—
76C2×C5×C3⋊C8D411yescharacteristic
77C2×C5×C3⋊C8D412yes—
78C2×C5×C3⋊C8D411yescharacteristic
79C2×C5×C3⋊C8C2312yes—
80C3×#689—24no—
81C3×#688—24no—
82C3×#681—21no—
83C3×#681C2312yes—
84C2×C3×#168—21no—
85#6656—24no—
86#6652—24no—
87#6649—24no—
88D5×C3⋊C8—24no—
89C2×C3×#137—51no—
90C2×#949—51no—
91C2×#948—51no—
92C22×#215D511yescharacteristic, complemented
93C2×#836—51no—
94#5203—58no—
95C2×#823—51no—
96C2×#822—51no—
97C22×C5×Q8C2×D311yescharacteristic
98C22×C5×D4—31no—
99C2×#709C2×D311yescharacteristic
100C2×C5×SD16—34no—
101C2×C5×SD16—61no—
102C2×C5×SD16—61no—
103C2×C5×SD16—62no—
104C22×C5×C8—31no—
105C2×#689—21no—
106#4088—22no—
107#4088C2×D314yescomplemented
108C2×#688—21no—
109C2×#687—61no—
110#4078—34no—
111#4078—62no—
112C2×#686—61no—
113C2×#681—31no—
114C2×#681—31no—
115C2×#681C2×D311yescharacteristic
116#4047—34no—
117#4047—62no—
118C2×#676—61no—
119C2×C8×D5—61no—
120#3968—34no—
121#3965—34no—
122#3951—34no—
123C2×#471—151noSylow
124C23×C3×C5#4111yescharacteristic
125C22×C5×D3—22no—
126C22×C5×D3—41no—
127C22×C5×D3—41no—
128C22×C5×D3—82no—
129C22×C3×D5—21no—
130C3×C5×Q8—22no—
131C3×C5×Q8—22no—
132C3×C5×Q8—41no—
133C3×C5×Q8—41no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—41no—
136C2×C3×C4×C5—41no—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5#4111yescharacteristic
142C2×C3×C4×C5C2411yescharacteristic
143C5×D12—22no—
144C5×D12—22no—
145C5×D12—41no—
146C5×D12—41no—
147C3×C22⋊D5—22no—
148C3×C22⋊D5—22no—
149C2×C3×Dic5—21no—
150C3×D20—21no—
151C3×D20C2×D412yes—
152C3×C4×D5—22no—
153C3×C4×D5—22no—
154C3×Dic10—21no—
155C3×Dic10C2×D412yes—
156C3⋊#168—22no—
157C3⋊#168—22no—
158C3×#168—22no—
159C5×C3⋊C8C2×D412yes—
160C5×C3⋊C8C2×D412yes—
161C2×C3×#41—51no—
162C22×C3×Q8C2×D511yescharacteristic
163C22×D12C2×D511yescharacteristic
164C3×#137—54no—
165C3×#137—102no—
166C2×C3×Q16—101no—
167C2×C3×SD16—101no—
168C2×C3×M16—51no—
169#949—54no—
170#949—102no—
171#948—54no—
172#948—102no—
173C2×#215—21no—
174C2×#215—21no—
175C2×#215—22no—
176C2×#215—101no—
177C2×#215C2×D514yescomplemented
178C2×#213—101no—
179C2×#208—51no—
180C2×#208—51no—
181C2×#208—101no—
182C22×C3⋊C8—101no—
183C22×C3⋊C8C2×D511yescharacteristic
184#836—54no—
185#823—54no—
186#822—54no—
187C24×C5—61no—
188C2×C5×Q8—21no—
189C2×C5×Q8—21no—
190C2×C5×Q8—21no—
191C2×C5×Q8—21no—
192C2×C5×Q8—21no—
193C2×C5×Q8C22×D312yes—
194C2×C5×D4—32no—
195C2×C5×D4—61no—
196C2×C5×D4—61no—
197C2×C5×D4—61no—
198C2×C5×D4—61no—
199C2×C5×D4—61no—
200C22×C4×C5—21no—
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—21no—
203#709—21no—
204#709—21no—
205#709#6712yes—
206#709C22×D312yes—
207C2×D20#6711yescharacteristic
208C2×C4×D5—21no—
209C2×Dic10#6711yescharacteristic
210C5×SD16—64no—
211C5×SD16—64no—
212C2×C5×C8—31no—
213C2×C5×C8—31no—
214C2×C5×C8—32no—
215C2×C5×C8—32no—
216#689—24no—
217#688—24no—
218#687—64no—
219#686—64no—
220#681—21no—
221#681—32no—
222#681—32no—
223#681—61no—
224#681—61no—
225#681C22×D312yes—
226C2×#168—21no—
227C2×#168—61no—
228C2×#168—61no—
229#676—64no—
230C8×D5—64no—
231C2×#137—51no—
232C2×AGL(1,ℤ/8)—151no—
233C22×SD16—31no—
234C2×#131—151no—
235#471—158no—
236C2×#108—151no—
237C2×#101—151no—
238C2×#100—151no—
239C22×C3×C5—22no—
240C22×C3×C5#12111yescharacteristic
241C22×C3×C5#12111yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C2×C5×D3—42no—
244C2×C5×D3—82no—
245C2×C5×D3—82no—
246C2×C5×D3—82no—
247C2×C3×D5—22no—
248C2×C3×D5—42no—
249C3×C4×C5—42no—
250C3×C4×C5#12111yescharacteristic
251C3×C4×C5#12111yescharacteristic
252C3×C4×C5C22×D411yescharacteristic
253C3×C4×C5C22×D411yescharacteristic
254C3×Dic5—22no—
255C23×D3—21no—
256C3×#41—52no—
257C3×#41—52no—
258C3×#41—101no—
259C3×#41—101no—
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—21no—
264C2×C3×Q8—21no—
265C2×C3×Q8—51no—
266C2×C3×Q8C22×D512yes—
267C2×C3×D4—51no—
268C2×C3×D4—101no—
269C22×C3×C4—21no—
270C22×C3×C4—101no—
271C22×C3×C4C22×D511yescharacteristic
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12C22×D512yes—
278C3×Q16—104no—
279C3×SD16—104no—
280C3×M16—52no—
281C3×M16—101no—
282C2×C3×C8—101no—
283#215—24no—
284#215—24no—
285#215—104no—
286#213—104no—
287#208—52no—
288#208—52no—
289#208—101no—
290#208—101no—
291#208—104no—
292C2×C3⋊C8—101no—
293C2×C3⋊C8—101no—
294C2×C3⋊C8—104no—
295C2×C3⋊C8C22⋊D511yescharacteristic
296C2×C3⋊C8C22⋊D511yescharacteristic
297C2×C3⋊C8C22⋊D512yes—
298C2×C3⋊C8C22×D512yes—
299C23×C5—62no—
300C23×C5—121no—
301C23×C5—121no—
302C23×C5—242no—
303C23×C5#23711yescharacteristic
304C22×D5—21no—
305C5×Q8—22no—
306C5×Q8—22no—
307C5×Q8—41no—
308C5×Q8—41no—
309C5×D4—62no—
310C5×D4—62no—
311C5×D4—121no—
312C5×D4—121no—
313C2×C4×C5—22no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5D3×D411yescharacteristic
317C2×C4×C5D3×D411yescharacteristic
318C2×C4×C5#23711yescharacteristic
319C2×C4×C5C2×#6711yescharacteristic
320C2×C4×C5C2×#6711yescharacteristic
321C2×C4×C5C23×D311yescharacteristic
322C22⋊D5—22no—
323C22⋊D5—22no—
324C2×Dic5—21no—
325D20—21no—
326D20C2×#6712yes—
327C4×D5—22no—
328C4×D5—22no—
329Dic10—21no—
330Dic10C2×#6712yes—
331C5×C8—32no—
332C5×C8—32no—
333#168—22no—
334#168—62no—
335#168—62no—
336C2×#41—51no—
337C22×Q8D3×D511yescharacteristic
338C22×D4—31no—
339#137—54no—
340#137—102no—
341AGL(1,ℤ/8)—154no—
342AGL(1,ℤ/8)—302no—
343C2×Q16—101no—
344C2×SD16—34no—
345C2×SD16—61no—
346C2×SD16—61no—
347C2×SD16—62no—
348C2×SD16—101no—
349C2×SD16—301no—
350C2×D8—301no—
351#131—154no—
352#131—302no—
353C2×M16—51no—
354C2×M16—151no—
355C2×M16—151no—
356C2×M16—301no—
357C22×C8—31no—
358C22×C8—301no—
359#108—154no—
360#101—154no—
361#100—154no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5#47112yescomplemented
365C2×C3×C5C2×#12111yescharacteristic
366C3×D5—42no—
367C5×D3—82no—
368C23×C3—101no—
369C23×C3#71111yescharacteristic
370C22×D3—22no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3—82no—
374C3×Q8—22no—
375C3×Q8—22no—
376C3×Q8—41no—
377C3×Q8—41no—
378C3×Q8—52no—
379C3×Q8—101no—
380C3×D4—52no—
381C3×D4—102no—
382C3×D4—102no—
383C3×D4—101no—
384C2×C3×C4—22no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—101no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4D4×D511yescharacteristic
391C2×C3×C4D4×D511yescharacteristic
392C2×C3×C4#71111yescharacteristic
393C2×C3×C4C2×C22⋊D511yescharacteristic
394C2×C3×C4C2×C22⋊D511yescharacteristic
395C2×C3×C4C23×D511yescharacteristic
396D12—22no—
397D12—22no—
398D12—41no—
399D12—41no—
400C3×C8—102no—
401C3⋊C8—102no—
402C3⋊C8—102no—
403C3⋊C8C2×C22⋊D512yes—
404C3⋊C8C2×C22⋊D512yes—
405C22×C5—22no—
406C22×C5—122no—
407C22×C5—242no—
408C22×C5—242no—
409C22×C5—242no—
410C22×C5#93911yescharacteristic
411C22×C5#93911yescharacteristic
412C22×C5C2×#23711yescharacteristic
413C2×D5—22no—
414C2×D5—42no—
415C4×C5—42no—
416C4×C5#93911yescharacteristic
417C4×C5#93911yescharacteristic
418C4×C5C2×D3×D411yescharacteristic
419C4×C5C22×#6711yescharacteristic
420Dic5—22no—
421C24—61no—
422#41—52no—
423#41—52no—
424#41—101no—
425#41—101no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—51no—
432C2×Q8C2×D3×D512yes—
433C2×D4—32no—
434C2×D4—51no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4—61no—
439C2×D4—61no—
440C2×D4—101no—
441C22×C4—21no—
442C22×C4—101no—
443C22×C4C2×D3×D511yescharacteristic
444Q16—104no—
445SD16—64no—
446SD16—64no—
447SD16—104no—
448SD16—304no—
449D8—304no—
450M16—52no—
451M16—101no—
452M16—152no—
453M16—152no—
454M16—304no—
455M16—301no—
456M16—301no—
457C2×C8—31no—
458C2×C8—31no—
459C2×C8—32no—
460C2×C8—32no—
461C2×C8—101no—
462C2×C8—304no—
463C2×C8—301no—
464C2×C8—301no—
465C3×C5C2×#47111yescharacteristic, complemented, Hall
466C22×C3—22no—
467C22×C3—102no—
468C22×C3—202no—
469C22×C3#408411yescharacteristic
470C22×C3#408411yescharacteristic
471C22×C3C2×#71111yescharacteristic
472C2×D3—42no—
473C2×D3—82no—
474C2×D3—82no—
475C2×D3—82no—
476C3×C4—42no—
477C3×C4—102no—
478C3×C4#408411yescharacteristic
479C3×C4#408411yescharacteristic
480C3×C4C2×D4×D511yescharacteristic
481C3×C4C22×C22⋊D511yescharacteristic
482C2×C5—21no—
483C2×C5—21no—
484C2×C5—242no—
485C2×C5#520312yescomplemented
486C2×C5C2×#93911yescharacteristic
487D5—42no—
488C23—62no—
489C23—101no—
490C23—121no—
491C23—121no—
492C23—242no—
493C23#678011yescharacteristic
494Q8—22no—
495Q8—22no—
496Q8—41no—
497Q8—41no—
498Q8—52no—
499Q8—101no—
500D4—52no—
501D4—62no—
502D4—62no—
503D4—102no—
504D4—102no—
505D4—101no—
506D4—121no—
507D4—121no—
508C2×C4—22no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—101no—
512C2×C4—102no—
513C2×C4—102no—
514C2×C4#678011yescharacteristic
515C2×C4D5×#6711yescharacteristic
516C2×C4D5×#6711yescharacteristic
517C2×C4D3×C22⋊D511yescharacteristic
518C2×C4D3×C22⋊D511yescharacteristic
519C2×C4C22×D3×D511yescharacteristic
520C8—32no—
521C8—32no—
522C8—102no—
523C8—302no—
524C8—302no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—202no—
528C2×C3#6546612yescomplemented
529C2×C3C2×#408411yescharacteristic
530D3—82no—
531C5C2×#520311yescharacteristic, complemented, Sylow
532C22—22no—
533C22—102no—
534C22—122no—
535C22—202no—
536C22—242no—
537C22—242no—
538C22—242no—
539C22#9154911yescharacteristic
540C22#9154911yescharacteristic
541C22C2×#678011yescharacteristic
542C4—42no—
543C4—102no—
544C4#9154911yescharacteristic
545C4#9154911yescharacteristic
546C4C2×D5×#6711yescharacteristic
547C4C2×D3×C22⋊D511yescharacteristic
548C3C2×#6546611yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—202no—
552C2—242no—
553C2#1174937612yesdirect product factor
554C2C2×#9154911yescharacteristic
subgroupG/H
centerC22#91549
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5#121
prime radicalC2×#91299C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C5×#215C2semidirect
2. C2×C3×#4088C2semidirect
4. C2×#91283C2semidirect
5. C2×#91120C2semidirect
6. #11749376C2direct (N × H)
7. C2×#90993C2semidirect
8. C2×#90959C2semidirect
18. C2×C5×#215C22semidirect
22. C3×#4088C22semidirect
31. #91283C22semidirect
33. #91120C22semidirect
34. #90993C22semidirect
35. #90959C22semidirect
38. C2×#4088D3semidirect
92. C22×#215D5semidirect
107. #4088C2×D3semidirect
177. C2×#215C2×D5semidirect
364. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
485. C2×C5#5203semidirect
528. C2×C3#65466semidirect
531. C5C2×#5203semidirect
548. C3C2×#65466semidirect
553. C2#11749376direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2152
C2×C3×#40882
C2×#912992
C2×#912832
C2×#911202
#117493762
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