Finite Group Databasebeta

← C2×#11748197 #14429344

Subgroups — C2×#11748197 #14429344

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×#91797C211yesmaximal, characteristic
2C2×#91315C211yesmaximal, characteristic, complemented
3C22×#6658C211yesmaximal, characteristic, complemented
4C2×#91291C211yesmaximal, characteristic, complemented
5C2×C5×#822C211yesmaximal, characteristic, complemented
6C2×C3×#3956C211yesmaximal, characteristic, complemented
7C2×#90960C211yesmaximal, characteristic, complemented
8#11748197C218yesmaximal, direct product factor
9C2×#65187—31nomaximal, Hall
10C2×#6817C2211yescharacteristic
11C22×D60C2211yescharacteristic
12C22×C3×Dic10C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14#91797—22no—
15#91797C2214yes—
16C2×D120—21no—
17C2×#6706—21no—
18C2×C5×#208C2211yescharacteristic
19C22×C5×C3⋊C8C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21C2×#6662—21no—
22#91315—22no—
23#91315C2214yescomplemented
24C2×#6658—21no—
25C2×#6658—21no—
26C2×#6658—22no—
27C2×#6658—21no—
28C2×#6658C2214yescomplemented
29C2×#6651—21no—
30#91291—22no—
31#91291C2214yescomplemented
32C2×#6648—21no—
33C5×#822C2214yescomplemented
34C3×#3956C2214yescomplemented
35#90960C2214yescomplemented
36C2×#4754—51nomaximal, Hall
37C2×#4055—31no—
38C2×#4054—31no—
39C22×#677—31no—
40C2×#4047—31no—
41C2×C5×#108—31no—
42C2×#3956D311yescharacteristic, complemented
43C2×#3955—31no—
44#65187—38no—
45C23×D15—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×#1220—21no—
48#6817—21no—
49#6817—21no—
50#6817D412yes—
51#6817C2312yes—
52C2×D60—21no—
53C2×D60—21no—
54C2×D60—21no—
55C2×D60—21no—
56C2×D60—21no—
57C2×D60D411yescharacteristic
58C2×D60C2312yes—
59C2×C4×D15—21no—
60C2×Dic30D411yescharacteristic
61C22×C3×Dic5—21no—
62C2×C3×Dic10—21no—
63C2×C3×Dic10—21no—
64C2×C3×Dic10—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—21no—
67C2×C3×Dic10C2312yes—
68C3×C5×M16—21no—
69C3×C5×M16C2312yes—
70C2×C3×C5×C8—21no—
71D120—24no—
72#6706—24no—
73C5×#208—21no—
74C5×#208C2312yes—
75C2×C5×C3⋊C8—21no—
76C2×C5×C3⋊C8D411yescharacteristic
77C2×C5×C3⋊C8D412yes—
78C2×C5×C3⋊C8D411yescharacteristic
79C2×C5×C3⋊C8C2312yes—
80C3×#681—21no—
81C3×#681C2312yes—
82C2×C3×#168—21no—
83#6662—24no—
84#6658—24no—
85#6658—24no—
86#6658—24no—
87#6651—24no—
88#6648—24no—
89C2×#942—51no—
90C22×#215—51no—
91C2×#908—51no—
92C2×#907—51no—
93C2×C3×#101—51no—
94C2×#823—51no—
95C2×#822D511yescharacteristic, complemented
96#4754—58no—
97C2×#709—31no—
98C22×D20—31no—
99C22×Dic10C2×D311yescharacteristic
100C2×C5×M16—31no—
101C2×C5×M16C2×D311yescharacteristic
102C22×C5×C8—31no—
103C2×#681C2×D311yescharacteristic
104#4055—34no—
105#4055—62no—
106#4054—34no—
107#4054—62no—
108C2×Dic20—61no—
109C2×D40—61no—
110C2×#677—34no—
111C2×#677—61no—
112C2×#677—61no—
113C2×#677—61no—
114C2×#677—62no—
115C2×#677—61no—
116#4047—34no—
117#4047—62no—
118C2×#676—61no—
119C2×C8×D5—61no—
120C5×#108—34no—
121#3956C2×D314yescomplemented
122#3955—34no—
123C2×#471—151noSylow
124C23×C3×C5#4111yescharacteristic
125C22×D15—21no—
126C22×D15—22no—
127C22×D15—41no—
128C22×D15—41no—
129C22×D15—82no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5#4111yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136#1220—22no—
137#1220—22no—
138C2×Dic15—21no—
139D60—21no—
140D60—22no—
141D60—22no—
142D60—41no—
143D60—41no—
144D60C2×D412yes—
145C4×D15—22no—
146C4×D15—22no—
147Dic30—21no—
148Dic30C2×D412yes—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—41no—
151C2×C3×Dic5—41no—
152C3×Dic10—22no—
153C3×Dic10—22no—
154C3×Dic10—41no—
155C3×Dic10—41no—
156C3×C5×C8—22no—
157C3×#168—22no—
158C5×C3⋊C8—22no—
159C5×C3⋊C8C2×D412yes—
160C5×C3⋊C8C2×D412yes—
161C22×C3×Q8—51no—
162C2×#235—51no—
163C22×D12—51no—
164C2×C3×M16—51no—
165C2×C3×M16C2×D511yescharacteristic
166C2×#216—101no—
167#942—54no—
168#942—102no—
169C2×#215—54no—
170C2×#215—101no—
171C2×#215—101no—
172C2×#215—101no—
173C2×#215—102no—
174C2×#208C2×D511yescharacteristic
175C22×C3⋊C8C2×D511yescharacteristic
176#908—54no—
177#908—102no—
178#907—54no—
179#907—102no—
180C2×D24—101no—
181C2×#204—101no—
182C2×ΓL(1,𝔽25)—101no—
183C2×D3×C8—101no—
184C3×#101—54no—
185#823—54no—
186#822C2×D514yescomplemented
187C23×D5—61no—
188C22×C4×C5C22×D311yescharacteristic
189C2×C22⋊D5—61no—
190C22×Dic5—21no—
191#709—32no—
192#709—32no—
193#709—61no—
194#709—61no—
195C2×D20—31no—
196C2×D20—32no—
197C2×D20—61no—
198C2×D20—61no—
199C2×D20—61no—
200C2×D20—61no—
201C2×D20—61no—
202C2×C4×D5—61no—
203C2×Dic10—21no—
204C2×Dic10—21no—
205C2×Dic10—21no—
206C2×Dic10—21no—
207C2×Dic10—21no—
208C2×Dic10—31no—
209C2×Dic10C22×D312yes—
210C5×M16—21no—
211C5×M16—32no—
212C5×M16—61no—
213C5×M16C22×D312yes—
214C2×C5×C8—21no—
215C2×C5×C8—31no—
216C2×C5×C8—31no—
217C2×C5×C8—32no—
218C2×C5×C8—32no—
219C2×C5×C8—61no—
220#681—21no—
221#681C22×D312yes—
222C2×#168—21no—
223Dic20—64no—
224D40—64no—
225#677—64no—
226#677—64no—
227#677—64no—
228#677—64no—
229#676—64no—
230C8×D5—64no—
231C2×#137—151no—
232C2×AGL(1,ℤ/8)—151no—
233C22×SD16—151no—
234C2×#131—151no—
235#471—158no—
236C2×#108—31no—
237C2×#101—51no—
238C2×#100—151no—
239C22×C3×C5—22no—
240C22×C3×C5#12111yescharacteristic
241C22×C3×C5#12111yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C2×D15—22no—
244C2×D15—42no—
245C2×D15—42no—
246C2×D15—82no—
247C2×D15—82no—
248C2×D15—82no—
249C3×C4×C5#12111yescharacteristic
250C3×C4×C5#12111yescharacteristic
251C3×C4×C5C22×D411yescharacteristic
252C3×C4×C5C22×D411yescharacteristic
253Dic15—22no—
254C3×Dic5—42no—
255C23×D3—101no—
256C2×C3×Q8—52no—
257C2×C3×Q8—101no—
258C2×C3×Q8—101no—
259C2×C3×Q8—101no—
260C2×C3×Q8—101no—
261C2×C3×Q8—101no—
262C22×C3×C4—101no—
263C22×C3×C4C22×D511yescharacteristic
264C2×#67—101no—
265#235—52no—
266#235—52no—
267#235—101no—
268#235—101no—
269C2×D12—51no—
270C2×D12—52no—
271C2×D12—101no—
272C2×D12—101no—
273C2×D12—101no—
274C2×D12—101no—
275C2×D12—101no—
276C2×C4×D3—101no—
277C2×Dic6—51no—
278C3×M16—21no—
279C3×M16—52no—
280C3×M16—101no—
281C3×M16C22×D512yes—
282C2×C3×C8—21no—
283C2×C3×C8—101no—
284#216—104no—
285#215—104no—
286#215—104no—
287#215—104no—
288#208—21no—
289#208C22×D512yes—
290C2×C3⋊C8—21no—
291C2×C3⋊C8D2011yescharacteristic
292C2×C3⋊C8D2011yescharacteristic
293C2×C3⋊C8D2012yes—
294C2×C3⋊C8C22×D512yes—
295D24—104no—
296#204—104no—
297ΓL(1,𝔽25)—104no—
298D3×C8—104no—
299C23×C5#23511yescharacteristic
300C22×D5—61no—
301C22×D5—62no—
302C22×D5—121no—
303C22×D5—121no—
304C22×D5—242no—
305C2×C4×C5#23511yescharacteristic
306C2×C4×C5D3×D411yescharacteristic
307C2×C4×C5D3×D411yescharacteristic
308C2×C4×C5D3×D411yescharacteristic
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C22⋊D5—62no—
312C22⋊D5—62no—
313C2×Dic5—22no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—61no—
317D20—32no—
318D20—61no—
319D20—62no—
320D20—62no—
321D20—121no—
322D20—121no—
323C4×D5—62no—
324C4×D5—62no—
325Dic10—22no—
326Dic10—22no—
327Dic10—32no—
328Dic10—41no—
329Dic10—41no—
330Dic10—61no—
331C5×C8—22no—
332C5×C8—32no—
333C5×C8—32no—
334C5×C8—62no—
335#168—22no—
336C2×#41—151no—
337C22×Q8—51no—
338C22×D4—151no—
339#137—154no—
340#137—302no—
341AGL(1,ℤ/8)—154no—
342AGL(1,ℤ/8)—302no—
343C2×Q16—301no—
344C2×SD16—154no—
345C2×SD16—301no—
346C2×SD16—301no—
347C2×SD16—301no—
348C2×SD16—302no—
349C2×SD16—301no—
350C2×D8—301no—
351#131—154no—
352#131—302no—
353C2×M16—31no—
354C2×M16—51no—
355C2×M16—301no—
356C2×M16D3×D511yescharacteristic
357C22×C8—31no—
358C22×C8—301no—
359#108—34no—
360#101—54no—
361#100—154no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5#47112yescomplemented
365C2×C3×C5C2×#12111yescharacteristic
366D15—42no—
367D15—82no—
368C23×C3#71311yescharacteristic
369C22×D3—101no—
370C22×D3—102no—
371C22×D3—201no—
372C22×D3—201no—
373C22×D3—402no—
374C3×Q8—102no—
375C3×Q8—102no—
376C3×Q8—201no—
377C3×Q8—201no—
378C2×C3×C4—102no—
379C2×C3×C4—201no—
380C2×C3×C4—201no—
381C2×C3×C4C2×D2011yescharacteristic
382C2×C3×C4C2×D2011yescharacteristic
383C2×C3×C4D4×D511yescharacteristic
384C2×C3×C4D4×D511yescharacteristic
385C2×C3×C4#71311yescharacteristic
386C2×C3×C4C23×D511yescharacteristic
387#67—102no—
388#67—102no—
389C2×Dic3—101no—
390D12—52no—
391D12—102no—
392D12—102no—
393D12—101no—
394D12—201no—
395D12—201no—
396C4×D3—102no—
397C4×D3—102no—
398Dic6—52no—
399Dic6—101no—
400C3×C8—22no—
401C3×C8—102no—
402C3⋊C8—22no—
403C3⋊C8C2×D2012yes—
404C3⋊C8C2×D2012yes—
405C22×C5—22no—
406C22×C5#88411yescharacteristic
407C22×C5#88411yescharacteristic
408C22×C5C2×#23511yescharacteristic
409C2×D5—62no—
410C2×D5—122no—
411C2×D5—122no—
412C2×D5—242no—
413C2×D5—242no—
414C2×D5—242no—
415C4×C5#88411yescharacteristic
416C4×C5#88411yescharacteristic
417C4×C5C2×D3×D411yescharacteristic
418C4×C5C2×D3×D411yescharacteristic
419Dic5—42no—
420Dic5—62no—
421C24—301no—
422#41—152no—
423#41—152no—
424#41—301no—
425#41—301no—
426C2×Q8—52no—
427C2×Q8—101no—
428C2×Q8—101no—
429C2×Q8—101no—
430C2×Q8—101no—
431C2×Q8—101no—
432C2×Q8—151no—
433C2×D4—151no—
434C2×D4—152no—
435C2×D4—301no—
436C2×D4—301no—
437C2×D4—301no—
438C2×D4—301no—
439C2×D4—301no—
440C2×D4—301no—
441C22×C4—101no—
442C22×C4—301no—
443C22×C4C2×D3×D511yescharacteristic
444Q16—304no—
445SD16—304no—
446SD16—304no—
447SD16—304no—
448SD16—304no—
449D8—304no—
450M16—21no—
451M16—32no—
452M16—52no—
453M16—61no—
454M16—101no—
455M16—304no—
456M16C2×D3×D512yes—
457C2×C8—21no—
458C2×C8—31no—
459C2×C8—31no—
460C2×C8—32no—
461C2×C8—32no—
462C2×C8—61no—
463C2×C8—101no—
464C2×C8—304no—
465C3×C5C2×#47111yescharacteristic, complemented, Hall
466C22×C3—22no—
467C22×C3#404111yescharacteristic
468C22×C3#404111yescharacteristic
469C22×C3C2×#71311yescharacteristic
470C2×D3—102no—
471C2×D3—202no—
472C2×D3—202no—
473C2×D3—402no—
474C2×D3—402no—
475C2×D3—402no—
476C3×C4—202no—
477C3×C4#404111yescharacteristic
478C3×C4#404111yescharacteristic
479C3×C4C22×D2011yescharacteristic
480C3×C4C2×D4×D511yescharacteristic
481Dic3—102no—
482C2×C5—21no—
483C2×C5—21no—
484C2×C5#475412yescomplemented
485C2×C5C2×#88411yescharacteristic
486D5—122no—
487D5—242no—
488C23—301no—
489C23—302no—
490C23—601no—
491C23—601no—
492C23—1202no—
493C23#677311yescharacteristic
494Q8—102no—
495Q8—102no—
496Q8—152no—
497Q8—201no—
498Q8—201no—
499Q8—301no—
500D4—152no—
501D4—302no—
502D4—302no—
503D4—301no—
504D4—302no—
505D4—302no—
506D4—601no—
507D4—601no—
508C2×C4—102no—
509C2×C4—201no—
510C2×C4—201no—
511C2×C4—301no—
512C2×C4—302no—
513C2×C4—302no—
514C2×C4#677311yescharacteristic
515C2×C4D3×D2011yescharacteristic
516C2×C4D3×D2011yescharacteristic
517C2×C4#679011yescharacteristic
518C2×C4#679011yescharacteristic
519C2×C4C22×D3×D511yescharacteristic
520C8—22no—
521C8—32no—
522C8—32no—
523C8—62no—
524C8—102no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3#6518712yescomplemented
528C2×C3C2×#404111yescharacteristic
529D3—202no—
530D3—402no—
531C5C2×#475411yescharacteristic, complemented, Sylow
532C22—22no—
533C22—302no—
534C22—602no—
535C22—602no—
536C22—1202no—
537C22—1202no—
538C22—1202no—
539C22#9145911yescharacteristic
540C22#9145911yescharacteristic
541C22C2×#677311yescharacteristic
542C4—202no—
543C4—302no—
544C4#9145911yescharacteristic
545C4#9145911yescharacteristic
546C4C2×D3×D2011yescharacteristic
547C4C2×#679011yescharacteristic
548C3C2×#6518711yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—602no—
552C2—1202no—
553C2#1174819712yesdirect product factor
554C2C2×#9145911yescharacteristic
subgroupG/H
centerC22#91459
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#121
prime radicalC2×#91797C2
hypercenterC2×M16D3×D5
hypocenterC3×C5C2×#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#91315C2semidirect
3. C22×#6658C2semidirect
4. C2×#91291C2semidirect
5. C2×C5×#822C2semidirect
6. C2×C3×#3956C2semidirect
7. C2×#90960C2semidirect
8. #11748197C2direct (N × H)
23. #91315C22semidirect
28. C2×#6658C22semidirect
31. #91291C22semidirect
33. C5×#822C22semidirect
34. C3×#3956C22semidirect
35. #90960C22semidirect
42. C2×#3956D3semidirect
95. C2×#822D5semidirect
121. #3956C2×D3semidirect
186. #822C2×D5semidirect
364. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
484. C2×C5#4754semidirect
527. C2×C3#65187semidirect
531. C5C2×#4754semidirect
548. C3C2×#65187semidirect
553. C2#11748197direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917972
C2×#913152
C22×#66582
C2×#912912
C2×C5×#8222
C2×C3×#39562
C2×#909602
#117481972
C2×#651873
C2×#47545