Finite Group Databasebeta

← #14424530

Subgroups — #14424530

Order 1920.

1400 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92098C211yesmaximal, characteristic
2C22×C3×C5×Q16C211yesmaximal, characteristic, complemented
3#11756575C211yesmaximal, characteristic, complemented
4C2×#91831C211yesmaximal, characteristic, complemented
5#11751326C211yesmaximal, characteristic, complemented
6#11751288C214yesmaximal, complemented
7#11751287C214yesmaximal, complemented
8#11751214C211yesmaximal, characteristic, complemented
9#11751211C211yesmaximal, characteristic, complemented
10#10615615—31nomaximal, Hall
11C22×C3×C5×Q8C2211yescharacteristic
12C22×C3×C5×Q8C2211yescharacteristic
13#92098—24no—
14#92098—24no—
15C2×#6821—21no—
16C2×#6821C2212yes—
17C2×Q8×D15—21no—
18C2×Q8×D15C2212yes—
19C2×#6817—22no—
20C2×#6817C2211yescharacteristic
21C2×#6817C2211yescharacteristic
22C2×C3×C5×Q16—24no—
23C2×C3×C5×Q16C2214yes—
24C22×C3×C5×C8C2211yescharacteristic
25#91836—21no—
26#91835C2214yes—
27#91833—21no—
28C2×#6718C2212yes—
29#91831—24no—
30C2×#6717C2212yes—
31#91818—22no—
32#91815C2211yescharacteristic
33C2×#6710C2211yescharacteristic
34#91119C2214yes—
35#91105C2212yes—
36#91104C2214yes—
37#91100C2212yes—
38#83884—51nomaximal, Hall
39C2×#4147—31no—
40C22×C5×Q16D311yescharacteristic, complemented
41#66150—31no—
42C2×#4088—31no—
43#65514—31no—
44#65476—34no—
45#65475—34no—
46#65402—31no—
47#65399—31no—
48C2×C3×C5×Q8—21no—
49C2×C3×C5×Q8—22no—
50C2×C3×C5×Q8—21no—
51C2×C3×C5×Q8—22no—
52C2×C3×C5×Q8—22no—
53C2×C3×C5×Q8D414yes—
54C2×C3×C5×Q8C2312yes—
55C2×C3×C5×Q8C2312yes—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—21no—
60C2×#1220D412yes—
61#6821—28no—
62#6821—24no—
63#6821—24no—
64Q8×D15—28no—
65Q8×D15—24no—
66Q8×D15—24no—
67#6817—216no—
68#6817—22no—
69#6817—22no—
70#6817—22no—
71#6817D414yes—
72C2×D60—22no—
73C2×D60D411yescharacteristic
74C2×D60C2311yescharacteristic
75C2×C4×D15—22no—
76C2×C4×D15—21no—
77C2×C4×D15—22no—
78C2×C4×D15C2312yes—
79C2×Dic30—22no—
80C2×Dic30D411yescharacteristic
81C2×Dic30C2311yescharacteristic
82C3×C5×Q16—28no—
83C2×C3×C5×C8—22no—
84C2×C3×C5×C8C2312yes—
85#6719—21no—
86#6718—24no—
87#6717—24no—
88#6714—24no—
89C4⋊Dic15C2312yes—
90#6712—24no—
91C4×Dic15—21no—
92#6710—22no—
93C2×C3⋊#168C2312yes—
94C2×#1007—51no—
95C22×C3×Q16D511yescharacteristic, complemented
96#5816—51no—
97C2×#942—51no—
98#5225—51no—
99#5187—54no—
100#5186—54no—
101#5113—51no—
102#5110—51no—
103C22×C5×Q8C2×D311yescharacteristic
104C22×C5×Q8C2×D311yescharacteristic
105#4147—64no—
106#4147—64no—
107C2×#713—32no—
108C2×#713—61no—
109C2×Q8×D5—32no—
110C2×Q8×D5—61no—
111C2×#709—31no—
112C2×#709—31no—
113C2×#709—62no—
114C2×C5×Q16—24no—
115C2×C5×Q16C2×D314yes—
116C22×C5×C8C2×D311yescharacteristic
117#4093—61no—
118#4092—34no—
119#4090—61no—
120C2×#689—32no—
121#4088—64no—
122C2×#688—32no—
123#4075—62no—
124#4072—31no—
125C2×#681—31no—
126#3967—34no—
127#3953—32no—
128#3952—34no—
129#3948—32no—
130#3011—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×D15—21no—
133C22×D15C2×D412yes—
134C3×C5×Q8—24no—
135C3×C5×Q8—22no—
136C3×C5×Q8—22no—
137C3×C5×Q8—22no—
138C3×C5×Q8—42no—
139C3×C5×Q8C2×D414yes—
140C2×C3×C4×C5—24no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—42no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5C2411yescharacteristic
148#1220—24no—
149#1220—24no—
150C2×Dic15—21no—
151C2×Dic15—22no—
152C2×Dic15C2×D412yes—
153D60—28no—
154D60—22no—
155D60—21no—
156D60C2×D412yes—
157C4×D15—28no—
158C4×D15—28no—
159C4×D15—24no—
160C4×D15—22no—
161C4×D15—22no—
162Dic30—28no—
163Dic30—22no—
164Dic30—21no—
165Dic30C2×D412yes—
166C3×C5×C8—22no—
167C3⋊#168—22no—
168C22×C3×Q8C2×D511yescharacteristic
169C22×C3×Q8C2×D511yescharacteristic
170#1007—104no—
171#1007—104no—
172C2×#239—52no—
173C2×#239—101no—
174C2×D3×Q8—52no—
175C2×D3×Q8—101no—
176C2×#235—51no—
177C2×#235—51no—
178C2×#235—102no—
179C2×C3×Q16—24no—
180C2×C3×Q16C2×D514yes—
181C22×C3×C8C2×D511yescharacteristic
182#947—101no—
183#946—54no—
184#944—101no—
185C2×#216—52no—
186#942—104no—
187C2×#215—52no—
188#929—102no—
189#926—51no—
190C2×#208—51no—
191#835—54no—
192#821—52no—
193(C2×D3)⋊C8—54no—
194#816—52no—
195C2×C5×Q8—21no—
196C2×C5×Q8—22no—
197C2×C5×Q8—21no—
198C2×C5×Q8—22no—
199C2×C5×Q8—22no—
200C2×C5×Q8#6714yes—
201C2×C5×Q8C22×D312yes—
202C2×C5×Q8C22×D312yes—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5C22×D311yescharacteristic
206C2×C22⋊D5—32no—
207C2×C22⋊D5—61no—
208#713—64no—
209#713—68no—
210#713—64no—
211Q8×D5—64no—
212Q8×D5—68no—
213Q8×D5—64no—
214#709—34no—
215#709—616no—
216#709—62no—
217#709—62no—
218#709—62no—
219C2×D20—31no—
220C2×D20—31no—
221C2×D20—62no—
222C2×C4×D5—32no—
223C2×C4×D5—62no—
224C2×C4×D5—62no—
225C2×C4×D5—61no—
226C2×Dic10—31no—
227C2×Dic10—31no—
228C2×Dic10—62no—
229C5×Q16—28no—
230C2×C5×C8—22no—
231C2×C5×C8C22×D312yes—
232C22⋊Dic5—61no—
233#689—64no—
234#688—64no—
235#685—64no—
236C4⋊Dic5—32no—
237#683—64no—
238C4×Dic5—61no—
239#681—62no—
240C2×#168—32no—
241C2×2−1+4—151no—
242C2×#137—151no—
243C22×Q16D1511yescharacteristic, complemented
244#536—151no—
245#452—154no—
246#451—154no—
247#419—151no—
248#416—151no—
249#408—151no—
250C22×C3×C5—22no—
251C22×C3×C5#12012yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×D15—22no—
254C2×D15—22no—
255C2×D15—24no—
256C2×D15—42no—
257C3×C4×C5—24no—
258C3×C4×C5—42no—
259C3×C4×C5#12012yes—
260C3×C4×C5C22×D411yescharacteristic
261C3×C4×C5C22×D411yescharacteristic
262Dic15—22no—
263Dic15—22no—
264Dic15—42no—
265C2×C3×Q8—21no—
266C2×C3×Q8—22no—
267C2×C3×Q8—21no—
268C2×C3×Q8—22no—
269C2×C3×Q8—22no—
270C2×C3×Q8C22⋊D514yes—
271C2×C3×Q8C22×D512yes—
272C2×C3×Q8C22×D512yes—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4C22×D511yescharacteristic
276C2×#67—52no—
277C2×#67—101no—
278#239—104no—
279#239—108no—
280#239—104no—
281D3×Q8—104no—
282D3×Q8—108no—
283D3×Q8—104no—
284#235—54no—
285#235—1016no—
286#235—102no—
287#235—102no—
288#235—102no—
289C2×D12—51no—
290C2×D12—51no—
291C2×D12—102no—
292C2×C4×D3—52no—
293C2×C4×D3—102no—
294C2×C4×D3—102no—
295C2×C4×D3—101no—
296C2×Dic6—51no—
297C2×Dic6—51no—
298C2×Dic6—102no—
299C3×Q16—28no—
300C2×C3×C8—22no—
301C2×C3×C8C22×D512yes—
302#217—101no—
303#216—104no—
304#215—104no—
305(C2×D3)⋊C4—104no—
306C4⋊Dic3—52no—
307Dic3⋊C4—104no—
308C4×Dic3—101no—
309#208—102no—
310C2×C3⋊C8—52no—
311C23×C5D3×D411yescharacteristic
312C22×D5—32no—
313C22×D5—61no—
314C5×Q8—24no—
315C5×Q8—22no—
316C5×Q8—22no—
317C5×Q8—22no—
318C5×Q8—42no—
319C5×Q8C2×#6714yes—
320C2×C4×C5—24no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—42no—
324C2×C4×C5D3×D411yescharacteristic
325C2×C4×C5D3×D412yes—
326C2×C4×C5C2×#6712yes—
327C2×C4×C5C23×D311yescharacteristic
328C22⋊D5—64no—
329C22⋊D5—64no—
330C2×Dic5—32no—
331C2×Dic5—61no—
332C2×Dic5—62no—
333D20—32no—
334D20—68no—
335D20—62no—
336D20—61no—
337C4×D5—68no—
338C4×D5—68no—
339C4×D5—64no—
340C4×D5—62no—
341C4×D5—62no—
342Dic10—32no—
343Dic10—68no—
344Dic10—62no—
345Dic10—61no—
346C5×C8—22no—
347#168—62no—
3482−1+4—304no—
3492−1+4—304no—
350C2×#41—151no—
351C2×#41—152no—
352C2×#41—151no—
353C2×#41—302no—
354C2×#41—301no—
355C22×Q8—152no—
356C22×Q8—301no—
357C22×Q8C2×D1511yescharacteristic
358C22×Q8C2×D1511yescharacteristic
359#137—304no—
360C2×Q16—24no—
361C2×Q16—152no—
362C2×Q16C2×D1514yes—
363C2×SD16—152no—
364C2×M16—151no—
365C22×C8C2×D1511yescharacteristic
366C4⋊Q8—301no—
367#124—301no—
368#123—302no—
369C22⋊Q8—154no—
370#117—151no—
371#103—154no—
372#103—152no—
373#102—152no—
374C22⋊C8—154no—
375C2×C3×C5—22no—
376C2×C3×C5C2×#12011yescharacteristic
377C2×C3×C5#57812yes—
378D15—42no—
379D15—42no—
380C23×C3D4×D511yescharacteristic
381C22×D3—52no—
382C22×D3—101no—
383C3×Q8—22no—
384C3×Q8—24no—
385C3×Q8—22no—
386C3×Q8—22no—
387C3×Q8—42no—
388C3×Q8C2×C22⋊D514yes—
389C2×C3×C4—22no—
390C2×C3×C4—24no—
391C2×C3×C4—22no—
392C2×C3×C4—42no—
393C2×C3×C4D4×D512yes—
394C2×C3×C4D4×D511yescharacteristic
395C2×C3×C4C2×C22⋊D512yes—
396C2×C3×C4C23×D511yescharacteristic
397#67—104no—
398#67—104no—
399C2×Dic3—52no—
400C2×Dic3—101no—
401C2×Dic3—102no—
402D12—52no—
403D12—108no—
404D12—101no—
405D12—102no—
406C4×D3—108no—
407C4×D3—108no—
408C4×D3—102no—
409C4×D3—102no—
410C4×D3—104no—
411Dic6—52no—
412Dic6—108no—
413Dic6—101no—
414Dic6—102no—
415C3×C8—22no—
416C3⋊C8—102no—
417C22×C5—22no—
418C22×C5#93712yes—
419C22×C5C2×D3×D411yescharacteristic
420C2×D5—64no—
421C2×D5—62no—
422C2×D5—62no—
423C2×D5—122no—
424C4×C5—24no—
425C4×C5—42no—
426C4×C5#93712yes—
427C4×C5C2×D3×D411yescharacteristic
428C4×C5C22×#6711yescharacteristic
429Dic5—62no—
430Dic5—62no—
431Dic5—122no—
432#41—154no—
433#41—3016no—
434#41—304no—
435#41—308no—
436#41—304no—
437#41—302no—
438#41—302no—
439#41—302no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—21no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—151no—
446C2×Q8—151no—
447C2×Q8—302no—
448C2×Q8—304no—
449C2×Q8—308no—
450C2×Q8—304no—
451C2×Q8#122014yes—
452C2×Q8C22×D1512yes—
453C2×Q8C22×D1512yes—
454C2×D4—152no—
455C2×D4—151no—
456C2×D4—151no—
457C2×D4—302no—
458C2×D4—301no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—152no—
462C22×C4—302no—
463C22×C4—302no—
464C22×C4—301no—
465C22×C4C22×D1511yescharacteristic
466Q16—28no—
467Q16—304no—
468SD16—304no—
469M16—302no—
470C2×C8—22no—
471C2×C8—152no—
472C2×C8C22×D1512yes—
473C4⋊C4—152no—
474C4⋊C4—304no—
475C22⋊C4—304no—
476C22⋊C4—301no—
477C42—301no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3#408312yes—
481C22×C3C2×D4×D511yescharacteristic
482C2×D3—104no—
483C2×D3—102no—
484C2×D3—102no—
485C2×D3—202no—
486C3×C4—24no—
487C3×C4—42no—
488C3×C4#408312yes—
489C3×C4C2×D4×D511yescharacteristic
490C3×C4C22×C22⋊D511yescharacteristic
491Dic3—102no—
492Dic3—102no—
493Dic3—202no—
494C2×C5—22no—
495C2×C5#576612yes—
496C2×C5C2×#93711yescharacteristic
497D5—122no—
498D5—122no—
499C23—152no—
500C23—301no—
501C23D4×D1511yescharacteristic
502Q8—24no—
503Q8—22no—
504Q8—22no—
505Q8—22no—
506Q8—42no—
507Q8—152no—
508Q8—308no—
509Q8—302no—
510Q8—301no—
511Q8C2×#122014yes—
512D4—152no—
513D4—308no—
514D4—304no—
515D4—304no—
516D4—302no—
517D4—301no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—42no—
522C2×C4—152no—
523C2×C4—308no—
524C2×C4—308no—
525C2×C4—301no—
526C2×C4—304no—
527C2×C4—302no—
528C2×C4—302no—
529C2×C4—302no—
530C2×C4D4×D1511yescharacteristic
531C2×C4D4×D1512yes—
532C2×C4C2×#122012yes—
533C2×C4C23×D1511yescharacteristic
534C8—22no—
535C8—302no—
536C2×C3—22no—
537C2×C3#6610012yes—
538C2×C3C2×#408311yescharacteristic
539D3—202no—
540D3—202no—
541C5#8388411yescharacteristic, complemented, Sylow
542C22—22no—
543C22—302no—
544C22—302no—
545C22—304no—
546C22—602no—
547C22#9182612yes—
548C22C2×D4×D1511yescharacteristic
549C4—24no—
550C4—42no—
551C4—302no—
552C4—302no—
553C4—602no—
554C4#9182612yes—
555C4C2×D4×D1511yescharacteristic
556C4C22×#122011yescharacteristic
557C3#1061561511yescharacteristic, complemented, Sylow
558C2—22no—
559C2—602no—
560C2—602no—
561C2#1175652512yes—
562C2C2×#9182611yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×Q16C2
socleC22×C3×C5C22×D4
prime radicalC2×#92098C2
hypercenterC22×Q16D15
hypocenterC3×C5#3011
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
2. C22×C3×C5×Q16C2semidirect
3. #11756575C2semidirect
4. C2×#91831C2semidirect
5. #11751326C2semidirect
6. #11751288C2semidirect
7. #11751287C2semidirect
8. #11751214C2semidirect
9. #11751211C2semidirect
40. C22×C5×Q16D3semidirect
95. C22×C3×Q16D5semidirect
243. C22×Q16D15semidirect
478. C3×C5#3011semidirect
541. C5#83884semidirect
557. C3#10615615semidirect

Maximal subgroups

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

subgroupindex
C2×#920982
C22×C3×C5×Q162
#117565752
C2×#918312
#117513262
#117512882
#117512872
#117512142
#117512112
#106156153
#838845