Finite Group Databasebeta

← C2×#11749401 #14423378

Subgroups — C2×#11749401 #14423378

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic10C211yesmaximal, characteristic
2C22×#6718C211yesmaximal, characteristic, complemented
3C2×C5×#946C211yesmaximal, characteristic
4C22×C3×#689C211yesmaximal, characteristic, complemented
5#11749401C218yesmaximal, direct product factor
6C2×#90975C211yesmaximal, characteristic, complemented
7C2×#90970C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊#168C211yesmaximal, characteristic
9C2×#65339—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×Dic30C2211yescharacteristic
12C22×C4×C5×D3C2211yescharacteristic
13C22×C3×Dic10C2211yescharacteristic
14C22×#1204—21no—
15C22×D3×Dic5—21no—
16C2×D3×Dic10—24no—
17C2×D3×Dic10—22no—
18C2×D3×Dic10—24no—
19C2×D3×Dic10C2214yes—
20C2×#6718—24no—
21C2×#6718C2214yescomplemented
22C22×C3⋊#168C2211yescharacteristic
23C5×#946—22no—
24C5×#946C2214yes—
25C2×C5×(C2×D3)⋊C4—21no—
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C2×C5×Dic3⋊C4—21no—
28C2×C3×#689—24no—
29C2×C3×#689C2214yescomplemented
30C22×C3×#168C2211yescharacteristic
31#90975C2214yescomplemented
32#90970C2214yescomplemented
33(C2×D3)⋊#168C2214yes—
34C2×#5186—51nomaximal, Hall
35C23×Dic10—31no—
36C2×C5×C22⋊Q8—31no—
37C22×#689—31no—
38C22×#689D311yescharacteristic, complemented
39C2×C22⋊#168—31no—
40#65339—38no—
41C2×#3942—31no—
42C2×#3942—31no—
43C23×C5×D3D411yescharacteristic
44C2×C3×C5×Q8—21no—
45C2×C3×C5×Q8—22no—
46C2×C3×C5×Q8—22no—
47C2×C3×C5×Q8C2312yes—
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5C2311yescharacteristic
50C22×Dic15—21no—
51C2×Dic30—21no—
52C2×Dic30—22no—
53C2×Dic30D414yes—
54C2×Dic30C2312yes—
55C22×C5×Dic3—21no—
56C22×C5×Dic3D411yescharacteristic
57C2×C4×C5×D3—22no—
58C2×C4×C5×D3—22no—
59C2×C4×C5×D3D412yes—
60C2×C4×C5×D3C2312yes—
61C22×C3×Dic5—21no—
62C2×C3×Dic10—21no—
63C2×C3×Dic10—22no—
64C2×C3×Dic10D414yes—
65C2×C3×Dic10C2312yes—
66C2×#1204—28no—
67C2×#1204—24no—
68C2×D3×Dic5—28no—
69C2×D3×Dic5—24no—
70D3×Dic10—216no—
71D3×Dic10—28no—
72D3×Dic10—28no—
73#6718—28no—
74C2×C3⋊#168—22no—
75C2×C3⋊#168C2312yes—
76C5×(C2×D3)⋊C4—24no—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3C2312yes—
79C5×Dic3⋊C4—24no—
80C3×#689—28no—
81C2×C3×#168—22no—
82C2×C3×#168C2312yes—
83C22×D3×Q8—51no—
84C22×C3×Q16—51no—
85C2×#946D511yescharacteristic
86C22×#216—51no—
87C2×#835—51no—
88#5186—58no—
89C2×(C2×D3)⋊C8—51no—
90C2×#816—51no—
91C22×C5×Q8C2×D311yescharacteristic
92C23×C4×C5—31no—
93C23×Dic5—61no—
94C22×Dic10—31no—
95C22×Dic10—34no—
96C22×Dic10—64no—
97C22×Dic10—62no—
98C22×Dic10—61no—
99C22×Dic10—64no—
100C22×Dic10C2×D311yescharacteristic
101C5×C22⋊Q8—34no—
102C5×C22⋊Q8—62no—
103C2×C5×C4⋊C4—31no—
104C2×C5×C4⋊C4—61no—
105C2×C5×C22⋊C4—61no—
106C2×#689—24no—
107C2×#689—34no—
108C2×#689—64no—
109C2×#689C2×D314yescomplemented
110C22×#168—31no—
111C22×#168C2×D311yescharacteristic
112C22⋊#168—34no—
113#3942—34no—
114#3942—34no—
115C2×#451—151noSylow
116C23×C3×C5C2×D411yescharacteristic
117C22×C5×D3—22no—
118C22×C5×D3—22no—
119C22×C5×D3Q1614yescomplemented
120C22×C5×D3C2×D412yes—
121C3×C5×Q8—22no—
122C3×C5×Q8—22no—
123C3×C5×Q8—42no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—42no—
126C2×C3×C4×C5C2×D411yescharacteristic
127C2×C3×C4×C5C2×D412yes—
128C2×C3×C4×C5C2×D412yes—
129C2×C3×C4×C5C2411yescharacteristic
130C2×Dic15—24no—
131C2×Dic15—22no—
132Dic30—24no—
133Dic30—22no—
134Dic30C2×D414yes—
135C2×C5×Dic3—22no—
136C2×C5×Dic3—22no—
137C2×C5×Dic3—42no—
138C2×C5×Dic3C2×D412yes—
139C4×C5×D3—24no—
140C4×C5×D3—22no—
141C4×C5×D3—22no—
142C2×C3×Dic5—24no—
143C2×C3×Dic5—22no—
144C3×Dic10—24no—
145C3×Dic10—22no—
146C3×Dic10C2×D414yes—
147#1204—216no—
148D3×Dic5—216no—
149C3⋊#168—22no—
150C3×#168—22no—
151C22×C3×Q8—51no—
152C22×C3×Q8C2×D511yescharacteristic
153C2×D3×Q8—54no—
154C2×D3×Q8—104no—
155C2×D3×Q8—104no—
156C2×D3×Q8—102no—
157C22×C4×D3—101no—
158C22×C4×D3C2×D511yescharacteristic
159C22×Dic6—51no—
160C22×Dic6—101no—
161C2×C3×Q16—54no—
162C2×C3×Q16—104no—
163C22×C3×C8—51no—
164#946—22no—
165#946C2×D514yes—
166C2×#216—54no—
167C2×#216—104no—
168C2×(C2×D3)⋊C4—21no—
169C2×C4⋊Dic3C2×D511yescharacteristic
170C2×Dic3⋊C4—21no—
171C22×C3⋊C8—51no—
172#835—54no—
173(C2×D3)⋊C8—54no—
174#816—54no—
175C24×C5—31no—
176C2×C5×Q8—21no—
177C2×C5×Q8—22no—
178C2×C5×Q8—22no—
179C2×C5×Q8C22×D312yes—
180C22×C4×C5—21no—
181C22×C4×C5—31no—
182C22×C4×C5—32no—
183C22×C4×C5—32no—
184C22×C4×C5—62no—
185C22×C4×C5—62no—
186C22×C4×C5—61no—
187C22×C4×C5C22×D311yescharacteristic
188C22×Dic5—21no—
189C22×Dic5—64no—
190C22×Dic5—68no—
191C22×Dic5—61no—
192C2×Dic10—21no—
193C2×Dic10—22no—
194C2×Dic10—34no—
195C2×Dic10—32no—
196C2×Dic10—68no—
197C2×Dic10—616no—
198C2×Dic10—64no—
199C2×Dic10—68no—
200C2×Dic10—61no—
201C2×Dic10—62no—
202C2×Dic10—68no—
203C2×Dic10#6714yes—
204C2×Dic10C22×D312yes—
205C5×C4⋊C4—32no—
206C5×C4⋊C4—64no—
207C5×C4⋊C4—61no—
208C5×C22⋊C4—64no—
209#689—28no—
210#689—68no—
211C2×#168—22no—
212C2×#168—32no—
213C2×#168—62no—
214C2×#168C22×D312yes—
215C23×Q8—151no—
216C22×Q16—51no—
217C22×Q16—151no—
218C2×C22⋊Q8—31no—
219#451—158no—
220C2×#103—151no—
221C2×#103—151no—
222C2×C22⋊C8—151no—
223C22×C3×C5#12012yes—
224C22×C3×C5C2×Q1612yes—
225C22×C3×C5#13712yes—
226C22×C3×C5C22×D411yescharacteristic
227C2×C5×D3—22no—
228C2×C5×D3—22no—
229C2×C5×D3—28no—
230C2×C5×D3C2×Q1614yescomplemented
231C3×C4×C5—42no—
232C3×C4×C5#12012yes—
233C3×C4×C5C22×D411yescharacteristic
234C3×C4×C5C22×D411yescharacteristic
235Dic15—24no—
236C3×Dic5—24no—
237C5×Dic3—22no—
238C5×Dic3—42no—
239C23×D3C22⋊D511yescharacteristic
240C2×C3×Q8—21no—
241C2×C3×Q8—22no—
242C2×C3×Q8—22no—
243C2×C3×Q8—54no—
244C2×C3×Q8—52no—
245C2×C3×Q8—102no—
246C2×C3×Q8—101no—
247C2×C3×Q8C22×D512yes—
248C22×C3×C4—21no—
249C22×C3×C4—101no—
250C22×C3×C4C22×D511yescharacteristic
251C22×Dic3—21no—
252C22×Dic3—101no—
253C22×Dic3C22⋊D511yescharacteristic
254D3×Q8—108no—
255D3×Q8—108no—
256D3×Q8—1016no—
257C2×C4×D3—22no—
258C2×C4×D3—22no—
259C2×C4×D3—108no—
260C2×C4×D3—104no—
261C2×C4×D3C22⋊D512yes—
262C2×C4×D3C22×D512yes—
263C2×Dic6—54no—
264C2×Dic6—52no—
265C2×Dic6—108no—
266C2×Dic6—102no—
267C2×Dic6—101no—
268C2×Dic6—104no—
269C3×Q16—108no—
270C2×C3×C8—52no—
271C2×C3×C8—102no—
272#216—108no—
273(C2×D3)⋊C4—24no—
274C4⋊Dic3—21no—
275C4⋊Dic3C22×D512yes—
276Dic3⋊C4—24no—
277C2×C3⋊C8—52no—
278C2×C3⋊C8—102no—
279C23×C5—34no—
280C23×C5—32no—
281C23×C5—62no—
282C23×C5—62no—
283C23×C5D3×D411yescharacteristic
284C5×Q8—22no—
285C5×Q8—22no—
286C5×Q8—42no—
287C2×C4×C5—22no—
288C2×C4×C5—32no—
289C2×C4×C5—42no—
290C2×C4×C5—62no—
291C2×C4×C5—64no—
292C2×C4×C5—62no—
293C2×C4×C5—62no—
294C2×C4×C5—62no—
295C2×C4×C5—122no—
296C2×C4×C5D3×D411yescharacteristic
297C2×C4×C5D3×D412yes—
298C2×C4×C5C2×#6712yes—
299C2×C4×C5C23×D311yescharacteristic
300C2×Dic5—24no—
301C2×Dic5—22no—
302C2×Dic5—616no—
303C2×Dic5—64no—
304C2×Dic5—62no—
305Dic10—24no—
306Dic10—22no—
307Dic10—34no—
308Dic10—616no—
309Dic10—64no—
310Dic10—62no—
311Dic10C2×#6714yes—
312#168—22no—
313#168—62no—
314C22×Q8—51no—
315C22×Q8—154no—
316C22×Q8—151no—
317C22×Q8—301no—
318C22×Q8—302no—
319C22×Q8—304no—
320C22×Q8—304no—
321C22×Q8D3×D511yescharacteristic
322C23×C4—31no—
323C23×C4—301no—
324C2×Q16—54no—
325C2×Q16—104no—
326C2×Q16—154no—
327C2×Q16—304no—
328C22×C8—51no—
329C22×C8—151no—
330C22⋊Q8—34no—
331C22⋊Q8—62no—
332C2×C4⋊C4—31no—
333C2×C4⋊C4—61no—
334C2×C22⋊C4—61no—
335#103—154no—
336#103—154no—
337C22⋊C8—154no—
338C2×C3×C5#45114yescomplemented
339C2×C3×C5C2×#12011yescharacteristic
340C2×C3×C5C22×Q1611yescharacteristic
341C2×C3×C5C2×#13711yescharacteristic
342C5×D3—24no—
343C23×C3C2×C22⋊D511yescharacteristic
344C22×D3—22no—
345C22×D3—22no—
346C22×D3#68914yescomplemented
347C22×D3C2×C22⋊D512yes—
348C3×Q8—22no—
349C3×Q8—22no—
350C3×Q8—42no—
351C3×Q8—54no—
352C3×Q8—102no—
353C3×Q8—104no—
354C2×C3×C4—22no—
355C2×C3×C4—42no—
356C2×C3×C4—102no—
357C2×C3×C4—104no—
358C2×C3×C4D4×D512yes—
359C2×C3×C4D4×D512yes—
360C2×C3×C4C2×C22⋊D511yescharacteristic
361C2×C3×C4C23×D511yescharacteristic
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—42no—
365C2×Dic3—102no—
366C2×Dic3—104no—
367C2×Dic3C2×C22⋊D512yes—
368C4×D3—22no—
369C4×D3—22no—
370C4×D3—24no—
371C4×D3—1016no—
372Dic6—54no—
373Dic6—1016no—
374Dic6—102no—
375Dic6—104no—
376C3×C8—102no—
377C3⋊C8—102no—
378C22×C5—34no—
379C22×C5—68no—
380C22×C5—62no—
381C22×C5—62no—
382C22×C5D3×Q1612yes—
383C22×C5#91812yes—
384C22×C5#93712yes—
385C22×C5C2×D3×D411yescharacteristic
386C4×C5—42no—
387C4×C5—62no—
388C4×C5—122no—
389C4×C5#93712yes—
390C4×C5C2×D3×D411yescharacteristic
391C4×C5C22×#6711yescharacteristic
392Dic5—24no—
393Dic5—64no—
394C24—31no—
395C2×Q8—21no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—54no—
399C2×Q8—52no—
400C2×Q8—101no—
401C2×Q8—102no—
402C2×Q8—154no—
403C2×Q8—152no—
404C2×Q8—304no—
405C2×Q8—308no—
406C2×Q8—308no—
407C2×Q8—308no—
408C2×Q8—3016no—
409C2×Q8—302no—
410C2×Q8—301no—
411C2×Q8C2×D3×D512yes—
412C22×C4—21no—
413C22×C4—31no—
414C22×C4—32no—
415C22×C4—32no—
416C22×C4—62no—
417C22×C4—62no—
418C22×C4—61no—
419C22×C4—101no—
420C22×C4—304no—
421C22×C4—308no—
422C22×C4—301no—
423C22×C4C2×D3×D511yescharacteristic
424Q16—108no—
425Q16—308no—
426C2×C8—52no—
427C2×C8—102no—
428C2×C8—152no—
429C2×C8—302no—
430C4⋊C4—32no—
431C4⋊C4—64no—
432C4⋊C4—61no—
433C22⋊C4—64no—
434C3×C5C2×#45111yescharacteristic, complemented, Hall
435C22×C3#408312yes—
436C22×C3C2×#68912yes—
437C22×C3#409712yes—
438C22×C3C22×C22⋊D511yescharacteristic
439C2×D3—28no—
440C2×D3—22no—
441C2×D3—22no—
442C2×D3C2×#68914yescomplemented
443C3×C4—42no—
444C3×C4—104no—
445C3×C4#408312yes—
446C3×C4C2×D4×D511yescharacteristic
447C3×C4C2×D4×D511yescharacteristic
448Dic3—22no—
449Dic3—42no—
450Dic3—104no—
451C2×C5—64no—
452C2×C5#518614yescomplemented
453C2×C5C2×D3×Q1611yescharacteristic
454C2×C5C2×#91811yescharacteristic
455C2×C5C2×#93711yescharacteristic
456C23—34no—
457C23—32no—
458C23—62no—
459C23—62no—
460C23D3×C22⋊D511yescharacteristic
461Q8—22no—
462Q8—22no—
463Q8—42no—
464Q8—54no—
465Q8—102no—
466Q8—104no—
467Q8—154no—
468Q8—3016no—
469Q8—302no—
470Q8—304no—
471C2×C4—22no—
472C2×C4—32no—
473C2×C4—42no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—64no—
478C2×C4—62no—
479C2×C4—102no—
480C2×C4—104no—
481C2×C4—122no—
482C2×C4—3016no—
483C2×C4—302no—
484C2×C4—304no—
485C2×C4D5×#6712yes—
486C2×C4D3×C22⋊D511yescharacteristic
487C2×C4#679012yes—
488C2×C4C22×D3×D511yescharacteristic
489C8—102no—
490C8—302no—
491C2×C3#6533914yescomplemented
492C2×C3C2×#408311yescharacteristic
493C2×C3C22×#68911yescharacteristic
494C2×C3C2×#409711yescharacteristic
495D3—24no—
496C5C2×#518611yescharacteristic, complemented, Sylow
497C22—34no—
498C22—68no—
499C22—62no—
500C22—62no—
501C22D3×#68912yes—
502C22#9151012yes—
503C22#9157712yes—
504C22C2×D3×C22⋊D511yescharacteristic
505C4—42no—
506C4—62no—
507C4—104no—
508C4—122no—
509C4—304no—
510C4#9157712yes—
511C4C2×D5×#6711yescharacteristic
512C4C2×#679011yescharacteristic
513C3C2×#6533911yescharacteristic, complemented, Sylow
514C2—64no—
515C2#1174940114yesdirect product factor
516C2C2×D3×#68911yescharacteristic
517C2C2×#9151011yescharacteristic
518C2C2×#9157711yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC23×C5×D3D4
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#451
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×#6718C2semidirect
4. C22×C3×#689C2semidirect
5. #11749401C2direct (N × H)
6. C2×#90975C2semidirect
7. C2×#90970C2semidirect
21. C2×#6718C22semidirect
29. C2×C3×#689C22semidirect
31. #90975C22semidirect
32. #90970C22semidirect
38. C22×#689D3semidirect
109. C2×#689C2×D3semidirect
119. C22×C5×D3Q16semidirect
230. C2×C5×D3C2×Q16semidirect
338. C2×C3×C5#451semidirect
346. C22×D3#689semidirect
434. C3×C5C2×#451semidirect
442. C2×D3C2×#689semidirect
452. C2×C5#5186semidirect
491. C2×C3#65339semidirect
496. C5C2×#5186semidirect
513. C3C2×#65339semidirect
515. C2#11749401direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Dic102
C22×#67182
C2×C5×#9462
C22×C3×#6892
#117494012
C2×#909752
C2×#909702
C2×(C2×D3)⋊#1682
C2×#653393
C2×#51865