Finite Group Databasebeta

← C2×#11749405 #14423526

Subgroups — C2×#11749405 #14423526

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6772C211yesmaximal, characteristic
2C22×#6718C211yesmaximal, characteristic, complemented
3C22×C5×#215C211yesmaximal, characteristic, complemented
4C2×C3×#4092C211yesmaximal, characteristic, complemented
5#11749405C218yesmaximal, direct product factor
6C2×#90974C211yesmaximal, characteristic, complemented
7C2×#90966C211yesmaximal, characteristic, complemented
8C2×#90955C211yesmaximal, characteristic, complemented
9C2×#65462—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×Dic30C2211yescharacteristic
12C22×C5×D12C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C22×#1201—21no—
15C22×D3×Dic5—21no—
16C2×#6772—24no—
17C2×#6772—24no—
18C2×#6772—22no—
19C2×#6772C2214yes—
20C2×#6718—24no—
21C2×#6718C2214yescomplemented
22C22×C3⋊#168C2211yescharacteristic
23C2×C5×#215—24no—
24C2×C5×#215C2214yescomplemented
25C22×C5×C3⋊C8C2211yescharacteristic
26C3×#4092—22no—
27C3×#4092C2214yescomplemented
28C2×C3×#685—21no—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683—21no—
31#90974C2214yescomplemented
32#90966C2214yescomplemented
33#90955C2214yescomplemented
34C2×#5047—51nomaximal, Hall
35C22×#711—31no—
36C22×C5×SD16—31no—
37C2×#4092D311yescharacteristic, complemented
38C22×#689—31no—
39C2×#3964—31no—
40#65462—38no—
41C2×#3952—31no—
42C2×#3948—31no—
43C23×C5×D3—21no—
44C23×C3×D5D411yescharacteristic
45C2×C3×C5×Q8—21no—
46C2×C3×C5×Q8—22no—
47C2×C3×C5×Q8—22no—
48C2×C3×C5×Q8C2312yes—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5C2311yescharacteristic
51C22×Dic15—21no—
52C2×Dic30—21no—
53C2×Dic30—22no—
54C2×Dic30D414yes—
55C2×Dic30C2312yes—
56C2×C5×D12—21no—
57C2×C5×D12—22no—
58C2×C5×D12D414yes—
59C2×C5×D12C2312yes—
60C22×C3×Dic5—21no—
61C22×C3×Dic5D411yescharacteristic
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5D412yes—
65C2×C3×C4×D5C2312yes—
66C2×#1201—28no—
67C2×#1201—24no—
68C2×D3×Dic5—28no—
69C2×D3×Dic5—24no—
70#6772—216no—
71#6772—28no—
72#6772—28no—
73#6718—28no—
74C2×C3⋊#168—22no—
75C2×C3⋊#168C2312yes—
76C5×#215—28no—
77C2×C5×C3⋊C8—22no—
78C2×C5×C3⋊C8C2312yes—
79C3×#685—24no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2312yes—
82C3×#683—24no—
83C22×#235—51no—
84C2×C3×C22⋊Q8—51no—
85C22×#216—51no—
86C22×#215D511yescharacteristic, complemented
87C2×#830—51no—
88#5047—58no—
89C2×#810—51no—
90C2×#809—51no—
91C22×C5×Q8C2×D311yescharacteristic
92C22×C5×D4—31no—
93C22×C22⋊D5—61no—
94C23×Dic5—61no—
95C2×#711—34no—
96C2×#711—64no—
97C2×#711—64no—
98C2×#711—62no—
99C22×C4×D5C2×D311yescharacteristic
100C22×Dic10—31no—
101C2×C5×SD16—34no—
102C2×C5×SD16—64no—
103C22×C5×C8—31no—
104#4092—22no—
105#4092C2×D314yescomplemented
106C2×#689—34no—
107C2×#689—64no—
108C2×#685—21no—
109C2×C4⋊Dic5C2×D311yescharacteristic
110C2×#683—21no—
111C22×#168—31no—
112#3964—34no—
113#3952—34no—
114#3948—34no—
115C2×#452—151noSylow
116C23×C3×C5C2×D411yescharacteristic
117C22×C5×D3—24no—
118C22×C5×D3—22no—
119C22×C5×D3—42no—
120C22×C5×D3—42no—
121C22×C3×D5—22no—
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5C2×D412yes—
125C3×C5×Q8—22no—
126C3×C5×Q8—22no—
127C3×C5×Q8—42no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—42no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—24no—
135C2×Dic15—22no—
136Dic30—24no—
137Dic30—22no—
138Dic30C2×D414yes—
139C5×D12—24no—
140C5×D12—22no—
141C5×D12C2×D414yes—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—42no—
145C2×C3×Dic5C2×D412yes—
146C3×C4×D5—24no—
147C3×C4×D5—22no—
148C3×C4×D5—22no—
149#1201—216no—
150D3×Dic5—216no—
151C3⋊#168—22no—
152C5×C3⋊C8—22no—
153C22×C3×Q8C2×D511yescharacteristic
154C23×C3×C4—51no—
155C22×#67—101no—
156C2×#235—54no—
157C2×#235—104no—
158C2×#235—102no—
159C2×#235—104no—
160C22×D12C2×D511yescharacteristic
161C22×C4×D3—101no—
162C22×Dic6—51no—
163C3×C22⋊Q8—54no—
164C3×C22⋊Q8—102no—
165C2×C3×C4⋊C4—51no—
166C2×C3×C4⋊C4—101no—
167C2×C3×C22⋊C4—101no—
168C2×#216—54no—
169C2×#216—104no—
170C2×#215—24no—
171C2×#215C2×D514yescomplemented
172C22×C3⋊C8—51no—
173C22×C3⋊C8C2×D511yescharacteristic
174#830—54no—
175#810—54no—
176#809—54no—
177C24×C5—61no—
178C23×D5#6711yescharacteristic
179C2×C5×Q8—21no—
180C2×C5×Q8—22no—
181C2×C5×Q8—22no—
182C2×C5×Q8C22×D312yes—
183C2×C5×D4—34no—
184C2×C5×D4—32no—
185C2×C5×D4—62no—
186C2×C5×D4—61no—
187C22×C4×C5—21no—
188C22×C4×C5C22×D311yescharacteristic
189C2×C22⋊D5—68no—
190C2×C22⋊D5—64no—
191C22×Dic5—21no—
192C22×Dic5—68no—
193C22×Dic5—61no—
194C22×Dic5—64no—
195C22×Dic5#6711yescharacteristic
196#711—68no—
197#711—68no—
198#711—616no—
199C2×C4×D5—22no—
200C2×C4×D5—22no—
201C2×C4×D5#6712yes—
202C2×C4×D5C22×D312yes—
203C2×Dic10—34no—
204C2×Dic10—32no—
205C2×Dic10—62no—
206C2×Dic10—61no—
207C5×SD16—68no—
208C2×C5×C8—32no—
209C2×C5×C8—62no—
210#689—68no—
211#685—24no—
212C4⋊Dic5—21no—
213C4⋊Dic5C22×D312yes—
214#683—24no—
215C2×#168—32no—
216C2×#168—62no—
217C22×#41—151no—
218C22×Q16—151no—
219C22×SD16—31no—
220C2×C22⋊Q8—51no—
221#452—158no—
222C2×#103—151no—
223C2×#102—151no—
224C2×C22⋊C8—151no—
225C22×C3×C5#12012yes—
226C22×C3×C5#13512yes—
227C22×C3×C5#13712yes—
228C22×C3×C5C22×D411yescharacteristic
229C2×C5×D3—24no—
230C2×C5×D3—42no—
231C2×C5×D3—42no—
232C2×C5×D3—48no—
233C2×C3×D5—22no—
234C2×C3×D5—22no—
235C2×C3×D5—22no—
236C2×C3×D5—44no—
237C3×C4×C5—42no—
238C3×C4×C5#12012yes—
239C3×C4×C5C22×D411yescharacteristic
240C3×C4×C5C22×D411yescharacteristic
241Dic15—24no—
242C3×Dic5—22no—
243C3×Dic5—42no—
244C24×C3—51no—
245C23×D3—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—22no—
248C2×C3×Q8—22no—
249C2×C3×Q8C22×D512yes—
250C22×C3×C4—21no—
251C22×C3×C4—51no—
252C22×C3×C4—52no—
253C22×C3×C4—52no—
254C22×C3×C4—102no—
255C22×C3×C4—102no—
256C22×C3×C4—101no—
257C22×C3×C4C22×D511yescharacteristic
258C2×#67—104no—
259C2×#67—108no—
260C22×Dic3—101no—
261#235—108no—
262#235—1016no—
263#235—108no—
264C2×D12—21no—
265C2×D12—22no—
266C2×D12C22⋊D514yes—
267C2×D12C22×D512yes—
268C2×C4×D3—104no—
269C2×C4×D3—108no—
270C2×Dic6—54no—
271C2×Dic6—52no—
272C2×Dic6—101no—
273C2×Dic6—102no—
274C3×C4⋊C4—52no—
275C3×C4⋊C4—104no—
276C3×C4⋊C4—101no—
277C3×C22⋊C4—104no—
278#216—108no—
279#215—28no—
280C2×C3⋊C8—22no—
281C2×C3⋊C8—52no—
282C2×C3⋊C8—102no—
283C2×C3⋊C8C22×D512yes—
284C23×C5—64no—
285C23×C5—62no—
286C23×C5—122no—
287C23×C5—122no—
288C23×C5C2×#6711yescharacteristic
289C22×D5—22no—
290C22×D5—22no—
291C22×D5—22no—
292C22×D5C2×#6712yes—
293C5×Q8—22no—
294C5×Q8—22no—
295C5×Q8—42no—
296C5×D4—34no—
297C5×D4—64no—
298C5×D4—62no—
299C2×C4×C5—22no—
300C2×C4×C5—42no—
301C2×C4×C5D3×D412yes—
302C2×C4×C5D3×D412yes—
303C2×C4×C5C2×#6711yescharacteristic
304C2×C4×C5C23×D311yescharacteristic
305C22⋊D5—616no—
306C2×Dic5—22no—
307C2×Dic5—22no—
308C2×Dic5—42no—
309C2×Dic5—616no—
310C2×Dic5—64no—
311C2×Dic5—62no—
312C2×Dic5C2×#6712yes—
313C4×D5—24no—
314C4×D5—22no—
315C4×D5—22no—
316Dic10—34no—
317Dic10—64no—
318Dic10—62no—
319C5×C8—62no—
320#168—62no—
321C2×#41—154no—
322C2×#41—302no—
323C2×#41—304no—
324C2×#41—304no—
325C22×Q8—151no—
326C22×Q8D3×D511yescharacteristic
327C22×D4—31no—
328C22×D4—301no—
329C23×C4—51no—
330C23×C4—301no—
331C2×Q16—154no—
332C2×Q16—304no—
333C2×SD16—34no—
334C2×SD16—64no—
335C22×C8—31no—
336C22×C8—151no—
337C22⋊Q8—54no—
338C22⋊Q8—102no—
339C2×C4⋊C4—51no—
340C2×C4⋊C4—101no—
341C2×C22⋊C4—101no—
342#103—154no—
343#102—154no—
344C22⋊C8—154no—
345C2×C3×C5#45214yescomplemented
346C2×C3×C5C2×#12011yescharacteristic
347C2×C3×C5C2×#13511yescharacteristic
348C2×C3×C5C2×#13711yescharacteristic
349C3×D5—42no—
350C5×D3—44no—
351C23×C3—52no—
352C23×C3—102no—
353C23×C3—102no—
354C23×C3—102no—
355C23×C3D4×D511yescharacteristic
356C22×D3—22no—
357C22×D3—24no—
358C22×D3—42no—
359C22×D3—42no—
360C3×Q8—22no—
361C3×Q8—22no—
362C3×Q8—42no—
363C2×C3×C4—22no—
364C2×C3×C4—42no—
365C2×C3×C4—52no—
366C2×C3×C4—102no—
367C2×C3×C4—102no—
368C2×C3×C4—102no—
369C2×C3×C4—104no—
370C2×C3×C4—102no—
371C2×C3×C4—202no—
372C2×C3×C4D4×D511yescharacteristic
373C2×C3×C4D4×D512yes—
374C2×C3×C4C2×C22⋊D512yes—
375C2×C3×C4C23×D511yescharacteristic
376#67—1016no—
377C2×Dic3—102no—
378C2×Dic3—104no—
379D12—22no—
380D12—24no—
381D12C2×C22⋊D514yes—
382C4×D3—1016no—
383Dic6—54no—
384Dic6—102no—
385Dic6—104no—
386C3⋊C8—22no—
387C3⋊C8—102no—
388C22×C5—64no—
389C22×C5—122no—
390C22×C5—128no—
391C22×C5—122no—
392C22×C5#93712yes—
393C22×C5#94212yes—
394C22×C5#95012yes—
395C22×C5C22×#6711yescharacteristic
396C2×D5—22no—
397C2×D5—22no—
398C2×D5—22no—
399C2×D5—44no—
400C4×C5—42no—
401C4×C5#93712yes—
402C4×C5C2×D3×D411yescharacteristic
403C4×C5C2×D3×D411yescharacteristic
404Dic5—22no—
405Dic5—42no—
406Dic5—64no—
407C24—51no—
408C24—61no—
409#41—308no—
410#41—308no—
411#41—3016no—
412C2×Q8—21no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—154no—
416C2×Q8—152no—
417C2×Q8—301no—
418C2×Q8—302no—
419C2×Q8C2×D3×D512yes—
420C2×D4—34no—
421C2×D4—32no—
422C2×D4—61no—
423C2×D4—62no—
424C2×D4—304no—
425C2×D4—308no—
426C22×C4—21no—
427C22×C4—51no—
428C22×C4—52no—
429C22×C4—52no—
430C22×C4—102no—
431C22×C4—102no—
432C22×C4—101no—
433C22×C4—304no—
434C22×C4—308no—
435C22×C4—301no—
436C22×C4C2×D3×D511yescharacteristic
437Q16—308no—
438SD16—68no—
439C2×C8—32no—
440C2×C8—62no—
441C2×C8—152no—
442C2×C8—302no—
443C4⋊C4—52no—
444C4⋊C4—104no—
445C4⋊C4—101no—
446C22⋊C4—104no—
447C3×C5C2×#45211yescharacteristic, complemented, Hall
448C22×C3—102no—
449C22×C3—102no—
450C22×C3—102no—
451C22×C3—204no—
452C22×C3#406112yes—
453C22×C3#406212yes—
454C22×C3#408312yes—
455C22×C3C2×D4×D511yescharacteristic
456C2×D3—24no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—48no—
460C3×C4—42no—
461C3×C4—102no—
462C3×C4—202no—
463C3×C4#408312yes—
464C3×C4C2×D4×D511yescharacteristic
465C3×C4C22×C22⋊D511yescharacteristic
466Dic3—104no—
467C2×C5—124no—
468C2×C5#504714yescomplemented
469C2×C5C2×#93711yescharacteristic
470C2×C5C2×#94211yescharacteristic
471C2×C5C2×#95011yescharacteristic
472D5—42no—
473C23—52no—
474C23—62no—
475C23—64no—
476C23—102no—
477C23—102no—
478C23—102no—
479C23—122no—
480C23—122no—
481C23D5×#6711yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—42no—
485Q8—154no—
486Q8—302no—
487Q8—304no—
488D4—34no—
489D4—62no—
490D4—64no—
491D4—3016no—
492C2×C4—22no—
493C2×C4—42no—
494C2×C4—52no—
495C2×C4—102no—
496C2×C4—102no—
497C2×C4—102no—
498C2×C4—104no—
499C2×C4—102no—
500C2×C4—202no—
501C2×C4—3016no—
502C2×C4—302no—
503C2×C4—304no—
504C2×C4D5×#6711yescharacteristic
505C2×C4D3×C22⋊D512yes—
506C2×C4#679012yes—
507C2×C4C22×D3×D511yescharacteristic
508C8—62no—
509C8—302no—
510C2×C3—202no—
511C2×C3#6546214yescomplemented
512C2×C3C2×#406111yescharacteristic
513C2×C3C2×#406211yescharacteristic
514C2×C3C2×#408311yescharacteristic
515D3—44no—
516C5C2×#504711yescharacteristic, complemented, Sylow
517C22—64no—
518C22—102no—
519C22—102no—
520C22—102no—
521C22—128no—
522C22—122no—
523C22—122no—
524C22—204no—
525C22#9151312yes—
526C22#9151412yes—
527C22#9157712yes—
528C22C2×D5×#6711yescharacteristic
529C4—42no—
530C4—102no—
531C4—202no—
532C4—304no—
533C4#9157712yes—
534C4C2×D3×C22⋊D511yescharacteristic
535C4C2×#679011yescharacteristic
536C3C2×#6546211yescharacteristic, complemented, Sylow
537C2—124no—
538C2—202no—
539C2#1174940514yesdirect product factor
540C2C2×#9151311yescharacteristic
541C2C2×#9151411yescharacteristic
542C2C2×#9157711yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC22×#6772C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#452
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
3. C22×C5×#215C2semidirect
4. C2×C3×#4092C2semidirect
5. #11749405C2direct (N × H)
6. C2×#90974C2semidirect
7. C2×#90966C2semidirect
8. C2×#90955C2semidirect
21. C2×#6718C22semidirect
24. C2×C5×#215C22semidirect
27. C3×#4092C22semidirect
31. #90974C22semidirect
32. #90966C22semidirect
33. #90955C22semidirect
37. C2×#4092D3semidirect
86. C22×#215D5semidirect
105. #4092C2×D3semidirect
171. C2×#215C2×D5semidirect
345. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
468. C2×C5#5047semidirect
511. C2×C3#65462semidirect
516. C5C2×#5047semidirect
536. C3C2×#65462semidirect
539. C2#11749405direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67722
C22×#67182
C22×C5×#2152
C2×C3×#40922
#117494052
C2×#909742
C2×#909662
C2×#909552
C2×#654623
C2×#50475