Finite Group Databasebeta

← C2×#11753434 #14482961

Subgroups — C2×#11753434 #14482961

Order 1920.

3136 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D15⋊Q8C212yesmaximal, complemented
2C2×#91782C211yesmaximal, characteristic
3C2×C5×#888C211yesmaximal, characteristic, complemented
4C2×C3×#4034C211yesmaximal, characteristic, complemented
5C2×#91470C211yesmaximal, characteristic, complemented
6C2×C4×#1204C211yesmaximal, characteristic, complemented
7C2×#91428C211yesmaximal, characteristic
8C2×#91424C212yesmaximal, complemented
9C2×#91418C211yesmaximal, characteristic
10C2×#91411C212yesmaximal, complemented
11C2×#91377C212yesmaximal, complemented
12#11753434C2116yesmaximal, direct product factor
13C2×#66061—31nomaximal, Hall
14C22×D60C2211yescharacteristic
15C22×C4×D15C2212yes—
16C22×C5×Dic6C2212yes—
17C22×C3×Dic10C2212yes—
18C22×#1204C2212yes—
19C22×#1204C2211yescharacteristic
20C22×#1200C2212yes—
21C22×#1200C2212yes—
22C2×D15⋊Q8—216no—
23C2×D15⋊Q8C22116yescomplemented
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×#6714C2212yes—
26C2×C4×Dic15C2211yescharacteristic
27#91782C2218yes—
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C5×Dic3⋊C4C2212yes—
30C2×C4×C5×Dic3C2211yescharacteristic
31C5×#888C2218yescomplemented
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×C3×#683C2212yes—
34C2×C3×C4×Dic5C2211yescharacteristic
35C3×#4034C2218yescomplemented
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×#6669C2211yescharacteristic
38C2×#6669C2212yes—
39C2×#6668C2211yescharacteristic
40C2×#6667C2212yes—
41C2×#6667C2212yes—
42#91470C2218yescomplemented
43C4×#1204C2218yescomplemented
44#91428C2218yes—
45#91424C22116yescomplemented
46#91418C2218yes—
47#91411C22116yescomplemented
48#91377C22116yescomplemented
49C2×#5727—51nomaximal, Hall
50C22×Q8×D5—32no—
51C2×C5×C4⋊Q8—31no—
52C2×#4092—32no—
53#66061—316no—
54C2×#4042—32no—
55C2×#4042—32no—
56C2×#4039—31no—
57C2×#4039—31no—
58C2×#4034—31no—
59C2×#4034D311yescharacteristic, complemented
60C2×C4×D20—31no—
61C2×C4×Dic10—31no—
62C23×D15C2312yes—
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C2×D60Q818yescomplemented
68C2×D60C2314yes—
69C2×C4×D15—28no—
70C2×C4×D15C2318yes—
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2312yes—
73C22×C5×Dic3C2311yescharacteristic
74C2×C5×Dic6—28no—
75C2×C5×Dic6C2318yes—
76C22×C3×Dic5C2312yes—
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2311yescharacteristic
79C2×C3×Dic10—28no—
80C2×C3×Dic10C2318yes—
81C2×#1204—28no—
82C2×#1204D418yescomplemented
83C2×#1204C2318yes—
84C2×#1204C2314yes—
85C2×#1200—28no—
86C2×#1200—28no—
87C2×#1200C2318yes—
88C2×#1200C2318yes—
89D15⋊Q8—264no—
90C3×C5×C4⋊C4C2314yes—
91#6714C2318yes—
92C4×Dic15C2314yes—
93C5×C4⋊Dic3C2314yes—
94C5×Dic3⋊C4C2318yes—
95C4×C5×Dic3C2314yes—
96C3×C4⋊Dic5C2314yes—
97C3×#683C2318yes—
98C3×C4×Dic5C2314yes—
99Dic3⋊Dic5C2314yes—
100#6669C2318yes—
101#6669C2314yes—
102#6668C2314yes—
103#6667C2318yes—
104#6667C2318yes—
105C22×D3×Q8—52no—
106C2×C3×C4⋊Q8—51no—
107C2×#946—52no—
108#5727—516no—
109C2×#896—52no—
110C2×#896—52no—
111C2×#893—51no—
112C2×#893—51no—
113C2×#888—51no—
114C2×#888D511yescharacteristic, complemented
115C2×C4×D12—51no—
116C2×C4×Dic6—51no—
117C22×C5×Q8—32no—
118C2×Q8×D5—316no—
119C2×Q8×D5—616no—
120C22×D20—31no—
121C22×C4×D5—32no—
122C22×C4×D5—32no—
123C22×C4×D5—32no—
124C22×Dic10—31no—
125C22×Dic10—32no—
126C22×Dic10C2×D312yes—
127C5×C4⋊Q8—38no—
128C2×C5×C4⋊C4—31no—
129C2×C5×C4⋊C4—32no—
130C2×C5×C4⋊C4C2×D311yescharacteristic
131C2×C42×C5—31no—
132#4092—316no—
133C2×#685—32no—
134C2×#685—32no—
135C2×#685—32no—
136C2×C4⋊Dic5—31no—
137C2×C4⋊Dic5C2×D311yescharacteristic
138C2×#683—31no—
139C2×#683—31no—
140C2×#683—32no—
141C2×#683C2×D312yes—
142C2×C4×Dic5—31no—
143C2×C4×Dic5C2×D311yescharacteristic
144#4042—316no—
145#4042—316no—
146#4039—38no—
147#4039—38no—
148#4034—38no—
149#4034C2×D318yescomplemented
150C4×D20—38no—
151C4×Dic10—38no—
152C2×D4×Q8—151noSylow
153C23×C3×C5C2411yescharacteristic
154C22×D15—24no—
155C22×D15—24no—
156C22×D15C2×Q818yescomplemented
157C22×D15C2414yes—
158C2×C3×C4×C5—24no—
159C2×C3×C4×C5C2×Q814yescomplemented
160C2×C3×C4×C5C2414yes—
161C2×C3×C4×C5C2412yes—
162C2×Dic15—22no—
163C2×Dic15C2×D414yes—
164C2×Dic15C2412yes—
165C2×Dic15C2412yes—
166D60C2×Q8116yescomplemented
167C4×D15—216no—
168C2×C5×Dic3—24no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3C2×D414yes—
171C2×C5×Dic3C2412yes—
172C2×C5×Dic3C2414yes—
173C2×C5×Dic3C2412yes—
174C5×Dic6—216no—
175C2×C3×Dic5—24no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5C2×D414yes—
178C2×C3×Dic5C2412yes—
179C2×C3×Dic5C2414yes—
180C2×C3×Dic5C2412yes—
181C3×Dic10—216no—
182#1204—216no—
183#1204C2×D4116yescomplemented
184#1200—216no—
185#1200—216no—
186C22×C3×Q8—52no—
187C2×D3×Q8—516no—
188C2×D3×Q8—1016no—
189C22×D12—51no—
190C22×C4×D3—52no—
191C22×C4×D3—52no—
192C22×C4×D3—52no—
193C22×Dic6—51no—
194C22×Dic6—52no—
195C22×Dic6C2×D512yes—
196C3×C4⋊Q8—58no—
197C2×C3×C4⋊C4—51no—
198C2×C3×C4⋊C4—52no—
199C2×C3×C4⋊C4C2×D511yescharacteristic
200C2×C3×C42—51no—
201#946—516no—
202C2×(C2×D3)⋊C4—52no—
203C2×(C2×D3)⋊C4—52no—
204C2×(C2×D3)⋊C4—52no—
205C2×C4⋊Dic3—51no—
206C2×C4⋊Dic3C2×D511yescharacteristic
207C2×Dic3⋊C4—51no—
208C2×Dic3⋊C4—51no—
209C2×Dic3⋊C4—52no—
210C2×Dic3⋊C4C2×D512yes—
211C2×C4×Dic3—51no—
212C2×C4×Dic3C2×D511yescharacteristic
213#896—516no—
214#896—516no—
215#893—58no—
216#893—58no—
217#888—58no—
218#888C2×D518yescomplemented
219C4×D12—58no—
220C4×Dic6—58no—
221C23×D5—32no—
222C2×C5×Q8—38no—
223C2×C5×Q8—68no—
224C22×C4×C5—31no—
225C22×C4×C5—31no—
226C22×C4×C5—32no—
227C22×C4×C5C22×D312yes—
228C22×C4×C5C22×D311yescharacteristic
229C22×Dic5—31no—
230C22×Dic5—31no—
231C22×Dic5C22×D312yes—
232C22×Dic5C22×D311yescharacteristic
233C22×Dic5C22×D311yescharacteristic
234Q8×D5—664no—
235C2×D20—38no—
236C2×D20—34no—
237C2×C4×D5—38no—
238C2×C4×D5—38no—
239C2×C4×D5—38no—
240C2×C4×D5—68no—
241C2×C4×D5—68no—
242C2×C4×D5—68no—
243C2×Dic10—28no—
244C2×Dic10—38no—
245C2×Dic10—34no—
246C2×Dic10—38no—
247C2×Dic10—68no—
248C2×Dic10C22×D318yes—
249C5×C4⋊C4—38no—
250C5×C4⋊C4—34no—
251C5×C4⋊C4C22×D314yes—
252C42×C5—34no—
253#685—38no—
254#685—38no—
255#685—38no—
256C4⋊Dic5—34no—
257C4⋊Dic5C22×D314yes—
258#683—34no—
259#683—34no—
260#683—38no—
261#683C22×D318yes—
262C4×Dic5—34no—
263C4×Dic5C22×D314yes—
264C23×Q8—152no—
265D4×Q8—1516no—
266C2×C4⋊Q8—31no—
267C2×C4⋊Q8—51no—
268C2×C4⋊Q8—151no—
269C2×C22⋊Q8—152no—
270C2×C22⋊Q8—152no—
271C2×C22⋊Q8—152no—
272C2×C4×Q8—151no—
273C2×C4×D4—151no—
274C2×C4×D4—151no—
275C2×C4×D4—151no—
276C22×C3×C5C22×D412yes—
277C22×C3×C5C22×Q812yes—
278C22×C3×C52−1+412yes—
279C22×C3×C5C2511yescharacteristic
280C2×D15—216no—
281C2×D15—24no—
282C2×D15—24no—
283C2×D15C22×Q818yescomplemented
284C3×C4×C5—24no—
285C3×C4×C5C22×Q814yescomplemented
286Dic15—22no—
287Dic15C22×D414yes—
288C3×Dic5—24no—
289C3×Dic5—22no—
290C3×Dic5C22×D414yes—
291C5×Dic3—24no—
292C5×Dic3—22no—
293C5×Dic3C22×D414yes—
294C23×D3—52no—
295C2×C3×Q8—58no—
296C2×C3×Q8—108no—
297C22×C3×C4—51no—
298C22×C3×C4—51no—
299C22×C3×C4—52no—
300C22×C3×C4C22×D512yes—
301C22×C3×C4C22×D511yescharacteristic
302C22×Dic3—51no—
303C22×Dic3—51no—
304C22×Dic3C22×D511yescharacteristic
305C22×Dic3C22×D512yes—
306C22×Dic3C22×D511yescharacteristic
307D3×Q8—1064no—
308C2×D12—58no—
309C2×D12—54no—
310C2×C4×D3—58no—
311C2×C4×D3—58no—
312C2×C4×D3—58no—
313C2×C4×D3—108no—
314C2×C4×D3—108no—
315C2×C4×D3—108no—
316C2×Dic6—28no—
317C2×Dic6—58no—
318C2×Dic6—54no—
319C2×Dic6—58no—
320C2×Dic6—108no—
321C2×Dic6C22×D518yes—
322C3×C4⋊C4—58no—
323C3×C4⋊C4—54no—
324C3×C4⋊C4C22×D514yes—
325C3×C42—54no—
326(C2×D3)⋊C4—58no—
327(C2×D3)⋊C4—58no—
328(C2×D3)⋊C4—58no—
329C4⋊Dic3—54no—
330C4⋊Dic3C22×D514yes—
331Dic3⋊C4—54no—
332Dic3⋊C4—58no—
333Dic3⋊C4—54no—
334Dic3⋊C4C22×D518yes—
335C4×Dic3—54no—
336C4×Dic3C22×D514yes—
337C23×C5C23×D311yescharacteristic
338C22×D5—38no—
339C22×D5—34no—
340C22×D5—64no—
341C22×D5—64no—
342C5×Q8—616no—
343C2×C4×C5—24no—
344C2×C4×C5—34no—
345C2×C4×C5—32no—
346C2×C4×C5—32no—
347C2×C4×C5—34no—
348C2×C4×C5—64no—
349C2×C4×C5—62no—
350C2×C4×C5D3×Q814yescomplemented
351C2×C4×C5C23×D314yes—
352C2×C4×C5C23×D312yes—
353C2×Dic5—24no—
354C2×Dic5—22no—
355C2×Dic5—34no—
356C2×Dic5—32no—
357C2×Dic5—32no—
358C2×Dic5—62no—
359C2×Dic5D3×D414yes—
360C2×Dic5C23×D312yes—
361C2×Dic5C23×D314yes—
362C2×Dic5C23×D312yes—
363D20—316no—
364C4×D5—616no—
365C4×D5—616no—
366C4×D5—616no—
367Dic10—216no—
368Dic10—316no—
369Dic10—616no—
370C22×Q8—32no—
371C22×Q8—52no—
372C22×Q8—151no—
373C22×Q8—152no—
374C22×Q8—1516no—
375C22×Q8—3016no—
376C22×D4—151no—
377C23×C4—152no—
378C23×C4—152no—
379C23×C4—152no—
380C4⋊Q8—38no—
381C4⋊Q8—58no—
382C4⋊Q8—158no—
383C22⋊Q8—1516no—
384C22⋊Q8—1516no—
385C22⋊Q8—1516no—
386C4×Q8—158no—
387C4×D4—158no—
388C4×D4—158no—
389C4×D4—158no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—51no—
393C2×C4⋊C4—52no—
394C2×C4⋊C4—151no—
395C2×C4⋊C4—151no—
396C2×C4⋊C4—151no—
397C2×C4⋊C4—152no—
398C2×C4⋊C4D3×D511yescharacteristic
399C2×C22⋊C4—152no—
400C2×C22⋊C4—152no—
401C2×C22⋊C4—152no—
402C2×C42—31no—
403C2×C42—51no—
404C2×C42—151no—
405C2×C3×C5D4×Q814yescomplemented
406C2×C3×C5C23×D411yescharacteristic
407C2×C3×C5C23×Q811yescharacteristic
408C2×C3×C5C2×2−1+411yescharacteristic
409D15—28no—
410C23×C3C23×D511yescharacteristic
411C22×D3—58no—
412C22×D3—54no—
413C22×D3—104no—
414C22×D3—104no—
415C3×Q8—1016no—
416C2×C3×C4—24no—
417C2×C3×C4—54no—
418C2×C3×C4—52no—
419C2×C3×C4—52no—
420C2×C3×C4—54no—
421C2×C3×C4—104no—
422C2×C3×C4—102no—
423C2×C3×C4Q8×D514yescomplemented
424C2×C3×C4C23×D514yes—
425C2×C3×C4C23×D512yes—
426C2×Dic3—24no—
427C2×Dic3—22no—
428C2×Dic3—54no—
429C2×Dic3—52no—
430C2×Dic3—52no—
431C2×Dic3—102no—
432C2×Dic3D4×D514yes—
433C2×Dic3C23×D512yes—
434C2×Dic3C23×D514yes—
435C2×Dic3C23×D512yes—
436D12—516no—
437C4×D3—1016no—
438C4×D3—1016no—
439C4×D3—1016no—
440Dic6—216no—
441Dic6—516no—
442Dic6—1016no—
443C22×C5C2×D3×D412yes—
444C22×C5C2×D3×Q812yes—
445C22×C5#100712yes—
446C22×C5C24×D311yescharacteristic
447C2×D5—38no—
448C2×D5—64no—
449C2×D5—64no—
450C2×D5—616no—
451C4×C5—24no—
452C4×C5—34no—
453C4×C5—64no—
454C4×C5—62no—
455C4×C5C2×D3×Q814yescomplemented
456Dic5—24no—
457Dic5—22no—
458Dic5—34no—
459Dic5—62no—
460Dic5C2×D3×D414yes—
461C24—152no—
462C2×Q8—38no—
463C2×Q8—58no—
464C2×Q8—68no—
465C2×Q8—108no—
466C2×Q8—154no—
467C2×Q8—158no—
468C2×Q8—158no—
469C2×Q8—308no—
470C2×Q8—3064no—
471C2×D4—158no—
472C2×D4—154no—
473C22×C4—31no—
474C22×C4—31no—
475C22×C4—32no—
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—52no—
479C22×C4—158no—
480C22×C4—158no—
481C22×C4—151no—
482C22×C4—151no—
483C22×C4—158no—
484C22×C4—308no—
485C22×C4—308no—
486C22×C4—308no—
487C22×C4C2×D3×D512yes—
488C22×C4C2×D3×D511yescharacteristic
489C4⋊C4—34no—
490C4⋊C4—38no—
491C4⋊C4—54no—
492C4⋊C4—58no—
493C4⋊C4—154no—
494C4⋊C4—154no—
495C4⋊C4—154no—
496C4⋊C4—158no—
497C4⋊C4C2×D3×D514yes—
498C22⋊C4—158no—
499C22⋊C4—158no—
500C22⋊C4—158no—
501C42—34no—
502C42—54no—
503C42—154no—
504C3×C5C2×D4×Q811yescharacteristic, complemented, Hall
505C22×C3C2×D4×D512yes—
506C22×C3C2×Q8×D512yes—
507C22×C3#414712yes—
508C22×C3C24×D511yescharacteristic
509C2×D3—58no—
510C2×D3—1016no—
511C2×D3—104no—
512C2×D3—104no—
513C3×C4—24no—
514C3×C4—54no—
515C3×C4—104no—
516C3×C4—102no—
517C3×C4C2×Q8×D514yescomplemented
518Dic3—24no—
519Dic3—22no—
520Dic3—54no—
521Dic3—102no—
522Dic3C2×D4×D514yes—
523C2×C5#572714yescomplemented
524C2×C5C22×D3×D411yescharacteristic
525C2×C5C22×D3×Q811yescharacteristic
526C2×C5C2×#100711yescharacteristic
527D5—68no—
528C23—158no—
529C23—154no—
530C23—304no—
531C23—304no—
532C23C22×D3×D511yescharacteristic
533Q8—616no—
534Q8—1016no—
535Q8—1516no—
536Q8—3016no—
537D4—1516no—
538C2×C4—24no—
539C2×C4—34no—
540C2×C4—32no—
541C2×C4—32no—
542C2×C4—34no—
543C2×C4—54no—
544C2×C4—52no—
545C2×C4—52no—
546C2×C4—54no—
547C2×C4—64no—
548C2×C4—62no—
549C2×C4—104no—
550C2×C4—102no—
551C2×C4—154no—
552C2×C4—152no—
553C2×C4—152no—
554C2×C4—3016no—
555C2×C4—3016no—
556C2×C4—3016no—
557C2×C4—302no—
558C2×C4D15⋊Q814yescomplemented
559C2×C4C22×D3×D514yes—
560C2×C4C22×D3×D512yes—
561C2×C3#6606114yescomplemented
562C2×C3C22×D4×D511yescharacteristic
563C2×C3C22×Q8×D511yescharacteristic
564C2×C3C2×#414711yescharacteristic
565D3—108no—
566C5C2×#572711yescharacteristic, complemented, Sylow
567C22—158no—
568C22—3016no—
569C22—304no—
570C22—304no—
571C22C2×D15⋊Q812yes—
572C22D3×D4×D512yes—
573C22#9202912yes—
574C22C23×D3×D511yescharacteristic
575C4—24no—
576C4—34no—
577C4—54no—
578C4—64no—
579C4—62no—
580C4—104no—
581C4—102no—
582C4—154no—
583C4—302no—
584C4C2×D15⋊Q814yescomplemented
585C3C2×#6606111yescharacteristic, complemented, Sylow
586C2—308no—
587C2#1175343414yesdirect product factor
588C2C22×D15⋊Q811yescharacteristic
589C2C2×D3×D4×D511yescharacteristic
590C2C2×#9202911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC22×D60C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×D4×Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D15⋊Q8C2semidirect
3. C2×C5×#888C2semidirect
4. C2×C3×#4034C2semidirect
5. C2×#91470C2semidirect
6. C2×C4×#1204C2semidirect
8. C2×#91424C2semidirect
10. C2×#91411C2semidirect
11. C2×#91377C2semidirect
12. #11753434C2direct (N × H)
23. C2×D15⋊Q8C22semidirect
31. C5×#888C22semidirect
35. C3×#4034C22semidirect
42. #91470C22semidirect
43. C4×#1204C22semidirect
45. #91424C22semidirect
47. #91411C22semidirect
48. #91377C22semidirect
59. C2×#4034D3semidirect
67. C2×D60Q8semidirect
82. C2×#1204D4semidirect
114. C2×#888D5semidirect
149. #4034C2×D3semidirect
156. C22×D15C2×Q8semidirect
159. C2×C3×C4×C5C2×Q8semidirect
166. D60C2×Q8semidirect
183. #1204C2×D4semidirect
218. #888C2×D5semidirect
283. C2×D15C22×Q8semidirect
285. C3×C4×C5C22×Q8semidirect
350. C2×C4×C5D3×Q8semidirect
405. C2×C3×C5D4×Q8semidirect
423. C2×C3×C4Q8×D5semidirect
455. C4×C5C2×D3×Q8semidirect
504. C3×C5C2×D4×Q8semidirect
517. C3×C4C2×Q8×D5semidirect
523. C2×C5#5727semidirect
558. C2×C4D15⋊Q8semidirect
561. C2×C3#66061semidirect
566. C5C2×#5727semidirect
584. C4C2×D15⋊Q8semidirect
585. C3C2×#66061semidirect
587. C2#11753434direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D15⋊Q82
C2×#917822
C2×C5×#8882
C2×C3×#40342
C2×#914702
C2×C4×#12042
C2×#914282
C2×#914242
C2×#914182
C2×#914112
C2×#913772
#117534342
C2×#660613
C2×#57275