Finite Group Databasebeta

← C2×#11756381 #14480113

Subgroups — C2×#11756381 #14480113

Order 1920.

2336 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic
2C2×Q8×Dic15C211yesmaximal, characteristic, complemented
3C2×#91833C211yesmaximal, characteristic, complemented
4C2×#91813C211yesmaximal, characteristic
5C22×C4×Dic15C211yesmaximal, characteristic
6#11756381C2116yesmaximal, direct product factor
7C2×#91778C212yesmaximal, complemented
8C2×#91777C211yesmaximal, characteristic, complemented
9C2×#91776C212yesmaximal, complemented
10C2×#91776C211yesmaximal, characteristic, complemented
11C2×#91767C212yesmaximal
12C2×#91766C212yesmaximal
13C2×#65956—31nomaximal, Hall
14C22×C3×C5×Q8C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×Dic15C2211yescharacteristic
17C23×Dic15C2211yescharacteristic
18C22×Dic30C2211yescharacteristic
19C22×Dic30C2212yes—
20C3×C5×C22⋊Q8C2218yes—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2212yes—
23C2×C3×C5×C22⋊C4C2212yes—
24C2×#6719C2212yes—
25Q8×Dic15C2218yescomplemented
26#91833C2218yescomplemented
27C2×C4⋊Dic15C2212yes—
28C2×C4⋊Dic15C2211yescharacteristic
29#91813C2218yes—
30C2×#6712C2212yes—
31C2×#6712C2212yes—
32C2×#6712C2212yes—
33C2×#6712C2212yes—
34C2×#6712C2212yes—
35C2×C4×Dic15C2211yescharacteristic
36C2×C4×Dic15C2212yes—
37C2×C4×Dic15C2211yescharacteristic
38C2×C4×Dic15C2218yes—
39C2×C4×Dic15C2212yes—
40C2×C4×Dic15C2211yescharacteristic
41C2×C4×Dic15C2211yescharacteristic
42#91778C22116yescomplemented
43#91777C2218yescomplemented
44#91776C2218yescomplemented
45#91776C22116yescomplemented
46#91767C22116yes—
47#91766C22116yes—
48C2×#5622—51nomaximal, Hall
49C2×C5×C22⋊Q8D311yescharacteristic
50C2×Q8×Dic5—31no—
51C2×#4090—31no—
52C2×#4070—31no—
53C22×C4×Dic5—31no—
54#65956—316no—
55C2×#4035—32no—
56C2×#4034—31no—
57C2×#4033—31no—
58C2×#4033—32no—
59C2×#4024—32no—
60C2×#4023—32no—
61C24×C3×C5C2311yescharacteristic
62C2×C3×C5×Q8—24no—
63C2×C3×C5×Q8C2314yes—
64C22×C3×C4×C5—24no—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2314yes—
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2312yes—
69C22×C3×C4×C5C2311yescharacteristic
70C22×Dic15—24no—
71C22×Dic15Q818yescomplemented
72C22×Dic15C2314yes—
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2312yes—
75C22×Dic15C2312yes—
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2314yes—
79C22×Dic15C2311yescharacteristic
80C2×Dic30—24no—
81C2×Dic30—28no—
82C2×Dic30C2318yes—
83C2×Dic30C2314yes—
84C3×C5×C4⋊C4C2314yes—
85C3×C5×C4⋊C4C2318yes—
86C3×C5×C22⋊C4C2318yes—
87#6719C2318yes—
88C4⋊Dic15C2318yes—
89C4⋊Dic15C2314yes—
90#6712C2318yes—
91#6712C2318yes—
92#6712C2318yes—
93#6712C2318yes—
94#6712C2318yes—
95C4×Dic15C2318yes—
96C4×Dic15C2318yes—
97C4×Dic15C2314yes—
98C4×Dic15C2314yes—
99C4×Dic15C2314yes—
100C4×Dic15C2314yes—
101C2×C3×C22⋊Q8D511yescharacteristic
102C2×Q8×Dic3—51no—
103C2×#944—51no—
104C2×#924—51no—
105C22×C4×Dic3—51no—
106#5622—516no—
107C2×#889—52no—
108C2×#888—51no—
109C2×#887—51no—
110C2×#887—52no—
111C2×#878—52no—
112C2×#877—52no—
113C22×C5×Q8C2×D311yescharacteristic
114C23×C4×C5C2×D311yescharacteristic
115C23×Dic5—31no—
116C23×Dic5—31no—
117C22×Dic10—32no—
118C22×Dic10—31no—
119C5×C22⋊Q8C2×D318yes—
120C2×C5×C4⋊C4C2×D311yescharacteristic
121C2×C5×C4⋊C4C2×D312yes—
122C2×C5×C22⋊C4C2×D312yes—
123C2×C22⋊Dic5—32no—
124Q8×Dic5—38no—
125#4090—38no—
126C2×C4⋊Dic5—32no—
127C2×C4⋊Dic5—31no—
128#4070—38no—
129C2×#683—32no—
130C2×#683—32no—
131C2×#683—32no—
132C2×#683—32no—
133C2×#683—32no—
134C2×C4×Dic5—32no—
135C2×C4×Dic5—32no—
136C2×C4×Dic5—31no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—31no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—38no—
141#4035—316no—
142#4034—38no—
143#4033—38no—
144#4033—316no—
145#4024—316no—
146#4023—316no—
147C2×#533—151noSylow
148C23×C3×C5—22no—
149C23×C3×C5—22no—
150C23×C3×C5C2×Q814yes—
151C23×C3×C5C2412yes—
152C23×C3×C5C2411yescharacteristic
153C3×C5×Q8—28no—
154C2×C3×C4×C5—24no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—24no—
157C2×C3×C4×C5—28no—
158C2×C3×C4×C5#4114yes—
159C2×C3×C4×C5C2412yes—
160C2×C3×C4×C5C2414yes—
161C2×C3×C4×C5C2414yes—
162C2×C3×C4×C5C2412yes—
163C2×Dic15—24no—
164C2×Dic15—24no—
165C2×Dic15—22no—
166C2×Dic15—28no—
167C2×Dic15C2×Q814yes—
168C2×Dic15C2×Q814yes—
169C2×Dic15C2×Q8116yescomplemented
170C2×Dic15#4114yes—
171C2×Dic15C2412yes—
172C2×Dic15C2414yes—
173C2×Dic15C2414yes—
174C2×Dic15C2412yes—
175C2×Dic15C2412yes—
176C2×Dic15C2412yes—
177Dic30—28no—
178Dic30—216no—
179C22×C3×Q8C2×D511yescharacteristic
180C23×C3×C4C2×D511yescharacteristic
181C23×Dic3—51no—
182C23×Dic3—51no—
183C22×Dic6—52no—
184C22×Dic6—51no—
185C3×C22⋊Q8C2×D518yes—
186C2×C3×C4⋊C4C2×D511yescharacteristic
187C2×C3×C4⋊C4C2×D512yes—
188C2×C3×C22⋊C4C2×D512yes—
189C2×#217—52no—
190Q8×Dic3—58no—
191#944—58no—
192C2×C4⋊Dic3—52no—
193C2×C4⋊Dic3—51no—
194#924—58no—
195C2×Dic3⋊C4—52no—
196C2×Dic3⋊C4—52no—
197C2×Dic3⋊C4—52no—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4—52no—
200C2×C4×Dic3—52no—
201C2×C4×Dic3—52no—
202C2×C4×Dic3—51no—
203C2×C4×Dic3—51no—
204C2×C4×Dic3—51no—
205C2×C4×Dic3—51no—
206C2×C4×Dic3—58no—
207#889—516no—
208#888—58no—
209#887—58no—
210#887—516no—
211#878—516no—
212#877—516no—
213C24×C5C22×D311yescharacteristic
214C2×C5×Q8—24no—
215C2×C5×Q8C22×D314yes—
216C22×C4×C5—24no—
217C22×C4×C5C22×D312yes—
218C22×C4×C5C22×D312yes—
219C22×C4×C5C22×D311yescharacteristic
220C22×C4×C5C22×D314yes—
221C22×C4×C5C22×D311yescharacteristic
222C22×Dic5—38no—
223C22×Dic5—31no—
224C22×Dic5—34no—
225C22×Dic5—31no—
226C22×Dic5—31no—
227C22×Dic5—32no—
228C22×Dic5—32no—
229C22×Dic5—34no—
230C22×Dic5—31no—
231C22×Dic5—64no—
232C2×Dic10—38no—
233C2×Dic10—34no—
234C2×Dic10—68no—
235C2×Dic10—64no—
236C5×C4⋊C4C22×D314yes—
237C5×C4⋊C4C22×D318yes—
238C5×C22⋊C4C22×D318yes—
239C22⋊Dic5—38no—
240C4⋊Dic5—38no—
241C4⋊Dic5—34no—
242#683—38no—
243#683—38no—
244#683—38no—
245#683—38no—
246#683—38no—
247C4×Dic5—38no—
248C4×Dic5—38no—
249C4×Dic5—34no—
250C4×Dic5—34no—
251C4×Dic5—34no—
252C4×Dic5—34no—
253#533—1516no—
254C2×C4⋊Q8—151no—
255C2×C4⋊Q8—151no—
256C2×#125—152no—
257C2×C22⋊Q8—151no—
258C2×C22⋊Q8—152no—
259C2×C22⋊Q8D1511yescharacteristic
260C2×C4×Q8—151no—
261C2×C4×Q8—151no—
262C2×C4×Q8—152no—
263C2×#117—152no—
264C22×C42—151no—
265C22×C3×C5—28no—
266C22×C3×C5—22no—
267C22×C3×C5—22no—
268C22×C3×C5C22×Q814yes—
269C22×C3×C5C22×Q812yes—
270C22×C3×C5C2×#4112yes—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5C2511yescharacteristic
273C3×C4×C5—24no—
274C3×C4×C5—22no—
275C3×C4×C5—24no—
276C3×C4×C5C2×#4114yes—
277Dic15—24no—
278Dic15—24no—
279Dic15—22no—
280Dic15C22×Q814yes—
281Dic15C22×Q814yes—
282Dic15C2×#4114yes—
283C24×C3C22×D511yescharacteristic
284C2×C3×Q8—24no—
285C2×C3×Q8C22×D514yes—
286C22×C3×C4—24no—
287C22×C3×C4C22×D511yescharacteristic
288C22×C3×C4C22×D514yes—
289C22×C3×C4C22×D512yes—
290C22×C3×C4C22×D512yes—
291C22×C3×C4C22×D511yescharacteristic
292C22×Dic3—58no—
293C22×Dic3—54no—
294C22×Dic3—51no—
295C22×Dic3—51no—
296C22×Dic3—51no—
297C22×Dic3—54no—
298C22×Dic3—51no—
299C22×Dic3—52no—
300C22×Dic3—52no—
301C22×Dic3—104no—
302C2×Dic6—58no—
303C2×Dic6—54no—
304C2×Dic6—108no—
305C2×Dic6—104no—
306C3×C4⋊C4C22×D514yes—
307C3×C4⋊C4C22×D518yes—
308C3×C22⋊C4C22×D518yes—
309#217—58no—
310C4⋊Dic3—58no—
311C4⋊Dic3—54no—
312Dic3⋊C4—58no—
313Dic3⋊C4—58no—
314Dic3⋊C4—58no—
315Dic3⋊C4—58no—
316Dic3⋊C4—58no—
317C4×Dic3—58no—
318C4×Dic3—58no—
319C4×Dic3—54no—
320C4×Dic3—54no—
321C4×Dic3—54no—
322C4×Dic3—54no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5D3×Q814yes—
326C23×C5C23×D312yes—
327C23×C5C23×D311yescharacteristic
328C5×Q8—28no—
329C2×C4×C5—22no—
330C2×C4×C5—24no—
331C2×C4×C5—24no—
332C2×C4×C5—28no—
333C2×C4×C5#23714yes—
334C2×C4×C5C23×D312yes—
335C2×C4×C5C23×D314yes—
336C2×C4×C5C23×D314yes—
337C2×C4×C5C23×D312yes—
338C2×Dic5—34no—
339C2×Dic5—34no—
340C2×Dic5—316no—
341C2×Dic5—34no—
342C2×Dic5—32no—
343C2×Dic5—32no—
344C2×Dic5—32no—
345C2×Dic5—32no—
346C2×Dic5—34no—
347C2×Dic5—34no—
348C2×Dic5—68no—
349C2×Dic5—64no—
350C2×Dic5—64no—
351C2×Dic5—62no—
352Dic10—616no—
353Dic10—68no—
354C22×Q8—152no—
355C22×Q8—151no—
356C22×Q8C2×D1511yescharacteristic
357C23×C4—151no—
358C23×C4—151no—
359C23×C4C2×D1511yescharacteristic
360C4⋊Q8—158no—
361C4⋊Q8—158no—
362#125—1516no—
363C22⋊Q8—158no—
364C22⋊Q8—1516no—
365C22⋊Q8C2×D1518yes—
366C4×Q8—158no—
367C4×Q8—158no—
368C4×Q8—1516no—
369#117—1516no—
370C2×C4⋊C4—152no—
371C2×C4⋊C4—152no—
372C2×C4⋊C4—152no—
373C2×C4⋊C4—152no—
374C2×C4⋊C4—152no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—151no—
377C2×C4⋊C4C2×D1512yes—
378C2×C4⋊C4C2×D1511yescharacteristic
379C2×C22⋊C4—152no—
380C2×C22⋊C4C2×D1512yes—
381C2×C42—152no—
382C2×C42—152no—
383C2×C42—151no—
384C2×C42—151no—
385C2×C42—151no—
386C2×C42—151no—
387C2×C42—158no—
388C2×C3×C5—24no—
389C2×C3×C5#53314yescomplemented
390C2×C3×C5C23×Q811yescharacteristic
391C2×C3×C5C22×#4111yescharacteristic
392C2×C3×C5C22×#4111yescharacteristic
393C23×C3—22no—
394C23×C3—22no—
395C23×C3Q8×D514yes—
396C23×C3C23×D512yes—
397C23×C3C23×D511yescharacteristic
398C3×Q8—28no—
399C2×C3×C4—22no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—28no—
403C2×C3×C4#71114yes—
404C2×C3×C4C23×D512yes—
405C2×C3×C4C23×D514yes—
406C2×C3×C4C23×D514yes—
407C2×C3×C4C23×D512yes—
408C2×Dic3—54no—
409C2×Dic3—54no—
410C2×Dic3—516no—
411C2×Dic3—54no—
412C2×Dic3—52no—
413C2×Dic3—52no—
414C2×Dic3—52no—
415C2×Dic3—52no—
416C2×Dic3—54no—
417C2×Dic3—54no—
418C2×Dic3—108no—
419C2×Dic3—104no—
420C2×Dic3—104no—
421C2×Dic3—102no—
422Dic6—1016no—
423Dic6—108no—
424C22×C5—22no—
425C22×C5—22no—
426C22×C5—28no—
427C22×C5C2×#23712yes—
428C22×C5C2×D3×Q814yes—
429C22×C5C2×D3×Q812yes—
430C22×C5D3×#4112yes—
431C22×C5C24×D311yescharacteristic
432C4×C5—22no—
433C4×C5—24no—
434C4×C5—24no—
435C4×C5C2×#23714yes—
436Dic5—34no—
437Dic5—34no—
438Dic5—34no—
439Dic5—64no—
440Dic5—64no—
441Dic5—62no—
442C24C22×D1511yescharacteristic
443C2×Q8—24no—
444C2×Q8—158no—
445C2×Q8—154no—
446C2×Q8—308no—
447C2×Q8—304no—
448C2×Q8C22×D1514yes—
449C22×C4—24no—
450C22×C4—158no—
451C22×C4—154no—
452C22×C4—151no—
453C22×C4—151no—
454C22×C4—151no—
455C22×C4—154no—
456C22×C4—151no—
457C22×C4—152no—
458C22×C4—152no—
459C22×C4—304no—
460C22×C4C22×D1514yes—
461C22×C4C22×D1511yescharacteristic
462C22×C4C22×D1512yes—
463C22×C4C22×D1512yes—
464C22×C4C22×D1511yescharacteristic
465C4⋊C4—158no—
466C4⋊C4—158no—
467C4⋊C4—158no—
468C4⋊C4—158no—
469C4⋊C4—158no—
470C4⋊C4—158no—
471C4⋊C4—154no—
472C4⋊C4C22×D1518yes—
473C4⋊C4C22×D1514yes—
474C22⋊C4—158no—
475C22⋊C4C22×D1518yes—
476C42—154no—
477C42—154no—
478C42—154no—
479C42—154no—
480C42—158no—
481C42—158no—
482C3×C5C2×#53311yescharacteristic, complemented, Hall
483C22×C3—28no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3C2×#71112yes—
487C22×C3C2×Q8×D514yes—
488C22×C3C2×Q8×D512yes—
489C22×C3D5×#4112yes—
490C22×C3C24×D511yescharacteristic
491C3×C4—22no—
492C3×C4—24no—
493C3×C4—24no—
494C3×C4C2×#71114yes—
495Dic3—54no—
496Dic3—54no—
497Dic3—54no—
498Dic3—104no—
499Dic3—104no—
500Dic3—102no—
501C2×C5—24no—
502C2×C5#562214yescomplemented
503C2×C5C22×#23711yescharacteristic
504C2×C5C22×D3×Q811yescharacteristic
505C2×C5C2×D3×#4111yescharacteristic
506C23—22no—
507C23—22no—
508C23Q8×D1514yes—
509C23C23×D1512yes—
510C23C23×D1511yescharacteristic
511Q8—28no—
512Q8—3016no—
513Q8—308no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—28no—
518C2×C4—1516no—
519C2×C4—154no—
520C2×C4—154no—
521C2×C4—154no—
522C2×C4—152no—
523C2×C4—152no—
524C2×C4—152no—
525C2×C4—152no—
526C2×C4—154no—
527C2×C4—154no—
528C2×C4—308no—
529C2×C4—304no—
530C2×C4—302no—
531C2×C4—304no—
532C2×C4#681914yes—
533C2×C4C23×D1512yes—
534C2×C4C23×D1514yes—
535C2×C4C23×D1514yes—
536C2×C4C23×D1512yes—
537C2×C3—24no—
538C2×C3#6595614yescomplemented
539C2×C3C22×#71111yescharacteristic
540C2×C3C22×Q8×D511yescharacteristic
541C2×C3C2×D5×#4111yescharacteristic
542C5C2×#562211yescharacteristic, complemented, Sylow
543C22—22no—
544C22—22no—
545C22—28no—
546C22C2×#681912yes—
547C22C2×Q8×D1514yes—
548C22C2×Q8×D1512yes—
549C22#41×D1512yes—
550C22C24×D1511yescharacteristic
551C4—22no—
552C4—24no—
553C4—24no—
554C4—154no—
555C4—154no—
556C4—154no—
557C4—304no—
558C4—302no—
559C4—304no—
560C4C2×#681914yes—
561C3C2×#6595611yescharacteristic, complemented, Sylow
562C2—24no—
563C2#1175638114yesdirect product factor
564C2C22×#681911yescharacteristic
565C2C22×Q8×D1511yescharacteristic
566C2C2×#41×D1511yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC2×C3×C5×C22⋊Q8C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C22⋊Q8D15
hypocenterC3×C5C2×#533
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic15C2semidirect
3. C2×#91833C2semidirect
6. #11756381C2direct (N × H)
7. C2×#91778C2semidirect
8. C2×#91777C2semidirect
9. C2×#91776C2semidirect
10. C2×#91776C2semidirect
25. Q8×Dic15C22semidirect
26. #91833C22semidirect
42. #91778C22semidirect
43. #91777C22semidirect
44. #91776C22semidirect
45. #91776C22semidirect
71. C22×Dic15Q8semidirect
169. C2×Dic15C2×Q8semidirect
389. C2×C3×C5#533semidirect
482. C3×C5C2×#533semidirect
502. C2×C5#5622semidirect
538. C2×C3#65956semidirect
542. C5C2×#5622semidirect
561. C3C2×#65956semidirect
563. C2#11756381direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C22⋊Q82
C2×Q8×Dic152
C2×#918332
C2×#918132
C22×C4×Dic152
#117563812
C2×#917782
C2×#917772
C2×#917762
C2×#917672
C2×#917662
C2×#659563
C2×#56225