Finite Group Databasebeta

← #14326152

Subgroups — #14326152

Order 1920.

1640 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×D3×Q8C211yesmaximal, characteristic
2C2×#91344C211yesmaximal, characteristic, complemented
3C2×Dic5×Dic6C211yesmaximal, characteristic, complemented
4#11751330C211yesmaximal, characteristic, complemented
5C3×#65519C211yesmaximal, characteristic, complemented
6#11748786C211yesmaximal, characteristic
7#11748782C212yesmaximal
8#11748719C212yesmaximal
9C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic
10#11748692C212yesmaximal, complemented
11#11748692C212yesmaximal, complemented
12Q8×C22⋊Dic5—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×C5×D3×Q8—24no—
15C2×C5×D3×Q8—24no—
16C2×C5×D3×Q8C418yescomplemented
17C22×C4×C5×D3C2211yescharacteristic
18C22×C4×C5×D3C2212yes—
19C22×C5×Dic6C2212yes—
20C22×C5×Dic6C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×C4×Dic5C2211yescharacteristic
25C2×Dic3⋊Dic5C2212yes—
26C2×Dic3⋊Dic5C2212yes—
27C2×(C2×D3)⋊Dic5C2211yescharacteristic
28C2×(C2×D3)⋊Dic5C2212yes—
29C2×(C2×D3)⋊Dic5C2211yescharacteristic
30C2×Dic3×Dic5C2212yes—
31C2×Dic3×Dic5C2212yes—
32#91344—24no—
33Dic5×Dic6—24no—
34#91115C2212yes—
35#91115C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38#90994C2211yescharacteristic
39#90994C2211yescharacteristic
40#90994C2212yes—
41#76614—51nomaximal, Hall
42C23×C5×Q8—31no—
43C2×Q8×Dic5—31no—
44C2×Q8×Dic5—31no—
45#65519—32no—
46#65519—32no—
47#65519—31no—
48#65519D311yescharacteristic, complemented
49#65501—31no—
50#65501—32no—
51C4×C22⋊Dic5—31no—
52C4×C22⋊Dic5—32no—
53C23×C5×D3C2311yescharacteristic
54C2×C3×C5×Q8—22no—
55C2×C3×C5×Q8—22no—
56C2×C3×C5×Q8C2×C414yes—
57C22×C3×C4×C5C2312yes—
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15C2312yes—
60C22×Dic15C2311yescharacteristic
61C22×Dic15C2311yescharacteristic
62C22×C5×Dic3C2311yescharacteristic
63C22×C5×Dic3C2312yes—
64C5×D3×Q8—232no—
65C2×C4×C5×D3—22no—
66C2×C4×C5×D3—22no—
67C2×C4×C5×D3—24no—
68C2×C4×C5×D3—24no—
69C2×C4×C5×D3C2×C414yes—
70C2×C4×C5×D3C2×C418yes—
71C2×C5×Dic6—24no—
72C2×C5×Dic6—24no—
73C2×C5×Dic6C2×C418yes—
74C2×C5×Dic6C2×C414yes—
75C2×C5×Dic6D414yes—
76C2×C5×Dic6D414yes—
77C22×C3×Dic5C2312yes—
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2311yescharacteristic
80C4⋊Dic15—22no—
81C4×Dic15—22no—
82C3×C4⋊Dic5—22no—
83C3×C4×Dic5—22no—
84Dic3⋊Dic5—24no—
85Dic3⋊Dic5—24no—
86(C2×D3)⋊Dic5—22no—
87(C2×D3)⋊Dic5—24no—
88(C2×D3)⋊Dic5Q814yescomplemented
89Dic3×Dic5—24no—
90Dic3×Dic5—24no—
91C22×D3×Q8D511yescharacteristic
92C2×#887—51no—
93C2×C4×Dic6—51no—
94C3×#391—51no—
95#5229—51no—
96#4987—51no—
97C4×(C2×D3)⋊C4—51no—
98#4667—52no—
99#4666—52no—
100#4646—52no—
101#4646—52no—
102C22×C5×Q8—38no—
103C22×C5×Q8—31no—
104C22×C5×Q8—32no—
105C22×C5×Q8—64no—
106C22×C5×Q8—64no—
107C22×C5×Q8C2×D311yescharacteristic
108C23×C4×C5—32no—
109C23×C4×C5—31no—
110C2×C22⋊Dic5—31no—
111C2×C22⋊Dic5—32no—
112C2×C22⋊Dic5—31no—
113Q8×Dic5—64no—
114Q8×Dic5—64no—
115C2×C4⋊Dic5—31no—
116C2×C4⋊Dic5—32no—
117C2×C4⋊Dic5—32no—
118C2×C4⋊Dic5C2×D311yescharacteristic
119C2×C4×Dic5—31no—
120C2×C4×Dic5—32no—
121C2×C4×Dic5—32no—
122C2×C4×Dic5C2×D311yescharacteristic
123#3963—32no—
124#3963—32no—
125#3963—31no—
126#3963—31no—
127#3963—32no—
128#3963C2×D312yes—
129#3963C2×D312yes—
130Q8×C22⋊C4—151noSylow
131C23×C3×C5C2411yescharacteristic
132C22×C5×D3—21no—
133C22×C5×D3—21no—
134C22×C5×D3—21no—
135C22×C5×D3—21no—
136C22×C5×D3C22×C412yes—
137C22×C5×D3C2×Q812yes—
138C22×C5×D3#4112yes—
139C3×C5×Q8—28no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C22×C414yes—
143C2×C3×C4×C5C22×C412yes—
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2×D412yes—
146C2×Dic15—21no—
147C2×Dic15—21no—
148C2×Dic15—22no—
149C2×Dic15—21no—
150C2×Dic15—22no—
151C2×Dic15—21no—
152C2×Dic15—22no—
153C2×Dic15—21no—
154C2×Dic15C2×Q812yescomplemented
155C2×C5×Dic3—21no—
156C2×C5×Dic3—21no—
157C2×C5×Dic3C22×C412yes—
158C2×C5×Dic3C22×C414yes—
159C2×C5×Dic3C2×D414yes—
160C2×C5×Dic3C2×D414yes—
161C4×C5×D3—28no—
162C4×C5×D3—216no—
163C5×Dic6—216no—
164C5×Dic6C22⋊C4116yescomplemented
165C2×C3×Dic5—21no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—21no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5C2×Q812yescomplemented
174C22×C3×Q8C2×D511yescharacteristic
175C2×D3×Q8—24no—
176C2×D3×Q8—24no—
177C2×D3×Q8Dic518yescomplemented
178C22×C4×D3C2×D512yes—
179C22×C4×D3C2×D511yescharacteristic
180C22×Dic6C2×D512yes—
181C22×Dic6C2×D511yescharacteristic
182C2×C3×C4⋊C4—51no—
183C2×C3×C42—51no—
184C2×(C2×D3)⋊C4—51no—
185C2×(C2×D3)⋊C4—52no—
186C2×(C2×D3)⋊C4—51no—
187C2×C4⋊Dic3—51no—
188C2×Dic3⋊C4—52no—
189C2×Dic3⋊C4—52no—
190C2×C4×Dic3—51no—
191C2×C4×Dic3—52no—
192C2×C4×Dic3—52no—
193#887—104no—
194C4×Dic6—104no—
195C3×#95—52no—
196C3×#95—52no—
197C3⋊#95—52no—
198C3⋊#95—52no—
199C3⋊#95—51no—
200C3⋊#95—51no—
201C3⋊#95—52no—
202C24×C5—31no—
203C2×C5×Q8—22no—
204C2×C5×Q8—22no—
205C2×C5×Q8—34no—
206C2×C5×Q8—38no—
207C2×C5×Q8—34no—
208C2×C5×Q8—34no—
209C2×C5×Q8—64no—
210C2×C5×Q8—64no—
211C2×C5×Q8—632no—
212C2×C5×Q8C4×D314yes—
213C22×C4×C5—32no—
214C22×C4×C5—31no—
215C22×C4×C5—38no—
216C22×C4×C5—34no—
217C22×C4×C5—64no—
218C22×C4×C5—64no—
219C22×C4×C5—62no—
220C22×C4×C5—62no—
221C22×C4×C5C22×D312yes—
222C22×C4×C5C22×D311yescharacteristic
223C22×Dic5—31no—
224C22×Dic5—32no—
225C22×Dic5—31no—
226C22×Dic5C22×D312yes—
227C22×Dic5C22×D311yescharacteristic
228C22×Dic5C22×D311yescharacteristic
229C22⋊Dic5—34no—
230C22⋊Dic5—62no—
231C22⋊Dic5—64no—
232C4⋊Dic5—22no—
233C4⋊Dic5—64no—
234C4⋊Dic5—64no—
235C4⋊Dic5—62no—
236C4×Dic5—22no—
237C4×Dic5—64no—
238C4×Dic5—64no—
239C4×Dic5—62no—
240C23×Q8—31no—
241C2×C4×Q8—151no—
242C2×C4×Q8—151no—
243#391—51no—
244#391—152no—
245#391—152no—
246#391—151no—
247#380—152no—
248#380—151no—
249C4×C22⋊C4—152no—
250C4×C22⋊C4—151no—
251C22×C3×C5C23×C411yescharacteristic
252C22×C3×C5C22×D411yescharacteristic
253C22×C3×C5C22×D411yescharacteristic
254C22×C3×C5C22×Q811yescharacteristic
255C22×C3×C5C2×#4111yescharacteristic
256C22×C3×C52−1+411yescharacteristic
257C22×C3×C52−1+411yescharacteristic
258C2×C5×D3—22no—
259C2×C5×D3—22no—
260C2×C5×D3—22no—
261C2×C5×D3—22no—
262C2×C5×D3—22no—
263C2×C5×D3—22no—
264C2×C5×D3C4×Q814yescomplemented
265C3×C4×C5—24no—
266C3×C4×C5C2×C22⋊C414yes—
267Dic15—22no—
268Dic15—42no—
269Dic15—41no—
270C3×Dic5—22no—
271C3×Dic5—41no—
272C3×Dic5—42no—
273C5×Dic3—22no—
274C5×Dic3C2×C22⋊C418yes—
275C23×D3C22×D511yescharacteristic
276C2×C3×Q8—22no—
277C2×C3×Q8—22no—
278C2×C3×Q8C2×Dic514yes—
279C22×C3×C4—51no—
280C22×C3×C4—52no—
281C22×C3×C4—51no—
282C22×C3×C4C22×D512yes—
283C22×C3×C4C22×D511yescharacteristic
284C22×Dic3—51no—
285C22×Dic3—51no—
286C22×Dic3—52no—
287C22×Dic3C22×D511yescharacteristic
288C22×Dic3C22×D512yes—
289D3×Q8—232no—
290C2×C4×D3—22no—
291C2×C4×D3—22no—
292C2×C4×D3—24no—
293C2×C4×D3—24no—
294C2×C4×D3C2×Dic514yes—
295C2×C4×D3C2×Dic518yes—
296C2×Dic6—24no—
297C2×Dic6—24no—
298C2×Dic6C2×Dic518yes—
299C2×Dic6C2×Dic514yes—
300C2×Dic6C22⋊D514yes—
301C2×Dic6C22⋊D514yes—
302C3×C4⋊C4—102no—
303C3×C42—102no—
304(C2×D3)⋊C4—54no—
305(C2×D3)⋊C4—104no—
306(C2×D3)⋊C4—102no—
307C4⋊Dic3—102no—
308Dic3⋊C4—104no—
309Dic3⋊C4—104no—
310C4×Dic3—102no—
311C4×Dic3—104no—
312C4×Dic3—104no—
313C23×C5—32no—
314C23×C5—32no—
315C23×C5—32no—
316C23×C5—61no—
317C23×C5—61no—
318C23×C5—61no—
319C23×C5—61no—
320C23×C5C23×D311yescharacteristic
321C5×Q8—28no—
322C5×Q8—316no—
323C5×Q8—616no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—34no—
327C2×C4×C5—34no—
328C2×C4×C5—34no—
329C2×C4×C5—32no—
330C2×C4×C5—616no—
331C2×C4×C5—61no—
332C2×C4×C5—61no—
333C2×C4×C5—68no—
334C2×C4×C5C2×C4×D314yes—
335C2×C4×C5C2×C4×D312yes—
336C2×C4×C5D3×D412yes—
337C2×C4×C5D3×D412yes—
338C2×Dic5—21no—
339C2×Dic5—21no—
340C2×Dic5—21no—
341C2×Dic5—22no—
342C2×Dic5—21no—
343C2×Dic5—21no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—32no—
347C2×Dic5—61no—
348C2×Dic5—61no—
349C2×Dic5—62no—
350C2×Dic5—61no—
351C2×Dic5—62no—
352C2×Dic5—62no—
353C2×Dic5—61no—
354C2×Dic5—61no—
355C2×Dic5D3×Q812yescomplemented
356C22×Q8—38no—
357C22×Q8—31no—
358C22×Q8—32no—
359C22×Q8—64no—
360C22×Q8—64no—
361C22×Q8D3×D511yescharacteristic
362C23×C4—32no—
363C23×C4—31no—
364C4×Q8—304no—
365C4×Q8—304no—
366C2×C4⋊C4—51no—
367C2×C4⋊C4—152no—
368C2×C4⋊C4—152no—
369C2×C4⋊C4—151no—
370C2×C22⋊C4—151no—
371C2×C22⋊C4—151no—
372C2×C22⋊C4—152no—
373C2×C42—51no—
374C2×C42—152no—
375C2×C42—152no—
376C2×C42—151no—
377#95—52no—
378#95—52no—
379#95—151no—
380#95—151no—
381#95—152no—
382#95—152no—
383#95—152no—
384C2×C3×C5C22×C22⋊C411yescharacteristic
385C2×C3×C5C2×C4×Q811yescharacteristic
386C2×C3×C5#51911yescharacteristic
387C2×C3×C5#54811yescharacteristic
388C2×C3×C5#54811yescharacteristic
389C2×C3×C5D4×Q811yescharacteristic
390C2×C3×C5D4×Q811yescharacteristic
391C5×D3—24no—
392C23×C3C23×D511yescharacteristic
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3Q8×D512yes—
398C22×D3#71312yes—
399C22×D3C22×Dic512yes—
400C3×Q8—28no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—52no—
404C2×C3×C4—101no—
405C2×C3×C4—101no—
406C2×C3×C4—102no—
407C2×C3×C4—101no—
408C2×C3×C4—102no—
409C2×C3×C4—101no—
410C2×C3×C4—102no—
411C2×C3×C4—101no—
412C2×C3×C4C22×Dic514yes—
413C2×C3×C4C22×Dic512yes—
414C2×C3×C4C2×C22⋊D512yes—
415C2×C3×C4C2×C22⋊D512yes—
416C2×Dic3—21no—
417C2×Dic3—21no—
418C2×Dic3—52no—
419C2×Dic3—101no—
420C2×Dic3—101no—
421C2×Dic3—101no—
422C2×Dic3—102no—
423C2×Dic3—101no—
424C2×Dic3—102no—
425C2×Dic3—101no—
426C2×Dic3—102no—
427C2×Dic3C22×Dic512yes—
428C2×Dic3C22×Dic514yes—
429C2×Dic3C2×C22⋊D514yes—
430C2×Dic3C2×C22⋊D514yes—
431C4×D3—28no—
432C4×D3—216no—
433Dic6—216no—
434Dic6C22⋊Dic5116yescomplemented
435C22×C5—34no—
436C22×C5—62no—
437C22×C5—62no—
438C22×C5—62no—
439C22×C5—62no—
440C22×C5—62no—
441C22×C5—62no—
442C22×C5C22×C4×D311yescharacteristic
443C22×C5C2×D3×D411yescharacteristic
444C22×C5C2×D3×D411yescharacteristic
445C22×C5C2×D3×Q811yescharacteristic
446C22×C5#100711yescharacteristic
447C22×C5D3×#4111yescharacteristic
448C22×C5#101011yescharacteristic
449C4×C5—24no—
450C4×C5—38no—
451C4×C5—62no—
452C4×C5D3×C22⋊C414yes—
453Dic5—22no—
454Dic5—41no—
455Dic5—42no—
456Dic5—62no—
457Dic5—122no—
458Dic5—121no—
459C24—31no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—34no—
463C2×Q8—38no—
464C2×Q8—34no—
465C2×Q8—34no—
466C2×Q8—64no—
467C2×Q8—64no—
468C2×Q8—632no—
469C2×Q8D3×Dic514yes—
470C22×C4—32no—
471C22×C4—31no—
472C22×C4—38no—
473C22×C4—34no—
474C22×C4—51no—
475C22×C4—51no—
476C22×C4—52no—
477C22×C4—64no—
478C22×C4—64no—
479C22×C4—62no—
480C22×C4—62no—
481C22×C4—151no—
482C22×C4—151no—
483C22×C4—152no—
484C22×C4C2×D3×D512yes—
485C22×C4C2×D3×D511yescharacteristic
486C4⋊C4—102no—
487C4⋊C4—304no—
488C4⋊C4—304no—
489C4⋊C4—302no—
490C22⋊C4—154no—
491C22⋊C4—304no—
492C22⋊C4—302no—
493C42—102no—
494C42—304no—
495C42—304no—
496C42—302no—
497C3×C5Q8×C22⋊C411yescharacteristic, complemented, Hall
498C22×C3C2×Q8×D511yescharacteristic
499C22×C3C2×#71311yescharacteristic
500C22×C3#414711yescharacteristic
501C22×C3#414711yescharacteristic
502C22×C3C23×Dic511yescharacteristic
503C22×C3C22×C22⋊D511yescharacteristic
504C22×C3C22×C22⋊D511yescharacteristic
505C2×D3—22no—
506C2×D3—22no—
507C2×D3—22no—
508C2×D3—22no—
509C2×D3—22no—
510C2×D3—22no—
511C2×D3Q8×Dic514yescomplemented
512C3×C4—24no—
513C3×C4—102no—
514C3×C4—202no—
515C3×C4—201no—
516C3×C4C2×C22⋊Dic514yes—
517Dic3—22no—
518Dic3—102no—
519Dic3—201no—
520Dic3—202no—
521Dic3C2×C22⋊Dic518yes—
522C2×C5—64no—
523C2×C5C2×D3×C22⋊C411yescharacteristic
524C2×C5C4×D3×Q811yescharacteristic
525C2×C5#557211yescharacteristic
526C2×C5#563211yescharacteristic
527C2×C5#563311yescharacteristic
528C2×C5#567711yescharacteristic
529C2×C5#572711yescharacteristic
530C23—32no—
531C23—32no—
532C23—32no—
533C23—61no—
534C23—61no—
535C23—61no—
536C23—61no—
537C23C22×D3×D511yescharacteristic
538Q8—28no—
539Q8—316no—
540Q8—616no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—34no—
544C2×C4—34no—
545C2×C4—34no—
546C2×C4—32no—
547C2×C4—52no—
548C2×C4—616no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—68no—
552C2×C4—101no—
553C2×C4—101no—
554C2×C4—102no—
555C2×C4—101no—
556C2×C4—102no—
557C2×C4—101no—
558C2×C4—101no—
559C2×C4—102no—
560C2×C4—152no—
561C2×C4—301no—
562C2×C4—301no—
563C2×C4—301no—
564C2×C4—302no—
565C2×C4—301no—
566C2×C4—302no—
567C2×C4—301no—
568C2×C4—302no—
569C2×C4C2×D3×Dic514yes—
570C2×C4C2×D3×Dic512yes—
571C2×C4D3×C22⋊D512yes—
572C2×C4D3×C22⋊D512yes—
573C2×C3C2×Q8×Dic511yescharacteristic
574C2×C3#6614611yescharacteristic
575C2×C3Q8×C22⋊D511yescharacteristic
576C2×C3Q8×C22⋊D511yescharacteristic
577C2×C3#6615111yescharacteristic
578C2×C3#6615111yescharacteristic
579C2×C3C22×C22⋊Dic511yescharacteristic
580D3—24no—
581C5#7661411yescharacteristic, complemented, Sylow
582C22—34no—
583C22—62no—
584C22—62no—
585C22—62no—
586C22—62no—
587C22—62no—
588C22—62no—
589C22#9202811yescharacteristic
590C22#9202911yescharacteristic
591C22D3×Q8×D511yescharacteristic
592C22D3×#71311yescharacteristic
593C22C22×D3×Dic511yescharacteristic
594C22C2×D3×C22⋊D511yescharacteristic
595C22C2×D3×C22⋊D511yescharacteristic
596C4—24no—
597C4—38no—
598C4—62no—
599C4—102no—
600C4—202no—
601C4—201no—
602C4—302no—
603C4—601no—
604C4—602no—
605C4D3×C22⋊Dic514yes—
606C3Q8×C22⋊Dic511yescharacteristic, complemented, Sylow
607C2—64no—
608C2#1175514411yescharacteristic
609C2D3×Q8×Dic511yescharacteristic
610C2#1175522911yescharacteristic
611C2#1175523011yescharacteristic
612C2#1175523411yescharacteristic
613C2#1175523511yescharacteristic
614C2C2×D3×C22⋊Dic511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×Q8C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5Q8×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#91344C2semidirect
3. C2×Dic5×Dic6C2semidirect
4. #11751330C2semidirect
5. C3×#65519C2semidirect
10. #11748692C2semidirect
11. #11748692C2semidirect
16. C2×C5×D3×Q8C4semidirect
48. #65519D3semidirect
88. (C2×D3)⋊Dic5Q8semidirect
154. C2×Dic15C2×Q8semidirect
164. C5×Dic6C22⋊C4semidirect
173. C2×C3×Dic5C2×Q8semidirect
177. C2×D3×Q8Dic5semidirect
264. C2×C5×D3C4×Q8semidirect
355. C2×Dic5D3×Q8semidirect
434. Dic6C22⋊Dic5semidirect
497. C3×C5Q8×C22⋊C4semidirect
511. C2×D3Q8×Dic5semidirect
581. C5#76614semidirect
606. C3Q8×C22⋊Dic5semidirect

Maximal subgroups

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

subgroupindex
C22×C5×D3×Q82
C2×#913442
C2×Dic5×Dic62
#117513302
C3×#655192
#117487862
#117487822
#117487192
C4×(C2×D3)⋊Dic52
#117486922
Q8×C22⋊Dic53
#766145