Finite Group Databasebeta

← Dic3×#4024 #14321825

Subgroups — Dic3×#4024 #14321825

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4024C211yesmaximal, characteristic
2C22×Dic3×Dic5C211yesmaximal, characteristic
3C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
4#11751051C211yesmaximal, characteristic
5C5×Dic3×C22⋊C4C211yesmaximal, characteristic
6#11749515C211yesmaximal, characteristic
7#11749506C211yesmaximal, characteristic
8Dic3×C22⋊Dic5C211yesmaximal, characteristic
9#11748698C211yesmaximal, characteristic, complemented
10Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
11#11748691C211yesmaximal, characteristic, complemented
12#11748680C211yesmaximal, characteristic, complemented
13#11748672C211yesmaximal, characteristic, complemented
14Dic3×#683C211yesmaximal, characteristic, complemented
15Dic3×#683C211yesmaximal, characteristic, complemented
16C4×#4024—31nomaximal, Hall
17C23×Dic15C2211yescharacteristic
18C23×C5×Dic3C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×C4⋊Dic15C2211yescharacteristic
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C3×#4024C418yescomplemented
33C2×#6668C2211yescharacteristic
34C2×#6668C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×#6668C2211yescharacteristic
37C2×Dic3×Dic5—24no—
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44Dic3×Dic10—24no—
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55Dic3×C22⋊Q8—51nomaximal, Hall
56C22×C4×Dic5—31no—
57C2×#4024D311yescharacteristic
58C2×C4×Dic10—31no—
59C4×C5×C22⋊C4—31no—
60C4×C22⋊Dic5—31no—
61#65239—31no—
62#65235—31no—
63#65231—31no—
64C4×C4⋊Dic5—31no—
65C4×#683—31no—
66C4×#683—31no—
67#64944—31no—
68#64943—31no—
69#64936—31no—
70#64935—31no—
71C24×C3×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15—22no—
75C22×Dic15—22no—
76C22×Dic15—22no—
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×C5×Dic3—22no—
82C22×C5×Dic3—22no—
83C22×C5×Dic3Q814yescomplemented
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C3×Dic5—22no—
89C22×C3×Dic5—22no—
90C22×C3×Dic5C2×C414yes—
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×C3×Dic10—22no—
96C2×C3×Dic10—22no—
97C2×C3×Dic10C2×C414yescomplemented
98C3×C5×C22⋊C4C2×C414yes—
99#6719—22no—
100C4⋊Dic15—22no—
101C4⋊Dic15—22no—
102C5×#217—22no—
103C4×C5×Dic3—22no—
104C4×C5×Dic3—22no—
105C3×C22⋊Dic5C2×C414yes—
106C3×C4⋊Dic5C2×C414yescomplemented
107C3×#683C2×C414yescomplemented
108C3×#683C2×C414yescomplemented
109#6668—22no—
110#6668—22no—
111#6668—22no—
112#6668—22no—
113Dic3×Dic5—22no—
114Dic3×Dic5—22no—
115Dic3×Dic5—22no—
116Dic3×Dic5—22no—
117Dic3×Dic5—22no—
118Dic3×Dic5D414yes—
119C2×C3×C22⋊Q8—51no—
120C2×Q8×Dic3—51no—
121C22×C4×Dic3—51no—
122#5229—51no—
123#5212—51no—
124#4984—51no—
125#4980—51no—
126#4980—51no—
127Dic3×C4⋊C4—51no—
128Dic3×C4⋊C4—51no—
129Dic3×C4⋊C4—51no—
130#4950—51no—
131#4950—51no—
132Dic3×C22⋊C4—51no—
133Dic3×C22⋊C4D511yescharacteristic
134C23×C4×C5—31no—
135C23×Dic5—31no—
136C23×Dic5C2×D311yescharacteristic
137C22×Dic10C2×D311yescharacteristic
138C2×C5×C22⋊C4—31no—
139C2×C5×C22⋊C4C2×D311yescharacteristic
140C2×C42×C5—31no—
141C2×C42×C5—31no—
142C2×C22⋊Dic5—31no—
143C2×C22⋊Dic5C2×D311yescharacteristic
144C2×C4⋊Dic5—31no—
145C2×C4⋊Dic5—31no—
146C2×C4⋊Dic5C2×D311yescharacteristic
147C2×#683—31no—
148C2×#683—31no—
149C2×#683—31no—
150C2×#683—31no—
151C2×#683C2×D311yescharacteristic
152C2×#683C2×D311yescharacteristic
153C2×C4×Dic5—31no—
154C2×C4×Dic5—31no—
155C2×C4×Dic5—31no—
156C2×C4×Dic5—31no—
157C2×C4×Dic5—31no—
158C2×C4×Dic5—31no—
159C2×C4×Dic5—64no—
160#4024Dic318yesdirect product factor
161C4×Dic10—64no—
162C5×#95—31no—
163C5×#95—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172C4×C22⋊Q8—151noSylow
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5C22×C412yes—
178C23×C3×C5C2×Q812yes—
179C23×C3×C5#4112yes—
180C23×C3×C5C2411yescharacteristic
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5C22×C412yes—
186C2×C3×C4×C5C22×C412yes—
187C2×Dic15—28no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15C2×D412yes—
199C2×Dic15#4112yes—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—28no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3C2×D412yes—
210C2×C5×Dic3C2×Q812yes—
211C2×C5×Dic3C2×Q812yes—
212C2×C5×Dic3#4112yes—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—28no—
220C2×C3×Dic5C22×C412yes—
221C2×C3×Dic5C22×C412yes—
222C2×C3×Dic5C22×C412yes—
223C2×C3×Dic5C22×C412yes—
224C2×C3×Dic5C2×D412yes—
225C2×C3×Dic5#4112yes—
226C3×Dic10—28no—
227C22×C3×Q8—51no—
228C23×C3×C4—51no—
229C23×Dic3—51no—
230C23×Dic3C2×D511yescharacteristic
231C3×C22⋊Q8—58no—
232C2×C3×C4⋊C4—51no—
233C2×C3×C4⋊C4—51no—
234C2×C3×C4⋊C4—51no—
235C2×C3×C22⋊C4—51no—
236C2×C3×C22⋊C4C2×D511yescharacteristic
237C2×#217—51no—
238C2×#217C2×D511yescharacteristic
239Q8×Dic3—104no—
240C2×C4⋊Dic3—51no—
241C2×C4⋊Dic3—51no—
242C2×C4⋊Dic3—51no—
243C2×C4⋊Dic3—51no—
244C2×C4⋊Dic3—51no—
245C2×C4⋊Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3—51no—
249C2×C4×Dic3—51no—
250C2×C4×Dic3—51no—
251C2×C4×Dic3—51no—
252C2×C4×Dic3—104no—
253C2×C4×Dic3C2×D511yescharacteristic
254C2×C4×Dic3C2×D511yescharacteristic
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95—51no—
260C3⋊#95—51no—
261C3⋊#95—51no—
262C3⋊#95—51no—
263C3⋊#95C2×D511yescharacteristic
264C3⋊#95C2×D511yescharacteristic
265C24×C5C22×D311yescharacteristic
266C22×C4×C5—31no—
267C22×C4×C5—34no—
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C22×C4×C5—31no—
271C22×C4×C5—62no—
272C22×C4×C5—62no—
273C22×C4×C5C22×D311yescharacteristic
274C22×C4×C5C22×D311yescharacteristic
275C22×Dic5—22no—
276C22×Dic5—22no—
277C22×Dic5—31no—
278C22×Dic5—31no—
279C22×Dic5—31no—
280C22×Dic5—31no—
281C22×Dic5—62no—
282C22×Dic5—62no—
283C22×Dic5—62no—
284C22×Dic5C2×Dic314yes—
285C22×Dic5C22×D311yescharacteristic
286C22×Dic5C22×D311yescharacteristic
287C22×Dic5C22×D311yescharacteristic
288C22×Dic5C22×D311yescharacteristic
289C2×Dic10—22no—
290C2×Dic10—22no—
291C2×Dic10C2×Dic314yescomplemented
292C5×C22⋊C4—62no—
293C5×C22⋊C4C2×Dic314yes—
294C42×C5—62no—
295C42×C5—62no—
296C22⋊Dic5—62no—
297C22⋊Dic5C2×Dic314yes—
298C4⋊Dic5—62no—
299C4⋊Dic5—62no—
300C4⋊Dic5C2×Dic314yescomplemented
301#683—62no—
302#683—62no—
303#683—62no—
304#683—62no—
305#683C2×Dic314yescomplemented
306#683C2×Dic314yescomplemented
307C4×Dic5—34no—
308C4×Dic5—62no—
309C4×Dic5—62no—
310C4×Dic5—62no—
311C4×Dic5—62no—
312C4×Dic5—62no—
313C2×C22⋊Q8—51no—
314C2×C4×Q8—151no—
315C22×C42—151no—
316#391—151no—
317#389—151no—
318#387—151no—
319#387—151no—
320#385—151no—
321#385—151no—
322#380—151no—
323C4×C4⋊C4—151no—
324C4×C4⋊C4—151no—
325C4×C4⋊C4—151no—
326C4×C22⋊C4—31no—
327C4×C22⋊C4—151no—
328C22×C3×C5—22no—
329C22×C3×C5—22no—
330C22×C3×C5—22no—
331C22×C3×C5—22no—
332C22×C3×C5—22no—
333C22×C3×C5—22no—
334C22×C3×C5C4×Q814yescomplemented
335C22×C3×C5C23×C411yescharacteristic
336C22×C3×C5C22×D411yescharacteristic
337C22×C3×C5C22×Q811yescharacteristic
338C22×C3×C5C2×#4111yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C3×C4×C5—22no—
343C3×C4×C5—22no—
344Dic15—22no—
345Dic15—22no—
346Dic15—41no—
347Dic15—41no—
348C3×Dic5—22no—
349C3×Dic5—22no—
350C3×Dic5—22no—
351C3×Dic5C4×D414yes—
352C5×Dic3—22no—
353C5×Dic3—41no—
354C5×Dic3—41no—
355C5×Dic3C22⋊Q814yescomplemented
356C24×C3C22×D511yescharacteristic
357C2×C3×Q8—54no—
358C2×C3×Q8—102no—
359C2×C3×Q8—102no—
360C22×C3×C4—51no—
361C22×C3×C4—54no—
362C22×C3×C4—51no—
363C22×C3×C4—51no—
364C22×C3×C4—51no—
365C22×C3×C4—102no—
366C22×C3×C4—102no—
367C22×C3×C4C22×D511yescharacteristic
368C22×C3×C4C22×D511yescharacteristic
369C22×Dic3—22no—
370C22×Dic3—22no—
371C22×Dic3—51no—
372C22×Dic3—51no—
373C22×Dic3—51no—
374C22×Dic3—51no—
375C22×Dic3—102no—
376C22×Dic3—102no—
377C22×Dic3—102no—
378C22×Dic3Dic1014yescomplemented
379C22×Dic3C22×D511yescharacteristic
380C22×Dic3C22×D511yescharacteristic
381C22×Dic3C22×D511yescharacteristic
382C22×Dic3C22×D511yescharacteristic
383C3×C4⋊C4—54no—
384C3×C4⋊C4—54no—
385C3×C4⋊C4—54no—
386C3×C22⋊C4—54no—
387C3×C22⋊C4C4×D514yes—
388#217—22no—
389#217—102no—
390C4⋊Dic3—102no—
391C4⋊Dic3—102no—
392C4⋊Dic3—102no—
393C4⋊Dic3—102no—
394C4⋊Dic3—102no—
395C4⋊Dic3—102no—
396C4×Dic3—22no—
397C4×Dic3—22no—
398C4×Dic3—54no—
399C4×Dic3—102no—
400C4×Dic3—102no—
401C4×Dic3—102no—
402C4×Dic3—102no—
403C4×Dic3—102no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5—21no—
408C23×C5D3×Q812yes—
409C23×C5#23912yes—
410C23×C5C22×Dic312yes—
411C23×C5C23×D311yescharacteristic
412C2×C4×C5—21no—
413C2×C4×C5—21no—
414C2×C4×C5—21no—
415C2×C4×C5—21no—
416C2×C4×C5—32no—
417C2×C4×C5—32no—
418C2×C4×C5—32no—
419C2×C4×C5—32no—
420C2×C4×C5—68no—
421C2×C4×C5—61no—
422C2×C4×C5—61no—
423C2×C4×C5—61no—
424C2×C4×C5—61no—
425C2×C4×C5—61no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5C22×Dic312yes—
430C2×C4×C5C22×Dic312yes—
431C2×Dic5—21no—
432C2×Dic5—21no—
433C2×Dic5—21no—
434C2×Dic5—21no—
435C2×Dic5—21no—
436C2×Dic5—21no—
437C2×Dic5—28no—
438C2×Dic5—32no—
439C2×Dic5—32no—
440C2×Dic5—68no—
441C2×Dic5—61no—
442C2×Dic5—61no—
443C2×Dic5—61no—
444C2×Dic5—61no—
445C2×Dic5—61no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5D3×D412yes—
452C2×Dic5#23712yes—
453C2×Dic5C22×Dic312yes—
454C2×Dic5C22×Dic312yes—
455C2×Dic5C22×Dic312yes—
456C2×Dic5C22×Dic312yes—
457Dic10—28no—
458C22×Q8—51no—
459C23×C4—31no—
460C23×C4—51no—
461C23×C4—151no—
462C22⋊Q8—58no—
463C4×Q8—304no—
464C2×C4⋊C4—51no—
465C2×C4⋊C4—51no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—151no—
468C2×C4⋊C4—151no—
469C2×C4⋊C4—151no—
470C2×C4⋊C4—151no—
471C2×C4⋊C4—151no—
472C2×C4⋊C4—151no—
473C2×C22⋊C4—31no—
474C2×C22⋊C4—51no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4D3×D511yescharacteristic
477C2×C42—31no—
478C2×C42—31no—
479C2×C42—151no—
480C2×C42—151no—
481C2×C42—151no—
482C2×C42—151no—
483C2×C42—151no—
484C2×C42—151no—
485C2×C42—304no—
486#95—31no—
487#95—31no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494#95—151no—
495#95—151no—
496C2×C3×C5—24no—
497C2×C3×C5C2×C4×D411yescharacteristic
498C2×C3×C5C2×C4×Q811yescharacteristic
499C2×C3×C5C4×#4111yescharacteristic
500C2×C3×C5C2×C22⋊Q811yescharacteristic
501C2×C3×C5#52511yescharacteristic
502C2×C3×C5#52911yescharacteristic
503C2×C3×C5#53311yescharacteristic
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3C2×Dic1012yes—
509C23×C3C2×C4×D512yes—
510C23×C3#70912yes—
511C23×C3C23×D511yescharacteristic
512C3×Q8—108no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—52no—
518C2×C3×C4—52no—
519C2×C3×C4—52no—
520C2×C3×C4—52no—
521C2×C3×C4—52no—
522C2×C3×C4—52no—
523C2×C3×C4—108no—
524C2×C3×C4—101no—
525C2×C3×C4—101no—
526C2×C3×C4—101no—
527C2×C3×C4—101no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4C2×C4×D512yes—
531C2×C3×C4C2×C4×D512yes—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—28no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—52no—
542C2×Dic3—52no—
543C2×Dic3—108no—
544C2×Dic3—101no—
545C2×Dic3—101no—
546C2×Dic3—101no—
547C2×Dic3—101no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3C2×Dic1012yes—
555C2×Dic3C2×Dic1012yes—
556C2×Dic3D4×D512yes—
557C2×Dic3#71112yes—
558C22×C5—22no—
559C22×C5—22no—
560C22×C5—22no—
561C22×C5—22no—
562C22×C5—22no—
563C22×C5—22no—
564C22×C5Q8×Dic314yescomplemented
565C22×C5C2×D3×D411yescharacteristic
566C22×C5C2×#23711yescharacteristic
567C22×C5C2×D3×Q811yescharacteristic
568C22×C5C2×#23911yescharacteristic
569C22×C5D3×#4111yescharacteristic
570C22×C5D3×#4111yescharacteristic
571C22×C5C23×Dic311yescharacteristic
572C4×C5—22no—
573C4×C5—22no—
574C4×C5—34no—
575C4×C5—62no—
576C4×C5—121no—
577C4×C5—121no—
578Dic5—22no—
579Dic5—22no—
580Dic5—22no—
581Dic5—62no—
582Dic5—62no—
583Dic5—121no—
584Dic5—121no—
585Dic5D4×Dic314yes—
586C24C2×D3×D511yescharacteristic
587C2×Q8—54no—
588C2×Q8—102no—
589C2×Q8—102no—
590C22×C4—31no—
591C22×C4—34no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—51no—
596C22×C4—54no—
597C22×C4—51no—
598C22×C4—51no—
599C22×C4—51no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—151no—
605C22×C4—151no—
606C22×C4—151no—
607C22×C4—151no—
608C22×C4—302no—
609C22×C4—302no—
610C22×C4—302no—
611C22×C4C2×D3×D511yescharacteristic
612C22×C4C2×D3×D511yescharacteristic
613C4⋊C4—54no—
614C4⋊C4—54no—
615C4⋊C4—54no—
616C4⋊C4—302no—
617C4⋊C4—302no—
618C4⋊C4—302no—
619C4⋊C4—302no—
620C4⋊C4—302no—
621C4⋊C4—302no—
622C22⋊C4—54no—
623C22⋊C4—62no—
624C22⋊C4—302no—
625C22⋊C4D5×Dic314yes—
626C42—62no—
627C42—62no—
628C42—154no—
629C42—302no—
630C42—302no—
631C42—302no—
632C42—302no—
633C42—302no—
634C3×C5C4×C22⋊Q811yescharacteristic, complemented, Hall
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3C4×Dic1014yescomplemented
642C22×C3C22×Dic1011yescharacteristic
643C22×C3C22×C4×D511yescharacteristic
644C22×C3C2×#70911yescharacteristic
645C22×C3C2×D4×D511yescharacteristic
646C22×C3C2×#71111yescharacteristic
647C22×C3D5×#4111yescharacteristic
648C22×C3D5×#4111yescharacteristic
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—54no—
652C3×C4—102no—
653C3×C4—102no—
654C3×C4—102no—
655Dic3—22no—
656Dic3—41no—
657Dic3—41no—
658Dic3—102no—
659Dic3—102no—
660Dic3—201no—
661Dic3—201no—
662Dic3#402414yesdirect product factor
663C2×C5—24no—
664C2×C5#562211yescharacteristic
665C2×C5#562411yescharacteristic
666C2×C5D3×C22⋊Q811yescharacteristic
667C2×C5#562711yescharacteristic
668C2×C5C2×D4×Dic311yescharacteristic
669C2×C5C2×Q8×Dic311yescharacteristic
670C2×C5Dic3×#4111yescharacteristic
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23D3×Dic1012yes—
676C23#676912yes—
677C23C2×D5×Dic312yes—
678C23C22×D3×D511yescharacteristic
679Q8—108no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—32no—
687C2×C4—32no—
688C2×C4—52no—
689C2×C4—52no—
690C2×C4—52no—
691C2×C4—52no—
692C2×C4—52no—
693C2×C4—52no—
694C2×C4—68no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—108no—
704C2×C4—101no—
705C2×C4—101no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—101no—
710C2×C4—152no—
711C2×C4—152no—
712C2×C4—308no—
713C2×C4—301no—
714C2×C4—301no—
715C2×C4—301no—
716C2×C4—301no—
717C2×C4—301no—
718C2×C4—301no—
719C2×C4—301no—
720C2×C4—301no—
721C2×C4—301no—
722C2×C4—301no—
723C2×C4C2×D5×Dic312yes—
724C2×C4C2×D5×Dic312yes—
725C2×C3—24no—
726C2×C3C2×C4×Dic1011yescharacteristic
727C2×C3C2×#402411yescharacteristic
728C2×C3#6585111yescharacteristic
729C2×C3C4×#71111yescharacteristic
730C2×C3#6587211yescharacteristic
731C2×C3C4×D4×D511yescharacteristic
732C2×C3#6588111yescharacteristic
733C5Dic3×C22⋊Q811yescharacteristic, complemented, Sylow
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22Dic3×Dic1014yescomplemented
741C22C2×D3×Dic1011yescharacteristic
742C22C2×#676911yescharacteristic
743C22D3×D4×D511yescharacteristic
744C22D5×#23711yescharacteristic
745C22D3×#71111yescharacteristic
746C22#9202411yescharacteristic
747C22C22×D5×Dic311yescharacteristic
748C4—22no—
749C4—22no—
750C4—34no—
751C4—54no—
752C4—62no—
753C4—102no—
754C4—102no—
755C4—102no—
756C4—121no—
757C4—121no—
758C4—302no—
759C4—302no—
760C4—601no—
761C4—601no—
762C3C4×#402411yescharacteristic, complemented, Sylow
763C2—24no—
764C2#1175278011yescharacteristic
765C2D3×#402411yescharacteristic
766C2#1175284911yescharacteristic
767C2#1175295611yescharacteristic
768C2C2×Dic3×Dic1011yescharacteristic
769C2D4×D5×Dic311yescharacteristic
770C2Dic3×#71111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C4×C22⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×Dic3×Dic10C2semidirect
9. #11748698C2semidirect
10. Dic3×C4⋊Dic5C2semidirect
11. #11748691C2semidirect
12. #11748680C2semidirect
13. #11748672C2semidirect
14. Dic3×#683C2semidirect
15. Dic3×#683C2semidirect
32. C3×#4024C4semidirect
83. C22×C5×Dic3Q8semidirect
97. C2×C3×Dic10C2×C4semidirect
106. C3×C4⋊Dic5C2×C4semidirect
107. C3×#683C2×C4semidirect
108. C3×#683C2×C4semidirect
160. #4024Dic3direct (N × H)
291. C2×Dic10C2×Dic3semidirect
300. C4⋊Dic5C2×Dic3semidirect
305. #683C2×Dic3semidirect
306. #683C2×Dic3semidirect
334. C22×C3×C5C4×Q8semidirect
355. C5×Dic3C22⋊Q8semidirect
378. C22×Dic3Dic10semidirect
564. C22×C5Q8×Dic3semidirect
634. C3×C5C4×C22⋊Q8semidirect
641. C22×C3C4×Dic10semidirect
662. Dic3#4024direct (N × H)
733. C5Dic3×C22⋊Q8semidirect
740. C22Dic3×Dic10semidirect
762. C3C4×#4024semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40242
C22×Dic3×Dic52
C2×Dic3×Dic102
#117510512
C5×Dic3×C22⋊C42
#117495152
#117495062
Dic3×C22⋊Dic52
#117486982
Dic3×C4⋊Dic52
#117486912
#117486802
#117486722
Dic3×#6832
C4×#40243
Dic3×C22⋊Q85