Finite Group Databasebeta

← #29695471

Subgroups — #29695471

Order 15616.

1490 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#92418C211yesmaximal, characteristic, complemented
2C2×#16839758C212yesmaximal, complemented
3#21448768C211yesmaximal, characteristic, complemented
4#21446743C211yesmaximal, characteristic, complemented
5#21446622C211yesmaximal, characteristic, complemented
6#21446243C212yesmaximal, complemented
7#21446132C212yesmaximal, complemented
8#21445819C211yesmaximal, characteristic, complemented
9#21445759C212yesmaximal, complemented
10C4×#14519698C211yesmaximal, characteristic, complemented
11C2×C61×#547C211yesmaximal, characteristic
12C23×#92418C2212yes—
13C2×#14519736C2212yes—
14D4×#92418—24no—
15C2×C4⋊#92418C2211yescharacteristic
16#16839758—28no—
17C2×#14519701C2212yes—
18C2×#14519701C2212yes—
19C2×#14519701C2212yes—
20C2×#14519701C2212yes—
21C2×#14519698C2211yescharacteristic
22C2×#14519698C2212yes—
23C2×#14519698C2211yescharacteristic
24C2×C22⋊#92418C2212yes—
25C2×C4×#92418C2211yescharacteristic
26#16839665—21no—
27#16839655—22no—
28#16839632C2211yescharacteristic
29#16839622C2212yes—
30C4⋊C4×Dic61—21no—
31C4×C4⋊Dic61C2211yescharacteristic
32#16839524C2211yescharacteristic
33#16839524C2211yescharacteristic
34#16839524C2212yes—
35C22×#41×C61C2212yes—
36C61×#547—24no—
37C61×#547C418yescomplemented
38C2×C4⋊Q8×C61C2211yescharacteristic
39C2×#123×C61—22no—
40C2×C22⋊Q8×C61C2212yes—
41C2×#121×C61—21no—
42C2×C4×D4×C61C2211yescharacteristic
43C2×C4×D4×C61C2211yescharacteristic
44C22×C4⋊C4×C61—21no—
45C22×#92418—24no—
46C22×#92418—24no—
47C22×#92418—42no—
48C22×#92418C2311yescharacteristic
49C22×#92418C2312yes—
50C22×#92418C2311yescharacteristic
51#14519736—24no—
52#14519736—42no—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61C2312yes—
56C2×C4⋊Dic61C2311yescharacteristic
57C2×C4⋊Dic61C2311yescharacteristic
58C2×C22⋊Dic61—22no—
59C2×C22⋊Dic61—22no—
60C2×C4×Dic61—22no—
61C2×C4×Dic61—21no—
62C4⋊#92418—22no—
63#14519701—24no—
64#14519701—24no—
65#14519701—42no—
66#14519701—42no—
67#14519698—24no—
68#14519698—22no—
69#14519698D414yescomplemented
70C22⋊#92418—24no—
71C4×#92418—22no—
72#14519684—21no—
73#14519684—22no—
74C2×#41×C61—24no—
75C2×#41×C61—24no—
76C2×#41×C61—24no—
77C2×#41×C61—42no—
78C2×#41×C61—42no—
79C2×#41×C61C2×C418yes—
80C22×Q8×C61C2312yes—
81C22×D4×C61—22no—
82C22×D4×C61D411yescharacteristic
83C22×D4×C61C2311yescharacteristic
84C23×C4×C61—22no—
85C23×C4×C61—21no—
86C23×C4×C61C2312yes—
87C4⋊Q8×C61—22no—
88C4⋊Q8×C61C2×C414yes—
89#123×C61—216no—
90C22⋊Q8×C61—24no—
91C22⋊Q8×C61C2×C418yes—
92#121×C61—28no—
93C4×D4×C61—22no—
94C4×D4×C61C2×C414yes—
95C4×D4×C61C2×C414yes—
96C4×D4×C61D414yes—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—22no—
100C2×C4⋊C4×C61—28no—
101C2×C4⋊C4×C61D411yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C22⋊C4×C61—22no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61D412yes—
106C2×C42×C61C2311yescharacteristic
107C24×C61—21no—
108C24×C61C2×D412yes—
109#41×C61—216no—
110#41×C61—48no—
111#41×C61—48no—
112#41×C61—48no—
113C2×Q8×C61—22no—
114C2×Q8×C61—22no—
115C2×Q8×C61—22no—
116C2×Q8×C61—22no—
117C2×Q8×C61—22no—
118C2×Q8×C61C22×C414yes—
119C2×D4×C61—28no—
120C2×D4×C61—22no—
121C2×D4×C61—22no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—44no—
126C2×D4×C61—44no—
127C2×D4×C61C22⋊C414yes—
128C2×D4×C61C22×C412yes—
129C2×D4×C61C2×D412yes—
130C2×D4×C61#4112yes—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61—24no—
138C22×C4×C61—28no—
139C22×C4×C61—44no—
140C22×C4×C61—44no—
141C22×C4×C61—42no—
142C22×C4×C61—42no—
143C22×C4×C61C22×C414yes—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D412yes—
146C22×C4×C61C2×D414yes—
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2411yescharacteristic
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—22no—
152C4⋊C4×C61—24no—
153C4⋊C4×C61—28no—
154C4⋊C4×C61—24no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61C22⋊C414yes—
157C4⋊C4×C61C22×C412yes—
158C22⋊C4×C61—28no—
159C22⋊C4×C61—24no—
160C22⋊C4×C61C22⋊C418yes—
161C42×C61C22×C412yes—
162C42×C61C2×D412yes—
163C22⋊Dic61—44no—
164C22⋊Dic61—82no—
165C4⋊Dic61—21no—
166C4⋊Dic61—22no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—22no—
170C4⋊Dic61—42no—
171C4⋊Dic61—81no—
172C4⋊Dic61C2×D412yes—
173C4×Dic61—44no—
174C4×Dic61—42no—
175C2×#92418—21no—
176C2×#92418—21no—
177C2×#92418—21no—
178C2×#92418—22no—
179C2×#92418—22no—
180C2×#92418—21no—
181C2×#92418—21no—
182C2×#92418—22no—
183C2×#92418—48no—
184C2×#92418C2×D412yes—
185C23×C61—22no—
186C23×C61—22no—
187C23×C61—22no—
188C23×C61—22no—
189C23×C61—22no—
190C23×C61—22no—
191C23×C61—22no—
192C23×C61—22no—
193C23×C61—22no—
194C23×C61—41no—
195C23×C61—41no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61C2×C22⋊C414yes—
199C23×C61C22×D411yescharacteristic
200Q8×C61—24no—
201Q8×C61—24no—
202Q8×C61—42no—
203Q8×C61—42no—
204D4×C61—22no—
205D4×C61—22no—
206D4×C61—22no—
207D4×C61—28no—
208D4×C61—416no—
209D4×C61C4×D414yes—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—24no—
215C2×C4×C61—24no—
216C2×C4×C61—24no—
217C2×C4×C61—24no—
218C2×C4×C61—22no—
219C2×C4×C61—24no—
220C2×C4×C61—416no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—48no—
226C2×C4×C61C2×C22⋊C412yes—
227C2×C4×C61C2×C22⋊C414yes—
228C2×C4×C61C2×C22⋊C412yes—
229C2×C4×C61#13512yes—
230C2×C4×C61#13512yes—
231C2×C4×C61C23×C411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61H(5,𝔽2)11yescharacteristic
236C2×C4×C61H(5,𝔽2)11yescharacteristic
237C2×Dic61—22no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—42no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—41no—
246#92418—22no—
247#92418—42no—
248#92418—41no—
249#22417—611nomaximal, Sylow
250C22×C61—24no—
251C22×C61—24no—
252C22×C61—24no—
253C22×C61—24no—
254C22×C61—42no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61—42no—
258C22×C61—42no—
259C22×C61—42no—
260C22×C61—42no—
261C22×C61—42no—
262C22×C61—42no—
263C22×C61—42no—
264C22×C61C22×C22⋊C411yescharacteristic
265C22×C61D4211yescharacteristic
266C22×C61#54611yescharacteristic
267C22×C61C2×#13511yescharacteristic
268C22×C61C2×#13511yescharacteristic
269C22×C61#57711yescharacteristic
270C22×C61#57811yescharacteristic
271C4×C61—24no—
272C4×C61—22no—
273C4×C61—44no—
274C4×C61—42no—
275C4×C61#41614yescomplemented
276C4×C61C2×C4×D411yescharacteristic
277C4×C61#51811yescharacteristic
278C4×C61D4211yescharacteristic
279C4×C61#54611yescharacteristic
280Dic61—42no—
281Dic61—82no—
282Dic61—81no—
283C2×#547D6111yescharacteristic
284C2×C8×D4—611no—
285C2×#416—612no—
286#2354—611no—
287#1981—611no—
288#1956—611no—
289#1892—612no—
290#1873—612no—
291#1802—611no—
292#1788—612no—
293C4×#102—611no—
294C2×C61—44no—
295C2×C61—44no—
296C2×C61D4×C22⋊C411yescharacteristic
297C2×C61C2×#41611yescharacteristic
298C2×C61#289811yescharacteristic
299C2×C61#328311yescharacteristic
300C2×C61#328411yescharacteristic
301C2×C61#330211yescharacteristic
302C2×C61#330311yescharacteristic
303C22×#41C2×D6112yes—
304C23×C8—612no—
305#547—24no—
306#547Dic6118yescomplemented
307C2×C4⋊Q8C2×D6111yescharacteristic
308C2×#123—22no—
309C2×C22⋊Q8C2×D6112yes—
310C2×#121—21no—
311C2×C4×D4C2×D6111yescharacteristic
312C2×C4×D4C2×D6111yescharacteristic
313C2×#117—612no—
314C22×C4⋊C4—21no—
315C8×D4—1224no—
316C2×C4⋊C8—611no—
317#416—1228no—
318C2×#103—612no—
319C2×#103—612no—
320C2×#103—612no—
321C2×#103—612no—
322C2×#102—611no—
323C2×#102—612no—
324C2×#102—611no—
325C2×C22⋊C8—612no—
326C2×C4×C8—611no—
327#390—1221no—
328#388—1222no—
329#384—611no—
330#380—612no—
331C4×C4⋊C4—611no—
332C4×C4⋊C4—1221no—
333#340—612no—
334#340—611no—
335#340—611no—
336C61#2241711yescharacteristic, complemented, Sylow
337C2×#41—24no—
338C2×#41—24no—
339C2×#41—24no—
340C2×#41—42no—
341C2×#41—42no—
342C2×#41C2×Dic6118yes—
343C22×Q8C22×D6112yes—
344C22×D4—22no—
345C22×D4C22⋊D6111yescharacteristic
346C22×D4C22×D6111yescharacteristic
347C23×C4—21no—
348C23×C4—22no—
349C23×C4C22×D6112yes—
350C22×C8—611no—
351C22×C8—612no—
352C22×C8—611no—
353C22×C8—1224no—
354C22×C8—1224no—
355C22×C8—2442no—
356C4⋊Q8—22no—
357C4⋊Q8C2×Dic6114yes—
358#123—216no—
359C22⋊Q8—24no—
360C22⋊Q8C2×Dic6118yes—
361#121—28no—
362C4×D4—22no—
363C4×D4C2×Dic6114yes—
364C4×D4C2×Dic6114yes—
365C4×D4C22⋊D6114yes—
366#117—1224no—
367#117—2442no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—612no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4C22⋊D6111yescharacteristic
378C2×C4⋊C4C22×D6111yescharacteristic
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—1222no—
382C2×C22⋊C4—1222no—
383C2×C22⋊C4C22⋊D6112yes—
384C2×C42—1222no—
385C2×C42—1221no—
386C2×C42C22×D6111yescharacteristic
387C4⋊C8—1222no—
388#103—1224no—
389#103—1224no—
390#103—2442no—
391#103—2442no—
392#102—614no—
393#102—1224no—
394#102—1222no—
395C22⋊C8—1224no—
396C4×C8—1222no—
397#95—1221no—
398#95—1222no—
399C24—21no—
400C24C2×C22⋊D6112yes—
401#41—216no—
402#41—48no—
403#41—48no—
404#41—48no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8C22×Dic6114yes—
411C2×D4—28no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4C22⋊Dic6114yes—
420C2×D4D4×D6112yes—
421C2×D4#1175822412yes—
422C2×D4C22×Dic6112yes—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—28no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1222no—
438C22×C4C22×Dic6114yes—
439C22×C4C2×C22⋊D6114yes—
440C22×C4C2×C22⋊D6112yes—
441C22×C4C2×C22⋊D6111yescharacteristic
442C22×C4C2×C22⋊D6111yescharacteristic
443C22×C4C23×D6111yescharacteristic
444C2×C8—612no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8—1222no—
448C2×C8—1221no—
449C2×C8—1222no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1222no—
453C2×C8—2448no—
454C4⋊C4—21no—
455C4⋊C4—24no—
456C4⋊C4—28no—
457C4⋊C4—24no—
458C4⋊C4—612no—
459C4⋊C4—1221no—
460C4⋊C4—1222no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1222no—
464C4⋊C4—4881no—
465C4⋊C4—2442no—
466C4⋊C4C22⋊Dic6114yes—
467C4⋊C4C22×Dic6112yes—
468C22⋊C4—28no—
469C22⋊C4—24no—
470C22⋊C4—4882no—
471C22⋊C4—2444no—
472C22⋊C4C22⋊Dic6118yes—
473C42—2444no—
474C42—2442no—
475C42C22×Dic6112yes—
476C42C2×C22⋊D6112yes—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C2×C22⋊Dic6114yes—
491C23C22×C22⋊D6111yescharacteristic
492Q8—24no—
493Q8—24no—
494Q8—42no—
495Q8—42no—
496D4—22no—
497D4—28no—
498D4—22no—
499D4—22no—
500D4—416no—
501D4D4×Dic6114yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—416no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—48no—
518C2×C4—1222no—
519C2×C4—2441no—
520C2×C4—2442no—
521C2×C4—2441no—
522C2×C4—2442no—
523C2×C4—2442no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4C2×C22⋊Dic6112yes—
528C2×C4C2×C22⋊Dic6114yes—
529C2×C4C2×C22⋊Dic6112yes—
530C2×C4#1451979712yes—
531C2×C4#1451979712yes—
532C2×C4C23×Dic6111yescharacteristic
533C2×C4C2×D4×D6111yescharacteristic
534C2×C4C22×C22⋊D6111yescharacteristic
535C2×C4C2×#1175822411yescharacteristic
536C2×C4#1451982211yescharacteristic
537C2×C4#1451982211yescharacteristic
538C8—1222no—
539C8—2442no—
540C8—2441no—
541C22—24no—
542C22—24no—
543C22—24no—
544C22—24no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22C22×C22⋊Dic6111yescharacteristic
556C22D4×C22⋊D6111yescharacteristic
557C22#1684040611yescharacteristic
558C22C2×#1451979711yescharacteristic
559C22C2×#1451979711yescharacteristic
560C22#1684057011yescharacteristic
561C22#1684057711yescharacteristic
562C4—22no—
563C4—24no—
564C4—44no—
565C4—42no—
566C4—4881no—
567C4—4882no—
568C4—2442no—
569C4#1683975814yescomplemented
570C4C2×D4×Dic6111yescharacteristic
571C4#1684023711yescharacteristic
572C4D4×C22⋊D6111yescharacteristic
573C4#1684040611yescharacteristic
574C2—44no—
575C2—44no—
576C2D4×C22⋊Dic6111yescharacteristic
577C2C2×#1683975811yescharacteristic
578C2#2145435211yescharacteristic
579C2#2145753711yescharacteristic
580C2#2145754511yescharacteristic
581C2#2145773611yescharacteristic
582C2#2145774711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#547C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#547D61
hypocenterC61#22417
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×D4×#92418C2semidirect
2. C2×#16839758C2semidirect
3. #21448768C2semidirect
4. #21446743C2semidirect
5. #21446622C2semidirect
6. #21446243C2semidirect
7. #21446132C2semidirect
8. #21445819C2semidirect
9. #21445759C2semidirect
10. C4×#14519698C2semidirect
37. C61×#547C4semidirect
69. #14519698D4semidirect
275. C4×C61#416semidirect
306. #547Dic61semidirect
336. C61#22417semidirect
569. C4#16839758semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#924182
C2×#168397582
#214487682
#214467432
#214466222
#214462432
#214461322
#214458192
#214457592
C4×#145196982
C2×C61×#5472
#2241761