Finite Group Databasebeta

← #29575341

Subgroups — #29575341

Order 15616.

726 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C8×D61C211yesmaximal, characteristic
2C4×#14519753C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic
4C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
5#21443659C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C2×C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C22×C8×D61—21no—
9C2×#14519753C411yescharacteristic
10C2×C42×D61C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519689—21no—
13C2×C4×#92418C2211yescharacteristic
14C2×C8×Dic61—21no—
15C4×C8×D61—22no—
16C4×C8×D61—22no—
17#16839669C411yescharacteristic
18#16839658C411yescharacteristic
19#16839643—21no—
20#16839633—21no—
21#16839619C411yescharacteristic
22C4×#11758196—21no—
23C4×C4⋊Dic61C2211yescharacteristic
24C4×#11758198—21no—
25#16839516—21no—
26Q8⋊#92418—22no—
27C2×C4×Q8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4×C8×C61C2211yescharacteristic
30C61×Q8⋊C8—22no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×#92418—21no—
35C22×#92418—21no—
36C2×C8×D61—24no—
37C2×C8×D61—24no—
38C2×C8×D61—24no—
39#14519753—22no—
40#14519753C814yescomplemented
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C42×D61—21no—
52C42×D61—21no—
53C42×D61—21no—
54C42×D61—21no—
55C4⋊#92418—21no—
56C4⋊#92418—21no—
57#14519689—42no—
58C4×#92418—21no—
59C4×#92418D412yes—
60C8×Dic61—24no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66C22×Q8×C61C2×C411yescharacteristic
67C22×C8×C61—21no—
68C22×C8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61—21no—
71C4×Q8×C61—21no—
72C4×Q8×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61C2×C411yescharacteristic
75C2×C42×C61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4×C8×C61—21no—
80C4×C8×C61D412yes—
81C23×D61C22⋊C411yescharacteristic
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61C2×C812yescomplemented
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61C22×C411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C22×Dic61C22⋊C411yescharacteristic
98C2×C4×D61—22no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—21no—
109C2×C4×D61—22no—
110C2×C4×D61C2×C812yes—
111C2×C4×D61M1612yes—
112C2×C4×D61SD1612yes—
113C2×C4×D61Q1612yes—
114C2×C8×C61—22no—
115C2×C8×C61—22no—
116C2×C8×C61—22no—
117C2×C8×C61—41no—
118C2×C8×C61—41no—
119C2×C8×C61—41no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—41no—
123C4⋊C4×C61—41no—
124C42×C61—41no—
125C42×C61—41no—
126C42×C61C2×D411yescharacteristic
127C42×C61C2×D411yescharacteristic
128C42×C61#4111yescharacteristic
129C42×C61#4111yescharacteristic
130#11758198—24no—
131#11758198—42no—
132C4⋊Dic61—21no—
133C4⋊Dic61—21no—
134C4⋊Dic61—21no—
135C4⋊Dic61C2×C812yescomplemented
136#11758196—24no—
137#11758196—42no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61—21no—
142C4×Dic61—21no—
143C4×Dic61—21no—
144C4×Dic61—41no—
145C4×Dic61—41no—
146C2×#92418—22no—
147C2×#92418—22no—
148C2×#92418—22no—
149C2×#92418—41no—
150C2×#92418—41no—
151C2×#92418—41no—
152C8×D61—216no—
153C23×C61C2×C22⋊C411yescharacteristic
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61C22⋊C812yes—
159C22×D61#10312yes—
160C22×D61#10412yes—
161Q8×C61—22no—
162Q8×C61—22no—
163Q8×C61—41no—
164Q8×C61—41no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—22no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61C4×D411yescharacteristic
174C2×C4×C61C4×D411yescharacteristic
175C2×C4×C61#12011yescharacteristic
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12311yescharacteristic
179C2×C4×C61C22×C811yescharacteristic
180C2×C4×C61C2×M1611yescharacteristic
181C2×C4×C61#13111yescharacteristic
182C2×C4×C61#13111yescharacteristic
183C2×C4×C61C2×SD1611yescharacteristic
184C2×C4×C61C2×Q1611yescharacteristic
185C2×C4×C61#13511yescharacteristic
186C2×C4×C61#13511yescharacteristic
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—21no—
193C2×Dic61—22no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61C22⋊C812yes—
200C2×Dic61#10312yes—
201C2×Dic61#10412yes—
202C4×D61—24no—
203C4×D61—24no—
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—22no—
210C4×D61—22no—
211C4×D61—22no—
212C8×C61—24no—
213C8×C61—81no—
214#92418—24no—
215#92418—81no—
216#9071—611nomaximal, Sylow
217C22×C61#38611yescharacteristic
218C22×C61C2×C22⋊C811yescharacteristic
219C22×C61#40811yescharacteristic
220C22×C61C2×#10311yescharacteristic
221C22×C61#41611yescharacteristic
222C22×C61C2×#10411yescharacteristic
223C22×C61C2×#10411yescharacteristic
224C2×D61—22no—
225C2×D61—22no—
226C2×D61—22no—
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—22no—
230C2×D61Q8⋊C814yescomplemented
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—42no—
234C4×C61—81no—
235C4×C61C8×D411yescharacteristic
236C4×C61C8×D411yescharacteristic
237C4×C61#43511yescharacteristic
238C4×C61#43511yescharacteristic
239C4×C61#46511yescharacteristic
240C4×C61#46511yescharacteristic
241C4×C61#46711yescharacteristic
242C4×C61#46711yescharacteristic
243Dic61—22no—
244Dic61—22no—
245Dic61—22no—
246Dic61—42no—
247Dic61—81no—
248C22×C4×C8—611no—
249C4×C22⋊Q8—611no—
250#1797—611no—
251C2×Q8⋊C8—611no—
252C2×Q8⋊C8D6111yescharacteristic, complemented
253#1279—611no—
254#1279—611no—
255C2×C61C2×Q8⋊C811yescharacteristic
256C2×C61#147611yescharacteristic
257C2×C61#149311yescharacteristic
258C2×C61#149411yescharacteristic
259C2×C61#186911yescharacteristic
260C2×C61#189211yescharacteristic
261C2×C61#189611yescharacteristic
262D61—24no—
263C23×C8—1221no—
264C2×C22⋊Q8—611no—
265C2×C4×Q8C2×D6111yescharacteristic
266C22×C42—611no—
267C2×C4⋊C8—611no—
268C2×C4⋊C8C2×D6111yescharacteristic
269C2×C22⋊C8—1221no—
270C2×C4×C8—611no—
271C2×C4×C8—1222no—
272C2×C4×C8—1221no—
273C2×C4×C8—1222no—
274C2×C4×C8C2×D6111yescharacteristic
275#391—611no—
276#389—611no—
277#387—1221no—
278#385—1221no—
279#380—611no—
280C4×C4⋊C4—611no—
281C4×C4⋊C4—1221no—
282C4×C22⋊C4—1221no—
283#336—1221no—
284Q8⋊C8—22no—
285Q8⋊C8—1222no—
286C61#907111yescharacteristic, complemented, Sylow
287C22×Q8C4×D6111yescharacteristic
288C23×C4—611no—
289C23×C4—611no—
290C23×C4—611no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—1224no—
294C22×C8—1224no—
295C22×C8—1224no—
296C22×C8—1221no—
297C22×C8—1221no—
298C22⋊Q8—614no—
299C22⋊Q8—1222no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—611no—
306C2×C4⋊C4—611no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4C4×D6111yescharacteristic
310C2×C22⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C42—21no—
313C2×C42—611no—
314C2×C42—611no—
315C2×C42—611no—
316C2×C42—1221no—
317C2×C42—1221no—
318C2×C42—1221no—
319C2×C42—1221no—
320C2×C42—1221no—
321C2×C42C22×D6111yescharacteristic
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8—1221no—
325C4⋊C8—1221no—
326C22⋊C8—2442no—
327C4×C8—21no—
328C4×C8—612no—
329C4×C8—1224no—
330C4×C8—1221no—
331C4×C8C22⋊D6112yes—
332#95—1221no—
333#95—1221no—
334#95—1221no—
335#95—1221no—
336#95—1221no—
337C24—611no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8C8×D6112yescomplemented
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—612no—
350C22×C4—612no—
351C22×C4—612no—
352C22×C4—612no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4—1221no—
360C22×C4—1221no—
361C22×C4—1221no—
362C22×C4—1221no—
363C22×C4—1221no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4—1221no—
367C22×C4C2×C4×D6111yescharacteristic
368C22×C4D4×D6111yescharacteristic
369C22×C4D4×D6111yescharacteristic
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—41no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—12216no—
377C2×C8—1222no—
378C2×C8—1222no—
379C2×C8—1222no—
380C2×C8—2441no—
381C2×C8—2441no—
382C2×C8—2441no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—612no—
388C4⋊C4—1224no—
389C4⋊C4—1221no—
390C4⋊C4—1221no—
391C4⋊C4—1221no—
392C4⋊C4—2442no—
393C22⋊C4—1224no—
394C22⋊C4—2442no—
395C42—41no—
396C42—41no—
397C42—1221no—
398C42—1221no—
399C42—1221no—
400C42—1221no—
401C42—1221no—
402C42—1221no—
403C42—2441no—
404C42—2441no—
405C42#1175822211yescharacteristic
406C42D4×D6111yescharacteristic
407C42#1175822411yescharacteristic
408C42C2×C22⋊D6111yescharacteristic
409C23—612no—
410C23—612no—
411C23—612no—
412C23—1221no—
413C23—1221no—
414C23—1221no—
415C23—1221no—
416C23C22⋊C4×D6111yescharacteristic
417Q8—22no—
418Q8—22no—
419Q8—41no—
420Q8—41no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—612no—
430C2×C4—612no—
431C2×C4—612no—
432C2×C4—1224no—
433C2×C4—1224no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1222no—
441C2×C4—1222no—
442C2×C4—1222no—
443C2×C4—1222no—
444C2×C4—1222no—
445C2×C4—1222no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4#1451973711yescharacteristic
455C2×C4C4×C22⋊D6111yescharacteristic
456C2×C4#1451974511yescharacteristic
457C2×C4#1451974811yescharacteristic
458C2×C4#1451975011yescharacteristic
459C2×C4#1451975911yescharacteristic
460C2×C4C2×C8×D6111yescharacteristic
461C2×C4M16×D6111yescharacteristic
462C2×C4#1451978311yescharacteristic
463C2×C4#1451978511yescharacteristic
464C2×C4SD16×D6111yescharacteristic
465C2×C4Q16×D6111yescharacteristic
466C2×C4#1451979811yescharacteristic
467C2×C4#1451980011yescharacteristic
468C8—24no—
469C8—81no—
470C8—1224no—
471C8—4881no—
472C22—614no—
473C22—1222no—
474C22—1222no—
475C22—1222no—
476C22—1222no—
477C22—1222no—
478C22—1222no—
479C22#1683963811yescharacteristic
480C22C22⋊C8×D6111yescharacteristic
481C22#1683972711yescharacteristic
482C22#103×D6111yescharacteristic
483C22#1683975711yescharacteristic
484C22#104×D6111yescharacteristic
485C22#104×D6111yescharacteristic
486C4—21no—
487C4—21no—
488C4—42no—
489C4—81no—
490C4—1222no—
491C4—1222no—
492C4—1222no—
493C4—4881no—
494C4—2442no—
495C4#1683982511yescharacteristic
496C4C8×C22⋊D6111yescharacteristic
497C4#1683983111yescharacteristic
498C4#1683983611yescharacteristic
499C4#1683998811yescharacteristic
500C4#1683999411yescharacteristic
501C4#1684000011yescharacteristic
502C4#1684000211yescharacteristic
503C2—1224no—
504C2Q8⋊C8×D6111yescharacteristic
505C2#2144420011yescharacteristic
506C2#2144427211yescharacteristic
507C2#2144427811yescharacteristic
508C2#2144610811yescharacteristic
509C2#2144623911yescharacteristic
510C2#2144625911yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenterC2×Q8⋊C8D61
hypocenterC61#9071
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×Q8⋊#92418C2semidirect
5. #21443659C2semidirect
6. #21443658C2semidirect
7. C2×C61×Q8⋊C8C2semidirect
40. #14519753C8semidirect
87. C2×Q8×C61C2×C8semidirect
135. C4⋊Dic61C2×C8semidirect
230. C2×D61Q8⋊C8semidirect
252. C2×Q8⋊C8D61semidirect
286. C61#9071semidirect
343. C2×Q8C8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C8×D612
C4×#145197532
#214457962
C2×Q8⋊#924182
#214436592
#214436582
C2×C61×Q8⋊C82
#907161