Finite Group Databasebeta

← #29574009

Subgroups — #29574009

Order 15616.

612 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448436C211yesmaximal, characteristic
2#21446012C211yesmaximal, characteristic
3C2×#16839487C211yesmaximal, characteristic
4#21444069C211yesmaximal, characteristic
5#21443699C211yesmaximal, characteristic
6#21443697C211yesmaximal, characteristic
7C61×#1853C211yesmaximal, characteristic
8C2×#14519733—21no—
9C22×#11758196C2211yescharacteristic
10C2×#14519708—21no—
11C2×C22⋊#92418C2211yescharacteristic
12#16839659—21no—
13#16839659—21no—
14#16839657—21no—
15#16839657—21no—
16#16839622C2211yescharacteristic
17#16839620—21no—
18C2×#14519684—21no—
19C2×#14519684—21no—
20C2×#14519684C2211yescharacteristic
21#16839524—21no—
22#16839487C414yescomplemented
23C22×C4⋊C4×C61C2211yescharacteristic
24C2×#106×C61—21no—
25C2×C22⋊C8×C61C2211yescharacteristic
26C61×#380C2211yescharacteristic
27C61×#340—21no—
28C23×Dic61—21no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31C22×#92418—21no—
32#14519733—42no—
33#14519733—42no—
34C2×C4⋊Dic61D411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196C2×C412yes—
45C2×#11758196Q812yes—
46C2×C22⋊Dic61—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49#14519708—42no—
50C22⋊#92418—21no—
51C22⋊#92418C2×C412yes—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—42no—
58#14519684—42no—
59C23×C4×C61—21no—
60C23×C4×C61C2311yescharacteristic
61C22×C8×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—42no—
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C22⋊C4×C61—21no—
68#106×C61—42no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61C2×C412yes—
71#95×C61—21no—
72C24×C61C2×D411yescharacteristic
73C22×C4×C61—22no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61C22×C411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×Q811yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—22no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—41no—
100C22×Dic61—41no—
101C22×Dic61—41no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61—41no—
105C22×Dic61—41no—
106C22×Dic61—41no—
107C22×Dic61C4⋊C412yes—
108C22×Dic61C4⋊C412yes—
109C22×Dic61SD1612yes—
110C22×Dic61SD1612yes—
111C2×C8×C61—22no—
112C2×C8×C61—41no—
113C2×C8×C61—41no—
114C4⋊C4×C61—22no—
115C4⋊C4×C61—22no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊Dic61—41no—
123C22⋊Dic61—41no—
124C4⋊Dic61—41no—
125C4⋊Dic61—41no—
126#11758196—22no—
127#11758196—22no—
128#11758196—22no—
129#11758196—22no—
130#11758196—42no—
131#11758196—42no—
132#11758196—81no—
133#11758196—81no—
134C4×Dic61—42no—
135C4×Dic61—42no—
136C2×#92418—22no—
137C2×#92418—41no—
138C2×#92418—41no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—21no—
142C23×C61—21no—
143C23×C61C2×C4⋊C411yescharacteristic
144C23×C61#12011yescharacteristic
145C23×C61#12311yescharacteristic
146C23×C61C2×SD1611yescharacteristic
147C23×C61C2×SD1611yescharacteristic
148C23×C61AGL(1,ℤ/8)11yescharacteristic
149C23×C61#13711yescharacteristic
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—42no—
166C2×C4×C61—41no—
167C2×C4×C61—81no—
168C2×C4×C61—81no—
169C2×C4×C61—81no—
170C2×C4×C61—81no—
171C2×C4×C61C4×D411yescharacteristic
172C2×C4×C61C4×D411yescharacteristic
173C2×C4×C61C22⋊Q811yescharacteristic
174C2×C4×C61C22⋊Q811yescharacteristic
175C2×Dic61—22no—
176C2×Dic61—22no—
177C2×Dic61—22no—
178C2×Dic61—22no—
179C2×Dic61—22no—
180C2×Dic61—22no—
181C2×Dic61—22no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61—42no—
187C2×Dic61—42no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—81no—
195C2×Dic61—81no—
196C2×Dic61—81no—
197C2×Dic61—81no—
198C2×Dic61—81no—
199C2×Dic61#10614yescomplemented
200C8×C61—42no—
201#92418—42no—
202#8857—611nomaximal, Sylow
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61#38511yescharacteristic
216C22×C61C2×#10611yescharacteristic
217C22×C61#42811yescharacteristic
218C22×C61#44811yescharacteristic
219C22×C61#45011yescharacteristic
220C22×C61#45411yescharacteristic
221C22×C61#45611yescharacteristic
222C22×C61B(4,𝔽2)11yescharacteristic
223C22×C61#45811yescharacteristic
224C22×C61#48111yescharacteristic
225C22×C61#48311yescharacteristic
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—82no—
231C4×C61—81no—
232C4×C61—81no—
233Dic61—24no—
234Dic61—42no—
235Dic61—82no—
236Dic61—81no—
237Dic61—81no—
238#2316—611no—
239#1853—611no—
240#1853D6111yescharacteristic
241C2×#324—611no—
242#1441—611no—
243#1294—611no—
244#1294—611no—
245C2×C61—21no—
246C2×C61—21no—
247C2×C61—21no—
248C2×C61—21no—
249C2×C61#159911yescharacteristic
250C2×C61#160411yescharacteristic
251C2×C61#161111yescharacteristic
252C2×C61#161611yescharacteristic
253C2×C61#185311yescharacteristic
254C2×C61#185711yescharacteristic
255C2×C61#186711yescharacteristic
256C2×#117—1221no—
257C22×C4⋊C4—611no—
258C22×C4⋊C4C2×D6111yescharacteristic
259C2×#106—21no—
260C2×#106—1221no—
261C2×C22⋊C8—611no—
262C2×C22⋊C8C2×D6111yescharacteristic
263#389—1221no—
264#389—1221no—
265#389—1221no—
266#389—1221no—
267#380—611no—
268#380—1221no—
269#380C2×D6111yescharacteristic
270C2×#95—611no—
271C2×#95—1221no—
272C2×#95—1221no—
273#340—21no—
274#340—1221no—
275#324—614no—
276C61#885711yescharacteristic, complemented, Sylow
277C23×C4—21no—
278C23×C4—611no—
279C23×C4—611no—
280C23×C4—1221no—
281C23×C4C22×D6111yescharacteristic
282C22×C8—21no—
283C22×C8—1221no—
284#117—2442no—
285#117—2442no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—612no—
290C2×C4⋊C4—612no—
291C2×C4⋊C4—611no—
292C2×C4⋊C4—611no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4—1221no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4—1221no—
299C2×C4⋊C4—1221no—
300C2×C4⋊C4—1221no—
301C2×C4⋊C4C22⋊D6111yescharacteristic
302C2×C4⋊C4C22⋊D6111yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—1221no—
305C2×C42—1221no—
306C2×C42—1221no—
307#106—42no—
308#106—2442no—
309C22⋊C8—21no—
310C22⋊C8—612no—
311C22⋊C8—1221no—
312C22⋊C8C4×D6112yes—
313#95—21no—
314#95—1221no—
315#95—1221no—
316#95—1221no—
317#95—1221no—
318#95—1221no—
319#95—2442no—
320#95—2442no—
321C24D4×D6111yescharacteristic
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—612no—
334C22×C4—612no—
335C22×C4—612no—
336C22×C4—612no—
337C22×C4—1221no—
338C22×C4—1221no—
339C22×C4—1221no—
340C22×C4—1221no—
341C22×C4—1221no—
342C22×C4—1221no—
343C22×C4—1222no—
344C22×C4—1221no—
345C22×C4—1221no—
346C22×C4—2441no—
347C22×C4—2441no—
348C22×C4—2441no—
349C22×C4—2441no—
350C22×C4—2441no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4—2441no—
354C22×C4C2×C4×D6111yescharacteristic
355C22×C4#1175822211yescharacteristic
356C22×C4D4×D6111yescharacteristic
357C22×C4Q8×D6111yescharacteristic
358C22×C4#1175822611yescharacteristic
359C22×C4C2×C22⋊D6111yescharacteristic
360C2×C8—22no—
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—1222no—
364C2×C8—2441no—
365C2×C8—2441no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—1222no—
373C4⋊C4—1222no—
374C4⋊C4—1222no—
375C4⋊C4—1222no—
376C4⋊C4—4881no—
377C4⋊C4—4881no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4—2442no—
381C4⋊C4—2442no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C42—2442no—
387C42—2442no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23C4⋊C4×D6111yescharacteristic
393C23#1451974511yescharacteristic
394C23#1451976211yescharacteristic
395C23SD16×D6111yescharacteristic
396C23SD16×D6111yescharacteristic
397C23#1451980411yescharacteristic
398C23#1451980611yescharacteristic
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—614no—
421C2×C4—1222no—
422C2×C4—1222no—
423C2×C4—1222no—
424C2×C4—1222no—
425C2×C4—1222no—
426C2×C4—1222no—
427C2×C4—1222no—
428C2×C4—4881no—
429C2×C4—4881no—
430C2×C4—4881no—
431C2×C4—4881no—
432C2×C4—4881no—
433C2×C4—2442no—
434C2×C4—2442no—
435C2×C4—2442no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2442no—
445C2×C4C4×C22⋊D6111yescharacteristic
446C2×C4#1451973911yescharacteristic
447C2×C4#1451975311yescharacteristic
448C2×C4#1451975511yescharacteristic
449C8—42no—
450C8—2442no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22#1683963311yescharacteristic
464C22#106×D6111yescharacteristic
465C22#1683980111yescharacteristic
466C22#1683989911yescharacteristic
467C22#1683991111yescharacteristic
468C22#1683993311yescharacteristic
469C22#1683994311yescharacteristic
470C22#1683994811yescharacteristic
471C22#1683995111yescharacteristic
472C22#1684008211yescharacteristic
473C22#1684009411yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—82no—
479C4—81no—
480C4—81no—
481C4—1224no—
482C4—4882no—
483C4—4881no—
484C4—4881no—
485C4—2442no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2#2144475711yescharacteristic
491C2#2144478611yescharacteristic
492C2#2144482511yescharacteristic
493C2#2144485411yescharacteristic
494C2#2144601011yescharacteristic
495C2#2144603211yescharacteristic
496C2#2144609811yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1853C2
socleC23×C61#120
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1853D61
hypocenterC61#8857
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
22. #16839487C4semidirect
199. C2×Dic61#106semidirect
276. C61#8857semidirect

Maximal subgroups

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

subgroupindex
#214484362
#214460122
C2×#168394872
#214440692
#214436992
#214436972
C61×#18532
#885761