Finite Group Databasebeta

← #29606275

Subgroups — #29606275

Order 15616.

1246 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21444087C211yesmaximal, characteristic
2#21444076C212yesmaximal
3#21444053C212yesmaximal
4#21444051C211yesmaximal, characteristic
5#21444051C212yesmaximal
6#21444051C212yesmaximal
7#21444048C212yesmaximal
8#95×Dic61C212yesmaximal
9C2×C61×#398C211yesmaximal, characteristic
10C22×C4⋊Dic61C2212yes—
11C22×C4×Dic61C2211yescharacteristic
12C22×C4×Dic61C2212yes—
13C22×C4×Dic61C2212yes—
14C2×#14519684C2212yes—
15C2×#14519684C2212yes—
16C2×#14519684C2212yes—
17C2×#14519684C2212yes—
18C2×#14519684C2212yes—
19C2×#14519684C2212yes—
20C2×#14519684C2211yescharacteristic
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2211yescharacteristic
24C2×#14519684C2211yescharacteristic
25C2×#14519684C2212yes—
26C22×C4⋊C4×C61C2212yes—
27C22×C4⋊C4×C61C2211yescharacteristic
28C22×C4⋊C4×C61C2211yescharacteristic
29C61×#398C418yescomplemented
30C2×#95×C61C2212yes—
31C2×#95×C61C2211yescharacteristic
32C23×Dic61C2312yes—
33C23×Dic61C2312yes—
34C23×Dic61C2312yes—
35C23×Dic61C2312yes—
36C2×C4⋊Dic61—24no—
37C2×C4⋊Dic61—24no—
38C2×C4⋊Dic61—42no—
39C2×C4×Dic61—24no—
40C2×C4×Dic61—24no—
41C2×C4×Dic61—24no—
42C2×C4×Dic61—24no—
43C2×C4×Dic61—41no—
44C2×C4×Dic61—42no—
45C2×C4×Dic61—42no—
46C2×C4×Dic61—42no—
47#14519684—24no—
48#14519684—24no—
49#14519684—24no—
50#14519684—24no—
51#14519684—24no—
52#14519684—24no—
53#14519684—41no—
54#14519684—42no—
55#14519684—41no—
56#14519684—42no—
57#14519684—41no—
58#14519684Q818yes—
59C23×C4×C61C2311yescharacteristic
60C23×C4×C61C2312yes—
61C23×C4×C61C2311yescharacteristic
62C23×C4×C61C2311yescharacteristic
63C23×C4×C61C2312yes—
64C2×C4⋊C4×C61—42no—
65C2×C4⋊C4×C61—42no—
66C2×C4⋊C4×C61—41no—
67C2×C4⋊C4×C61—41no—
68C2×C4⋊C4×C61—41no—
69C2×C4⋊C4×C61—41no—
70C2×C4⋊C4×C61C2×C414yes—
71C2×C4⋊C4×C61C2×C414yes—
72C2×C4⋊C4×C61C2×C418yes—
73#95×C61C2×C418yes—
74#95×C61C2×C414yes—
75C24×C61C2411yescharacteristic
76C22×C4×C61—22no—
77C22×C4×C61—22no—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61—22no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—22no—
92C22×C4×C61—22no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—21no—
98C22×C4×C61C22×C412yes—
99C22×C4×C61C22×C412yes—
100C22×C4×C61C22×C414yes—
101C22×C4×C61C22×C412yes—
102C22×C4×C61C22×C414yes—
103C22×C4×C61C2×Q814yes—
104C22×C4×C61#4114yes—
105C22×Dic61—22no—
106C22×Dic61—22no—
107C22×Dic61—22no—
108C22×Dic61—22no—
109C22×Dic61—22no—
110C22×Dic61—22no—
111C22×Dic61—22no—
112C22×Dic61—22no—
113C22×Dic61—22no—
114C22×Dic61—22no—
115C22×Dic61—22no—
116C22×Dic61—22no—
117C22×Dic61—22no—
118C22×Dic61—22no—
119C22×Dic61—22no—
120C22×Dic61—22no—
121C22×Dic61—22no—
122C22×Dic61—22no—
123C22×Dic61—22no—
124C22×Dic61—22no—
125C22×Dic61—22no—
126C22×Dic61—22no—
127C22×Dic61—22no—
128C22×Dic61C2×Q814yes—
129C22×Dic61C2×Q814yes—
130C22×Dic61#4114yes—
131C22×Dic61#4114yes—
132C22×Dic61#4114yes—
133C4⋊C4×C61—48no—
134C4⋊C4×C61—44no—
135C4⋊C4×C61—44no—
136C4⋊Dic61—48no—
137C4×Dic61—44no—
138C4×Dic61—48no—
139C4×Dic61—48no—
140C23×C61C23×C411yescharacteristic
141C23×C61C22×Q812yes—
142C23×C61C2×#4112yes—
143C23×C61C2×#4112yes—
144C23×C61C2×#4112yes—
145C23×C61C2×#4112yes—
146C23×C61H(5,𝔽2)11yescharacteristic
147C23×C61H(5,𝔽2)12yes—
148C23×C61H(5,𝔽2)11yescharacteristic
149C2×C4×C61—24no—
150C2×C4×C61—24no—
151C2×C4×C61—24no—
152C2×C4×C61—24no—
153C2×C4×C61—24no—
154C2×C4×C61—24no—
155C2×C4×C61—22no—
156C2×C4×C61—24no—
157C2×C4×C61—24no—
158C2×C4×C61—24no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—24no—
162C2×C4×C61—22no—
163C2×C4×C61—24no—
164C2×C4×C61—22no—
165C2×C4×C61—42no—
166C2×C4×C61—42no—
167C2×C4×C61—42no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61C4×Q818yes—
178C2×Dic61—24no—
179C2×Dic61—24no—
180C2×Dic61—24no—
181C2×Dic61—24no—
182C2×Dic61—24no—
183C2×Dic61—24no—
184C2×Dic61—24no—
185C2×Dic61—24no—
186C2×Dic61—24no—
187C2×Dic61—24no—
188C2×Dic61—24no—
189C2×Dic61—24no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61#12518yes—
206#14246—611nomaximal, Sylow
207C22×C61C2×C4×Q812yes—
208C22×C61C4×#4111yescharacteristic
209C22×C61C4×#4112yes—
210C22×C61#51811yescharacteristic
211C22×C61#51811yescharacteristic
212C22×C61C2×#12512yes—
213C22×C61#52912yes—
214C22×C61#52912yes—
215C22×C61#53312yes—
216C22×C61#53812yes—
217C22×C61#54012yes—
218C22×C61#55112yes—
219C22×C61#55112yes—
220C22×C61#55111yescharacteristic
221C22×C61#55312yes—
222C22×C61#55412yes—
223C22×C61#55412yes—
224C22×C61#55412yes—
225C22×C61#55511yescharacteristic
226C22×C61Q8211yescharacteristic
227C22×C61#55911yescharacteristic
228C4×C61—28no—
229C4×C61—42no—
230C4×C61—44no—
231C4×C61—42no—
232C4×C61—42no—
233Dic61—28no—
234Dic61—44no—
235Dic61—44no—
236Dic61—82no—
237C2×#398D6111yescharacteristic
238#1445—611no—
239#1442—612no—
240#1436—612no—
241#1436—612no—
242#1436—612no—
243#1436—611no—
244C4⋊#95—612no—
245C4×#95—612no—
246C2×C61C4×#12512yes—
247C2×C61#233311yescharacteristic
248C2×C61#236812yes—
249C2×C61#236911yescharacteristic
250C2×C61#237411yescharacteristic
251C2×C61#250512yes—
252C2×C61#250712yes—
253C2×C61#253112yes—
254C2×C61#258912yes—
255C22×C4⋊C4—612no—
256C22×C4⋊C4C2×D6112yes—
257C22×C4⋊C4C2×D6111yescharacteristic
258C22×C4⋊C4C2×D6111yescharacteristic
259C22×C42—611no—
260C22×C42—612no—
261C22×C42—612no—
262#398Dic6118yescomplemented
263C2×#95—612no—
264C2×#95—612no—
265C2×#95—612no—
266C2×#95—612no—
267C2×#95—612no—
268C2×#95—612no—
269C2×#95—612no—
270C2×#95—611no—
271C2×#95—612no—
272C2×#95—612no—
273C2×#95—611no—
274C2×#95—611no—
275C2×#95C2×D6112yes—
276C2×#95C2×D6111yescharacteristic
277C61#1424611yescharacteristic, complemented, Sylow
278C23×C4—612no—
279C23×C4—612no—
280C23×C4—612no—
281C23×C4—612no—
282C23×C4C22×D6111yescharacteristic
283C23×C4C22×D6111yescharacteristic
284C23×C4C22×D6112yes—
285C23×C4C22×D6111yescharacteristic
286C23×C4C22×D6112yes—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—1224no—
294C2×C4⋊C4—1224no—
295C2×C4⋊C4—2442no—
296C2×C4⋊C4C2×Dic6114yes—
297C2×C4⋊C4C2×Dic6114yes—
298C2×C4⋊C4C2×Dic6118yes—
299C2×C42—1224no—
300C2×C42—1224no—
301C2×C42—1224no—
302C2×C42—1224no—
303C2×C42—2442no—
304C2×C42—2441no—
305C2×C42—2442no—
306C2×C42—2442no—
307#95—618no—
308#95—1224no—
309#95—1224no—
310#95—1224no—
311#95—1224no—
312#95—1224no—
313#95—1224no—
314#95—2441no—
315#95—2442no—
316#95—2441no—
317#95—2442no—
318#95—2441no—
319#95C2×Dic6118yes—
320#95C2×Dic6114yes—
321C24C23×D6111yescharacteristic
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—614no—
345C22×C4—614no—
346C22×C4—614no—
347C22×C4—614no—
348C22×C4—614no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1222no—
356C22×C4—1222no—
357C22×C4—1222no—
358C22×C4—1222no—
359C22×C4—1222no—
360C22×C4—1222no—
361C22×C4—1222no—
362C22×C4—1222no—
363C22×C4—1222no—
364C22×C4—1222no—
365C22×C4—1222no—
366C22×C4—1222no—
367C22×C4—1222no—
368C22×C4—1222no—
369C22×C4—1222no—
370C22×C4—1222no—
371C22×C4—1222no—
372C22×C4Q8×D6114yes—
373C22×C4#1175822614yes—
374C22×C4C22×Dic6112yes—
375C22×C4C22×Dic6112yes—
376C22×C4C22×Dic6114yes—
377C22×C4C22×Dic6112yes—
378C22×C4C22×Dic6114yes—
379C4⋊C4—48no—
380C4⋊C4—44no—
381C4⋊C4—44no—
382C4⋊C4—2448no—
383C42—2448no—
384C42—2444no—
385C42—2448no—
386C23C23×Dic6111yescharacteristic
387C23C2×Q8×D6112yes—
388C23#41×D6112yes—
389C23#41×D6112yes—
390C23#41×D6112yes—
391C23C2×#1175822612yes—
392C23#1451982211yescharacteristic
393C23#1451982212yes—
394C23#1451982211yescharacteristic
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—618no—
424C2×C4—1224no—
425C2×C4—1224no—
426C2×C4—1224no—
427C2×C4—1224no—
428C2×C4—1224no—
429C2×C4—1224no—
430C2×C4—1224no—
431C2×C4—1224no—
432C2×C4—1224no—
433C2×C4—1224no—
434C2×C4—1224no—
435C2×C4—1224no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2442no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4—2442no—
446C2×C4—2442no—
447C2×C4—2442no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4Q8×Dic6118yes—
452C22C2×Q8×Dic6112yes—
453C22#41×Dic6111yescharacteristic
454C22#41×Dic6112yes—
455C22#1684023711yescharacteristic
456C22#1684023711yescharacteristic
457C22#125×D6112yes—
458C22#1684029712yes—
459C22#1684029712yes—
460C22#1684031812yes—
461C22#1684034412yes—
462C22#1684036212yes—
463C22#1684043912yes—
464C22#1684043912yes—
465C22#1684044011yescharacteristic
466C22#1684045712yes—
467C22#1684046612yes—
468C22#1684046612yes—
469C22#1684047312yes—
470C22#1684047811yescharacteristic
471C22#1684049211yescharacteristic
472C22#1684049611yescharacteristic
473C4—28no—
474C4—42no—
475C4—44no—
476C4—42no—
477C4—42no—
478C4—1228no—
479C4—4882no—
480C4—2444no—
481C4—2444no—
482C2#125×Dic6112yes—
483C2#2144858611yescharacteristic
484C2#2144890412yes—
485C2#2144890911yescharacteristic
486C2#2144895511yescharacteristic
487C2#2145032112yes—
488C2#2145034112yes—
489C2#2145066112yes—
490C2#2145127312yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#398C2
socle, prime radical, cosocleC24×C61C24
hypercenterC2×#398D61
hypocenterC61#14246
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
29. C61×#398C4semidirect
262. #398Dic61semidirect
277. C61#14246semidirect

Maximal subgroups

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

subgroupindex
#214440872
#214440762
#214440532
#214440512
#214440482
#95×Dic612
C2×C61×#3982
#1424661