Finite Group Databasebeta

← #30599209

Subgroups — #30599209

Order 15616.

1158 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461642C212yesmaximal
2#21460657C212yesmaximal, complemented
3#21460657C212yesmaximal, complemented
4C2×#95×D61C211yesmaximal, characteristic
5C2×#14519834—22no—
6C2×#14519834—22no—
7C2×C22⋊#92420C2214yes—
8C23×C4×D61C411yescharacteristic
9C23×C4×D61C411yescharacteristic
10C23×C4×D61C2211yescharacteristic
11C2×#14519684C411yescharacteristic
12C2×#14519684C2211yescharacteristic
13C2×#14519684C2211yescharacteristic
14#95×D61—22no—
15#95×D61—22no—
16C2×#95×C61C411yescharacteristic
17C22×#92420—24no—
18#14519834—44no—
19#14519834—44no—
20C22⋊#92420—24no—
21C22⋊#92420—24no—
22C24×D61C2×C411yescharacteristic
23C23×Dic61C2×C411yescharacteristic
24C23×Dic61C2×C411yescharacteristic
25C23×Dic61C2311yescharacteristic
26C22×C4×D61—21no—
27C22×C4×D61—21no—
28C22×C4×D61—21no—
29C22×C4×D61—21no—
30C22×C4×D61—22no—
31C22×C4×D61—22no—
32C22×C4×D61—22no—
33C22×C4×D61—22no—
34C22×C4×D61—22no—
35C22×C4×D61—42no—
36C22×C4×D61—42no—
37C22×C4×D61—42no—
38C22×C4×D61—42no—
39C22×C4×D61—42no—
40C22×C4×D61—42no—
41C22×C4×D61C814yescomplemented
42C22×C4×D61D412yes—
43C22×C4×D61D412yes—
44#14519684—22no—
45#14519684—22no—
46#14519684—22no—
47C23×C4×C61C2×C411yescharacteristic
48C23×C4×C61C2×C411yescharacteristic
49C23×C4×C61C2×C411yescharacteristic
50#95×C61—22no—
51C24×C61C22×C411yescharacteristic
52C23×D61—21no—
53C23×D61—21no—
54C23×D61—21no—
55C23×D61—21no—
56C23×D61—22no—
57C23×D61—22no—
58C23×D61—22no—
59C23×D61—22no—
60C23×D61C22⋊C411yescharacteristic
61C23×D61C22⋊C411yescharacteristic
62C23×D61C2×C812yes—
63C23×D61M1612yes—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C22×C4×C61C22⋊C412yes—
77C22×C4×C61C2×C812yes—
78C22×C4×C61M1612yes—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61—41no—
89C22×Dic61C2×C812yes—
90C22×Dic61M1612yes—
91C22×Dic61C2×D412yes—
92C22×Dic61#4112yes—
93C22×Dic61#4112yes—
94C2×C4×D61—24no—
95C2×C4×D61—24no—
96C2×C4×D61—24no—
97C2×C4×D61—24no—
98C2×C4×D61—24no—
99C2×C4×D61—24no—
100C2×C4×D61—24no—
101C2×C4×D61—24no—
102C2×C4×D61—42no—
103C2×C4×D61—42no—
104C2×C4×D61—48no—
105C2×C4×D61—48no—
106C2×C4×D61—48no—
107C2×C4×D61—42no—
108C2×C4×D61—42no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—48no—
112C2×C4×D61—48no—
113C2×C4×D61—42no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×C4×D61—42no—
117C2×C4×D61—48no—
118C2×#92420—44no—
119C2×#92420—44no—
120C2×#92420—44no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61C2×C22⋊C411yescharacteristic
126C23×C61#11711yescharacteristic
127C23×C61#11711yescharacteristic
128C23×C61C22×C811yescharacteristic
129C23×C61C2×M1611yescharacteristic
130C23×C61C2×M1611yescharacteristic
131C23×C61C2×M1611yescharacteristic
132C22×D61—24no—
133C22×D61—24no—
134C22×D61—24no—
135C22×D61—24no—
136C22×D61—24no—
137C22×D61—24no—
138C22×D61—24no—
139C22×D61—24no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—24no—
153C22×D61—24no—
154C22×D61—24no—
155C22×D61—24no—
156C22×D61C22⋊C812yes—
157C22×D61C22⋊C812yes—
158C22×D61#9912yes—
159C22×D61#9912yes—
160C22×D61#10012yes—
161C22×D61#10112yes—
162C2×C4×C61—22no—
163C2×C4×C61—22no—
164C2×C4×C61—22no—
165C2×C4×C61—22no—
166C2×C4×C61—22no—
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—41no—
174C2×C4×C61—41no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×Dic61—22no—
178C2×Dic61—22no—
179C2×Dic61—22no—
180C2×Dic61—22no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—42no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61#12314yes—
192C4×D61—48no—
193C4×D61—48no—
194C4×D61—48no—
195C4×D61—48no—
196C4×D61—48no—
197C4×D61—48no—
198#92420—84no—
199#8698—611nomaximal, Sylow
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
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#38111yescharacteristic
213C22×C61C2×C22⋊C811yescharacteristic
214C22×C61#40711yescharacteristic
215C22×C61C2×#9911yescharacteristic
216C22×C61C2×#9911yescharacteristic
217C22×C61C2×#10011yescharacteristic
218C22×C61C2×#10111yescharacteristic
219C22×C61#43111yescharacteristic
220C22×C61#43111yescharacteristic
221C22×C61#43211yescharacteristic
222C22×C61#43211yescharacteristic
223C2×D61—28no—
224C2×D61—28no—
225C2×D61—28no—
226C2×D61—28no—
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—22no—
230C2×D61—22no—
231C2×D61—22no—
232C2×D61—22no—
233C2×D61—22no—
234C2×D61—22no—
235C2×D61—22no—
236C2×D61—22no—
237C2×D61—22no—
238C2×D61—22no—
239C2×D61#32314yes—
240C2×D61#32414yes—
241C4×C61—42no—
242C4×C61—42no—
243C4×C61—42no—
244Dic61—24no—
245Dic61—42no—
246Dic61—42no—
247C22×#95—611no—
248#1779—612no—
249#1280—612no—
250#1280—612no—
251C2×C61—21no—
252C2×C61—21no—
253C2×C61—21no—
254C2×C61—21no—
255C2×C61C2×#32311yescharacteristic
256C2×C61C2×#32411yescharacteristic
257C2×C61#146211yescharacteristic
258C2×C61#146311yescharacteristic
259C2×C61#181711yescharacteristic
260C2×C61#181911yescharacteristic
261C2×C61#182111yescharacteristic
262D61—24no—
263D61—24no—
264C24×C4—611no—
265C24×C4—611no—
266C24×C4—611no—
267C2×C22⋊C8—614no—
268C2×C22⋊C8—1222no—
269C2×C22⋊C8—1222no—
270C2×#95—611no—
271C2×#95—611no—
272C2×#95—611no—
273C2×#95—1222no—
274C2×#95—1222no—
275C2×#95#692311yescharacteristic
276C61#869811yescharacteristic, complemented, Sylow
277C25—611no—
278C23×C4—611no—
279C23×C4—611no—
280C23×C4—611no—
281C23×C4—612no—
282C23×C4—612no—
283C23×C4—614no—
284C23×C4—1222no—
285C23×C4—1222no—
286C23×C4—1222no—
287C23×C4—1222no—
288C23×C4—1221no—
289C23×C4—1221no—
290C23×C4—1221no—
291C23×C4—1221no—
292C23×C4—1222no—
293C23×C4—2442no—
294C23×C4—2442no—
295C23×C4—2442no—
296C23×C4—2442no—
297C23×C4—2442no—
298C23×C4—2442no—
299C23×C4C2×#692311yescharacteristic
300C23×C4C2×#692311yescharacteristic
301C23×C4C2×#692311yescharacteristic
302C22×C8—1224no—
303C22⋊C8—1224no—
304C22⋊C8—1224no—
305C22⋊C8—2444no—
306C22⋊C8—2444no—
307#95—22no—
308#95—1222no—
309#95—1222no—
310#95—1222no—
311C24—611no—
312C24—611no—
313C24—612no—
314C24—612no—
315C24—1222no—
316C24—1222no—
317C24—1222no—
318C24—1222no—
319C24—1221no—
320C24—1221no—
321C24—1221no—
322C24—1221no—
323C24C22×#692311yescharacteristic
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—612no—
337C22×C4—612no—
338C22×C4—612no—
339C22×C4—612no—
340C22×C4—612no—
341C22×C4—1224no—
342C22×C4—1224no—
343C22×C4—1224no—
344C22×C4—1224no—
345C22×C4—1224no—
346C22×C4—1224no—
347C22×C4—1224no—
348C22×C4—1224no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—2442no—
354C22×C4—2442no—
355C22×C4—2442no—
356C22×C4—2442no—
357C22×C4—2442no—
358C22×C4—2442no—
359C22×C4—2448no—
360C22×C4—2448no—
361C22×C4—2448no—
362C22×C4—2448no—
363C22×C4—2442no—
364C22×C4—2442no—
365C22×C4—2442no—
366C22×C4—2442no—
367C22×C4—2448no—
368C22×C4—2448no—
369C22×C4—2441no—
370C22×C4—2441no—
371C22×C4—2441no—
372C22×C4—2441no—
373C22×C4—2441no—
374C22×C4—2441no—
375C22×C4D61⋊C812yes—
376C22×C4#1175821312yes—
377C22×C4C22⋊#692312yes—
378C2×C8—2444no—
379C2×C8—2444no—
380C2×C8—2444no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—612no—
386C23—612no—
387C23—612no—
388C23—612no—
389C23—612no—
390C23—612no—
391C23—1224no—
392C23—1224no—
393C23—1224no—
394C23—1224no—
395C23—1224no—
396C23—1224no—
397C23—1224no—
398C23—1224no—
399C23—1224no—
400C23—1224no—
401C23—1224no—
402C23—1224no—
403C23—1221no—
404C23—1221no—
405C23—1221no—
406C23—1221no—
407C23—1221no—
408C23—1221no—
409C23—1221no—
410C23—1221no—
411C23—1222no—
412C23—1222no—
413C23—1222no—
414C23—1222no—
415C23C2×C22⋊#692311yescharacteristic
416C23#1451985611yescharacteristic
417C23#1451985611yescharacteristic
418C23C2×D61⋊C811yescharacteristic
419C23D61⋊M1611yescharacteristic
420C23D61⋊M1611yescharacteristic
421C23C2×#1175821311yescharacteristic
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—614no—
438C2×C4—1222no—
439C2×C4—1222no—
440C2×C4—1222no—
441C2×C4—1222no—
442C2×C4—2448no—
443C2×C4—2448no—
444C2×C4—2448no—
445C2×C4—2448no—
446C2×C4—2448no—
447C2×C4—2448no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4—2442no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2442no—
457C2×C4—2442no—
458C8—4884no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—614no—
472C22—614no—
473C22—1228no—
474C22—1228no—
475C22—1228no—
476C22—1228no—
477C22—1222no—
478C22—1222no—
479C22—1222no—
480C22—1222no—
481C22—1222no—
482C22—1222no—
483C22—1222no—
484C22—1222no—
485C22—1222no—
486C22—1222no—
487C22—1222no—
488C22—1222no—
489C22#1684070511yescharacteristic
490C22D61⋊(C22⋊C8)11yescharacteristic
491C22#1684073311yescharacteristic
492C22D61⋊#9911yescharacteristic
493C22D61⋊#9911yescharacteristic
494C22D61⋊#10011yescharacteristic
495C22D61⋊#10111yescharacteristic
496C22#1684078011yescharacteristic
497C22#1684078111yescharacteristic
498C22#1684078411yescharacteristic
499C22#1684078511yescharacteristic
500C4—42no—
501C4—42no—
502C4—42no—
503C4—1224no—
504C4—2442no—
505C4—2442no—
506C2—21no—
507C2—21no—
508C2—21no—
509C2—21no—
510C2—1224no—
511C2—1224no—
512C2D61⋊#32311yescharacteristic
513C2D61⋊#32411yescharacteristic
514C2#2146106511yescharacteristic
515C2#2146106811yescharacteristic
516C2#2146171111yescharacteristic
517C2#2146171511yescharacteristic
518C2#2146171911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC2×#95×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC2×#95#6923
hypocenterC61#8698
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. #21460657C2semidirect
3. #21460657C2semidirect
41. C22×C4×D61C8semidirect
276. C61#8698semidirect

Maximal subgroups

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

subgroupindex
#214616422
#214606572
C2×#95×D612
#869861