Finite Group Databasebeta

← #30598818

Subgroups — #30598818

Order 15616.

898 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461675C212yesmaximal, complemented
2C2×#16840606C212yesmaximal
3#21460657C212yesmaximal, complemented
4C2×#16839609C211yesmaximal, characteristic
5C2×#14519844—22no—
6C2×C22⋊#92420C2214yes—
7#16840628—22no—
8#16840606—24no—
9C23×C4×D61C411yescharacteristic
10C22×#11758198C411yescharacteristic
11C22×#11758198C2211yescharacteristic
12C22×C4×Dic61C411yescharacteristic
13C22×C4×Dic61C2211yescharacteristic
14#16839609—22no—
15#16839609—22no—
16C2×#14519684C2211yescharacteristic
17C2×#95×C61C411yescharacteristic
18C22×#92420—24no—
19#14519844—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—22no—
29C22×C4×D61—42no—
30C22×C4×D61—42no—
31C22×C4×D61C814yescomplemented
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×#11758198—22no—
35C2×#11758198—22no—
36C2×#11758198—22no—
37C2×#11758198D412yes—
38C2×#11758198Q812yes—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—42no—
42C2×C4×Dic61—42no—
43C2×C4×Dic61D412yes—
44C2×C4×Dic61D412yes—
45#14519684—22no—
46C23×C4×C61C2×C411yescharacteristic
47C23×C4×C61C2×C411yescharacteristic
48C23×C4×C61C2×C411yescharacteristic
49#95×C61—22no—
50C24×C61C22×C411yescharacteristic
51C23×D61—21no—
52C23×D61—21no—
53C23×D61—21no—
54C23×D61—21no—
55C23×D61—41no—
56C23×D61—41no—
57C23×D61—41no—
58C23×D61—41no—
59C23×D61C4⋊C412yes—
60C23×D61C2×C812yes—
61C23×D61M1612yes—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C22⋊C412yes—
75C22×C4×C61C4⋊C412yes—
76C22×C4×C61C2×C812yes—
77C22×Dic61—22no—
78C22×Dic61—22no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C2×C812yes—
88C22×Dic61M1612yes—
89C22×Dic61M1612yes—
90C22×Dic61C2×D412yes—
91C22×Dic61C2×D411yescharacteristic
92C22×Dic61C2×Q811yescharacteristic
93C22×Dic61#4112yes—
94C2×C4×D61—24no—
95C2×C4×D61—24no—
96C2×C4×D61—42no—
97C2×C4×D61—42no—
98C2×C4×D61—48no—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101C2×C4×D61—48no—
102C2×#92420—44no—
103C2×#92420—44no—
104C2×#92420—44no—
105#11758198—28no—
106#11758198—24no—
107#11758198—24no—
108C4×Dic61—24no—
109C4×Dic61—42no—
110C4×Dic61—42no—
111C4×Dic61—42no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61C2×C22⋊C411yescharacteristic
117C23×C61C2×C4⋊C411yescharacteristic
118C23×C61#11711yescharacteristic
119C23×C61C22×C811yescharacteristic
120C23×C61C2×M1611yescharacteristic
121C23×C61C2×M1611yescharacteristic
122C23×C61C2×M1611yescharacteristic
123C22×D61—22no—
124C22×D61—22no—
125C22×D61—22no—
126C22×D61—22no—
127C22×D61—22no—
128C22×D61—22no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—42no—
134C22×D61—42no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—42no—
140C22×D61—42no—
141C22×D61—42no—
142C22×D61—42no—
143C22×D61—42no—
144C22×D61—42no—
145C22×D61C4⋊C814yescomplemented
146C2×C4×C61—22no—
147C2×C4×C61—22no—
148C2×C4×C61—22no—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—42no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—42no—
160C2×C4×C61—42no—
161C2×Dic61—22no—
162C2×Dic61—21no—
163C2×Dic61—22no—
164C2×Dic61—21no—
165C2×Dic61—24no—
166C2×Dic61—24no—
167C2×Dic61—22no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—42no—
171C2×Dic61—42no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—42no—
175C2×Dic61C22⋊C812yes—
176C2×Dic61C22⋊C812yes—
177C2×Dic61#9912yes—
178C2×Dic61#10012yes—
179C2×Dic61#12112yes—
180C2×Dic61C22⋊Q812yes—
181C4×D61—48no—
182C4×D61—48no—
183#92420—84no—
184#8557—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61#38011yescharacteristic
198C22×C61C2×C22⋊C811yescharacteristic
199C22×C61#40711yescharacteristic
200C22×C61C2×#9911yescharacteristic
201C22×C61#41011yescharacteristic
202C22×C61C2×#10011yescharacteristic
203C22×C61#41311yescharacteristic
204C22×C61C2×C4⋊C811yescharacteristic
205C22×C61#42311yescharacteristic
206C22×C61#43111yescharacteristic
207C22×C61#43211yescharacteristic
208C2×D61—24no—
209C2×D61—44no—
210C2×D61—44no—
211C2×D61—44no—
212C2×D61—42no—
213C2×D61—42no—
214C2×D61—42no—
215C2×D61—42no—
216C2×D61—42no—
217C2×D61—42no—
218C2×D61—44no—
219C4×C61—42no—
220C4×C61—42no—
221C4×C61—42no—
222Dic61—22no—
223Dic61—22no—
224Dic61—22no—
225Dic61—42no—
226Dic61#32314yescomplemented
227C2×C4×C22⋊C4—611no—
228#1797—612no—
229C2×#323—612no—
230#1280—612no—
231C2×C61—21no—
232C2×C61—21no—
233C2×C61—21no—
234C2×C61—21no—
235C2×C61C2×#32311yescharacteristic
236C2×C61#145811yescharacteristic
237C2×C61#146511yescharacteristic
238C2×C61#146611yescharacteristic
239C2×C61#179711yescharacteristic
240C2×C61#179911yescharacteristic
241C2×C61#180011yescharacteristic
242D61—44no—
243C24×C4—611no—
244C22×C22⋊C4—611no—
245C22×C22⋊C4—611no—
246C22×C42—611no—
247C22×C42—611no—
248C2×C4⋊C8—1222no—
249C2×C22⋊C8—614no—
250C4×C22⋊C4—1222no—
251C4×C22⋊C4—1222no—
252C2×#95—611no—
253C2×#95#692311yescharacteristic
254#336—1222no—
255#323—1224no—
256C61#855711yescharacteristic, complemented, Sylow
257C25—611no—
258C23×C4—611no—
259C23×C4—611no—
260C23×C4—611no—
261C23×C4—614no—
262C23×C4—1222no—
263C23×C4—1221no—
264C23×C4—1221no—
265C23×C4—2442no—
266C23×C4—2442no—
267C23×C4C2×#692311yescharacteristic
268C23×C4C2×#692311yescharacteristic
269C23×C4C2×#692311yescharacteristic
270C22×C8—1224no—
271C2×C22⋊C4—612no—
272C2×C22⋊C4—612no—
273C2×C22⋊C4—1222no—
274C2×C22⋊C4—1222no—
275C2×C22⋊C4—1222no—
276C2×C22⋊C4—1222no—
277C2×C22⋊C4—1222no—
278C2×C42—612no—
279C2×C42—612no—
280C2×C42—1221no—
281C2×C42—1221no—
282C2×C42—2442no—
283C2×C42—2442no—
284C4⋊C8—2444no—
285C22⋊C8—1224no—
286C22⋊C8—1224no—
287#95—22no—
288#95—1222no—
289C24—612no—
290C24—612no—
291C24—612no—
292C24—1221no—
293C24—1221no—
294C24—1221no—
295C24—1221no—
296C24—2441no—
297C24—2441no—
298C24—2441no—
299C24—2441no—
300C24C22×#692311yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—611no—
314C22×C4—612no—
315C22×C4—611no—
316C22×C4—612no—
317C22×C4—612no—
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—612no—
321C22×C4—612no—
322C22×C4—1224no—
323C22×C4—1224no—
324C22×C4—1222no—
325C22×C4—1222no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—2442no—
329C22×C4—2442no—
330C22×C4—2448no—
331C22×C4—2442no—
332C22×C4—2442no—
333C22×C4—2448no—
334C22×C4—2441no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4—2441no—
338C22×C4D61⋊C812yes—
339C22×C4C4⋊#692312yes—
340C22×C4C22⋊#692312yes—
341C2×C8—2444no—
342C2×C8—2444no—
343C2×C8—2444no—
344C22⋊C4—1224no—
345C22⋊C4—1224no—
346C22⋊C4—1228no—
347C42—1224no—
348C42—2442no—
349C42—2442no—
350C42—2442no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—614no—
356C23—1222no—
357C23—1222no—
358C23—1222no—
359C23—1222no—
360C23—1222no—
361C23—1222no—
362C23—2442no—
363C23—2442no—
364C23—2442no—
365C23—2442no—
366C23—2442no—
367C23—2442no—
368C23—2442no—
369C23—2442no—
370C23—2442no—
371C23—2442no—
372C23—2442no—
373C23—2442no—
374C23—2441no—
375C23—2441no—
376C23—2441no—
377C23—2441no—
378C23C2×C22⋊#692311yescharacteristic
379C23C2×C4⋊#692311yescharacteristic
380C23#1451985611yescharacteristic
381C23C2×D61⋊C811yescharacteristic
382C23D61⋊M1611yescharacteristic
383C23D61⋊M1611yescharacteristic
384C23D61⋊M1611yescharacteristic
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—612no—
401C2×C4—612no—
402C2×C4—612no—
403C2×C4—612no—
404C2×C4—612no—
405C2×C4—612no—
406C2×C4—1224no—
407C2×C4—1224no—
408C2×C4—1222no—
409C2×C4—1221no—
410C2×C4—1222no—
411C2×C4—1221no—
412C2×C4—1222no—
413C2×C4—2448no—
414C2×C4—2448no—
415C2×C4—2441no—
416C2×C4—2442no—
417C2×C4—2441no—
418C2×C4—2442no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2442no—
422C8—4884no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—1224no—
436C22—2444no—
437C22—2444no—
438C22—2444no—
439C22—2444no—
440C22—2442no—
441C22—2442no—
442C22—2442no—
443C22—2442no—
444C22—2442no—
445C22—2442no—
446C22#1684070411yescharacteristic
447C22D61⋊(C22⋊C8)11yescharacteristic
448C22#1684073411yescharacteristic
449C22D61⋊#9911yescharacteristic
450C22#1684074311yescharacteristic
451C22D61⋊#10011yescharacteristic
452C22#1684074911yescharacteristic
453C22D61⋊(C4⋊C8)11yescharacteristic
454C22#1684076711yescharacteristic
455C22#1684078011yescharacteristic
456C22#1684078511yescharacteristic
457C4—42no—
458C4—42no—
459C4—42no—
460C4—614no—
461C4—1222no—
462C4—1222no—
463C4—1222no—
464C4—2442no—
465C2—21no—
466C2—21no—
467C2—21no—
468C2—21no—
469C2—2444no—
470C2D61⋊#32311yescharacteristic
471C2#2146105311yescharacteristic
472C2#2146107711yescharacteristic
473C2#2146108011yescharacteristic
474C2#2146167611yescharacteristic
475C2#2146168211yescharacteristic
476C2#2146168411yescharacteristic
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#8557
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
1. #21461675C2semidirect
3. #21460657C2semidirect
31. C22×C4×D61C8semidirect
145. C22×D61C4⋊C8semidirect
226. Dic61#323semidirect
256. C61#8557semidirect

Maximal subgroups

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

subgroupindex
#214616752
C2×#168406062
#214606572
C2×#168396092
#855761