Finite Group Databasebeta

← #30596802

Subgroups — #30596802

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3#21460692C214yesmaximal, complemented
4#21448198C211yesmaximal, characteristic
5C22×D61⋊C8—21no—
6C22×C22⋊#6923—21no—
7C22×C4×#6923—21no—
8C2×#14519834C2212yes—
9D61⋊(C22⋊C8)—22no—
10D61⋊(C22⋊C8)C414yescomplemented
11C2×C22⋊#92420—21no—
12C4×C22⋊#6923—22no—
13C4×C22⋊#6923C414yescomplemented
14C2×(C2×#6923)⋊C4C2212yes—
15C23×C4×D61C2211yescharacteristic
16C2×#14519736C411yescharacteristic, complemented
17#16839623—21no—
18#16839619C412yescomplemented
19#16839619C2212yes—
20#16839617—21no—
21C4×#11758198—21no—
22C4×#11758198—21no—
23C2×#117×C61C411yescharacteristic, complemented
24C23×#6923—22no—
25C2×D61⋊C8—24no—
26C2×D61⋊C8—42no—
27C2×D61⋊C8—42no—
28C22×#92420—22no—
29C2×C22⋊#6923—28no—
30C2×C22⋊#6923—24no—
31C2×C4×#6923—24no—
32C2×C4×#6923—42no—
33C2×C4×#6923—42no—
34#14519834—22no—
35#14519834C2×C414yes—
36C22⋊#92420—24no—
37(C2×#6923)⋊C4—22no—
38(C2×#6923)⋊C4C2×C414yes—
39C24×D61D411yescharacteristic
40C23×Dic61D411yescharacteristic
41C22×C4×D61—42no—
42C22×C4×D61—42no—
43C22×C4×D61C2×C411yescharacteristic
44C22×C4×D61C2×C412yes—
45C22×C4×D61C2×C412yes—
46C22×C4×D61D411yescharacteristic
47C22×C4×D61D411yescharacteristic
48C22×C4×D61D412yes—
49C22×C4×D61Q812yes—
50C22×C4×D61C2311yescharacteristic
51#14519736—42no—
52C2×C4⋊Dic61C2×C412yes—
53C2×C22⋊Dic61—21no—
54C2×#11758198—22no—
55C2×#11758198—22no—
56C2×C4×Dic61—21no—
57#14519684—22no—
58#14519684—22no—
59C23×C4×C61C2×C411yescharacteristic
60#117×C61—42no—
61C2×C4⋊C4×C61C2×C412yes—
62C2×C22⋊C4×C61—21no—
63C2×C42×C61—21no—
64C24×C61C22⋊C411yescharacteristic
65C23×D61—24no—
66C23×D61—24no—
67C23×D61—41no—
68C23×D61—41no—
69C23×D61C22⋊C412yes—
70C23×D61C22⋊C411yescharacteristic
71C23×D61C4⋊C412yes—
72C23×D61C2×D411yescharacteristic
73C22×#6923—28no—
74C22×#6923—24no—
75C22×#6923—42no—
76C22×#6923—42no—
77C22×#6923—44no—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61C4212yes—
82C22×C4×C61C22⋊C411yescharacteristic
83C22×C4×C61C4⋊C412yes—
84C22×C4×C61C22×C411yescharacteristic
85C22×Dic61—22no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C412yes—
90C22×Dic61C4⋊C412yes—
91C22×Dic61C2×D411yescharacteristic
92C2×C4×D61—22no—
93C2×C4×D61—22no—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—44no—
97C2×C4×D61—44no—
98C2×C4×D61—44no—
99C2×C4×D61—44no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61C4212yes—
105C2×C4×D61C22⋊C412yes—
106C2×C4×D61C22⋊C412yes—
107C2×C4×D61C4⋊C412yes—
108C2×C4×D61C4⋊C412yes—
109C2×C4×D61C4⋊C412yes—
110C2×C4×D61C22×C411yescharacteristic
111C2×C4×D61C22×C411yescharacteristic
112C2×C4×D61C2×D411yescharacteristic
113C2×C4×D61C2×Q811yescharacteristic
114C22⋊#6923—216no—
115C2×#92420—24no—
116C2×#92420—42no—
117C2×#92420—42no—
118C4×#6923—48no—
119D61⋊C8—48no—
120C4⋊C4×C61—42no—
121C22⋊C4×C61—42no—
122C42×C61—42no—
123C22⋊Dic61—42no—
124#11758198—44no—
125#11758198—44no—
126C4⋊Dic61—42no—
127C4×Dic61—42no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—22no—
131C23×C61—22no—
132C23×C61#9512yes—
133C23×C61C2×C22⋊C411yescharacteristic
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—22no—
139C22×D61—22no—
140C22×D61—24no—
141C22×D61—24no—
142C22×D61—24no—
143C22×D61—24no—
144C22×D61—42no—
145C22×D61—42no—
146C22×D61—48no—
147C22×D61—48no—
148C22×D61#9512yes—
149C22×D61#10414yes—
150C22×D61C2×C22⋊C411yescharacteristic
151C22×D61C2×C4⋊C411yescharacteristic
152C22×D61#13514yes—
153C2×#6923—28no—
154C2×#6923—44no—
155C2×#6923—48no—
156C2×#6923—48no—
157C2×#6923—44no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—24no—
161C2×C4×C61—24no—
162C2×C4×C61—42no—
163C2×C4×C61—42no—
164C2×C4×C61—42no—
165C2×C4×C61#9512yes—
166C2×C4×C61#9912yes—
167C2×C4×C61#9912yes—
168C2×C4×C61C2×C4211yescharacteristic
169C2×C4×C61C2×C4⋊C411yescharacteristic
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—42no—
175C2×Dic61—42no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61#9512yes—
180C2×Dic61C2×C22⋊C411yescharacteristic
181C2×Dic61C2×C4⋊C411yescharacteristic
182C4×D61—24no—
183C4×D61—24no—
184C4×D61—24no—
185C4×D61—24no—
186C4×D61—42no—
187C4×D61—42no—
188C4×D61—41no—
189C4×D61—41no—
190C4×D61—41no—
191C4×D61—41no—
192#92420—44no—
193#8012—611nomaximal, Sylow
194C22×C61—22no—
195C22×C61—22no—
196C22×C61—22no—
197C22×C61—42no—
198C22×C61—42no—
199C22×C61C2×#9511yescharacteristic
200C22×C61C2×#9911yescharacteristic
201C22×C61C2×#9911yescharacteristic
202C22×C61#41612yes—
203C22×C61C2×#10412yes—
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—22no—
207C2×D61—21no—
208C2×D61—22no—
209C2×D61—21no—
210C2×D61—24no—
211C2×D61—24no—
212C2×D61—24no—
213C2×D61—24no—
214C2×D61—48no—
215C2×D61—48no—
216C2×D61#33914yes—
217C2×D61#41612yes—
218C2×D61#42712yes—
219#6923—48no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—82no—
223C4×C61#34214yes—
224Dic61—21no—
225Dic61—22no—
226Dic61—21no—
227Dic61—82no—
228C22×C22⋊C8—611no—
229#2280—611no—
230C2×C4×C22⋊C4—611no—
231#1294—614no—
232C2×C61—42no—
233C2×C61#150112yes—
234C2×C61#150112yes—
235C2×C61C2×#33911yescharacteristic
236C2×C61#173511yescharacteristic
237C2×C61C2×#34211yescharacteristic
238D61—22no—
239D61—24no—
240D61—22no—
241C24×C4—611no—
242C23×C8—1221no—
243C2×#117—611no—
244C2×#117#692311yescharacteristic, complemented
245C22×C22⋊C4—1221no—
246C22×C42—1221no—
247C2×C22⋊C8—612no—
248C2×C22⋊C8—614no—
249C2×C22⋊C8—1221no—
250C2×C22⋊C8—1222no—
251#381—1221no—
252#380—612no—
253#380—612no—
254#379—1221no—
255C4×C22⋊C4—614no—
256C4×C22⋊C4—1221no—
257C4×C22⋊C4—1221no—
258C4×C22⋊C4—1222no—
259C2×#95—612no—
260C61#801211yescharacteristic, complemented, Sylow
261C25—611no—
262C23×C4—611no—
263C23×C4—611no—
264C23×C4—611no—
265C23×C4—612no—
266C23×C4—612no—
267C23×C4—612no—
268C23×C4—612no—
269C23×C4—611no—
270C23×C4—611no—
271C23×C4—1222no—
272C23×C4—2442no—
273C23×C4—2442no—
274C23×C4C2×#692311yescharacteristic
275C22×C8—1222no—
276C22×C8—1224no—
277C22×C8—2442no—
278C22×C8—2442no—
279#117—42no—
280#117—2442no—
281C2×C4⋊C4—612no—
282C2×C4⋊C4C2×#692312yes—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—1224no—
285C2×C22⋊C4—1228no—
286C2×C22⋊C4—1222no—
287C2×C22⋊C4—1222no—
288C2×C22⋊C4—1221no—
289C2×C42—21no—
290C2×C42—1224no—
291C2×C42—1221no—
292C2×C42—2442no—
293C2×C42—2442no—
294C22⋊C8—614no—
295C22⋊C8—1224no—
296C22⋊C8—1222no—
297#95—614no—
298#95—1222no—
299#95—1222no—
300#95—1222no—
301C24—611no—
302C24—611no—
303C24—612no—
304C24—612no—
305C24—1224no—
306C24—1224no—
307C24—2441no—
308C24—2441no—
309C24C22⋊#692311yescharacteristic
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—612no—
316C22×C4—612no—
317C22×C4—612no—
318C22×C4—612no—
319C22×C4—612no—
320C22×C4—612no—
321C22×C4—611no—
322C22×C4—611no—
323C22×C4—612no—
324C22×C4—611no—
325C22×C4—612no—
326C22×C4—611no—
327C22×C4—1222no—
328C22×C4—1222no—
329C22×C4—1222no—
330C22×C4—1222no—
331C22×C4—1224no—
332C22×C4—1228no—
333C22×C4—1222no—
334C22×C4—2444no—
335C22×C4—2444no—
336C22×C4—2444no—
337C22×C4—2444no—
338C22×C4—2441no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4—2441no—
343C22×C4—2441no—
344C22×C4—2444no—
345C22×C4—2442no—
346C22×C4—2442no—
347C22×C4C4×#692312yes—
348C22×C4C4⋊#692312yes—
349C22×C4C22⋊#692311yescharacteristic
350C22×C4C22×#692311yescharacteristic
351C2×C8—1224no—
352C2×C8—2448no—
353C2×C8—2442no—
354C2×C8—2442no—
355C4⋊C4—42no—
356C4⋊C4—2442no—
357C22⋊C4—42no—
358C22⋊C4—12216no—
359C22⋊C4—2444no—
360C22⋊C4—2444no—
361C22⋊C4—2442no—
362C42—42no—
363C42—2448no—
364C42—2442no—
365C23—21no—
366C23—21no—
367C23—22no—
368C23—22no—
369C23—614no—
370C23—614no—
371C23—612no—
372C23—611no—
373C23—611no—
374C23—1224no—
375C23—1224no—
376C23—1224no—
377C23—1224no—
378C23—1221no—
379C23—1221no—
380C23—1221no—
381C23—1221no—
382C23—1222no—
383C23—1222no—
384C23—2442no—
385C23—2442no—
386C23—2448no—
387C23—2448no—
388C23(C2×#6923)⋊C412yes—
389C23C2×C22⋊#692311yescharacteristic
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—612no—
398C2×C4—611no—
399C2×C4—611no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1224no—
405C2×C4—1224no—
406C2×C4—1224no—
407C2×C4—1224no—
408C2×C4—1228no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2442no—
412C2×C4—2441no—
413C2×C4—2442no—
414C2×C4—2441no—
415C2×C4—2442no—
416C2×C4—2442no—
417C2×C4—2442no—
418C2×C4—2442no—
419C2×C4—2442no—
420C2×C4—2444no—
421C2×C4—2444no—
422C2×C4—2448no—
423C2×C4—2448no—
424C2×C4(C2×#6923)⋊C412yes—
425C2×C4#1451983512yes—
426C2×C4#1451983612yes—
427C2×C4C2×C4×#692311yescharacteristic
428C2×C4C2×C4⋊#692311yescharacteristic
429C8—2444no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—42no—
434C22—42no—
435C22—612no—
436C22—612no—
437C22—614no—
438C22—1222no—
439C22—1221no—
440C22—1222no—
441C22—1221no—
442C22—1224no—
443C22—1224no—
444C22—1224no—
445C22—1224no—
446C22—1221no—
447C22—1221no—
448C22—2448no—
449C22—2448no—
450C22C2×(C2×#6923)⋊C411yescharacteristic
451C22C2×#1451983511yescharacteristic
452C22C2×#1451983611yescharacteristic
453C22#1684075212yes—
454C22D61⋊#10412yes—
455C4—21no—
456C4—21no—
457C4—82no—
458C4—1221no—
459C4—1222no—
460C4—1221no—
461C4—4882no—
462C4—2448no—
463C4#1684064014yes—
464C2—42no—
465C2—1222no—
466C2—1222no—
467C2—1224no—
468C2#2146119412yes—
469C2#2146119612yes—
470C2#2146149511yescharacteristic
471C2#2146150411yescharacteristic
472C2C2×#1684064011yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenterC2×#117#6923
hypocenterC61#8012
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #21460692C2semidirect
10. D61⋊(C22⋊C8)C4semidirect
13. C4×C22⋊#6923C4semidirect
16. C2×#14519736C4semidirect
18. #16839619C4semidirect
23. C2×#117×C61C4semidirect
244. C2×#117#6923semidirect
260. C61#8012semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊(C22⋊C8)2
C2×C4×C22⋊#69232
#214606922
#214481982
#801261