Finite Group Databasebeta

← #30602430

Subgroups — #30602430

Order 15616.

1374 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840734C211yesmaximal, characteristic
2C2×#16840734C211yesmaximal, characteristic
3C2×#16840643C214yesmaximal, complemented
4C2×#117×D61C211yesmaximal, characteristic
5C22×#11758217C2212yes—
6C22×#11758217C2212yes—
7#16840734—22no—
8#16840734—21no—
9#16840734—21no—
10#16840734—21no—
11#16840734—21no—
12#16840734C414yescomplemented
13C2×#14519834—22no—
14C2×#14519834C414yescomplemented
15#16840643—28no—
16C23×C4×D61C2211yescharacteristic
17C2×#14519736C411yescharacteristic
18C2×#14519735—21no—
19C2×#14519734—21no—
20C2×#14519733C2212yes—
21#117×D61—28no—
22C2×C4⋊C4×D61—21no—
23C2×C22⋊C4×D61C412yes—
24C2×C42×D61—21no—
25C2×#117×C61C411yescharacteristic
26C2×#11758217—22no—
27C2×#11758217—22no—
28C2×#11758217—22no—
29C2×#11758217—24no—
30C2×#11758217—24no—
31C2×#11758217—24no—
32C2×#11758217—24no—
33C2×#11758217C2×C414yescomplemented
34C22×#92420—22no—
35C22×#92420C2×C414yescomplemented
36#14519834—24no—
37#14519834—24no—
38#14519834—24no—
39#14519834—24no—
40C24×D61C2×C411yescharacteristic
41C23×Dic61C2311yescharacteristic
42C22×C4×D61—24no—
43C22×C4×D61—24no—
44C22×C4×D61—22no—
45C22×C4×D61C2×C412yes—
46C22×C4×D61C2×C412yes—
47C22×C4×D61D412yes—
48C22×C4×D61D411yescharacteristic
49C22×C4×D61D411yescharacteristic
50C22×C4×D61D411yescharacteristic
51C22×C4×D61D411yescharacteristic
52C22×C4×D61Q812yes—
53#14519736—24no—
54#14519735—28no—
55#14519734—28no—
56#14519733—24no—
57#14519733D418yes—
58C2×C4⋊Dic61—21no—
59C2×#11758196—22no—
60C4⋊C4×D61—28no—
61C2×C22⋊Dic61C2×C412yes—
62C2×#11758198—22no—
63C22⋊C4×D61—24no—
64C22⋊C4×D61—24no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61—22no—
67C42×D61—28no—
68C23×C4×C61C2×C411yescharacteristic
69#117×C61—24no—
70C2×C4⋊C4×C61—21no—
71C2×C22⋊C4×C61C2×C412yes—
72C2×C42×C61—21no—
73C24×C61C22×C411yescharacteristic
74C23×D61—22no—
75C23×D61—22no—
76C23×D61—44no—
77C23×D61C4212yes—
78C23×D61C22⋊C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C23×D61C4⋊C412yes—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—22no—
84C22×C4×C61C4212yes—
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C4⋊C412yes—
88C22×Dic61—22no—
89C22×Dic61C22×C411yescharacteristic
90C22×Dic61C22×C411yescharacteristic
91C22×Dic61C2×D411yescharacteristic
92C22×Dic61C2×D411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94C22×Dic61C2×D414yes—
95C22×Dic61C2×Q811yescharacteristic
96C22×Dic61#4114yes—
97C2×C4×D61—28no—
98C2×C4×D61—28no—
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—22no—
103C2×C4×D61—28no—
104C2×C4×D61—28no—
105C2×C4×D61—22no—
106C2×C4×D61—22no—
107C2×C4×D61—22no—
108C2×C4×D61—22no—
109C2×C4×D61—28no—
110C2×C4×D61—48no—
111C2×C4×D61C22⋊C412yes—
112C2×C4×D61C22⋊C412yes—
113C2×C4×D61C22⋊C412yes—
114C2×C4×D61C22⋊C412yes—
115C2×C4×D61C4⋊C412yes—
116C2×C4×D61C4⋊C412yes—
117C2×C4×D61C4⋊C412yes—
118C2×C4×D61C4⋊C412yes—
119#11758217—28no—
120#11758217—42no—
121#11758217—42no—
122#11758217—44no—
123#11758217—42no—
124#11758217—42no—
125C2×#92420—24no—
126C2×#92420—24no—
127C2×#92420—28no—
128C2×#92420—44no—
129C4⋊C4×C61—24no—
130C22⋊C4×C61—22no—
131C22⋊C4×C61C22⋊C414yes—
132C42×C61—24no—
133C22⋊Dic61—22no—
134C22⋊Dic61C22⋊C414yes—
135#11758198—28no—
136C4⋊Dic61—24no—
137#11758196—28no—
138C4×Dic61—24no—
139C4×Dic61—28no—
140C23×C61—42no—
141C23×C61C2×C4211yescharacteristic
142C23×C61C2×C22⋊C411yescharacteristic
143C23×C61C2×C22⋊C412yes—
144C23×C61C2×C4⋊C411yescharacteristic
145C23×C61#11712yes—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—24no—
149C22×D61—24no—
150C22×D61—21no—
151C22×D61—24no—
152C22×D61—21no—
153C22×D61—24no—
154C22×D61—24no—
155C22×D61—42no—
156C22×D61—42no—
157C22×D61—42no—
158C22×D61—48no—
159C22×D61—48no—
160C22×D61#9512yes—
161C22×D61#9512yes—
162C2×C4×C61—24no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—24no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—24no—
169C2×C4×C61—44no—
170C2×C4×C61#9512yes—
171C2×C4×C61#9512yes—
172C2×Dic61—24no—
173C2×Dic61—44no—
174C2×Dic61C2×C22⋊C411yescharacteristic
175C2×Dic61C2×C22⋊C411yescharacteristic
176C2×Dic61C2×C4⋊C411yescharacteristic
177C2×Dic61C2×C4⋊C411yescharacteristic
178C2×Dic61C4×D414yes—
179C2×Dic61C4×D414yes—
180C2×Dic61#12012yes—
181C2×Dic61#12012yes—
182C2×Dic61#12114yes—
183C2×Dic61C22⋊Q814yes—
184C2×Dic61#12312yes—
185C2×Dic61#12312yes—
186C4×D61—24no—
187C4×D61—24no—
188C4×D61—24no—
189C4×D61—24no—
190C4×D61—24no—
191C4×D61—24no—
192C4×D61—24no—
193C4×D61—24no—
194C4×D61—416no—
195#92420—44no—
196#92420—44no—
197#10738—611nomaximal, Sylow
198C22×C61—22no—
199C22×C61—22no—
200C22×C61—22no—
201C22×C61—42no—
202C22×C61—42no—
203C22×C61C2×#9511yescharacteristic
204C22×C61C4×C22⋊C412yes—
205C22×C61#37911yescharacteristic
206C22×C61#38012yes—
207C22×C61#38111yescharacteristic
208C2×D61—24no—
209C2×D61—24no—
210C2×D61—22no—
211C2×D61—22no—
212C2×D61—22no—
213C2×D61—22no—
214C2×D61—22no—
215C2×D61—48no—
216C2×D61—48no—
217C2×D61—42no—
218C2×D61—42no—
219C2×D61#34414yescomplemented
220C4×C61—22no—
221C4×C61—22no—
222C4×C61—44no—
223Dic61—44no—
224Dic61#38512yes—
225Dic61#38512yes—
226Dic61#38612yes—
227Dic61#38612yes—
228C22×#117—611no—
229C2×#407—611no—
230C2×#407—611no—
231C2×#344—614no—
232C2×C61—21no—
233C2×C61—21no—
234C2×C61—22no—
235C2×C61—22no—
236C2×C61C22⋊#9511yescharacteristic
237C2×C61C2×#34412yes—
238D61—24no—
239D61—42no—
240C24×C4—611no—
241C22×M16—612no—
242C22×M16—612no—
243C2×#117—611no—
244C2×#117—612no—
245C2×#117—1221no—
246C2×#117—1221no—
247C2×#117—1228no—
248C2×#117#692311yescharacteristic
249C22×C4⋊C4—1221no—
250C22×C22⋊C4—612no—
251C22×C42—1221no—
252#407—614no—
253#407—1222no—
254#407—1221no—
255#407—1221no—
256#407—1221no—
257#407—1221no—
258C2×C22⋊C8—614no—
259C2×C22⋊C8—1222no—
260#344—1228no—
261C61#1073811yescharacteristic, complemented, Sylow
262C25—611no—
263C23×C4—611no—
264C23×C4—612no—
265C23×C4—612no—
266C23×C4—612no—
267C23×C4—612no—
268C23×C4—611no—
269C23×C4—611no—
270C23×C4—611no—
271C23×C4—611no—
272C23×C4—1224no—
273C23×C4—1224no—
274C23×C4—1222no—
275C23×C4C2×#692311yescharacteristic
276C2×M16—614no—
277C2×M16—1224no—
278C2×M16—1224no—
279C2×M16—1222no—
280C2×M16—1222no—
281C2×M16—1222no—
282C2×M16—1224no—
283C2×M16—1224no—
284C22×C8—614no—
285C22×C8—1222no—
286#117—24no—
287#117—618no—
288#117—1228no—
289#117—1224no—
290#117—1224no—
291#117—1228no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—1228no—
294C2×C4⋊C4—1222no—
295C2×C4⋊C4—1221no—
296C2×C22⋊C4—612no—
297C2×C22⋊C4—1224no—
298C2×C22⋊C4—1222no—
299C2×C22⋊C4—1224no—
300C2×C22⋊C4C2×#692312yes—
301C2×C42—21no—
302C2×C42—1228no—
303C2×C42—1222no—
304C2×C42—1221no—
305C22⋊C8—1224no—
306C22⋊C8—1224no—
307C22⋊C8—1224no—
308C22⋊C8—1224no—
309C24—611no—
310C24—612no—
311C24—612no—
312C24—611no—
313C24—1222no—
314C24—1222no—
315C24—2444no—
316C24C22×#692311yescharacteristic
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—611no—
321C22×C4—611no—
322C22×C4—611no—
323C22×C4—611no—
324C22×C4—614no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—614no—
328C22×C4—612no—
329C22×C4—612no—
330C22×C4—612no—
331C22×C4—612no—
332C22×C4—612no—
333C22×C4—612no—
334C22×C4—612no—
335C22×C4—612no—
336C22×C4—1222no—
337C22×C4—1222no—
338C22×C4—1222no—
339C22×C4—1222no—
340C22×C4—1228no—
341C22×C4—1228no—
342C22×C4—1222no—
343C22×C4—1222no—
344C22×C4—1222no—
345C22×C4—1222no—
346C22×C4—1228no—
347C22×C4—1228no—
348C22×C4—1228no—
349C22×C4—1222no—
350C22×C4—2448no—
351C22×C4C4×#692312yes—
352C22×C4C4⋊#692312yes—
353C22×C4C22⋊#692311yescharacteristic
354C22×C4C22⋊#692311yescharacteristic
355M16—1228no—
356M16—2444no—
357M16—2442no—
358M16—2442no—
359M16—2442no—
360M16—2442no—
361C2×C8—1224no—
362C2×C8—1224no—
363C2×C8—1228no—
364C2×C8—2444no—
365C4⋊C4—24no—
366C4⋊C4—1228no—
367C4⋊C4—1224no—
368C22⋊C4—22no—
369C22⋊C4—614no—
370C22⋊C4—1228no—
371C22⋊C4—1222no—
372C22⋊C4C22⋊#692314yes—
373C42—24no—
374C42—1228no—
375C42—1224no—
376C23—42no—
377C23—612no—
378C23—612no—
379C23—1224no—
380C23—1224no—
381C23—1224no—
382C23—1221no—
383C23—1221no—
384C23—1224no—
385C23—1221no—
386C23—1224no—
387C23—1221no—
388C23—2442no—
389C23—2442no—
390C23—2442no—
391C23—2448no—
392C23—2448no—
393C23C2×C4×#692311yescharacteristic
394C23C2×C22⋊#692311yescharacteristic
395C23C2×C22⋊#692312yes—
396C23C2×C4⋊#692311yescharacteristic
397C23#1451985612yes—
398C2×C4—24no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—24no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—24no—
405C2×C4—44no—
406C2×C4—614no—
407C2×C4—614no—
408C2×C4—612no—
409C2×C4—612no—
410C2×C4—611no—
411C2×C4—611no—
412C2×C4—611no—
413C2×C4—611no—
414C2×C4—614no—
415C2×C4—614no—
416C2×C4—612no—
417C2×C4—612no—
418C2×C4—1224no—
419C2×C4—1224no—
420C2×C4—1224no—
421C2×C4—1224no—
422C2×C4—1224no—
423C2×C4—1224no—
424C2×C4—1224no—
425C2×C4—1224no—
426C2×C4—1224no—
427C2×C4—24416no—
428C2×C4—2444no—
429C2×C4(C2×#6923)⋊C412yes—
430C2×C4(C2×#6923)⋊C412yes—
431C8—2444no—
432C8—2444no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—42no—
437C22—42no—
438C22—614no—
439C22—1224no—
440C22—1224no—
441C22—1222no—
442C22—1222no—
443C22—1222no—
444C22—1222no—
445C22—1222no—
446C22—2448no—
447C22—2448no—
448C22—2442no—
449C22—2442no—
450C22C2×(C2×#6923)⋊C411yescharacteristic
451C22C4×C22⋊#692312yes—
452C22#1684070311yescharacteristic
453C22#1684070412yes—
454C22#1684070511yescharacteristic
455C4—22no—
456C4—22no—
457C4—44no—
458C4—612no—
459C4—612no—
460C4—612no—
461C4—612no—
462C4—2444no—
463C2—21no—
464C2—21no—
465C2—22no—
466C2—22no—
467C2—1224no—
468C2—2442no—
469C2#2146099311yescharacteristic
470C2#2146152712yes—
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#10738
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. C2×#16840643C2semidirect
12. #16840734C4semidirect
14. C2×#14519834C4semidirect
33. C2×#11758217C2×C4semidirect
35. C22×#92420C2×C4semidirect
219. C2×D61#344semidirect
261. C61#10738semidirect

Maximal subgroups

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

subgroupindex
C2×#168407342
C2×#168406432
C2×#117×D612
#1073861