Finite Group Databasebeta

← #29597092

Subgroups — #29597092

Order 15616.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic488C211yesmaximal, characteristic
2C2×#16839856C211yesmaximal, characteristic
3C2×#16839565C211yesmaximal, characteristic
4C2×#16839565C211yesmaximal, characteristic
5#21446678C211yesmaximal, characteristic
6#21443896C211yesmaximal, characteristic
7C61×#1380C211yesmaximal, characteristic
8C22×Dic244C2211yescharacteristic
9C22×Dic244C2211yescharacteristic
10C2×#14519742—21no—
11C2×Dic488—22no—
12C2×Dic488—22no—
13C2×Dic488C414yescomplemented
14C22×#11758185C2211yescharacteristic
15#16839856—22no—
16#16839856—22no—
17C2×#14519700—21no—
18C2×#14519700—21no—
19C2×C8×Dic61C2211yescharacteristic
20#16839667—21no—
21#16839565—22no—
22#16839565—22no—
23C22×C16×C61C2211yescharacteristic
24C2×#107×C61C2211yescharacteristic
25C2×#107×C61C2211yescharacteristic
26C22×Dic122—21no—
27C22×Dic122—21no—
28C2×Dic244—21no—
29C2×Dic244—21no—
30C2×Dic244—21no—
31C2×Dic244—21no—
32C2×Dic244—21no—
33C2×Dic244—21no—
34C2×Dic244—21no—
35C2×Dic244—21no—
36C2×Dic244C2×C412yes—
37C2×Dic244C2×C412yes—
38C2×Dic244D412yes—
39C2×Dic244D412yes—
40C22×#92418D411yescharacteristic
41#14519742—24no—
42#14519742—42no—
43C2×#11758196—41no—
44C2×C4×Dic61—41no—
45C2×C4×Dic61D411yescharacteristic
46Dic488—28no—
47C2×#11758185—21no—
48C2×#11758185—21no—
49C2×#11758185—21no—
50#14519700—24no—
51#14519700—42no—
52C8×Dic61—21no—
53C8×Dic61—21no—
54#14519684—41no—
55#14519684—41no—
56C22×C8×C61C2311yescharacteristic
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61C2×C412yes—
62#107×C61—21no—
63#107×C61—21no—
64#107×C61—21no—
65#107×C61D412yes—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—41no—
70C22×Dic61—41no—
71C22×Dic61D811yescharacteristic
72C22×Dic61D811yescharacteristic
73C2×Dic122—22no—
74C2×Dic122—22no—
75C2×Dic122—22no—
76C2×Dic122—22no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×C8×C61C22×C411yescharacteristic
86C2×C8×C61C2×D411yescharacteristic
87C2×C8×C61C2×D411yescharacteristic
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61#4111yescharacteristic
90C2×C8×C61#4111yescharacteristic
91C4⋊C4×C61—22no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95#11758196—44no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—44no—
99C2×#92418—21no—
100C2×#92418—21no—
101C2×#92418—21no—
102Dic244—22no—
103Dic244—22no—
104Dic244—22no—
105Dic244—22no—
106Dic244—22no—
107Dic244—41no—
108Dic244—41no—
109Dic244C22⋊C414yes—
110C16×C61—22no—
111#11758185—41no—
112C23×C61C2×D811yescharacteristic
113C2×C4×C61—42no—
114C2×C4×C61—81no—
115C2×C4×C61—81no—
116C2×C4×C61—81no—
117C2×C4×C61—81no—
118C2×C4×C61—81no—
119C2×C4×C61C4×D411yescharacteristic
120C2×C4×C61#12011yescharacteristic
121C2×C4×C61#12111yescharacteristic
122C2×C4×C61#13511yescharacteristic
123C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—42no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136C2×Dic61Q3212yescomplemented
137Dic122—24no—
138Dic122—42no—
139Dic122—42no—
140Dic122—42no—
141Dic122—42no—
142Dic122—42no—
143Dic122—81no—
144Dic122—81no—
145C8×C61C2×C22⋊C411yescharacteristic
146C8×C61C4×D411yescharacteristic
147C8×C61#12111yescharacteristic
148C8×C61#12311yescharacteristic
149#92418—41no—
150#13015—611nomaximal, Sylow
151C22×C61C4×D811yescharacteristic
152C22×C61#44711yescharacteristic
153C22×C61#45911yescharacteristic
154C22×C61C2×Q3211yescharacteristic
155C22×C61#50811yescharacteristic
156C22×C61#51011yescharacteristic
157C22×C61#51011yescharacteristic
158C4×C61—82no—
159C4×C61—161no—
160C4×C61#38611yescharacteristic
161C4×C61#44211yescharacteristic
162C4×C61#44911yescharacteristic
163C4×C61#46311yescharacteristic
164Dic61—22no—
165Dic61—44no—
166Dic61—41no—
167Dic61—82no—
168C22×Q32—611no—
169C2×C4×Q16—611no—
170C2×#358—611no—
171C2×#358—611no—
172#1969—611no—
173#1380D6111yescharacteristic
174#1374—611no—
175C2×C61#187911yescharacteristic
176C2×C61C4×Q3211yescharacteristic
177C2×C61#217611yescharacteristic
178C2×C61#218811yescharacteristic
179C2×C61#218911yescharacteristic
180C2×C61#220911yescharacteristic
181C2×C61#221111yescharacteristic
182C22×Q16—611no—
183C22×Q16—611no—
184C2×C4×Q8—1221no—
185C2×Q32—614no—
186C2×Q32—1222no—
187C2×Q32—1222no—
188C22×C16—611no—
189C22×C16C2×D6111yescharacteristic
190C4×Q16—1222no—
191C4×Q16—1222no—
192C2×#107C2×D6111yescharacteristic
193C2×#107C2×D6111yescharacteristic
194C2×#103—1221no—
195C2×#103—1221no—
196C2×C4×C8—611no—
197#391—1221no—
198#358—1222no—
199#358—1222no—
200C61#1301511yescharacteristic, complemented, Sylow
201C22×Q8—1221no—
202C22×Q8—1221no—
203C2×Q16—612no—
204C2×Q16—612no—
205C2×Q16—612no—
206C2×Q16—612no—
207C2×Q16—1221no—
208C2×Q16—1221no—
209C2×Q16—1221no—
210C2×Q16—1221no—
211C2×Q16—1221no—
212C2×Q16—1221no—
213C2×Q16—1221no—
214C2×Q16—1221no—
215C22×C8—611no—
216C22×C8C22×D6111yescharacteristic
217C4×Q8—1224no—
218C4×Q8—2442no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—2441no—
222C2×C42—611no—
223C2×C42—2441no—
224Q32—1228no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—1221no—
228C2×C16—1221no—
229C2×C16—1221no—
230C2×C16C4×D6112yes—
231#107—21no—
232#107—21no—
233#107—21no—
234#107D24412yes—
235#103—1224no—
236#103—2442no—
237C4×C8—1221no—
238C4×C8—1221no—
239#95—2441no—
240#95—2441no—
241C2×Q8—1222no—
242C2×Q8—1222no—
243C2×Q8—1222no—
244C2×Q8—1222no—
245C2×Q8—2441no—
246C2×Q8—2441no—
247C2×Q8—2441no—
248C2×Q8—2441no—
249C2×Q8—2441no—
250C2×Q8—2441no—
251C2×Q8—2441no—
252C2×Q8—2441no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—2441no—
258C22×C4—2441no—
259C22×C4D4×D6111yescharacteristic
260Q16—614no—
261Q16—1222no—
262Q16—1222no—
263Q16—1222no—
264Q16—1222no—
265Q16—1222no—
266Q16—2441no—
267Q16—2441no—
268C2×C8—1221no—
269C2×C8—1221no—
270C2×C8—1221no—
271C2×C8C2×C4×D6111yescharacteristic
272C2×C8C2×D24411yescharacteristic
273C2×C8#1175822211yescharacteristic
274C2×C8D4×D6111yescharacteristic
275C2×C8D4×D6111yescharacteristic
276C2×C8#1175822611yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—2444no—
282C42—1221no—
283C42—1221no—
284C42—2444no—
285C16—22no—
286C16—2441no—
287C23D8×D6111yescharacteristic
288Q8—1224no—
289Q8—4881no—
290Q8—4881no—
291Q8—2442no—
292Q8—2442no—
293Q8—2442no—
294Q8—2442no—
295Q8—2442no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—612no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—4881no—
309C2×C4—4881no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4—2442no—
314C2×C4#1451973911yescharacteristic
315C2×C4#1451974711yescharacteristic
316C2×C4#1451975011yescharacteristic
317C2×C4#1451980011yescharacteristic
318C2×C4#1451980411yescharacteristic
319C2×C4#1451980411yescharacteristic
320C8—2441no—
321C8C22⋊C4×D6111yescharacteristic
322C8C4×D24411yescharacteristic
323C8#1451975211yescharacteristic
324C8#1451976211yescharacteristic
325C22#1683984411yescharacteristic
326C22#1683989711yescharacteristic
327C22#1683995611yescharacteristic
328C22Q32×D6111yescharacteristic
329C22#1684019111yescharacteristic
330C22#1684020111yescharacteristic
331C22#1684020111yescharacteristic
332C4—82no—
333C4—161no—
334C4—1222no—
335C4—4882no—
336C4—2444no—
337C4—2441no—
338C4#1683964011yescharacteristic
339C4#1683987311yescharacteristic
340C4#1683991011yescharacteristic
341C4#1683998011yescharacteristic
342C2#2144616811yescharacteristic
343C2#2144767711yescharacteristic
344C2#2144768911yescharacteristic
345C2#2144775411yescharacteristic
346C2#2144776011yescharacteristic
347C2#2144786811yescharacteristic
348C2#2144788011yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1380C2
socle, prime radicalC23×C61C2×D8
cosocleC22×C8×C61C23
hypercenter#1380D61
hypocenterC61#13015
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
13. C2×Dic488C4semidirect
136. C2×Dic61Q32semidirect
200. C61#13015semidirect

Maximal subgroups

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

subgroupindex
C22×Dic4882
C2×#168398562
C2×#168395652
#214466782
#214438962
C61×#13802
#1301561