Finite Group Databasebeta

← #29597090

Subgroups — #29597090

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×C4×Dic244C211yesmaximal, characteristic
3C2×#16839567C211yesmaximal, characteristic
4C2×#16839567C211yesmaximal, characteristic
5#21446680C211yesmaximal, characteristic
6#21443911C211yesmaximal, characteristic
7C61×#1374C211yesmaximal, characteristic
8C22×Dic244C2211yescharacteristic
9C22×Dic244C2211yescharacteristic
10C2×C4×Dic122—21no—
11C2×Dic488—22no—
12C2×Dic488—22no—
13C2×Dic488C414yescomplemented
14C4×Dic244—22no—
15C4×Dic244—22no—
16C2×#14519711C2211yescharacteristic
17C2×#14519711C2211yescharacteristic
18C2×#14519702—21no—
19C2×#14519702—21no—
20#16839668—21no—
21#16839567—22no—
22#16839567—22no—
23C22×C16×C61C2211yescharacteristic
24C22×C16×C61C2211yescharacteristic
25C2×C4×C8×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—
40C4×Dic122—24no—
41C4×Dic122—42no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×#11758196—41no—
45C2×C4×Dic61—41no—
46Dic488—28no—
47#14519711—21no—
48#14519711—21no—
49#14519711—21no—
50#14519711D412yes—
51#14519702—24no—
52#14519702—42no—
53#14519684—41no—
54#14519684—41no—
55C22×C8×C61D411yescharacteristic
56C22×C8×C61C2311yescharacteristic
57C2×C42×C61D411yescharacteristic
58C2×C16×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C2×C16×C61—21no—
63C2×C16×C61C2×C412yes—
64C4×C8×C61—21no—
65C4×C8×C61—21no—
66C22×C4×C61D811yescharacteristic
67C22×C4×C61D811yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—41no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61—41no—
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×C61—21no—
86C2×C8×C61—21no—
87C2×C8×C61—21no—
88C2×C8×C61C22×C411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C2×C8×C61C2×D411yescharacteristic
91C2×C8×C61C2×D411yescharacteristic
92C2×C8×C61#4111yescharacteristic
93C2×C8×C61#4111yescharacteristic
94C42×C61—21no—
95C42×C61—21no—
96C4⋊Dic61—22no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100#11758196—44no—
101C4×Dic61—44no—
102Dic244—22no—
103Dic244—22no—
104Dic244—22no—
105Dic244—22no—
106Dic244—22no—
107Dic244—41no—
108Dic244—41no—
109Dic244C22⋊C414yes—
110C16×C61—22no—
111C16×C61—41no—
112C23×C61C2×D811yescharacteristic
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61Q3212yescomplemented
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—42no—
126C2×Dic61—42no—
127C2×Dic61—42no—
128C2×Dic61—42no—
129C2×Dic61—42no—
130C2×Dic61—81no—
131C2×Dic61—81no—
132C2×Dic61—81no—
133C2×Dic61—81no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137Dic122—24no—
138Dic122—42no—
139Dic122—42no—
140Dic122—42no—
141Dic122—42no—
142Dic122—42no—
143Dic122—81no—
144Dic122—81no—
145C8×C61—41no—
146C8×C61C2×C22⋊C411yescharacteristic
147C8×C61C4×D411yescharacteristic
148C8×C61#12111yescharacteristic
149C8×C61#12311yescharacteristic
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—22no—
159C4×C61—41no—
160C4×C61#38611yescharacteristic
161C4×C61#44211yescharacteristic
162C4×C61#44911yescharacteristic
163C4×C61#46311yescharacteristic
164Dic61—44no—
165Dic61—82no—
166Dic61—82no—
167Dic61—161no—
168C22×Q32—611no—
169C2×C4×Q16—611no—
170C2×#358—611no—
171C2×#358—611no—
172#1969—611no—
173#1380—611no—
174#1374D6111yescharacteristic
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×C16C2×D6111yescharacteristic
189C22×C16C2×D6111yescharacteristic
190C4×Q16—1222no—
191C4×Q16—1222no—
192C2×#107—611no—
193C2×#107—611no—
194C2×#103—1221no—
195C2×#103—1221no—
196C2×C4×C8C2×D6111yescharacteristic
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×C8D24411yescharacteristic
216C22×C8C22×D6111yescharacteristic
217C4×Q8—1224no—
218C4×Q8—2442no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—2441no—
222C2×C42—2441no—
223C2×C42D24411yescharacteristic
224Q32—1228no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—21no—
228C2×C16—21no—
229C2×C16—21no—
230C2×C16C4×D6112yes—
231#107—612no—
232#107—1221no—
233#107—1221no—
234#107—1221no—
235#103—1224no—
236#103—2442no—
237C4×C8—21no—
238C4×C8—21no—
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—2441no—
254C22×C4—2441no—
255C22×C4—2441no—
256C22×C4—2441no—
257C22×C4D48811yescharacteristic
258C22×C4D48811yescharacteristic
259C22×C4C2×D24411yescharacteristic
260Q16—614no—
261Q16—1222no—
262Q16—1222no—
263Q16—1222no—
264Q16—1222no—
265Q16—1222no—
266Q16—2441no—
267Q16—2441no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8C2×C4×D6111yescharacteristic
272C2×C8#1175822211yescharacteristic
273C2×C8D4×D6111yescharacteristic
274C2×C8D4×D6111yescharacteristic
275C2×C8D4×D6111yescharacteristic
276C2×C8#1175822611yescharacteristic
277C4⋊C4—1222no—
278C4⋊C4—2444no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C42—21no—
283C42—21no—
284C42—2444no—
285C16—22no—
286C16—41no—
287C23C2×D48811yescharacteristic
288Q8—1224no—
289Q8—4881no—
290Q8—4881no—
291Q8—2442no—
292Q8—2442no—
293Q8—2442no—
294Q8—2442no—
295Q8—2442no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—4881no—
302C2×C4—4881no—
303C2×C4—4881no—
304C2×C4—4881no—
305C2×C4—4881no—
306C2×C4—4881no—
307C2×C4—4881no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4Dic48812yescomplemented
314C2×C4C4×D24411yescharacteristic
315C2×C4#1451974711yescharacteristic
316C2×C4#1451975211yescharacteristic
317C2×C4#1451979911yescharacteristic
318C2×C4#1451980511yescharacteristic
319C2×C4#1451980511yescharacteristic
320C8—41no—
321C8C22⋊C4×D6111yescharacteristic
322C8#1451973911yescharacteristic
323C8#1451975011yescharacteristic
324C8#1451976211yescharacteristic
325C22C4×D48811yescharacteristic
326C22#1683989811yescharacteristic
327C22#1683995811yescharacteristic
328C22C2×Dic48811yescharacteristic
329C22#1684019411yescharacteristic
330C22#1684020511yescharacteristic
331C22#1684020511yescharacteristic
332C4—22no—
333C4—41no—
334C4—9761no—
335C4—4882no—
336C4—4882no—
337C4—2444no—
338C4#1683964011yescharacteristic
339C4#1683987511yescharacteristic
340C4#1683990911yescharacteristic
341C4#1683997811yescharacteristic
342C2#2144616611yescharacteristic
343C2C4×Dic48811yescharacteristic
344C2#2144769111yescharacteristic
345C2#2144775511yescharacteristic
346C2#2144776111yescharacteristic
347C2#2144787011yescharacteristic
348C2#2144788211yescharacteristic
subgroupG/H
centerC23C2×D488
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1374C2
socle, prime radicalC23×C61C2×D8
cosocleC22×C8×C61C23
hypercenter#1374D61
hypocenterC61#13015
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
13. C2×Dic488C4semidirect
118. C2×C4×C61Q32semidirect
200. C61#13015semidirect
313. C2×C4Dic488semidirect

Maximal subgroups

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

subgroupindex
C22×Dic4882
C2×C4×Dic2442
C2×#168395672
#214466802
#214439112
C61×#13742
#1301561