Finite Group Databasebeta

← #29680554

Subgroups — #29680554

Order 15616.

894 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#92418C211yesmaximal, characteristic
2#21448217C211yesmaximal, characteristic
3#21445981C212yesmaximal, complemented
4#21445949C212yesmaximal, complemented
5#21445846C212yesmaximal
6#21445842C212yesmaximal
7C4×#14519710C212yesmaximal, complemented
8C4×#14519708C212yesmaximal, complemented
9C61×#2283C211yesmaximal, characteristic
10C23×#92418C2211yescharacteristic
11C23×#92418C2211yescharacteristic
12C2×#14519710C2214yes—
13C2×#14519708C2214yes—
14C2×C4×#92418C418yescomplemented
15C2×C4×#92418C2211yescharacteristic
16C2×C4×#92418C2211yescharacteristic
17C2×C4×#92418C2211yescharacteristic
18C2×C4×#92418C2211yescharacteristic
19#16839630—21no—
20#16839628C2212yes—
21#16839625—21no—
22#16839622C2212yes—
23C4×C4⋊Dic61C2212yes—
24C4×C22⋊Dic61—21no—
25#16839608—21no—
26#16839524C2214yes—
27#16839524C2214yes—
28C22×C42×C61C2211yescharacteristic
29C61×#383—21no—
30C61×#382C2212yes—
31C61×#381—21no—
32C61×#380C2212yes—
33C4×C4⋊C4×C61C2212yes—
34C4×C22⋊C4×C61—21no—
35C61×#376—21no—
36C22×#92418—24no—
37C22×#92418—24no—
38C22×#92418C2×C414yes—
39C22×#92418C2×C414yes—
40C22×#92418C2311yescharacteristic
41C22×#92418C2311yescharacteristic
42C22×#92418C2311yescharacteristic
43C22×#92418C2311yescharacteristic
44C2×C4⋊Dic61C2314yes—
45C2×C22⋊Dic61—22no—
46C2×C4×Dic61—22no—
47#14519710—28no—
48#14519708—28no—
49C4×#92418C2×C414yes—
50C4×#92418C2×C414yes—
51C4×#92418C2×C414yes—
52C4×#92418C2×C414yes—
53#14519684—22no—
54#14519684—22no—
55#14519684—22no—
56#14519684—22no—
57C23×C4×C61D411yescharacteristic
58C23×C4×C61D411yescharacteristic
59C23×C4×C61C2311yescharacteristic
60C2×C4⋊C4×C61C2314yes—
61C2×C22⋊C4×C61—22no—
62C2×C42×C61—22no—
63C2×C42×C61C2×C414yes—
64C2×C42×C61D411yescharacteristic
65C2×C42×C61D411yescharacteristic
66C2×C42×C61Q814yes—
67C2×C42×C61C2311yescharacteristic
68C2×C42×C61C2311yescharacteristic
69#95×C61—22no—
70#95×C61—22no—
71#95×C61—22no—
72#95×C61—22no—
73C24×C61C2×D411yescharacteristic
74C22×C4×C61—24no—
75C22×C4×C61—24no—
76C22×C4×C61—22no—
77C22×C4×C61—22no—
78C22×C4×C61—24no—
79C22×C4×C61C4⋊C414yes—
80C22×C4×C61C4⋊C414yes—
81C22×C4×C61C22×C412yes—
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×Q812yes—
88C22×C4×C61C2411yescharacteristic
89C22×Dic61—24no—
90C4⋊C4×C61—24no—
91C4⋊C4×C61—24no—
92C22⋊C4×C61—44no—
93C42×C61—44no—
94C42×C61C4⋊C414yes—
95C42×C61C4⋊C414yes—
96C42×C61C22×C412yes—
97C42×C61C22×C412yes—
98C42×C61C2×Q812yes—
99C42×C61C2×Q812yes—
100C22⋊Dic61—44no—
101C4⋊Dic61—24no—
102C4⋊Dic61—24no—
103C4×Dic61—44no—
104C2×#92418—22no—
105C2×#92418—22no—
106C2×#92418—28no—
107C2×#92418—28no—
108C2×#92418C22×C412yes—
109C2×#92418C22×C412yes—
110C2×#92418C22×C412yes—
111C2×#92418C22×C412yes—
112C2×#92418#4114yes—
113C2×#92418#4114yes—
114C23×C61—22no—
115C23×C61—22no—
116C23×C61C2×C4⋊C412yes—
117C23×C61#13514yes—
118C23×C61C22×D411yescharacteristic
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—22no—
123C2×C4×C61—28no—
124C2×C4×C61—22no—
125C2×C4×C61—22no—
126C2×C4×C61—24no—
127C2×C4×C61—28no—
128C2×C4×C61—44no—
129C2×C4×C61—44no—
130C2×C4×C61—44no—
131C2×C4×C61C2×C4⋊C412yes—
132C2×C4×C61C2×C4⋊C412yes—
133C2×C4×C61C2×C4⋊C412yes—
134C2×C4×C61C2×C4⋊C412yes—
135C2×C4×C61C2×C4⋊C412yes—
136C2×C4×C61#13514yes—
137C2×C4×C61C23×C411yescharacteristic
138C2×C4×C61C22×Q811yescharacteristic
139C2×C4×C61C2×#4112yes—
140C2×C4×C61C2×#4112yes—
141C2×Dic61—44no—
142C2×Dic61—44no—
143C2×Dic61—44no—
144#92418—22no—
145#92418—22no—
146#92418#11714yes—
147#92418#11714yes—
148#20818—611nomaximal, Sylow
149C22×C61—22no—
150C22×C61—28no—
151C22×C61—22no—
152C22×C61#42714yes—
153C22×C61C22×C4⋊C411yescharacteristic
154C22×C61#53212yes—
155C22×C61C2×#13512yes—
156C22×C61C2×#13512yes—
157C4×C61—22no—
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—22no—
161C4×C61—84no—
162C4×C61#42714yes—
163C4×C61C2×#11711yescharacteristic
164C4×C61C2×#11711yescharacteristic
165C4×C61#53312yes—
166Dic61—84no—
167C22×C4×C8—611no—
168#2283—611no—
169#2283D6111yescharacteristic
170#1846—612no—
171#1835—612no—
172#1808—612no—
173#1807—612no—
174C4×#107—612no—
175C4×#106—612no—
176C2×C61—24no—
177C2×C61#228511yescharacteristic
178C2×C61C2×#42711yescharacteristic
179C2×C61C2×#42711yescharacteristic
180C2×C61#316814yes—
181C23×C8—611no—
182C23×C8—611no—
183C22×C42C2×D6111yescharacteristic
184C2×#107—614no—
185C2×#106—614no—
186C2×C4×C8—618no—
187C2×C4×C8—611no—
188C2×C4×C8—611no—
189C2×C4×C8—611no—
190C2×C4×C8—611no—
191#383—21no—
192#383—1221no—
193#382—612no—
194#382C2×D6112yes—
195#381—21no—
196#381—1221no—
197#380—612no—
198#380C2×D6112yes—
199C4×C4⋊C4—612no—
200C4×C4⋊C4C2×D6112yes—
201C4×C22⋊C4—21no—
202C4×C22⋊C4—1221no—
203#376—21no—
204#376—1221no—
205#340—614no—
206#340—614no—
207C61#2081811yescharacteristic, complemented, Sylow
208C23×C4C22⋊D6111yescharacteristic
209C23×C4C22⋊D6111yescharacteristic
210C23×C4C22×D6111yescharacteristic
211C22×C8—611no—
212C22×C8—611no—
213C22×C8—614no—
214C22×C8—614no—
215C22×C8—611no—
216C22×C8—611no—
217C22×C8—1224no—
218C22×C8—1224no—
219C2×C4⋊C4—614no—
220C2×C4⋊C4C22×D6114yes—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—1222no—
223C2×C42—22no—
224C2×C42—1222no—
225C2×C42Dic12214yes—
226C2×C42C4×D6114yes—
227C2×C42C22⋊D6111yescharacteristic
228C2×C42C22⋊D6111yescharacteristic
229C2×C42C22×D6111yescharacteristic
230C2×C42C22×D6111yescharacteristic
231#107—1228no—
232#106—1228no—
233C4×C8—614no—
234C4×C8—614no—
235C4×C8—614no—
236C4×C8—614no—
237#95—22no—
238#95—22no—
239#95—22no—
240#95—22no—
241#95—1222no—
242#95—1222no—
243#95—1222no—
244#95—1222no—
245C24C2×C22⋊D6111yescharacteristic
246C22×C4—24no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—1224no—
252C22×C4#1175819614yes—
253C22×C4#1175819614yes—
254C22×C4C2×Dic12212yes—
255C22×C4C2×C4×D6112yes—
256C22×C4C2×C22⋊D6111yescharacteristic
257C22×C4C2×C22⋊D6111yescharacteristic
258C22×C4C2×C22⋊D6111yescharacteristic
259C22×C4C2×C22⋊D6111yescharacteristic
260C22×C4C2×C22⋊D6111yescharacteristic
261C22×C4C23×D6111yescharacteristic
262C2×C8—612no—
263C2×C8—612no—
264C2×C8—614no—
265C2×C8—614no—
266C2×C8—612no—
267C2×C8—612no—
268C2×C8—1228no—
269C2×C8—1228no—
270C2×C8—1222no—
271C2×C8—1222no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—1224no—
275C4⋊C4—1224no—
276C22⋊C4—44no—
277C22⋊C4—2444no—
278C42—44no—
279C42—2444no—
280C42#1175819614yes—
281C42#1175819614yes—
282C42C2×Dic12212yes—
283C42C2×Dic12212yes—
284C42C2×C4×D6112yes—
285C42C2×C4×D6112yes—
286C23—22no—
287C23—22no—
288C23C2×#1175819612yes—
289C23#1451979714yes—
290C23C22×C22⋊D6111yescharacteristic
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—28no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—28no—
299C2×C4—24no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—2444no—
304C2×C4—2444no—
305C2×C4—2444no—
306C2×C4C2×#1175819612yes—
307C2×C4C2×#1175819612yes—
308C2×C4C2×#1175819612yes—
309C2×C4C2×#1175819612yes—
310C2×C4C2×#1175819612yes—
311C2×C4#1451979714yes—
312C2×C4C22×C4×D6111yescharacteristic
313C2×C4C22×Dic12211yescharacteristic
314C2×C4#41×D6112yes—
315C2×C4#41×D6112yes—
316C8—614no—
317C8—614no—
318C8—1222no—
319C8—1222no—
320C22—22no—
321C22—22no—
322C22—28no—
323C22#1683979814yes—
324C22C22×#1175819611yescharacteristic
325C22#1684030812yes—
326C22C2×#1451979712yes—
327C22C2×#1451979712yes—
328C4—22no—
329C4—22no—
330C4—22no—
331C4—22no—
332C4—84no—
333C4—4884no—
334C4#1683979814yes—
335C4#117×D6111yescharacteristic
336C4#117×D6111yescharacteristic
337C4#1684031512yes—
338C2—24no—
339C2#2144822211yescharacteristic
340C2C2×#1683979811yescharacteristic
341C2C2×#1683979811yescharacteristic
342C2#2145638314yes—
subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2283C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
cosocleC22×C4×C61C24
hypercenter#2283D61
hypocenterC61#20818
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
3. #21445981C2semidirect
4. #21445949C2semidirect
7. C4×#14519710C2semidirect
8. C4×#14519708C2semidirect
14. C2×C4×#92418C4semidirect
207. C61#20818semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#924182
#214482172
#214459812
#214459492
#214458462
#214458422
C4×#145197102
C4×#145197082
C61×#22832
#2081861