Finite Group Databasebeta

← #30597643

Subgroups — #30597643

Order 15616.

516 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519841C211yesmaximal, characteristic
2C4×C8×#6923C211yesmaximal, characteristic, complemented
3#21461111C211yesmaximal, characteristic
4#21461029C211yesmaximal, characteristic, complemented
5#21460650C211yesmaximal, characteristic, complemented
6#21460646C211yesmaximal, characteristic, complemented
7#21454782C211yesmaximal, characteristic
8#16840781C2211yescharacteristic
9C2×#14519841C412yes—
10C4×#11758213C2211yescharacteristic
11C4×D61⋊C8C2211yescharacteristic
12C2×C8×#6923—21no—
13C2×C8×#6923—21no—
14C42×#6923C2211yescharacteristic
15#16840632C412yes—
16#16840612C412yescomplemented
17D4⋊#92420C412yescomplemented
18#92420⋊C8—21no—
19#16840603—21no—
20C4×#11758224C2211yescharacteristic
21#16839892C411yescharacteristic, complemented
22#16839889C411yescharacteristic, complemented
23#16839840C411yescharacteristic, complemented
24#16839836—21no—
25#16839831—21no—
26#16839814C2211yescharacteristic
27#16839812—21no—
28M16×Dic61—21no—
29C4×C8×D61C2211yescharacteristic
30C61×#436C411yescharacteristic, complemented
31C2×#11758213C2×C412yes—
32C2×D61⋊C8—21no—
33C2×C4×#6923—21no—
34C2×C4×#6923—21no—
35C2×C4×#6923C2×C412yes—
36C4⋊#92420C2×C412yes—
37#14519841—24no—
38#14519834—21no—
39#14519832—21no—
40C4×#92420—21no—
41C4×#92420—21no—
42C4×#92420—21no—
43C4×#92420C2×C412yes—
44C8×#6923—24no—
45C8×#6923—24no—
46C2×#11758224C2×C411yescharacteristic
47C2×#11758194—21no—
48C2×C8×D61D411yescharacteristic
49C2×C8×D61D411yescharacteristic
50C4×Dic122C2×C411yescharacteristic
51#14519742C2×C411yescharacteristic
52D4×Dic61C2×C411yescharacteristic
53C4×C22⋊D61—21no—
54#14519737—21no—
55#14519735C2×C411yescharacteristic
56#14519733—21no—
57C2×C4×Dic61—21no—
58C42×D61C2311yescharacteristic
59C4⋊#92418C2×C411yescharacteristic
60#14519706—21no—
61#14519706—21no—
62C22⋊#92418—21no—
63#14519689—21no—
64#14519687—21no—
65#14519687—21no—
66C4×#92418C2×C411yescharacteristic
67C8×Dic61—21no—
68C8×Dic61D411yescharacteristic
69C8×Dic61D411yescharacteristic
70C2×M16×C61—21no—
71C4×D4×C61C2×C411yescharacteristic
72C4⋊C8×C61C2×C411yescharacteristic
73C22⋊C8×C61—21no—
74C4×C8×C61C2×C411yescharacteristic
75C22×#6923—22no—
76C2×D4×C61C4211yescharacteristic
77C22×C4×C61—21no—
78C2×C22⋊D61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81#11758224—22no—
82#11758224—22no—
83C2×C4×D61C22×C411yescharacteristic
84C2×C4×D61C2×D411yescharacteristic
85C2×C4×D61#4111yescharacteristic
86C2×Dic122C4211yescharacteristic
87C2×#92420—22no—
88C2×#92420—22no—
89C2×#92420—22no—
90C4×#6923—22no—
91C4×#6923—22no—
92C4×#6923—24no—
93C4×#6923—22no—
94C4×#6923M1614yescomplemented
95#11758213—22no—
96#11758213—22no—
97D61⋊C8—22no—
98D61⋊C8—22no—
99M16×C61—42no—
100C2×C8×C61—21no—
101C2×C8×C61C22⋊C411yescharacteristic
102C2×C8×C61C22⋊C411yescharacteristic
103C4⋊C4×C61C4211yescharacteristic
104C22⋊C4×C61—21no—
105C42×C61C22×C411yescharacteristic
106C22⋊Dic61—21no—
107#11758198—21no—
108C4⋊Dic61C4211yescharacteristic
109#11758196—21no—
110#11758196—21no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61C22×C411yescharacteristic
115C4×Dic61C2×D411yescharacteristic
116C4×Dic61#4111yescharacteristic
117#11758194—42no—
118C2×#92418—21no—
119C2×#92418C22⋊C411yescharacteristic
120C2×#92418C22⋊C411yescharacteristic
121C8×D61—22no—
122C8×D61—22no—
123C23×C61—21no—
124C22×D61C4×D411yescharacteristic
125C2×#6923—24no—
126C2×#6923—24no—
127C2×#6923—24no—
128D4×C61—21no—
129D4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61C2×C4211yescharacteristic
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61#11711yescharacteristic
136C22⋊D61—42no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61C4×D411yescharacteristic
142C2×Dic61C4×D411yescharacteristic
143C2×Dic61C4×D411yescharacteristic
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—22no—
147C4×D61C2×M1612yes—
148C4×D61#13112yes—
149Dic122—21no—
150Dic122—21no—
151#92420—24no—
152#92420—42no—
153#92420—42no—
154C8×C61—21no—
155C8×C61—41no—
156C8×C61#10412yescomplemented
157#92418—21no—
158#92418—41no—
159#92418#10412yescomplemented
160#8194—611nomaximal, Sylow
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C4×C22⋊C411yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61#43512yes—
168#6923—28no—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61C4×M1611yescharacteristic
172C4×C61#40511yescharacteristic
173C4×C61C2×#10411yescharacteristic
174C4×C61C2×#10411yescharacteristic
175Dic61—21no—
176Dic61—41no—
177Dic61—41no—
178Dic61#43612yes—
179Dic61#44312yes—
180#2965—611no—
181C4×#104—611no—
182C42×C8—611no—
183#1476—611no—
184#1451—611no—
185#1278—611no—
186#1276—611no—
187C2×C61—81no—
188C2×C61#175311yescharacteristic
189C2×C61C4×#10411yescharacteristic
190C2×C61#176411yescharacteristic
191D61—22no—
192C4×#41—611no—
193#446—611no—
194#446—611no—
195#436—611no—
196#436#692311yescharacteristic, complemented
197#435—1221no—
198#435—1221no—
199#431—611no—
200#431—611no—
201#431—1221no—
202C2×#104—612no—
203C4×M16—611no—
204C4×M16—1221no—
205C2×C4×C8—611no—
206C2×C4×C8—611no—
207C2×C4×C8—1221no—
208C2×C4×C8—1221no—
209C43—611no—
210#339—612no—
211Q8⋊C8—612no—
212D4⋊C8—612no—
213#322—1221no—
214#322—1221no—
215C61#819411yescharacteristic, complemented, Sylow
216C2×#41—611no—
217C2×M16—21no—
218C2×M16—612no—
219C2×M16—1221no—
220C22×C8—611no—
221C22×C8—611no—
222C22×C8—1221no—
223C4×Q8—611no—
224C4×Q8—611no—
225C4×D4—611no—
226C4×D4—1221no—
227C4×D4—1221no—
228C4×D4C2×#692311yescharacteristic
229#117—611no—
230#117—1221no—
231C2×C42—611no—
232C2×C42—612no—
233C2×C42—1221no—
234C2×C42—1221no—
235C2×C42—1221no—
236C4⋊C8—612no—
237C4⋊C8—611no—
238C4⋊C8—1221no—
239C4⋊C8—1221no—
240C4⋊C8C2×#692311yescharacteristic
241#104—1224no—
242C22⋊C8—21no—
243C22⋊C8—1221no—
244C22⋊C8—1221no—
245C22⋊C8—1221no—
246#97—1221no—
247#97—1221no—
248#97—1221no—
249C4×C8—611no—
250C4×C8—611no—
251C4×C8—612no—
252C4×C8—611no—
253C4×C8—1221no—
254C4×C8—1221no—
255C4×C8—1221no—
256C4×C8—1221no—
257C4×C8—1224no—
258C4×C8—1224no—
259C4×C8C2×#692311yescharacteristic
260#41—1222no—
261#41—1222no—
262C2×Q8—611no—
263C2×D4—1221no—
264C2×D4C4×#692311yescharacteristic
265C22×C4—21no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1222no—
272M16—42no—
273M16—1222no—
274M16—1222no—
275M16—2442no—
276C2×C8—21no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8—1222no—
280C2×C8—1222no—
281C2×C8—1222no—
282C2×C8—1222no—
283C2×C8—1222no—
284C2×C8—1222no—
285C2×C8—1222no—
286C2×C8—1221no—
287C2×C8C22⋊#692311yescharacteristic
288C2×C8C22⋊#692311yescharacteristic
289C4⋊C4—611no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4C4×#692311yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C42—611no—
297C42—611no—
298C42—611no—
299C42—614no—
300C42—1221no—
301C42—1221no—
302C42—1222no—
303C42—1222no—
304C42—1222no—
305C42—1224no—
306C42—1221no—
307C42C22×#692311yescharacteristic
308C23—21no—
309C23—611no—
310Q8—1221no—
311Q8—1221no—
312D4—21no—
313D4—21no—
314D4—2442no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—612no—
321C2×C4—612no—
322C2×C4—611no—
323C2×C4—1222no—
324C2×C4—1224no—
325C2×C4—1224no—
326C2×C4—1224no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4C2×C4×#692311yescharacteristic
334C2×C4C2×C22⋊#692311yescharacteristic
335C2×C4#1451985611yescharacteristic
336C8—21no—
337C8—41no—
338C8—612no—
339C8—1224no—
340C8—1221no—
341C8—2442no—
342C8—2442no—
343C8—2441no—
344C8#1451984112yescomplemented
345C22—41no—
346C22—41no—
347C22—41no—
348C22—612no—
349C22—1221no—
350C22—1221no—
351C22C4×C22⋊#692311yescharacteristic
352C4—21no—
353C4—41no—
354C4—612no—
355C4—612no—
356C4—1228no—
357C4—1221no—
358C4—2441no—
359C4—2441no—
360C4M16×#692311yescharacteristic
361C4#1684072811yescharacteristic
362C4C2×#1451984111yescharacteristic
363C4D61⋊#10411yescharacteristic
364C2—81no—
365C2—1222no—
366C2#2146155911yescharacteristic
367C2C4×#1451984111yescharacteristic
368C2#2146159311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61C4×C22⋊C4
prime radicalC2×#11758224C2×C4
cosocleC42×D61C23
hypercenter#436#6923
hypocenterC61#8194
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
2. C4×C8×#6923C2semidirect
4. #21461029C2semidirect
5. #21460650C2semidirect
6. #21460646C2semidirect
16. #16840612C4semidirect
17. D4⋊#92420C4semidirect
21. #16839892C4semidirect
22. #16839889C4semidirect
23. #16839840C4semidirect
30. C61×#436C4semidirect
94. C4×#6923M16semidirect
156. C8×C61#104semidirect
159. #92418#104semidirect
196. #436#6923semidirect
215. C61#8194semidirect
344. C8#14519841semidirect

Maximal subgroups

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

subgroupindex
C4×#145198412
C4×C8×#69232
#214611112
#214610292
#214606502
#214606462
#214547822
#819461