Finite Group Databasebeta

← #29575430

Subgroups — #29575430

Order 15616.

480 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454899C211yesmaximal, characteristic
2C2×#16839870C211yesmaximal, characteristic
3#21444215C211yesmaximal, characteristic
4#21444213C211yesmaximal, characteristic
5#21444142C211yesmaximal, characteristic
6#21443650C211yesmaximal, characteristic
7C61×#1281C211yesmaximal, characteristic
8C22×Dic244C411yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11C8×Dic122—22no—
12#16839886—22no—
13#16839870—22no—
14#16839870—22no—
15#16839815C2211yescharacteristic
16#16839815C2211yescharacteristic
17#16839812—22no—
18C2×#14519709C411yescharacteristic
19C2×#14519702C411yescharacteristic
20C2×#14519702C411yescharacteristic
21#16839494—22no—
22#16839492—22no—
23#16839487—22no—
24C61×#431C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C2×#97×C61C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×Dic122C2×C411yescharacteristic
29C2×Dic244—22no—
30C2×Dic244—22no—
31C2×Dic244C814yescomplemented
32C4×Dic122—21no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122D412yes—
39C4×Dic122D412yes—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46#14519709—22no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49#14519706—24no—
50#14519702—22no—
51#14519702—22no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C4×#92418—21no—
55C4×#92418D412yes—
56C8×Dic61—24no—
57C22×C8×C61C2×C411yescharacteristic
58C22×C8×C61C2×C411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61D412yes—
64#97×C61—21no—
65#97×C61—21no—
66C4×C8×C61—21no—
67C4×C8×C61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61#4111yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C2×Dic122—21no—
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×Dic122—21no—
79C2×Dic122—21no—
80C2×Dic122—21no—
81C2×Dic122—21no—
82C2×Dic122—21no—
83C2×Dic122C22⋊C412yes—
84C2×Dic122C2×C812yes—
85C2×Dic122C2×C812yes—
86C2×Dic122M1612yes—
87C2×C8×C61—21no—
88C2×C8×C61—21no—
89C2×C8×C61—21no—
90C2×C8×C61—22no—
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C2×C8×C61—41no—
94C2×C8×C61C2×C812yes—
95C42×C61C2×D411yescharacteristic
96C42×C61C2×D411yescharacteristic
97C42×C61C2×D411yescharacteristic
98C42×C61#4111yescharacteristic
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61C22⋊C412yes—
103#11758196—22no—
104#11758196—22no—
105#11758196—41no—
106#11758196—41no—
107C4×Dic61—22no—
108C4×Dic61—22no—
109C4×Dic61—41no—
110C4×Dic61—41no—
111C2×#92418—22no—
112C2×#92418—41no—
113Dic244—28no—
114C23×C61C4×D411yescharacteristic
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61C2×C22⋊C411yescharacteristic
118C2×C4×C61C4×D411yescharacteristic
119C2×C4×C61#12011yescharacteristic
120C2×C4×C61#12111yescharacteristic
121C2×C4×C61#12111yescharacteristic
122C2×C4×C61#12311yescharacteristic
123C2×C4×C61C22×C811yescharacteristic
124C2×C4×C61C2×M1611yescharacteristic
125C2×C4×C61#13111yescharacteristic
126C2×C4×C61#13111yescharacteristic
127C2×Dic61—22no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—22no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137Dic122—22no—
138Dic122—22no—
139Dic122—22no—
140Dic122—22no—
141Dic122—22no—
142Dic122—41no—
143Dic122—41no—
144Dic122C22⋊C814yes—
145C8×C61—22no—
146C8×C61—42no—
147C8×C61—41no—
148C8×C61—81no—
149#92418—42no—
150#92418—81no—
151#9088—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61#38611yescharacteristic
155C22×C61C8×D411yescharacteristic
156C22×C61#43511yescharacteristic
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61C2×C22⋊C811yescharacteristic
162C4×C61#40811yescharacteristic
163C4×C61C8×D411yescharacteristic
164C4×C61#43511yescharacteristic
165Dic61—24no—
166Dic61—42no—
167Dic61—42no—
168Dic61—81no—
169#2982—611no—
170C2×#441—611no—
171#1479—611no—
172#1479—611no—
173#1461—611no—
174#1281D6111yescharacteristic
175#1275—611no—
176C2×C61—21no—
177C2×C61—21no—
178C2×C61#186911yescharacteristic
179C2×C61#190211yescharacteristic
180C2×C61#190511yescharacteristic
181C22×Q16—611no—
182C2×C4×Q8—611no—
183C2×C4×Q8—611no—
184C8×Q8—1222no—
185C8×Q8—1222no—
186#441—1222no—
187#441—1222no—
188#431—611no—
189#431—611no—
190#431—1222no—
191#431C2×D6111yescharacteristic
192#431C2×D6111yescharacteristic
193C2×#106—611no—
194C2×#103—611no—
195C2×#103—611no—
196C2×#97C2×D6111yescharacteristic
197Q8⋊C8—1222no—
198Q8⋊C8—1222no—
199#324—1222no—
200C61#908811yescharacteristic, complemented, Sylow
201C22×Q8—611no—
202C22×Q8—611no—
203C2×Q16—614no—
204C2×Q16—1222no—
205C2×Q16—1222no—
206C22×C8C4×D6111yescharacteristic
207C22×C8C4×D6111yescharacteristic
208C4×Q8—612no—
209C4×Q8—612no—
210C4×Q8—1221no—
211C4×Q8—1221no—
212C4×Q8—1221no—
213C4×Q8—1221no—
214C4×Q8—1221no—
215C4×Q8—1221no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C42—1221no—
221C2×C42—1221no—
222C2×C42C22×D6111yescharacteristic
223#106—1222no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—1224no—
227C4⋊C8—1221no—
228C4⋊C8—1221no—
229#103—1222no—
230#103—1222no—
231C22⋊C8—21no—
232C22⋊C8—1221no—
233C22⋊C8—1221no—
234C22⋊C8D24412yes—
235#97—21no—
236#97—21no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8—612no—
240C4×C8—1224no—
241C4×C8—1221no—
242C2×Q8—612no—
243C2×Q8—612no—
244C2×Q8—612no—
245C2×Q8—612no—
246C2×Q8—1221no—
247C2×Q8—1221no—
248C2×Q8—1221no—
249C2×Q8—1221no—
250C2×Q8—1221no—
251C2×Q8—1221no—
252C2×Q8—1221no—
253C2×Q8—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4C2×C4×D6111yescharacteristic
259C22×C4C2×D24411yescharacteristic
260C22×C4#1175822211yescharacteristic
261Q16—1228no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—22no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—41no—
269C2×C8—1222no—
270C2×C8—2441no—
271C2×C8C8×D6112yes—
272C4⋊C4—612no—
273C4⋊C4—1221no—
274C4⋊C4—1222no—
275C4⋊C4—1222no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C42—1222no—
281C42—1222no—
282C42—2441no—
283C42—2441no—
284C42D4×D6111yescharacteristic
285C42D4×D6111yescharacteristic
286C42D4×D6111yescharacteristic
287C42#1175822611yescharacteristic
288C23C4×D24411yescharacteristic
289Q8—614no—
290Q8—1222no—
291Q8—1222no—
292Q8—1222no—
293Q8—1222no—
294Q8—1222no—
295Q8—2441no—
296Q8—2441no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—1222no—
300C2×C4—1222no—
301C2×C4—1222no—
302C2×C4—1222no—
303C2×C4—1222no—
304C2×C4—4881no—
305C2×C4—4881no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4C22⋊C4×D6111yescharacteristic
310C2×C4#1451973911yescharacteristic
311C2×C4#1451974711yescharacteristic
312C2×C4#1451975011yescharacteristic
313C2×C4#1451975211yescharacteristic
314C2×C4#1451976211yescharacteristic
315C2×C4C2×C8×D6111yescharacteristic
316C2×C4M16×D6111yescharacteristic
317C2×C4#1451978311yescharacteristic
318C2×C4#1451978511yescharacteristic
319C8—22no—
320C8—42no—
321C8—41no—
322C8—81no—
323C8—4881no—
324C8—2442no—
325C22—21no—
326C22—21no—
327C22#1683964011yescharacteristic
328C22C8×D24411yescharacteristic
329C22#1683983511yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—1224no—
335C4—4881no—
336C4—2442no—
337C4—2442no—
338C4C22⋊C8×D6111yescharacteristic
339C4#1683972711yescharacteristic
340C4#1683982711yescharacteristic
341C4#1683983211yescharacteristic
342C2—21no—
343C2—21no—
344C2#2144611011yescharacteristic
345C2#2144629111yescharacteristic
346C2#2144631211yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1281C2
socleC22×C61#386
prime radicalC23×C61C4×D4
cosocleC2×C42×C61C23
hypercenter#1281D61
hypocenterC61#9088
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
31. C2×Dic244C8semidirect
200. C61#9088semidirect

Maximal subgroups

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

subgroupindex
#214548992
C2×#168398702
#214442152
#214442132
#214441422
#214436502
C61×#12812
#908861