Finite Group Databasebeta

← #29589889

Subgroups — #29589889

Order 15616.

320 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454796C211yesmaximal, characteristic
2#21447616C211yesmaximal, characteristic, complemented
3C4⋊C16×D61C211yesmaximal, characteristic, complemented
4Q8⋊#11758185C211yesmaximal, characteristic, complemented
5#21443775C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic, complemented
7C61×Q8⋊C16C211yesmaximal, characteristic, complemented
8#16840299C411yescharacteristic
9C2×C16×D61—21no—
10#16839893C411yescharacteristic
11#16839839C411yescharacteristic
12#16839832—21no—
13C8×D244—21no—
14C8×D244C2211yescharacteristic
15#16839822—21no—
16#16839818C411yescharacteristic
17#16839716—21no—
18C4×C8×D61C2211yescharacteristic
19C4⋊#11758185C2211yescharacteristic
20#16839580—21no—
21#16839580—21no—
22#16839541—21no—
23C4×#11758185C2211yescharacteristic
24C8×Q8×C61C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C4×C16×C61C2211yescharacteristic
27C2×#11758189—21no—
28C2×C8×D61—21no—
29C2×C8×D61D411yescharacteristic
30C2×C8×D61D411yescharacteristic
31#14519772—21no—
32#14519768C811yescharacteristic
33#14519766C811yescharacteristic
34#14519762—21no—
35#14519753C811yescharacteristic
36#14519752C811yescharacteristic
37C4×D244—21no—
38C4×D244C2×C411yescharacteristic
39#14519734—21no—
40C42×D61C2×C411yescharacteristic
41C2×#11758185—21no—
42C2×#11758185—21no—
43C16×D61—42no—
44C4⋊#92418—21no—
45C4⋊#92418C2×C411yescharacteristic
46#14519689—21no—
47#14519689—21no—
48#14519689—21no—
49#14519688—21no—
50#14519687—21no—
51C4×#92418C2×C411yescharacteristic
52C8×Dic61D411yescharacteristic
53C8×Dic61D411yescharacteristic
54C4×Q8×C61C2×C411yescharacteristic
55C2×C16×C61—21no—
56C2×C16×C61—21no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61C2×C411yescharacteristic
59C4×C8×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×Q8×C61C2×C811yescharacteristic
62C2×D244—21no—
63C2×D244C2×C811yescharacteristic
64C2×C4×D61—21no—
65C2×C4×D61C22⋊C411yescharacteristic
66C2×C4×D61C2×C811yescharacteristic
67C2×C4×D61M1611yescharacteristic
68C2×C8×C61—21no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61C2×C811yescharacteristic
73C42×C61—21no—
74C42×C61C22×C411yescharacteristic
75#11758198—21no—
76#11758198—21no—
77#11758198—21no—
78#11758198—21no—
79#11758198—21no—
80C4⋊Dic61—21no—
81C4⋊Dic61C2×C811yescharacteristic
82#11758196—21no—
83#11758196—21no—
84C4×Dic61C22⋊C411yescharacteristic
85C4×Dic61C2×C811yescharacteristic
86C4×Dic61M1611yescharacteristic
87C2×#92418—21no—
88C2×#92418C22⋊C411yescharacteristic
89C2×#92418C22⋊C411yescharacteristic
90#11758189—42no—
91C8×D61—21no—
92C8×D61—21no—
93C8×D61—41no—
94C8×D61—41no—
95C8×D61—41no—
96C16×C61—41no—
97C16×C61—41no—
98#11758185—41no—
99#11758185—41no—
100C22×D61—21no—
101C22×D61C22⋊C811yescharacteristic
102Q8×C61—21no—
103Q8×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61C22×C811yescharacteristic
108C2×C4×C61C2×M1611yescharacteristic
109C2×Dic61—21no—
110C2×Dic61C22⋊C811yescharacteristic
111C2×Dic61C22⋊C811yescharacteristic
112C2×Dic61C22⋊C811yescharacteristic
113D244—21no—
114D244—21no—
115D244—42no—
116C4×D61—22no—
117C4×D61—21no—
118C4×D61—21no—
119C4×D61—21no—
120C4×D61—21no—
121C4×D61—41no—
122C4×D61—41no—
123C8×C61—21no—
124C8×C61—41no—
125C8×C61AGL(1,ℤ/8)11yescharacteristic
126C8×C61#13711yescharacteristic
127#92418—21no—
128#92418—21no—
129#92418—41no—
130#11622—611nomaximal, Sylow
131C22×C61C2×C22⋊C811yescharacteristic
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—41no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61#35012yes—
138C4×C61—21no—
139C4×C61—41no—
140C4×C61—41no—
141C4×C61#41711yescharacteristic
142C4×C61#42111yescharacteristic
143C4×C61#50411yescharacteristic
144C4×C61#50411yescharacteristic
145Dic61—21no—
146Dic61—21no—
147Dic61—21no—
148Dic61—41no—
149#2966—611no—
150#2162—611no—
151C2×C4⋊C16—611no—
152Q8⋊C16—611no—
153Q8⋊C16D6111yescharacteristic, complemented
154D4⋊C16—611no—
155D4⋊C16—611no—
156C2×C61#147711yescharacteristic
157C2×C61#211311yescharacteristic
158C2×C61C2×#35011yescharacteristic
159D61—22no—
160D61—81no—
161#529—611no—
162C22×C16—1221no—
163#446—611no—
164C8×Q8C2×D6111yescharacteristic
165#436—611no—
166#435—1221no—
167C8×D4—611no—
168C8×D4—1221no—
169#433—1221no—
170#432—611no—
171#405—1221no—
172C2×C4×C8—611no—
173C4⋊C16—611no—
174C4⋊C16—1221no—
175C4⋊C16—1221no—
176C4⋊C16C2×D6111yescharacteristic
177C22⋊C16—1221no—
178C4×C16—611no—
179C4×C16C2×D6111yescharacteristic
180C61#1162211yescharacteristic, complemented, Sylow
181C2×M16—1221no—
182C22×C8—611no—
183C22×C8—611no—
184C22×C8—1221no—
185#126—1221no—
186#125—611no—
187#124—611no—
188#123—1221no—
189C22⋊Q8—611no—
190#121—611no—
191C4×Q8C4×D6111yescharacteristic
192C4×D4—611no—
193C4×D4—1221no—
194#117—1221no—
195C2×C42—611no—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16—1221no—
199C2×C16—1221no—
200C2×C16—2442no—
201C4⋊C8—21no—
202C4⋊C8—611no—
203C4⋊C8—1221no—
204C4⋊C8C4×D6111yescharacteristic
205C22⋊C8—1221no—
206C22⋊C8—1221no—
207C22⋊C8—1221no—
208#97—1221no—
209#97—1221no—
210C4×C8—21no—
211C4×C8—611no—
212C4×C8—611no—
213C4×C8—611no—
214C4×C8C22×D6111yescharacteristic
215C2×Q8C8×D6111yescharacteristic
216C2×D4—611no—
217C2×D4—1221no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—1221no—
222M16—2442no—
223C2×C8—21no—
224C2×C8—611no—
225C2×C8—611no—
226C2×C8—1221no—
227C2×C8—1221no—
228C2×C8—1221no—
229C2×C8—2441no—
230C2×C8—2441no—
231C2×C8—2441no—
232C2×C8D4×D6111yescharacteristic
233C2×C8D4×D6111yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—611no—
236C4⋊C4—1221no—
237C4⋊C4—1221no—
238C4⋊C4—1221no—
239C4⋊C4C8×D6111yescharacteristic
240C22⋊C4—1221no—
241C22⋊C4—1221no—
242C22⋊C4—1221no—
243C22⋊C4—1221no—
244C22⋊C4—1221no—
245C42—21no—
246C42—611no—
247C42—611no—
248C42—611no—
249C42C2×C4×D6111yescharacteristic
250C16—41no—
251C16—41no—
252C16—2441no—
253C16—2441no—
254C23—611no—
255C23—1221no—
256Q8—21no—
257Q8—21no—
258D4—1221no—
259D4—1221no—
260D4—2442no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—611no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—1222no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4C22⋊C4×D6111yescharacteristic
275C2×C4C2×C8×D6111yescharacteristic
276C2×C4M16×D6111yescharacteristic
277C8—21no—
278C8—41no—
279C8—1221no—
280C8—1221no—
281C8—2441no—
282C8#1451980411yescharacteristic
283C8#1451980911yescharacteristic
284C22—612no—
285C22—1221no—
286C22—1221no—
287C22—2441no—
288C22—2441no—
289C22—2441no—
290C22C22⋊C8×D6111yescharacteristic
291C4—21no—
292C4—41no—
293C4—41no—
294C4—1221no—
295C4—1221no—
296C4—1221no—
297C4—2441no—
298C4#1683976211yescharacteristic
299C4#1683977711yescharacteristic
300C4#1684017811yescharacteristic
301C4#1684018011yescharacteristic
302C2—1222no—
303C2—4881no—
304C2#2144420511yescharacteristic
305C2#2144743111yescharacteristic
306C2#350×D6111yescharacteristic
subgroupG/H
centerC2×C8D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC4×C8C22×D61
FittingC61×Q8⋊C16C2
socleC22×C61C2×C22⋊C8
prime radical#14519752C8
cosocleC4×C8×C61C23
hypercenterQ8⋊C16D61
hypocenterC61#11622
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
2. #21447616C2semidirect
3. C4⋊C16×D61C2semidirect
4. Q8⋊#11758185C2semidirect
5. #21443775C2semidirect
6. #21443773C2semidirect
7. C61×Q8⋊C16C2semidirect
153. Q8⋊C16D61semidirect
180. C61#11622semidirect

Maximal subgroups

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

subgroupindex
#214547962
#214476162
C4⋊C16×D612
Q8⋊#117581852
#214437752
#214437732
C61×Q8⋊C162
#1162261