Finite Group Databasebeta

← #29589879

Subgroups — #29589879

Order 15616.

318 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 91 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#21454793C211yesmaximal, characteristic
2#21447621C211yesmaximal, characteristic, complemented
3#21447412C211yesmaximal, characteristic, complemented
4#21443801C211yesmaximal, characteristic, complemented
5#21443778C211yesmaximal, characteristic, complemented
6#21443776C211yesmaximal, characteristic, complemented
7C61×#1338C211yesmaximal, characteristic, complemented
8#16840299C411yescharacteristic
9C2×#14519716—21no—
10Q8×#92418C411yescharacteristic
11#16839841C2211yescharacteristic
12#16839835—21no—
13#16839827—21no—
14#16839827C411yescharacteristic
15#16839822—21no—
16#16839818C411yescharacteristic
17#16839719—21no—
18C4×C8×D61C2211yescharacteristic
19C4⋊#11758185C2211yescharacteristic
20#16839541—21no—
21#16839538C2211yescharacteristic
22#16839537—21no—
23C16×Dic61—21no—
24C61×#446C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#346C2211yescharacteristic
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
41#14519716—24no—
42C2×#11758185—21no—
43C2×#11758185—21no—
44C4⋊#92418—21no—
45C4⋊#92418C2×C411yescharacteristic
46#14519689—21no—
47#14519689—21no—
48#14519689—21no—
49#14519687—21no—
50C4×#92418—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
59#97×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—41no—
91#11758189—41no—
92C8×D61—21no—
93C8×D61—21no—
94C8×D61—22no—
95C8×D61—42no—
96C16×C61—22no—
97C16×C61—41no—
98#11758185—22no—
99#11758185—41no—
100C22×D61—21no—
101C22×D61C22⋊C811yescharacteristic
102Q8×C61—41no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61C2×C22⋊C411yescharacteristic
106C2×C4×C61C22×C811yescharacteristic
107C2×C4×C61C2×M1611yescharacteristic
108C2×Dic61—21no—
109C2×Dic61C22⋊C811yescharacteristic
110C2×Dic61C22⋊C811yescharacteristic
111C2×Dic61C22⋊C811yescharacteristic
112D244—41no—
113D244—42no—
114C4×D61—21no—
115C4×D61—21no—
116C4×D61—41no—
117C4×D61—41no—
118C4×D61—41no—
119C4×D61—41no—
120C8×C61—21no—
121C8×C61—41no—
122C8×C61#13511yescharacteristic
123C8×C61#13511yescharacteristic
124#92418—21no—
125#92418—41no—
126#92418#10412yes—
127#11620—611nomaximal, Sylow
128C22×C61C2×C22⋊C811yescharacteristic
129C2×D61—21no—
130C2×D61—21no—
131C2×D61—21no—
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—41no—
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—41no—
138C4×C61—41no—
139C4×C61#41611yescharacteristic
140C4×C61C2×#10411yescharacteristic
141Dic61—21no—
142Dic61—21no—
143Dic61—21no—
144Dic61—41no—
145#2966—611no—
146#2163—611no—
147C4×M32—611no—
148#1338—611no—
149#1338D6111yescharacteristic, complemented
150#1330—611no—
151#1330—611no—
152C2×C61#147611yescharacteristic
153C2×C61#211511yescharacteristic
154C2×C61#211711yescharacteristic
155D61—41no—
156D61—81no—
157#529—611no—
158C2×M32—1221no—
159#446C2×D6111yescharacteristic
160C8×Q8—611no—
161#436—611no—
162#435—1221no—
163C8×D4—611no—
164C8×D4—1221no—
165#433—1221no—
166#432—611no—
167#405—1221no—
168C2×C4×C8—611no—
169C4⋊C16—611no—
170C4⋊C16C2×D6111yescharacteristic
171C22⋊C16—1221no—
172#346—611no—
173#346—1221no—
174#346C2×D6111yescharacteristic
175C4×C16—1221no—
176C61#1162011yescharacteristic, complemented, Sylow
177C2×M16—1221no—
178C22×C8—611no—
179C22×C8—611no—
180C22×C8—1221no—
181#126—1221no—
182#125—611no—
183#124—611no—
184#123—1221no—
185C22⋊Q8—611no—
186#121—611no—
187C4×Q8C4×D6111yescharacteristic
188C4×D4—611no—
189C4×D4—1221no—
190#117—1221no—
191C2×C42—611no—
192M32—1224no—
193C2×C16—21no—
194C2×C16—21no—
195C2×C16—1221no—
196C2×C16—1221no—
197C4⋊C8—21no—
198C4⋊C8—611no—
199C4⋊C8—1221no—
200C4⋊C8C4×D6111yescharacteristic
201C22⋊C8—1221no—
202C22⋊C8—1221no—
203C22⋊C8—1221no—
204#97—21no—
205#97—1221no—
206C4×C8—611no—
207C4×C8—611no—
208C4×C8—611no—
209C4×C8—1221no—
210C4×C8C22×D6111yescharacteristic
211C2×Q8C8×D6111yescharacteristic
212C2×D4—611no—
213C2×D4—1221no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—1221no—
218M16—2441no—
219M16—2441no—
220C2×C8—21no—
221C2×C8—611no—
222C2×C8—611no—
223C2×C8—1222no—
224C2×C8—1221no—
225C2×C8—1221no—
226C2×C8—1221no—
227C2×C8—2442no—
228C2×C8D4×D6111yescharacteristic
229C2×C8D4×D6111yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—611no—
232C4⋊C4—1221no—
233C4⋊C4—1221no—
234C4⋊C4—1221no—
235C4⋊C4C8×D6111yescharacteristic
236C22⋊C4—1221no—
237C22⋊C4—1221no—
238C22⋊C4—1221no—
239C22⋊C4—1221no—
240C22⋊C4—1221no—
241C42—21no—
242C42—611no—
243C42—611no—
244C42—611no—
245C42C2×C4×D6111yescharacteristic
246C16—22no—
247C16—41no—
248C16—1222no—
249C16—2441no—
250C23—611no—
251C23—1221no—
252Q8—41no—
253D4—2441no—
254D4—2442no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—611no—
258C2×C4—611no—
259C2×C4—611no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4C22⋊C4×D6111yescharacteristic
268C2×C4C2×C8×D6111yescharacteristic
269C2×C4M16×D6111yescharacteristic
270C8—21no—
271C8—41no—
272C8—612no—
273C8—1221no—
274C8—2441no—
275C8#1451979811yescharacteristic
276C8#1451980011yescharacteristic
277C22—1221no—
278C22—1221no—
279C22—1221no—
280C22—2441no—
281C22—2441no—
282C22—2441no—
283C22C22⋊C8×D6111yescharacteristic
284C4—21no—
285C4—21no—
286C4—41no—
287C4—41no—
288C4—1221no—
289C4—1221no—
290C4—1221no—
291C4—2441no—
292C4#1683975711yescharacteristic
293C4#104×D6111yescharacteristic
294C2—4881no—
295C2—2441no—
296C2#2144420011yescharacteristic
297C2#2144743811yescharacteristic
298C2#2144744511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC4×C8C22×D61
FittingC61×#1338C2
socleC22×C61C2×C22⋊C8
prime radical#14519752C8
cosocleC4×C8×C61C23
hypercenter#1338D61
hypocenterC61#11620
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1338

Complements

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

NH ≅ G/Ntype
2. #21447621C2semidirect
3. #21447412C2semidirect
4. #21443801C2semidirect
5. #21443778C2semidirect
6. #21443776C2semidirect
7. C61×#1338C2semidirect
149. #1338D61semidirect
176. C61#11620semidirect

Maximal subgroups

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

subgroupindex
#214547932
#214476212
#214474122
#214438012
#214437782
#214437762
C61×#13382
#1162061