Finite Group Databasebeta

← #29589877

Subgroups — #29589877

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#21454797C211yesmaximal, characteristic
2#21447621C211yesmaximal, characteristic, complemented
3#21447412C211yesmaximal, characteristic, complemented
4#21443802C211yesmaximal, characteristic, complemented
5#21443800C211yesmaximal, characteristic, complemented
6#21443777C211yesmaximal, characteristic, complemented
7C61×#1330C211yesmaximal, characteristic, complemented
8#16840294C411yescharacteristic
9C2×#14519716—21no—
10#16839892C2211yescharacteristic
11#16839886C411yescharacteristic
12#16839831—21no—
13D4×#92418C411yescharacteristic
14#16839825—21no—
15#16839820—21no—
16#16839818C411yescharacteristic
17#16839720—21no—
18C4×C8×D61C2211yescharacteristic
19C4⋊#11758185C2211yescharacteristic
20#16839541—21no—
21#16839538C2211yescharacteristic
22#16839537—21no—
23C16×Dic61—21no—
24C61×#436C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#346C2211yescharacteristic
27C22×#92418—21no—
28C2×C8×D61D411yescharacteristic
29C2×C8×D61D411yescharacteristic
30#14519770—21no—
31#14519768C811yescharacteristic
32#14519764C811yescharacteristic
33#14519759—21no—
34#14519757C811yescharacteristic
35#14519748C811yescharacteristic
36C4×Dic122C2×C411yescharacteristic
37C4×C22⋊D61—21no—
38#14519736—21no—
39C42×D61C2×C411yescharacteristic
40#14519716—24no—
41C2×#11758185—21no—
42C2×#11758185—21no—
43C4⋊#92418C2×C411yescharacteristic
44#14519706—21no—
45#14519706—21no—
46C22⋊#92418—21no—
47#14519689—21no—
48#14519687—21no—
49#14519687—21no—
50C4×#92418C2×C411yescharacteristic
51C8×Dic61—21no—
52C8×Dic61D411yescharacteristic
53C8×Dic61D411yescharacteristic
54C2×M16×C61—21no—
55C4×D4×C61C2×C411yescharacteristic
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58C4⋊C8×C61C2×C411yescharacteristic
59C22⋊C8×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×D4×C61C2×C811yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C2×C4×D61C22⋊C411yescharacteristic
65C2×C4×D61C2×C811yescharacteristic
66C2×C4×D61M1611yescharacteristic
67C2×Dic122C2×C811yescharacteristic
68M16×C61—41no—
69M16×C61—41no—
70C2×C8×C61—21no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61C2×C811yescharacteristic
74C22⋊C4×C61—21no—
75C42×C61C22×C411yescharacteristic
76C22⋊Dic61—21no—
77C22⋊Dic61—21no—
78C22⋊Dic61—21no—
79#11758198—21no—
80C4⋊Dic61—21no—
81C4⋊Dic61—21no—
82C4⋊Dic61C2×C811yescharacteristic
83#11758196—21no—
84#11758196—21no—
85C4×Dic61—21no—
86C4×Dic61C22⋊C411yescharacteristic
87C4×Dic61C2×C811yescharacteristic
88C4×Dic61M1611yescharacteristic
89C2×#92418—21no—
90C2×#92418—42no—
91C2×#92418C22⋊C411yescharacteristic
92C2×#92418C22⋊C411yescharacteristic
93C8×D61—21no—
94C8×D61—21no—
95C8×D61—22no—
96C16×C61—22no—
97C16×C61—41no—
98#11758185—22no—
99#11758185—41no—
100C23×C61—21no—
101C22×D61C22⋊C811yescharacteristic
102D4×C61—41no—
103C2×C4×C61—21no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61C2×C22⋊C411yescharacteristic
107C2×C4×C61C22×C811yescharacteristic
108C2×C4×C61C2×M1611yescharacteristic
109C22⋊D61—42no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61C22⋊C811yescharacteristic
113C2×Dic61C22⋊C811yescharacteristic
114C2×Dic61C22⋊C811yescharacteristic
115C4×D61—21no—
116C4×D61—21no—
117C4×D61—41no—
118C4×D61—41no—
119Dic122—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×C61—41no—
129C22×C61—41no—
130C22×C61—41no—
131C22×C61C2×C22⋊C811yescharacteristic
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—21no—
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—41no—
138C4×C61#41611yescharacteristic
139C4×C61C2×#10411yescharacteristic
140Dic61—21no—
141Dic61—21no—
142Dic61—21no—
143Dic61—41no—
144Dic61—41no—
145#2966—611no—
146#2163—611no—
147C4×M32—611no—
148#1338—611no—
149#1338—611no—
150#1330—611no—
151#1330D6111yescharacteristic, complemented
152C2×C61—81no—
153C2×C61#147611yescharacteristic
154C2×C61#211511yescharacteristic
155C2×C61#211711yescharacteristic
156D61—41no—
157#529—611no—
158C2×M32—1221no—
159#446—611no—
160C8×Q8—611no—
161#436C2×D6111yescharacteristic
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—21no—
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×Q8—611no—
188C4×D4—1221no—
189C4×D4C4×D6111yescharacteristic
190#117—1221no—
191C2×C42—611no—
192M32—1224no—
193C2×C16—21no—
194C2×C16—21no—
195C2×C16—1221no—
196C2×C16—1221no—
197C4⋊C8—611no—
198C4⋊C8—1221no—
199C4⋊C8—1221no—
200C4⋊C8C4×D6111yescharacteristic
201C22⋊C8—21no—
202C22⋊C8—1221no—
203C22⋊C8—1221no—
204#97—1221no—
205#97—1221no—
206C4×C8—611no—
207C4×C8—611no—
208C4×C8—611no—
209C4×C8—1221no—
210C4×C8C22×D6111yescharacteristic
211C2×Q8—611no—
212C2×D4—1221no—
213C2×D4C8×D6111yescharacteristic
214C22×C4—21no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—611no—
218M16—41no—
219M16—41no—
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—611no—
231C4⋊C4—1221no—
232C4⋊C4—1221no—
233C4⋊C4—1221no—
234C4⋊C4—1221no—
235C4⋊C4C8×D6111yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—1221no—
238C22⋊C4—1221no—
239C22⋊C4—1221no—
240C22⋊C4—1221no—
241C42—611no—
242C42—611no—
243C42—611no—
244C42—1221no—
245C42C2×C4×D6111yescharacteristic
246C16—22no—
247C16—41no—
248C16—1222no—
249C16—2441no—
250C23—21no—
251C23—611no—
252Q8—2441no—
253D4—41no—
254D4—2442no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—611no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
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#1451979611yescharacteristic
276C8#1451979811yescharacteristic
277C22—41no—
278C22—41no—
279C22—41no—
280C22—1221no—
281C22—1221no—
282C22—1221no—
283C22C22⋊C8×D6111yescharacteristic
284C4—21no—
285C4—21no—
286C4—41no—
287C4—1221no—
288C4—1221no—
289C4—1221no—
290C4—2441no—
291C4—2441no—
292C4#1683975511yescharacteristic
293C4#104×D6111yescharacteristic
294C2—81no—
295C2—2441no—
296C2#2144419811yescharacteristic
297C2#2144743811yescharacteristic
298C2#2144744511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC4×C8C22×D61
FittingC61×#1330C2
socleC22×C61C2×C22⋊C8
prime radical#14519748C8
cosocleC4×C8×C61C23
hypercenter#1330D61
hypocenterC61#11620
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #21447621C2semidirect
3. #21447412C2semidirect
4. #21443802C2semidirect
5. #21443800C2semidirect
6. #21443777C2semidirect
7. C61×#1330C2semidirect
151. #1330D61semidirect
176. C61#11620semidirect

Maximal subgroups

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

subgroupindex
#214547972
#214476212
#214474122
#214438022
#214438002
#214437772
C61×#13302
#1162061