Finite Group Databasebeta

← #29589231

Subgroups — #29589231

Order 15616.

310 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 87 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#21454462C211yesmaximal, characteristic
2#21447619C211yesmaximal, characteristic, complemented
3#21447615C211yesmaximal, characteristic, complemented
4#21443761C211yesmaximal, characteristic, complemented
5#21443744C211yesmaximal, characteristic
6#21443744C211yesmaximal, characteristic
7C61×#1323C211yesmaximal, characteristic, complemented
8#16840230C411yescharacteristic
9#16839822—21no—
10#16839822—21no—
11#16839814—21no—
12#16839814—21no—
13#16839789C411yescharacteristic
14#16839730C411yescharacteristic
15#16839728C2211yescharacteristic
16M16×Dic61C411yescharacteristic
17C2×C8×Dic61C2211yescharacteristic
18#16839580—21no—
19#16839580—21no—
20C22⋊#11758185C2211yescharacteristic
21C22⋊#11758185C2211yescharacteristic
22#16839537—21no—
23C16×Dic61—21no—
24C61×#424C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×C22⋊C16C2211yescharacteristic
27C2×#11758222C2×C411yescharacteristic
28C2×#11758194C2×C411yescharacteristic
29C22×#92418C2×C411yescharacteristic
30#14519742C811yescharacteristic
31#14519742C811yescharacteristic
32#14519739C811yescharacteristic
33#14519739C811yescharacteristic
34#14519737—21no—
35#14519737—21no—
36#14519734—21no—
37C2×C4×Dic61C2×C411yescharacteristic
38C42×D61—21no—
39C2×#11758185—21no—
40C2×#11758185—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43#14519689—21no—
44#14519689—21no—
45#14519689—21no—
46#14519689—21no—
47#14519687—21no—
48C8×Dic61—21no—
49C8×Dic61D411yescharacteristic
50C8×Dic61D411yescharacteristic
51C8×Dic61D411yescharacteristic
52C8×Dic61D411yescharacteristic
53C2×M16×C61C2×C411yescharacteristic
54C22×C8×C61C2311yescharacteristic
55#117×C61C2×C411yescharacteristic
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C22×C4×C61C22×C411yescharacteristic
61C2×C22⋊D61—21no—
62C22×Dic61M1611yescharacteristic
63C22×Dic61M1611yescharacteristic
64#11758222—41no—
65#11758222—41no—
66C2×D244C2×C811yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×Dic122C2×C811yescharacteristic
71M16×C61—41no—
72C2×C8×C61—21no—
73C2×C8×C61—41no—
74C2×C8×C61C2×D411yescharacteristic
75C2×C8×C61C2×D411yescharacteristic
76C4⋊C4×C61C2×C811yescharacteristic
77C4⋊C4×C61C2×C811yescharacteristic
78C22⋊C4×C61—21no—
79C42×C61—21no—
80#11758198—21no—
81#11758198—21no—
82#11758196—21no—
83#11758196—21no—
84C4×Dic61—21no—
85C4×Dic61—21no—
86C4×Dic61C22⋊C411yescharacteristic
87C4×Dic61C22⋊C411yescharacteristic
88C4×Dic61C2×C811yescharacteristic
89C4×Dic61C2×C811yescharacteristic
90#11758194—41no—
91C2×#92418—21no—
92C2×#92418—41no—
93C2×#92418C22⋊C411yescharacteristic
94C2×#92418C22⋊C411yescharacteristic
95C16×C61—41no—
96C16×C61—41no—
97#11758185—41no—
98#11758185—41no—
99C23×C61C2×M1611yescharacteristic
100C22×D61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61C2×C22⋊C411yescharacteristic
106C2×C4×C61C22×C811yescharacteristic
107C22⋊D61—42no—
108C2×Dic61—22no—
109C2×Dic61—21no—
110C2×Dic61—41no—
111C2×Dic61C22⋊C811yescharacteristic
112C2×Dic61C22⋊C811yescharacteristic
113C2×Dic61C22⋊C811yescharacteristic
114C2×Dic61C22⋊C811yescharacteristic
115D244—41no—
116C4×D61—42no—
117C4×D61—41no—
118C4×D61—41no—
119C4×D61—42no—
120Dic122—41no—
121C8×C61—21no—
122C8×C61—21no—
123C8×C61—41no—
124#92418—21no—
125#92418—21no—
126#92418—41no—
127#11464—611nomaximal, Sylow
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61C2×C22⋊C811yescharacteristic
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—41no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61—41no—
138C4×C61#41011yescharacteristic
139C4×C61#41311yescharacteristic
140Dic61—21no—
141Dic61—21no—
142Dic61—21no—
143Dic61—41no—
144Dic61#35012yes—
145#2922—611no—
146#2163—611no—
147#2162—611no—
148#1323—611no—
149#1323D6111yescharacteristic, complemented
150#1315—611no—
151#1315—611no—
152C2×C61—41no—
153C2×C61#145811yescharacteristic
154C2×C61C2×#35011yescharacteristic
155C2×C61#211711yescharacteristic
156D61—81no—
157C4×#41—611no—
158#433—1221no—
159#433—1221no—
160#431—1221no—
161#431—1221no—
162#424—611no—
163#424C2×D6111yescharacteristic
164#408—611no—
165#408—611no—
166C4×M16—611no—
167C2×C4×C8—611no—
168C4⋊C16—1221no—
169C4⋊C16—1221no—
170C22⋊C16—611no—
171C22⋊C16—611no—
172C22⋊C16C2×D6111yescharacteristic
173C22⋊C16C2×D6111yescharacteristic
174#346—1221no—
175C4×C16—1221no—
176C61#1146411yescharacteristic, complemented, Sylow
177C2×#41—611no—
178C2×M16—611no—
179C2×M16C4×D6111yescharacteristic
180C22×C8—611no—
181C22×C8C22×D6111yescharacteristic
182C4×Q8—611no—
183C4×Q8—611no—
184C4×D4—611no—
185C4×D4—611no—
186C4×D4—1221no—
187C4×D4—1221no—
188#117—1221no—
189#117C4×D6111yescharacteristic
190C2×C42—611no—
191C2×C42—1221no—
192C2×C16—21no—
193C2×C16—21no—
194C2×C16—1221no—
195C2×C16—1221no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—1221no—
199C4⋊C8—1221no—
200C22⋊C8—1221no—
201C22⋊C8—1221no—
202C22⋊C8—1221no—
203C22⋊C8—1221no—
204#97—1221no—
205C4×C8—611no—
206C4×C8—611no—
207C4×C8—611no—
208C4×C8—611no—
209C4×C8—1221no—
210#41—2441no—
211#41—2441no—
212C2×Q8—611no—
213C2×D4—611no—
214C2×D4—1221no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4—1221no—
220C22×C4C2×C4×D6111yescharacteristic
221M16—41no—
222M16—2441no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8—611no—
226C2×C8—611no—
227C2×C8—1221no—
228C2×C8—2441no—
229C2×C8D4×D6111yescharacteristic
230C2×C8D4×D6111yescharacteristic
231C4⋊C4—1221no—
232C4⋊C4—1221no—
233C4⋊C4C8×D6111yescharacteristic
234C4⋊C4C8×D6111yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—1221no—
237C22⋊C4—1221no—
238C42—21no—
239C42—611no—
240C42—611no—
241C42—611no—
242C42—611no—
243C42—1221no—
244C42—1221no—
245C16—41no—
246C16—41no—
247C16—2441no—
248C16—2441no—
249C23—1221no—
250C23M16×D6111yescharacteristic
251Q8—2441no—
252D4—2441no—
253D4—2442no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—611no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—1222no—
263C2×C4—1221no—
264C2×C4—2442no—
265C2×C4—2442no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4C22⋊C4×D6111yescharacteristic
270C2×C4C2×C8×D6111yescharacteristic
271C8—21no—
272C8—21no—
273C8—41no—
274C8—1221no—
275C8—1221no—
276C8—2441no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—2441no—
281C22—2441no—
282C22—2441no—
283C22C22⋊C8×D6111yescharacteristic
284C4—21no—
285C4—41no—
286C4—41no—
287C4—612no—
288C4—1221no—
289C4—1221no—
290C4—1221no—
291C4—2441no—
292C4#1683973411yescharacteristic
293C4#1683974511yescharacteristic
294C2—41no—
295C2—4881no—
296C2#2144413211yescharacteristic
297C2#350×D6111yescharacteristic
298C2#2144744511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#1323C2
socleC22×C61C2×C22⋊C8
prime radicalC2×#11758222C2×C4
cosocleC22×C8×C61C23
hypercenter#1323D61
hypocenterC61#11464
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #21447619C2semidirect
3. #21447615C2semidirect
4. #21443761C2semidirect
7. C61×#1323C2semidirect
149. #1323D61semidirect
176. C61#11464semidirect

Maximal subgroups

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

subgroupindex
#214544622
#214476192
#214476152
#214437612
#214437442
C61×#13232
#1146461