Finite Group Databasebeta

← #29590603

Subgroups — #29590603

Order 15616.

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

normal subgroups only

This group has 482 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#21450818C211yesmaximal, characteristic
2#21444163C211yesmaximal, characteristic, complemented
3#21443821C214yesmaximal, complemented
4C4×#101×C61C211yesmaximal, characteristic, complemented
5C2×#14519774C411yescharacteristic
6C2×#14519766—21no—
7#16839819—21no—
8#16839679C412yes—
9#16839679C2212yes—
10#16839664—21no—
11#16839664—21no—
12#16839663—21no—
13C4×C4⋊Dic61C411yescharacteristic
14#16839488—21no—
15#16839488C2212yes—
16C2×C4×Q8×C61C2211yescharacteristic
17C2×#101×C61—21no—
18C4×M16×C61—21no—
19C61×#343C2212yes—
20C22×D244—21no—
21C22×D244—21no—
22C22×D244C2×C412yes—
23#14519774—41no—
24#14519774—41no—
25#14519766—44no—
26C2×C4⋊Dic61—21no—
27C2×#11758198—22no—
28C2×#11758198—22no—
29C2×#11758198—22no—
30C2×#11758198—22no—
31C2×C4×Dic61—21no—
32C4⋊#92418—41no—
33C22⋊#92418—22no—
34#14519688—41no—
35#14519684C2×C412yes—
36C22×Q8×C61D411yescharacteristic
37C2×M16×C61—22no—
38C4×Q8×C61—41no—
39C4×Q8×C61—41no—
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C4⋊C4×C61D411yescharacteristic
42C2×C4⋊C4×C61C2311yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C2×C42×C61D411yescharacteristic
46#101×C61—24no—
47#97×C61—41no—
48C4×C8×C61—41no—
49C23×D61—22no—
50C2×Q8×C61—22no—
51C2×Q8×C61—22no—
52C2×Q8×C61—41no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22×C411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×Dic61—22no—
61C2×D244—42no—
62C2×D244—42no—
63C2×D244—42no—
64C2×D244—42no—
65C2×D244—42no—
66C2×D244—41no—
67C2×D244—41no—
68C2×D244—42no—
69C2×D244—82no—
70M16×C61—24no—
71M16×C61—42no—
72C2×C8×C61—42no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C42×C61—21no—
77C42×C61—21no—
78C42×C61—21no—
79C42×C61—21no—
80C42×C61—21no—
81C42×C61—21no—
82#11758198—44no—
83#11758198—44no—
84#11758198—82no—
85#11758198—82no—
86C4⋊Dic61—42no—
87C4×Dic61—42no—
88C2×#92418—42no—
89C23×C61C2×C22⋊C411yescharacteristic
90C22×D61—42no—
91C22×D61—42no—
92C22×D61—42no—
93C22×D61—42no—
94C22×D61—42no—
95C22×D61—42no—
96C22×D61—42no—
97Q8×C61—44no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61#9911yescharacteristic
113C2×C4×C61#9911yescharacteristic
114C2×C4×C61#10412yes—
115C2×C4×C61AGL(1,ℤ/8)12yes—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119D244—82no—
120D244—84no—
121D244—84no—
122D244—82no—
123C8×C61—44no—
124#92418—82no—
125#11781—611nomaximal, Sylow
126C22×C61—21no—
127C22×C61—21no—
128C22×C61C2×#9911yescharacteristic
129C22×C61#41811yescharacteristic
130C22×C61C2×#10411yescharacteristic
131C2×D61—82no—
132C2×D61—82no—
133C2×D61—82no—
134C2×D61—82no—
135C2×D61—82no—
136C2×D61—82no—
137C2×D61—82no—
138C4×C61—21no—
139C4×C61—22no—
140C4×C61—22no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61#35512yes—
146Dic61—82no—
147#2548—611no—
148C4×#101D6111yescharacteristic, complemented
149#1467—611no—
150#1345—614no—
151C2×C61—21no—
152C2×C61—21no—
153C2×C61#150711yescharacteristic
154C2×C61#212211yescharacteristic
155C2×C61C2×#35511yescharacteristic
156D61—162no—
157C2×#127—611no—
158C2×#124—1221no—
159C2×C4×Q8C2×D6111yescharacteristic
160#432—1221no—
161C2×#101—21no—
162C4×M16—21no—
163#394—612no—
164#394—612no—
165#390—1221no—
166#390—1221no—
167#390—1221no—
168C4×C4⋊C4—611no—
169#343C2×D6112yes—
170#324—612no—
171#324—1221no—
172C61#1178111yescharacteristic, complemented, Sylow
173C22×Q8C22⋊D6111yescharacteristic
174C22×D4—612no—
175C22×D4—1221no—
176C22×D4—1221no—
177C2×M16—22no—
178#127—2441no—
179#127—2441no—
180#124—2444no—
181C4×Q8—41no—
182C4×Q8—41no—
183C2×C4⋊C4—1221no—
184C2×C4⋊C4C4×D6111yescharacteristic
185C2×C4⋊C4D24411yescharacteristic
186C2×C4⋊C4C22×D6111yescharacteristic
187C2×C22⋊C4—1222no—
188C2×C22⋊C4—1222no—
189C2×C22⋊C4—1222no—
190C2×C22⋊C4—1222no—
191C2×C42—1221no—
192C2×C42C4×D6111yescharacteristic
193C2×C42D24411yescharacteristic
194C2×C42C22⋊D6111yescharacteristic
195C4⋊C8—2441no—
196#101—24no—
197C22⋊C8—1222no—
198#97—41no—
199#97—2441no—
200C4×C8—41no—
201#95—612no—
202C24—1222no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C2×D4—4882no—
207C2×D4—2442no—
208C2×D4—2442no—
209C2×D4—2442no—
210C2×D4—2442no—
211C2×D4—2442no—
212C2×D4—2441no—
213C2×D4—2441no—
214C2×D4—2442no—
215C22×C4—1222no—
216C22×C4#1175819811yescharacteristic
217C22×C4#1175819811yescharacteristic
218C22×C4#1175819811yescharacteristic
219C22×C4#1175819811yescharacteristic
220C22×C4C2×C4×D6111yescharacteristic
221C22×C4C2×D24411yescharacteristic
222C22×C4C2×C22⋊D6111yescharacteristic
223M16—24no—
224M16—42no—
225C2×C8—42no—
226C2×C8—2442no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—2442no—
231C22⋊C4—4882no—
232C22⋊C4—4882no—
233C22⋊C4—2444no—
234C22⋊C4—2444no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—2442no—
242C23—2442no—
243C23—2442no—
244C23—2442no—
245C23—2442no—
246C23—2442no—
247C23—2442no—
248C23—2442no—
249C23C2×#1175819811yescharacteristic
250Q8—44no—
251D4—4882no—
252D4—4884no—
253D4—4884no—
254D4—4882no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4—2442no—
272C2×C4#1451969111yescharacteristic
273C2×C4#1451969111yescharacteristic
274C2×C4#1451970512yes—
275C2×C4#1451980212yes—
276C8—44no—
277C8—4882no—
278C22—21no—
279C22—21no—
280C22—4882no—
281C22—4882no—
282C22—4882no—
283C22—4882no—
284C22—4882no—
285C22—4882no—
286C22—4882no—
287C22C2×#1451969111yescharacteristic
288C22#1683976611yescharacteristic
289C22C2×#1451970511yescharacteristic
290C4—21no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—4882no—
298C4#1683955812yes—
299C2—21no—
300C2—21no—
301C2—9762no—
302C2#2144433411yescharacteristic
303C2#2144747011yescharacteristic
304C2C2×#1683955811yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC4×#101×C61C2
socleC22×C61C2×#99
prime radicalC2×#14519774C4
cosocleC2×C4⋊C4×C61C23
hypercenterC4×#101D61
hypocenterC61#11781
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. #21444163C2semidirect
3. #21443821C2semidirect
4. C4×#101×C61C2semidirect
148. C4×#101D61semidirect
172. C61#11781semidirect

Maximal subgroups

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

subgroupindex
#214508182
#214441632
#214438212
C4×#101×C612
#1178161