Finite Group Databasebeta

← #29599438

Subgroups — #29599438

Order 15616.

496 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C2×#16839552C212yesmaximal
2#21446233C212yesmaximal
3#21446028C211yesmaximal, characteristic
4#21443944C211yesmaximal, characteristic
5C61×#2724C211yesmaximal, characteristic
6#16840237C2211yescharacteristic
7#16839802—21no—
8C2×#14519694C2211yescharacteristic
9C2×#14519692C2212yes—
10#16839625—22no—
11#16839552—24no—
12#16839528—22no—
13#16839522—21no—
14C2×#123×C61C2212yes—
15C61×#398—21no—
16C61×#397—22no—
17C61×#390C2211yescharacteristic
18C61×#389—21no—
19C61×#385—22no—
20C2×#11758194—21no—
21D4×Dic61—41no—
22D4×Dic61—41no—
23#14519736—21no—
24C2×C22⋊Dic61—22no—
25C2×C22⋊Dic61—22no—
26#14519710—41no—
27#14519708—41no—
28#14519694—21no—
29#14519694D412yes—
30#14519692—22no—
31#14519692—22no—
32#14519684—42no—
33#14519684—42no—
34C22×D4×C61C2311yescharacteristic
35C23×C4×C61D412yes—
36#123×C61—22no—
37#123×C61—22no—
38#123×C61—22no—
39#123×C61—22no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C22⋊C4×C61—22no—
46C2×C22⋊C4×C61—22no—
47C2×C22⋊C4×C61D412yes—
48C2×C42×C61D411yescharacteristic
49#95×C61—22no—
50#95×C61—22no—
51#95×C61—21no—
52C24×C61C2×D412yes—
53C2×D4×C61—41no—
54C2×D4×C61—41no—
55C2×D4×C61C2×D411yescharacteristic
56C2×D4×C61#4111yescharacteristic
57C2×D4×C61#4112yes—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—22no—
64C22×C4×C61—42no—
65C22×C4×C61—42no—
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—42no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—42no—
73C4⋊C4×C61—42no—
74C4⋊C4×C61—81no—
75C4⋊C4×C61—81no—
76C22⋊C4×C61—22no—
77C22⋊C4×C61—22no—
78C22⋊C4×C61—44no—
79C22⋊C4×C61—42no—
80C22⋊C4×C61—42no—
81C42×C61—41no—
82C22⋊Dic61—42no—
83C22⋊Dic61—41no—
84C22⋊Dic61—42no—
85C22⋊Dic61—42no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4×Dic61—41no—
89#11758194—22no—
90#11758194—41no—
91C2×#92418—41no—
92C23×C61—22no—
93C23×C61—22no—
94C23×C61—42no—
95C23×C61—42no—
96C23×C61#12011yescharacteristic
97C23×C61#12112yes—
98C23×C61#12312yes—
99D4×C61—41no—
100D4×C61—41no—
101D4×C61—42no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—22no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61—42no—
110C2×C4×C61—44no—
111C2×C4×C61—42no—
112C2×C4×C61—42no—
113C2×C4×C61—41no—
114C2×C4×C61—42no—
115C2×C4×C61—42no—
116C2×C4×C61—82no—
117C2×C4×C61#12111yescharacteristic
118C2×C4×C61#12411yescharacteristic
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—82no—
122C2×Dic61—82no—
123C2×Dic61—82no—
124C2×Dic61—82no—
125C2×Dic61—82no—
126#92418—42no—
127#13421—611nomaximal, Sylow
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—22no—
131C22×C61—22no—
132C22×C61—42no—
133C22×C61—42no—
134C22×C61—42no—
135C22×C61—42no—
136C22×C61—82no—
137C22×C61#39411yescharacteristic
138C22×C61B(4,𝔽2)11yescharacteristic
139C22×C61#45811yescharacteristic
140C4×C61—21no—
141C4×C61—21no—
142C4×C61—42no—
143C4×C61—82no—
144C4×C61—81no—
145C4×C61—82no—
146Dic61—81no—
147Dic61—81no—
148Dic61—162no—
149#2724D6111yescharacteristic
150C2×#352—612no—
151#1890—612no—
152#1856—611no—
153#1393—611no—
154C2×C61—21no—
155C2×C61—21no—
156C2×C61—42no—
157C2×C61—42no—
158C2×C61#204411yescharacteristic
159C2×C61#219811yescharacteristic
160C2×C61#220111yescharacteristic
161C2×#123C2×D6112yes—
162#518—611no—
163#428—1221no—
164C2×#100—611no—
165C2×#99—612no—
166#398—21no—
167#397—22no—
168#390C2×D6111yescharacteristic
169#389—21no—
170#385—22no—
171#381—1222no—
172#352—1224no—
173#342—1222no—
174#339—1221no—
175C61#1342111yescharacteristic, complemented, Sylow
176C22×D4C22×D6111yescharacteristic
177C23×C4C22⋊D6112yes—
178C2×M16—1221no—
179#123—22no—
180#123—22no—
181#123—22no—
182#123—22no—
183C4×D4—2441no—
184C4×D4—2441no—
185#117—1221no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C22⋊D6111yescharacteristic
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—1222no—
194C2×C22⋊C4—1222no—
195C2×C22⋊C4C22⋊D6112yes—
196C2×C42C22⋊D6111yescharacteristic
197#107—2441no—
198#106—2441no—
199#100—612no—
200#100—1221no—
201#99—1222no—
202#99—1222no—
203#95—22no—
204#95—22no—
205#95—21no—
206#95—2442no—
207#95—2442no—
208C24C2×C22⋊D6112yes—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4D4×D6111yescharacteristic
212C2×D4#1175822411yescharacteristic
213C2×D4#1175822412yes—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—1222no—
223C22×C4—1222no—
224C22×C4—2442no—
225C22×C4C2×C22⋊D6111yescharacteristic
226M16—1222no—
227M16—2441no—
228C2×C8—2441no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—81no—
234C4⋊C4—81no—
235C4⋊C4—1221no—
236C4⋊C4—1221no—
237C22⋊C4—22no—
238C22⋊C4—22no—
239C22⋊C4—44no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—2442no—
243C22⋊C4—2442no—
244C22⋊C4—2442no—
245C22⋊C4—2441no—
246C42—41no—
247C42—2441no—
248C23—22no—
249C23—22no—
250C23—42no—
251C23—42no—
252C23#1451974611yescharacteristic
253C23#1451974912yes—
254C23#1451975812yes—
255D4—41no—
256D4—41no—
257D4—42no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—44no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—82no—
273C2×C4—4882no—
274C2×C4—4882no—
275C2×C4—4882no—
276C2×C4—4882no—
277C2×C4—4882no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4#1451974811yescharacteristic
281C2×C4#1451976411yescharacteristic
282C8—2442no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—22no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—82no—
292C22#1683967611yescharacteristic
293C22#1683994911yescharacteristic
294C22#1683995211yescharacteristic
295C4—21no—
296C4—21no—
297C4—42no—
298C4—82no—
299C4—81no—
300C4—82no—
301C4—9762no—
302C4—4881no—
303C4—4881no—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—42no—
308C2#2144706711yescharacteristic
309C2#2144781511yescharacteristic
310C2#2144783211yescharacteristic
subgroupG/H
centerC22#16839949
commutator, prime radical, cosocleC22×D4×C61C23
FrattiniC22×D4C22×D61
FittingC61×#2724C2
socleC22×C61B(4,𝔽2)
hypercenter#2724D61
hypocenterC61#13421
LCSG ▷ C22×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2724

Complements

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

NH ≅ G/Ntype
175. C61#13421semidirect

Maximal subgroups

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

subgroupindex
C2×#168395522
#214462332
#214460282
#214439442
C61×#27242
#1342161