Finite Group Databasebeta

← #29568846

Subgroups — #29568846

Order 15616.

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

normal subgroups only

This group has 536 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#21446955C212yesmaximal, complemented
2#21446918C211yesmaximal, characteristic, complemented
3#21443645C211yesmaximal, characteristic, complemented
4#21443640C212yesmaximal, complemented
5C61×#2733C211yesmaximal, characteristic
6C22×#11758202—21no—
7C2×#14519777C2211yescharacteristic
8C2×#14519700—21no—
9C2×#14519698—22no—
10#16839524—22no—
11#16839517C2211yescharacteristic
12#16839517C2212yes—
13C2×#124×C61—21no—
14C61×#394—21no—
15C61×#392—22no—
16C61×#391C2211yescharacteristic
17C61×#390C2212yes—
18C61×#388—22no—
19C22×Dic122—21no—
20C2×#11758202—42no—
21C2×#11758202—42no—
22C2×#11758202—42no—
23C22×#92418—21no—
24C22×#92418—22no—
25#14519777—42no—
26C2×C4⋊Dic61—22no—
27#14519700—42no—
28#14519698—44no—
29C22×Q8×C61D411yescharacteristic
30C22×D4×C61—21no—
31C22×D4×C61—21no—
32C22×D4×C61D412yes—
33#124×C61—42no—
34#124×C61—42no—
35C2×C4⋊C4×C61D411yescharacteristic
36C2×C4⋊C4×C61D412yes—
37C2×C22⋊C4×C61—22no—
38C2×C22⋊C4×C61—22no—
39C2×C22⋊C4×C61—22no—
40C2×C22⋊C4×C61—22no—
41C2×C42×C61—21no—
42C2×C42×C61C2311yescharacteristic
43#95×C61—21no—
44#95×C61—22no—
45C24×C61—22no—
46C2×Q8×C61—21no—
47C2×Q8×C61—41no—
48C2×Q8×C61—41no—
49C2×Q8×C61D812yes—
50C2×D4×C61—22no—
51C2×D4×C61—22no—
52C2×D4×C61—42no—
53C2×D4×C61—42no—
54C2×D4×C61—42no—
55C2×D4×C61—81no—
56C2×D4×C61—81no—
57C2×D4×C61—81no—
58C2×D4×C61—82no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—22no—
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D412yes—
64C22×Dic61—41no—
65C2×Dic122—22no—
66C2×Dic122—41no—
67C2×Dic122—41no—
68C2×Dic122—41no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C4⋊C4×C61—42no—
72C4⋊C4×C61—41no—
73C22⋊C4×C61—44no—
74C22⋊C4×C61—42no—
75C22⋊C4×C61—42no—
76C22⋊C4×C61—42no—
77C22⋊C4×C61—42no—
78C22⋊C4×C61—82no—
79C42×C61—41no—
80C42×C61—42no—
81#11758202—48no—
82C4⋊Dic61—24no—
83C4⋊Dic61—42no—
84C2×#92418—22no—
85C2×#92418—41no—
86C2×#92418—41no—
87C2×#92418—42no—
88C2×#92418—42no—
89C2×#92418—42no—
90C23×C61—42no—
91C23×C61—42no—
92C23×C61—42no—
93C23×C61—42no—
94C23×C61—42no—
95C23×C61—42no—
96C23×C61—42no—
97C23×C61#12011yescharacteristic
98Q8×C61—42no—
99Q8×C61—81no—
100D4×C61—44no—
101D4×C61—82no—
102D4×C61—84no—
103D4×C61—84no—
104C2×C4×C61—21no—
105C2×C4×C61—22no—
106C2×C4×C61—22no—
107C2×C4×C61—21no—
108C2×C4×C61—22no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—42no—
112C2×C4×C61—42no—
113C2×C4×C61—41no—
114C2×C4×C61—42no—
115C2×C4×C61—42no—
116C2×C4×C61C2×D811yescharacteristic
117C2×C4×C61#13512yes—
118C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C61#13712yes—
120C2×Dic61—42no—
121C2×Dic61—81no—
122C2×Dic61—81no—
123Dic122—42no—
124Dic122—42no—
125Dic122—81no—
126Dic122—81no—
127#92418—42no—
128#92418—82no—
129#7758—611nomaximal, Sylow
130C22×C61—82no—
131C22×C61—82no—
132C22×C61—82no—
133C22×C61—82no—
134C22×C61—82no—
135C22×C61—82no—
136C22×C61—82no—
137C22×C61#44711yescharacteristic
138C22×C61#45212yes—
139C22×C61#45311yescharacteristic
140C22×C61#45512yes—
141C22×C61B(4,𝔽2)11yescharacteristic
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—22no—
145C4×C61—22no—
146C4×C61—42no—
147C4×C61—82no—
148C4×C61—81no—
149Dic61—82no—
150#2733D6111yescharacteristic
151#2023—612no—
152#2016—611no—
153#1272—611no—
154#1270—612no—
155C2×C61—162no—
156C2×C61#159511yescharacteristic
157C2×C61#160612yes—
158C2×C61#163411yescharacteristic
159C2×C61#164112yes—
160C2×C61#165911yescharacteristic
161C22×Q16—1221no—
162C2×C4⋊Q8—611no—
163C2×#124—21no—
164C2×#103—1221no—
165C2×#102—1222no—
166#394—21no—
167#392—22no—
168#391C2×D6111yescharacteristic
169#390C2×D6112yes—
170#388—22no—
171#340—1222no—
172#336—611no—
173#336—612no—
174C61#775811yescharacteristic, complemented, Sylow
175C22×Q8—1221no—
176C22×Q8C22⋊D6111yescharacteristic
177C22×D4—21no—
178C22×D4—21no—
179C22×D4C22⋊D6112yes—
180C2×Q16—2442no—
181C2×Q16—2442no—
182C2×Q16—2442no—
183C22×C8—1221no—
184C22×C8—1222no—
185C4⋊Q8—2442no—
186#124—42no—
187#124—42no—
188C2×C4⋊C4—1222no—
189C2×C4⋊C4C22⋊D6112yes—
190C2×C4⋊C4C22⋊D6111yescharacteristic
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C42—21no—
196C2×C42C22×D6111yescharacteristic
197#103—2442no—
198#102—2444no—
199#95—21no—
200#95—22no—
201C24—22no—
202C2×Q8—21no—
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8—1222no—
206C2×Q8—2441no—
207C2×Q8—2441no—
208C2×Q8—2441no—
209C2×Q8—2441no—
210C2×Q8—2441no—
211C2×Q8#1175819912yes—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—81no—
218C2×D4—81no—
219C2×D4—82no—
220C2×D4—81no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—2441no—
225C22×C4C2×C22⋊D6111yescharacteristic
226C22×C4C2×C22⋊D6112yes—
227Q16—2448no—
228C2×C8—1222no—
229C2×C8—2442no—
230C2×C8—2442no—
231C2×C8—2442no—
232C2×C8—2441no—
233C2×C8—2441no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C4⋊C4—1224no—
237C4⋊C4—2442no—
238C22⋊C4—44no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—82no—
244C42—41no—
245C42—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—42no—
253C23#1451974611yescharacteristic
254Q8—42no—
255Q8—81no—
256Q8—4881no—
257Q8—4881no—
258Q8—2442no—
259Q8—2442no—
260D4—44no—
261D4—82no—
262D4—84no—
263D4—84no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—4881no—
277C2×C4—4881no—
278C2×C4—2442no—
279C2×C4C2×#1175819911yescharacteristic
280C2×C4#1451979712yes—
281C2×C4#1451980311yescharacteristic
282C2×C4#1451980712yes—
283C8—4882no—
284C8—2442no—
285C22—82no—
286C22—82no—
287C22—82no—
288C22—82no—
289C22—82no—
290C22—82no—
291C22—82no—
292C22#1683989611yescharacteristic
293C22#1683992412yes—
294C22#1683993011yescharacteristic
295C22#1683994012yes—
296C22#1683994911yescharacteristic
297C4—21no—
298C4—21no—
299C4—22no—
300C4—22no—
301C4—42no—
302C4—81no—
303C4—82no—
304C4—4882no—
305C2—162no—
306C2#2144473711yescharacteristic
307C2#2144479912yes—
308C2#2144496411yescharacteristic
309C2#2144501212yes—
310C2#2144512511yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#2733C2
socleC23×C61#120
hypercenter#2733D61
hypocenterC61#7758
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #21446955C2semidirect
2. #21446918C2semidirect
3. #21443645C2semidirect
4. #21443640C2semidirect
174. C61#7758semidirect

Maximal subgroups

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

subgroupindex
#214469552
#214469182
#214436452
#214436402
C61×#27332
#775861