Finite Group Databasebeta

← #29579652

Subgroups — #29579652

Order 15616.

402 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 123 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×#16840113C211yesmaximal, characteristic
2#21446808C211yesmaximal, characteristic
3#21446808C211yesmaximal, characteristic
4#21444575C211yesmaximal, characteristic
5#21444503C211yesmaximal, characteristic
6#21444499C211yesmaximal, characteristic
7C61×#1451C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9C2×#14519777C2211yescharacteristic
10#16840113—22no—
11#16840113—22no—
12#16839786C2211yescharacteristic
13#16839786C2211yescharacteristic
14C2×#14519702C414yes—
15#16839530—22no—
16#16839530—22no—
17#16839513—22no—
18#16839510—22no—
19#16839509—22no—
20C61×#431C2211yescharacteristic
21C4×M16×C61C2211yescharacteristic
22C2×C4×C8×C61C2211yescharacteristic
23C61×#322—22no—
24C22×Dic122—21no—
25C22×Dic122C2×C412yes—
26C2×#11758194—21no—
27C2×#11758194—21no—
28#14519777—21no—
29#14519777—21no—
30#14519777—21no—
31#14519777—21no—
32#14519777—21no—
33#14519777—21no—
34#14519777—21no—
35#14519777—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C412yes—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44#14519702—28no—
45C2×M16×C61D412yes—
46C22×C8×C61C2×C412yes—
47C2×C42×C61C2311yescharacteristic
48C4⋊C8×C61D412yes—
49C22⋊C8×C61—21no—
50#97×C61—21no—
51C4×C8×C61—21no—
52C4×C8×C61—21no—
53C4×C8×C61D412yes—
54C4×C8×C61D412yes—
55C22×C4×C61C22×C411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61#4111yescharacteristic
58C22×Dic61—22no—
59C22×Dic61—22no—
60C2×Dic122—22no—
61C2×Dic122—22no—
62C2×Dic122—44no—
63C2×Dic122—41no—
64C2×Dic122—41no—
65C2×Dic122—82no—
66M16×C61—22no—
67M16×C61—22no—
68C2×C8×C61—22no—
69C2×C8×C61—22no—
70C2×C8×C61—42no—
71C2×C8×C61C22⋊C414yes—
72C42×C61C2×D411yescharacteristic
73C42×C61C2×D411yescharacteristic
74C42×C61C2×D411yescharacteristic
75C42×C61#4111yescharacteristic
76C4⋊Dic61—22no—
77C4⋊Dic61—22no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84#11758194—42no—
85#11758194—42no—
86C2×#92418—41no—
87C2×#92418—41no—
88C23×C61C4×D411yescharacteristic
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61C2×C22⋊C411yescharacteristic
92C2×C4×C61C4×D411yescharacteristic
93C2×C4×C61#12111yescharacteristic
94C2×C4×C61#12111yescharacteristic
95C2×C4×C61#12411yescharacteristic
96C2×C4×C61#12711yescharacteristic
97C2×C4×C61#13712yes—
98C2×C4×C61#13712yes—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—82no—
102C2×Dic61—82no—
103Dic122—44no—
104Dic122—82no—
105Dic122—82no—
106Dic122—82no—
107C8×C61—24no—
108C8×C61—42no—
109C8×C61—42no—
110#92418—81no—
111#92418—81no—
112#9803—611nomaximal, Sylow
113C22×C61—21no—
114C22×C61—21no—
115C22×C61#39011yescharacteristic
116C22×C61#44112yes—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61#41312yes—
120C4×C61#47012yes—
121C4×C61#47112yes—
122C4×C61#49711yescharacteristic
123C4×C61#49711yescharacteristic
124Dic61—82no—
125Dic61—82no—
126C2×#487—611no—
127#1997—611no—
128#1997—611no—
129#1566—611no—
130#1549—611no—
131#1548—611no—
132#1451D6111yescharacteristic
133C2×C61—22no—
134C2×C61#196711yescharacteristic
135C2×C61#197111yescharacteristic
136C2×C61#197711yescharacteristic
137C2×C4⋊Q8—611no—
138C2×C4⋊Q8—611no—
139#487—1222no—
140#487—1222no—
141#431C2×D6111yescharacteristic
142#423—611no—
143#423—611no—
144C2×#103—614no—
145C4×M16C2×D6111yescharacteristic
146C2×C4×C8C2×D6111yescharacteristic
147#343—1222no—
148#343—1222no—
149#334—1222no—
150#333—1222no—
151#332—1222no—
152#322—22no—
153C61#980311yescharacteristic, complemented, Sylow
154C22×Q8—612no—
155C22×Q8—1221no—
156C2×M16—1221no—
157C2×M16—1221no—
158C2×M16D24412yes—
159C22×C8C4×D6112yes—
160C4⋊Q8—1221no—
161C4⋊Q8—1221no—
162C4⋊Q8—1221no—
163C4⋊Q8—1221no—
164C4⋊Q8—1221no—
165C4⋊Q8—1221no—
166C4⋊Q8—1221no—
167C4⋊Q8—1221no—
168C2×C4⋊C4—612no—
169C2×C4⋊C4—1221no—
170C2×C4⋊C4—1221no—
171C2×C4⋊C4—1221no—
172C2×C42C22×D6111yescharacteristic
173C4⋊C8—1221no—
174C4⋊C8—1221no—
175C4⋊C8—1221no—
176C4⋊C8—1221no—
177C4⋊C8D24412yes—
178#103—1228no—
179C22⋊C8—21no—
180#97—21no—
181C4×C8—21no—
182C4×C8—21no—
183C4×C8D24412yes—
184C4×C8C22⋊D6112yes—
185C2×Q8—1222no—
186C2×Q8—1222no—
187C2×Q8—4882no—
188C2×Q8—2444no—
189C2×Q8—2441no—
190C2×Q8—2441no—
191C22×C4—1222no—
192C22×C4—1222no—
193C22×C4C2×C4×D6111yescharacteristic
194C22×C4C2×D24411yescharacteristic
195C22×C4#1175822211yescharacteristic
196M16—22no—
197M16—22no—
198M16—2442no—
199M16—2442no—
200C2×C8—22no—
201C2×C8—22no—
202C2×C8—42no—
203C2×C8—2441no—
204C2×C8—2441no—
205C2×C8#1175819814yes—
206C4⋊C4—1222no—
207C4⋊C4—1222no—
208C4⋊C4—2441no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C4⋊C4—2441no—
214C42C2×D24411yescharacteristic
215C42C2×D24411yescharacteristic
216C42#1175822211yescharacteristic
217C42C2×C22⋊D6111yescharacteristic
218C23C4×D24411yescharacteristic
219Q8—4882no—
220Q8—4882no—
221Q8—4882no—
222Q8—2444no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—4882no—
226C2×C4—4882no—
227C2×C4—2442no—
228C2×C4—2442no—
229C2×C4C2×#1175819811yescharacteristic
230C2×C4C4×D24411yescharacteristic
231C2×C4#1451975111yescharacteristic
232C2×C4#1451975111yescharacteristic
233C2×C4#1451976511yescharacteristic
234C2×C4#1451977411yescharacteristic
235C2×C4#1451981012yes—
236C2×C4#1451981012yes—
237C8—24no—
238C8—42no—
239C8—42no—
240C8—4881no—
241C8—4881no—
242C22—21no—
243C22—21no—
244C22#1683966411yescharacteristic
245C22#1683987012yes—
246C4—21no—
247C4—21no—
248C4—4882no—
249C4—4882no—
250C4#1683974412yes—
251C4#1684002012yes—
252C4#1684002512yes—
253C4#1684015611yescharacteristic
254C4#1684015611yescharacteristic
255C2—22no—
256C2#2144666811yescharacteristic
257C2#2144669011yescharacteristic
258C2#2144672211yescharacteristic
subgroupG/H
centerC22#16839664
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1451C2
socleC22×C61#390
prime radicalC23×C61C4×D4
cosocleC2×C42×C61C23
hypercenter#1451D61
hypocenterC61#9803
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1451

Complements

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

NH ≅ G/Ntype
153. C61#9803semidirect

Maximal subgroups

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

subgroupindex
C2×#168401132
#214468082
#214445752
#214445032
#214444992
C61×#14512
#980361