Finite Group Databasebeta

← #29579651

Subgroups — #29579651

Order 15616.

402 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16840114C211yesmaximal, characteristic
2#21446808C211yesmaximal, characteristic
3#21444574C211yesmaximal, characteristic
4#21444504C211yesmaximal, characteristic
5#21444501C211yesmaximal, characteristic
6#21444106C211yesmaximal, characteristic
7C61×#1997C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9#16840114—22no—
10#16840114—22no—
11#16839815C2211yescharacteristic
12#16839786C2211yescharacteristic
13C2×#14519700C414yes—
14C2×C4×#92418C2211yescharacteristic
15#16839530—22no—
16#16839512—22no—
17#16839510—22no—
18#16839508—22no—
19#16839484—22no—
20C2×C4⋊Q8×C61C2211yescharacteristic
21C61×#423C2211yescharacteristic
22C4×M16×C61C2211yescharacteristic
23C61×#343—22no—
24C22×Dic122C2×C412yes—
25C2×#11758194—21no—
26C22×#92418C2×C412yes—
27#14519777—21no—
28#14519777—21no—
29#14519777—21no—
30#14519777—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C4⋊#92418—21no—
34C4⋊#92418—21no—
35C4⋊#92418D412yes—
36#14519700—28no—
37C22⋊#92418—21no—
38C4×#92418—21no—
39C4×#92418D412yes—
40C4×#92418D412yes—
41C22×Q8×C61—21no—
42C2×M16×C61—21no—
43C2×M16×C61D412yes—
44C4⋊Q8×C61—21no—
45C4⋊Q8×C61—21no—
46C4⋊Q8×C61—21no—
47C4⋊Q8×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61C2×C412yes—
50C2×C42×C61C2311yescharacteristic
51C4⋊C8×C61—21no—
52C4⋊C8×C61—21no—
53#97×C61—21no—
54C4×C8×C61—21no—
55C2×Q8×C61—41no—
56C2×Q8×C61—41no—
57C2×Q8×C61—82no—
58C22×C4×C61—22no—
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61#4111yescharacteristic
62C22×Dic61—22no—
63C2×Dic122—22no—
64C2×Dic122—22no—
65C2×Dic122—44no—
66M16×C61—22no—
67M16×C61—22no—
68M16×C61—42no—
69C2×C8×C61—22no—
70C2×C8×C61—41no—
71C4⋊C4×C61—22no—
72C4⋊C4×C61—22no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C42×C61C2×D411yescharacteristic
76C42×C61C2×D411yescharacteristic
77C42×C61C2×D411yescharacteristic
78C42×C61#4111yescharacteristic
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83#11758194—42no—
84C2×#92418—22no—
85C2×#92418—42no—
86C2×#92418—41no—
87C2×#92418C22⋊C414yes—
88C23×C61C4×D411yescharacteristic
89Q8×C61—82no—
90Q8×C61—82no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—42no—
94C2×C4×C61—82no—
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61C4×D411yescharacteristic
97C2×C4×C61#12111yescharacteristic
98C2×C4×C61#12111yescharacteristic
99C2×C4×C61#12411yescharacteristic
100C2×C4×C61#12711yescharacteristic
101C2×C4×C61#13712yes—
102C2×C4×C61#13712yes—
103C2×Dic61—42no—
104C2×Dic61—82no—
105Dic122—44no—
106Dic122—82no—
107C8×C61—42no—
108C8×C61—81no—
109#92418—24no—
110#92418—42no—
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—82no—
120C4×C61#41312yes—
121C4×C61#47012yes—
122C4×C61#47112yes—
123C4×C61#49711yescharacteristic
124C4×C61#49711yescharacteristic
125Dic61—82no—
126C2×#487—611no—
127#1997—611no—
128#1997D6111yescharacteristic
129#1566—611no—
130#1549—611no—
131#1548—611no—
132#1451—611no—
133C2×C61—22no—
134C2×C61#196711yescharacteristic
135C2×C61#197111yescharacteristic
136C2×C61#197711yescharacteristic
137C2×C4⋊Q8—611no—
138C2×C4⋊Q8C2×D6111yescharacteristic
139#487—1222no—
140#487—1222no—
141#431—611no—
142#423—611no—
143#423C2×D6111yescharacteristic
144C2×#103—614no—
145C4×M16C2×D6111yescharacteristic
146C2×C4×C8—611no—
147#343—22no—
148#343—1222no—
149#334—1222no—
150#333—1222no—
151#332—1222no—
152#322—1222no—
153C61#980311yescharacteristic, complemented, Sylow
154C22×Q8—21no—
155C22×Q8—612no—
156C2×M16—21no—
157C2×M16—1221no—
158C2×M16C22⋊D6112yes—
159C22×C8—612no—
160C4⋊Q8—21no—
161C4⋊Q8—21no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164C4⋊Q8—1221no—
165C4⋊Q8—1221no—
166C4⋊Q8—1221no—
167C4⋊Q8—1221no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—1221no—
170C2×C4⋊C4—1221no—
171C2×C4⋊C4C4×D6112yes—
172C2×C42C22×D6111yescharacteristic
173C4⋊C8—21no—
174C4⋊C8—21no—
175C4⋊C8—612no—
176C4⋊C8—1221no—
177C4⋊C8—1221no—
178#103—1228no—
179C22⋊C8—1221no—
180#97—21no—
181C4×C8—21no—
182C4×C8—612no—
183C4×C8—612no—
184C4×C8—1221no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8—82no—
188C2×Q8—1222no—
189C2×Q8—1222no—
190C2×Q8—2444no—
191C22×C4—22no—
192C22×C4—1222no—
193C22×C4C2×C4×D6111yescharacteristic
194C22×C4#1175822211yescharacteristic
195C22×C4C2×C22⋊D6111yescharacteristic
196M16—22no—
197M16—22no—
198M16—42no—
199M16—2442no—
200C2×C8—22no—
201C2×C8—41no—
202C2×C8—614no—
203C2×C8—1222no—
204C2×C8—2442no—
205C2×C8—2441no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C4⋊C4—2441no—
214C42D4×D6111yescharacteristic
215C42D4×D6111yescharacteristic
216C42D4×D6111yescharacteristic
217C42#1175822411yescharacteristic
218C23C4×C22⋊D6111yescharacteristic
219Q8—82no—
220Q8—82no—
221Q8—4882no—
222Q8—2444no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—82no—
227C2×C4—4882no—
228C2×C4—2442no—
229C2×C4C22⋊C4×D6111yescharacteristic
230C2×C4#1451973711yescharacteristic
231C2×C4#1451974911yescharacteristic
232C2×C4#1451975011yescharacteristic
233C2×C4#1451976311yescharacteristic
234C2×C4#1451977311yescharacteristic
235C2×C4#1451980712yes—
236C2×C4#1451980812yes—
237C8—42no—
238C8—81no—
239C8—1224no—
240C8—4881no—
241C8—2442no—
242C22—21no—
243C22—21no—
244C22#1683966211yescharacteristic
245C22#1683986712yes—
246C4—21no—
247C4—21no—
248C4—82no—
249C4—4882no—
250C4#1683974512yes—
251C4#1684001812yes—
252C4#1684002412yes—
253C4#1684015411yescharacteristic
254C4#1684015711yescharacteristic
255C2—22no—
256C2#2144666711yescharacteristic
257C2#2144668911yescharacteristic
258C2#2144671911yescharacteristic
subgroupG/H
centerC22#16839662
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1997C2
socleC22×C61#390
prime radicalC23×C61C4×D4
cosocleC2×C42×C61C23
hypercenter#1997D61
hypocenterC61#9803
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

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×#168401142
#214468082
#214445742
#214445042
#214445012
#214441062
C61×#19972
#980361