Finite Group Databasebeta

← #29579598

Subgroups — #29579598

Order 15616.

426 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 121 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×#16840158C211yesmaximal, characteristic
2#21446809C211yesmaximal, characteristic
3#21446662C211yesmaximal, characteristic
4#21444574C211yesmaximal, characteristic
5#21444490C211yesmaximal, characteristic
6#21444100C211yesmaximal, characteristic
7C61×#1549C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9#16840158—21no—
10#16840158—21no—
11#16840158—22no—
12C2×#14519708C414yes—
13#16839786C2211yescharacteristic
14C2×#14519695—22no—
15C4×#11758194C2211yescharacteristic
16C2×C4×#92418C2211yescharacteristic
17#16839531—22no—
18#16839512—22no—
19#16839507—22no—
20#16839484—21no—
21C8×#92418—21no—
22C2×C4⋊Q8×C61C2211yescharacteristic
23C61×#431C2211yescharacteristic
24C61×#423C2211yescharacteristic
25C61×#332—22no—
26C22×Dic122—21no—
27C2×#11758194—21no—
28C2×#11758194D412yes—
29C22×#92418C2×C412yes—
30#14519777—21no—
31#14519777—21no—
32#14519777—21no—
33#14519777—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C412yes—
36#14519708—24no—
37#14519708—24no—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40#14519695—44no—
41#14519688—21no—
42C4×#92418—21no—
43C4×#92418D411yescharacteristic
44C4×#92418D411yescharacteristic
45C4×#92418D412yes—
46C22×Q8×C61—21no—
47C2×M16×C61—21no—
48C4⋊Q8×C61—21no—
49C4⋊Q8×C61—21no—
50C4⋊Q8×C61—21no—
51C4⋊Q8×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C412yes—
54C2×C42×C61C2311yescharacteristic
55C4⋊C8×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61D412yes—
58C22⋊C8×C61—21no—
59C4×C8×C61—21no—
60C2×Q8×C61—41no—
61C2×Q8×C61—41no—
62C2×Q8×C61—82no—
63C22×C4×C61—22no—
64C22×C4×C61C22×C411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61#4111yescharacteristic
67C22×Dic61—22no—
68C2×Dic122—41no—
69C2×Dic122—41no—
70C2×Dic122—42no—
71C2×Dic122—42no—
72M16×C61—42no—
73C2×C8×C61—22no—
74C2×C8×C61—41no—
75C4⋊C4×C61—22no—
76C4⋊C4×C61—22no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C42×C61C2×D411yescharacteristic
80C42×C61C2×D411yescharacteristic
81C42×C61C2×D411yescharacteristic
82C42×C61#4111yescharacteristic
83C4⋊Dic61—22no—
84C4⋊Dic61—22no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87#11758194—22no—
88#11758194—42no—
89#11758194SD1614yes—
90C2×#92418—22no—
91C2×#92418—24no—
92C2×#92418—41no—
93C2×#92418C22⋊C412yes—
94C2×#92418C22⋊C412yes—
95C23×C61C4×D411yescharacteristic
96Q8×C61—82no—
97Q8×C61—82no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—42no—
101C2×C4×C61—82no—
102C2×C4×C61C2×C22⋊C411yescharacteristic
103C2×C4×C61C4×D411yescharacteristic
104C2×C4×C61#12111yescharacteristic
105C2×C4×C61#12111yescharacteristic
106C2×C4×C61#12411yescharacteristic
107C2×C4×C61#12711yescharacteristic
108C2×C4×C61C2×SD1612yes—
109C2×C4×C61#13512yes—
110C2×Dic61—42no—
111C2×Dic61—44no—
112Dic122—82no—
113Dic122—81no—
114Dic122—81no—
115C8×C61—42no—
116C8×C61—81no—
117#92418—22no—
118#92418—24no—
119#92418—81no—
120#92418#10114yescomplemented
121#9794—611nomaximal, Sylow
122C22×C61—21no—
123C22×C61—21no—
124C22×C61#39011yescharacteristic
125C22×C61C4×SD1612yes—
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—82no—
129C4×C61C2×#10112yes—
130C4×C61#46512yes—
131C4×C61#47112yes—
132C4×C61#49211yescharacteristic
133C4×C61#49511yescharacteristic
134Dic61—82no—
135C2×#498—611no—
136#1997—611no—
137#1966—611no—
138#1566—611no—
139#1549D6111yescharacteristic
140#1546—611no—
141C8×M16—611no—
142C2×C61—22no—
143C2×C61#196611yescharacteristic
144C2×C61#196811yescharacteristic
145C2×C61#197711yescharacteristic
146C2×C4⋊Q8—611no—
147C2×C4⋊Q8C2×D6111yescharacteristic
148#498—1221no—
149#498—1221no—
150#498—1222no—
151#431C2×D6111yescharacteristic
152C2×#106—614no—
153#423—611no—
154#423C2×D6111yescharacteristic
155C2×#101—1222no—
156C4×M16—611no—
157C2×C4×C8—611no—
158#343—1222no—
159#334—1222no—
160#332—22no—
161#332—1222no—
162#322—1221no—
163C82—1221no—
164C61#979411yescharacteristic, complemented, Sylow
165C22×Q8—21no—
166C22×Q8—1221no—
167C2×M16—21no—
168C2×M16—612no—
169C2×M16—1221no—
170C22×C8—612no—
171C4⋊Q8—21no—
172C4⋊Q8—21no—
173C4⋊Q8—21no—
174C4⋊Q8—21no—
175C4⋊Q8—1221no—
176C4⋊Q8—1221no—
177C4⋊Q8—1221no—
178C4⋊Q8—1221no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—612no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4C4×D6112yes—
183C2×C42C22×D6111yescharacteristic
184#106—1224no—
185#106—1224no—
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—1221no—
189C4⋊C8—1221no—
190C4⋊C8C22⋊D6112yes—
191#101—2444no—
192C22⋊C8—21no—
193#97—1221no—
194C4×C8—21no—
195C4×C8—611no—
196C4×C8—611no—
197C4×C8—612no—
198C4×C8—1221no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8—82no—
202C2×Q8—2441no—
203C2×Q8—2441no—
204C2×Q8—2442no—
205C2×Q8—2442no—
206C22×C4—22no—
207C22×C4—1222no—
208C22×C4C2×C4×D6111yescharacteristic
209C22×C4D4×D6111yescharacteristic
210C22×C4#1175822411yescharacteristic
211M16—42no—
212M16—614no—
213M16—1222no—
214M16—2442no—
215C2×C8—22no—
216C2×C8—41no—
217C2×C8—612no—
218C2×C8—612no—
219C2×C8—1224no—
220C2×C8—1222no—
221C2×C8—2441no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—1222no—
227C4⋊C4—1222no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C42#1175822211yescharacteristic
231C42D4×D6111yescharacteristic
232C42D4×D6111yescharacteristic
233C42C2×C22⋊D6111yescharacteristic
234C23#1451973711yescharacteristic
235Q8—82no—
236Q8—82no—
237Q8—4882no—
238Q8—4881no—
239Q8—4881no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—82no—
244C2×C4—2444no—
245C2×C4—2442no—
246C2×C4C22⋊C4×D6111yescharacteristic
247C2×C4C4×C22⋊D6111yescharacteristic
248C2×C4#1451974911yescharacteristic
249C2×C4#1451975011yescharacteristic
250C2×C4#1451976311yescharacteristic
251C2×C4#1451977311yescharacteristic
252C2×C4SD16×D6112yes—
253C2×C4#1451980012yes—
254C8—42no—
255C8—81no—
256C8—614no—
257C8—1224no—
258C8—1222no—
259C8—4881no—
260C22—21no—
261C22—21no—
262C22#1683966211yescharacteristic
263C22#1683984712yes—
264C4—21no—
265C4—21no—
266C4—82no—
267C4—4882no—
268C4#101×D6112yes—
269C4#1683999412yes—
270C4#1684002312yes—
271C4#1684013311yescharacteristic
272C4#1684014711yescharacteristic
273C2—22no—
274C2#2144666111yescharacteristic
275C2#2144667011yescharacteristic
276C2#2144672511yescharacteristic
subgroupG/H
centerC22#16839662
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1549C2
socleC22×C61#390
prime radicalC23×C61C4×D4
cosocleC2×C42×C61C23
hypercenter#1549D61
hypocenterC61#9794
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
120. #92418#101semidirect
164. C61#9794semidirect

Maximal subgroups

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

subgroupindex
C2×#168401582
#214468092
#214466622
#214445742
#214444902
#214441002
C61×#15492
#979461