Finite Group Databasebeta

← #21447112

Subgroups — #21447112

Order 7808.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14519803C211yesmaximal, characteristic
2C2×#14519713C211yesmaximal, characteristic, complemented
3#16839761C211yesmaximal, characteristic, complemented
4C2×#14519694C211yesmaximal, characteristic, complemented
5#16839728C211yesmaximal, characteristic, complemented
6#16839531C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519803—22no—
10#14519803—22no—
11C2×#11758200—21no—
12C2×#11758199—21no—
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15C2×#11758194C2211yescharacteristic
16#14519713—22no—
17#14519700—21no—
18#14519697—21no—
19#14519694—22no—
20#14519689—22no—
21C22×D4×C61C2211yescharacteristic
22C22×C8×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24#102×C61—22no—
25C24×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61D412yes—
32C22×C4×C61—21no—
33C22×C4×C61C2311yescharacteristic
34C2×C22⋊D61—21no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38#11758222—21no—
39C2×D244D411yescharacteristic
40C2×C4×D61—21no—
41C2×Dic122D411yescharacteristic
42C2×C8×C61—21no—
43C2×C8×C61—21no—
44C2×C8×C61D412yes—
45C4⋊C4×C61—21no—
46C4⋊C4×C61—21no—
47#11758200—24no—
48#11758199—24no—
49#11758194—21no—
50#11758194—21no—
51#11758194—21no—
52#11758194—21no—
53#11758194—21no—
54#11758194D412yes—
55C2×#92418—21no—
56C2×#92418—21no—
57C2×#92418—21no—
58C23×C61—22no—
59C23×C61—41no—
60C23×C61—41no—
61C23×C61—81no—
62C23×C61—81no—
63C23×C61#4111yescharacteristic
64C22×D61—21no—
65D4×C61—22no—
66D4×C61—22no—
67D4×C61—41no—
68D4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61—81no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C2×C4×C61#4111yescharacteristic
77C22⋊D61—41no—
78C22⋊D61—41no—
79C2×Dic61—21no—
80D244—21no—
81D244—21no—
82C4×D61—41no—
83C4×D61—41no—
84Dic122—21no—
85Dic122—21no—
86C8×C61—22no—
87#92418—22no—
88#92418—41no—
89#92418—41no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61—42no—
93C22×C61—82no—
94C22×C61—82no—
95C22×C61—81no—
96C22×C61—81no—
97C22×C61#12111yescharacteristic
98C22×C61#12311yescharacteristic
99C22×C61#12411yescharacteristic
100C2×D61—41no—
101C2×D61—41no—
102C2×D61—41no—
103C4×C61—81no—
104C4×C61#12011yescharacteristic
105C4×C61#12111yescharacteristic
106C4×C61#12111yescharacteristic
107C4×C61#12311yescharacteristic
108Dic61—41no—
109#2051—611nomaximal, Sylow
110C2×C61—21no—
111C2×C61—21no—
112C2×C61—82no—
113C2×C61#39411yescharacteristic
114C2×C61#47111yescharacteristic
115C2×C61#47211yescharacteristic
116D61—81no—
117C2×AGL(1,ℤ/8)—611no—
118C2×#108—611no—
119#417—611no—
120C2×#102D6111yescharacteristic, complemented
121C2×#100—611no—
122#408—611no—
123#343—611no—
124C61#205111yescharacteristic, complemented, Sylow
125C2×#41—611no—
126C22×D4C2×D6111yescharacteristic
127AGL(1,ℤ/8)—1222no—
128AGL(1,ℤ/8)—1222no—
129C2×SD16—1221no—
130C2×D8—1221no—
131C2×M16—611no—
132C2×M16—611no—
133C2×M16—611no—
134C22×C8C2×D6111yescharacteristic
135C2×C4⋊C4C2×D6111yescharacteristic
136#108—1222no—
137#103—1221no—
138#102—22no—
139#102—1221no—
140#100—1222no—
141C22⋊C8—1222no—
142C24—21no—
143#41—1221no—
144#41—1221no—
145#41—1221no—
146#41—1221no—
147C2×Q8—611no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—611no—
154C2×D4—1221no—
155C2×D4D24412yes—
156C22×C4—21no—
157C22×C4—1221no—
158C22×C4C22×D6111yescharacteristic
159SD16—1224no—
160D8—1224no—
161M16—612no—
162M16—1221no—
163M16—1221no—
164M16—1221no—
165M16—1221no—
166M16—1221no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—1221no—
170C2×C8—1221no—
171C2×C8—1221no—
172C2×C8C22⋊D6112yes—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C23—22no—
176C23—41no—
177C23—41no—
178C23—81no—
179C23—81no—
180C23—1221no—
181C23#1175822411yescharacteristic
182Q8—1221no—
183Q8—1221no—
184D4—22no—
185D4—22no—
186D4—41no—
187D4—41no—
188D4—1221no—
189D4—1221no—
190D4—2441no—
191D4—2441no—
192C2×C4—41no—
193C2×C4—81no—
194C2×C4—1221no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4C2×D24411yescharacteristic
198C2×C4#1175822211yescharacteristic
199C2×C4D4×D6111yescharacteristic
200C2×C4D4×D6111yescharacteristic
201C2×C4#1175822411yescharacteristic
202C2×C4C2×C22⋊D6111yescharacteristic
203C8—22no—
204C8—1222no—
205C8—2441no—
206C8—2441no—
207C22—21no—
208C22—21no—
209C22—42no—
210C22—82no—
211C22—82no—
212C22—81no—
213C22—81no—
214C22—2441no—
215C22—2441no—
216C22—2441no—
217C22#1451974811yescharacteristic
218C22#1451976111yescharacteristic
219C22#1451976311yescharacteristic
220C4—81no—
221C4—2441no—
222C4#1451974711yescharacteristic
223C4#1451974911yescharacteristic
224C4#1451975111yescharacteristic
225C4#1451975911yescharacteristic
226C2—21no—
227C2—21no—
228C2—82no—
229C2—4881no—
230C2#1683967811yescharacteristic
231C2#1684002211yescharacteristic
232C2#1684002911yescharacteristic
subgroupG/H
centerC22#14519748
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC22×C61#121
hypercenterC2×#102D61
hypocenterC61#2051
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14519713C2semidirect
3. #16839761C2semidirect
4. C2×#14519694C2semidirect
5. #16839728C2semidirect
6. #16839531C2semidirect
7. C2×#102×C61C2semidirect
120. C2×#102D61semidirect
124. C61#2051semidirect