Finite Group Databasebeta

← #21447113

Subgroups — #21447113

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×#14519805C211yesmaximal, characteristic
2#16839764C211yesmaximal, characteristic, complemented
3C2×#14519699C211yesmaximal, characteristic, complemented
4C2×#14519693C211yesmaximal, characteristic, complemented
5#16839728C211yesmaximal, characteristic, complemented
6#16839530C211yesmaximal, characteristic, complemented
7C2×#108×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×D244C2211yescharacteristic
10#14519805—22no—
11#14519805—22no—
12C2×#11758190—21no—
13C2×D488—21no—
14C2×#11758194C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16#14519702—21no—
17#14519699—21no—
18#14519699—22no—
19#14519693—22no—
20#14519689—22no—
21C2×M16×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23C22×C8×C61C2211yescharacteristic
24#108×C61—22no—
25C23×D61—21no—
26C22×C4×C61C2311yescharacteristic
27C2×C22⋊D61—21no—
28C22×Dic61—21no—
29#11758222—21no—
30#11758222—21no—
31#11758222—21no—
32#11758222—21no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244—21no—
36C2×D244—21no—
37C2×D244—21no—
38C2×D244D412yes—
39C2×D244D411yescharacteristic
40C2×C4×D61—21no—
41C2×Dic122D411yescharacteristic
42M16×C61—21no—
43M16×C61—21no—
44M16×C61—21no—
45M16×C61D412yes—
46C2×C8×C61—21no—
47C2×C8×C61—21no—
48C2×C8×C61—21no—
49C2×C8×C61—21no—
50C2×C8×C61D412yes—
51C4⋊Dic61—21no—
52C4⋊Dic61—21no—
53#11758194—21no—
54#11758194—21no—
55C2×#92418—21no—
56D488—24no—
57#11758190—24no—
58C23×C61#4111yescharacteristic
59C22×D61—21no—
60C22×D61—22no—
61C22×D61—41no—
62C22×D61—41no—
63C22×D61—81no—
64C22×D61—81no—
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C22⋊D61—41no—
72C22⋊D61—41no—
73C2×Dic61—21no—
74C2×Dic61—41no—
75C2×Dic61—81no—
76D244—22no—
77D244—21no—
78D244—22no—
79D244—21no—
80D244—41no—
81D244—41no—
82C4×D61—41no—
83C4×D61—41no—
84Dic122—21no—
85Dic122—21no—
86C8×C61—22no—
87C8×C61—22no—
88C8×C61—41no—
89#92418—41no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61#12111yescharacteristic
93C22×C61#12311yescharacteristic
94C22×C61#12411yescharacteristic
95C2×D61—41no—
96C2×D61—42no—
97C2×D61—41no—
98C2×D61—41no—
99C2×D61—82no—
100C2×D61—81no—
101C2×D61—81no—
102C2×D61—82no—
103C4×C61#12011yescharacteristic
104C4×C61#12111yescharacteristic
105C4×C61#12111yescharacteristic
106C4×C61#12311yescharacteristic
107Dic61—41no—
108Dic61—81no—
109#2051—611nomaximal, Sylow
110C2×C61—21no—
111C2×C61—21no—
112C2×C61#39411yescharacteristic
113C2×C61#47111yescharacteristic
114C2×C61#47211yescharacteristic
115D61—81no—
116D61—82no—
117C2×AGL(1,ℤ/8)—611no—
118C2×#108D6111yescharacteristic, complemented
119#417—611no—
120C2×#102—611no—
121C2×#100—611no—
122#408—611no—
123#343—611no—
124C61#205111yescharacteristic, complemented, Sylow
125C2×#41—611no—
126C22×D4—611no—
127AGL(1,ℤ/8)—1222no—
128AGL(1,ℤ/8)—1222no—
129C2×SD16—1221no—
130C2×D8—1221no—
131C2×M16—611no—
132C2×M16C2×D6111yescharacteristic
133C2×M16C2×D6111yescharacteristic
134C22×C8C2×D6111yescharacteristic
135C2×C4⋊C4—611no—
136#108—22no—
137#103—1221no—
138#102—1221no—
139#102—1222no—
140#100—1222no—
141C22⋊C8—1222no—
142C24—1221no—
143#41—1221no—
144#41—1221no—
145#41—1221no—
146#41—1221no—
147C2×Q8—611no—
148C2×D4—612no—
149C2×D4—611no—
150C2×D4—1221no—
151C2×D4—1221no—
152C2×D4—1221no—
153C2×D4—1221no—
154C2×D4—1221no—
155C2×D4—1221no—
156C22×C4—1221no—
157C22×C4—1221no—
158C22×C4C22×D6111yescharacteristic
159SD16—1224no—
160D8—1224no—
161M16—21no—
162M16—21no—
163M16—21no—
164M16—1221no—
165M16—1221no—
166M16C22⋊D6112yes—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—21no—
170C2×C8—21no—
171C2×C8—1221no—
172C2×C8D24412yes—
173C4⋊C4—1221no—
174C4⋊C4—1221no—
175C23—1222no—
176C23—1221no—
177C23—4881no—
178C23—4881no—
179C23—2441no—
180C23—2441no—
181C23#1175822611yescharacteristic
182Q8—1221no—
183Q8—1221no—
184D4—1221no—
185D4—1222no—
186D4—1222no—
187D4—1221no—
188D4—2441no—
189D4—2441no—
190D4—2441no—
191D4—2441no—
192C2×C4—1221no—
193C2×C4—4881no—
194C2×C4—2441no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4C2×D24411yescharacteristic
198C2×C4#1175822211yescharacteristic
199C2×C4D4×D6111yescharacteristic
200C2×C4D4×D6111yescharacteristic
201C2×C4#1175822611yescharacteristic
202C2×C4C2×C22⋊D6111yescharacteristic
203C8—22no—
204C8—22no—
205C8—41no—
206C8—2441no—
207C22—21no—
208C22—21no—
209C22—4882no—
210C22—4882no—
211C22—4881no—
212C22—4881no—
213C22—2441no—
214C22—2441no—
215C22—2441no—
216C22—2442no—
217C22#1451975211yescharacteristic
218C22#1451976211yescharacteristic
219C22#1451976611yescharacteristic
220C4—4881no—
221C4—2441no—
222C4#1451974511yescharacteristic
223C4#1451975111yescharacteristic
224C4#1451975211yescharacteristic
225C4#1451976211yescharacteristic
226C2—21no—
227C2—21no—
228C2—4882no—
229C2—4881no—
230C2#1683967911yescharacteristic
231C2#1684002611yescharacteristic
232C2#1684003311yescharacteristic
subgroupG/H
centerC22#14519752
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#108×C61C2
socleC22×C61#121
hypercenterC2×#108D61
hypocenterC61#2051
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
2. #16839764C2semidirect
3. C2×#14519699C2semidirect
4. C2×#14519693C2semidirect
5. #16839728C2semidirect
6. #16839530C2semidirect
7. C2×#108×C61C2semidirect
118. C2×#108D61semidirect
124. C61#2051semidirect