Finite Group Databasebeta

← #21447093

Subgroups — #21447093

Order 7808.

274 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 65 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×#14519802C211yesmaximal, characteristic
2#16839811C211yesmaximal, characteristic, complemented
3#16839766C211yesmaximal, characteristic, complemented
4#16839746C211yesmaximal, characteristic, complemented
5C2×#14519693C211yesmaximal, characteristic, complemented
6#16839532C211yesmaximal, characteristic, complemented
7C61×#421C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9#14519802—22no—
10#14519802—22no—
11C2×#11758201—21no—
12C2×#11758199—21no—
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15C2×#11758194C2211yescharacteristic
16#14519713—22no—
17#14519697—22no—
18#14519696—21no—
19#14519694—21no—
20#14519693—22no—
21C2×#41×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23#117×C61C2211yescharacteristic
24#104×C61—22no—
25C23×D61—21no—
26#41×C61—21no—
27#41×C61—21no—
28#41×C61—21no—
29#41×C61—21no—
30C2×Q8×C61D411yescharacteristic
31C2×D4×C61—21no—
32C2×D4×C61D411yescharacteristic
33C22×C4×C61—21no—
34C22×C4×C61C2311yescharacteristic
35C2×D244—21no—
36C2×D244—21no—
37C2×D244—21no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244D412yes—
41M16×C61—21no—
42M16×C61D412yes—
43C2×C8×C61—21no—
44C4⋊C4×C61—21no—
45C22⋊C4×C61—21no—
46C42×C61—21no—
47#11758201—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—21no—
59C23×C61#4111yescharacteristic
60C22×D61—22no—
61C22×D61—41no—
62C22×D61—41no—
63C22×D61—82no—
64Q8×C61—21no—
65Q8×C61—21no—
66D4×C61—21no—
67D4×C61—21no—
68D4×C61—41no—
69D4×C61—41no—
70C2×C4×C61—21no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61#4111yescharacteristic
79C2×C4×C61#4111yescharacteristic
80D244—22no—
81D244—22no—
82D244—41no—
83D244—41no—
84C8×C61—22no—
85#92418—22no—
86#92418—41no—
87#92418—41no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61—81no—
91C22×C61#12111yescharacteristic
92C22×C61#12311yescharacteristic
93C22×C61#12411yescharacteristic
94C2×D61—42no—
95C2×D61—82no—
96C2×D61—82no—
97C2×D61—82no—
98C4×C61—41no—
99C4×C61—81no—
100C4×C61#12011yescharacteristic
101C4×C61#12111yescharacteristic
102C4×C61#12111yescharacteristic
103C4×C61#12311yescharacteristic
104#2048—611nomaximal, Sylow
105C2×C61—21no—
106C2×C61—21no—
107C2×C61—21no—
108C2×C61—81no—
109C2×C61#39411yescharacteristic
110D61—82no—
111C2×AGL(1,ℤ/8)—611no—
112#430—611no—
113#421D6111yescharacteristic, complemented
114#418—611no—
115#413—611no—
116C2×#100—611no—
117#344—611no—
118C61#204811yescharacteristic, complemented, Sylow
119C2×#41C2×D6111yescharacteristic
120C22×D4—611no—
121AGL(1,ℤ/8)—1222no—
122AGL(1,ℤ/8)—1222no—
123C2×SD16—1221no—
124C2×D8—1221no—
125C2×M16—611no—
126C2×M16—611no—
127C2×M16—611no—
128C2×M16C2×D6111yescharacteristic
129#117C2×D6111yescharacteristic
130#108—1222no—
131#104—22no—
132#102—1222no—
133#101—1221no—
134#100—1221no—
135#100—1222no—
136C24—1221no—
137#41—21no—
138#41—21no—
139#41—21no—
140#41—21no—
141C2×Q8D24411yescharacteristic
142C2×D4—21no—
143C2×D4—612no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4D24411yescharacteristic
150C22×C4—21no—
151C22×C4C22×D6111yescharacteristic
152SD16—1224no—
153D8—1224no—
154M16—21no—
155M16—612no—
156M16—1221no—
157M16—1221no—
158M16—1221no—
159M16—1221no—
160M16—1221no—
161M16C22⋊D6112yes—
162C2×C8—21no—
163C2×C8—1221no—
164C2×C8—1221no—
165C2×C8—1221no—
166C4⋊C4—21no—
167C22⋊C4—21no—
168C42—21no—
169C23—21no—
170C23—1222no—
171C23—4882no—
172C23—2441no—
173C23—2441no—
174C23#1175822411yescharacteristic
175Q8—21no—
176Q8—21no—
177D4—21no—
178D4—21no—
179D4—41no—
180D4—41no—
181D4—1222no—
182D4—1222no—
183D4—2441no—
184D4—2441no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4C2×D24411yescharacteristic
190C2×C4#1175822211yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C2×C4D4×D6111yescharacteristic
193C2×C4#1175822411yescharacteristic
194C2×C4C2×C22⋊D6111yescharacteristic
195C8—22no—
196C8—1222no—
197C8—2441no—
198C8—2441no—
199C22—41no—
200C22—41no—
201C22—81no—
202C22—4882no—
203C22—4882no—
204C22—4882no—
205C22—2442no—
206C22#1451974811yescharacteristic
207C22#1451976111yescharacteristic
208C22#1451976311yescharacteristic
209C4—41no—
210C4—81no—
211C4#1451974711yescharacteristic
212C4#1451974911yescharacteristic
213C4#1451975111yescharacteristic
214C4#1451975911yescharacteristic
215C2—21no—
216C2—21no—
217C2—21no—
218C2—81no—
219C2—4882no—
220C2#1683967811yescharacteristic
subgroupG/H
centerC2#16839678
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#421C2
socleC2×C61#394
hypercenter#421D61
hypocenterC61#2048
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #16839811C2semidirect
3. #16839766C2semidirect
4. #16839746C2semidirect
5. C2×#14519693C2semidirect
6. #16839532C2semidirect
7. C61×#421C2semidirect
113. #421D61semidirect
118. C61#2048semidirect