Finite Group Databasebeta

← #21447094

Subgroups — #21447094

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×#14519805C211yesmaximal, characteristic
2#16839778C211yesmaximal, characteristic, complemented
3#16839768C211yesmaximal, characteristic, complemented
4#16839744C211yesmaximal, characteristic, complemented
5C2×#14519693C211yesmaximal, characteristic, complemented
6#16839534C211yesmaximal, characteristic, complemented
7C61×#430C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×D244C2211yescharacteristic
10#14519805—22no—
11#14519805—22no—
12C2×#11758190—21no—
13C2×D488—21no—
14C2×#11758194C2211yescharacteristic
15#14519736C2211yescharacteristic
16#14519703—22no—
17#14519699—22no—
18#14519695—21no—
19#14519693—21no—
20#14519693—22no—
21C2×M16×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23C2×M16×C61C2211yescharacteristic
24#108×C61—22no—
25C23×D61—21no—
26C22×C4×C61C2311yescharacteristic
27C2×C22⋊D61—21no—
28#11758222—21no—
29#11758222—21no—
30#11758222—21no—
31#11758222—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244—21no—
36C2×D244—21no—
37C2×D244D412yes—
38C2×D244D411yescharacteristic
39C2×C4×D61—21no—
40C2×Dic122D411yescharacteristic
41M16×C61—21no—
42M16×C61—21no—
43M16×C61—21no—
44M16×C61—21no—
45M16×C61D412yes—
46M16×C61D412yes—
47C2×C8×C61—21no—
48C2×C8×C61—21no—
49C2×C8×C61—21no—
50C22⋊Dic61—21no—
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—22no—
60C22×D61—21no—
61C22×D61—41no—
62C22×D61—41no—
63C22×D61—82no—
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61#4111yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C22⋊D61—41no—
71C22⋊D61—41no—
72C2×Dic61—21no—
73C2×Dic61—41no—
74D244—22no—
75D244—21no—
76D244—21no—
77D244—22no—
78D244—41no—
79D244—41no—
80C4×D61—41no—
81C4×D61—41no—
82Dic122—21no—
83Dic122—21no—
84C8×C61—22no—
85C8×C61—22no—
86C8×C61—41no—
87#92418—41no—
88C22×C61—41no—
89C22×C61#12111yescharacteristic
90C22×C61#12311yescharacteristic
91C22×C61#12411yescharacteristic
92C2×D61—41no—
93C2×D61—42no—
94C2×D61—82no—
95C2×D61—82no—
96C2×D61—81no—
97C2×D61—82no—
98C4×C61#12011yescharacteristic
99C4×C61#12111yescharacteristic
100C4×C61#12111yescharacteristic
101C4×C61#12311yescharacteristic
102Dic61—41no—
103Dic61—81no—
104#2048—611nomaximal, Sylow
105C2×C61—21no—
106C2×C61—21no—
107C2×C61—21no—
108C2×C61#39411yescharacteristic
109D61—81no—
110D61—82no—
111C2×AGL(1,ℤ/8)—611no—
112#430D6111yescharacteristic, complemented
113#421—611no—
114#418—611no—
115#413—611no—
116C2×#100—611no—
117#344—611no—
118C61#204811yescharacteristic, complemented, Sylow
119C2×#41—611no—
120C22×D4—611no—
121AGL(1,ℤ/8)—1222no—
122AGL(1,ℤ/8)—1222no—
123C2×SD16—1221no—
124C2×D8—1221no—
125C2×M16—611no—
126C2×M16C2×D6111yescharacteristic
127C2×M16C2×D6111yescharacteristic
128C2×M16C2×D6111yescharacteristic
129#117—611no—
130#108—22no—
131#104—1222no—
132#102—1222no—
133#101—1221no—
134#100—1221no—
135#100—1222no—
136C24—1221no—
137#41—1221no—
138#41—1221no—
139#41—1221no—
140#41—1221no—
141C2×Q8—611no—
142C2×D4—611no—
143C2×D4—612no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4—1221no—
150C22×C4—1221no—
151C22×C4C22×D6111yescharacteristic
152SD16—1224no—
153D8—1224no—
154M16—21no—
155M16—21no—
156M16—21no—
157M16—21no—
158M16—1221no—
159M16—1221no—
160M16D24412yes—
161M16C22⋊D6112yes—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—1221no—
166C4⋊C4—1221no—
167C22⋊C4—1221no—
168C42—1221no—
169C23—1222no—
170C23—1221no—
171C23—4882no—
172C23—2441no—
173C23—2441no—
174C23#1175822611yescharacteristic
175Q8—1221no—
176Q8—1221no—
177D4—1221no—
178D4—1222no—
179D4—1221no—
180D4—1222no—
181D4—2441no—
182D4—2441no—
183D4—2441no—
184D4—2441no—
185C2×C4—1221no—
186C2×C4—2441no—
187C2×C4—2441no—
188C2×C4—2441no—
189C2×C4C2×D24411yescharacteristic
190C2×C4#1175822211yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C2×C4D4×D6111yescharacteristic
193C2×C4#1175822611yescharacteristic
194C2×C4C2×C22⋊D6111yescharacteristic
195C8—22no—
196C8—22no—
197C8—41no—
198C8—2441no—
199C22—41no—
200C22—4881no—
201C22—4882no—
202C22—4882no—
203C22—4882no—
204C22—2441no—
205C22—2442no—
206C22#1451975211yescharacteristic
207C22#1451976211yescharacteristic
208C22#1451976611yescharacteristic
209C4—4881no—
210C4—2441no—
211C4#1451974511yescharacteristic
212C4#1451975111yescharacteristic
213C4#1451975211yescharacteristic
214C4#1451976211yescharacteristic
215C2—21no—
216C2—21no—
217C2—21no—
218C2—4882no—
219C2—4881no—
220C2#1683967911yescharacteristic
subgroupG/H
centerC2#16839679
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#430C2
socleC2×C61#394
hypercenter#430D61
hypocenterC61#2048
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
2. #16839778C2semidirect
3. #16839768C2semidirect
4. #16839744C2semidirect
5. C2×#14519693C2semidirect
6. #16839534C2semidirect
7. C61×#430C2semidirect
112. #430D61semidirect
118. C61#2048semidirect