Finite Group Databasebeta

← #21447097

Subgroups — #21447097

Order 7808.

254 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14519808C211yesmaximal, characteristic
2#16839810C211yesmaximal, characteristic, complemented
3#16839780C211yesmaximal, characteristic
4#16839744C211yesmaximal, characteristic
5C2×#14519696C211yesmaximal, characteristic, complemented
6#16839532C211yesmaximal, characteristic, complemented
7C61×#419C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—22no—
10#14519808—22no—
11C2×#11758202—21no—
12C2×#11758201—21no—
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15C2×#11758194C2211yescharacteristic
16#14519712—22no—
17#14519705—22no—
18#14519696—22no—
19#14519695—21no—
20#14519693—21no—
21C22×Q8×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23#117×C61C2211yescharacteristic
24#103×C61—22no—
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61D412yes—
31C22×C4×C61—21no—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—21no—
34#11758222—21no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38C2×D244D411yescharacteristic
39C2×C4×D61—21no—
40C2×Dic122D411yescharacteristic
41M16×C61—21no—
42M16×C61—21no—
43C2×C8×C61—21no—
44C4⋊C4×C61—21no—
45C22⋊C4×C61—21no—
46C42×C61—21no—
47#11758202—24no—
48#11758201—24no—
49#11758194—21no—
50#11758194—21no—
51#11758194—21no—
52#11758194—21no—
53#11758194D412yes—
54#11758194D412yes—
55C2×#92418—21no—
56C2×#92418—21no—
57C2×#92418—21no—
58C23×C61#4111yescharacteristic
59C22×D61—21no—
60Q8×C61—22no—
61Q8×C61—22no—
62Q8×C61—41no—
63Q8×C61—41no—
64C2×C4×C61—22no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C22⋊D61—41no—
75C22⋊D61—41no—
76C2×Dic61—21no—
77D244—21no—
78D244—21no—
79C4×D61—41no—
80C4×D61—41no—
81Dic122—21no—
82Dic122—21no—
83C8×C61—41no—
84#92418—22no—
85#92418—22no—
86#92418—41no—
87C22×C61—41no—
88C22×C61#12111yescharacteristic
89C22×C61#12311yescharacteristic
90C22×C61#12411yescharacteristic
91C2×D61—41no—
92C2×D61—81no—
93C4×C61—42no—
94C4×C61—81no—
95C4×C61#12011yescharacteristic
96C4×C61#12111yescharacteristic
97C4×C61#12111yescharacteristic
98C4×C61#12311yescharacteristic
99Dic61—41no—
100#2049—611nomaximal, Sylow
101C2×C61—21no—
102C2×C61—21no—
103C2×C61—21no—
104C2×C61#39411yescharacteristic
105D61—81no—
106C2×#137—611no—
107#430—611no—
108#421—611no—
109#419D6111yescharacteristic, complemented
110#413—611no—
111C2×#101—611no—
112#344—611no—
113C61#204911yescharacteristic, complemented, Sylow
114C2×#41—611no—
115C22×Q8C2×D6111yescharacteristic
116#137—1222no—
117#137—1222no—
118C2×Q16—1221no—
119C2×SD16—1221no—
120C2×M16—611no—
121C2×M16—611no—
122C2×M16—611no—
123C2×M16C2×D6111yescharacteristic
124#117C2×D6111yescharacteristic
125#108—1222no—
126#104—1222no—
127#103—22no—
128#101—1221no—
129#101—1222no—
130#100—1221no—
131#41—1221no—
132#41—1221no—
133#41—1221no—
134#41—1221no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—611no—
141C2×Q8C22⋊D6112yes—
142C2×D4—611no—
143C2×D4—1221no—
144C22×C4—21no—
145C22×C4—1221no—
146C22×C4C22×D6111yescharacteristic
147Q16—1224no—
148SD16—1224no—
149M16—21no—
150M16—21no—
151M16—612no—
152M16—612no—
153M16—1221no—
154M16—1221no—
155M16—1221no—
156M16—1221no—
157C2×C8—21no—
158C2×C8—1221no—
159C2×C8—1221no—
160C2×C8—1221no—
161C4⋊C4—21no—
162C22⋊C4—21no—
163C42—21no—
164C23—1221no—
165C23#1175822411yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—1221no—
171Q8—1221no—
172D4—1221no—
173D4—1221no—
174D4—2441no—
175D4—2441no—
176C2×C4—22no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—1221no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4#1175822211yescharacteristic
184C2×C4#1175822211yescharacteristic
185C2×C4D4×D6111yescharacteristic
186C2×C4D4×D6111yescharacteristic
187C2×C4D4×D6111yescharacteristic
188C2×C4C2×C22⋊D6111yescharacteristic
189C8—41no—
190C8—1222no—
191C8—1222no—
192C8—2441no—
193C22—41no—
194C22—4881no—
195C22—2441no—
196C22#1451974911yescharacteristic
197C22#1451975911yescharacteristic
198C22#1451976311yescharacteristic
199C4—42no—
200C4—81no—
201C4—2441no—
202C4#1451974511yescharacteristic
203C4#1451975011yescharacteristic
204C4#1451975011yescharacteristic
205C4#1451976011yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—4881no—
210C2#1683967711yescharacteristic
subgroupG/H
centerC2#16839677
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#419C2
socleC2×C61#394
hypercenter#419D61
hypocenterC61#2049
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. #16839810C2semidirect
5. C2×#14519696C2semidirect
6. #16839532C2semidirect
7. C61×#419C2semidirect
109. #419D61semidirect
113. C61#2049semidirect