Finite Group Databasebeta

← #21447766

Subgroups — #21447766

Order 7808.

226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 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
1#16840559C211yesmaximal, characteristic, complemented
2#16840200C211yesmaximal, characteristic, complemented
3#16840197C211yesmaximal, characteristic, complemented
4#16840016C211yesmaximal, characteristic, complemented
5#16839571C211yesmaximal, characteristic, complemented
6#16839543C211yesmaximal, characteristic, complemented
7C61×#360C211yesmaximal, characteristic, complemented
8#41×D61—21no—
9#14519809—21no—
10#14519806—21no—
11#14519804—21no—
12#14519801—21no—
13#14519799C2211yescharacteristic
14#14519797—21no—
15C2×D488C2211yescharacteristic, complemented
16C2×#11758189C2211yescharacteristic
17#14519752—21no—
18#14519722—21no—
19#14519720—21no—
20D976—21no—
21#14519718—21no—
22#14519717C2211yescharacteristic, complemented
23#14519697—21no—
24#135×C61C2211yescharacteristic
25M32×C61C2211yescharacteristic, complemented
26#106×C61C2211yescharacteristic, complemented
27#41×C61—21no—
28#11758226—21no—
29Q8×D61—21no—
30#11758224—21no—
31#11758224—41no—
32D4×D61—21no—
33D4×D61—41no—
34#11758222—21no—
35#11758222—41no—
36C2×D244—21no—
37C2×D244—41no—
38C2×C4×D61—41no—
39C2×C4×D61D411yescharacteristic
40Q16×C61D411yescharacteristic, complemented
41SD16×C61—21no—
42D8×C61D411yescharacteristic, complemented
43C2×C8×C61C2311yescharacteristic
44C4⋊C4×C61—21no—
45#11758202—21no—
46#11758201—21no—
47#11758200—21no—
48#11758199—21no—
49#11758198—41no—
50C2×#92418D411yescharacteristic
51Dic244D411yescharacteristic, complemented
52D488—21no—
53D488—21no—
54D488D411yescharacteristic, complemented
55#11758190—21no—
56#11758189—21no—
57#11758189—21no—
58C16×C61—21no—
59#11758185—21no—
60C22×D61—41no—
61C22×D61—41no—
62C22×D61D811yescharacteristic
63Q8×C61—21no—
64D4×C61—21no—
65D4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61C2×D411yescharacteristic
69C22⋊D61—41no—
70C22⋊D61—41no—
71C22⋊D61—41no—
72C2×Dic61—41no—
73C2×Dic61D811yescharacteristic
74D244—21no—
75D244—41no—
76D244—41no—
77D244—41no—
78D244—82no—
79C4×D61—21no—
80C4×D61—21no—
81C4×D61—41no—
82C4×D61—41no—
83C4×D61—41no—
84Dic122—21no—
85Dic122—41no—
86C8×C61C2×D411yescharacteristic
87C8×C61C2×D411yescharacteristic
88#92418—21no—
89C22×C61—41no—
90C22×C61C2×D811yescharacteristic
91C2×D61—21no—
92C2×D61—41no—
93C2×D61—41no—
94C2×D61—82no—
95C2×D61—81no—
96C2×D61—81no—
97C2×D61—81no—
98C4×C61—41no—
99C4×C61—81no—
100C4×C61#12011yescharacteristic
101C4×C61AGL(1,ℤ/8)11yescharacteristic
102Dic61—21no—
103Dic61—41no—
104#2190—611nomaximal, Sylow
105C2×C61—21no—
106C2×C61—81no—
107C2×C61#44711yescharacteristic
108D61—41no—
109D61—81no—
110D61—161no—
111#575—611no—
112#509—611no—
113#509—611no—
114#469—611no—
115#360—611no—
116#360D6111yescharacteristic, complemented
117#349—611no—
118C61#219011yescharacteristic, complemented, Sylow
119C2×#41—1221no—
120#137—1221no—
121#137—1221no—
122AGL(1,ℤ/8)—1221no—
123AGL(1,ℤ/8)—1221no—
124#135—611no—
125#135—1221no—
126#135C2×D6111yescharacteristic
127C2×D8—611no—
128C2×M16—611no—
129#121—1221no—
130SD32—1221no—
131SD32—1221no—
132D16—1221no—
133D16—1221no—
134M32—611no—
135M32C2×D6111yescharacteristic, complemented
136#106C2×D6111yescharacteristic, complemented
137#102—1221no—
138#41—21no—
139#41—1221no—
140#41—1221no—
141#41—1221no—
142#41—2441no—
143#41—2441no—
144C2×Q8—1221no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—2441no—
148C2×D4—2441no—
149C22×C4—611no—
150C22×C4—2441no—
151Q16—611no—
152Q16—1221no—
153Q16D24411yescharacteristic, complemented
154SD16—21no—
155SD16—1221no—
156SD16—1221no—
157SD16—1221no—
158D8—611no—
159D8—1221no—
160D8—1221no—
161D8—1221no—
162D8D24411yescharacteristic, complemented
163M16—1221no—
164M16—1221no—
165C2×C8—611no—
166C2×C8C22×D6111yescharacteristic
167C4⋊C4—21no—
168C22⋊C4—2441no—
169C16—21no—
170C16—1221no—
171C23—611no—
172C23—2441no—
173C23—2441no—
174Q8—21no—
175Q8—1221no—
176Q8—2441no—
177D4—21no—
178D4—41no—
179D4—1221no—
180D4—4882no—
181D4—2441no—
182D4—2441no—
183D4—2441no—
184D4—2441no—
185D4—2441no—
186D4—2441no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—611no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—2441no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4—2441no—
196C2×C4D4×D6111yescharacteristic
197C8—1221no—
198C8C2×D24411yescharacteristic
199C8D4×D6111yescharacteristic
200C22—41no—
201C22—1221no—
202C22—4881no—
203C22—4881no—
204C22—4882no—
205C22—4881no—
206C22—2441no—
207C22—2441no—
208C22D8×D6111yescharacteristic
209C4—41no—
210C4—81no—
211C4—1221no—
212C4—2441no—
213C4#1451974711yescharacteristic
214C4#1451980411yescharacteristic
215C2—21no—
216C2—81no—
217C2—9761no—
218C2—4881no—
219C2—2441no—
220C2#1683989711yescharacteristic
subgroupG/H
centerC2#16839897
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#360C2
socleC2×C61#447
hypercenter#360D61
hypocenterC61#2190
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
1. #16840559C2semidirect
2. #16840200C2semidirect
3. #16840197C2semidirect
4. #16840016C2semidirect
5. #16839571C2semidirect
6. #16839543C2semidirect
7. C61×#360C2semidirect
15. C2×D488C22semidirect
22. #14519717C22semidirect
25. M32×C61C22semidirect
26. #106×C61C22semidirect
40. Q16×C61D4semidirect
42. D8×C61D4semidirect
51. Dic244D4semidirect
54. D488D4semidirect
116. #360D61semidirect
118. C61#2190semidirect
135. M32C2×D61semidirect
136. #106C2×D61semidirect
153. Q16D244semidirect
162. D8D244semidirect