Finite Group Databasebeta

← #360×D109 #28364762

Subgroups — #360×D109 #28364762

Order 13952.

232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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#135×D109C211yesmaximal, characteristic
2M32×D109C211yesmaximal, characteristic, complemented
3#106×D109C211yesmaximal, characteristic, complemented
4#20294837C211yesmaximal, characteristic, complemented
5#20294836C211yesmaximal, characteristic, complemented
6#20294835C211yesmaximal, characteristic, complemented
7#360×C109C211yesmaximal, characteristic, complemented
8#41×D109—21no—
9#16812722C411yescharacteristic, complemented
10#16812721C2211yescharacteristic
11#16812720—21no—
12#16812719—21no—
13#16812718C411yescharacteristic, complemented
14Q16×D109C411yescharacteristic, complemented
15SD16×D109—21no—
16D8×D109C411yescharacteristic, complemented
17C2×C8×D109C2211yescharacteristic
18C4⋊C4×D109—21no—
19#16812639C2211yescharacteristic, complemented
20#16812638—21no—
21C16×D109—21no—
22#16812631C2211yescharacteristic, complemented
23#16812630—21no—
24#135×C109C2211yescharacteristic
25M32×C109C2211yescharacteristic, complemented
26#106×C109C2211yescharacteristic, complemented
27#13182030—21no—
28#13182029—21no—
29#13182029—41no—
30#13182028—21no—
31#13182028—41no—
32Q8×D109—21no—
33D4×D109—21no—
34D4×D109—41no—
35C2×C4×D109—41no—
36C2×C4×D109—41no—
37C2×C4×D109D411yescharacteristic
38Dic436C2×C411yescharacteristic, complemented
39#13182019—21no—
40#13182018—21no—
41#13182017—21no—
42#13182016—21no—
43D872C2×C411yescharacteristic, complemented
44#13182014—21no—
45C2×#11724784D411yescharacteristic
46C8×D109C2×C411yescharacteristic
47C8×D109C2×C411yescharacteristic
48C8×D109D411yescharacteristic
49C8×D109D411yescharacteristic
50C4⋊Dic109—21no—
51#13182008—41no—
52#13182004—21no—
53#41×C109—21no—
54Q16×C109C2×C411yescharacteristic, complemented
55SD16×C109—21no—
56D8×C109C2×C411yescharacteristic, complemented
57C2×C8×C109C2311yescharacteristic
58C4⋊C4×C109—21no—
59C16×C109—21no—
60C22×D109—41no—
61C22×D109D811yescharacteristic
62Q8×C109—21no—
63D4×C109—21no—
64D4×C109—41no—
65C2×C4×C109—41no—
66C2×C4×C109—41no—
67C2×C4×C109C2×D411yescharacteristic
68C22⋊D109—41no—
69C22⋊D109—41no—
70C22⋊D109—41no—
71C2×Dic109—41no—
72C2×Dic109—41no—
73C2×Dic109D811yescharacteristic
74D436—21no—
75D436—41no—
76C4×D109—41no—
77C4×D109—41no—
78C4×D109—41no—
79C4×D109—82no—
80C4×D109C22⋊C411yescharacteristic
81C4×D109C22⋊C411yescharacteristic
82C4×D109SD1611yescharacteristic
83C4×D109SD1611yescharacteristic
84Dic218—21no—
85Dic218—41no—
86C8×C109C22×C411yescharacteristic
87C8×C109C2×D411yescharacteristic
88#11724784C22⋊C411yescharacteristic
89#11724784C22⋊C411yescharacteristic
90C22×C109—41no—
91C22×C109C2×D811yescharacteristic
92C2×D109—22no—
93C2×D109—41no—
94C2×D109—82no—
95C2×D109#10211yescharacteristic
96C2×D109#10211yescharacteristic
97C4×C109—41no—
98C4×C109—81no—
99C4×C109C2×C22⋊C411yescharacteristic
100C4×C109C2×SD1611yescharacteristic
101Dic109—41no—
102Dic109—81no—
103Dic109#10211yescharacteristic
104Dic109#10211yescharacteristic
105C2×C109—21no—
106C2×C109—81no—
107C2×C109C2×#10211yescharacteristic
108D109—21no—
109D109—81no—
110D109#36012yesdirect product factor
111C2×#360—1091nomaximal, Sylow
112C109C2×#36011yescharacteristic, complemented, Sylow
113C2×#135—1091no—
114C2×M32—1091no—
115C2×#106—1091no—
116#360—1091no—
117#360—1091no—
118#360—1091no—
119#360D10911yescharacteristic, direct product factor
120C2×#41—2181no—
121#135—1091no—
122#135—1091no—
123#135—1091no—
124#135—2181no—
125#135—2181no—
126#135C2×D10911yescharacteristic
127C2×Q16—1091no—
128C2×SD16—2181no—
129C2×D8—1091no—
130C22×C8—1091no—
131C2×C4⋊C4—2181no—
132M32—1091no—
133M32—2181no—
134M32C2×D10911yescharacteristic, complemented
135C2×C16—2181no—
136#106—1091no—
137#106—2181no—
138#106C2×D10911yescharacteristic, complemented
139#41—21no—
140#41—4361no—
141#41—4361no—
142#41—2181no—
143#41—2181no—
144#41—2181no—
145C2×Q8—2181no—
146C2×D4—4361no—
147C2×D4—2181no—
148C22×C4—1091no—
149C22×C4—4361no—
150C22×C4—4361no—
151Q16—1091no—
152Q16—2181no—
153Q16C4×D10911yescharacteristic, complemented
154SD16—21no—
155SD16—2181no—
156SD16—2181no—
157SD16—2181no—
158D8—1091no—
159D8—2181no—
160D8C4×D10911yescharacteristic, complemented
161C2×C8—1091no—
162C2×C8—1091no—
163C2×C8—1091no—
164C2×C8—1091no—
165C2×C8—1091no—
166C2×C8C22×D10911yescharacteristic
167C4⋊C4—21no—
168C4⋊C4—4361no—
169C4⋊C4—2181no—
170C16—21no—
171C16—2181no—
172C23—1091no—
173C23—4361no—
174Q8—21no—
175Q8—4361no—
176Q8—2181no—
177D4—21no—
178D4—41no—
179D4—4361no—
180D4—4361no—
181D4—4361no—
182D4—4361no—
183D4—2181no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—8722no—
187C2×C4—1091no—
188C2×C4—1091no—
189C2×C4—1091no—
190C2×C4—1091no—
191C2×C4—1091no—
192C2×C4—4361no—
193C2×C4—4361no—
194C2×C4—4361no—
195C2×C4—4361no—
196C2×C4—4361no—
197C2×C4D4×D10911yescharacteristic
198C8—1091no—
199C8—1091no—
200C8C2×C4×D10911yescharacteristic
201C8D4×D10911yescharacteristic
202C22—41no—
203C22—8722no—
204C22—1091no—
205C22—1091no—
206C22—4361no—
207C22—2182no—
208C22D8×D10911yescharacteristic
209C4—41no—
210C4—81no—
211C4—8721no—
212C4—1091no—
213C4—1091no—
214C4—4361no—
215C4C22⋊C4×D10911yescharacteristic
216C4SD16×D10911yescharacteristic
217C2—21no—
218C2—81no—
219C2—8721no—
220C2—1092no—
221C2—2181no—
222C2#102×D10911yescharacteristic
subgroupG/H
centerC2#102×D109
commutatorC8×C109C22×C4
FrattiniC2×C8C22×D109
Fitting#360×C109C2
socleC2×C109C2×#102
prime radical#135×D109C2
cosocleC2×C8×C109C23
hypercenter#360D109
hypocenterC109C2×#360
LCSG ▷ C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. M32×D109C2semidirect
3. #106×D109C2semidirect
4. #20294837C2semidirect
5. #20294836C2semidirect
6. #20294835C2semidirect
7. #360×C109C2semidirect
9. #16812722C4semidirect
13. #16812718C4semidirect
14. Q16×D109C4semidirect
16. D8×D109C4semidirect
19. #16812639C22semidirect
22. #16812631C22semidirect
25. M32×C109C22semidirect
26. #106×C109C22semidirect
38. Dic436C2×C4semidirect
43. D872C2×C4semidirect
54. Q16×C109C2×C4semidirect
56. D8×C109C2×C4semidirect
110. D109#360direct (N × H)
112. C109C2×#360semidirect
119. #360D109direct (N × H)
134. M32C2×D109semidirect
138. #106C2×D109semidirect
153. Q16C4×D109semidirect
160. D8C4×D109semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#135×D1092
M32×D1092
#106×D1092
#202948372
#202948362
#202948352
#360×C1092
C2×#360109