Finite Group Databasebeta

← #28362095

Subgroups — #28362095

Order 13952.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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#20295698C211yesmaximal, characteristic, complemented
2#20295402C211yesmaximal, characteristic, complemented
3#20295218C211yesmaximal, characteristic, complemented
4#20294769C211yesmaximal, characteristic, complemented
5Q8⋊#11724784C211yesmaximal, characteristic, complemented
6#20294753C211yesmaximal, characteristic, complemented
7#460×C109C211yesmaximal, characteristic, complemented
8C2×#13182030—21no—
9C2×#13182014—21no—
10C2×#13182014—22no—
11#16812696—21no—
12#16812696C2211yescharacteristic
13#16812674—22no—
14#16812674—21no—
15C4×D436—21no—
16C4×D436C2211yescharacteristic
17C4⋊#11724784C2211yescharacteristic
18#16812620—21no—
19C4×#11724784C2211yescharacteristic
20C2×SD16×C109—21no—
21#127×C109C2211yescharacteristic
22C4×Q8×C109C2211yescharacteristic
23C4⋊C8×C109C2211yescharacteristic
24#102×C109—21no—
25#13182030—42no—
26#13182030—42no—
27C2×D436—22no—
28C2×D436—21no—
29C2×D436—21no—
30C2×D436—22no—
31C2×D436D411yescharacteristic
32C2×D436D412yes—
33C2×C4×D109—22no—
34C2×C4×D109—21no—
35#13182014—44no—
36#13182014—42no—
37C2×#11724784—21no—
38C2×#11724784—21no—
39C4⋊Dic109D411yescharacteristic
40#13182006—22no—
41#13182006—21no—
42C2×Q8×C109D411yescharacteristic
43C2×D4×C109—21no—
44C2×D4×C109—21no—
45C2×D4×C109—21no—
46SD16×C109—42no—
47C2×C8×C109—21no—
48C4⋊C4×C109—21no—
49C4⋊C4×C109D411yescharacteristic
50C42×C109—21no—
51C42×C109C2311yescharacteristic
52C23×C109—41no—
53C22×D109—21no—
54C22×D109—22no—
55Q8×C109—21no—
56Q8×C109D812yescomplemented
57D4×C109—42no—
58D4×C109—41no—
59D4×C109—41no—
60D4×C109—41no—
61D4×C109—41no—
62C2×C4×C109—21no—
63C2×C4×C109—21no—
64C2×C4×C109C2×D411yescharacteristic
65C2×C4×C109C2×D411yescharacteristic
66C2×C4×C109C2×D411yescharacteristic
67C2×Dic109—21no—
68D436—21no—
69D436—21no—
70D436—42no—
71D436—44no—
72D436—41no—
73D436—41no—
74D436—41no—
75D436—41no—
76D436—82no—
77C4×D109—44no—
78C4×D109—41no—
79C4×D109—41no—
80C8×C109—41no—
81#11724784—22no—
82#11724784—41no—
83C22×C109—81no—
84C22×C109—81no—
85C22×C109—81no—
86C22×C109#12011yescharacteristic
87C2×D109—42no—
88C2×D109—41no—
89C2×D109—41no—
90C2×D109—42no—
91C2×D109—42no—
92C2×D109—41no—
93C4×C109—22no—
94C4×C109—21no—
95C4×C109—41no—
96C4×C109C2×D811yescharacteristic
97C4×C109#13511yescharacteristic
98C4×C109AGL(1,ℤ/8)11yescharacteristic
99C4×C109AGL(1,ℤ/8)11yescharacteristic
100Dic109—41no—
101C2×C109—161no—
102C2×C109#44711yescharacteristic
103C2×C109#44911yescharacteristic
104C2×C109#45311yescharacteristic
105D109—81no—
106D109—82no—
107#1621—1091nomaximal, Sylow
108C109#162111yescharacteristic, complemented, Sylow
109#550—1091no—
110#493—1091no—
111#460D10911yescharacteristic, complemented
112#459—1091no—
113#331—1091no—
114Q8⋊C8—1091no—
115D4⋊C8—1091no—
116C2×#41—2181no—
117C2×SD16—21no—
118C2×D8—2181no—
119C2×D8—2182no—
120#127—1091no—
121#127—2181no—
122#127C2×D10911yescharacteristic
123#121—2182no—
124#121—2181no—
125C4×Q8C2×D10911yescharacteristic
126C4×D4—1091no—
127C4×D4—2181no—
128C4⋊C8—1091no—
129C4⋊C8C2×D10911yescharacteristic
130#102—21no—
131#102—2181no—
132C4×C8—1091no—
133#41—4362no—
134#41—4362no—
135C2×Q8C22⋊D10911yescharacteristic
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—1092no—
140C2×D4—1091no—
141C2×D4—2182no—
142C2×D4—2182no—
143C2×D4—2181no—
144C2×D4—2181no—
145C22×C4—2182no—
146C22×C4—2181no—
147SD16—42no—
148D8—4362no—
149D8—4364no—
150C2×C8—21no—
151C2×C8—2181no—
152C2×C8—2181no—
153C4⋊C4—21no—
154C4⋊C4—1091no—
155C4⋊C4C22⋊D10911yescharacteristic
156C22⋊C4—2182no—
157C22⋊C4—2181no—
158C42—21no—
159C42C22×D10911yescharacteristic
160C23—41no—
161C23—2182no—
162C23—2181no—
163Q8—21no—
164Q8#1318201412yescomplemented
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—8722no—
171D4—4362no—
172D4—4364no—
173D4—4361no—
174D4—4361no—
175D4—4361no—
176D4—4361no—
177D4—2181no—
178D4—2181no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—4364no—
182C2×C4—4361no—
183C2×C4—4361no—
184C2×C4—2181no—
185C2×C4D4×D10911yescharacteristic
186C2×C4D4×D10911yescharacteristic
187C2×C4C2×C22⋊D10911yescharacteristic
188C8—41no—
189C8—4361no—
190C8—2182no—
191C22—81no—
192C22—81no—
193C22—81no—
194C22—4362no—
195C22—4361no—
196C22—4361no—
197C22—4362no—
198C22—4362no—
199C22—4361no—
200C22#1681266711yescharacteristic
201C4—21no—
202C4—22no—
203C4—41no—
204C4—4361no—
205C4C2×#1318201411yescharacteristic
206C4#1681272011yescharacteristic
207C4#1681272411yescharacteristic
208C4#1681272611yescharacteristic
209C2—161no—
210C2—8722no—
211C2—8721no—
212C2#2029515911yescharacteristic
213C2#2029517011yescharacteristic
214C2#2029519211yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#460×C109C2
socleC22×C109#120
hypercenter#460D109
hypocenterC109#1621
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #20295698C2semidirect
2. #20295402C2semidirect
3. #20295218C2semidirect
4. #20294769C2semidirect
5. Q8⋊#11724784C2semidirect
6. #20294753C2semidirect
7. #460×C109C2semidirect
56. Q8×C109D8semidirect
108. C109#1621semidirect
111. #460D109semidirect
164. Q8#13182014semidirect

Maximal subgroups

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

subgroupindex
#202956982
#202954022
#202952182
#202947692
Q8⋊#117247842
#202947532
#460×C1092
#1621109