Finite Group Databasebeta

← #28362993

Subgroups — #28362993

Order 13952.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#16812747C211yesmaximal, characteristic
2C2×#16812625C212yesmaximal, complemented
3#20295028C212yesmaximal, complemented
4#20294933C211yesmaximal, characteristic, complemented
5C2×#101×C109C211yesmaximal, characteristic, complemented
6#16812747—24no—
7#16812747—22no—
8#16812747C414yescomplemented
9C2×#13182030—22no—
10C2×#13182029—22no—
11C2×#13182029C2212yes—
12C2×Q8×D109—22no—
13C2×C4⋊Dic109C2211yescharacteristic
14C2×C4×Dic109C2211yescharacteristic
15#16812625—24no—
16#16812624—22no—
17#16812621—22no—
18#16812606—22no—
19C22×Q8×C109C2211yescharacteristic
20C2×M16×C109C2212yes—
21#101×C109—22no—
22#13182030—28no—
23#13182030—28no—
24#13182029—28no—
25#13182029—28no—
26#13182029—22no—
27#13182029—22no—
28#13182029C2×C414yes—
29#13182029D414yes—
30C2×Dic218—22no—
31C2×Dic218D412yes—
32Q8×D109—28no—
33Q8×D109—28no—
34C2×D436—22no—
35C2×D436D412yes—
36C2×C22⋊D109—22no—
37C22×Dic109—21no—
38C22×Dic109—21no—
39C2×C4×D109—24no—
40C2×C4×D109—22no—
41C4⋊Dic109—22no—
42C4×Dic109—22no—
43C2×Q8×C109—22no—
44C2×Q8×C109—22no—
45C2×Q8×C109C2×C412yes—
46C2×Q8×C109D412yes—
47C22×C4×C109D412yes—
48C22×C4×C109C2311yescharacteristic
49M16×C109—22no—
50M16×C109—22no—
51C2×C8×C109—22no—
52C23×C109C2×D411yescharacteristic
53C22×D109—22no—
54Q8×C109—24no—
55Q8×C109—24no—
56C2×C4×C109—22no—
57C2×C4×C109—22no—
58C2×C4×C109C22⋊C414yes—
59C2×C4×C109C22×C411yescharacteristic
60C2×C4×C109C2×D412yes—
61C2×C4×C109C2×D412yes—
62C2×C4×C109C2×D411yescharacteristic
63C22⋊D109—24no—
64C22⋊D109—24no—
65C2×Dic109—22no—
66C2×Dic109—22no—
67C2×Dic109—41no—
68C2×Dic109—41no—
69C2×Dic109—42no—
70C2×Dic109—41no—
71D436—28no—
72D436—22no—
73D436C22⋊C414yes—
74C4×D109—216no—
75C4×D109—24no—
76C4×D109—24no—
77Dic218—28no—
78Dic218—22no—
79Dic218C22⋊C414yes—
80C8×C109—42no—
81C22×C109—21no—
82C22×C109—21no—
83C22×C109C2×C22⋊C411yescharacteristic
84C22×C109#12011yescharacteristic
85C22×C109#12011yescharacteristic
86C2×D109—24no—
87C2×D109—42no—
88C2×D109—42no—
89C4×C109—24no—
90C4×C109C2×C22⋊C412yes—
91C4×C109#12012yes—
92Dic109—24no—
93Dic109—42no—
94Dic109—81no—
95C2×C109—21no—
96C2×C109—21no—
97C2×C109#37911yescharacteristic
98C2×C109#45411yescharacteristic
99C2×C109#45611yescharacteristic
100D109—44no—
101#1793—1091nomaximal, Sylow
102C109#179311yescharacteristic, complemented, Sylow
103C2×2−1+4—1091no—
104C2×#104—1092no—
105#417—1092no—
106C2×#101D10911yescharacteristic, complemented
107#391—1091no—
1082−1+4—1094no—
1092−1+4—2184no—
1102−1+4—2182no—
111C2×#41—1092no—
112C2×#41—2182no—
113C2×#41—2182no—
114C22×Q8—2182no—
115C22×Q8C2×D10911yescharacteristic
116C2×M16C2×D10912yes—
117C2×C4⋊C4—1091no—
118C2×C42—1091no—
119#104—2184no—
120#103—2182no—
121#102—2182no—
122#101—22no—
123#95—2182no—
124#41—1094no—
125#41—1094no—
126#41—2188no—
127#41—2188no—
128#41—2188no—
129#41—2188no—
130#41—2182no—
131#41—2182no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—1092no—
135C2×Q8—2182no—
136C2×Q8—2188no—
137C2×Q8—2188no—
138C2×Q8C4×D10912yes—
139C2×Q8C22⋊D10912yes—
140C2×D4—1092no—
141C2×D4—2182no—
142C2×D4—2182no—
143C22×C4—2184no—
144C22×C4—2181no—
145C22×C4—2181no—
146C22×C4—2182no—
147C22×C4D43612yes—
148C22×C4C22×D10911yescharacteristic
149M16—22no—
150M16—22no—
151C2×C8—22no—
152C4⋊C4—2182no—
153C42—2182no—
154C23—2182no—
155C23C2×D43611yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—1094no—
159Q8—2188no—
160Q8—2182no—
161D4—1094no—
162D4—2188no—
163D4—2184no—
164D4—2184no—
165D4—2182no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—4362no—
169C2×C4—4361no—
170C2×C4—4361no—
171C2×C4—4361no—
172C2×C4—21816no—
173C2×C4—2182no—
174C2×C4—2182no—
175C2×C4—2184no—
176C2×C4—2184no—
177C2×C4#1318200614yes—
178C2×C4C2×C4×D10911yescharacteristic
179C2×C4D4×D10912yes—
180C2×C4D4×D10912yes—
181C2×C4C2×C22⋊D10911yescharacteristic
182C8—42no—
183C22—21no—
184C22—21no—
185C22—4362no—
186C22—4362no—
187C22—2184no—
188C22C2×#1318200611yescharacteristic
189C22#1681266911yescharacteristic
190C22#1681266911yescharacteristic
191C4—24no—
192C4—8721no—
193C4—4362no—
194C4—2184no—
195C4C22⋊C4×D10912yes—
196C4#1681266712yes—
197C2—21no—
198C2—21no—
199C2—4364no—
200C2#2029488111yescharacteristic
201C2#2029520111yescharacteristic
202C2#2029521111yescharacteristic
subgroupG/H
centerC22#16812669
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
FittingC2×#101×C109C2
socleC22×C109#120
prime radicalC2×#16812747C2
cosocleC22×C4×C109C23
hypercenterC2×#101D109
hypocenterC109#1793
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#16812625C2semidirect
3. #20295028C2semidirect
4. #20294933C2semidirect
5. C2×#101×C109C2semidirect
8. #16812747C4semidirect
102. C109#1793semidirect
106. C2×#101D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168127472
C2×#168126252
#202950282
#202949332
C2×#101×C1092
#1793109