Finite Group Databasebeta

← #28363007

Subgroups — #28363007

Order 13952.

536 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 121 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#20295043C212yesmaximal, complemented
2#20295035C212yesmaximal, complemented
3#20295010C211yesmaximal, characteristic, complemented
4#20295000C211yesmaximal, characteristic, complemented
5C2×2−1+4×C109C211yesmaximal, characteristic
6C2×#13182013C2212yes—
7#16812658C2212yes—
8#16812626—24no—
9#16812623—24no—
10#16812618—21no—
11#16812616—21no—
12#16812614—22no—
132−1+4×C109—24no—
142−1+4×C109—24no—
15C2×#41×C109—21no—
16C2×#41×C109—22no—
17C2×#41×C109C412yescomplemented
18C2×#41×C109C2211yescharacteristic
19C2×#41×C109C2211yescharacteristic
20C22×Q8×C109—21no—
21C22×Q8×C109C412yescomplemented
22C22×Q8×C109C2211yescharacteristic
23#13182013—22no—
24#13182013—22no—
25C2×#11724784—22no—
26C4⋊Dic109—22no—
27C22⋊Dic109—22no—
28C4×Dic109—22no—
29#41×C109—216no—
30#41×C109—28no—
31#41×C109—24no—
32#41×C109—24no—
33#41×C109—22no—
34#41×C109—22no—
35#41×C109—22no—
36#41×C109D414yes—
37C2×Q8×C109—28no—
38C2×Q8×C109—24no—
39C2×Q8×C109—24no—
40C2×Q8×C109—22no—
41C2×Q8×C109—21no—
42C2×Q8×C109—22no—
43C2×Q8×C109C2×C411yescharacteristic
44C2×Q8×C109C2×C412yes—
45C2×Q8×C109D414yes—
46C2×Q8×C109D411yescharacteristic
47C2×D4×C109—22no—
48C2×D4×C109—21no—
49C2×D4×C109C2×C411yescharacteristic
50C2×D4×C109D412yes—
51C2×D4×C109D411yescharacteristic
52C22×C4×C109—22no—
53C22×C4×C109—21no—
54C22×C4×C109—22no—
55C22×C4×C109—21no—
56C22×C4×C109C2×C412yes—
57C22×C4×C109C2311yescharacteristic
58C23×C109—21no—
59C23×C109C22⋊C412yes—
60C23×C109C2×D411yescharacteristic
61Q8×C109—28no—
62Q8×C109—21no—
63Q8×C109—22no—
64Q8×C109—24no—
65Q8×C109—22no—
66Q8×C109C22⋊C412yes—
67Q8×C109C22⋊C414yes—
68D4×C109—28no—
69D4×C109—24no—
70D4×C109—24no—
71D4×C109—21no—
72D4×C109—22no—
73D4×C109C22⋊C412yes—
74C2×C4×C109—28no—
75C2×C4×C109—28no—
76C2×C4×C109—21no—
77C2×C4×C109—22no—
78C2×C4×C109—24no—
79C2×C4×C109—22no—
80C2×C4×C109—22no—
81C2×C4×C109—24no—
82C2×C4×C109C22⋊C412yes—
83C2×C4×C109C22×C411yescharacteristic
84C2×C4×C109C2×D412yes—
85C2×C4×C109C2×D412yes—
86C2×C4×C109C2×D411yescharacteristic
87C2×Dic109—42no—
88#11724784—42no—
89C22×C109—22no—
90C22×C109—22no—
91C22×C109—41no—
92C22×C109—42no—
93C22×C109—42no—
94C22×C109C2×C22⋊C411yescharacteristic
95C22×C109#12012yes—
96C4×C109—24no—
97C4×C109—22no—
98C4×C109—22no—
99C4×C109C2×C22⋊C411yescharacteristic
100C4×C109C2×C22⋊C411yescharacteristic
101C4×C109#12012yes—
102Dic109—82no—
103C2×C109—22no—
104C2×C109—21no—
105C2×C109—42no—
106C2×C109—42no—
107C2×C109#37911yescharacteristic
108#1796—1091nomaximal, Sylow
109C109#179611yescharacteristic, complemented, Sylow
110C2×2−1+4D10911yescharacteristic
111#421—1092no—
112#419—1092no—
113#413—1091no—
114#410—1091no—
1152−1+4—24no—
1162−1+4—24no—
117C2×#41—21no—
118C2×#41—22no—
119C2×#41Dic10912yescomplemented
120C2×#41C2×D10911yescharacteristic
121C2×#41C2×D10911yescharacteristic
122C22×Q8—21no—
123C22×Q8Dic10912yescomplemented
124C22×Q8C2×D10911yescharacteristic
125C2×M16—1092no—
126#117—1092no—
127#104—2184no—
128#103—2184no—
129#101—2181no—
130#100—2181no—
131#99—2182no—
132#41—216no—
133#41—28no—
134#41—24no—
135#41—24no—
136#41—22no—
137#41—22no—
138#41—22no—
139#41C22⋊D10914yes—
140C2×Q8—28no—
141C2×Q8—24no—
142C2×Q8—24no—
143C2×Q8—22no—
144C2×Q8—21no—
145C2×Q8—22no—
146C2×Q8C2×Dic10911yescharacteristic
147C2×Q8C2×Dic10912yes—
148C2×Q8C22⋊D10914yes—
149C2×Q8C22⋊D10911yescharacteristic
150C2×D4—22no—
151C2×D4—21no—
152C2×D4C2×Dic10911yescharacteristic
153C2×D4C22⋊D10912yes—
154C2×D4C22⋊D10911yescharacteristic
155C22×C4—22no—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—21no—
159C22×C4C2×Dic10912yes—
160C22×C4C22×D10911yescharacteristic
161M16—2182no—
162M16—2182no—
163C2×C8—2182no—
164C4⋊C4—2182no—
165C22⋊C4—2182no—
166C42—2182no—
167C23—21no—
168C23C22⋊Dic10912yes—
169C23C2×C22⋊D10911yescharacteristic
170Q8—28no—
171Q8—21no—
172Q8—22no—
173Q8—24no—
174Q8—22no—
175Q8C22⋊Dic10912yes—
176Q8C22⋊Dic10914yes—
177D4—28no—
178D4—24no—
179D4—24no—
180D4—21no—
181D4—22no—
182D4C22⋊Dic10912yes—
183C2×C4—28no—
184C2×C4—28no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—4362no—
192C2×C4C22⋊Dic10912yes—
193C2×C4C22×Dic10911yescharacteristic
194C2×C4C2×C22⋊D10912yes—
195C2×C4C2×C22⋊D10912yes—
196C2×C4C2×C22⋊D10911yescharacteristic
197C8—4362no—
198C22—22no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22C2×C22⋊Dic10911yescharacteristic
204C22#1681266812yes—
205C4—24no—
206C4—22no—
207C4—22no—
208C4—8722no—
209C4C2×C22⋊Dic10911yescharacteristic
210C4C2×C22⋊Dic10911yescharacteristic
211C4#1681266812yes—
212C2—22no—
213C2—21no—
214C2—42no—
215C2—42no—
216C2#2029488211yescharacteristic
subgroupG/H
centerC2#20294882
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting, prime radicalC2×2−1+4×C109C2
socleC2×C109#379
cosocleC22×C4×C109C23
hypercenterC2×2−1+4D109
hypocenterC109#1796
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20295043C2semidirect
2. #20295035C2semidirect
3. #20295010C2semidirect
4. #20295000C2semidirect
17. C2×#41×C109C4semidirect
21. C22×Q8×C109C4semidirect
109. C109#1796semidirect
119. C2×#41Dic109semidirect
123. C22×Q8Dic109semidirect

Maximal subgroups

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

subgroupindex
#202950432
#202950352
#202950102
#202950002
C2×2−1+4×C1092
#1796109