Finite Group Databasebeta

← #34044667

Subgroups — #34044667

Order 19072.

536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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×#18011958C211yesmaximal, characteristic
2#23749641C212yesmaximal, complemented
3#23749635C212yesmaximal, complemented
4#23749599C211yesmaximal, characteristic, complemented
5#413×C149C211yesmaximal, characteristic, complemented
6#18011958—24no—
7#18011958—24no—
8C2×#14558736C412yescomplemented
9C2×#14558736C2211yescharacteristic
10C2×#14558735—22no—
11C2×#14558735—21no—
12C22×Dic298C412yescomplemented
13C22×Dic298C2211yescharacteristic
14C2×Q8×D149—21no—
15#18011870C2212yes—
16#18011837—24no—
17#18011836—24no—
18#18011826—22no—
19C2×#41×C149C2211yescharacteristic
20C2×M16×C149C2212yes—
21#101×C149—21no—
22#100×C149—21no—
23#14558736—24no—
24#14558736—24no—
25#14558736—22no—
26#14558736D414yes—
27#14558735—216no—
28#14558735—28no—
29C2×Dic298—24no—
30C2×Dic298—24no—
31C2×Dic298—22no—
32C2×Dic298—21no—
33C2×Dic298—22no—
34C2×Dic298C2×C411yescharacteristic
35C2×Dic298C2×C412yes—
36C2×Dic298D414yes—
37Q8×D149—28no—
38C2×D596C2×C411yescharacteristic
39C2×C22⋊D149—22no—
40C2×C22⋊D149—21no—
41C22×Dic149—22no—
42C22×Dic149—21no—
43C2×C4×D149—22no—
44C2×C4×D149—21no—
45C4⋊Dic149—22no—
46C22⋊Dic149—22no—
47C4×Dic149—22no—
48#41×C149—22no—
49#41×C149—22no—
50C2×Q8×C149D411yescharacteristic
51C2×D4×C149D412yes—
52C2×D4×C149D411yescharacteristic
53C22×C4×C149C2×C412yes—
54C22×C4×C149C2311yescharacteristic
55M16×C149—22no—
56M16×C149—22no—
57C2×C8×C149—22no—
58C22×D149—21no—
59Dic298—28no—
60Dic298—21no—
61Dic298—22no—
62Dic298—24no—
63Dic298C22⋊C412yes—
64Dic298C22⋊C414yes—
65D596—21no—
66D596C22⋊C412yes—
67C22⋊D149—28no—
68C22⋊D149—24no—
69C2×Dic149—28no—
70C2×Dic149—22no—
71C2×Dic149—21no—
72C2×Dic149—24no—
73C2×Dic149—42no—
74C4×D149—28no—
75C4×D149—24no—
76C23×C149C22⋊C412yes—
77C23×C149C2×D411yescharacteristic
78Q8×C149—22no—
79D4×C149—24no—
80D4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—22no—
83C2×C4×C149C22⋊C412yes—
84C2×C4×C149C22×C411yescharacteristic
85C2×C4×C149C2×D412yes—
86C2×C4×C149C2×D412yes—
87C2×C4×C149C2×D411yescharacteristic
88C8×C149—42no—
89C22×C149—22no—
90C22×C149—41no—
91C22×C149—42no—
92C22×C149C2×C22⋊C411yescharacteristic
93C22×C149#12012yes—
94C2×D149—22no—
95C2×D149—42no—
96C4×C149—22no—
97C4×C149C2×C22⋊C411yescharacteristic
98C4×C149C2×C22⋊C411yescharacteristic
99C4×C149#12012yes—
100Dic149—24no—
101Dic149—22no—
102Dic149—82no—
103C2×C149—22no—
104C2×C149—21no—
105C2×C149—42no—
106C2×C149#37911yescharacteristic
107D149—42no—
108C149#179611yescharacteristic, complemented, Sylow
109#1796—1491nomaximal, Sylow
110C2×2−1+4—1491no—
111#421—1492no—
112#419—1492no—
113#413D14911yescharacteristic, complemented
114#410—1491no—
1152−1+4—2984no—
1162−1+4—2984no—
117C2×#41—2981no—
118C2×#41—2982no—
119C2×#41—1492no—
120C2×#41—1491no—
121C2×#41C2×D14911yescharacteristic
122C22×Q8—2981no—
123C22×Q8—1492no—
124C22×Q8—1491no—
125C2×M16C2×D14912yes—
126#117—1492no—
127#104—2984no—
128#103—2984no—
129#101—21no—
130#100—21no—
131#99—2982no—
132#41—22no—
133#41—22no—
134#41—2984no—
135#41—2984no—
136#41—29816no—
137#41—2988no—
138#41—2982no—
139#41—1494no—
140C2×Q8—2984no—
141C2×Q8—2984no—
142C2×Q8—2988no—
143C2×Q8—2982no—
144C2×Q8—2981no—
145C2×Q8—2982no—
146C2×Q8—1491no—
147C2×Q8—1492no—
148C2×Q8—1494no—
149C2×Q8C22⋊D14911yescharacteristic
150C2×D4—2981no—
151C2×D4—2982no—
152C2×D4—1491no—
153C2×D4C22⋊D14911yescharacteristic
154C2×D4D59612yes—
155C22×C4—2981no—
156C22×C4—2982no—
157C22×C4—2981no—
158C22×C4—2982no—
159C22×C4C4×D14912yes—
160C22×C4C22×D14911yescharacteristic
161M16—22no—
162M16—22no—
163C2×C8—22no—
164C4⋊C4—2982no—
165C22⋊C4—2982no—
166C42—2982no—
167C23—2981no—
168C23#1455871312yes—
169C23C2×D59611yescharacteristic
170Q8—22no—
171Q8—2988no—
172Q8—2981no—
173Q8—2982no—
174Q8—2984no—
175Q8—1492no—
176Q8—1494no—
177D4—24no—
178D4—22no—
179D4—2988no—
180D4—2984no—
181D4—2981no—
182D4—1492no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—2988no—
186C2×C4—2988no—
187C2×C4—2982no—
188C2×C4—2981no—
189C2×C4—2984no—
190C2×C4—2984no—
191C2×C4—5962no—
192C2×C4#1455871312yes—
193C2×C4C2×C4×D14911yescharacteristic
194C2×C4D4×D14912yes—
195C2×C4D4×D14912yes—
196C2×C4C2×C22⋊D14911yescharacteristic
197C8—42no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—2982no—
202C22—5962no—
203C22C2×#1455871311yescharacteristic
204C22#1801188112yes—
205C4—22no—
206C4—2984no—
207C4—2982no—
208C4—11922no—
209C4C22⋊C4×D14911yescharacteristic
210C4C22⋊C4×D14911yescharacteristic
211C4#1801187912yes—
212C2—22no—
213C2—21no—
214C2—42no—
215C2—5962no—
216C2#2374948011yescharacteristic
subgroupG/H
centerC2#23749480
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#413×C149C2
socleC2×C149#379
prime radicalC2×#18011958C2
cosocleC22×C4×C149C23
hypercenter#413D149
hypocenterC149#1796
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #23749641C2semidirect
3. #23749635C2semidirect
4. #23749599C2semidirect
5. #413×C149C2semidirect
8. C2×#14558736C4semidirect
12. C22×Dic298C4semidirect
108. C149#1796semidirect
113. #413D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119582
#237496412
#237496352
#237495992
#413×C1492
#1796149