Finite Group Databasebeta

← #34077590

Subgroups — #34077590

Order 19328.

704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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×#18012787C211yesmaximal, characteristic
2#23752978C212yesmaximal, complemented
3#23752195C214yesmaximal, complemented
4#23752194C212yesmaximal, complemented
5C2×#18012658C211yesmaximal, characteristic, complemented
6#101×D151C214yesmaximal, complemented
7C2×#101×C151C211yesmaximal, characteristic, complemented
8#18012787—24no—
9#18012787—24no—
10C2×#14559005C412yes—
11C2×#14559005C2212yes—
12C2×#14559004C414yes—
13C2×#14559004C2211yescharacteristic
14C2×#14559004C2211yescharacteristic
15C2×Q8×D151C412yes—
16C2×Q8×D151C2212yes—
17#18012747—24no—
18#18012745—24no—
19C2×#14558988C2212yes—
20M16×D151C2218yes—
21#18012658C2214yes—
22#18012657C2214yes—
23#18012655C2214yes—
24C22×Q8×C151C2211yescharacteristic
25C2×M16×C151C2212yes—
26#101×C151C2214yes—
27#14559005—28no—
28#14559005—28no—
29#14559004—28no—
30#14559004—28no—
31#14559004—22no—
32#14559004—22no—
33#14559004D414yes—
34#14559004D414yes—
35C2×Dic302C2×C414yes—
36C2×Dic302C2×C411yescharacteristic
37C2×Dic302C2311yescharacteristic
38Q8×D151—28no—
39Q8×D151—28no—
40C2×D604C2×C414yes—
41C2×D604C2×C411yescharacteristic
42C2×D604C2311yescharacteristic
43C2×C22⋊D151C2×C412yes—
44C2×C22⋊D151C2×C412yes—
45C2×C4×D151C2×C414yes—
46C2×C4×D151C2×C412yes—
47C2×C4×D151C2×C414yes—
48C2×C4×D151C2312yes—
49#14558988—22no—
50#14558988C2314yes—
51#14558987—28no—
52C2×C151⋊C8—22no—
53C8×D151—28no—
54C2×Q8×C151—22no—
55C2×Q8×C151—22no—
56C2×Q8×C151C2×C412yes—
57C2×Q8×C151C2312yes—
58C22×C4×C151C2×C412yes—
59C22×C4×C151C2311yescharacteristic
60M16×C151—22no—
61M16×C151C2314yes—
62C2×C8×C151—22no—
63C22×D151C22×C412yes—
64C22×D151C22×C412yes—
65Dic302—22no—
66Dic302—28no—
67Dic302C22⋊C414yes—
68D604—28no—
69D604—22no—
70D604C22⋊C414yes—
71C22⋊D151—22no—
72C22⋊D151—22no—
73C22⋊D151C22⋊C414yes—
74C22⋊D151C22⋊C414yes—
75C2×Dic151C22×C412yes—
76C2×Dic151C22×C412yes—
77C4×D151—28no—
78C4×D151—24no—
79C4×D151—28no—
80C4×D151C2×D418yes—
81C151⋊C8—24no—
82C23×C151C22×C411yescharacteristic
83Q8×C151—24no—
84Q8×C151—24no—
85C2×C4×C151—22no—
86C2×C4×C151—22no—
87C2×C4×C151C22×C414yes—
88C2×C4×C151C22×C411yescharacteristic
89C2×C4×C151C2×D412yes—
90C2×C4×C151C2×D412yes—
91C2×C4×C151C2411yescharacteristic
92C8×C151—24no—
93C22×C151—41no—
94C22×C151C2×C22⋊C411yescharacteristic
95C22×C151C2×C22⋊C411yescharacteristic
96C22×C151C23×C411yescharacteristic
97C2×D151—22no—
98C2×D151—42no—
99C2×D151—42no—
100C2×D151C2×C22⋊C414yes—
101C4×C151—24no—
102C4×C151C2×C22⋊C412yes—
103C4×C151C22×D412yes—
104Dic151—22no—
105Dic151C2×C22⋊C414yes—
106C2×C151—21no—
107C2×C151—21no—
108C2×C151—21no—
109C2×C151C22×C22⋊C411yescharacteristic
110D151—24no—
111D151—42no—
112C151#288911yescharacteristic, complemented, Sylow
113#2889—1511nomaximal, Sylow
114C2×2−1+4—1511no—
115#568—1512no—
116#413—1512no—
117#413—1514no—
118C2×#101—1511no—
119C2×#101—1514no—
120C2×#101D15111yescharacteristic, complemented
1212−1+4—3024no—
1222−1+4—3024no—
123C2×#41—1512no—
124C2×#41—1512no—
125C2×#41—1514no—
126C2×#41—1511no—
127C2×#41—1511no—
128C22×Q8—1512no—
129C22×Q8—1512no—
130C22×Q8C2×D15111yescharacteristic
131#131—3024no—
132#131—3024no—
133C2×M16—1512no—
134C2×M16—1518no—
135C2×M16C2×D15112yes—
136#101—1514no—
137#101—1514no—
138#101C2×D15114yes—
139#100—1514no—
140#41—3028no—
141#41—3028no—
142#41—3028no—
143#41—3028no—
144#41—3022no—
145#41—3022no—
146#41—1514no—
147#41—1514no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—3028no—
151C2×Q8—3028no—
152C2×Q8—1514no—
153C2×Q8—1511no—
154C2×Q8—1511no—
155C2×Q8C4×D15112yes—
156C2×Q8C22×D15112yes—
157C2×D4—1512no—
158C2×D4—1512no—
159C2×D4—1514no—
160C2×D4—1511no—
161C2×D4—1511no—
162C22×C4—1514no—
163C22×C4—1514no—
164C22×C4—1512no—
165C22×C4—1512no—
166C22×C4C4×D15112yes—
167C22×C4C22×D15111yescharacteristic
168M16—22no—
169M16—3028no—
170M16—3022no—
171M16—1514no—
172M16C22×D15114yes—
173C2×C8—22no—
174C2×C8—3028no—
175C2×C8—3022no—
176C23—1512no—
177C23—1512no—
178C23C2×C4×D15111yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—3028no—
182Q8—3022no—
183Q8—1514no—
184D4—3028no—
185D4—3022no—
186D4—3022no—
187D4—3022no—
188D4—1514no—
189D4—1514no—
190D4—1514no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—3028no—
194C2×C4—3028no—
195C2×C4—3024no—
196C2×C4—1512no—
197C2×C4—1512no—
198C2×C4—1518no—
199C2×C4C2×C4×D15114yes—
200C2×C4C2×C4×D15111yescharacteristic
201C2×C4D4×D15112yes—
202C2×C4D4×D15112yes—
203C2×C4C23×D15111yescharacteristic
204C8—24no—
205C8—3024no—
206C22—41no—
207C22—3022no—
208C22—6042no—
209C22—6042no—
210C22—1514no—
211C22C22⋊C4×D15111yescharacteristic
212C22C22⋊C4×D15111yescharacteristic
213C22C22×C4×D15111yescharacteristic
214C4—24no—
215C4—3022no—
216C4—1514no—
217C4C22⋊C4×D15112yes—
218C4C2×D4×D15112yes—
219C2—21no—
220C2—21no—
221C2—21no—
222C2—3024no—
223C2—6042no—
224C2C2×C22⋊C4×D15111yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D151
commutatorC22×C151C23×C4
FrattiniC2×C4C23×D151
FittingC2×#101×C151C2
socleC2×C151C22×C22⋊C4
prime radicalC2×#18012787C2
cosocleC2×C4×C151C24
hypercenterC2×#101D151
hypocenterC151#2889
LCSG ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #23752978C2semidirect
3. #23752195C2semidirect
4. #23752194C2semidirect
5. C2×#18012658C2semidirect
6. #101×D151C2semidirect
7. C2×#101×C151C2semidirect
112. C151#2889semidirect
120. C2×#101D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127872
#237529782
#237521952
#237521942
C2×#180126582
#101×D1512
C2×#101×C1512
#2889151