Finite Group Databasebeta

← #34045831

Subgroups — #34045831

Order 19072.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#18011910C211yesmaximal, characteristic
2C2×#18011836C211yesmaximal, characteristic
3C2×#18011834C211yesmaximal, characteristic
4#23749530C211yesmaximal, characteristic
5#23749387C211yesmaximal, characteristic
6#23749379C211yesmaximal, characteristic
7#340×C149C211yesmaximal, characteristic
8C22×Dic298—21no—
9C22×Dic298C2211yescharacteristic
10C22×#11924746C2211yescharacteristic
11#18011910—22no—
12#18011910—22no—
13C2×C4⋊Dic149C2211yescharacteristic
14C2×#14558715—21no—
15C2×C4×Dic149C2211yescharacteristic
16#18011836—22no—
17#18011834—22no—
18#18011818—21no—
19#18011818—21no—
20C22×C8×C149C2211yescharacteristic
21C2×C4⋊C4×C149C2211yescharacteristic
22C2×C4⋊C4×C149C2211yescharacteristic
23C2×Dic298—24no—
24C2×Dic298—21no—
25C2×Dic298—21no—
26C2×Dic298—21no—
27C2×Dic298—21no—
28C2×Dic298—21no—
29C2×Dic298—42no—
30C2×Dic298—42no—
31C2×Dic298Q812yescomplemented
32C22×Dic149—21no—
33C22×Dic149—21no—
34C22×Dic149D411yescharacteristic
35C22×Dic149D411yescharacteristic
36C2×#11924746—21no—
37C2×#11924746—21no—
38C2×#11924746—21no—
39C4⋊Dic149—21no—
40C4⋊Dic149D412yes—
41#14558715—24no—
42C4×Dic149—21no—
43C4×Dic149—21no—
44C22×C4×C149—21no—
45C22×C4×C149—21no—
46C22×C4×C149C2311yescharacteristic
47C2×C8×C149—21no—
48C2×C8×C149—21no—
49C2×C8×C149—21no—
50C4⋊C4×C149—21no—
51C4⋊C4×C149—21no—
52C4⋊C4×C149—21no—
53C4⋊C4×C149D412yes—
54Dic298—22no—
55Dic298—22no—
56Dic298—48no—
57Dic298—41no—
58Dic298—41no—
59C2×Dic149—21no—
60C2×Dic149—21no—
61C2×Dic149—21no—
62C2×Dic149—21no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65C2×Dic149—41no—
66C2×Dic149—41no—
67C2×Dic149—41no—
68C2×Dic149—41no—
69C2×Dic149SD1612yes—
70C2×Dic149Q1612yes—
71#11924746—41no—
72C23×C149C2×D411yescharacteristic
73C2×C4×C149—22no—
74C2×C4×C149—41no—
75C2×C4×C149—41no—
76C2×C4×C149—41no—
77C2×C4×C149—41no—
78C2×C4×C149—41no—
79C2×C4×C149C2×D411yescharacteristic
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2×Q811yescharacteristic
82C2×C4×C149#4111yescharacteristic
83C2×C4×C149#4111yescharacteristic
84C2×C4×C149#4111yescharacteristic
85C8×C149—41no—
86C22×C149#12011yescharacteristic
87C22×C149C22⋊Q811yescharacteristic
88C22×C149#12411yescharacteristic
89C22×C149C2×SD1611yescharacteristic
90C22×C149C2×Q1611yescharacteristic
91C22×C149AGL(1,ℤ/8)11yescharacteristic
92C22×C149#13711yescharacteristic
93C4×C149—42no—
94C4×C149—81no—
95C4×C149C22⋊Q811yescharacteristic
96C4×C149C22⋊Q811yescharacteristic
97C4×C149#12411yescharacteristic
98C4×C149#12411yescharacteristic
99Dic149—22no—
100Dic149—22no—
101Dic149—42no—
102Dic149—42no—
103C2×C149#39311yescharacteristic
104C2×C149#45011yescharacteristic
105C2×C149#45111yescharacteristic
106C2×C149#47511yescharacteristic
107C2×C149#47711yescharacteristic
108C2×C149#48711yescharacteristic
109C2×C149#48911yescharacteristic
110C149#202411yescharacteristic, complemented, Sylow
111#2024—1491nomaximal, Sylow
112C2×C4⋊Q8—1491no—
113C2×#103—1491no—
114C2×#103—1491no—
115#391—1491no—
116#340—1491no—
117#340D14911yescharacteristic
118#336—1491no—
119C22×Q8—2981no—
120C22×Q8—1491no—
121C22×C8—1491no—
122C22×C8C2×D14911yescharacteristic
123C4⋊Q8—2982no—
124C4⋊Q8—2982no—
125C2×C4⋊C4—2981no—
126C2×C4⋊C4—1491no—
127C2×C4⋊C4C2×D14911yescharacteristic
128C2×C4⋊C4C2×D14911yescharacteristic
129C2×C42—1491no—
130#103—2982no—
131#103—2982no—
132#95—2981no—
133#95—2981no—
134C2×Q8—2984no—
135C2×Q8—2981no—
136C2×Q8—2981no—
137C2×Q8—2981no—
138C2×Q8—2981no—
139C2×Q8—2981no—
140C2×Q8—5962no—
141C2×Q8—5962no—
142C2×Q8—1492no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—2981no—
146C22×C4—2981no—
147C22×C4—1491no—
148C22×C4—1491no—
149C22×C4C22×D14911yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—2981no—
154C2×C8—2981no—
155C2×C8—2981no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—2984no—
160C4⋊C4—2981no—
161C4⋊C4—1492no—
162C4⋊C4D59612yes—
163C42—2981no—
164C42—2981no—
165C23D4×D14911yescharacteristic
166Q8—2982no—
167Q8—2982no—
168Q8—5968no—
169Q8—5961no—
170Q8—5961no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—2981no—
178C2×C4—2981no—
179C2×C4—2981no—
180C2×C4—2981no—
181C2×C4—2982no—
182C2×C4—2982no—
183C2×C4—5961no—
184C2×C4—5961no—
185C2×C4—5961no—
186C2×C4—5961no—
187C2×C4—1492no—
188C2×C4—1492no—
189C2×C4D4×D14911yescharacteristic
190C2×C4C2×D59611yescharacteristic
191C2×C4Q8×D14911yescharacteristic
192C2×C4#1455873511yescharacteristic
193C2×C4#1455873611yescharacteristic
194C2×C4#1455873611yescharacteristic
195C8—41no—
196C8—5961no—
197C22#1801188111yescharacteristic
198C22#1801188911yescharacteristic
199C22#1801189711yescharacteristic
200C22SD16×D14911yescharacteristic
201C22Q16×D14911yescharacteristic
202C22#1801193511yescharacteristic
203C22#1801194011yescharacteristic
204C4—42no—
205C4—81no—
206C4—2982no—
207C4—2982no—
208C4—5962no—
209C4—5962no—
210C4#1801188911yescharacteristic
211C4#1801189111yescharacteristic
212C4#1801189711yescharacteristic
213C4#1801189911yescharacteristic
214C2#2374953811yescharacteristic
215C2#2374977711yescharacteristic
216C2#2374978211yescharacteristic
217C2#2374990911yescharacteristic
218C2#2374991911yescharacteristic
219C2#2374997411yescharacteristic
220C2#2374998311yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#340×C149C2
socle, prime radicalC23×C149C2×D4
hypercenter#340D149
hypocenterC149#2024
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
31. C2×Dic298Q8semidirect
110. C149#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#180119102
C2×#180118362
C2×#180118342
#237495302
#237493872
#237493792
#340×C1492
#2024149