Finite Group Databasebeta

← #34045561

Subgroups — #34045561

Order 19072.

304 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C22×#14558726C211yesmaximal, characteristic
2C2×#18011842C211yesmaximal, characteristic
3C2×#18011835C211yesmaximal, characteristic
4C2×#18011834C211yesmaximal, characteristic
5C2×#18011822C211yesmaximal, characteristic
6#23749531C211yesmaximal, characteristic
7#391×C149C211yesmaximal, characteristic
8C22×Dic298C2211yescharacteristic
9C2×#14558726—22no—
10C2×#14558726—22no—
11C2×#14558726C414yescomplemented
12C22×#11924746C2211yescharacteristic
13C22×#11924746C2211yescharacteristic
14C2×C4⋊Dic149C2211yescharacteristic
15#18011842—22no—
16#18011835—22no—
17#18011834—22no—
18#18011822—22no—
19#18011818—22no—
20C22×Q8×C149C2211yescharacteristic
21C2×C4⋊C4×C149C2211yescharacteristic
22C2×C42×C149C2211yescharacteristic
23#95×C149—22no—
24C2×Dic298—21no—
25C2×Dic298—21no—
26C2×Dic298—21no—
27C2×Dic298—21no—
28C2×Dic298—21no—
29C2×Dic298C2×C412yes—
30C22×Dic149—21no—
31C22×Dic149—21no—
32#14558726—28no—
33C2×#11924746—21no—
34C2×#11924746—21no—
35C2×#11924746C2×C412yes—
36C2×#11924746D412yes—
37C2×#11924746D412yes—
38C2×#11924746D412yes—
39C4⋊Dic149—21no—
40C4⋊Dic149—21no—
41C2×Q8×C149—21no—
42C2×Q8×C149—21no—
43C2×Q8×C149—21no—
44C2×Q8×C149—21no—
45C2×Q8×C149—21no—
46C2×Q8×C149C2×C412yes—
47C22×C4×C149—21no—
48C22×C4×C149—21no—
49C22×C4×C149D412yes—
50C22×C4×C149C2311yescharacteristic
51C4⋊C4×C149—21no—
52C4⋊C4×C149—21no—
53C42×C149—21no—
54C42×C149—21no—
55Dic298—22no—
56Dic298—22no—
57Dic298—41no—
58Dic298—41no—
59C2×Dic149—22no—
60C2×Dic149—41no—
61C2×Dic149—41no—
62C2×Dic149—41no—
63C2×Dic149—42no—
64#11924746—22no—
65#11924746C22⋊C414yes—
66C23×C149C2×D411yescharacteristic
67Q8×C149—22no—
68Q8×C149—22no—
69Q8×C149—41no—
70Q8×C149—41no—
71C2×C4×C149—22no—
72C2×C4×C149—22no—
73C2×C4×C149—22no—
74C2×C4×C149—22no—
75C2×C4×C149—41no—
76C2×C4×C149—41no—
77C2×C4×C149—41no—
78C2×C4×C149—42no—
79C2×C4×C149C22×C411yescharacteristic
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149#4111yescharacteristic
84C2×C4×C149#4111yescharacteristic
85C22×C149C4×D411yescharacteristic
86C22×C149#12111yescharacteristic
87C22×C149#12711yescharacteristic
88C22×C149#13712yes—
89C22×C149#13712yes—
90C4×C149—42no—
91C4×C149—42no—
92C4×C149—81no—
93C4×C149C2×C22⋊C411yescharacteristic
94C4×C149C4×D411yescharacteristic
95C4×C149#12111yescharacteristic
96C4×C149#12411yescharacteristic
97Dic149—42no—
98Dic149—81no—
99C2×C149#39011yescharacteristic
100C2×C149#44112yes—
101C2×C149#47012yes—
102C2×C149#49711yescharacteristic
103C2×C149#49711yescharacteristic
104C149#197111yescharacteristic, complemented, Sylow
105#1971—1491nomaximal, Sylow
106C22×Q16—1491no—
107C2×#106—1491no—
108C2×#103—1491no—
109C2×#103—1491no—
110C2×#97—1491no—
111#391—1491no—
112#391D14911yescharacteristic
113C22×Q8—1491no—
114C22×Q8C2×D14911yescharacteristic
115C2×Q16—2982no—
116C2×Q16—2982no—
117C2×Q16—1494no—
118C22×C8—1491no—
119C22×C8—1491no—
120C2×C4⋊C4—1491no—
121C2×C4⋊C4C2×D14911yescharacteristic
122C2×C42C2×D14911yescharacteristic
123#106—2982no—
124#103—2982no—
125#103—2982no—
126#97—2982no—
127#95—22no—
128#95—2982no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—2981no—
135C2×Q8—2981no—
136C2×Q8—2981no—
137C2×Q8—2981no—
138C2×Q8—2981no—
139C2×Q8—1492no—
140C2×Q8C4×D14912yes—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—2981no—
144C22×C4—2981no—
145C22×C4C22⋊D14912yes—
146C22×C4C22×D14911yescharacteristic
147Q16—2988no—
148C2×C8—2981no—
149C2×C8—2981no—
150C2×C8—1492no—
151C2×C8—1492no—
152C2×C8—1492no—
153C2×C8—1492no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—2981no—
157C4⋊C4—2981no—
158C42—21no—
159C42—21no—
160C23C2×C22⋊D14911yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165Q8—2982no—
166Q8—2982no—
167Q8—5961no—
168Q8—5961no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—2982no—
178C2×C4—5961no—
179C2×C4—5961no—
180C2×C4—5961no—
181C2×C4—5962no—
182C2×C4C2×C4×D14911yescharacteristic
183C2×C4D4×D14911yescharacteristic
184C2×C4D4×D14911yescharacteristic
185C2×C4D4×D14911yescharacteristic
186C2×C4#1455873511yescharacteristic
187C2×C4#1455873611yescharacteristic
188C8—2982no—
189C8—1494no—
190C22C4×C22⋊D14911yescharacteristic
191C22#1801188311yescharacteristic
192C22#1801190711yescharacteristic
193C22#1801194112yes—
194C22#1801194212yes—
195C4—42no—
196C4—42no—
197C4—81no—
198C4—5962no—
199C4—11921no—
200C4C22⋊C4×D14911yescharacteristic
201C4#1801187111yescharacteristic
202C4#1801188411yescharacteristic
203C4#1801189711yescharacteristic
204C2#2374952511yescharacteristic
205C2#2374973012yes—
206C2#2374988112yes—
207C2#2375001711yescharacteristic
208C2#2375002011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#391×C149C2
socle, prime radicalC23×C149C2×D4
cosocleC22×C4×C149C23
hypercenter#391D149
hypocenterC149#1971
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
11. C2×#14558726C4semidirect
104. C149#1971semidirect

Maximal subgroups

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

subgroupindex
C22×#145587262
C2×#180118422
C2×#180118352
C2×#180118342
C2×#180118222
#237495312
#391×C1492
#1971149