Finite Group Databasebeta

← #34044723

Subgroups — #34044723

Order 19072.

316 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14558719C211yesmaximal, characteristic
2C2×#18011844C211yesmaximal, characteristic, complemented
3C2×#18011842C211yesmaximal, characteristic, complemented
4#23749482C211yesmaximal, characteristic
5#23749482C211yesmaximal, characteristic
6#23749388C211yesmaximal, characteristic, complemented
7#340×C149C211yesmaximal, characteristic, complemented
8C22×C4×D149C2211yescharacteristic
9C2×#14558719—22no—
10C2×#14558719—22no—
11C2×#14558719C414yescomplemented
12C22×#11924746C2211yescharacteristic
13C2×C4⋊Dic149C2211yescharacteristic
14C2×C4⋊Dic149C2211yescharacteristic
15C2×#14558713—21no—
16C2×#14558713—21no—
17#18011844—22no—
18#18011842—22no—
19#18011818—21no—
20#18011818—21no—
21C22×C8×C149C2211yescharacteristic
22C2×C4⋊C4×C149C2211yescharacteristic
23C2×C4⋊C4×C149C2211yescharacteristic
24C23×D149D411yescharacteristic
25C22×Dic149—21no—
26C22×Dic149—21no—
27C22×Dic149D411yescharacteristic
28C2×C4×D149—21no—
29C2×C4×D149—21no—
30C2×C4×D149—21no—
31C2×C4×D149—21no—
32C2×C4×D149C2×C412yes—
33C2×C4×D149Q812yes—
34#14558719—28no—
35C2×#11924746C2×C412yes—
36C2×#11924746D412yes—
37C2×#11924746D412yes—
38C4⋊Dic149—21no—
39C4⋊Dic149—21no—
40C4⋊Dic149—21no—
41C4⋊Dic149—21no—
42#14558713—42no—
43#14558713—42no—
44C22×C4×C149—21no—
45C22×C4×C149—21no—
46C22×C4×C149C2311yescharacteristic
47C2×C8×C149—21no—
48C2×C8×C149—21no—
49C2×C8×C149C2×C412yes—
50C4⋊C4×C149—21no—
51C4⋊C4×C149—21no—
52C4⋊C4×C149—21no—
53C4⋊C4×C149—21no—
54C22×D149—21no—
55C22×D149—21no—
56C22×D149—21no—
57C22×D149—21no—
58C22×D149—21no—
59C22×D149—21no—
60C22×D149C4⋊C412yes—
61C2×Dic149—21no—
62C2×Dic149—21no—
63C2×Dic149—41no—
64C2×Dic149—41no—
65C2×Dic149—41no—
66C2×Dic149—41no—
67C2×Dic149—41no—
68C2×Dic149—41no—
69C2×Dic149C4⋊C412yes—
70C4×D149—22no—
71C4×D149—22no—
72C4×D149—22no—
73C4×D149—22no—
74#11924746C22⋊C414yescomplemented
75C23×C149C2×D411yescharacteristic
76C2×C4×C149—41no—
77C2×C4×C149—41no—
78C2×C4×C149—41no—
79C2×C4×C149—41no—
80C2×C4×C149—41no—
81C2×C4×C149—41no—
82C2×C4×C149C22×C411yescharacteristic
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2×Q811yescharacteristic
86C2×C4×C149#4111yescharacteristic
87C2×C4×C149#4111yescharacteristic
88C8×C149—22no—
89C22×C149C2×C4⋊C411yescharacteristic
90C22×C149#12111yescharacteristic
91C22×C149#12111yescharacteristic
92C22×C149AGL(1,ℤ/8)11yescharacteristic
93C22×C149AGL(1,ℤ/8)11yescharacteristic
94C22×C149#13711yescharacteristic
95C22×C149#13711yescharacteristic
96C2×D149—22no—
97C2×D149—22no—
98C2×D149—22no—
99C2×D149—41no—
100C2×D149—41no—
101C2×D149—41no—
102C2×D149—41no—
103C4×C149—81no—
104C4×C149—81no—
105C4×C149C2×C22⋊C411yescharacteristic
106C4×C149#11711yescharacteristic
107C4×C149C22⋊Q811yescharacteristic
108C4×C149C22⋊Q811yescharacteristic
109Dic149—22no—
110Dic149—81no—
111Dic149—81no—
112C2×C149#38011yescharacteristic
113C2×C149#42811yescharacteristic
114C2×C149#42811yescharacteristic
115C2×C149#46811yescharacteristic
116C2×C149#46811yescharacteristic
117C2×C149#46911yescharacteristic
118C2×C149#47011yescharacteristic
119D149—42no—
120C149#180911yescharacteristic, complemented, Sylow
121#1809—1491nomaximal, Sylow
122C22×M16—1491no—
123C2×#107—1491no—
124C2×#106—1491no—
125#380—1491no—
126#380—1491no—
127#340—1491no—
128#340D14911yescharacteristic, complemented
129C23×C4—1491no—
130C2×M16—2982no—
131C2×M16—2982no—
132C2×M16—1494no—
133C22×C8—1491no—
134C22×C8C2×D14911yescharacteristic
135C2×C4⋊C4—1491no—
136C2×C4⋊C4—1491no—
137C2×C4⋊C4C2×D14911yescharacteristic
138C2×C4⋊C4C2×D14911yescharacteristic
139C2×C22⋊C4—2981no—
140C2×C22⋊C4—2981no—
141#107—2982no—
142#106—2982no—
143#95—2981no—
144#95—2981no—
145C24—1491no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—2981no—
149C22×C4—2981no—
150C22×C4—2981no—
151C22×C4—2981no—
152C22×C4—2981no—
153C22×C4—2981no—
154C22×C4—1491no—
155C22×C4—1492no—
156C22×C4—1492no—
157C22×C4C22×D14911yescharacteristic
158M16—2988no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—1492no—
162C2×C8—1492no—
163C2×C8—1492no—
164C2×C8C4×D14912yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—2981no—
170C4⋊C4—2981no—
171C4⋊C4—2981no—
172C4⋊C4—2981no—
173C22⋊C4—5962no—
174C22⋊C4—5962no—
175C23—2981no—
176C23—2981no—
177C23—2981no—
178C23—2981no—
179C23—2981no—
180C23—2981no—
181C23—1492no—
182C23D4×D14911yescharacteristic
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2981no—
190C2×C4—2981no—
191C2×C4—2982no—
192C2×C4—2982no—
193C2×C4—2982no—
194C2×C4—2982no—
195C2×C4—5961no—
196C2×C4—5961no—
197C2×C4—5961no—
198C2×C4—5961no—
199C2×C4—5961no—
200C2×C4—5961no—
201C2×C4—1492no—
202C2×C4C2×C4×D14911yescharacteristic
203C2×C4D4×D14911yescharacteristic
204C2×C4D4×D14911yescharacteristic
205C2×C4Q8×D14911yescharacteristic
206C2×C4#1455873611yescharacteristic
207C2×C4#1455873611yescharacteristic
208C8—22no—
209C8—1494no—
210C22—2982no—
211C22—2982no—
212C22—2982no—
213C22—5961no—
214C22—5961no—
215C22—5961no—
216C22—5961no—
217C22C4⋊C4×D14911yescharacteristic
218C22#1801188411yescharacteristic
219C22#1801188411yescharacteristic
220C22#1801193511yescharacteristic
221C22#1801193811yescharacteristic
222C22#1801194011yescharacteristic
223C22#1801194311yescharacteristic
224C4—81no—
225C4—81no—
226C4—2982no—
227C4—11921no—
228C4—11921no—
229C4C22⋊C4×D14911yescharacteristic
230C4#1801186811yescharacteristic
231C4#1801188911yescharacteristic
232C4#1801188911yescharacteristic
233C2—5962no—
234C2#2374948411yescharacteristic
235C2#2374966411yescharacteristic
236C2#2374966611yescharacteristic
237C2#2374987011yescharacteristic
238C2#2374987411yescharacteristic
239C2#2374987711yescharacteristic
240C2#2374988211yescharacteristic
subgroupG/H
centerC23D4×D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#340×C149C2
socleC23×C149C2×D4
prime radicalC23×D149D4
cosocleC22×C4×C149C23
hypercenter#340D149
hypocenterC149#1809
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#18011844C2semidirect
3. C2×#18011842C2semidirect
6. #23749388C2semidirect
7. #340×C149C2semidirect
11. C2×#14558719C4semidirect
74. #11924746C22⋊C4semidirect
120. C149#1809semidirect
128. #340D149semidirect

Maximal subgroups

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

subgroupindex
C22×#145587192
C2×#180118442
C2×#180118422
#237494822
#237493882
#340×C1492
#1809149