Finite Group Databasebeta

← #34046007

Subgroups — #34046007

Order 19072.

324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14558724C211yesmaximal, characteristic
2C2×#18011840C211yesmaximal, characteristic, complemented
3C2×#18011836C211yesmaximal, characteristic, complemented
4#23749530C211yesmaximal, characteristic, complemented
5#23749528C211yesmaximal, characteristic
6#23749387C211yesmaximal, characteristic, complemented
7C2×#102×C149C211yesmaximal, characteristic
8C22×Dic298C2211yescharacteristic
9C2×#14558724—22no—
10C2×#14558724—22no—
11C2×#14558724—22no—
12C22×#11924746C2211yescharacteristic
13C2×C4⋊Dic149C2211yescharacteristic
14C2×C22⋊Dic149—21no—
15C2×C22⋊Dic149—21no—
16C2×C4×Dic149C2211yescharacteristic
17#18011840—22no—
18#18011836—22no—
19#18011818—21no—
20#18011818—21no—
21C22×D4×C149C2211yescharacteristic
22C22×C8×C149C2211yescharacteristic
23C2×C4⋊C4×C149C2211yescharacteristic
24#102×C149—22no—
25C2×Dic298—21no—
26C2×Dic298—21no—
27C2×Dic298—21no—
28C2×Dic298—21no—
29C2×Dic298—21no—
30C2×Dic298D412yes—
31C22×Dic149—21no—
32C22×Dic149—21no—
33C22×Dic149D411yescharacteristic
34C22×Dic149D411yescharacteristic
35#14558724—28no—
36C2×#11924746—21no—
37C2×#11924746—21no—
38C2×#11924746D412yes—
39C4⋊Dic149—21no—
40C4⋊Dic149—21no—
41C22⋊Dic149—42no—
42C22⋊Dic149—42no—
43C4×Dic149—21no—
44C4×Dic149—21no—
45C24×C149—21no—
46C2×D4×C149—21no—
47C2×D4×C149—21no—
48C2×D4×C149—21no—
49C2×D4×C149—21no—
50C2×D4×C149—21no—
51C2×D4×C149D412yes—
52C22×C4×C149—21no—
53C22×C4×C149C2311yescharacteristic
54C2×C8×C149—21no—
55C2×C8×C149—21no—
56C2×C8×C149—21no—
57C4⋊C4×C149—21no—
58C4⋊C4×C149—21no—
59Dic298—22no—
60Dic298—22no—
61Dic298—41no—
62Dic298—41no—
63C2×Dic149—21no—
64C2×Dic149—21no—
65C2×Dic149—22no—
66C2×Dic149—21no—
67C2×Dic149—21no—
68C2×Dic149—21no—
69C2×Dic149—41no—
70C2×Dic149—41no—
71C2×Dic149—41no—
72C2×Dic149—41no—
73C2×Dic149—41no—
74C2×Dic149SD1612yescomplemented
75#11924746—22no—
76C23×C149—22no—
77C23×C149—41no—
78C23×C149—41no—
79C23×C149—41no—
80C23×C149—41no—
81C23×C149—41no—
82C23×C149—41no—
83C23×C149C2×D411yescharacteristic
84D4×C149—22no—
85D4×C149—22no—
86D4×C149—41no—
87D4×C149—41no—
88C2×C4×C149—41no—
89C2×C4×C149—41no—
90C2×C4×C149—41no—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149#4111yescharacteristic
95C2×C4×C149#4111yescharacteristic
96C2×C4×C149#4111yescharacteristic
97C8×C149—41no—
98C22×C149—42no—
99C22×C149—42no—
100C22×C149—42no—
101C22×C149—81no—
102C22×C149—81no—
103C22×C149—81no—
104C22×C149—81no—
105C22×C149#12111yescharacteristic
106C22×C149#12111yescharacteristic
107C22×C149#12111yescharacteristic
108C22×C149C2×SD1611yescharacteristic
109C22×C149#13511yescharacteristic
110C22×C149AGL(1,ℤ/8)11yescharacteristic
111C22×C149#13711yescharacteristic
112C4×C149—81no—
113C4×C149#12011yescharacteristic
114C4×C149#12311yescharacteristic
115C4×C149#12311yescharacteristic
116C4×C149#12411yescharacteristic
117Dic149—22no—
118Dic149—42no—
119Dic149—41no—
120Dic149—81no—
121C2×C149—82no—
122C2×C149#39411yescharacteristic
123C2×C149#46011yescharacteristic
124C2×C149#46111yescharacteristic
125C2×C149#46311yescharacteristic
126C2×C149#46411yescharacteristic
127C2×C149#46511yescharacteristic
128C2×C149#46811yescharacteristic
129C149#205511yescharacteristic, complemented, Sylow
130#2055—1491nomaximal, Sylow
131C22×SD16—1491no—
132C2×C4⋊C8—1491no—
133C2×#103—1491no—
134C2×#102D14911yescharacteristic
135#391—1491no—
136#390—1491no—
137#340—1491no—
138C22×Q8—1491no—
139C22×D4C2×D14911yescharacteristic
140C2×SD16—2982no—
141C2×SD16—2982no—
142C2×SD16—2982no—
143C22×C8—1491no—
144C22×C8C2×D14911yescharacteristic
145C2×C4⋊C4—1491no—
146C2×C4⋊C4C2×D14911yescharacteristic
147C2×C22⋊C4—2981no—
148C2×C22⋊C4—2981no—
149C2×C42—1491no—
150C4⋊C8—2982no—
151#103—2982no—
152#102—22no—
153#95—2981no—
154#95—2981no—
155C24—21no—
156C2×Q8—2981no—
157C2×Q8—2981no—
158C2×Q8—2981no—
159C2×Q8—2981no—
160C2×Q8—2981no—
161C2×Q8—1492no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4C22⋊D14912yes—
168C22×C4—21no—
169C22×C4—2981no—
170C22×C4—2981no—
171C22×C4—1491no—
172C22×C4—1491no—
173C22×C4C22×D14911yescharacteristic
174SD16—2988no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—2981no—
179C2×C8—2981no—
180C2×C8—1492no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—2981no—
184C4⋊C4—2981no—
185C22⋊C4—5962no—
186C22⋊C4—5962no—
187C42—2981no—
188C42—2981no—
189C23—22no—
190C23—41no—
191C23—41no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23D4×D14911yescharacteristic
197Q8—2982no—
198Q8—2982no—
199Q8—5961no—
200Q8—5961no—
201D4—22no—
202D4—22no—
203D4—41no—
204D4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—2981no—
209C2×C4—2981no—
210C2×C4—2981no—
211C2×C4—2981no—
212C2×C4—2981no—
213C2×C4—2982no—
214C2×C4—5961no—
215C2×C4—5961no—
216C2×C4—5961no—
217C2×C4—5961no—
218C2×C4—5961no—
219C2×C4—1492no—
220C2×C4D4×D14911yescharacteristic
221C2×C4D4×D14911yescharacteristic
222C2×C4C2×C22⋊D14911yescharacteristic
223C2×C4#1455873511yescharacteristic
224C2×C4#1455873611yescharacteristic
225C2×C4#1455873611yescharacteristic
226C8—41no—
227C8—2982no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—81no—
235C22#1801188311yescharacteristic
236C22#1801188411yescharacteristic
237C22#1801188411yescharacteristic
238C22SD16×D14911yescharacteristic
239C22#1801193011yescharacteristic
240C22#1801193511yescharacteristic
241C22#1801194011yescharacteristic
242C4—81no—
243C4—2982no—
244C4—5962no—
245C4—5961no—
246C4—11921no—
247C4#1801187911yescharacteristic
248C4#1801189311yescharacteristic
249C4#1801189411yescharacteristic
250C4#1801189711yescharacteristic
251C2—82no—
252C2#2374954011yescharacteristic
253C2#2374982411yescharacteristic
254C2#2374982811yescharacteristic
255C2#2374983811yescharacteristic
256C2#2374984611yescharacteristic
257C2#2374985311yescharacteristic
258C2#2374987011yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#102×C149C2
socleC23×C149C2×D4
prime radicalC22×D4×C149C22
hypercenterC2×#102D149
hypocenterC149#2055
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#18011840C2semidirect
3. C2×#18011836C2semidirect
4. #23749530C2semidirect
6. #23749387C2semidirect
74. C2×Dic149SD16semidirect
129. C149#2055semidirect

Maximal subgroups

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

subgroupindex
C22×#145587242
C2×#180118402
C2×#180118362
#237495302
#237495282
#237493872
C2×#102×C1492
#2055149