Finite Group Databasebeta

← #34046005

Subgroups — #34046005

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×#14558723C211yesmaximal, characteristic
2C2×#18011840C211yesmaximal, characteristic, complemented
3C2×#18011833C211yesmaximal, characteristic
4#23749532C211yesmaximal, characteristic, complemented
5#23749526C211yesmaximal, characteristic
6#23749387C211yesmaximal, characteristic, complemented
7C2×#103×C149C211yesmaximal, characteristic, complemented
8C22×D596C2211yescharacteristic
9C2×#14558723—22no—
10C2×#14558723—22no—
11C2×#14558723—22no—
12C22×#11924746C2211yescharacteristic
13C2×C4⋊Dic149C2211yescharacteristic
14C2×#14558713—21no—
15C2×#14558713—21no—
16C2×C4×Dic149C2211yescharacteristic
17#18011840—22no—
18#18011833—22no—
19#18011818—21no—
20#18011818—21no—
21C22×Q8×C149C2211yescharacteristic
22C22×C8×C149C2211yescharacteristic
23C2×C4⋊C4×C149C2211yescharacteristic
24#103×C149—22no—
25C23×D149—21no—
26C2×D596—21no—
27C2×D596—21no—
28C2×D596—21no—
29C2×D596—21no—
30C2×D596—21no—
31C2×D596D412yes—
32C22×Dic149—21no—
33C22×Dic149D411yescharacteristic
34C22×Dic149D411yescharacteristic
35#14558723—28no—
36C2×#11924746—21no—
37C2×#11924746—21no—
38C2×#11924746D412yes—
39C4⋊Dic149—21no—
40C4⋊Dic149—21no—
41#14558713—42no—
42#14558713—42no—
43C4×Dic149—21no—
44C4×Dic149—21no—
45C2×Q8×C149—21no—
46C2×Q8×C149—21no—
47C2×Q8×C149—21no—
48C2×Q8×C149—21no—
49C2×Q8×C149—21no—
50C2×Q8×C149D412yes—
51C22×C4×C149—21no—
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—
59C22×D149—22no—
60C22×D149—41no—
61C22×D149—41no—
62C22×D149—41no—
63C22×D149—41no—
64C22×D149—41no—
65C22×D149—41no—
66D596—22no—
67D596—22no—
68D596—41no—
69D596—41no—
70C2×Dic149—21no—
71C2×Dic149—21no—
72C2×Dic149—21no—
73C2×Dic149—21no—
74C2×Dic149—21no—
75C2×Dic149—41no—
76C2×Dic149—41no—
77C2×Dic149—41no—
78C2×Dic149SD1612yescomplemented
79#11924746—22no—
80C23×C149C2×D411yescharacteristic
81Q8×C149—22no—
82Q8×C149—22no—
83Q8×C149—41no—
84Q8×C149—41no—
85C2×C4×C149—22no—
86C2×C4×C149—41no—
87C2×C4×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#12111yescharacteristic
99C22×C149#12111yescharacteristic
100C22×C149#12111yescharacteristic
101C22×C149C2×SD1611yescharacteristic
102C22×C149#13511yescharacteristic
103C22×C149AGL(1,ℤ/8)11yescharacteristic
104C22×C149#13711yescharacteristic
105C2×D149—42no—
106C2×D149—42no—
107C2×D149—42no—
108C2×D149—81no—
109C2×D149—81no—
110C2×D149—81no—
111C2×D149—81no—
112C4×C149—42no—
113C4×C149—81no—
114C4×C149#12011yescharacteristic
115C4×C149#12311yescharacteristic
116C4×C149#12311yescharacteristic
117C4×C149#12411yescharacteristic
118Dic149—22no—
119Dic149—41no—
120Dic149—81no—
121C2×C149#39411yescharacteristic
122C2×C149#46011yescharacteristic
123C2×C149#46111yescharacteristic
124C2×C149#46311yescharacteristic
125C2×C149#46411yescharacteristic
126C2×C149#46511yescharacteristic
127C2×C149#46811yescharacteristic
128D149—82no—
129C149#205511yescharacteristic, complemented, Sylow
130#2055—1491nomaximal, Sylow
131C22×SD16—1491no—
132C2×C4⋊C8—1491no—
133C2×#103D14911yescharacteristic, complemented
134C2×#102—1491no—
135#391—1491no—
136#390—1491no—
137#340—1491no—
138C22×Q8C2×D14911yescharacteristic
139C22×D4—1491no—
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—22no—
152#102—2982no—
153#95—2981no—
154#95—2981no—
155C24—2981no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D14912yes—
162C2×D4—2981no—
163C2×D4—2981no—
164C2×D4—2981no—
165C2×D4—2981no—
166C2×D4—2981no—
167C2×D4—1492no—
168C22×C4—21no—
169C22×C4—21no—
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—2982no—
190C23—5961no—
191C23—5961no—
192C23—5961no—
193C23—5961no—
194C23—5961no—
195C23—5961no—
196C23D4×D14911yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—2982no—
202D4—2982no—
203D4—5961no—
204D4—5961no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2981no—
212C2×C4—2981no—
213C2×C4—2981no—
214C2×C4—2981no—
215C2×C4—2981no—
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—5962no—
229C22—5962no—
230C22—5962no—
231C22—11921no—
232C22—11921no—
233C22—11921no—
234C22—11921no—
235C22#1801188311yescharacteristic
236C22#1801188411yescharacteristic
237C22#1801188411yescharacteristic
238C22SD16×D14911yescharacteristic
239C22#1801193411yescharacteristic
240C22#1801193811yescharacteristic
241C22#1801194311yescharacteristic
242C4—42no—
243C4—81no—
244C4—2982no—
245C4—5961no—
246C4—11921no—
247C4#1801187911yescharacteristic
248C4#1801189311yescharacteristic
249C4#1801189411yescharacteristic
250C4#1801189711yescharacteristic
251C2—11922no—
252C2#2374954011yescharacteristic
253C2#2374982311yescharacteristic
254C2#2374982911yescharacteristic
255C2#2374984311yescharacteristic
256C2#2374984911yescharacteristic
257C2#2374985711yescharacteristic
258C2#2374987411yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#103×C149C2
socleC23×C149C2×D4
prime radicalC22×D596C22
hypercenterC2×#103D149
hypocenterC149#2055
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#18011840C2semidirect
4. #23749532C2semidirect
6. #23749387C2semidirect
7. C2×#103×C149C2semidirect
78. C2×Dic149SD16semidirect
129. C149#2055semidirect
133. C2×#103D149semidirect

Maximal subgroups

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

subgroupindex
C22×#145587232
C2×#180118402
C2×#180118332
#237495322
#237495262
#237493872
C2×#103×C1492
#2055149