Finite Group Databasebeta

← #34046010

Subgroups — #34046010

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×#14558725C211yesmaximal, characteristic
2C2×#18011840C211yesmaximal, characteristic, complemented
3C2×#18011834C211yesmaximal, characteristic, complemented
4C2×#18011831C211yesmaximal, characteristic
5#23749530C211yesmaximal, characteristic, complemented
6#23749526C211yesmaximal, characteristic
7#340×C149C211yesmaximal, characteristic, complemented
8C22×Dic298C2211yescharacteristic
9C22×D596C2211yescharacteristic
10C2×#14558725—22no—
11C2×#14558725—22no—
12C2×#14558725—22no—
13C22×#11924746C2211yescharacteristic
14C2×#14558713—21no—
15C2×#14558713—21no—
16C2×C4×Dic149C2211yescharacteristic
17#18011840—22no—
18#18011834—22no—
19#18011831—22no—
20#18011818—21no—
21#18011818—21no—
22C22×C8×C149C2211yescharacteristic
23C2×C4⋊C4×C149C2211yescharacteristic
24C2×C4⋊C4×C149C2211yescharacteristic
25C23×D149—21no—
26C2×Dic298—21no—
27C2×Dic298—21no—
28C2×Dic298—21no—
29C2×Dic298—21no—
30C2×Dic298—21no—
31C2×Dic298D412yes—
32C2×D596—21no—
33C2×D596—21no—
34C2×D596—21no—
35C2×D596—21no—
36C2×D596—21no—
37C2×D596D412yes—
38C22×Dic149—21no—
39C22×Dic149D411yescharacteristic
40C22×Dic149D411yescharacteristic
41#14558725—28no—
42C2×#11924746—21no—
43C2×#11924746—21no—
44C2×#11924746—21no—
45#14558713—42no—
46#14558713—42no—
47C4×Dic149—21no—
48C4×Dic149—21no—
49C22×C4×C149—21no—
50C22×C4×C149—21no—
51C22×C4×C149C2311yescharacteristic
52C2×C8×C149—21no—
53C2×C8×C149—21no—
54C2×C8×C149D412yes—
55C4⋊C4×C149—21no—
56C4⋊C4×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—
66Dic298—22no—
67Dic298—22no—
68Dic298—41no—
69Dic298—41no—
70D596—22no—
71D596—22no—
72D596—41no—
73D596—41no—
74C2×Dic149—21no—
75C2×Dic149—21no—
76C2×Dic149—22no—
77C2×Dic149—21no—
78C2×Dic149—21no—
79C2×Dic149—21no—
80C2×Dic149—41no—
81C2×Dic149—41no—
82C2×Dic149SD1612yescomplemented
83#11924746—41no—
84C23×C149C2×D411yescharacteristic
85C2×C4×C149—41no—
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—22no—
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—81no—
113C4×C149—81no—
114C4×C149#12011yescharacteristic
115C4×C149#12311yescharacteristic
116C4×C149#12311yescharacteristic
117C4×C149#12411yescharacteristic
118Dic149—22no—
119Dic149—42no—
120Dic149—41no—
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×#103—1491no—
134C2×#102—1491no—
135#391—1491no—
136#390—1491no—
137#340D14911yescharacteristic, complemented
138C22×Q8—1491no—
139C22×D4—1491no—
140C2×SD16—2982no—
141C2×SD16—2982no—
142C2×SD16—2982no—
143C22×C8—1491no—
144C22×C8C2×D14911yescharacteristic
145C2×C4⋊C4C2×D14911yescharacteristic
146C2×C4⋊C4C2×D14911yescharacteristic
147C2×C22⋊C4—2981no—
148C2×C22⋊C4—2981no—
149C2×C42—1491no—
150C4⋊C8—2982no—
151#103—2982no—
152#102—2982no—
153#95—2981no—
154#95—2981no—
155C24—2981no—
156C2×Q8—2981no—
157C2×Q8—2981no—
158C2×Q8—2981no—
159C2×Q8—2981no—
160C2×Q8—2981no—
161C2×Q8—1492no—
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—2981no—
178C2×C8—2981no—
179C2×C8—2981no—
180C2×C8D59612yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—21no—
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—2982no—
198Q8—2982no—
199Q8—5961no—
200Q8—5961no—
201D4—2982no—
202D4—2982no—
203D4—5961no—
204D4—5961no—
205C2×C4—41no—
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—2982no—
216C2×C4—2981no—
217C2×C4—5961no—
218C2×C4—5961no—
219C2×C4—1492no—
220C2×C4D4×D14911yescharacteristic
221C2×C4D4×D14911yescharacteristic
222C2×C4C2×D59611yescharacteristic
223C2×C4#1455873611yescharacteristic
224C2×C4#1455873611yescharacteristic
225C2×C4#1455873711yescharacteristic
226C8—22no—
227C8—5961no—
228C22—5962no—
229C22—5962no—
230C22—5962no—
231C22—11921no—
232C22—11921no—
233C22—11921no—
234C22—11921no—
235C22#1801188411yescharacteristic
236C22#1801188411yescharacteristic
237C22#1801188611yescharacteristic
238C22SD16×D14911yescharacteristic
239C22#1801193211yescharacteristic
240C22#1801193511yescharacteristic
241C22#1801194311yescharacteristic
242C4—81no—
243C4—81no—
244C4—2982no—
245C4—5962no—
246C4—5961no—
247C4#1801188111yescharacteristic
248C4#1801189611yescharacteristic
249C4#1801189611yescharacteristic
250C4#1801189911yescharacteristic
251C2—11922no—
252C2#2374954311yescharacteristic
253C2#2374982411yescharacteristic
254C2#2374982911yescharacteristic
255C2#2374983911yescharacteristic
256C2#2374985011yescharacteristic
257C2#2374985511yescharacteristic
258C2#2374987211yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#340×C149C2
socleC23×C149C2×D4
prime radicalC22×D596C22
hypercenter#340D149
hypocenterC149#2055
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
2. C2×#18011840C2semidirect
3. C2×#18011834C2semidirect
5. #23749530C2semidirect
7. #340×C149C2semidirect
82. C2×Dic149SD16semidirect
129. C149#2055semidirect
137. #340D149semidirect

Maximal subgroups

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

subgroupindex
C22×#145587252
C2×#180118402
C2×#180118342
C2×#180118312
#237495302
#237495262
#340×C1492
#2055149