Finite Group Databasebeta

← #34060680

Subgroups — #34060680

Order 19072.

324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×#18011998C211yesmaximal, characteristic, complemented
2C2×#18011976C211yesmaximal, characteristic, complemented
3C2×#18011975C211yesmaximal, characteristic, complemented
4#23750600C211yesmaximal, characteristic, complemented
5#23750501C211yesmaximal, characteristic, complemented
6(C2×#10597010)⋊C8C211yesmaximal, characteristic, complemented
7C2×#18011932C211yesmaximal, characteristic
8#18011998—22no—
9#18011998—22no—
10C2×#14558746C2211yescharacteristic
11C2×#14558746C2211yescharacteristic
12C2×#14558745—21no—
13C2×D149⋊C8C2211yescharacteristic
14C22×#11924753—21no—
15C2×C4×#10597010C2211yescharacteristic
16#18011976—22no—
17#18011975—22no—
18#18011968—21no—
19#18011968—21no—
20C2×#14558737C2211yescharacteristic
21C2×#14558735C2211yescharacteristic
22#18011932—22no—
23#18011932—22no—
24C2×#14558726C411yescharacteristic, complemented
25C2×#14558725C411yescharacteristic, complemented
26C2×#14558721C411yescharacteristic, complemented
27C2×C8×D149C2211yescharacteristic
28C2×SD16×C149C411yescharacteristic, complemented
29C22×#10597010—21no—
30#14558746—21no—
31#14558746—21no—
32#14558746—21no—
33#14558746D412yes—
34#14558745—24no—
35D149⋊C8—21no—
36D149⋊C8—21no—
37C2×#11924753—24no—
38C2×#11924753—21no—
39C2×#11924753—21no—
40C2×#11924753D411yescharacteristic
41C2×#11924753D411yescharacteristic
42C4×#10597010—21no—
43C4×#10597010—21no—
44#14558737—21no—
45#14558737—21no—
46#14558737—21no—
47#14558737—21no—
48#14558735—21no—
49#14558735—21no—
50#14558735D412yes—
51#14558735D412yes—
52C2×Dic298C2×C411yescharacteristic
53C2×D596—21no—
54C2×D596C2×C411yescharacteristic
55C2×C22⋊D149—21no—
56C22×Dic149—21no—
57C2×C4×D149—21no—
58C2×C4×D149C2311yescharacteristic
59#14558726—22no—
60#14558725—22no—
61#14558721—22no—
62C2×#11924746C2×C411yescharacteristic
63C8×D149—21no—
64C8×D149—21no—
65C2×Q8×C149C2×C411yescharacteristic
66C2×D4×C149C2×C411yescharacteristic
67SD16×C149—22no—
68C2×C8×C149C2×C411yescharacteristic
69C2×#10597010—22no—
70C2×#10597010—41no—
71C2×#10597010—41no—
72#11924753—21no—
73#11924753—22no—
74#11924753—21no—
75#11924753—41no—
76C22×D149—21no—
77C22×D149#4111yescharacteristic
78Dic298—21no—
79Dic298C22⋊C412yes—
80D596—21no—
81D596—21no—
82D596—41no—
83D596—41no—
84C22⋊D149—22no—
85C22⋊D149—22no—
86C2×Dic149—21no—
87C2×Dic149—22no—
88C2×Dic149—22no—
89C2×Dic149C2×D411yescharacteristic
90C4×D149—41no—
91C4×D149—41no—
92C4×D149C2×D411yescharacteristic
93C4×D149C2×D411yescharacteristic
94C4×D149C2×D411yescharacteristic
95C4×D149#4111yescharacteristic
96#11924746—21no—
97C23×C149—21no—
98Q8×C149—21no—
99Q8×C149—21no—
100D4×C149—21no—
101D4×C149C22⋊C412yes—
102C2×C4×C149—21no—
103C2×C4×C149C22×C411yescharacteristic
104C8×C149—21no—
105C22×C149—22no—
106C22×C149—41no—
107C22×C149—41no—
108C22×C149C4×D411yescharacteristic
109C2×D149—21no—
110C2×D149—21no—
111C2×D149—41no—
112C2×D149—41no—
113C2×D149—41no—
114C2×D149#12111yescharacteristic
115C2×D149#12311yescharacteristic
116#10597010—42no—
117C4×C149—41no—
118C4×C149C2×C22⋊C411yescharacteristic
119C4×C149C4×D411yescharacteristic
120Dic149—22no—
121Dic149#12011yescharacteristic
122Dic149#12111yescharacteristic
123C2×C149—42no—
124C2×C149#38611yescharacteristic
125C2×C149#44311yescharacteristic
126C2×C149#44411yescharacteristic
127D149—21no—
128D149—21no—
129D149—81no—
130C149#187611yescharacteristic, complemented, Sylow
131#1876—1491nomaximal, Sylow
132C2×#135—1491no—
133C2×#131—1491no—
134C2×#104—1491no—
135C2×#104—1491no—
136#408—1491no—
137#341—1491no—
138#336—1491no—
139C2×#41—1491no—
140C2×#41—1491no—
141#135—2982no—
142#135—2982no—
143C2×Q16—1491no—
144C2×SD16—1491no—
145C2×SD16#1059701011yescharacteristic, complemented
146C2×D8—1491no—
147#131—2982no—
148#131—2982no—
149C2×M16—2981no—
150C2×M16—1491no—
151C2×M16—1491no—
152C22×C8—2981no—
153C22×C8—1491no—
154C22×C8—1491no—
155C2×C42—1491no—
156#104—2982no—
157#104—2982no—
158C22⋊C8—2981no—
159C22⋊C8—2981no—
160#41—2981no—
161#41—2981no—
162#41—2981no—
163#41—2981no—
164#41—2981no—
165#41—2981no—
166#41—1492no—
167#41—1492no—
168C2×Q8—1491no—
169C2×Q8C2×#1059701011yescharacteristic
170C2×D4—2981no—
171C2×D4—2981no—
172C2×D4—1491no—
173C2×D4C2×#1059701011yescharacteristic
174C22×C4—2981no—
175C22×C4—2981no—
176C22×C4—2981no—
177C22×C4—1491no—
178Q16—2982no—
179SD16—22no—
180SD16—2982no—
181D8—2982no—
182M16—2984no—
183M16—2981no—
184M16—2981no—
185M16—2981no—
186M16—1492no—
187C2×C8—2981no—
188C2×C8—2981no—
189C2×C8—2984no—
190C2×C8—2981no—
191C2×C8—2981no—
192C2×C8—2981no—
193C2×C8—2981no—
194C2×C8—1491no—
195C2×C8—1491no—
196C2×C8—1491no—
197C2×C8C2×#1059701011yescharacteristic
198C42—2981no—
199C42—2981no—
200C23—21no—
201C23—2981no—
202C23—1491no—
203Q8—21no—
204Q8—21no—
205Q8—2981no—
206Q8—1492no—
207D4—21no—
208D4—2982no—
209D4—2982no—
210D4—2981no—
211D4—2981no—
212D4—5961no—
213D4—5961no—
214D4C22⋊#1059701012yes—
215C2×C4—21no—
216C2×C4—2981no—
217C2×C4—2982no—
218C2×C4—2982no—
219C2×C4—2982no—
220C2×C4—5961no—
221C2×C4—5961no—
222C2×C4—5961no—
223C2×C4—5961no—
224C2×C4—1491no—
225C2×C4—1491no—
226C2×C4—1491no—
227C2×C4—1491no—
228C2×C4—1491no—
229C2×C4C22×#1059701011yescharacteristic
230C8—21no—
231C8—2981no—
232C8—2982no—
233C8—2981no—
234C8—2981no—
235C8—5961no—
236C22—22no—
237C22—41no—
238C22—41no—
239C22—2981no—
240C22—2981no—
241C22—5961no—
242C22—5961no—
243C22—5961no—
244C22—1491no—
245C22—1491no—
246C22D4×#1059701011yescharacteristic
247C4—41no—
248C4—2982no—
249C4—5962no—
250C4—1491no—
251C4—1491no—
252C4C2×C22⋊#1059701011yescharacteristic
253C4D4×#1059701011yescharacteristic
254C2—42no—
255C2—2981no—
256C2—2981no—
257C2—11921no—
258C2#2375057311yescharacteristic
259C2#2375066811yescharacteristic
260C2#2375067011yescharacteristic
subgroupG/H
centerC22D4×#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×SD16×C149C4
socleC22×C149C4×D4
prime radicalC2×#18011932C2
cosocleC2×C4×D149C23
hypercenterC2×SD16#10597010
hypocenterC149#1876
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#18011998C2semidirect
2. C2×#18011976C2semidirect
3. C2×#18011975C2semidirect
4. #23750600C2semidirect
5. #23750501C2semidirect
6. (C2×#10597010)⋊C8C2semidirect
24. C2×#14558726C4semidirect
25. C2×#14558725C4semidirect
26. C2×#14558721C4semidirect
28. C2×SD16×C149C4semidirect
130. C149#1876semidirect
145. C2×SD16#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119982
C2×#180119762
C2×#180119752
#237506002
#237505012
(C2×#10597010)⋊C82
C2×#180119322
#1876149