Finite Group Databasebeta

← #34045192

Subgroups — #34045192

Order 19072.

332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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
1#23750423C211yesmaximal, characteristic
2#23749642C211yesmaximal, characteristic, complemented
3C2×#18011839C211yesmaximal, characteristic, complemented
4#23749598C211yesmaximal, characteristic, complemented
5#23749395C211yesmaximal, characteristic, complemented
6#23749385C211yesmaximal, characteristic, complemented
7C4×#41×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9#18011942—21no—
10#18011941C412yescomplemented
11#18011937—21no—
12#18011936C412yescomplemented
13#18011931—22no—
14C2×#14558720C2211yescharacteristic
15C2×#14558720C2211yescharacteristic
16#18011870C2211yescharacteristic
17#18011839—21no—
18#18011839—21no—
19#18011838—22no—
20#18011825—22no—
21C2×#41×C149C2211yescharacteristic
22C4×Q8×C149—21no—
23C4×D4×C149—21no—
24C4×D4×C149—22no—
25#117×C149—21no—
26#117×C149C2211yescharacteristic
27C2×C42×C149—21no—
28C2×C42×C149C2211yescharacteristic
29#14558736—21no—
30#14558736—21no—
31#14558736—21no—
32#14558736—21no—
33C2×Dic298C2×C411yescharacteristic, complemented
34C2×D596C2×C411yescharacteristic, complemented
35C2×C22⋊D149—21no—
36C2×C4×D149—21no—
37#14558726—22no—
38#14558724—22no—
39#14558723—22no—
40#14558721—22no—
41#14558720—21no—
42#14558720—21no—
43#14558720—21no—
44#14558720C2×C412yescomplemented
45C2×#11924746—21no—
46C2×#11924746—21no—
47C4⋊Dic149—21no—
48C22⋊Dic149—21no—
49C4×Dic149—21no—
50#41×C149—21no—
51#41×C149—21no—
52#41×C149C2×C412yes—
53#41×C149D412yes—
54C2×Q8×C149D411yescharacteristic
55C2×D4×C149—21no—
56C2×D4×C149D411yescharacteristic
57C22×C4×C149—21no—
58C22×C4×C149—22no—
59C22×C4×C149—21no—
60C22×C4×C149C2311yescharacteristic
61C4⋊C4×C149—22no—
62C4⋊C4×C149—21no—
63C22⋊C4×C149—22no—
64C22⋊C4×C149D412yes—
65C42×C149—22no—
66C42×C149—21no—
67C42×C149—21no—
68C42×C149D411yescharacteristic
69C42×C149D411yescharacteristic
70C22×D149—21no—
71Dic298—21no—
72Dic298—21no—
73D596—21no—
74D596—21no—
75C22⋊D149—41no—
76C22⋊D149—41no—
77C2×Dic149—21no—
78C2×Dic149—41no—
79C4×D149—41no—
80C4×D149—41no—
81#11924746—22no—
82#11924746—41no—
83C23×C149—21no—
84C23×C149C2×D411yescharacteristic
85Q8×C149—21no—
86Q8×C149C22⋊C412yes—
87D4×C149—22no—
88D4×C149—22no—
89D4×C149—21no—
90D4×C149C22⋊C412yes—
91C2×C4×C149—21no—
92C2×C4×C149—21no—
93C2×C4×C149—22no—
94C2×C4×C149—22no—
95C2×C4×C149—22no—
96C2×C4×C149—21no—
97C2×C4×C149—42no—
98C2×C4×C149—44no—
99C2×C4×C149C22×C411yescharacteristic
100C2×C4×C149C2×D411yescharacteristic
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149#4111yescharacteristic
104C2×C4×C149#4111yescharacteristic
105C22×C149—22no—
106C22×C149—41no—
107C22×C149—42no—
108C22×C149C4×D411yescharacteristic
109C22×C149#12011yescharacteristic
110C22×C149#12111yescharacteristic
111C2×D149—41no—
112C2×D149—81no—
113C4×C149—22no—
114C4×C149—22no—
115C4×C149—42no—
116C4×C149—41no—
117C4×C149C2×C22⋊C411yescharacteristic
118C4×C149C4×D411yescharacteristic
119C4×C149#12111yescharacteristic
120C4×C149#12311yescharacteristic
121Dic149—41no—
122Dic149—81no—
123C2×C149—21no—
124C2×C149—21no—
125C2×C149—21no—
126C2×C149—42no—
127C2×C149#38611yescharacteristic
128D149—81no—
129C149#190611yescharacteristic, complemented, Sylow
130#1906—1491nomaximal, Sylow
131#575—1491no—
132C4×#41D14911yescharacteristic, complemented
133#421—1491no—
134C2×#104—1491no—
135#410—1491no—
136#344—1491no—
137#339—1491no—
138C2×#41—1491no—
139C2×#41C2×D14911yescharacteristic
140#137—2981no—
141#137—1492no—
142AGL(1,ℤ/8)—2981no—
143AGL(1,ℤ/8)—1492no—
144#135—2982no—
145C2×M16—1491no—
146C2×M16—1491no—
147C4×Q8—21no—
148C4×D4—21no—
149C4×D4—22no—
150#117—21no—
151#117—1491no—
152#117C2×D14911yescharacteristic
153C2×C42—21no—
154C2×C42C2×D14911yescharacteristic
155#104—2982no—
156#104—2981no—
157#104—2981no—
158#99—2982no—
159#41—21no—
160#41—21no—
161#41—2981no—
162#41—2981no—
163#41—2981no—
164#41—2981no—
165#41C4×D14912yes—
166#41D59612yes—
167C2×Q8—1491no—
168C2×Q8C22⋊D14911yescharacteristic
169C2×D4—21no—
170C2×D4—2981no—
171C2×D4—1491no—
172C2×D4C22⋊D14911yescharacteristic
173C22×C4—21no—
174C22×C4—22no—
175C22×C4—21no—
176C22×C4—2981no—
177C22×C4C22×D14911yescharacteristic
178Q16—2982no—
179SD16—2982no—
180SD16—2982no—
181D8—2982no—
182M16—2981no—
183M16—2981no—
184M16—2981no—
185M16—1492no—
186C2×C8—2981no—
187C2×C8—2981no—
188C4⋊C4—22no—
189C4⋊C4—21no—
190C4⋊C4—2981no—
191C22⋊C4—22no—
192C22⋊C4—2981no—
193C22⋊C4C22⋊D14912yes—
194C42—22no—
195C42—21no—
196C42—21no—
197C42—2981no—
198C42C22⋊D14911yescharacteristic
199C42C22⋊D14911yescharacteristic
200C23—21no—
201C23—2981no—
202C23C2×C22⋊D14911yescharacteristic
203Q8—21no—
204Q8—2981no—
205Q8—2981no—
206Q8#1455871312yes—
207D4—22no—
208D4—22no—
209D4—21no—
210D4—2981no—
211D4—2981no—
212D4—5961no—
213D4—5961no—
214D4#1455871312yes—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—42no—
222C2×C4—44no—
223C2×C4—2981no—
224C2×C4—5961no—
225C2×C4—5961no—
226C2×C4—5961no—
227C2×C4C2×C4×D14911yescharacteristic
228C2×C4C2×C22⋊D14911yescharacteristic
229C2×C4C2×C22⋊D14911yescharacteristic
230C2×C4C2×D59611yescharacteristic
231C2×C4#1455873611yescharacteristic
232C2×C4#1455873611yescharacteristic
233C8—2982no—
234C8—5961no—
235C22—22no—
236C22—41no—
237C22—42no—
238C22—5961no—
239C22—11921no—
240C22C4×C22⋊D14911yescharacteristic
241C22#1801188011yescharacteristic
242C22#1801188511yescharacteristic
243C4—22no—
244C4—22no—
245C4—42no—
246C4—41no—
247C4—5961no—
248C4—11921no—
249C4C2×#1455871311yescharacteristic
250C4C4×C22⋊D14911yescharacteristic
251C4#1801188511yescharacteristic
252C4#1801189411yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—42no—
257C2—11921no—
258C2#2374950411yescharacteristic
subgroupG/H
centerC4#18011885
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC4×#41×C149C2
socleC2×C149#386
prime radical#23750423C2
cosocleC22×C4×C149C23
hypercenterC4×#41D149
hypocenterC149#1906
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. #23749642C2semidirect
3. C2×#18011839C2semidirect
4. #23749598C2semidirect
5. #23749395C2semidirect
6. #23749385C2semidirect
7. C4×#41×C149C2semidirect
10. #18011941C4semidirect
12. #18011936C4semidirect
33. C2×Dic298C2×C4semidirect
34. C2×D596C2×C4semidirect
44. #14558720C2×C4semidirect
129. C149#1906semidirect
132. C4×#41D149semidirect

Maximal subgroups

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

subgroupindex
#237504232
#237496422
C2×#180118392
#237495982
#237493952
#237493852
C4×#41×C1492
#1906149