Finite Group Databasebeta

← #34055311

Subgroups — #34055311

Order 19072.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#23750247C212yesmaximal, complemented
2#23750022C211yesmaximal, characteristic, complemented
3#23750010C211yesmaximal, characteristic, complemented
4#23749986C212yesmaximal, complemented
5#23749880C211yesmaximal, characteristic, complemented
6#23749879C211yesmaximal, characteristic
7#23749857C212yesmaximal, complemented
8#23749738C211yesmaximal, characteristic, complemented
9C4×#14558723C212yesmaximal, complemented
10#23749582C211yesmaximal, characteristic, complemented
11#441×C149C211yesmaximal, characteristic, complemented
12C2×#14558723C2212yes—
13C2×D1192C2211yescharacteristic
14C2×#14558719C2211yescharacteristic
15C2×C8×D149C2211yescharacteristic
16#18011910C2212yes—
17#18011905—22no—
18#18011900C2212yes—
19#18011899—22no—
20#18011896—22no—
21#18011889—22no—
22#18011887C2212yes—
23#18011886C2212yes—
24C4×D596C2212yes—
25#18011868C2211yescharacteristic
26#18011843C2211yescharacteristic
27#18011842C2212yes—
28#18011835C2212yes—
29#18011833C2212yes—
30#18011831C2212yes—
31#18011821C2211yescharacteristic
32C4×#11924746C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C2×Q16×C149C2211yescharacteristic
35C4×Q8×C149C2212yes—
36#106×C149C2211yescharacteristic
37#103×C149C2212yes—
38#97×C149C2211yescharacteristic
39C2×Dic298—22no—
40C2×D596—22no—
41C2×D596C2312yes—
42C2×C4×D149—22no—
43C2×C4×D149C2311yescharacteristic
44#14558723—24no—
45D1192—22no—
46#14558719—22no—
47C2×#11924746C2311yescharacteristic
48C2×#11924746C2311yescharacteristic
49C8×D149—22no—
50C4⋊Dic149C2312yes—
51#14558715—22no—
52#14558715—22no—
53#14558715D412yes—
54#14558713—22no—
55#14558713—22no—
56#14558713—22no—
57#14558713—22no—
58#14558713—22no—
59#14558713D412yes—
60C4×Dic149C2311yescharacteristic
61C2×Q8×C149C2312yes—
62Q16×C149—22no—
63C2×C8×C149C2311yescharacteristic
64C2×C8×C149C2311yescharacteristic
65C4⋊C4×C149—22no—
66C4⋊C4×C149C2312yes—
67C42×C149—22no—
68C42×C149C2311yescharacteristic
69C22×D149—22no—
70C22×D149C2×D411yescharacteristic
71Dic298—82no—
72D596—22no—
73D596—22no—
74D596—82no—
75C2×Dic149—22no—
76C2×Dic149C2×D411yescharacteristic
77C2×Dic149C2×D412yes—
78C4×D149—21no—
79C4×D149—21no—
80C4×D149—82no—
81#11924746—21no—
82#11924746#4112yes—
83Q8×C149—22no—
84Q8×C149—22no—
85C2×C4×C149—22no—
86C2×C4×C149—22no—
87C2×C4×C149C2×D412yes—
88C2×C4×C149C2411yescharacteristic
89C8×C149—21no—
90C8×C149#4112yes—
91C22×C149C22×D411yescharacteristic
92C2×D149—21no—
93C2×D149—22no—
94C2×D149—42no—
95C2×D149—42no—
96C2×D149—42no—
97C4×C149—22no—
98C4×C149—42no—
99C4×C149—42no—
100C4×C149C2×#4111yescharacteristic
101C4×C149C2×#4111yescharacteristic
102Dic149—21no—
103Dic149—22no—
104Dic149—42no—
105C2×C149#53211yescharacteristic
106C2×C149#57712yes—
107D149—41no—
108D149—82no—
109C149#317311yescharacteristic, complemented, Sylow
110#3173—1491nomaximal, Sylow
111#542—1492no—
112#498—1491no—
113#495—1491no—
114#489—1492no—
115#470—1491no—
116#469—1491no—
117#465—1492no—
118#442—1491no—
119#441D14911yescharacteristic, complemented
120C4×SD16—1492no—
121#405—1491no—
122C2×Q16C2×D14911yescharacteristic
123C2×SD16—1492no—
124C2×D8—1491no—
125C2×M16—1491no—
126C22×C8—1491no—
127C4⋊Q8—1492no—
128#126—2982no—
129#124—2982no—
130#124—1492no—
131#123—2982no—
132C22⋊Q8—2982no—
133C22⋊Q8—1492no—
134#121—1492no—
135C4×Q8C2×D14912yes—
136C4×D4—1492no—
137#117—1491no—
138#106—1491no—
139#106—1492no—
140#106C2×D14911yescharacteristic
141#103—1492no—
142#103C2×D14912yes—
143#102—1492no—
144#102—1492no—
145#97—1491no—
146#97C2×D14911yescharacteristic
147C4×C8—1491no—
148C4×C8—1491no—
149C2×Q8—2982no—
150C2×Q8C22×D14912yes—
151C2×D4—2982no—
152C2×D4—1492no—
153C22×C4—2982no—
154C22×C4—1491no—
155Q16—22no—
156SD16—2984no—
157D8—2982no—
158M16—2982no—
159C2×C8—2982no—
160C2×C8—1491no—
161C2×C8—1491no—
162C2×C8C22×D14911yescharacteristic
163C2×C8C22×D14911yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—2982no—
166C4⋊C4—2982no—
167C4⋊C4—1492no—
168C4⋊C4—1492no—
169C4⋊C4C22×D14912yes—
170C22⋊C4—2982no—
171C22⋊C4—2982no—
172C22⋊C4—2982no—
173C22⋊C4—2982no—
174C22⋊C4—2982no—
175C22⋊C4—1492no—
176C42—22no—
177C42—1491no—
178C42C22×D14911yescharacteristic
179C23—2982no—
180C23—1491no—
181Q8—22no—
182Q8—22no—
183Q8—11922no—
184D4—2982no—
185D4—2982no—
186D4—11922no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—2981no—
190C2×C4—2981no—
191C2×C4—2982no—
192C2×C4—1492no—
193C2×C4—1491no—
194C2×C4—11922no—
195C2×C4D4×D14912yes—
196C2×C4C23×D14911yescharacteristic
197C8—21no—
198C8—2981no—
199C8—1492no—
200C8#1455873612yes—
201C22—2981no—
202C22—2982no—
203C22—5962no—
204C22—5962no—
205C22—5962no—
206C22C2×D4×D14911yescharacteristic
207C4—22no—
208C4—42no—
209C4—42no—
210C4—2981no—
211C4—2982no—
212C4—5962no—
213C4#41×D14911yescharacteristic
214C4C2×#1455873611yescharacteristic
215C2—5961no—
216C2—11922no—
217C2#2375017211yescharacteristic
218C2#2375043412yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#441×C149C2
socleC22×C149C22×D4
prime radical#23749879C2
hypercenter#441D149
hypocenterC149#3173
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #23750247C2semidirect
2. #23750022C2semidirect
3. #23750010C2semidirect
4. #23749986C2semidirect
5. #23749880C2semidirect
7. #23749857C2semidirect
8. #23749738C2semidirect
9. C4×#14558723C2semidirect
10. #23749582C2semidirect
11. #441×C149C2semidirect
109. C149#3173semidirect
119. #441D149semidirect

Maximal subgroups

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

subgroupindex
#237502472
#237500222
#237500102
#237499862
#237498802
#237498792
#237498572
#237497382
C4×#145587232
#237495822
#441×C1492
#3173149