Finite Group Databasebeta

← #34054217

Subgroups — #34054217

Order 19072.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18011941C211yesmaximal, characteristic
2C22×#14558726C211yesmaximal, characteristic, complemented
3#23750102C211yesmaximal, characteristic, complemented
4#23749844C214yesmaximal, complemented
5#23749832C214yesmaximal, complemented
6#23749652C211yesmaximal, characteristic, complemented
7#23749634C211yesmaximal, characteristic, complemented
8#23749621C211yesmaximal, characteristic
9#536×C149C211yesmaximal, characteristic
10C22×Dic298C2211yescharacteristic
11#18011941—24no—
12C2×#14558726—24no—
13C2×#14558726C2214yes—
14C2×#14558726C2212yes—
15C2×#14558724C2212yes—
16C2×#14558720C2211yescharacteristic
17C22×#11924746C2211yescharacteristic
18C4×Dic298C2214yes—
19#18011876—22no—
20#18011870C2211yescharacteristic
21#18011867—22no—
22C4⋊#11924746C2214yes—
23#18011835C2214yes—
24#18011835C2212yes—
25#18011832C2212yes—
26C2×#41×C149C2211yescharacteristic
27C22×Q8×C149C2211yescharacteristic
28C4⋊Q8×C149C2212yes—
29#124×C149C2212yes—
30#123×C149—22no—
31C22⋊Q8×C149—22no—
32#117×C149C2211yescharacteristic
33C2×Dic298—21no—
34C2×Dic298—22no—
35C2×Dic298D414yes—
36C2×Dic298C2312yes—
37C22×Dic149—21no—
38#14558726—28no—
39#14558726—24no—
40#14558724—24no—
41#14558720—22no—
42C2×#11924746—22no—
43C2×#11924746C2312yes—
44C2×#11924746C2312yes—
45C4⋊Dic149C2312yes—
46#14558715—24no—
47C22⋊Dic149—21no—
48C4×Dic149—24no—
49C4×Dic149—21no—
50#41×C149—22no—
51#41×C149—22no—
52C2×Q8×C149—21no—
53C2×Q8×C149—22no—
54C2×Q8×C149—22no—
55C2×Q8×C149C2312yes—
56C2×Q8×C149C2311yescharacteristic
57C2×D4×C149—21no—
58C2×D4×C149C2311yescharacteristic
59C22×C4×C149—21no—
60C22×C4×C149—21no—
61C22×C4×C149C2311yescharacteristic
62C4⋊C4×C149—24no—
63C4⋊C4×C149D412yes—
64C22⋊C4×C149—24no—
65C22⋊C4×C149D412yes—
66C42×C149C2312yes—
67Dic298—24no—
68Dic298—22no—
69Dic298C2×D414yes—
70C2×Dic149—24no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73#11924746—22no—
74#11924746—22no—
75C23×C149—21no—
76C23×C149C2×D411yescharacteristic
77Q8×C149—22no—
78Q8×C149—21no—
79Q8×C149—22no—
80Q8×C149—21no—
81Q8×C149—42no—
82D4×C149—21no—
83D4×C149—21no—
84D4×C149—42no—
85C2×C4×C149—22no—
86C2×C4×C149—21no—
87C2×C4×C149—42no—
88C2×C4×C149—42no—
89C2×C4×C149C2×D412yes—
90C2×C4×C149C2×D414yes—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149#4112yes—
93C2×C4×C149C2411yescharacteristic
94C22×C149—22no—
95C22×C149—41no—
96C22×C149—42no—
97C22×C149#12112yes—
98C22×C149C22×D411yescharacteristic
99C4×C149—24no—
100C4×C149—41no—
101C4×C149—42no—
102C4×C149#12112yes—
103C4×C149C22×D411yescharacteristic
104C4×C149C2×#4111yescharacteristic
105Dic149—24no—
106Dic149—42no—
107C2×C149—22no—
108C2×C149—81no—
109C2×C149C2×#12111yescharacteristic
110C2×C149#57812yes—
111C149#304411yescharacteristic, complemented, Sylow
112#3044—1491nomaximal, Sylow
113C2×#137—1491no—
114C22×Q16—1491no—
115#536D14911yescharacteristic
116#519—1491no—
117#464—1494no—
118#462—1494no—
119#424—1491no—
120#419—1491no—
121#416—1491no—
122C2×#41C2×D14911yescharacteristic
123C22×Q8—1491no—
124C22×Q8C2×D14911yescharacteristic
125#137—2984no—
126C2×Q16—2984no—
127C2×Q16—1494no—
128C2×Q16—1492no—
129C2×SD16—1492no—
130C2×M16—1491no—
131C22×C8—1491no—
132C4⋊Q8C2×D14912yes—
133#124C2×D14912yes—
134#123—22no—
135C22⋊Q8—22no—
136C4×Q8—2982no—
137C4×Q8—1494no—
138#117—2982no—
139#117—1491no—
140#117C2×D14911yescharacteristic
141C4⋊C8—1494no—
142#103—1492no—
143#103—1494no—
144#102—1492no—
145#41—22no—
146#41—22no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—2981no—
151C2×Q8—2982no—
152C2×Q8—1494no—
153C2×Q8—1492no—
154C2×Q8C22×D14912yes—
155C2×Q8C22×D14911yescharacteristic
156C2×D4—21no—
157C2×D4C22×D14911yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—2981no—
161C22×C4C22×D14911yescharacteristic
162Q16—2988no—
163Q16—2984no—
164SD16—2984no—
165M16—2982no—
166C2×C8—2982no—
167C2×C8—1492no—
168C2×C8—1492no—
169C4⋊C4—24no—
170C4⋊C4—2984no—
171C4⋊C4—1492no—
172C4⋊C4C22⋊D14912yes—
173C22⋊C4—24no—
174C22⋊C4—2981no—
175C22⋊C4C22⋊D14912yes—
176C42—2984no—
177C42—2981no—
178C42C22×D14912yes—
179C23—21no—
180C23C2×C22⋊D14911yescharacteristic
181Q8—22no—
182Q8—21no—
183Q8—22no—
184Q8—21no—
185Q8—42no—
186Q8—2982no—
187Q8—2984no—
188Q8—1494no—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—2982no—
197C2×C4—2984no—
198C2×C4—2982no—
199C2×C4D4×D14912yes—
200C2×C4C2×C22⋊D14914yes—
201C2×C4C2×C22⋊D14911yescharacteristic
202C2×C4#1455873512yes—
203C2×C4C23×D14911yescharacteristic
204C8—2982no—
205C8—2982no—
206C22—22no—
207C22—42no—
208C22—41no—
209C22#1801188212yes—
210C22C22×C22⋊D14911yescharacteristic
211C4—24no—
212C4—41no—
213C4—42no—
214C4—2984no—
215C4—5962no—
216C4#1801188212yes—
217C4C2×D4×D14911yescharacteristic
218C4C2×#1455873511yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#1801188211yescharacteristic
222C2#2375044012yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#536×C149C2
socleC22×C149C22×D4
prime radicalC2×#41×C149C22
hypercenter#536D149
hypocenterC149#3044
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C22×#14558726C2semidirect
3. #23750102C2semidirect
4. #23749844C2semidirect
5. #23749832C2semidirect
6. #23749652C2semidirect
7. #23749634C2semidirect
111. C149#3044semidirect

Maximal subgroups

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

subgroupindex
C2×#180119412
C22×#145587262
#237501022
#237498442
#237498322
#237496522
#237496342
#237496212
#536×C1492
#3044149