Finite Group Databasebeta

← #34055647

Subgroups — #34055647

Order 19072.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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#23750182C211yesmaximal, characteristic, complemented
2#23750004C211yesmaximal, characteristic, complemented
3#23749997C211yesmaximal, characteristic, complemented
4#23749975C211yesmaximal, characteristic, complemented
5#23749971C211yesmaximal, characteristic, complemented
6#23749844C214yesmaximal, complemented
7#23749787C214yesmaximal, complemented
8#23749678C211yesmaximal, characteristic, complemented
9#532×C149C211yesmaximal, characteristic
10C2×#14558726C2214yes—
11C2×#14558724C2214yes—
12#18011911C2211yescharacteristic
13#18011911C2211yescharacteristic
14#18011903—21no—
15#18011890—21no—
16#18011890C2212yes—
17C4×Dic298—21no—
18C4×Dic298C2212yes—
19#18011870—21no—
20C4⋊#11924746C2212yes—
21#18011835C2214yes—
22#18011832C2214yes—
23C22⋊#11924746C2212yes—
24C4×#11924746C2211yescharacteristic
25C4×#11924746C2211yescharacteristic
26C2×#41×C149C2212yes—
27C4⋊Q8×C149C2211yescharacteristic
28#127×C149C2211yescharacteristic
29#124×C149C2212yes—
30#121×C149—21no—
31#121×C149—21no—
32C4×D4×C149—21no—
33C4×D4×C149—21no—
34C2×C42×C149C2211yescharacteristic
35C2×Dic298—21no—
36C2×Dic298C2312yes—
37#14558726—44no—
38#14558724—44no—
39C2×#11924746C2312yes—
40C2×#11924746C2312yes—
41C4⋊Dic149—21no—
42C4⋊Dic149—21no—
43C4⋊Dic149—21no—
44C4⋊Dic149C2312yes—
45#14558715—22no—
46#14558715—22no—
47C22⋊Dic149—22no—
48C4×Dic149—22no—
49#41×C149—44no—
50C2×Q8×C149C2312yes—
51C2×D4×C149—22no—
52C2×D4×C149—21no—
53C2×D4×C149—21no—
54C2×D4×C149C2312yes—
55C22×C4×C149—22no—
56C22×C4×C149D411yescharacteristic
57C22×C4×C149D411yescharacteristic
58C22×C4×C149C2311yescharacteristic
59C4⋊C4×C149—21no—
60C4⋊C4×C149—21no—
61C22⋊C4×C149—22no—
62C22⋊C4×C149—22no—
63C42×C149D411yescharacteristic
64C42×C149D411yescharacteristic
65C42×C149C2311yescharacteristic
66C42×C149C2311yescharacteristic
67Dic298—24no—
68Dic298—42no—
69C2×Dic149—22no—
70C2×Dic149—22no—
71#11924746—22no—
72#11924746—22no—
73C23×C149—22no—
74C23×C149C2×D411yescharacteristic
75Q8×C149—24no—
76D4×C149—24no—
77D4×C149—44no—
78D4×C149—42no—
79D4×C149—42no—
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—22no—
83C2×C4×C149—22no—
84C2×C4×C149—44no—
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2×D411yescharacteristic
90C2×C4×C149C2411yescharacteristic
91C22×C149—21no—
92C22×C149—21no—
93C22×C149—21no—
94C22×C149—42no—
95C22×C149—42no—
96C22×C149—42no—
97C22×C149C22×D411yescharacteristic
98C4×C149—21no—
99C4×C149—21no—
100C4×C149—21no—
101C4×C149—42no—
102C4×C149#13512yes—
103C4×C149#13712yes—
104C4×C149H(5,𝔽2)12yes—
105Dic149—42no—
106Dic149—42no—
107C2×C149—41no—
108C2×C149—82no—
109C2×C149#53511yescharacteristic
110C2×C149C2×#13511yescharacteristic
111C2×C149C2×#13711yescharacteristic
112C149#321011yescharacteristic, complemented, Sylow
113#3210—1491nomaximal, Sylow
114#533—1491no—
115#532D14911yescharacteristic
116#494—1491no—
117#492—1491no—
118#487—1491no—
119#486—1491no—
120#464—1494no—
121#452—1494no—
122#431—1491no—
123C2×#41C2×D14912yes—
124C2×Q16—1494no—
125C2×SD16—1494no—
126C4⋊Q8—1491no—
127C4⋊Q8—1491no—
128C4⋊Q8C2×D14911yescharacteristic
129#127C2×D14911yescharacteristic
130#125—2981no—
131#124C2×D14912yes—
132C22⋊Q8—2981no—
133C22⋊Q8—1492no—
134#121—21no—
135#121—21no—
136C4×Q8—2981no—
137C4×Q8—1492no—
138C4×D4—21no—
139C4×D4—21no—
140#117—2981no—
141C2×C42C2×D14911yescharacteristic
142C4⋊C8—1492no—
143#103—1494no—
144#102—1494no—
145C22⋊C8—1492no—
146C4×C8—1491no—
147C4×C8—1491no—
148#41—44no—
149C2×Q8—2981no—
150C2×Q8—1492no—
151C2×Q8C22×D14912yes—
152C2×D4—22no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4C22×D14912yes—
156C22×C4—22no—
157C22×C4C22⋊D14911yescharacteristic
158C22×C4C22⋊D14911yescharacteristic
159C22×C4C22×D14911yescharacteristic
160Q16—5964no—
161SD16—5964no—
162C2×C8—1492no—
163C2×C8—1492no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—2981no—
167C4⋊C4—2981no—
168C4⋊C4—2981no—
169C4⋊C4—2982no—
170C4⋊C4—2982no—
171C4⋊C4—1492no—
172C22⋊C4—22no—
173C22⋊C4—22no—
174C22⋊C4—2982no—
175C42—2982no—
176C42C22⋊D14911yescharacteristic
177C42C22⋊D14911yescharacteristic
178C42C22×D14911yescharacteristic
179C42C22×D14911yescharacteristic
180C23—22no—
181C23C2×C22⋊D14911yescharacteristic
182Q8—24no—
183Q8—2984no—
184Q8—5962no—
185D4—24no—
186D4—44no—
187D4—42no—
188D4—42no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—44no—
194C2×C4—2982no—
195C2×C4—2982no—
196C2×C4C2×C22⋊D14911yescharacteristic
197C2×C4C2×C22⋊D14911yescharacteristic
198C2×C4C2×C22⋊D14911yescharacteristic
199C2×C4C2×C22⋊D14911yescharacteristic
200C2×C4C2×C22⋊D14911yescharacteristic
201C2×C4C23×D14911yescharacteristic
202C8—2982no—
203C8—2982no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22C22×C22⋊D14911yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—5962no—
216C4—5962no—
217C4#1801193112yes—
218C4#1801194112yes—
219C4#1801195612yes—
220C2—41no—
221C2—82no—
222C2#2375019211yescharacteristic
223C2C2×#1801193111yescharacteristic
224C2C2×#1801194111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting, prime radical#532×C149C2
socleC22×C149C22×D4
hypercenter#532D149
hypocenterC149#3210
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #23750182C2semidirect
2. #23750004C2semidirect
3. #23749997C2semidirect
4. #23749975C2semidirect
5. #23749971C2semidirect
6. #23749844C2semidirect
7. #23749787C2semidirect
8. #23749678C2semidirect
112. C149#3210semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237500042
#237499972
#237499752
#237499712
#237498442
#237497872
#237496782
#532×C1492
#3210149