Finite Group Databasebeta

← #34055827

Subgroups — #34055827

Order 19072.

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

normal subgroups only

This group has 370 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#23750175C211yesmaximal, characteristic
2#23750028C211yesmaximal, characteristic, complemented
3#23750021C211yesmaximal, characteristic, complemented
4#23749973C211yesmaximal, characteristic, complemented
5#23749973C211yesmaximal, characteristic, complemented
6#23749949C214yesmaximal, complemented
7#23749922C214yesmaximal, complemented
8#23749678C211yesmaximal, characteristic, complemented
9#533×C149C211yesmaximal, characteristic, complemented
10C2×#14558736—21no—
11#18011911C2211yescharacteristic
12#18011908C2211yescharacteristic
13#18011899—21no—
14#18011885—21no—
15#18011885C2212yes—
16C4×D596—21no—
17C4×D596C2212yes—
18#18011844C2214yes—
19#18011842C2214yes—
20C4⋊#11924746C2212yes—
21#18011831C2214yes—
22#18011831C2214yes—
23C22⋊#11924746C2212yes—
24C4×#11924746C2211yescharacteristic
25C4×#11924746C2211yescharacteristic
26C4⋊Q8×C149C2211yescharacteristic
27C4⋊Q8×C149C2211yescharacteristic
28#125×C149C2212yes—
29C22⋊Q8×C149—21no—
30C22⋊Q8×C149—21no—
31C4×Q8×C149—21no—
32C4×Q8×C149—21no—
33#117×C149C2212yes—
34C2×C42×C149C2211yescharacteristic
35#14558736—44no—
36C2×Dic298—21no—
37C2×D596—21no—
38C2×D596—21no—
39C2×D596C2312yes—
40C2×C22⋊D149—22no—
41C2×C4×D149—22no—
42C2×#11924746C2312yes—
43C2×#11924746C2312yes—
44C4⋊Dic149—21no—
45C4⋊Dic149C2312yes—
46#14558713—22no—
47#14558713—22no—
48C2×Q8×C149—21no—
49C2×Q8×C149—21no—
50C22×C4×C149D411yescharacteristic
51C22×C4×C149D411yescharacteristic
52C22×C4×C149C2311yescharacteristic
53C4⋊C4×C149—22no—
54C4⋊C4×C149—22no—
55C4⋊C4×C149—21no—
56C4⋊C4×C149—21no—
57C4⋊C4×C149C2312yes—
58C4⋊C4×C149C2312yes—
59C22⋊C4×C149—22no—
60C42×C149—22no—
61C42×C149D411yescharacteristic
62C42×C149D411yescharacteristic
63C42×C149C2311yescharacteristic
64C42×C149C2311yescharacteristic
65C22×D149—22no—
66Dic298—42no—
67D596—24no—
68D596—42no—
69D596—42no—
70C22⋊D149—44no—
71C2×Dic149—22no—
72C4×D149—44no—
73#11924746—22no—
74#11924746—22no—
75C23×C149C2×D411yescharacteristic
76Q8×C149—42no—
77Q8×C149—42no—
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—22no—
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2411yescharacteristic
89C22×C149—21no—
90C22×C149—21no—
91C22×C149—21no—
92C22×C149C22×D411yescharacteristic
93C2×D149—42no—
94C2×D149—42no—
95C2×D149—42no—
96C4×C149—21no—
97C4×C149—21no—
98C4×C149—21no—
99C4×C149—42no—
100C4×C149—42no—
101C4×C149#13512yes—
102C4×C149AGL(1,ℤ/8)12yes—
103C4×C1492−1+412yes—
104Dic149—42no—
105C2×C149—41no—
106C2×C149#53611yescharacteristic
107C2×C149C2×#13511yescharacteristic
108C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
109D149—82no—
110C149#322811yescharacteristic, complemented, Sylow
111#3228—1491nomaximal, Sylow
112#533D14911yescharacteristic, complemented
113#532—1491no—
114#500—1491no—
115#498—1491no—
116#486—1491no—
117#486—1491no—
118#482—1494no—
119#478—1494no—
120#431—1491no—
121C2×#41—2981no—
122C4⋊Q8—1491no—
123C4⋊Q8C2×D14911yescharacteristic
124C4⋊Q8C2×D14911yescharacteristic
125#127—1491no—
126#125C2×D14912yes—
127#124—2981no—
128C22⋊Q8—21no—
129C22⋊Q8—21no—
130#121—2981no—
131#121—1492no—
132C4×Q8—21no—
133C4×Q8—21no—
134C4×D4—2981no—
135C4×D4—1492no—
136#117C2×D14912yes—
137C2×C42C2×D14911yescharacteristic
138#107—1494no—
139#106—1494no—
140C4⋊C8—1492no—
141#102—1494no—
142#102—1494no—
143C22⋊C8—1492no—
144C4×C8—1491no—
145C4×C8—1491no—
146#41—5964no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—2981no—
150C2×D4—2982no—
151C2×D4—2981no—
152C2×D4—2981no—
153C2×D4—1492no—
154C22×C4—2982no—
155C22×C4C22⋊D14911yescharacteristic
156C22×C4C22⋊D14911yescharacteristic
157C22×C4C22×D14911yescharacteristic
158C2×C8—1492no—
159C2×C8—1492no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—2981no—
165C4⋊C4—1492no—
166C4⋊C4C22×D14912yes—
167C4⋊C4C22×D14912yes—
168C22⋊C4—22no—
169C22⋊C4—2982no—
170C22⋊C4—2982no—
171C42—22no—
172C42C22⋊D14911yescharacteristic
173C42C22⋊D14911yescharacteristic
174C42C22×D14911yescharacteristic
175C42C22×D14911yescharacteristic
176C23—2982no—
177C23C2×C22⋊D14911yescharacteristic
178Q8—42no—
179Q8—42no—
180Q8—5962no—
181D4—2984no—
182D4—5964no—
183D4—5962no—
184D4—5962no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—2982no—
191C2×C4—5964no—
192C2×C4C2×C22⋊D14911yescharacteristic
193C2×C4C2×C22⋊D14911yescharacteristic
194C2×C4C2×C22⋊D14911yescharacteristic
195C2×C4C2×C22⋊D14911yescharacteristic
196C2×C4C2×C22⋊D14911yescharacteristic
197C2×C4C23×D14911yescharacteristic
198C8—2982no—
199C8—2982no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—5962no—
204C22—5962no—
205C22—5962no—
206C22C22×C22⋊D14911yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—42no—
211C4—42no—
212C4—5962no—
213C4#1801193112yes—
214C4#1801193612yes—
215C4#1801195912yes—
216C2—41no—
217C2—11922no—
218C2#2375019911yescharacteristic
219C2C2×#1801193111yescharacteristic
220C2C2×#1801193611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#533×C149C2
socleC22×C149C22×D4
prime radical#23750175C2
hypercenter#533D149
hypocenterC149#3228
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #23750028C2semidirect
3. #23750021C2semidirect
4. #23749973C2semidirect
5. #23749973C2semidirect
6. #23749949C2semidirect
7. #23749922C2semidirect
8. #23749678C2semidirect
9. #533×C149C2semidirect
110. C149#3228semidirect
112. #533D149semidirect

Maximal subgroups

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

subgroupindex
#237501752
#237500282
#237500212
#237499732
#237499492
#237499222
#237496782
#533×C1492
#3228149