Finite Group Databasebeta

← #34057264

Subgroups — #34057264

Order 19072.

336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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#23750313C212yesmaximal
2#23749968C212yesmaximal, complemented
3#23749962C212yesmaximal, complemented
4#23749929C212yesmaximal, complemented
5#23749884C212yesmaximal, complemented
6C4×Dic596C211yesmaximal, characteristic, complemented
7#23749704C211yesmaximal, characteristic
8#23749664C212yesmaximal, complemented
9#499×C149C211yesmaximal, characteristic, complemented
10C2×Dic596C2211yescharacteristic
11C2×#14558719C2212yes—
12#18011906—22no—
13#18011902—22no—
14#18011896—22no—
15#18011891C2212yes—
16#18011891C2212yes—
17C4×Dic298C2212yes—
18C4×D596C2211yescharacteristic
19#18011869—22no—
20#18011869C2212yes—
21C4⋊C4×D149C2212yes—
22#18011845C2211yescharacteristic
23#18011844C2212yes—
24#18011842C2212yes—
25C4⋊#11924746C2211yescharacteristic
26#18011836C2212yes—
27#18011834C2212yes—
28#18011834C2212yes—
29#18011823C2212yes—
30#125×C149C2212yes—
31#107×C149C2211yescharacteristic
32#107×C149C2211yescharacteristic
33#106×C149C2212yes—
34C4×C8×C149C2211yescharacteristic
35C2×Dic298C2312yes—
36C2×D596D411yescharacteristic
37C2×C4×D149—22no—
38C2×C4×D149C2312yes—
39Dic596—22no—
40#14558719—24no—
41C2×#11924746C2312yes—
42C4⋊Dic149—22no—
43C4⋊Dic149—22no—
44C4⋊Dic149D411yescharacteristic
45C4⋊Dic149C2312yes—
46#14558715—22no—
47#14558715—22no—
48#14558713—22no—
49#14558713—22no—
50#14558713—22no—
51#14558713D412yes—
52C4×Dic149—22no—
53C4×Dic149—22no—
54C2×C8×C149C2311yescharacteristic
55C2×C8×C149C2311yescharacteristic
56C4⋊C4×C149—22no—
57C4⋊C4×C149—22no—
58C4⋊C4×C149C2312yes—
59C4⋊C4×C149C2312yes—
60C42×C149C2311yescharacteristic
61C22×D149C2×D412yes—
62Dic298—22no—
63Dic298—22no—
64D596—41no—
65C2×Dic149—22no—
66C2×Dic149—22no—
67C2×Dic149C2×D412yes—
68C4×D149—22no—
69C4×D149—22no—
70C4×D149—44no—
71#11924746—22no—
72C2×C4×C149—22no—
73C2×C4×C149—22no—
74C2×C4×C149C2×D411yescharacteristic
75C2×C4×C149C2×D411yescharacteristic
76C2×C4×C149C2411yescharacteristic
77C8×C149—21no—
78C8×C149#4112yes—
79C22×C149C22×D411yescharacteristic
80C2×D149—22no—
81C2×D149—22no—
82C2×D149—22no—
83C4×C149—21no—
84C4×C149—21no—
85C4×C149—42no—
86C4×C149—42no—
87C4×C149C2×#4111yescharacteristic
88C4×C1492−1+411yescharacteristic
89Dic149—22no—
90Dic149—42no—
91Dic149—42no—
92C2×C149#54711yescharacteristic
93C2×C149#57511yescharacteristic
94C2×C149#57811yescharacteristic
95D149—42no—
96C149#335211yescharacteristic, complemented, Sylow
97#3352—1491nomaximal, Sylow
98#552—1492no—
99#499D14911yescharacteristic, complemented
100#485—1492no—
101#484—1492no—
102#479—1492no—
103#470—1492no—
104C4×Q16—1491no—
105#436—1491no—
106#428—1492no—
107C2×Q16—1491no—
108C2×M16—1492no—
109#126—2982no—
110#125—2982no—
111#125C2×D14912yes—
112#123—2982no—
113C22⋊Q8—1492no—
114C22⋊Q8—1492no—
115C4×Q8—1492no—
116C4×D4—1491no—
117#117—2982no—
118#117—1492no—
119C2×C4⋊C4—1492no—
120#107—1491no—
121#107—1492no—
122#107C2×D14911yescharacteristic
123#107C2×D14911yescharacteristic
124#106—1492no—
125#106C2×D14912yes—
126C4⋊C8—1491no—
127#103—1492no—
128#103—1492no—
129#103—1492no—
130C22⋊C8—1492no—
131C4×C8C2×D14911yescharacteristic
132C2×Q8—1492no—
133C2×D4—1491no—
134C22×C4—2982no—
135C22×C4—1492no—
136Q16—2982no—
137M16—2984no—
138C2×C8—1492no—
139C2×C8C22×D14911yescharacteristic
140C2×C8C22×D14911yescharacteristic
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—2982no—
144C4⋊C4—2982no—
145C4⋊C4—2982no—
146C4⋊C4—2982no—
147C4⋊C4—1492no—
148C4⋊C4—1491no—
149C4⋊C4C22×D14912yes—
150C4⋊C4C22×D14912yes—
151C22⋊C4—2982no—
152C22⋊C4—2982no—
153C22⋊C4—2982no—
154C22⋊C4—1492no—
155C42—2982no—
156C42—2982no—
157C42C22×D14911yescharacteristic
158C23—1492no—
159Q8—2982no—
160Q8—2982no—
161D4—5961no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—2982no—
165C2×C4—2982no—
166C2×C4—2982no—
167C2×C4—2982no—
168C2×C4—5964no—
169C2×C4—1492no—
170C2×C4D4×D14911yescharacteristic
171C2×C4D4×D14911yescharacteristic
172C2×C4C23×D14911yescharacteristic
173C8—21no—
174C8—2982no—
175C8#1455873712yes—
176C22—2982no—
177C22—2982no—
178C22—2982no—
179C22C2×D4×D14911yescharacteristic
180C4—21no—
181C4—21no—
182C4—42no—
183C4—42no—
184C4—2982no—
185C4—5962no—
186C4—5962no—
187C4C2×#1455873711yescharacteristic
188C4#1801195911yescharacteristic
189C2—5962no—
190C2#2375027811yescharacteristic
191C2#2375042211yescharacteristic
192C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#499×C149C2
socleC22×C149C22×D4
prime radicalC2×D596D4
hypercenter#499D149
hypocenterC149#3352
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
2. #23749968C2semidirect
3. #23749962C2semidirect
4. #23749929C2semidirect
5. #23749884C2semidirect
6. C4×Dic596C2semidirect
8. #23749664C2semidirect
9. #499×C149C2semidirect
96. C149#3352semidirect
99. #499D149semidirect

Maximal subgroups

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

subgroupindex
#237503132
#237499682
#237499622
#237499292
#237498842
C4×Dic5962
#237497042
#237496642
#499×C1492
#3352149