Finite Group Databasebeta

← #34057295

Subgroups — #34057295

Order 19072.

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

normal subgroups only

This group has 360 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#23750328C212yesmaximal, complemented
2#23749952C212yesmaximal, complemented
3#23749940C212yesmaximal, complemented
4#23749922C212yesmaximal, complemented
5#23749879C212yesmaximal, complemented
6C4×D1192C211yesmaximal, characteristic, complemented
7#23749704C211yesmaximal, characteristic, complemented
8#23749664C212yesmaximal, complemented
9#499×C149C211yesmaximal, characteristic, complemented
10C2×D1192C2211yescharacteristic
11C2×#14558719C2212yes—
12#18011906—22no—
13#18011896—22no—
14#18011886—22no—
15#18011886C2212yes—
16#18011886C2212yes—
17C4×D596C2212yes—
18C4×D596C2211yescharacteristic
19#18011873—22no—
20#18011869C2212yes—
21C4⋊C4×D149C2212yes—
22#18011845C2211yescharacteristic
23#18011844C2212yes—
24#18011842C2212yes—
25C4⋊#11924746C2211yescharacteristic
26#18011833C2212yes—
27#18011831C2212yes—
28#18011831C2212yes—
29#18011823C2212yes—
30#125×C149C2212yes—
31#107×C149C2211yescharacteristic
32#107×C149C2211yescharacteristic
33#106×C149C2212yes—
34C4×C8×C149C2211yescharacteristic
35C2×D596—22no—
36C2×D596—22no—
37C2×D596D411yescharacteristic
38C2×D596C2312yes—
39C2×C4×D149—22no—
40C2×C4×D149—22no—
41C2×C4×D149C2312yes—
42D1192—22no—
43#14558719—24no—
44C2×#11924746C2312yes—
45C4⋊Dic149D411yescharacteristic
46C4⋊Dic149C2312yes—
47#14558715—22no—
48#14558713—22no—
49#14558713—22no—
50#14558713—22no—
51#14558713—22no—
52#14558713D412yes—
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×D149—22no—
62C22×D149C2×D412yes—
63D596—22no—
64D596—22no—
65D596—41no—
66D596—44no—
67D596—82no—
68C2×Dic149—22no—
69C2×Dic149C2×D412yes—
70C4×D149—22no—
71C4×D149—22no—
72C4×D149—82no—
73C4×D149—82no—
74#11924746—22no—
75C2×C4×C149—22no—
76C2×C4×C149—22no—
77C2×C4×C149C2×D411yescharacteristic
78C2×C4×C149C2×D411yescharacteristic
79C2×C4×C149C2411yescharacteristic
80C8×C149—21no—
81C8×C149#4112yes—
82C22×C149C22×D411yescharacteristic
83C2×D149—22no—
84C2×D149—22no—
85C2×D149—22no—
86C2×D149—42no—
87C2×D149—42no—
88C2×D149—42no—
89C4×C149—21no—
90C4×C149—21no—
91C4×C149—42no—
92C4×C149—42no—
93C4×C149C2×#4111yescharacteristic
94C4×C1492−1+411yescharacteristic
95Dic149—22no—
96Dic149—42no—
97C2×C149#54711yescharacteristic
98C2×C149#57511yescharacteristic
99C2×C149#57611yescharacteristic
100D149—42no—
101D149—82no—
102C149#335511yescharacteristic, complemented, Sylow
103#3355—1491nomaximal, Sylow
104#553—1492no—
105#499D14911yescharacteristic, complemented
106#482—1492no—
107#480—1492no—
108#478—1492no—
109#469—1492no—
110C4×D8—1491no—
111#436—1491no—
112#428—1492no—
113C2×D8—1491no—
114C2×M16—1492no—
115#126—2982no—
116#125C2×D14912yes—
117#123—2982no—
118#121—2982no—
119#121—1492no—
120#121—1492no—
121C4×D4—2982no—
122C4×D4—1492no—
123C4×D4—1491no—
124#117—1492no—
125C2×C4⋊C4—1492no—
126#107—1491no—
127#107—1492no—
128#107C2×D14911yescharacteristic
129#107C2×D14911yescharacteristic
130#106—1492no—
131#106C2×D14912yes—
132C4⋊C8—1491no—
133#102—1492no—
134#102—1492no—
135#102—1492no—
136C22⋊C8—1492no—
137C4×C8C2×D14911yescharacteristic
138C2×D4—2982no—
139C2×D4—2982no—
140C2×D4—1491no—
141C2×D4—1492no—
142C22×C4—2982no—
143C22×C4—2982no—
144C22×C4—1492no—
145D8—2982no—
146M16—2984no—
147C2×C8—1492no—
148C2×C8C22×D14911yescharacteristic
149C2×C8C22×D14911yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—2982no—
153C4⋊C4—1492no—
154C4⋊C4—1491no—
155C4⋊C4C22×D14912yes—
156C4⋊C4C22×D14912yes—
157C22⋊C4—2982no—
158C22⋊C4—2982no—
159C22⋊C4—2982no—
160C22⋊C4—2982no—
161C22⋊C4—1492no—
162C42—2982no—
163C42C22×D14911yescharacteristic
164C23—2982no—
165C23—1492no—
166D4—2982no—
167D4—2982no—
168D4—5961no—
169D4—5964no—
170D4—11922no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—2982no—
174C2×C4—2982no—
175C2×C4—2982no—
176C2×C4—1492no—
177C2×C4—11922no—
178C2×C4—11922no—
179C2×C4D4×D14911yescharacteristic
180C2×C4D4×D14911yescharacteristic
181C2×C4C23×D14911yescharacteristic
182C8—21no—
183C8—2982no—
184C8#1455873712yes—
185C22—2982no—
186C22—2982no—
187C22—2982no—
188C22—5962no—
189C22—5962no—
190C22—5962no—
191C22C2×D4×D14911yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—42no—
196C4—2982no—
197C4—5962no—
198C4C2×#1455873711yescharacteristic
199C4#1801195911yescharacteristic
200C2—5962no—
201C2—11922no—
202C2#2375027811yescharacteristic
203C2#2375042211yescharacteristic
204C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#499×C149C2
socleC22×C149C22×D4
hypercenter#499D149
hypocenterC149#3355
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
1. #23750328C2semidirect
2. #23749952C2semidirect
3. #23749940C2semidirect
4. #23749922C2semidirect
5. #23749879C2semidirect
6. C4×D1192C2semidirect
7. #23749704C2semidirect
8. #23749664C2semidirect
9. #499×C149C2semidirect
102. C149#3355semidirect
105. #499D149semidirect

Maximal subgroups

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

subgroupindex
#237503282
#237499522
#237499402
#237499222
#237498792
C4×D11922
#237497042
#237496642
#499×C1492
#3355149