Finite Group Databasebeta

← #34057298

Subgroups — #34057298

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#23750325C212yesmaximal, complemented
2#23750027C211yesmaximal, characteristic, complemented
3#23749947C212yesmaximal, complemented
4#23749937C212yesmaximal, complemented
5#23749925C212yesmaximal, complemented
6#23749875C212yesmaximal, complemented
7#23749704C211yesmaximal, characteristic, complemented
8#23749666C212yesmaximal, complemented
9C4×D8×C149C211yesmaximal, characteristic, complemented
10C2×#14558719C2212yes—
11#18011904—22no—
12#18011903C2212yes—
13#18011894—22no—
14#18011884—22no—
15#18011882C2212yes—
16#18011882C2212yes—
17C4×D596C2211yescharacteristic
18C4×C22⋊D149—22no—
19#18011869C2212yes—
20C4⋊C4×D149C2212yes—
21#18011845C2211yescharacteristic
22#18011845C2211yescharacteristic
23#18011844C2212yes—
24#18011843C2212yes—
25#18011842C2212yes—
26C4⋊#11924746C2211yescharacteristic
27#18011832C2212yes—
28#18011832C2212yes—
29#18011823C2212yes—
30C2×D8×C149C2211yescharacteristic
31C4×D4×C149C2212yes—
32#107×C149C2211yescharacteristic
33#102×C149C2212yes—
34C4×C8×C149C2211yescharacteristic
35C2×D596D411yescharacteristic
36C2×C22⋊D149—22no—
37C2×C22⋊D149—22no—
38C2×C4×D149—22no—
39C2×C4×D149C2312yes—
40#14558719—24no—
41C2×#11924746C2312yes—
42C4⋊Dic149D411yescharacteristic
43C4⋊Dic149C2312yes—
44C4⋊Dic149C2312yes—
45#14558715—22no—
46#14558715—22no—
47#14558715—22no—
48C22⋊Dic149—22no—
49C22⋊Dic149—22no—
50#14558713—22no—
51#14558713D412yes—
52C4×Dic149—22no—
53C2×D4×C149C2312yes—
54C22×C4×C149—22no—
55D8×C149—22no—
56C2×C8×C149C2311yescharacteristic
57C2×C8×C149C2311yescharacteristic
58C4⋊C4×C149C2312yes—
59C22⋊C4×C149—22no—
60C42×C149C2311yescharacteristic
61C22×D149C2×D412yes—
62D596—41no—
63C22⋊D149—44no—
64C22⋊D149—82no—
65C2×Dic149—22no—
66C2×Dic149—22no—
67C2×Dic149C2×D412yes—
68C4×D149—22no—
69C4×D149—22no—
70C4×D149—82no—
71#11924746—22no—
72C23×C149—22no—
73D4×C149—22no—
74D4×C149—22no—
75C2×C4×C149—22no—
76C2×C4×C149—82no—
77C2×C4×C149C2×D411yescharacteristic
78C2×C4×C149C2×D411yescharacteristic
79C2×C4×C149C2411yescharacteristic
80C8×C149—21no—
81C8×C149#4112yes—
82C22×C149—42no—
83C22×C149—42no—
84C22×C149—42no—
85C22×C149C22×D411yescharacteristic
86C2×D149—22no—
87C2×D149—22no—
88C2×D149—22no—
89C4×C149—21no—
90C4×C149—21no—
91C4×C149—42no—
92C4×C149C2×#4111yescharacteristic
93C4×C1492−1+411yescharacteristic
94Dic149—22no—
95Dic149—42no—
96Dic149—42no—
97C2×C149—82no—
98C2×C149#54711yescharacteristic
99C2×C149#57511yescharacteristic
100C2×C149#57611yescharacteristic
101D149—42no—
102C149#335511yescharacteristic, complemented, Sylow
103#3355—1491nomaximal, Sylow
104#553—1492no—
105#499—1491no—
106#482—1492no—
107#480—1492no—
108#478—1492no—
109#469—1492no—
110C4×D8D14911yescharacteristic, complemented
111#436—1491no—
112#428—1492no—
113C2×D8C2×D14911yescharacteristic
114C2×M16—1492no—
115#126—2982no—
116#125—1492no—
117#123—2982no—
118#121—2982no—
119#121—1492no—
120#121—1492no—
121C4×D4—2982no—
122C4×D4—1491no—
123C4×D4C2×D14912yes—
124#117—1492no—
125C2×C4⋊C4—1492no—
126#107—1491no—
127#107—1491no—
128#107—1492no—
129#107C2×D14911yescharacteristic
130#106—1492no—
131#106—1492no—
132C4⋊C8—1491no—
133#102—1492no—
134#102—1492no—
135#102C2×D14912yes—
136C22⋊C8—1492no—
137C4×C8C2×D14911yescharacteristic
138C2×D4—2982no—
139C2×D4—2982no—
140C2×D4—1491no—
141C2×D4C22×D14912yes—
142C22×C4—22no—
143C22×C4—2982no—
144C22×C4—1492no—
145D8—22no—
146M16—2984no—
147C2×C8—1492no—
148C2×C8C22×D14911yescharacteristic
149C2×C8C22×D14911yescharacteristic
150C4⋊C4—2982no—
151C4⋊C4—2982no—
152C4⋊C4—2982no—
153C4⋊C4—1492no—
154C4⋊C4—1492no—
155C4⋊C4—1491no—
156C4⋊C4C22×D14912yes—
157C22⋊C4—22no—
158C22⋊C4—2982no—
159C22⋊C4—2982no—
160C22⋊C4—2982no—
161C22⋊C4—1492no—
162C42—2982no—
163C42C22×D14911yescharacteristic
164C23—22no—
165C23—1492no—
166D4—22no—
167D4—22no—
168D4—5961no—
169D4—5964no—
170D4—11922no—
171C2×C4—22no—
172C2×C4—82no—
173C2×C4—2982no—
174C2×C4—2982no—
175C2×C4—2982no—
176C2×C4—2982no—
177C2×C4—1492no—
178C2×C4—11922no—
179C2×C4D4×D14911yescharacteristic
180C2×C4D4×D14911yescharacteristic
181C2×C4C23×D14911yescharacteristic
182C8—21no—
183C8—2982no—
184C8#1455873612yes—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—2982no—
189C22—2982no—
190C22—2982no—
191C22C2×D4×D14911yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—2982no—
196C4—5962no—
197C4—5962no—
198C4C2×#1455873611yescharacteristic
199C4#1801195811yescharacteristic
200C2—82no—
201C2—5962no—
202C2#2375028011yescharacteristic
203C2#2375042211yescharacteristic
204C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×D8×C149C2
socleC22×C149C22×D4
hypercenterC4×D8D149
hypocenterC149#3355
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23750325C2semidirect
2. #23750027C2semidirect
3. #23749947C2semidirect
4. #23749937C2semidirect
5. #23749925C2semidirect
6. #23749875C2semidirect
7. #23749704C2semidirect
8. #23749666C2semidirect
9. C4×D8×C149C2semidirect
102. C149#3355semidirect
110. C4×D8D149semidirect

Maximal subgroups

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

subgroupindex
#237503252
#237500272
#237499472
#237499372
#237499252
#237498752
#237497042
#237496662
C4×D8×C1492
#3355149