Finite Group Databasebeta

← #34044652

Subgroups — #34044652

Order 19072.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#18011959C211yesmaximal, characteristic
2C2×#18011837C212yesmaximal, complemented
3#23749627C212yesmaximal, complemented
4#23749532C211yesmaximal, characteristic, complemented
5C2×#101×C149C211yesmaximal, characteristic, complemented
6#18011959—22no—
7#18011959—24no—
8#18011959C414yescomplemented
9C2×#14558737—22no—
10C2×#14558736—22no—
11C2×#14558736C2212yes—
12C2×Q8×D149—22no—
13C2×C4⋊Dic149C2211yescharacteristic
14C2×C4×Dic149C2211yescharacteristic
15#18011837—24no—
16#18011836—22no—
17#18011833—22no—
18#18011818—22no—
19C22×Q8×C149C2211yescharacteristic
20C2×M16×C149C2212yes—
21#101×C149—22no—
22#14558737—28no—
23#14558737—28no—
24#14558736—28no—
25#14558736—28no—
26#14558736—22no—
27#14558736—22no—
28#14558736C2×C414yes—
29#14558736D414yes—
30C2×Dic298—22no—
31C2×Dic298D412yes—
32Q8×D149—28no—
33Q8×D149—28no—
34C2×D596—22no—
35C2×D596D412yes—
36C2×C22⋊D149—22no—
37C22×Dic149—21no—
38C22×Dic149—21no—
39C2×C4×D149—24no—
40C2×C4×D149—22no—
41C4⋊Dic149—22no—
42C4×Dic149—22no—
43C2×Q8×C149—22no—
44C2×Q8×C149—22no—
45C2×Q8×C149C2×C412yes—
46C2×Q8×C149D412yes—
47C22×C4×C149D412yes—
48C22×C4×C149C2311yescharacteristic
49M16×C149—22no—
50M16×C149—22no—
51C2×C8×C149—22no—
52C22×D149—22no—
53Dic298—28no—
54Dic298—22no—
55Dic298C22⋊C414yes—
56D596—28no—
57D596—22no—
58D596C22⋊C414yes—
59C22⋊D149—24no—
60C22⋊D149—24no—
61C2×Dic149—22no—
62C2×Dic149—22no—
63C2×Dic149—41no—
64C2×Dic149—41no—
65C2×Dic149—42no—
66C2×Dic149—41no—
67C4×D149—216no—
68C4×D149—24no—
69C4×D149—24no—
70C23×C149C2×D411yescharacteristic
71Q8×C149—24no—
72Q8×C149—24no—
73C2×C4×C149—22no—
74C2×C4×C149—22no—
75C2×C4×C149C22⋊C414yes—
76C2×C4×C149C22×C411yescharacteristic
77C2×C4×C149C2×D412yes—
78C2×C4×C149C2×D412yes—
79C2×C4×C149C2×D411yescharacteristic
80C8×C149—42no—
81C22×C149—21no—
82C22×C149—21no—
83C22×C149C2×C22⋊C411yescharacteristic
84C22×C149#12011yescharacteristic
85C22×C149#12011yescharacteristic
86C2×D149—24no—
87C2×D149—42no—
88C2×D149—42no—
89C4×C149—24no—
90C4×C149C2×C22⋊C412yes—
91C4×C149#12012yes—
92Dic149—24no—
93Dic149—42no—
94Dic149—81no—
95C2×C149—21no—
96C2×C149—21no—
97C2×C149#37911yescharacteristic
98C2×C149#45411yescharacteristic
99C2×C149#45611yescharacteristic
100D149—44no—
101C149#179311yescharacteristic, complemented, Sylow
102#1793—1491nomaximal, Sylow
103C2×2−1+4—1491no—
104C2×#104—1492no—
105#417—1492no—
106C2×#101D14911yescharacteristic, complemented
107#391—1491no—
1082−1+4—2984no—
1092−1+4—2982no—
1102−1+4—1494no—
111C2×#41—2982no—
112C2×#41—2982no—
113C2×#41—1492no—
114C22×Q8—2982no—
115C22×Q8C2×D14911yescharacteristic
116C2×M16C2×D14912yes—
117C2×C4⋊C4—1491no—
118C2×C42—1491no—
119#104—2984no—
120#103—2982no—
121#102—2982no—
122#101—22no—
123#95—2982no—
124#41—2988no—
125#41—2988no—
126#41—2988no—
127#41—2982no—
128#41—2982no—
129#41—2988no—
130#41—1494no—
131#41—1494no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—2982no—
135C2×Q8—2988no—
136C2×Q8—2988no—
137C2×Q8—1492no—
138C2×Q8C4×D14912yes—
139C2×Q8C22⋊D14912yes—
140C2×D4—2982no—
141C2×D4—2982no—
142C2×D4—1492no—
143C22×C4—2984no—
144C22×C4—2982no—
145C22×C4—2981no—
146C22×C4—2981no—
147C22×C4D59612yes—
148C22×C4C22×D14911yescharacteristic
149M16—22no—
150M16—22no—
151C2×C8—22no—
152C4⋊C4—2982no—
153C42—2982no—
154C23—2982no—
155C23C2×D59611yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—2988no—
159Q8—2982no—
160Q8—1494no—
161D4—2988no—
162D4—2984no—
163D4—2984no—
164D4—2982no—
165D4—1494no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—29816no—
169C2×C4—2982no—
170C2×C4—2984no—
171C2×C4—2984no—
172C2×C4—2982no—
173C2×C4—5961no—
174C2×C4—5961no—
175C2×C4—5962no—
176C2×C4—5961no—
177C2×C4#1455871314yes—
178C2×C4C2×C4×D14911yescharacteristic
179C2×C4D4×D14912yes—
180C2×C4D4×D14912yes—
181C2×C4C2×C22⋊D14911yescharacteristic
182C8—42no—
183C22—21no—
184C22—21no—
185C22—2984no—
186C22—5962no—
187C22—5962no—
188C22C2×#1455871311yescharacteristic
189C22#1801188111yescharacteristic
190C22#1801188111yescharacteristic
191C4—24no—
192C4—2984no—
193C4—5962no—
194C4—11921no—
195C4C22⋊C4×D14912yes—
196C4#1801187912yes—
197C2—21no—
198C2—21no—
199C2—5964no—
200C2#2374948011yescharacteristic
201C2#2374980011yescharacteristic
202C2#2374981011yescharacteristic
subgroupG/H
centerC22#18011881
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC2×#101×C149C2
socleC22×C149#120
prime radicalC2×#18011959C2
cosocleC22×C4×C149C23
hypercenterC2×#101D149
hypocenterC149#1793
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#18011837C2semidirect
3. #23749627C2semidirect
4. #23749532C2semidirect
5. C2×#101×C149C2semidirect
8. #18011959C4semidirect
101. C149#1793semidirect
106. C2×#101D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119592
C2×#180118372
#237496272
#237495322
C2×#101×C1492
#1793149