Finite Group Databasebeta

← #34043740

Subgroups — #34043740

Order 19072.

240 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 49 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#23750212C211yesmaximal, characteristic
2#23749961C211yesmaximal, characteristic, complemented
3#23749941C211yesmaximal, characteristic, complemented
4#23749562C211yesmaximal, characteristic, complemented
5#23749361C211yesmaximal, characteristic, complemented
6#23749348C211yesmaximal, characteristic, complemented
7#327×C149C211yesmaximal, characteristic, complemented
8#18011906—21no—
9#18011897—21no—
10#18011895—21no—
11#18011890C2211yescharacteristic
12#18011883—21no—
13#18011879—21no—
14D4×Dic149—21no—
15C2×C4⋊Dic149—21no—
16C2×C4⋊Dic149C2211yescharacteristic
17C2×#14558713—21no—
18C2×#14558713C2211yescharacteristic
19#18011845—21no—
20#18011842—21no—
21#18011836—21no—
22#18011832—21no—
23C22⋊#11924746C2211yescharacteristic
24#121×C149C2211yescharacteristic
25C22⋊C8×C149C2211yescharacteristic
26#95×C149C2211yescharacteristic
27C23×D149D411yescharacteristic
28C2×Dic298D411yescharacteristic
29C2×C22⋊D149—21no—
30C2×C22⋊D149—21no—
31C22×Dic149—21no—
32C22×Dic149—21no—
33C22×Dic149D411yescharacteristic
34C2×#11924746—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149—21no—
37C4⋊Dic149—21no—
38C4⋊Dic149—42no—
39C4⋊Dic149D411yescharacteristic
40#14558715—21no—
41C22⋊Dic149—21no—
42C22⋊Dic149—21no—
43#14558713—21no—
44#14558713—21no—
45#14558713—21no—
46#14558713—21no—
47#14558713—42no—
48C4×Dic149—21no—
49C2×D4×C149—21no—
50C2×D4×C149D411yescharacteristic
51C22×C4×C149—21no—
52C22×C4×C149C2311yescharacteristic
53C2×C8×C149—21no—
54C4⋊C4×C149D411yescharacteristic
55C22⋊C4×C149—21no—
56C22×D149—21no—
57C22×D149—21no—
58C22×D149—21no—
59C22×D149—41no—
60C22×D149—41no—
61Dic298—41no—
62C22⋊D149—81no—
63C22⋊D149—81no—
64C2×Dic149—21no—
65C2×Dic149—21no—
66C2×Dic149—21no—
67C2×Dic149—41no—
68C2×Dic149—41no—
69C2×Dic149—41no—
70C2×Dic149—41no—
71C2×Dic149—81no—
72#11924746—41no—
73C23×C149—21no—
74C23×C149C2×D411yescharacteristic
75D4×C149—41no—
76D4×C149—41no—
77D4×C149—41no—
78C2×C4×C149—22no—
79C2×C4×C149—21no—
80C2×C4×C149—41no—
81C2×C4×C149—41no—
82C2×C4×C149—41no—
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×D411yescharacteristic
85C8×C149—41no—
86C22×C149—21no—
87C22×C149—21no—
88C22×C149—41no—
89C22×C149—41no—
90C22×C149—41no—
91C22×C149#12011yescharacteristic
92C22×C149#13511yescharacteristic
93C22×C149#13711yescharacteristic
94C2×D149—42no—
95C2×D149—41no—
96C2×D149—41no—
97C2×D149—41no—
98C2×D149—81no—
99C4×C149—21no—
100C4×C149—21no—
101C4×C149—42no—
102C4×C149—41no—
103Dic149—41no—
104Dic149—41no—
105Dic149—41no—
106Dic149—81no—
107C2×C149—21no—
108C2×C149—21no—
109C2×C149—81no—
110C2×C149#45211yescharacteristic
111C2×C149#45311yescharacteristic
112C2×C149#45811yescharacteristic
113D149—81no—
114C149#161811yescharacteristic, complemented, Sylow
115#1618—1491nomaximal, Sylow
116#538—1491no—
117#484—1491no—
118#481—1491no—
119#399—1491no—
120#328—1491no—
121#327D14911yescharacteristic, complemented
122#323—1491no—
123#126—2981no—
124#124—2981no—
125#123—2981no—
126C22⋊Q8—1491no—
127#121—2981no—
128#121C2×D14911yescharacteristic
129#120—2981no—
130C4×D4—2981no—
131C2×C4⋊C4—2981no—
132C2×C4⋊C4—1491no—
133C2×C22⋊C4—2981no—
134C2×C22⋊C4—1491no—
135#107—2981no—
136#106—2981no—
137#103—2981no—
138#102—2981no—
139C22⋊C8—1491no—
140C22⋊C8C2×D14911yescharacteristic
141#95C2×D14911yescharacteristic
142C24—1491no—
143C2×Q8—1491no—
144C2×D4—21no—
145C2×D4—2981no—
146C2×D4—2981no—
147C2×D4D59611yescharacteristic
148C22×C4—21no—
149C22×C4—2981no—
150C22×C4—2981no—
151C22×C4—1491no—
152C22×C4C22×D14911yescharacteristic
153C2×C8—21no—
154C2×C8—2981no—
155C4⋊C4—2981no—
156C4⋊C4—2981no—
157C4⋊C4—2981no—
158C4⋊C4—2981no—
159C4⋊C4—5962no—
160C4⋊C4—1491no—
161C4⋊C4D59611yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—2981no—
164C22⋊C4—2981no—
165C22⋊C4—2981no—
166C22⋊C4—2981no—
167C22⋊C4—2981no—
168C22⋊C4—2981no—
169C22⋊C4—5962no—
170C42—2981no—
171C23—21no—
172C23—2981no—
173C23—2981no—
174C23—2981no—
175C23—5961no—
176C23—5961no—
177C23D4×D14911yescharacteristic
178Q8—5961no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—11921no—
183D4—11921no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2981no—
190C2×C4—2981no—
191C2×C4—2981no—
192C2×C4—5961no—
193C2×C4—5961no—
194C2×C4—5961no—
195C2×C4—5961no—
196C2×C4—11921no—
197C2×C4D4×D14911yescharacteristic
198C2×C4C2×D59611yescharacteristic
199C8—41no—
200C8—5961no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—5962no—
207C22—5961no—
208C22—5961no—
209C22—5961no—
210C22—11921no—
211C22#1801188111yescharacteristic
212C22#1801193011yescharacteristic
213C22#1801194011yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—5961no—
219C4—5961no—
220C4—5961no—
221C4—11921no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—11921no—
226C2#2374978811yescharacteristic
227C2#2374979411yescharacteristic
228C2#2374981611yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#327×C149C2
socleC22×C149#120
prime radical#23750212C2
hypercenter#327D149
hypocenterC149#1618
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #23749961C2semidirect
3. #23749941C2semidirect
4. #23749562C2semidirect
5. #23749361C2semidirect
6. #23749348C2semidirect
7. #327×C149C2semidirect
114. C149#1618semidirect
121. #327D149semidirect

Maximal subgroups

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

subgroupindex
#237502122
#237499612
#237499412
#237495622
#237493612
#237493482
#327×C1492
#1618149