Finite Group Databasebeta

← #34057118

Subgroups — #34057118

Order 19072.

340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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#23750346C212yesmaximal
2#23750029C211yesmaximal, characteristic, complemented
3#23749964C212yesmaximal, complemented
4#23749963C212yesmaximal, complemented
5#23749908C212yesmaximal, complemented
6#23749863C211yesmaximal, characteristic, complemented
7Q16×Dic149C211yesmaximal, characteristic, complemented
8C8×C22⋊D149C211yesmaximal, characteristic
9#23749663C211yesmaximal, characteristic, complemented
10#23749662C211yesmaximal, characteristic, complemented
11#467×C149C211yesmaximal, characteristic, complemented
12C2×C8×D149C2211yescharacteristic
13#18011910C2212yes—
14#18011906—22no—
15#18011904—22no—
16#18011897—22no—
17#18011887C2212yes—
18Q8×Dic149C2212yes—
19#18011876—22no—
20C4×C22⋊D149C2211yescharacteristic
21#18011870C2212yes—
22#18011869C2212yes—
23#18011845C2211yescharacteristic
24#18011845C2211yescharacteristic
25#18011844C2212yes—
26#18011843C2212yes—
27#18011842C2212yes—
28#18011840C2211yescharacteristic
29#18011835C2212yes—
30#18011835C2212yes—
31C22⋊#11924746C2211yescharacteristic
32#18011823C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C2×Q16×C149C2211yescharacteristic
35C22×C8×C149C2211yescharacteristic
36C22⋊Q8×C149C2212yes—
37#107×C149C2211yescharacteristic
38#103×C149C2212yes—
39C2×Dic298—22no—
40C2×C22⋊D149D411yescharacteristic
41C2×C4×D149C2311yescharacteristic
42C2×#11924746C2311yescharacteristic
43C2×#11924746C2311yescharacteristic
44C8×D149—22no—
45C4⋊Dic149—22no—
46C4⋊Dic149C2312yes—
47C4⋊Dic149C2312yes—
48#14558715—22no—
49#14558715—22no—
50#14558715D411yescharacteristic
51C22⋊Dic149—22no—
52C22⋊Dic149D411yescharacteristic
53#14558713—22no—
54#14558713—22no—
55#14558713D411yescharacteristic
56C4×Dic149—22no—
57C4×Dic149—22no—
58C4×Dic149—22no—
59C4×Dic149C2311yescharacteristic
60C2×Q8×C149C2312yes—
61C22×C4×C149C2311yescharacteristic
62Q16×C149—22no—
63C2×C8×C149—22no—
64C2×C8×C149C2311yescharacteristic
65C2×C8×C149C2311yescharacteristic
66C4⋊C4×C149—22no—
67C4⋊C4×C149C2312yes—
68C22⋊C4×C149—22no—
69C22×D149C2×D411yescharacteristic
70Dic298—44no—
71C22⋊D149—22no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C2×Dic149C2×D411yescharacteristic
75C2×Dic149C2×D411yescharacteristic
76C2×Dic149C2×D411yescharacteristic
77C4×D149—21no—
78C4×D149—21no—
79#11924746—21no—
80#11924746—21no—
81C23×C149C2×D411yescharacteristic
82Q8×C149—22no—
83Q8×C149—22no—
84C2×C4×C149—21no—
85C2×C4×C149—21no—
86C2×C4×C149—22no—
87C2×C4×C149—22no—
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2411yescharacteristic
90C8×C149—21no—
91C8×C149#4112yes—
92C22×C149—21no—
93C22×C149—21no—
94C22×C149—21no—
95C22×C149C22×D411yescharacteristic
96C2×D149—21no—
97C2×D149—21no—
98C2×D149—21no—
99C4×C149—21no—
100C4×C149—42no—
101C4×C149—42no—
102C4×C149C2×#4111yescharacteristic
103C4×C1492−1+411yescharacteristic
104Dic149—21no—
105Dic149—21no—
106Dic149—42no—
107Dic149—42no—
108Dic149#13512yes—
109C2×C149—41no—
110C2×C149#54711yescharacteristic
111C2×C149C2×#13511yescharacteristic
112C2×C149#57811yescharacteristic
113D149—41no—
114C149#334211yescharacteristic, complemented, Sylow
115#3342—1491nomaximal, Sylow
116#556—1492no—
117#500—1491no—
118#485—1492no—
119#485—1492no—
120#475—1492no—
121#467—1491no—
122#467D14911yescharacteristic, complemented
123C4×Q16—1491no—
124C8×D4—1491no—
125#427—1491no—
126#427—1491no—
127C2×Q16C2×D14911yescharacteristic
128C22×C8—1491no—
129C22×C8C2×D14911yescharacteristic
130C4⋊Q8—1492no—
131#126—2982no—
132#126—2982no—
133#124—2982no—
134C22⋊Q8—1492no—
135C22⋊Q8C2×D14912yes—
136C4×Q8—2982no—
137C4×Q8—1492no—
138C4×D4—1491no—
139#117—1492no—
140#117—1492no—
141#107—1491no—
142#107—1491no—
143#107—1492no—
144#107C2×D14911yescharacteristic
145#106—1492no—
146#106—1492no—
147C4⋊C8—1491no—
148#103—1492no—
149#103—1492no—
150#103C2×D14912yes—
151C22⋊C8—1491no—
152C22⋊C8—1491no—
153C4×C8—1491no—
154C2×Q8—2982no—
155C2×Q8C22×D14912yes—
156C2×D4—1491no—
157C22×C4—1491no—
158C22×C4C22×D14911yescharacteristic
159Q16—22no—
160C2×C8—22no—
161C2×C8—2982no—
162C2×C8—1491no—
163C2×C8—1491no—
164C2×C8C22×D14911yescharacteristic
165C2×C8C22×D14911yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—2982no—
168C4⋊C4—2982no—
169C4⋊C4—2982no—
170C4⋊C4—1492no—
171C4⋊C4—1492no—
172C4⋊C4—1491no—
173C4⋊C4C22×D14912yes—
174C22⋊C4—22no—
175C22⋊C4—2982no—
176C22⋊C4—2982no—
177C22⋊C4—2982no—
178C22⋊C4—1491no—
179C22⋊C4—1491no—
180C42—2982no—
181C42—2982no—
182C42—2982no—
183C42—1491no—
184C23—1491no—
185C23D4×D14911yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—5964no—
189D4—2982no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—2981no—
195C2×C4—2981no—
196C2×C4—2982no—
197C2×C4—2982no—
198C2×C4—1491no—
199C2×C4—1491no—
200C2×C4—1491no—
201C2×C4D4×D14911yescharacteristic
202C2×C4C23×D14911yescharacteristic
203C8—21no—
204C8—2981no—
205C8—2981no—
206C8#1455873512yes—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—2981no—
211C22—2981no—
212C22—2981no—
213C22C2×D4×D14911yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—2981no—
218C4—2981no—
219C4—5962no—
220C4—5962no—
221C4—1492no—
222C4C2×#1455873511yescharacteristic
223C4#1801195811yescharacteristic
224C2—41no—
225C2—5961no—
226C2#2375027511yescharacteristic
227C2#135×D14911yescharacteristic
228C2#2375043811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#467×C149C2
socleC22×C149C22×D4
prime radicalC2×C22⋊D149D4
hypercenter#467D149
hypocenterC149#3342
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #23750029C2semidirect
3. #23749964C2semidirect
4. #23749963C2semidirect
5. #23749908C2semidirect
6. #23749863C2semidirect
7. Q16×Dic149C2semidirect
9. #23749663C2semidirect
10. #23749662C2semidirect
11. #467×C149C2semidirect
114. C149#3342semidirect
122. #467D149semidirect

Maximal subgroups

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

subgroupindex
#237503462
#237500292
#237499642
#237499632
#237499082
#237498632
Q16×Dic1492
C8×C22⋊D1492
#237496632
#237496622
#467×C1492
#3342149