Finite Group Databasebeta

← #34057059

Subgroups — #34057059

Order 19072.

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

normal subgroups only

This group has 342 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#23750314C212yesmaximal
2#23750026C211yesmaximal, characteristic, complemented
3#23749966C212yesmaximal, complemented
4#23749957C212yesmaximal, complemented
5#23749935C212yesmaximal, complemented
6#23749867C211yesmaximal, characteristic, complemented
7#23749866C211yesmaximal, characteristic, complemented
8#23749719C211yesmaximal, characteristic, complemented
9C8×C22⋊D149C211yesmaximal, characteristic
10#107×D149C211yesmaximal, characteristic, complemented
11#427×C149C211yesmaximal, characteristic, complemented
12C2×Dic596C2211yescharacteristic
13C2×C8×D149C2211yescharacteristic
14#18011904—22no—
15#18011903—22no—
16#18011902C2212yes—
17#18011893—22no—
18#18011891C2212yes—
19#18011890C2212yes—
20#18011876C2212yes—
21C4×C22⋊D149C2211yescharacteristic
22#18011868—22no—
23C4⋊C4×D149C2212yes—
24#18011845C2211yescharacteristic
25#18011844C2212yes—
26#18011842C2212yes—
27#18011840C2211yescharacteristic
28#18011836C2212yes—
29#18011834C2212yes—
30#18011834C2212yes—
31C22⋊#11924746C2211yescharacteristic
32#18011823C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C22×C8×C149C2211yescharacteristic
35#117×C149C2212yes—
36#107×C149C2211yescharacteristic
37#107×C149C2211yescharacteristic
38#106×C149C2212yes—
39C2×Dic298C2312yes—
40C2×C22⋊D149D411yescharacteristic
41C2×C4×D149—22no—
42C2×C4×D149C2311yescharacteristic
43Dic596—22no—
44C2×#11924746C2311yescharacteristic
45C2×#11924746C2311yescharacteristic
46C8×D149—22no—
47C4⋊Dic149—22no—
48C4⋊Dic149—22no—
49C4⋊Dic149C2312yes—
50#14558715—22no—
51#14558715—22no—
52#14558715—22no—
53#14558715—22no—
54#14558715D411yescharacteristic
55C22⋊Dic149—22no—
56C22⋊Dic149D411yescharacteristic
57#14558713—22no—
58#14558713D411yescharacteristic
59C4×Dic149—22no—
60C4×Dic149C2311yescharacteristic
61C22×C4×C149C2311yescharacteristic
62C2×C8×C149—22no—
63C2×C8×C149C2311yescharacteristic
64C2×C8×C149C2311yescharacteristic
65C4⋊C4×C149C2312yes—
66C4⋊C4×C149C2312yes—
67C22⋊C4×C149—22no—
68C42×C149—22no—
69C22×D149C2×D411yescharacteristic
70Dic298—22no—
71Dic298—22no—
72C22⋊D149—22no—
73C2×Dic149—22no—
74C2×Dic149—22no—
75C2×Dic149C2×D411yescharacteristic
76C2×Dic149C2×D411yescharacteristic
77C2×Dic149C2×D411yescharacteristic
78C4×D149—21no—
79C4×D149—21no—
80C4×D149—44no—
81#11924746—21no—
82#11924746—21no—
83C23×C149C2×D411yescharacteristic
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#13512yes—
99C4×C149—21no—
100C4×C149—42no—
101C4×C149—42no—
102C4×C149C2×#4111yescharacteristic
103C4×C1492−1+411yescharacteristic
104Dic149—21no—
105Dic149—21no—
106Dic149—21no—
107Dic149—42no—
108Dic149—42no—
109C2×C149—41no—
110C2×C149#54711yescharacteristic
111C2×C149C2×#13511yescharacteristic
112C2×C149#57811yescharacteristic
113D149—22no—
114C149#333611yescharacteristic, complemented, Sylow
115#3336—1491nomaximal, Sylow
116#552—1492no—
117#499—1491no—
118#485—1492no—
119#483—1492no—
120#479—1492no—
121#467—1491no—
122#467—1491no—
123C4×Q16—1491no—
124C8×D4—1491no—
125#427D14911yescharacteristic, complemented
126C2×#107—1491no—
127C2×Q16—1491no—
128C22×C8—1491no—
129C22×C8C2×D14911yescharacteristic
130#126—2982no—
131#125—2982no—
132#125—1492no—
133#123—2982no—
134C22⋊Q8—1492no—
135C22⋊Q8—1492no—
136C4×Q8—1492no—
137C4×D4—1491no—
138#117—2982no—
139#117C2×D14912yes—
140C2×C4⋊C4—1492no—
141#107—1491no—
142#107—1492no—
143#107C2×D14911yescharacteristic
144#107C2×D14911yescharacteristic
145#106—1492no—
146#106C2×D14912yes—
147C4⋊C8—1491no—
148#103—1492no—
149#103—1492no—
150#103—1492no—
151C22⋊C8—1491no—
152C22⋊C8—1491no—
153C4×C8—1491no—
154C2×Q8—1492no—
155C2×D4—1491no—
156C22×C4—2982no—
157C22×C4—1491no—
158C22×C4C22×D14911yescharacteristic
159Q16—2982no—
160C2×C8—22no—
161C2×C8—2982no—
162C2×C8—1491no—
163C2×C8—1491no—
164C2×C8C22×D14911yescharacteristic
165C2×C8C22×D14911yescharacteristic
166C4⋊C4—2982no—
167C4⋊C4—2982no—
168C4⋊C4—2982no—
169C4⋊C4—2982no—
170C4⋊C4—2982no—
171C4⋊C4—2982no—
172C4⋊C4—1492no—
173C4⋊C4—1491no—
174C4⋊C4C22×D14912yes—
175C4⋊C4C22×D14912yes—
176C22⋊C4—22no—
177C22⋊C4—2982no—
178C22⋊C4—2982no—
179C22⋊C4—1491no—
180C22⋊C4—1491no—
181C42—22no—
182C42—2982no—
183C42—1491no—
184C23—1491no—
185C23D4×D14911yescharacteristic
186Q8—2982no—
187Q8—2982no—
188D4—2982no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—2981no—
194C2×C4—2981no—
195C2×C4—2982no—
196C2×C4—2982no—
197C2×C4—5964no—
198C2×C4—1491no—
199C2×C4—1491no—
200C2×C4—1491no—
201C2×C4D4×D14911yescharacteristic
202C2×C4C23×D14911yescharacteristic
203C8—21no—
204C8—2981no—
205C8—2981no—
206C8#1455873612yes—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—2981no—
211C22—2981no—
212C22—1492no—
213C22C2×D4×D14911yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—2981no—
218C4—2981no—
219C4—2981no—
220C4—5962no—
221C4—5962no—
222C4C2×#1455873611yescharacteristic
223C4#1801195911yescharacteristic
224C2—41no—
225C2—2982no—
226C2#2375027611yescharacteristic
227C2#135×D14911yescharacteristic
228C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#427×C149C2
socleC22×C149C22×D4
prime radicalC2×C22⋊D149D4
hypercenter#427D149
hypocenterC149#3336
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #23750026C2semidirect
3. #23749966C2semidirect
4. #23749957C2semidirect
5. #23749935C2semidirect
6. #23749867C2semidirect
7. #23749866C2semidirect
8. #23749719C2semidirect
10. #107×D149C2semidirect
11. #427×C149C2semidirect
114. C149#3336semidirect
125. #427D149semidirect

Maximal subgroups

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

subgroupindex
#237503142
#237500262
#237499662
#237499572
#237499352
#237498672
#237498662
#237497192
C8×C22⋊D1492
#107×D1492
#427×C1492
#3336149