Finite Group Databasebeta

← #34057092

Subgroups — #34057092

Order 19072.

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

normal subgroups only

This group has 366 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#23750328C212yesmaximal, complemented
2#23749951C212yesmaximal, complemented
3#23749945C212yesmaximal, complemented
4#23749922C212yesmaximal, complemented
5#23749862C211yesmaximal, characteristic, complemented
6#23749862C211yesmaximal, characteristic, complemented
7C4×D1192C211yesmaximal, characteristic, complemented
8C8×D596C211yesmaximal, characteristic, complemented
9#23749662C211yesmaximal, characteristic, complemented
10#107×D149C211yesmaximal, characteristic, complemented
11#499×C149C211yesmaximal, characteristic, complemented
12C2×D1192C2211yescharacteristic
13C2×C8×D149C2211yescharacteristic
14C2×C8×D149C2211yescharacteristic
15#18011906—22no—
16#18011896—22no—
17#18011886—22no—
18#18011886C2212yes—
19#18011886C2212yes—
20C4×D596C2212yes—
21C4×D596C2211yescharacteristic
22#18011873—22no—
23#18011869C2212yes—
24C4⋊C4×D149C2212yes—
25#18011845C2211yescharacteristic
26#18011844C2212yes—
27#18011842C2212yes—
28C4⋊#11924746C2211yescharacteristic
29#18011833C2212yes—
30#18011831C2212yes—
31#18011831C2212yes—
32#18011823C2211yescharacteristic
33#18011823C2211yescharacteristic
34#125×C149C2212yes—
35#107×C149C2211yescharacteristic
36#107×C149C2211yescharacteristic
37#106×C149C2212yes—
38C4×C8×C149C2211yescharacteristic
39C2×D596—22no—
40C2×D596—22no—
41C2×D596D411yescharacteristic
42C2×D596C2312yes—
43C2×C4×D149—22no—
44C2×C4×D149—22no—
45C2×C4×D149C2311yescharacteristic
46C2×C4×D149C2311yescharacteristic
47D1192—22no—
48C2×#11924746C2311yescharacteristic
49C2×#11924746C2311yescharacteristic
50C8×D149—22no—
51C8×D149—22no—
52C4⋊Dic149D411yescharacteristic
53C4⋊Dic149C2312yes—
54#14558715—22no—
55#14558713—22no—
56#14558713—22no—
57#14558713—22no—
58#14558713—22no—
59#14558713D411yescharacteristic
60#14558713D411yescharacteristic
61C4×Dic149—22no—
62C2×C8×C149C2311yescharacteristic
63C2×C8×C149C2311yescharacteristic
64C4⋊C4×C149—22no—
65C4⋊C4×C149—22no—
66C4⋊C4×C149C2312yes—
67C4⋊C4×C149C2312yes—
68C42×C149C2311yescharacteristic
69C22×D149—22no—
70C22×D149C2×D411yescharacteristic
71C22×D149C2×D411yescharacteristic
72D596—22no—
73D596—22no—
74D596—22no—
75D596—44no—
76D596—82no—
77C2×Dic149—22no—
78C2×Dic149C2×D411yescharacteristic
79C2×Dic149C2×D411yescharacteristic
80C4×D149—21no—
81C4×D149—21no—
82C4×D149—21no—
83C4×D149—21no—
84C4×D149—82no—
85C4×D149—82no—
86#11924746—21no—
87#11924746—21no—
88C2×C4×C149—22no—
89C2×C4×C149—22no—
90C2×C4×C149C2×D411yescharacteristic
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2411yescharacteristic
93C8×C149—21no—
94C8×C149#4112yes—
95C22×C149C22×D411yescharacteristic
96C2×D149—21no—
97C2×D149—21no—
98C2×D149—21no—
99C2×D149—21no—
100C2×D149—21no—
101C2×D149—42no—
102C2×D149—42no—
103C2×D149—42no—
104C2×D149#13512yes—
105C4×C149—21no—
106C4×C149—21no—
107C4×C149—42no—
108C4×C149—42no—
109C4×C149C2×#4111yescharacteristic
110C4×C1492−1+411yescharacteristic
111Dic149—21no—
112Dic149—21no—
113Dic149—42no—
114C2×C149#54711yescharacteristic
115C2×C149C2×#13511yescharacteristic
116C2×C149#57611yescharacteristic
117D149—22no—
118D149—41no—
119D149—82no—
120C149#333911yescharacteristic, complemented, Sylow
121#3339—1491nomaximal, Sylow
122#553—1492no—
123#499D14911yescharacteristic, complemented
124#482—1492no—
125#481—1492no—
126#478—1492no—
127#466—1491no—
128#466—1491no—
129C4×D8—1491no—
130C8×D4—1491no—
131#427—1491no—
132C2×#107—1491no—
133C2×D8—1491no—
134C22×C8—1491no—
135C22×C8—1491no—
136#126—2982no—
137#125C2×D14912yes—
138#123—2982no—
139#121—2982no—
140#121—1492no—
141#121—1492no—
142C4×D4—2982no—
143C4×D4—1492no—
144C4×D4—1491no—
145#117—1492no—
146C2×C4⋊C4—1492no—
147#107—1491no—
148#107—1492no—
149#107C2×D14911yescharacteristic
150#107C2×D14911yescharacteristic
151#106—1492no—
152#106C2×D14912yes—
153C4⋊C8—1491no—
154#102—1492no—
155#102—1492no—
156#102—1492no—
157C22⋊C8—1491no—
158C22⋊C8—1491no—
159C4×C8C2×D14911yescharacteristic
160C2×D4—2982no—
161C2×D4—2982no—
162C2×D4—1491no—
163C2×D4—1492no—
164C22×C4—2982no—
165C22×C4—2982no—
166C22×C4—1491no—
167C22×C4—1491no—
168D8—2982no—
169C2×C8—2982no—
170C2×C8—2982no—
171C2×C8—1491no—
172C2×C8—1491no—
173C2×C8C22×D14911yescharacteristic
174C2×C8C22×D14911yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—2982no—
178C4⋊C4—1492no—
179C4⋊C4—1491no—
180C4⋊C4C22×D14912yes—
181C4⋊C4C22×D14912yes—
182C22⋊C4—2982no—
183C22⋊C4—2982no—
184C22⋊C4—2982no—
185C22⋊C4—2982no—
186C22⋊C4—1491no—
187C22⋊C4—1491no—
188C42—2982no—
189C42C22×D14911yescharacteristic
190C23—2982no—
191C23—1491no—
192C23—1491no—
193D4—2982no—
194D4—2982no—
195D4—2982no—
196D4—5964no—
197D4—11922no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—2981no—
201C2×C4—2981no—
202C2×C4—2981no—
203C2×C4—2981no—
204C2×C4—2982no—
205C2×C4—1491no—
206C2×C4—1491no—
207C2×C4—11922no—
208C2×C4—11922no—
209C2×C4D4×D14911yescharacteristic
210C2×C4D4×D14911yescharacteristic
211C2×C4C23×D14911yescharacteristic
212C8—21no—
213C8—2981no—
214C8—2981no—
215C8#1455873712yes—
216C22—2981no—
217C22—2981no—
218C22—2981no—
219C22—2981no—
220C22—2981no—
221C22—5962no—
222C22—5962no—
223C22—5962no—
224C22—1492no—
225C22C2×D4×D14911yescharacteristic
226C4—21no—
227C4—21no—
228C4—42no—
229C4—42no—
230C4—2981no—
231C4—2981no—
232C4—5962no—
233C4C2×#1455873711yescharacteristic
234C4#1801195911yescharacteristic
235C2—2982no—
236C2—5961no—
237C2—11922no—
238C2#2375027811yescharacteristic
239C2#135×D14911yescharacteristic
240C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#499×C149C2
socleC22×C149C22×D4
hypercenter#499D149
hypocenterC149#3339
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #23750328C2semidirect
2. #23749951C2semidirect
3. #23749945C2semidirect
4. #23749922C2semidirect
5. #23749862C2semidirect
6. #23749862C2semidirect
7. C4×D1192C2semidirect
8. C8×D596C2semidirect
9. #23749662C2semidirect
10. #107×D149C2semidirect
11. #499×C149C2semidirect
120. C149#3339semidirect
123. #499D149semidirect

Maximal subgroups

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

subgroupindex
#237503282
#237499512
#237499452
#237499222
#237498622
C4×D11922
C8×D5962
#237496622
#107×D1492
#499×C1492
#3339149