Finite Group Databasebeta

← #34057093

Subgroups — #34057093

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#23750319C212yesmaximal, complemented
2#23750026C211yesmaximal, characteristic, complemented
3#23749949C212yesmaximal, complemented
4#23749945C212yesmaximal, complemented
5#23749924C212yesmaximal, complemented
6#23749862C211yesmaximal, characteristic, complemented
7#23749861C211yesmaximal, characteristic, complemented
8#23749707C211yesmaximal, characteristic, complemented
9C8×C22⋊D149C211yesmaximal, characteristic, complemented
10#107×D149C211yesmaximal, characteristic, complemented
11#427×C149C211yesmaximal, characteristic, complemented
12C2×D1192C2211yescharacteristic
13C2×C8×D149C2211yescharacteristic
14#18011905—22no—
15#18011902C2212yes—
16#18011893—22no—
17#18011886C2212yes—
18#18011885C2212yes—
19#18011884—22no—
20C4×D596—22no—
21#18011873C2212yes—
22C4×C22⋊D149C2211yescharacteristic
23C4⋊C4×D149C2212yes—
24#18011845C2211yescharacteristic
25#18011844C2212yes—
26#18011842C2212yes—
27#18011840C2211yescharacteristic
28#18011833C2212yes—
29#18011831C2212yes—
30#18011831C2212yes—
31C22⋊#11924746C2211yescharacteristic
32#18011823C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C22×C8×C149C2211yescharacteristic
35#117×C149C2212yes—
36#107×C149C2211yescharacteristic
37#107×C149C2211yescharacteristic
38#106×C149C2212yes—
39C2×D596—22no—
40C2×D596C2312yes—
41C2×C22⋊D149—22no—
42C2×C22⋊D149D411yescharacteristic
43C2×C4×D149—22no—
44C2×C4×D149—22no—
45C2×C4×D149C2311yescharacteristic
46D1192—22no—
47C2×#11924746C2311yescharacteristic
48C2×#11924746C2311yescharacteristic
49C8×D149—22no—
50C4⋊Dic149—22no—
51C4⋊Dic149C2312yes—
52#14558715—22no—
53#14558715—22no—
54#14558715D411yescharacteristic
55C22⋊Dic149D411yescharacteristic
56#14558713—22no—
57#14558713—22no—
58#14558713—22no—
59#14558713D411yescharacteristic
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×D149—22no—
70C22×D149C2×D411yescharacteristic
71D596—22no—
72D596—22no—
73D596—44no—
74C22⋊D149—22no—
75C22⋊D149—82no—
76C2×Dic149—22no—
77C2×Dic149C2×D411yescharacteristic
78C2×Dic149C2×D411yescharacteristic
79C2×Dic149C2×D411yescharacteristic
80C4×D149—21no—
81C4×D149—21no—
82C4×D149—82no—
83C4×D149—82no—
84#11924746—21no—
85#11924746—21no—
86C23×C149C2×D411yescharacteristic
87C2×C4×C149—21no—
88C2×C4×C149—21no—
89C2×C4×C149—22no—
90C2×C4×C149—22no—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2411yescharacteristic
93C8×C149—21no—
94C8×C149#4112yes—
95C22×C149—21no—
96C22×C149—21no—
97C22×C149—21no—
98C22×C149C22×D411yescharacteristic
99C2×D149—21no—
100C2×D149—21no—
101C2×D149—42no—
102C2×D149—42no—
103C2×D149—42no—
104C2×D149#13512yes—
105C4×C149—21no—
106C4×C149—42no—
107C4×C149—42no—
108C4×C149C2×#4111yescharacteristic
109C4×C1492−1+411yescharacteristic
110Dic149—21no—
111Dic149—21no—
112Dic149—21no—
113Dic149—42no—
114C2×C149—41no—
115C2×C149#54711yescharacteristic
116C2×C149C2×#13511yescharacteristic
117C2×C149#57611yescharacteristic
118D149—22no—
119D149—82no—
120C149#333911yescharacteristic, complemented, Sylow
121#3339—1491nomaximal, Sylow
122#553—1492no—
123#499—1491no—
124#482—1492no—
125#481—1492no—
126#478—1492no—
127#466—1491no—
128#466—1491no—
129C4×D8—1491no—
130C8×D4—1491no—
131#427D14911yescharacteristic, complemented
132C2×#107—1491no—
133C2×D8—1491no—
134C22×C8—1491no—
135C22×C8C2×D14911yescharacteristic
136#126—2982no—
137#125—1492no—
138#123—2982no—
139#121—2982no—
140#121—1492no—
141#121—1492no—
142C4×D4—2982no—
143C4×D4—1492no—
144C4×D4—1491no—
145#117C2×D14912yes—
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×C8—1491no—
160C2×D4—2982no—
161C2×D4—2982no—
162C2×D4—1491no—
163C2×D4—1492no—
164C22×C4—2982no—
165C22×C4—2982no—
166C22×C4—1491no—
167C22×C4C22×D14911yescharacteristic
168D8—2982no—
169C2×C8—22no—
170C2×C8—2982no—
171C2×C8—1491no—
172C2×C8—1491no—
173C2×C8C22×D14911yescharacteristic
174C2×C8C22×D14911yescharacteristic
175C4⋊C4—2982no—
176C4⋊C4—2982no—
177C4⋊C4—2982no—
178C4⋊C4—1492no—
179C4⋊C4—1491no—
180C4⋊C4C22×D14912yes—
181C4⋊C4C22×D14912yes—
182C22⋊C4—22no—
183C22⋊C4—2982no—
184C22⋊C4—2982no—
185C22⋊C4—2982no—
186C22⋊C4—1491no—
187C22⋊C4—1491no—
188C42—22no—
189C42—1491no—
190C23—2982no—
191C23—1491no—
192C23D4×D14911yescharacteristic
193D4—2982no—
194D4—2982no—
195D4—2982no—
196D4—5964no—
197D4—11922no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—2981no—
203C2×C4—2981no—
204C2×C4—2982no—
205C2×C4—1491no—
206C2×C4—1491no—
207C2×C4—1491no—
208C2×C4—11922no—
209C2×C4—11922no—
210C2×C4D4×D14911yescharacteristic
211C2×C4C23×D14911yescharacteristic
212C8—21no—
213C8—2981no—
214C8—2981no—
215C8#1455873612yes—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—2981no—
220C22—2981no—
221C22—5962no—
222C22—5962no—
223C22—5962no—
224C22—1492no—
225C22C2×D4×D14911yescharacteristic
226C4—21no—
227C4—42no—
228C4—42no—
229C4—2981no—
230C4—2981no—
231C4—2981no—
232C4—5962no—
233C4C2×#1455873611yescharacteristic
234C4#1801195911yescharacteristic
235C2—41no—
236C2—2982no—
237C2—11922no—
238C2#2375027611yescharacteristic
239C2#135×D14911yescharacteristic
240C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#427×C149C2
socleC22×C149C22×D4
hypercenter#427D149
hypocenterC149#3339
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
1. #23750319C2semidirect
2. #23750026C2semidirect
3. #23749949C2semidirect
4. #23749945C2semidirect
5. #23749924C2semidirect
6. #23749862C2semidirect
7. #23749861C2semidirect
8. #23749707C2semidirect
9. C8×C22⋊D149C2semidirect
10. #107×D149C2semidirect
11. #427×C149C2semidirect
120. C149#3339semidirect
131. #427D149semidirect

Maximal subgroups

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

subgroupindex
#237503192
#237500262
#237499492
#237499452
#237499242
#237498622
#237498612
#237497072
C8×C22⋊D1492
#107×D1492
#427×C1492
#3339149