Finite Group Databasebeta

← #34055598

Subgroups — #34055598

Order 19072.

402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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#23750205C212yesmaximal, complemented
2#23749954C212yesmaximal, complemented
3#23749945C212yesmaximal, complemented
4#23749878C211yesmaximal, characteristic, complemented
5#23749856C212yesmaximal, complemented
6#23749786C212yesmaximal, complemented
7#23749773C212yesmaximal, complemented
8#23749593C211yesmaximal, characteristic, complemented
9#470×C149C211yesmaximal, characteristic, complemented
10C2×#14558737C2212yes—
11C2×#14558736C2211yescharacteristic
12C2×#14558723C2212yes—
13C2×D1192C2211yescharacteristic
14C22×#11924746C2211yescharacteristic
15#18011889—22no—
16#18011887C2212yes—
17#18011886—22no—
18#18011886C2212yes—
19#18011885C2212yes—
20#18011884—22no—
21#18011884—22no—
22C4⋊C4×D149C2212yes—
23#18011843C2211yescharacteristic
24#18011842C2212yes—
25#18011835C2212yes—
26#18011833C2212yes—
27#18011831C2212yes—
28#18011823C2212yes—
29#18011823C2212yes—
30C2×Q16×C149C2211yescharacteristic
31C2×M16×C149C2211yescharacteristic
32C22⋊Q8×C149C2212yes—
33#106×C149C2211yescharacteristic
34#103×C149C2212yes—
35#14558737—42no—
36#14558737—42no—
37#14558736—41no—
38#14558736—41no—
39C2×Dic298D411yescharacteristic
40C2×D596—22no—
41C2×D596—22no—
42C2×D596D411yescharacteristic
43C2×D596C2312yes—
44C2×C22⋊D149—22no—
45C2×C22⋊D149D412yes—
46C2×C4×D149—22no—
47C2×C4×D149—22no—
48C2×C4×D149C2312yes—
49#14558723—42no—
50D1192—41no—
51C2×#11924746—41no—
52C2×#11924746C2312yes—
53C4⋊Dic149C2312yes—
54#14558715—22no—
55#14558715—22no—
56#14558713—22no—
57#14558713—22no—
58#14558713—22no—
59C2×Q8×C149C2312yes—
60C22×C4×C149C2311yescharacteristic
61Q16×C149—41no—
62M16×C149—41no—
63C2×C8×C149C2311yescharacteristic
64C2×C8×C149C2311yescharacteristic
65C4⋊C4×C149—22no—
66C4⋊C4×C149C2312yes—
67C22⋊C4×C149—22no—
68C22×D149—22no—
69C22×D149C2×D412yes—
70Dic298—41no—
71D596—22no—
72D596—22no—
73D596—41no—
74D596—44no—
75D596—82no—
76C22⋊D149—42no—
77C22⋊D149—82no—
78C2×Dic149—22no—
79C2×Dic149C2×D412yes—
80C4×D149—22no—
81C4×D149—22no—
82C4×D149—44no—
83C4×D149—82no—
84#11924746—22no—
85C23×C149C2×D411yescharacteristic
86Q8×C149—22no—
87Q8×C149—22no—
88C2×C4×C149—21no—
89C2×C4×C149—21no—
90C2×C4×C149—22no—
91C2×C4×C149—22no—
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2411yescharacteristic
94C8×C149—21no—
95C8×C149—21no—
96C22×C149—21no—
97C22×C149—22no—
98C22×C149C22×D411yescharacteristic
99C2×D149—22no—
100C2×D149—22no—
101C2×D149—22no—
102C2×D149—42no—
103C2×D149—42no—
104C2×D149—42no—
105C4×C149—21no—
106C4×C149—42no—
107C4×C149—42no—
108C4×C149H(5,𝔽2)11yescharacteristic
109C4×C149H(5,𝔽2)11yescharacteristic
110Dic149—22no—
111Dic149—42no—
112C2×C149—41no—
113C2×C149#53411yescharacteristic
114C2×C149#57712yes—
115D149—42no—
116D149—82no—
117C149#320411yescharacteristic, complemented, Sylow
118#3204—1491nomaximal, Sylow
119#537—1492no—
120#483—1492no—
121#481—1492no—
122#470D14911yescharacteristic, complemented
123#469—1491no—
124#465—1492no—
125#452—1492no—
126#449—1492no—
127#408—1491no—
128C2×#41—1492no—
129C2×#41—1491no—
130C2×Q16C2×D14911yescharacteristic
131C2×SD16—1492no—
132C2×D8—1491no—
133C2×M16C2×D14911yescharacteristic
134C22×C8—1491no—
135C22⋊Q8—2982no—
136C22⋊Q8—1492no—
137C22⋊Q8C2×D14912yes—
138#121—2982no—
139#121—2982no—
140#121—2982no—
141#121—1492no—
142#121—1492no—
143C2×C4⋊C4—1492no—
144#106—1491no—
145#106—1492no—
146#106C2×D14911yescharacteristic
147#103—1492no—
148#103C2×D14912yes—
149#102—1492no—
150#102—1492no—
151C22⋊C8—1492no—
152C22⋊C8—1492no—
153#41—5961no—
154#41—5961no—
155#41—5962no—
156#41—5962no—
157C2×Q8—1491no—
158C2×Q8C22×D14912yes—
159C2×D4—2982no—
160C2×D4—2982no—
161C2×D4—2982no—
162C2×D4—1492no—
163C2×D4—1491no—
164C2×D4—1492no—
165C22×C4—2982no—
166C22×C4—2982no—
167C22×C4—1492no—
168C22×C4C22×D14911yescharacteristic
169Q16—41no—
170SD16—5962no—
171D8—5961no—
172M16—41no—
173C2×C8—5961no—
174C2×C8—1492no—
175C2×C8C22×D14911yescharacteristic
176C2×C8C22×D14911yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—2982no—
179C4⋊C4—2982no—
180C4⋊C4—1492no—
181C4⋊C4C22×D14912yes—
182C22⋊C4—22no—
183C22⋊C4—2982no—
184C22⋊C4—2982no—
185C22⋊C4—2982no—
186C23—2982no—
187C23—1492no—
188C23D4×D14911yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—5961no—
192D4—2982no—
193D4—2982no—
194D4—5961no—
195D4—5964no—
196D4—5962no—
197D4—11922no—
198D4—11922no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—2982no—
204C2×C4—2982no—
205C2×C4—2982no—
206C2×C4—5964no—
207C2×C4—1492no—
208C2×C4—11922no—
209C2×C4D4×D14911yescharacteristic
210C2×C4C23×D14911yescharacteristic
211C8—21no—
212C8—21no—
213C8—2982no—
214C22—22no—
215C22—21no—
216C22—2982no—
217C22—2982no—
218C22—2982no—
219C22—5962no—
220C22—5962no—
221C22—5962no—
222C22C2×D4×D14911yescharacteristic
223C4—21no—
224C4—42no—
225C4—42no—
226C4—2982no—
227C4—5962no—
228C4#1801195611yescharacteristic
229C4#1801195711yescharacteristic
230C2—41no—
231C2—5962no—
232C2—11922no—
233C2#2375018311yescharacteristic
234C2#2375043412yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#470×C149C2
socleC22×C149C22×D4
hypercenter#470D149
hypocenterC149#3204
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #23750205C2semidirect
2. #23749954C2semidirect
3. #23749945C2semidirect
4. #23749878C2semidirect
5. #23749856C2semidirect
6. #23749786C2semidirect
7. #23749773C2semidirect
8. #23749593C2semidirect
9. #470×C149C2semidirect
117. C149#3204semidirect
122. #470D149semidirect

Maximal subgroups

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

subgroupindex
#237502052
#237499542
#237499452
#237498782
#237498562
#237497862
#237497732
#237495932
#470×C1492
#3204149