Finite Group Databasebeta

← #34057724

Subgroups — #34057724

Order 19072.

350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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#23750354C211yesmaximal, characteristic, complemented
2#23750348C211yesmaximal, characteristic
3#23750019C212yesmaximal
4#23750005C211yesmaximal, characteristic, complemented
5#23749848C212yesmaximal
6#23749836C211yesmaximal, characteristic, complemented
7#23749836C212yesmaximal, complemented
8#23749831C211yesmaximal, characteristic
9#23749733C212yesmaximal, complemented
10C4×#14558725C211yesmaximal, characteristic
11#446×C149C211yesmaximal, characteristic, complemented
12C2×Dic596C2212yes—
13C2×Dic596C2212yes—
14C2×Dic596C2212yes—
15C2×#14558725C2211yescharacteristic
16C2×#14558725C2212yes—
17#18011911C2211yescharacteristic
18#18011911C2211yescharacteristic
19#18011911C2212yes—
20#18011906—22no—
21#18011902—22no—
22#18011902—21no—
23#18011899C2212yes—
24#18011887—21no—
25Q8×Dic149—21no—
26C4×Dic298C2211yescharacteristic
27C4×Dic298C2212yes—
28C4×Dic298C2212yes—
29C4×D596C2211yescharacteristic
30#18011869—21no—
31#18011843C2211yescharacteristic
32#18011836C2211yescharacteristic
33#18011836C2212yes—
34#18011836C2212yes—
35#18011833C2211yescharacteristic
36C4×Q8×C149C2211yescharacteristic
37C4⋊C8×C149C2211yescharacteristic
38C4⋊C8×C149C2212yes—
39#97×C149C2212yes—
40C4×C8×C149C2211yescharacteristic
41C2×Dic298C2311yescharacteristic
42C2×Dic298C2312yes—
43C2×Dic298C2312yes—
44C2×D596C2311yescharacteristic
45C2×C4×D149—21no—
46Dic596—24no—
47Dic596—42no—
48Dic596—42no—
49#14558725—22no—
50#14558725—42no—
51C4⋊Dic149—21no—
52C4⋊Dic149—21no—
53C4⋊Dic149—22no—
54C4⋊Dic149—21no—
55C4⋊Dic149—22no—
56C4⋊Dic149—21no—
57C4⋊Dic149C2311yescharacteristic
58C4⋊Dic149C2311yescharacteristic
59#14558715—22no—
60#14558715—22no—
61#14558715—21no—
62#14558713—21no—
63#14558713—22no—
64#14558713—22no—
65C4×Dic149—22no—
66C4×Dic149—22no—
67C4×Dic149—21no—
68C2×Q8×C149D411yescharacteristic
69C2×C8×C149C2312yes—
70C2×C8×C149C2311yescharacteristic
71C2×C8×C149C2311yescharacteristic
72C4⋊C4×C149D412yes—
73C4⋊C4×C149D411yescharacteristic
74C42×C149C2311yescharacteristic
75C42×C149C2312yes—
76C22×D149—21no—
77Dic298—21no—
78Dic298—22no—
79Dic298—22no—
80Dic298—22no—
81Dic298—21no—
82Dic298—22no—
83D596—21no—
84D596—21no—
85C2×Dic149—21no—
86C2×Dic149—22no—
87C2×Dic149—21no—
88C2×Dic149—22no—
89C2×Dic149—21no—
90C4×D149—42no—
91Q8×C149—22no—
92C2×C4×C149C2×D412yes—
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149C2×D412yes—
95C2×C4×C149C2×D411yescharacteristic
96C2×C4×C149C2411yescharacteristic
97C8×C149—22no—
98C8×C149—21no—
99C8×C149#4112yes—
100C22×C149C22×D411yescharacteristic
101C2×D149—41no—
102C2×D149—41no—
103C2×D149—41no—
104C4×C149—22no—
105C4×C149—22no—
106C4×C149—21no—
107C4×C149#13712yes—
108C4×C149C2×#4111yescharacteristic
109C4×C149H(5,𝔽2)11yescharacteristic
110Dic149—42no—
111Dic149—41no—
112Dic149—42no—
113Dic149—41no—
114Dic149—41no—
115C2×C149#55011yescharacteristic
116C2×C149C2×#13711yescharacteristic
117C2×C149#57811yescharacteristic
118D149—81no—
119C149#339811yescharacteristic, complemented, Sylow
120#3398—1491nomaximal, Sylow
121#557—1491no—
122#556—1491no—
123#497—1492no—
124#494—1491no—
125#464—1492no—
126#462—1492no—
127#462—1491no—
128#461—1491no—
129#446D14911yescharacteristic, complemented
130#441—1492no—
131C4×SD16—1491no—
132C2×Q16—1492no—
133C2×Q16—1492no—
134C2×Q16—1492no—
135C2×SD16—1491no—
136C2×SD16—1492no—
137C4⋊Q8—1491no—
138C4⋊Q8—1491no—
139C4⋊Q8—1492no—
140#126—2982no—
141#125—2981no—
142#125—2982no—
143#124—1492no—
144C22⋊Q8—2981no—
145C4×Q8—2981no—
146C4×Q8—1492no—
147C4×Q8—1491no—
148C4×Q8—1492no—
149C4×Q8C2×D14911yescharacteristic
150C4×D4—1491no—
151#117—2981no—
152#106—1491no—
153C4⋊C8C2×D14911yescharacteristic
154C4⋊C8C2×D14912yes—
155#103—1491no—
156#103—1492no—
157#103—1492no—
158#102—1491no—
159#97C2×D14912yes—
160C4×C8C2×D14911yescharacteristic
161C2×Q8—1492no—
162C2×Q8—1491no—
163C2×Q8—1492no—
164C2×Q8D59611yescharacteristic
165C2×D4—1491no—
166C22×C4—2981no—
167Q16—2984no—
168Q16—5962no—
169Q16—5962no—
170SD16—2982no—
171SD16—5962no—
172C2×C8C22×D14911yescharacteristic
173C2×C8C22×D14912yes—
174C2×C8C22×D14911yescharacteristic
175C4⋊C4—2981no—
176C4⋊C4—2982no—
177C4⋊C4—2981no—
178C4⋊C4—2982no—
179C4⋊C4—2982no—
180C4⋊C4—2981no—
181C4⋊C4—2982no—
182C4⋊C4—2981no—
183C4⋊C4—2981no—
184C4⋊C4—1491no—
185C4⋊C4—1491no—
186C4⋊C4D59611yescharacteristic
187C4⋊C4D59612yes—
188C22⋊C4—2982no—
189C22⋊C4—2981no—
190C22⋊C4—2982no—
191C42—2982no—
192C42—2982no—
193C42—2981no—
194C42C22×D14911yescharacteristic
195C42C22×D14912yes—
196C23—2981no—
197Q8—22no—
198Q8—2981no—
199Q8—2982no—
200Q8—2982no—
201Q8—2982no—
202Q8—2982no—
203Q8—2981no—
204D4—2981no—
205D4—2981no—
206C2×C4—2981no—
207C2×C4—2981no—
208C2×C4—2982no—
209C2×C4—2981no—
210C2×C4—2982no—
211C2×C4—5962no—
212C2×C4C2×D59612yes—
213C2×C4C2×D59612yes—
214C2×C4C2×D59611yescharacteristic
215C2×C4C2×D59611yescharacteristic
216C2×C4C23×D14911yescharacteristic
217C8—22no—
218C8—21no—
219C8#1455873712yes—
220C22—5961no—
221C22—5961no—
222C22—5961no—
223C22C22×D59611yescharacteristic
224C4—22no—
225C4—22no—
226C4—21no—
227C4—5961no—
228C4—5961no—
229C4—5962no—
230C4—5961no—
231C4—5962no—
232C4#1801194412yes—
233C4C2×#1455873711yescharacteristic
234C4#1801195711yescharacteristic
235C2—11921no—
236C2#2375029711yescharacteristic
237C2C2×#1801194411yescharacteristic
238C2#2375044211yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#446×C149C2
socleC22×C149C22×D4
prime radicalC2×D596C23
hypercenter#446D149
hypocenterC149#3398
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #23750354C2semidirect
4. #23750005C2semidirect
6. #23749836C2semidirect
7. #23749836C2semidirect
9. #23749733C2semidirect
11. #446×C149C2semidirect
119. C149#3398semidirect
129. #446D149semidirect

Maximal subgroups

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

subgroupindex
#237503542
#237503482
#237500192
#237500052
#237498482
#237498362
#237498312
#237497332
C4×#145587252
#446×C1492
#3398149