Finite Group Databasebeta

← #34057499

Subgroups — #34057499

Order 19072.

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

normal subgroups only

This group has 326 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#23750350C211yesmaximal, characteristic
2#23750350C211yesmaximal, characteristic
3#23749992C212yesmaximal
4#23749934C212yesmaximal
5#23749907C211yesmaximal, characteristic
6#23749834C212yesmaximal
7#23749832C211yesmaximal, characteristic
8#23749755C211yesmaximal, characteristic
9#23749729C212yesmaximal
10C4×Dic596C211yesmaximal, characteristic
11#487×C149C211yesmaximal, characteristic
12C2×Dic596C2211yescharacteristic
13C2×#14558726C2212yes—
14#18011909—21no—
15#18011909C2212yes—
16#18011902—21no—
17#18011902C2212yes—
18#18011901—22no—
19#18011901—22no—
20Q8×Dic149—21no—
21Q8×Dic149C2212yes—
22C4×Dic298C2211yescharacteristic
23C4×Dic298C2211yescharacteristic
24C4×Dic298C2211yescharacteristic
25#18011876—21no—
26#18011876C2212yes—
27#18011845C2211yescharacteristic
28#18011842C2212yes—
29C4⋊#11924746C2211yescharacteristic
30#18011840C2212yes—
31#18011836C2211yescharacteristic
32#18011836C2211yescharacteristic
33#18011835C2212yes—
34#18011834C2212yes—
35#18011821C2212yes—
36C4⋊Q8×C149C2211yescharacteristic
37C4⋊Q8×C149C2211yescharacteristic
38#103×C149C2212yes—
39#103×C149C2212yes—
40C4×C8×C149C2211yescharacteristic
41C2×Dic298D411yescharacteristic
42C2×Dic298C2311yescharacteristic
43C2×Dic298C2311yescharacteristic
44Dic596—22no—
45#14558726—24no—
46C2×#11924746C2312yes—
47C4⋊Dic149—22no—
48C4⋊Dic149—22no—
49C4⋊Dic149D411yescharacteristic
50C4⋊Dic149C2311yescharacteristic
51C4⋊Dic149C2311yescharacteristic
52#14558715—22no—
53#14558715—22no—
54#14558715—22no—
55#14558715—22no—
56#14558715—21no—
57#14558715—21no—
58#14558715D412yes—
59C4×Dic149—22no—
60C4×Dic149—22no—
61C4×Dic149—21no—
62C4×Dic149—21no—
63C4×Dic149C2312yes—
64C2×Q8×C149—21no—
65C2×Q8×C149C2312yes—
66C2×C8×C149C2311yescharacteristic
67C2×C8×C149C2311yescharacteristic
68C4⋊C4×C149—21no—
69C4⋊C4×C149—21no—
70C4⋊C4×C149—21no—
71C4⋊C4×C149C2312yes—
72C42×C149C2311yescharacteristic
73Dic298—22no—
74Dic298—21no—
75Dic298—21no—
76Dic298—21no—
77Dic298#4112yes—
78C2×Dic149—21no—
79C2×Dic149—21no—
80C2×Dic149—21no—
81C2×Dic149—21no—
82C2×Dic149C2×D412yes—
83C2×Dic149C2×D412yes—
84#11924746—22no—
85Q8×C149—22no—
86Q8×C149—22no—
87Q8×C149—42no—
88C2×C4×C149—22no—
89C2×C4×C149—22no—
90C2×C4×C149C2×D411yescharacteristic
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2411yescharacteristic
93C8×C149—21no—
94C8×C149—21no—
95C22×C149C22×D411yescharacteristic
96C4×C149—21no—
97C4×C149—42no—
98C4×C149—42no—
99C4×C149#13712yes—
100C4×C149C2×#4111yescharacteristic
101C4×C1492−1+411yescharacteristic
102Dic149—22no—
103Dic149—22no—
104Dic149—22no—
105Dic149—41no—
106Dic149—41no—
107Dic149—41no—
108C2×C149#54811yescharacteristic
109C2×C149C2×#13711yescharacteristic
110C2×C149#57811yescharacteristic
111C149#337411yescharacteristic, complemented, Sylow
112#3374—1491nomaximal, Sylow
113#557—1491no—
114#557—1491no—
115#491—1492no—
116#487D14911yescharacteristic
117#479—1492no—
118#475—1491no—
119#462—1491no—
120#462—1492no—
121#446—1491no—
122#441—1492no—
123C4×Q16—1491no—
124C2×Q16—1492no—
125C2×Q16—1491no—
126C4⋊Q8—2981no—
127C4⋊Q8—1492no—
128C4⋊Q8C2×D14911yescharacteristic
129C4⋊Q8C2×D14911yescharacteristic
130#125—2982no—
131#125—2982no—
132#125—2981no—
133#125—1492no—
134C4×Q8—2981no—
135C4×Q8—2981no—
136C4×Q8—1492no—
137C4×Q8—1492no—
138C4×Q8—1491no—
139C4×Q8—1491no—
140C4×Q8—1491no—
141#107—1491no—
142#106—1492no—
143C4⋊C8—1492no—
144C4⋊C8—1491no—
145#103—1492no—
146#103—1491no—
147#103—1491no—
148#103—1492no—
149#103C2×D14912yes—
150#103C2×D14912yes—
151#97—1492no—
152C4×C8C2×D14911yescharacteristic
153C2×Q8—21no—
154C2×Q8—1491no—
155C2×Q8—1491no—
156C2×Q8—1491no—
157C2×Q8C22×D14912yes—
158Q16—2982no—
159Q16—2984no—
160C2×C8—1492no—
161C2×C8C22×D14911yescharacteristic
162C2×C8C22×D14911yescharacteristic
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—2982no—
167C4⋊C4—2982no—
168C4⋊C4—2982no—
169C4⋊C4—2982no—
170C4⋊C4—2982no—
171C4⋊C4—2982no—
172C4⋊C4—2981no—
173C4⋊C4—2981no—
174C4⋊C4—1491no—
175C4⋊C4—1491no—
176C4⋊C4—1491no—
177C4⋊C4—1492no—
178C4⋊C4C22×D14912yes—
179C42—2982no—
180C42—2982no—
181C42—2981no—
182C42—2981no—
183C42—1492no—
184C42C22×D14911yescharacteristic
185Q8—22no—
186Q8—22no—
187Q8—42no—
188Q8—2982no—
189Q8—2981no—
190Q8—2981no—
191Q8—2981no—
192Q8—1492no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—2981no—
196C2×C4—2981no—
197C2×C4—2981no—
198C2×C4—2981no—
199C2×C4—1492no—
200C2×C4—1492no—
201C2×C4D4×D14911yescharacteristic
202C2×C4D4×D14911yescharacteristic
203C2×C4C23×D14911yescharacteristic
204C8—21no—
205C8—21no—
206C8—2982no—
207C22C2×D4×D14911yescharacteristic
208C4—21no—
209C4—42no—
210C4—42no—
211C4—2982no—
212C4—2982no—
213C4—2982no—
214C4—5961no—
215C4—5961no—
216C4—5961no—
217C4#1801194012yes—
218C4#41×D14911yescharacteristic
219C4#1801195811yescharacteristic
220C2#2375028311yescharacteristic
221C2C2×#1801194011yescharacteristic
222C2#2375043811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#487×C149C2
socle, prime radicalC22×C149C22×D4
hypercenter#487D149
hypocenterC149#3374
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
111. C149#3374semidirect

Maximal subgroups

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

subgroupindex
#237503502
#237499922
#237499342
#237499072
#237498342
#237498322
#237497552
#237497292
C4×Dic5962
#487×C1492
#3374149