Finite Group Databasebeta

← #34057627

Subgroups — #34057627

Order 19072.

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

normal subgroups only

This group has 326 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#23750355C211yesmaximal, characteristic
2#23750354C211yesmaximal, characteristic
3#23750033C212yesmaximal
4#23750021C211yesmaximal, characteristic
5#23749931C212yesmaximal
6#23749911C211yesmaximal, characteristic
7#23749908C212yesmaximal
8#23749752C211yesmaximal, characteristic
9#23749729C212yesmaximal
10C4×#14558726C211yesmaximal, characteristic
11#477×C149C211yesmaximal, characteristic
12C2×#14558726C2211yescharacteristic
13#18011911—21no—
14#18011911C2211yescharacteristic
15#18011910—21no—
16#18011910C2212yes—
17#18011909—22no—
18#18011902—22no—
19#18011902C2212yes—
20Q8×Dic149C2212yes—
21C4×Dic298—21no—
22C4×Dic298C2211yescharacteristic
23C4×Dic298C2211yescharacteristic
24#18011876—21no—
25#18011876C2212yes—
26#18011844C2211yescharacteristic
27#18011843C2212yes—
28#18011842C2212yes—
29#18011842C2212yes—
30#18011840C2212yes—
31#18011836C2212yes—
32#18011835C2211yescharacteristic
33#18011834C2211yescharacteristic
34#18011821C2212yes—
35C4×#11924746C2211yescharacteristic
36C4⋊Q8×C149C2211yescharacteristic
37C4×Q8×C149C2211yescharacteristic
38#107×C149C2212yes—
39C4⋊C8×C149C2211yescharacteristic
40#103×C149C2212yes—
41C2×Dic298—22no—
42C2×Dic298—21no—
43C2×Dic298D411yescharacteristic
44C2×Dic298C2311yescharacteristic
45#14558726Q814yescomplemented
46C2×#11924746C2311yescharacteristic
47C2×#11924746C2311yescharacteristic
48C4⋊Dic149—22no—
49C4⋊Dic149—22no—
50C4⋊Dic149—21no—
51C4⋊Dic149D411yescharacteristic
52C4⋊Dic149C2311yescharacteristic
53C4⋊Dic149C2312yes—
54#14558715—22no—
55#14558715—22no—
56#14558715—22no—
57#14558715—21no—
58#14558715D412yes—
59C4×Dic149—22no—
60C4×Dic149—22no—
61C4×Dic149—21no—
62C4×Dic149C2312yes—
63C2×Q8×C149—21no—
64C2×Q8×C149C2311yescharacteristic
65C2×C8×C149C2312yes—
66C4⋊C4×C149—21no—
67C4⋊C4×C149—21no—
68C4⋊C4×C149C2312yes—
69C4⋊C4×C149C2311yescharacteristic
70C42×C149—21no—
71C42×C149C2311yescharacteristic
72Dic298—22no—
73Dic298—21no—
74Dic298—42no—
75Dic298—82no—
76Dic298C2×Q812yes—
77C2×Dic149—21no—
78C2×Dic149—21no—
79C2×Dic149—22no—
80C2×Dic149C2×D412yes—
81C2×Dic149C2×D412yes—
82#11924746—21no—
83#11924746C2×Q812yes—
84Q8×C149—21no—
85Q8×C149—81no—
86Q8×C149C2×Q812yes—
87C2×C4×C149—21no—
88C2×C4×C149—22no—
89C2×C4×C149—21no—
90C2×C4×C149C2×D411yescharacteristic
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2411yescharacteristic
93C8×C149—22no—
94C22×C149C22×D411yescharacteristic
95C4×C149—22no—
96C4×C149—21no—
97C4×C149—41no—
98C4×C149—42no—
99C4×C149#13712yes—
100C4×C149C22×Q811yescharacteristic
101C4×C1492−1+411yescharacteristic
102Dic149—22no—
103Dic149—22no—
104Dic149—22no—
105Dic149—42no—
106Dic149—41no—
107C2×C149D4×Q811yescharacteristic
108C2×C149C2×#13711yescharacteristic
109C2×C149#57711yescharacteristic
110C149#338711yescharacteristic, complemented, Sylow
111#3387—1491nomaximal, Sylow
112Q82—1491no—
113#557—1491no—
114#501—1492no—
115#498—1491no—
116#479—1492no—
117#477D14911yescharacteristic
118#475—1491no—
119#475—1492no—
120#446—1491no—
121#441—1492no—
122C4×Q16—1491no—
123C2×Q16—1491no—
124C4⋊Q8—2981no—
125C4⋊Q8—2981no—
126C4⋊Q8—2982no—
127C4⋊Q8—1492no—
128C4⋊Q8—1491no—
129C4⋊Q8C2×D14911yescharacteristic
130#125—2982no—
131#125—1492no—
132C4×Q8—2981no—
133C4×Q8—2981no—
134C4×Q8—1492no—
135C4×Q8—1492no—
136C4×Q8—1491no—
137C4×Q8—1491no—
138C4×Q8C2×D14911yescharacteristic
139#107—1491no—
140#107C2×D14912yes—
141#106—1492no—
142#106—1492no—
143#106—1492no—
144C4⋊C8—1492no—
145C4⋊C8C2×D14911yescharacteristic
146#103—1491no—
147#103—1492no—
148#103—1491no—
149#103C2×D14912yes—
150#97—1492no—
151C4×C8—1491no—
152C2×Q8—21no—
153C2×Q8—2982no—
154C2×Q8—2981no—
155C2×Q8—1491no—
156C2×Q8—1491no—
157C2×Q8C22×D14911yescharacteristic
158Q16—1494no—
159C2×C8—1491no—
160C2×C8—1491no—
161C2×C8C22×D14912yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—2982no—
165C4⋊C4—2982no—
166C4⋊C4—2982no—
167C4⋊C4—2982no—
168C4⋊C4—2982no—
169C4⋊C4—2981no—
170C4⋊C4—2981no—
171C4⋊C4—1492no—
172C4⋊C4—1491no—
173C4⋊C4—1491no—
174C4⋊C4—1492no—
175C4⋊C4C22×D14911yescharacteristic
176C4⋊C4C22×D14912yes—
177C42—21no—
178C42—2982no—
179C42—2982no—
180C42—2981no—
181C42—1492no—
182C42C22×D14911yescharacteristic
183Q8—21no—
184Q8—81no—
185Q8—2982no—
186Q8—2981no—
187Q8—5962no—
188Q8—1492no—
189Q8—11922no—
190Q8Q8×D14912yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—2981no—
195C2×C4—2982no—
196C2×C4—2981no—
197C2×C4—1492no—
198C2×C4—1492no—
199C2×C4D4×D14911yescharacteristic
200C2×C4D4×D14911yescharacteristic
201C2×C4C23×D14911yescharacteristic
202C8—22no—
203C8—2981no—
204C8—1492no—
205C22C2×D4×D14911yescharacteristic
206C4—21no—
207C4—22no—
208C4—42no—
209C4—41no—
210C4—2982no—
211C4—2982no—
212C4—2982no—
213C4—5962no—
214C4—5961no—
215C4#1801194312yes—
216C4C2×Q8×D14911yescharacteristic
217C4#1801195811yescharacteristic
218C2#2375028811yescharacteristic
219C2C2×#1801194311yescharacteristic
220C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#477×C149C2
socle, prime radicalC22×C149C22×D4
hypercenter#477D149
hypocenterC149#3387
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
45. #14558726Q8semidirect
110. C149#3387semidirect

Maximal subgroups

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

subgroupindex
#237503552
#237503542
#237500332
#237500212
#237499312
#237499112
#237499082
#237497522
#237497292
C4×#145587262
#477×C1492
#3387149