Finite Group Databasebeta

← #34057628

Subgroups — #34057628

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#23750350C211yesmaximal, characteristic
3#23750032C212yesmaximal
4#23749935C212yesmaximal
5#23749917C211yesmaximal, characteristic
6#23749909C212yesmaximal
7#23749907C211yesmaximal, characteristic
8#23749755C211yesmaximal, characteristic
9#23749731C212yesmaximal
10C4×Dic596C211yesmaximal, characteristic
11#498×C149C211yesmaximal, characteristic
12C2×Dic596C2211yescharacteristic
13#18011910—21no—
14#18011910C2212yes—
15#18011909—22no—
16#18011909—21no—
17#18011902C2212yes—
18#18011901—22no—
19Q8×Dic149—21no—
20C4×Dic298C2211yescharacteristic
21C4×Dic298C2211yescharacteristic
22C4×Dic298C2211yescharacteristic
23#18011876—21no—
24#18011876C2212yes—
25#18011876C2212yes—
26#18011845C2211yescharacteristic
27#18011844C2212yes—
28#18011842C2212yes—
29C4⋊#11924746C2211yescharacteristic
30#18011840C2212yes—
31#18011836C2211yescharacteristic
32#18011836C2211yescharacteristic
33#18011834C2212yes—
34#18011834C2212yes—
35#18011821C2212yes—
36C4⋊Q8×C149C2211yescharacteristic
37C4⋊Q8×C149C2211yescharacteristic
38#106×C149C2212yes—
39#106×C149C2212yes—
40C4×C8×C149C2211yescharacteristic
41C2×Dic298—22no—
42C2×Dic298D411yescharacteristic
43C2×Dic298C2311yescharacteristic
44C2×Dic298C2311yescharacteristic
45Dic596Q814yescomplemented
46C2×#11924746C2312yes—
47C4⋊Dic149—22no—
48C4⋊Dic149D411yescharacteristic
49C4⋊Dic149C2311yescharacteristic
50C4⋊Dic149C2311yescharacteristic
51#14558715—22no—
52#14558715—22no—
53#14558715—22no—
54#14558715—22no—
55#14558715—21no—
56#14558715—21no—
57#14558715D412yes—
58C4×Dic149—22no—
59C4×Dic149—22no—
60C4×Dic149—21no—
61C4×Dic149—21no—
62C4×Dic149C2312yes—
63C2×Q8×C149—21no—
64C2×Q8×C149—21no—
65C2×C8×C149C2311yescharacteristic
66C2×C8×C149C2311yescharacteristic
67C4⋊C4×C149—21no—
68C4⋊C4×C149—21no—
69C4⋊C4×C149C2312yes—
70C4⋊C4×C149C2312yes—
71C42×C149C2311yescharacteristic
72Dic298—22no—
73Dic298—21no—
74Dic298—21no—
75Dic298—82no—
76Dic298C2×Q812yes—
77Dic298C2×Q812yes—
78C2×Dic149—21no—
79C2×Dic149—21no—
80C2×Dic149—21no—
81C2×Dic149—21no—
82C2×Dic149C2×D412yes—
83C2×Dic149C2×D412yes—
84#11924746—22no—
85Q8×C149—42no—
86Q8×C149—81no—
87C2×C4×C149—22no—
88C2×C4×C149—22no—
89C2×C4×C149C2×D411yescharacteristic
90C2×C4×C149C2×D411yescharacteristic
91C2×C4×C149C2411yescharacteristic
92C8×C149—21no—
93C8×C149C2×Q812yes—
94C22×C149C22×D411yescharacteristic
95C4×C149—21no—
96C4×C149—42no—
97C4×C149—42no—
98C4×C149#13712yes—
99C4×C149C22×Q811yescharacteristic
100C4×C1492−1+411yescharacteristic
101Dic149—22no—
102Dic149—22no—
103Dic149—22no—
104Dic149—22no—
105Dic149—41no—
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#498D14911yescharacteristic
116#479—1492no—
117#477—1491no—
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⋊Q8C2×D14911yescharacteristic
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×Q8—1491no—
139#107—1491no—
140#107—1492no—
141#106—1492no—
142#106C2×D14912yes—
143#106C2×D14912yes—
144C4⋊C8—1492no—
145C4⋊C8—1491no—
146#103—1491no—
147#103—1491no—
148#103—1492no—
149#103—1492no—
150#97—1492no—
151C4×C8C2×D14911yescharacteristic
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—2982no—
155C2×Q8—1491no—
156C2×Q8—1491no—
157C2×Q8—1491no—
158Q16—1494no—
159C2×C8—1492no—
160C2×C8C22×D14911yescharacteristic
161C2×C8C22×D14911yescharacteristic
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—1491no—
172C4⋊C4—1491no—
173C4⋊C4—1491no—
174C4⋊C4—1492no—
175C4⋊C4C22×D14912yes—
176C4⋊C4C22×D14912yes—
177C42—2982no—
178C42—2982no—
179C42—2981no—
180C42—2981no—
181C42—1492no—
182C42C22×D14911yescharacteristic
183Q8—42no—
184Q8—81no—
185Q8—2982no—
186Q8—2981no—
187Q8—2981no—
188Q8—1492no—
189Q8—1492no—
190Q8—11922no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—2981no—
194C2×C4—2981no—
195C2×C4—2981no—
196C2×C4—2981no—
197C2×C4—1492no—
198C2×C4—1492no—
199C2×C4D4×D14911yescharacteristic
200C2×C4D4×D14911yescharacteristic
201C2×C4C23×D14911yescharacteristic
202C8—21no—
203C8—2982no—
204C8Q8×D14912yes—
205C22C2×D4×D14911yescharacteristic
206C4—21no—
207C4—42no—
208C4—42no—
209C4—2982no—
210C4—2982no—
211C4—2982no—
212C4—2982no—
213C4—5961no—
214C4—5961no—
215C4#1801194012yes—
216C4C2×Q8×D14911yescharacteristic
217C4#1801195911yescharacteristic
218C2#2375029011yescharacteristic
219C2C2×#1801194011yescharacteristic
220C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#498×C149C2
socle, prime radicalC22×C149C22×D4
hypercenter#498D149
hypocenterC149#3387
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
45. Dic596Q8semidirect
110. C149#3387semidirect

Maximal subgroups

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

subgroupindex
#237503552
#237503502
#237500322
#237499352
#237499172
#237499092
#237499072
#237497552
#237497312
C4×Dic5962
#498×C1492
#3387149