Finite Group Databasebeta

← #34044705

Subgroups — #34044705

Order 19072.

292 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#18011876C211yesmaximal, characteristic
2C2×#18011840C211yesmaximal, characteristic
3C2×#18011836C211yesmaximal, characteristic
4C2×#18011834C211yesmaximal, characteristic
5#23749490C211yesmaximal, characteristic
6#23749387C211yesmaximal, characteristic
7#340×C149C211yesmaximal, characteristic
8C22×Dic298C2211yescharacteristic
9C22×#11924746C2211yescharacteristic
10#18011876—22no—
11#18011876C414yescomplemented
12C2×C4⋊Dic149C2211yescharacteristic
13C2×#14558715—21no—
14C2×C4×Dic149—21no—
15C2×C4×Dic149C2211yescharacteristic
16#18011840—22no—
17#18011836—22no—
18#18011834—22no—
19#18011818—21no—
20#18011818—21no—
21C22×C8×C149C2211yescharacteristic
22C2×C4⋊C4×C149C2211yescharacteristic
23C2×C4⋊C4×C149C2211yescharacteristic
24C2×Dic298—21no—
25C2×Dic298—21no—
26C2×Dic298—21no—
27C2×Dic298C2×C412yes—
28C2×Dic298D412yes—
29C2×Dic298Q812yes—
30C22×Dic149—21no—
31C22×Dic149—21no—
32C22×Dic149D411yescharacteristic
33C22×Dic149D411yescharacteristic
34C2×#11924746—21no—
35C2×#11924746—21no—
36C2×#11924746—21no—
37C4⋊Dic149—21no—
38C4⋊Dic149—21no—
39#14558715—24no—
40C4×Dic149—24no—
41C4×Dic149C2×C412yes—
42C4×Dic149D412yes—
43C22×C4×C149—21no—
44C22×C4×C149—21no—
45C22×C4×C149C2311yescharacteristic
46C2×C8×C149—21no—
47C2×C8×C149—21no—
48C2×C8×C149—21no—
49C4⋊C4×C149—21no—
50C4⋊C4×C149—21no—
51C4⋊C4×C149—21no—
52C4⋊C4×C149C2×C412yes—
53Dic298—22no—
54Dic298—22no—
55Dic298—22no—
56Dic298C4⋊C414yes—
57C2×Dic149—22no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—21no—
61C2×Dic149—21no—
62C2×Dic149—21no—
63C2×Dic149—21no—
64C2×Dic149—41no—
65C2×Dic149—41no—
66C2×Dic149—41no—
67C2×Dic149C22⋊C412yes—
68C2×Dic149C22⋊C412yes—
69#11924746—41no—
70C23×C149C2×D411yescharacteristic
71C2×C4×C149—22no—
72C2×C4×C149—41no—
73C2×C4×C149—41no—
74C2×C4×C149—41no—
75C2×C4×C149—41no—
76C2×C4×C149—41no—
77C2×C4×C149C22×C411yescharacteristic
78C2×C4×C149C2×D411yescharacteristic
79C2×C4×C149C2×D411yescharacteristic
80C2×C4×C149C2×Q811yescharacteristic
81C2×C4×C149#4111yescharacteristic
82C2×C4×C149#4111yescharacteristic
83C8×C149—41no—
84C22×C149C2×C22⋊C411yescharacteristic
85C22×C149#12111yescharacteristic
86C22×C149C22⋊Q811yescharacteristic
87C22×C149#13511yescharacteristic
88C22×C149#13511yescharacteristic
89C22×C149#13711yescharacteristic
90C22×C149#13711yescharacteristic
91C4×C149—42no—
92C4×C149—81no—
93C4×C149C2×C4⋊C411yescharacteristic
94C4×C149#11711yescharacteristic
95C4×C149#12111yescharacteristic
96C4×C149C22⋊Q811yescharacteristic
97Dic149—24no—
98Dic149—22no—
99Dic149—22no—
100Dic149—81no—
101C2×C149#38011yescharacteristic
102C2×C149#41611yescharacteristic
103C2×C149#41911yescharacteristic
104C2×C149#46411yescharacteristic
105C2×C149#46411yescharacteristic
106C2×C149#47911yescharacteristic
107C2×C149#47911yescharacteristic
108C149#180511yescharacteristic, complemented, Sylow
109#1805—1491nomaximal, Sylow
110C2×C4×Q8—1491no—
111C2×C4⋊C8—1491no—
112C2×#103—1491no—
113C2×#103—1491no—
114#382—1491no—
115#340—1491no—
116#340D14911yescharacteristic
117C22×Q8—1491no—
118C22×C8—1491no—
119C22×C8C2×D14911yescharacteristic
120C4×Q8—2982no—
121C4×Q8—1494no—
122C2×C4⋊C4—2981no—
123C2×C4⋊C4—1491no—
124C2×C4⋊C4C2×D14911yescharacteristic
125C2×C4⋊C4C2×D14911yescharacteristic
126C2×C42—2981no—
127C2×C42—1491no—
128C4⋊C8—2982no—
129#103—2982no—
130#103—2982no—
131#95—2981no—
132#95—2981no—
133C2×Q8—2981no—
134C2×Q8—2981no—
135C2×Q8—2981no—
136C2×Q8—1492no—
137C2×Q8—1492no—
138C2×Q8—1492no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—2981no—
142C22×C4—2981no—
143C22×C4—1491no—
144C22×C4—1491no—
145C22×C4C22×D14911yescharacteristic
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—2981no—
150C2×C8—2981no—
151C2×C8—2981no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—2984no—
156C4⋊C4—2981no—
157C4⋊C4—2981no—
158C4⋊C4C4×D14912yes—
159C42—2984no—
160C42—1492no—
161C42—1492no—
162C23D4×D14911yescharacteristic
163Q8—2982no—
164Q8—2982no—
165Q8—2982no—
166Q8—1494no—
167C2×C4—22no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—2981no—
174C2×C4—2981no—
175C2×C4—2981no—
176C2×C4—2981no—
177C2×C4—2982no—
178C2×C4—2982no—
179C2×C4—2982no—
180C2×C4—5961no—
181C2×C4—5961no—
182C2×C4—5961no—
183C2×C4—1492no—
184C2×C4—1492no—
185C2×C4C2×C4×D14911yescharacteristic
186C2×C4D4×D14911yescharacteristic
187C2×C4D4×D14911yescharacteristic
188C2×C4Q8×D14911yescharacteristic
189C2×C4#1455873611yescharacteristic
190C2×C4#1455873611yescharacteristic
191C8—41no—
192C8—5961no—
193C22C22⋊C4×D14911yescharacteristic
194C22#1801188411yescharacteristic
195C22#1801188911yescharacteristic
196C22#1801193011yescharacteristic
197C22#1801193211yescharacteristic
198C22#1801194011yescharacteristic
199C22#1801194311yescharacteristic
200C4—42no—
201C4—81no—
202C4—2982no—
203C4—2984no—
204C4—2982no—
205C4—11921no—
206C4C4⋊C4×D14911yescharacteristic
207C4#1801186811yescharacteristic
208C4#1801188411yescharacteristic
209C4#1801188911yescharacteristic
210C2#2374948411yescharacteristic
211C2#2374961811yescharacteristic
212C2#2374963211yescharacteristic
213C2#2374984611yescharacteristic
214C2#2374985011yescharacteristic
215C2#2374993111yescharacteristic
216C2#2374993511yescharacteristic
subgroupG/H
centerC23D4×D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#340×C149C2
socle, prime radicalC23×C149C2×D4
cosocleC22×C4×C149C23
hypercenter#340D149
hypocenterC149#1805
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
11. #18011876C4semidirect
108. C149#1805semidirect

Maximal subgroups

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

subgroupindex
C2×#180118762
C2×#180118402
C2×#180118362
C2×#180118342
#237494902
#237493872
#340×C1492
#1805149