Finite Group Databasebeta

← #34045722

Subgroups — #34045722

Order 19072.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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×#18011944C211yesmaximal, characteristic, complemented
2#23750192C211yesmaximal, characteristic
3C2×#18011898C211yesmaximal, characteristic, complemented
4C2×#18011837C211yesmaximal, characteristic, complemented
5#23749635C211yesmaximal, characteristic, complemented
6#23749386C211yesmaximal, characteristic, complemented
7C2×#100×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C22×Dic298C2211yescharacteristic
10#18011944—22no—
11#18011944—22no—
12C2×Dic596—21no—
13C2×#14558725—21no—
14#18011907—21no—
15#18011898—22no—
16#18011898—21no—
17#18011898—22no—
18#18011882—22no—
19#18011880—22no—
20#18011870C2211yescharacteristic
21C2×C22⋊Dic149—22no—
22C2×C4×Dic149C2211yescharacteristic
23#18011837—22no—
24#18011836—22no—
25C22×D4×C149C2211yescharacteristic
26C2×M16×C149C2211yescharacteristic
27C2×M16×C149C2211yescharacteristic
28#100×C149—22no—
29#14558736—21no—
30#14558736—21no—
31#14558736—21no—
32#14558736—21no—
33C2×Dic298—21no—
34C2×Dic298—21no—
35C2×Dic298—21no—
36C2×Dic298—21no—
37C2×Dic298—21no—
38C2×Dic298D411yescharacteristic
39C2×Dic298D412yescomplemented
40C2×D596D411yescharacteristic
41C2×C22⋊D149—24no—
42C2×C22⋊D149—21no—
43C22×Dic149—21no—
44C22×Dic149—21no—
45C2×C4×D149—21no—
46Dic596—24no—
47#14558725—24no—
48C4⋊Dic149D412yes—
49C22⋊Dic149—28no—
50C22⋊Dic149—24no—
51C22⋊Dic149—21no—
52C4×Dic149—21no—
53C4×Dic149—21no—
54C4×Dic149D412yescomplemented
55C24×C149D412yes—
56C2×D4×C149—21no—
57C2×D4×C149—21no—
58C2×D4×C149—21no—
59C2×D4×C149—21no—
60C2×D4×C149—21no—
61C2×D4×C149—21no—
62C22×C4×C149C2311yescharacteristic
63M16×C149—21no—
64M16×C149—21no—
65M16×C149—21no—
66M16×C149D412yescomplemented
67C2×C8×C149—21no—
68C2×C8×C149—21no—
69C22×D149—21no—
70Dic298—22no—
71Dic298—21no—
72Dic298—22no—
73Dic298—21no—
74Dic298—41no—
75Dic298—41no—
76D596—21no—
77D596—21no—
78C22⋊D149—41no—
79C22⋊D149—41no—
80C22⋊D149—84no—
81C2×Dic149—21no—
82C2×Dic149—22no—
83C2×Dic149—22no—
84C2×Dic149—22no—
85C2×Dic149—42no—
86C2×Dic149—41no—
87C2×Dic149—41no—
88C4×D149—41no—
89C4×D149—41no—
90C23×C149—22no—
91C23×C149—22no—
92C23×C149—22no—
93C23×C149—44no—
94C23×C149C2×D411yescharacteristic
95D4×C149—41no—
96D4×C149—41no—
97D4×C149—41no—
98D4×C149—41no—
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149C2×D411yescharacteristic
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149C2×D411yescharacteristic
104C2×C4×C149#4111yescharacteristic
105C8×C149—22no—
106C8×C149—41no—
107C22×C149—22no—
108C22×C149—44no—
109C22×C149—42no—
110C22×C149—44no—
111C22×C149—82no—
112C22×C149#12011yescharacteristic
113C22×C149#12011yescharacteristic
114C22×C149#12111yescharacteristic
115C2×D149—41no—
116C2×D149—42no—
117C4×C149#12011yescharacteristic
118C4×C149#12111yescharacteristic
119C4×C149#12111yescharacteristic
120C4×C149#12711yescharacteristic
121Dic149—42no—
122Dic149—41no—
123Dic149—42no—
124Dic149—42no—
125C2×C149—21no—
126C2×C149—21no—
127C2×C149—82no—
128C2×C149#39211yescharacteristic
129C2×C149#45512yes—
130D149—81no—
131C149#200411yescharacteristic, complemented, Sylow
132#2004—1491nomaximal, Sylow
133C2×#137—1491no—
134#535—1491no—
135C2×#124—1491no—
136C2×#104—1491no—
137#419—1491no—
138C2×#100D14911yescharacteristic, complemented
139#339—1491no—
140C2×#41—1491no—
141C22×Q8—1491no—
142C22×D4C2×D14911yescharacteristic
143#137—2982no—
144#137—2982no—
145C2×Q16—2981no—
146C2×SD16—2981no—
147C2×M16C2×D14911yescharacteristic
148C2×M16C2×D14911yescharacteristic
149#127—2981no—
150#124—2982no—
151#124—2981no—
152#124—2982no—
153#121—2982no—
154#120—2982no—
155#117—1491no—
156C2×C22⋊C4—2982no—
157C2×C42—1491no—
158#104—2982no—
159#103—2982no—
160#100—22no—
161C24D59612yes—
162#41—2981no—
163#41—2981no—
164#41—2981no—
165#41—2981no—
166C2×Q8—2981no—
167C2×Q8—2981no—
168C2×Q8—2981no—
169C2×Q8—2981no—
170C2×Q8—2981no—
171C2×Q8—1491no—
172C2×Q8—1492no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—2981no—
180C2×D4—2984no—
181C2×D4—1491no—
182C22×C4—2981no—
183C22×C4—2981no—
184C22×C4—2981no—
185C22×C4C22×D14911yescharacteristic
186Q16—2984no—
187SD16—2984no—
188M16—21no—
189M16—21no—
190M16—21no—
191M16C22⋊D14912yescomplemented
192C2×C8—21no—
193C2×C8—21no—
194C4⋊C4—1492no—
195C22⋊C4—2988no—
196C22⋊C4—2984no—
197C22⋊C4—2981no—
198C42—2981no—
199C42—2981no—
200C42—1492no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—2981no—
206C23C2×D59611yescharacteristic
207Q8—2982no—
208Q8—2981no—
209Q8—2982no—
210Q8—2981no—
211Q8—5961no—
212Q8—5961no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—2981no—
218D4—2981no—
219D4—5961no—
220D4—5961no—
221D4—11924no—
222C2×C4—2982no—
223C2×C4—2982no—
224C2×C4—2982no—
225C2×C4—2981no—
226C2×C4—5962no—
227C2×C4—5961no—
228C2×C4—5961no—
229C2×C4—5961no—
230C2×C4—5961no—
231C2×C4D4×D14911yescharacteristic
232C2×C4D4×D14911yescharacteristic
233C2×C4D4×D14911yescharacteristic
234C2×C4D4×D14911yescharacteristic
235C2×C4C2×C22⋊D14911yescharacteristic
236C2×C4#1455873611yescharacteristic
237C8—22no—
238C8—41no—
239C22—22no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—82no—
244C22—5961no—
245C22—5962no—
246C22#1801188111yescharacteristic
247C22#1801188111yescharacteristic
248C22#1801188511yescharacteristic
249C4—5962no—
250C4—5961no—
251C4—5962no—
252C4—5962no—
253C4#1801187911yescharacteristic
254C4#1801188411yescharacteristic
255C4#1801188411yescharacteristic
256C4#1801190711yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—11921no—
261C2#2374953411yescharacteristic
262C2#2374980512yes—
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#100×C149C2
socleC22×C149#120
prime radical#23750192C2
hypercenterC2×#100D149
hypocenterC149#2004
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#18011944C2semidirect
3. C2×#18011898C2semidirect
4. C2×#18011837C2semidirect
5. #23749635C2semidirect
6. #23749386C2semidirect
7. C2×#100×C149C2semidirect
39. C2×Dic298D4semidirect
54. C4×Dic149D4semidirect
66. M16×C149D4semidirect
131. C149#2004semidirect
138. C2×#100D149semidirect
191. M16C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119442
#237501922
C2×#180118982
C2×#180118372
#237496352
#237493862
C2×#100×C1492
#2004149