Finite Group Databasebeta

← #34045727

Subgroups — #34045727

Order 19072.

362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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×#18011942C211yesmaximal, characteristic
2#23750199C211yesmaximal, characteristic
3C2×#18011839C211yesmaximal, characteristic
4#23749634C211yesmaximal, characteristic, complemented
5C2×#18011830C211yesmaximal, characteristic, complemented
6#23749385C211yesmaximal, characteristic, complemented
7C2×C4⋊Q8×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9#18011942—22no—
10#18011942—22no—
11C2×#14558726—21no—
12C2×#14558723—21no—
13C2×#14558720C2211yescharacteristic
14C2×#14558720C2211yescharacteristic
15#18011909—21no—
16#18011900—21no—
17#18011894—22no—
18#18011887—22no—
19#18011870C2211yescharacteristic
20#18011839—22no—
21#18011835—22no—
22#18011830—22no—
23C22×Q8×C149C2211yescharacteristic
24C22×Q8×C149C2211yescharacteristic
25C4⋊Q8×C149—22no—
26C4⋊Q8×C149—22no—
27C2×C4⋊C4×C149—22no—
28C2×C42×C149C2211yescharacteristic
29#14558736—21no—
30#14558736—21no—
31#14558736—21no—
32#14558736—21no—
33C2×Dic298D411yescharacteristic
34C2×D596D411yescharacteristic
35C2×C22⋊D149—21no—
36C2×C4×D149—21no—
37#14558726—24no—
38#14558723—24no—
39#14558720—21no—
40#14558720—21no—
41#14558720—21no—
42#14558720D412yes—
43C2×#11924746—21no—
44C2×#11924746—21no—
45C4⋊Dic149D412yes—
46#14558715—24no—
47C22⋊Dic149—21no—
48#14558713—24no—
49C4×Dic149—21no—
50C2×Q8×C149—21no—
51C2×Q8×C149—21no—
52C2×Q8×C149—21no—
53C2×Q8×C149—21no—
54C2×Q8×C149—21no—
55C2×Q8×C149—21no—
56C2×Q8×C149—21no—
57C2×Q8×C149—21no—
58C2×Q8×C149—21no—
59C2×Q8×C149—21no—
60C2×Q8×C149—21no—
61C2×Q8×C149D412yes—
62C22×C4×C149—21no—
63C22×C4×C149—21no—
64C22×C4×C149D412yes—
65C22×C4×C149C2311yescharacteristic
66C4⋊C4×C149—28no—
67C42×C149—21no—
68C42×C149D412yes—
69C22×D149—21no—
70Dic298—21no—
71Dic298—21no—
72D596—21no—
73D596—21no—
74C22⋊D149—41no—
75C22⋊D149—41no—
76C2×Dic149—21no—
77C2×Dic149—22no—
78C4×D149—41no—
79C4×D149—41no—
80#11924746—22no—
81#11924746—41no—
82C23×C149C2×D411yescharacteristic
83Q8×C149—22no—
84Q8×C149—22no—
85Q8×C149—41no—
86Q8×C149—41no—
87Q8×C149—41no—
88Q8×C149—41no—
89Q8×C149—41no—
90Q8×C149—41no—
91C2×C4×C149—24no—
92C2×C4×C149—22no—
93C2×C4×C149—22no—
94C2×C4×C149—22no—
95C2×C4×C149—22no—
96C2×C4×C149—22no—
97C2×C4×C149—41no—
98C2×C4×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
105C22×C149—22no—
106C22×C149#12011yescharacteristic
107C22×C149#12011yescharacteristic
108C22×C149#12111yescharacteristic
109C2×D149—41no—
110C2×D149—42no—
111C4×C149—24no—
112C4×C149—42no—
113C4×C149—42no—
114C4×C149#12011yescharacteristic
115C4×C149#12111yescharacteristic
116C4×C149#12111yescharacteristic
117C4×C149#12711yescharacteristic
118Dic149—41no—
119Dic149—42no—
120C2×C149—21no—
121C2×C149—21no—
122C2×C149#39211yescharacteristic
123C2×C149#45612yes—
124D149—81no—
125C149#200511yescharacteristic, complemented, Sylow
126#2005—1491nomaximal, Sylow
127C2×#137—1491no—
128#536—1491no—
129C2×C4⋊Q8D14911yescharacteristic, complemented
130C2×#104—1491no—
131#419—1491no—
132C2×#101—1491no—
133#339—1491no—
134C2×#41—1491no—
135C22×Q8C2×D14911yescharacteristic
136C22×Q8C2×D14911yescharacteristic
137#137—2982no—
138#137—2982no—
139C2×Q16—2981no—
140C2×SD16—2981no—
141C2×M16—1491no—
142C2×M16—1491no—
143C4⋊Q8—22no—
144C4⋊Q8—22no—
145C4⋊Q8—2981no—
146#124—2981no—
147#123—2982no—
148C22⋊Q8—2982no—
149#117—1491no—
150C2×C4⋊C4—22no—
151C2×C42C2×D14911yescharacteristic
152#104—2982no—
153#103—2982no—
154#101—2982no—
155#41—2981no—
156#41—2981no—
157#41—2981no—
158#41—2981no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—1491no—
171C2×Q8C22⋊D14912yes—
172C2×D4—2981no—
173C2×D4—1491no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—2981no—
177C22×C4C22⋊D14912yes—
178C22×C4C22×D14911yescharacteristic
179Q16—2984no—
180SD16—2984no—
181M16—2981no—
182M16—2981no—
183M16—2981no—
184M16—1492no—
185C2×C8—2981no—
186C2×C8—2981no—
187C4⋊C4—28no—
188C4⋊C4—2984no—
189C4⋊C4—1492no—
190C22⋊C4—2984no—
191C22⋊C4—2981no—
192C42—21no—
193C42—2981no—
194C42C22⋊D14912yes—
195C23—2981no—
196C23C2×C22⋊D14911yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201Q8—41no—
202Q8—41no—
203Q8—41no—
204Q8—41no—
205Q8—2981no—
206Q8—2981no—
207D4—2981no—
208D4—2981no—
209D4—5961no—
210D4—5961no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—2982no—
220C2×C4—2981no—
221C2×C4—5961no—
222C2×C4—5961no—
223C2×C4D4×D14911yescharacteristic
224C2×C4D4×D14911yescharacteristic
225C2×C4D4×D14911yescharacteristic
226C2×C4C2×C22⋊D14911yescharacteristic
227C2×C4C2×C22⋊D14911yescharacteristic
228C2×C4#1455873511yescharacteristic
229C8—2982no—
230C8—5961no—
231C22—22no—
232C22—5961no—
233C22—5962no—
234C22#1801187911yescharacteristic
235C22#1801188011yescharacteristic
236C22#1801188311yescharacteristic
237C4—24no—
238C4—42no—
239C4—42no—
240C4—5961no—
241C4—5962no—
242C4#1801187911yescharacteristic
243C4#1801188211yescharacteristic
244C4#1801188311yescharacteristic
245C4#1801190711yescharacteristic
246C2—21no—
247C2—21no—
248C2—11921no—
249C2#2374953311yescharacteristic
250C2#2374980712yes—
subgroupG/H
centerC22#18011879
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×C4⋊Q8×C149C2
socleC22×C149#120
prime radicalC2×#14558736C22
hypercenterC2×C4⋊Q8D149
hypocenterC149#2005
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #23749634C2semidirect
5. C2×#18011830C2semidirect
6. #23749385C2semidirect
7. C2×C4⋊Q8×C149C2semidirect
125. C149#2005semidirect
129. C2×C4⋊Q8D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119422
#237501992
C2×#180118392
#237496342
C2×#180118302
#237493852
C2×C4⋊Q8×C1492
#2005149