Finite Group Databasebeta

← #398×D149 #34047920

Subgroups — #398×D149 #34047920

Order 19072.

692 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D149C211yesmaximal, characteristic
2C2×C4⋊C4×D149C211yesmaximal, characteristic
3C2×C4⋊C4×D149C212yesmaximal
4#23749559C212yesmaximal, complemented
5#23749558C212yesmaximal, complemented
6#23749557C211yesmaximal, characteristic, complemented
7#23749556C211yesmaximal, characteristic, complemented
8#23749555C211yesmaximal, characteristic, complemented
9#95×D149C212yesmaximal
10#95×D149C211yesmaximal, characteristic
11#398×C149C211yesmaximal, characteristic, complemented
12C22×C4×D149C2211yescharacteristic
13C22×C4×D149C2212yes—
14C22×C4×D149C2211yescharacteristic
15C22×C4×D149C2211yescharacteristic
16C22×C4×D149C2212yes—
17C2×C4⋊Dic149C2211yescharacteristic
18C2×C4⋊Dic149C2212yes—
19C2×C4⋊Dic149C2211yescharacteristic
20C2×#14558715C2212yes—
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2212yes—
23C2×#14558715C2212yes—
24C2×#14558715C2211yescharacteristic
25C4⋊C4×D149—24no—
26C4⋊C4×D149—28no—
27C4⋊C4×D149—24no—
28#18011818C2211yescharacteristic
29#18011818C2212yes—
30#18011818C2212yes—
31#18011818C2212yes—
32#18011818C2212yes—
33C2×C4⋊C4×C149C2211yescharacteristic
34C2×C4⋊C4×C149C2211yescharacteristic
35C2×C4⋊C4×C149C2212yes—
36#95×C149C2211yescharacteristic
37#95×C149C2212yes—
38C23×D149C2311yescharacteristic
39C22×Dic149C2311yescharacteristic
40C22×Dic149C2312yes—
41C22×Dic149C2311yescharacteristic
42C22×Dic149C2311yescharacteristic
43C22×Dic149C2312yes—
44C2×C4×D149—22no—
45C2×C4×D149—24no—
46C2×C4×D149—22no—
47C2×C4×D149—24no—
48C2×C4×D149—24no—
49C2×C4×D149—24no—
50C2×C4×D149—24no—
51C2×C4×D149—22no—
52C2×C4×D149—24no—
53C2×C4×D149—24no—
54C2×C4×D149D414yes—
55C2×C4×D149D414yes—
56C2×C4×D149Q818yes—
57C4⋊Dic149—22no—
58C4⋊Dic149—24no—
59C4⋊Dic149—22no—
60#14558715—22no—
61#14558715—24no—
62#14558715—24no—
63#14558715—24no—
64#14558715—22no—
65C22×C4×C149C2311yescharacteristic
66C22×C4×C149C2312yes—
67C22×C4×C149C2311yescharacteristic
68C22×C4×C149C2311yescharacteristic
69C22×C4×C149C2312yes—
70C4⋊C4×C149—24no—
71C4⋊C4×C149—22no—
72C4⋊C4×C149—22no—
73C22×D149C2×D412yes—
74C22×D149C2×D412yes—
75C22×D149C2×Q814yes—
76C22×D149#4112yes—
77C22×D149#4114yes—
78C2×Dic149—21no—
79C2×Dic149—22no—
80C2×Dic149—21no—
81C2×Dic149—22no—
82C2×Dic149—22no—
83C2×Dic149—22no—
84C2×Dic149—22no—
85C2×Dic149—21no—
86C2×Dic149—22no—
87C2×Dic149—22no—
88C2×Dic149C2×D412yes—
89C2×Dic149C2×D412yes—
90C2×Dic149C2×Q814yes—
91C4×D149—28no—
92C4×D149—216no—
93C4×D149—28no—
94C4×D149—48no—
95C4×D149—44no—
96C23×C149C2411yescharacteristic
97C2×C4×C149—21no—
98C2×C4×C149—22no—
99C2×C4×C149—21no—
100C2×C4×C149—22no—
101C2×C4×C149—22no—
102C2×C4×C149—22no—
103C2×C4×C149—22no—
104C2×C4×C149—21no—
105C2×C4×C149—22no—
106C2×C4×C149—22no—
107C2×C4×C149C2×D412yes—
108C2×C4×C149C2×D412yes—
109C2×C4×C149C2×Q814yes—
110C22×C149C22×D411yescharacteristic
111C22×C149C22×D411yescharacteristic
112C22×C149C22×Q812yes—
113C22×C149C2×#4111yescharacteristic
114C22×C149C2×#4112yes—
115C2×D149#12114yes—
116C2×D149C22⋊Q818yes—
117C2×D149#12314yes—
118C2×D149#12518yes—
119C2×D149C4⋊Q814yes—
120C4×C149—22no—
121C4×C149—24no—
122C4×C149—22no—
123C4×C149—42no—
124C4×C149—41no—
125Dic149—22no—
126Dic149—24no—
127Dic149—22no—
128Dic149—42no—
129Dic149—41no—
130C2×C149C2×#12111yescharacteristic
131C2×C149C2×C22⋊Q812yes—
132C2×C149C2×#12311yescharacteristic
133C2×C149C2×#12512yes—
134C2×C149C2×C4⋊Q811yescharacteristic
135D149#39818yesdirect product factor
136C149C2×#39811yescharacteristic, complemented, Sylow
137C2×#398—1491nomaximal, Sylow
138C22×C4⋊C4—1491no—
139C22×C4⋊C4—1492no—
140C22×C4⋊C4—1491no—
141#398—1491no—
142#398—1491no—
143#398—1492no—
144#398—1491no—
145#398—1492no—
146#398D14911yescharacteristic, direct product factor
147C2×#95—1492no—
148C2×#95—1491no—
149C23×C4—1492no—
150C23×C4—1491no—
151C23×C4—1491no—
152C23×C4—1491no—
153C23×C4—1492no—
154C2×C4⋊C4—2984no—
155C2×C4⋊C4—2984no—
156C2×C4⋊C4—2988no—
157C2×C4⋊C4—1492no—
158C2×C4⋊C4—1492no—
159C2×C4⋊C4—1491no—
160C2×C4⋊C4—1491no—
161C2×C4⋊C4—1492no—
162C2×C4⋊C4—1491no—
163C2×C4⋊C4—1492no—
164C2×C4⋊C4—1491no—
165C2×C4⋊C4C2×D14911yescharacteristic
166C2×C4⋊C4C2×D14911yescharacteristic
167C2×C4⋊C4C2×D14912yes—
168#95—1492no—
169#95—1492no—
170#95—1492no—
171#95—1491no—
172#95—1492no—
173#95C2×D14912yes—
174#95C2×D14911yescharacteristic
175C24—1491no—
176C22×C4—2982no—
177C22×C4—2984no—
178C22×C4—2982no—
179C22×C4—2984no—
180C22×C4—2984no—
181C22×C4—2984no—
182C22×C4—2984no—
183C22×C4—2982no—
184C22×C4—2984no—
185C22×C4—2984no—
186C22×C4—1491no—
187C22×C4—1492no—
188C22×C4—1492no—
189C22×C4—1491no—
190C22×C4—1491no—
191C22×C4—1494no—
192C22×C4—1494no—
193C22×C4—1498no—
194C22×C4C22×D14911yescharacteristic
195C22×C4C22×D14912yes—
196C22×C4C22×D14911yescharacteristic
197C22×C4C22×D14911yescharacteristic
198C22×C4C22×D14912yes—
199C4⋊C4—22no—
200C4⋊C4—24no—
201C4⋊C4—22no—
202C4⋊C4—2984no—
203C4⋊C4—2982no—
204C4⋊C4—2984no—
205C4⋊C4—2982no—
206C4⋊C4—2984no—
207C4⋊C4—2982no—
208C4⋊C4—2984no—
209C4⋊C4—2982no—
210C23—1492no—
211C23—1492no—
212C23—1494no—
213C23—1492no—
214C23—1494no—
215C23C23×D14911yescharacteristic
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—2988no—
227C2×C4—29816no—
228C2×C4—2988no—
229C2×C4—2981no—
230C2×C4—2982no—
231C2×C4—2981no—
232C2×C4—2982no—
233C2×C4—2982no—
234C2×C4—2982no—
235C2×C4—2982no—
236C2×C4—2981no—
237C2×C4—2982no—
238C2×C4—2982no—
239C2×C4—5968no—
240C2×C4—5964no—
241C2×C4—1492no—
242C2×C4—1492no—
243C2×C4—1494no—
244C2×C4D4×D14912yes—
245C2×C4D4×D14912yes—
246C2×C4Q8×D14914yes—
247C22—1498no—
248C22—1494no—
249C22—1494no—
250C22—1498no—
251C22—1494no—
252C22C2×D4×D14911yescharacteristic
253C22C2×D4×D14911yescharacteristic
254C22C2×Q8×D14912yes—
255C22#41×D14911yescharacteristic
256C22#41×D14912yes—
257C4—22no—
258C4—24no—
259C4—22no—
260C4—42no—
261C4—41no—
262C4—2982no—
263C4—2984no—
264C4—2982no—
265C4—5962no—
266C4—5961no—
267C2—1498no—
268C2#121×D14911yescharacteristic
269C2C22⋊Q8×D14912yes—
270C2#123×D14911yescharacteristic
271C2#125×D14912yes—
272C2C4⋊Q8×D14911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#398×C149C2
prime radicalC23×D149C23
hypercenter#398D149
hypocenterC149C2×#398
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
4. #23749559C2semidirect
5. #23749558C2semidirect
6. #23749557C2semidirect
7. #23749556C2semidirect
8. #23749555C2semidirect
11. #398×C149C2semidirect
135. D149#398direct (N × H)
136. C149C2×#398semidirect
146. #398D149direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D1492
#237495592
#237495582
#237495572
#237495562
#237495552
#95×D1492
#398×C1492
C2×#398149