Finite Group Databasebeta

← #34052744

Subgroups — #34052744

Order 19072.

464 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 464 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
1C2×#18011901C211yesmaximal, characteristic, complemented
2C2×#18011898C211yesmaximal, characteristic
3#23749561C212yesmaximal, complemented
4#23749553C212yesmaximal, complemented
5#23749548C212yesmaximal, complemented
6#23749548C212yesmaximal, complemented
7#23749546C211yesmaximal, characteristic, complemented
8#23749545C211yesmaximal, characteristic, complemented
9#23749539C211yesmaximal, characteristic
10#23749489C211yesmaximal, characteristic, complemented
11#394×C149C211yesmaximal, characteristic
12C22×Dic298C2211yescharacteristic
13#18011901—24no—
14#18011898—24no—
15C2×C4⋊Dic149C2211yescharacteristic
16C2×C4⋊Dic149C2212yes—
17C2×#14558715C2211yescharacteristic
18C2×#14558715C2211yescharacteristic
19C2×#14558715C2211yescharacteristic
20C2×#14558715C2211yescharacteristic
21C2×#14558715C2212yes—
22C2×#14558715C2212yes—
23C2×C22⋊Dic149C2212yes—
24C2×C22⋊Dic149C2212yes—
25C2×C22⋊Dic149C2212yes—
26C2×C22⋊Dic149C2212yes—
27C2×C4×Dic149C2211yescharacteristic
28#18011818C2211yescharacteristic
29#18011818C2212yes—
30#18011818C2212yes—
31#18011818C2212yes—
32C22×D4×C149C2211yescharacteristic
33C2×C4⋊C4×C149C2211yescharacteristic
34C2×C22⋊C4×C149C2212yes—
35C2×C22⋊C4×C149C2212yes—
36#95×C149C2211yescharacteristic
37C2×Dic298—22no—
38C2×Dic298—42no—
39C22×Dic149C2312yes—
40C22×Dic149C2312yes—
41C22×Dic149C2311yescharacteristic
42C22×Dic149C2311yescharacteristic
43C22×Dic149C2311yescharacteristic
44C22×Dic149C2311yescharacteristic
45C4⋊Dic149—22no—
46C4⋊Dic149—42no—
47#14558715—22no—
48#14558715—22no—
49#14558715—22no—
50#14558715—22no—
51#14558715—42no—
52#14558715—42no—
53C22⋊Dic149—24no—
54C22⋊Dic149—24no—
55C22⋊Dic149—42no—
56C22⋊Dic149—42no—
57C4×Dic149D414yes—
58C24×C149C2312yes—
59C2×D4×C149—22no—
60C2×D4×C149—42no—
61C22×C4×C149C2312yes—
62C22×C4×C149C2311yescharacteristic
63C22×C4×C149C2311yescharacteristic
64C22×C4×C149C2311yescharacteristic
65C4⋊C4×C149—22no—
66C22⋊C4×C149—42no—
67C22⋊C4×C149—42no—
68Dic298—44no—
69C2×Dic149—21no—
70C2×Dic149—22no—
71C2×Dic149—21no—
72C2×Dic149—22no—
73C2×Dic149—21no—
74C2×Dic149—21no—
75C2×Dic149—22no—
76C2×Dic149—22no—
77C2×Dic149—21no—
78C2×Dic149—22no—
79C2×Dic149—22no—
80C2×Dic149—22no—
81C2×Dic149—21no—
82C2×Dic149—22no—
83C2×Dic149C2×D412yes—
84C2×Dic149C2×D412yes—
85C23×C149—22no—
86C23×C149—22no—
87C23×C149—22no—
88C23×C149—22no—
89C23×C149—22no—
90C23×C149—22no—
91C23×C149—22no—
92C23×C149C2411yescharacteristic
93D4×C149—44no—
94C2×C4×C149—22no—
95C2×C4×C149—21no—
96C2×C4×C149—21no—
97C2×C4×C149—21no—
98C2×C4×C149—22no—
99C2×C4×C149—22no—
100C2×C4×C149—22no—
101C2×C4×C149—21no—
102C2×C4×C149—22no—
103C2×C4×C149C2×D412yes—
104C22×C149—42no—
105C22×C149—42no—
106C22×C149—42no—
107C22×C149—42no—
108C22×C149—42no—
109C22×C149—42no—
110C22×C149—42no—
111C22×C149C22×D411yescharacteristic
112C22×C149H(5,𝔽2)12yes—
113C22×C149H(5,𝔽2)11yescharacteristic
114C22×C1492−1+412yes—
115C22×C1492−1+411yescharacteristic
116C4×C149—22no—
117C4×C149—41no—
118C4×C149—41no—
119C4×C149—42no—
120Dic149—22no—
121Dic149—22no—
122Dic149—41no—
123Dic149—42no—
124Dic149—41no—
125Dic149—42no—
126C2×C149—82no—
127C2×C149#53511yescharacteristic
128C2×C149#53611yescharacteristic
129C2×C149#53711yescharacteristic
130C2×C149#56212yes—
131C2×C149#56312yes—
132C149#282011yescharacteristic, complemented, Sylow
133#2820—1491nomaximal, Sylow
134C2×#125—1491no—
135C2×#124—1491no—
136#399—1492no—
137#397—1492no—
138#396—1492no—
139#396—1492no—
140#395—1491no—
141#395—1491no—
142#394—1491no—
143#394D14911yescharacteristic
144#382—1491no—
145C22×Q8—1491no—
146C22×D4C2×D14911yescharacteristic
147#125—2984no—
148#124—2984no—
149C2×C4⋊C4—1491no—
150C2×C4⋊C4—1491no—
151C2×C4⋊C4—1491no—
152C2×C4⋊C4—1491no—
153C2×C4⋊C4—1491no—
154C2×C4⋊C4—1492no—
155C2×C4⋊C4—1492no—
156C2×C4⋊C4—1492no—
157C2×C4⋊C4C2×D14911yescharacteristic
158C2×C22⋊C4—1492no—
159C2×C22⋊C4—1492no—
160C2×C22⋊C4—1492no—
161C2×C22⋊C4—1492no—
162C2×C22⋊C4C2×D14912yes—
163C2×C22⋊C4C2×D14912yes—
164C2×C42—1491no—
165#95—1491no—
166#95—1492no—
167#95—1492no—
168#95—1492no—
169#95C2×D14911yescharacteristic
170C24C22×D14912yes—
171C2×Q8—2982no—
172C2×Q8—5962no—
173C2×D4—22no—
174C2×D4—42no—
175C22×C4—1492no—
176C22×C4—1491no—
177C22×C4—1492no—
178C22×C4—1491no—
179C22×C4—1491no—
180C22×C4—1491no—
181C22×C4C22×D14912yes—
182C22×C4C22×D14911yescharacteristic
183C22×C4C22×D14911yescharacteristic
184C22×C4C22×D14911yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—2982no—
187C4⋊C4—2982no—
188C4⋊C4—2982no—
189C4⋊C4—2982no—
190C4⋊C4—2982no—
191C4⋊C4—5962no—
192C4⋊C4—5962no—
193C4⋊C4—5962no—
194C22⋊C4—42no—
195C22⋊C4—42no—
196C22⋊C4—2984no—
197C22⋊C4—2984no—
198C22⋊C4—5962no—
199C22⋊C4—5962no—
200C42—1494no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23C23×D14911yescharacteristic
209Q8—5964no—
210D4—44no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—2981no—
221C2×C4—2982no—
222C2×C4—2981no—
223C2×C4—2982no—
224C2×C4—2981no—
225C2×C4—2981no—
226C2×C4—2981no—
227C2×C4—2982no—
228C2×C4—2982no—
229C2×C4—2982no—
230C2×C4—2982no—
231C2×C4—2982no—
232C2×C4—2981no—
233C2×C4—2982no—
234C2×C4—1492no—
235C2×C4—1492no—
236C2×C4D4×D14912yes—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22C2×D4×D14911yescharacteristic
245C22#1801195612yes—
246C22#1801195611yescharacteristic
247C22#1801195812yes—
248C22#1801195811yescharacteristic
249C4—22no—
250C4—41no—
251C4—41no—
252C4—42no—
253C4—2982no—
254C4—2982no—
255C4—5962no—
256C4—5961no—
257C4—5961no—
258C4—5962no—
259C2—82no—
260C2#2375019011yescharacteristic
261C2#2375019511yescharacteristic
262C2#2375020411yescharacteristic
263C2#2375037012yes—
264C2#2375037812yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, cosocleC23×C149C24
Fitting#394×C149C2
prime radicalC22×D4×C149C22
hypercenter#394D149
hypocenterC149#2820
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#18011901C2semidirect
3. #23749561C2semidirect
4. #23749553C2semidirect
5. #23749548C2semidirect
6. #23749548C2semidirect
7. #23749546C2semidirect
8. #23749545C2semidirect
10. #23749489C2semidirect
132. C149#2820semidirect

Maximal subgroups

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

subgroupindex
C2×#180119012
C2×#180118982
#237495612
#237495532
#237495482
#237495462
#237495452
#237495392
#237494892
#394×C1492
#2820149