Finite Group Databasebeta

← #34054173

Subgroups — #34054173

Order 19072.

480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18011940C212yesmaximal
2C4⋊Q8×D149C211yesmaximal, characteristic, complemented
3C4×#14558735C211yesmaximal, characteristic
4#23749836C211yesmaximal, characteristic, complemented
5#23749834C212yesmaximal, complemented
6#23749832C211yesmaximal, characteristic, complemented
7#23749830C211yesmaximal, characteristic, complemented
8#23749828C212yesmaximal, complemented
9#23749647C211yesmaximal, characteristic, complemented
10#23749632C212yesmaximal, complemented
11#461×C149C211yesmaximal, characteristic, complemented
12C2×#14558735C2211yescharacteristic
13C2×Q8×D149C2212yes—
14#18011940—28no—
15C2×Dic596C2212yes—
16C2×#14558726C2212yes—
17C2×#14558724C2212yes—
18C2×#14558719C2212yes—
19#18011911C2211yescharacteristic
20#18011910—21no—
21#18011910—21no—
22#18011909C2212yes—
23C4×Dic298C2211yescharacteristic
24#18011876C2211yescharacteristic
25D4×Dic149C2211yescharacteristic
26C4×C22⋊D149—21no—
27#18011871—21no—
28#18011869C2211yescharacteristic
29#18011867—21no—
30C4⋊C4×D149—21no—
31C4⋊C4×D149—21no—
32C2×C4×Dic149—21no—
33C42×D149C2211yescharacteristic
34C4⋊#11924746C2211yescharacteristic
35#18011840C2212yes—
36#18011836C2212yes—
37#18011835C2212yes—
38#18011834C2212yes—
39C2×SD16×C149C2212yes—
40C4⋊Q8×C149C2211yescharacteristic
41C4×D4×C149C2211yescharacteristic
42C4⋊C8×C149C2211yescharacteristic
43#103×C149C2212yes—
44#14558735—22no—
45#14558735D414yes—
46C2×Dic298—22no—
47C2×Dic298C2312yes—
48C2×Dic298C2311yescharacteristic
49Q8×D149—24no—
50Q8×D149—24no—
51C2×C22⋊D149—21no—
52C22×Dic149—21no—
53C22×Dic149—21no—
54C2×C4×D149—22no—
55C2×C4×D149D411yescharacteristic
56C2×C4×D149D411yescharacteristic
57C2×C4×D149C2311yescharacteristic
58Dic596—24no—
59#14558726—24no—
60#14558724—24no—
61#14558719—24no—
62C2×#11924746C2312yes—
63C4⋊Dic149—21no—
64C4⋊Dic149—21no—
65C4⋊Dic149C2311yescharacteristic
66#14558715—22no—
67#14558715—22no—
68#14558715—21no—
69#14558715—21no—
70C22⋊Dic149—21no—
71#14558713—21no—
72C4×Dic149—21no—
73C4×Dic149—21no—
74C4×Dic149—21no—
75C4×Dic149D411yescharacteristic
76C4×Dic149D411yescharacteristic
77C4×Dic149C2311yescharacteristic
78C2×Q8×C149C2312yes—
79C2×D4×C149C2311yescharacteristic
80C22×C4×C149—21no—
81SD16×C149—24no—
82C2×C8×C149C2312yes—
83C4⋊C4×C149—21no—
84C4⋊C4×C149—21no—
85C4⋊C4×C149C2311yescharacteristic
86C22⋊C4×C149—21no—
87C42×C149C2311yescharacteristic
88C22×D149C2×D411yescharacteristic
89Dic298—21no—
90Dic298—22no—
91Dic298—22no—
92Dic298—44no—
93Dic298C2×D412yes—
94C22⋊D149—24no—
95C2×Dic149—21no—
96C2×Dic149—24no—
97C2×Dic149—22no—
98C2×Dic149—21no—
99C2×Dic149—42no—
100C2×Dic149C2×D411yescharacteristic
101C2×Dic149C2×D411yescharacteristic
102C2×Dic149C2×D411yescharacteristic
103C4×D149—22no—
104C4×D149—22no—
105C4×D149—44no—
106C4×D149C2×D412yes—
107C4×D149#4112yes—
108#11924746—22no—
109C23×C149—21no—
110Q8×C149—22no—
111Q8×C149—22no—
112D4×C149—21no—
113D4×C149C2×D412yes—
114C2×C4×C149—22no—
115C2×C4×C149—21no—
116C2×C4×C149—42no—
117C2×C4×C149C2×D411yescharacteristic
118C2×C4×C149C2×D411yescharacteristic
119C2×C4×C149C2411yescharacteristic
120C8×C149—22no—
121C22×C149—22no—
122C22×C149—41no—
123C22×C149—41no—
124C22×C149C22×D411yescharacteristic
125C2×D149—21no—
126C2×D149—21no—
127C2×D149#12112yes—
128C4×C149—21no—
129C4×C149—42no—
130C4×C149—41no—
131C4×C149#13712yescomplemented
132C4×C149C22×D411yescharacteristic
133C4×C149C2×#4111yescharacteristic
134Dic149—22no—
135Dic149—21no—
136Dic149—42no—
137Dic149—41no—
138Dic149#12112yes—
139Dic149#13712yescomplemented
140C2×C149—42no—
141C2×C149C2×#12111yescharacteristic
142C2×C149C2×#13711yescharacteristic
143C2×C149C2×#13711yescharacteristic
144D149—22no—
145C149#303911yescharacteristic, complemented, Sylow
146#3039—1491nomaximal, Sylow
147C2×#137—1492no—
148C2×C4⋊Q8—1491no—
149C4×#41—1491no—
150#462—1491no—
151#462—1491no—
152#462—1492no—
153#461—1492no—
154#461—1491no—
155#461D14911yescharacteristic, complemented
156#423—1491no—
157#419—1492no—
158C2×#41—1491no—
159C22×Q8—1492no—
160#137—2988no—
161C2×Q16—1492no—
162C2×Q16—1492no—
163C2×SD16—1492no—
164C2×SD16C2×D14912yes—
165C2×M16—1492no—
166C4⋊Q8—2981no—
167C4⋊Q8—2981no—
168C4⋊Q8—1492no—
169C4⋊Q8—1491no—
170C4⋊Q8C2×D14911yescharacteristic
171C4×Q8—1491no—
172C4×Q8—1491no—
173C4×D4—2981no—
174C4×D4—2981no—
175C4×D4—1491no—
176C4×D4C2×D14911yescharacteristic
177#117—2981no—
178#117—1491no—
179C2×C4⋊C4—2981no—
180C2×C4⋊C4—2981no—
181C2×C42—2981no—
182C2×C42—1491no—
183C4⋊C8—1492no—
184C4⋊C8—1491no—
185C4⋊C8C2×D14911yescharacteristic
186#103—1492no—
187#103—1492no—
188#103—1492no—
189#103C2×D14912yes—
190#41—2982no—
191#41—1494no—
192C2×Q8—2982no—
193C2×Q8—2984no—
194C2×Q8—2984no—
195C2×Q8—1492no—
196C2×Q8—1491no—
197C2×Q8C22×D14912yes—
198C2×D4—2981no—
199C2×D4C22×D14911yescharacteristic
200C22×C4—21no—
201C22×C4—2982no—
202C22×C4—2981no—
203C22×C4—2981no—
204C22×C4—1491no—
205C22×C4—1491no—
206C22×C4—1491no—
207Q16—2984no—
208Q16—2984no—
209SD16—24no—
210SD16—2984no—
211M16—2984no—
212C2×C8—1492no—
213C2×C8C22×D14912yes—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—2982no—
217C4⋊C4—2982no—
218C4⋊C4—2981no—
219C4⋊C4—2981no—
220C4⋊C4—2981no—
221C4⋊C4—2981no—
222C4⋊C4—1491no—
223C4⋊C4C22×D14911yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—2981no—
226C22⋊C4—2981no—
227C42—2981no—
228C42—2981no—
229C42—2981no—
230C42—1491no—
231C42—1491no—
232C42—1491no—
233C42C22×D14911yescharacteristic
234C23—21no—
235C23—1491no—
236Q8—22no—
237Q8—22no—
238Q8—2981no—
239Q8—2982no—
240Q8—2982no—
241Q8—5964no—
242Q8—1492no—
243D4—21no—
244D4—2984no—
245D4D4×D14912yes—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—42no—
249C2×C4—2982no—
250C2×C4—2981no—
251C2×C4—2984no—
252C2×C4—2982no—
253C2×C4—2981no—
254C2×C4—2982no—
255C2×C4—5964no—
256C2×C4—5962no—
257C2×C4—1491no—
258C2×C4—1491no—
259C2×C4—1491no—
260C2×C4—1492no—
261C2×C4—1492no—
262C2×C4D4×D14911yescharacteristic
263C2×C4D4×D14911yescharacteristic
264C2×C4C23×D14911yescharacteristic
265C8—22no—
266C8—2982no—
267C22—22no—
268C22—41no—
269C22—41no—
270C22—2981no—
271C22—2981no—
272C22—1492no—
273C22C2×D4×D14911yescharacteristic
274C4—21no—
275C4—41no—
276C4—42no—
277C4—2981no—
278C4—2982no—
279C4—5961no—
280C4—5962no—
281C4—1492no—
282C4—1492no—
283C4#1801194012yescomplemented
284C4C2×D4×D14911yescharacteristic
285C4#41×D14911yescharacteristic
286C2—42no—
287C2—2982no—
288C2#121×D14911yescharacteristic
289C2#137×D14911yescharacteristic
290C2C2×#1801194011yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#461×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558735C22
hypercenter#461D149
hypocenterC149#3039
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D149C2semidirect
4. #23749836C2semidirect
5. #23749834C2semidirect
6. #23749832C2semidirect
7. #23749830C2semidirect
8. #23749828C2semidirect
9. #23749647C2semidirect
10. #23749632C2semidirect
11. #461×C149C2semidirect
131. C4×C149#137semidirect
139. Dic149#137semidirect
145. C149#3039semidirect
155. #461D149semidirect
283. C4#18011940semidirect

Maximal subgroups

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

subgroupindex
C2×#180119402
C4⋊Q8×D1492
C4×#145587352
#237498362
#237498342
#237498322
#237498302
#237498282
#237496472
#237496322
#461×C1492
#3039149