Finite Group Databasebeta

← #34044648

Subgroups — #34044648

Order 19072.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#18011958C211yesmaximal, characteristic
2C2×#18011838C211yesmaximal, characteristic, complemented
3C2×#18011837C211yesmaximal, characteristic, complemented
4#23749624C211yesmaximal, characteristic, complemented
5C2×#18011829C211yesmaximal, characteristic, complemented
6#23749530C211yesmaximal, characteristic, complemented
7#417×C149C211yesmaximal, characteristic, complemented
8#18011958—22no—
9#18011958—22no—
10#18011958—22no—
11#18011958C414yescomplemented
12C2×#14558736—21no—
13C2×#14558736C2211yescharacteristic
14C2×#14558735—21no—
15C2×#14558735—22no—
16C22×Dic298—21no—
17C22×Dic298C2211yescharacteristic
18C2×Q8×D149—21no—
19C2×#14558720C2211yescharacteristic
20C2×C4×Dic149C2211yescharacteristic
21#18011838—22no—
22#18011837—22no—
23#18011834—21no—
24#18011831—21no—
25#18011829—22no—
26#18011818—22no—
27C2×#41×C149C2211yescharacteristic
28C2×M16×C149C2211yescharacteristic
29C2×C4⋊C4×C149C2211yescharacteristic
30#103×C149—21no—
31#102×C149—21no—
32#14558736—24no—
33#14558736—24no—
34#14558736—21no—
35#14558736—21no—
36#14558736C2×C412yes—
37#14558736D412yes—
38#14558735—28no—
39#14558735—24no—
40#14558735—28no—
41#14558735—24no—
42C2×Dic298—22no—
43C2×Dic298—24no—
44C2×Dic298—24no—
45C2×Dic298—21no—
46C2×Dic298—21no—
47C2×Dic298—21no—
48C2×Dic298—21no—
49C2×Dic298C2×C412yes—
50C2×Dic298D411yescharacteristic
51C2×Dic298D412yes—
52Q8×D149—24no—
53Q8×D149—24no—
54C2×D596D411yescharacteristic
55C2×C22⋊D149—22no—
56C2×C22⋊D149—21no—
57C22×Dic149—22no—
58C22×Dic149—21no—
59C22×Dic149D412yes—
60C2×C4×D149—22no—
61C2×C4×D149—21no—
62#14558720—21no—
63#14558720—21no—
64C2×#11924746—21no—
65C4×Dic149—21no—
66C4×Dic149—21no—
67#41×C149—21no—
68#41×C149—21no—
69#41×C149C2×C412yes—
70#41×C149D412yes—
71C2×Q8×C149D411yescharacteristic
72C2×D4×C149—21no—
73C2×D4×C149D411yescharacteristic
74C22×C4×C149—21no—
75C22×C4×C149—21no—
76C22×C4×C149C2311yescharacteristic
77M16×C149—21no—
78M16×C149—21no—
79C2×C8×C149—21no—
80C4⋊C4×C149—21no—
81C4⋊C4×C149—21no—
82C22×D149—21no—
83Dic298—28no—
84Dic298—22no—
85Dic298—22no—
86Dic298—22no—
87Dic298—21no—
88Dic298—22no—
89Dic298C22⋊C412yes—
90D596—21no—
91D596C22⋊C412yes—
92C22⋊D149—28no—
93C22⋊D149—22no—
94C22⋊D149—22no—
95C2×Dic149—28no—
96C2×Dic149—21no—
97C2×Dic149—22no—
98C2×Dic149—22no—
99C2×Dic149—22no—
100C2×Dic149—41no—
101C2×Dic149—41no—
102C2×Dic149C22⋊C414yes—
103C4×D149—28no—
104C4×D149—22no—
105C4×D149—22no—
106#11924746—41no—
107C23×C149—21no—
108C23×C149C2×D411yescharacteristic
109Q8×C149—21no—
110Q8×C149C22⋊C412yes—
111D4×C149—22no—
112D4×C149—22no—
113D4×C149—21no—
114D4×C149C22⋊C412yes—
115C2×C4×C149—21no—
116C2×C4×C149—22no—
117C2×C4×C149—22no—
118C2×C4×C149—42no—
119C2×C4×C149—41no—
120C2×C4×C149C22×C411yescharacteristic
121C2×C4×C149C2×D411yescharacteristic
122C2×C4×C149C2×D411yescharacteristic
123C2×C4×C149C2×D411yescharacteristic
124C2×C4×C149C2×D411yescharacteristic
125C2×C4×C149C2×D411yescharacteristic
126C8×C149—41no—
127C22×C149—21no—
128C22×C149—21no—
129C22×C149—22no—
130C22×C149—41no—
131C22×C149—41no—
132C22×C149C2×C22⋊C411yescharacteristic
133C22×C149#12011yescharacteristic
134C22×C149#12011yescharacteristic
135C2×D149—22no—
136C2×D149—41no—
137C2×D149—41no—
138C4×C149—22no—
139C4×C149—81no—
140C4×C149C2×C22⋊C411yescharacteristic
141C4×C149C2×C22⋊C411yescharacteristic
142C4×C149#12011yescharacteristic
143C4×C149#12011yescharacteristic
144Dic149—22no—
145Dic149—24no—
146Dic149—42no—
147C2×C149—21no—
148C2×C149—21no—
149C2×C149—42no—
150C2×C149#37911yescharacteristic
151C2×C149#45411yescharacteristic
152C2×C149#45611yescharacteristic
153D149—42no—
154C149#179311yescharacteristic, complemented, Sylow
155#1793—1491nomaximal, Sylow
156C2×2−1+4—1491no—
157C2×#104—1491no—
158C2×#104—1491no—
159#417—1491no—
160#417D14911yescharacteristic, complemented
161C2×#101—1491no—
162#391—1491no—
1632−1+4—2982no—
1642−1+4—2982no—
1652−1+4—2982no—
1662−1+4—1494no—
167C2×#41—2981no—
168C2×#41—2981no—
169C2×#41—2982no—
170C2×#41—1491no—
171C2×#41C2×D14911yescharacteristic
172C22×Q8—2981no—
173C22×Q8—2981no—
174C22×Q8—1491no—
175C2×M16—1491no—
176C2×M16C2×D14911yescharacteristic
177C2×C4⋊C4C2×D14911yescharacteristic
178C2×C42—1491no—
179#104—2982no—
180#104—2982no—
181#103—21no—
182#103—2981no—
183#102—21no—
184#102—2981no—
185#101—2982no—
186#95—2982no—
187#41—21no—
188#41—21no—
189#41—2984no—
190#41—2984no—
191#41—2988no—
192#41—2984no—
193#41—2984no—
194#41—2988no—
195#41—2981no—
196#41—2981no—
197#41—1492no—
198#41—1492no—
199#41C4×D14912yes—
200#41D59612yes—
201C2×Q8—2982no—
202C2×Q8—2984no—
203C2×Q8—2984no—
204C2×Q8—2984no—
205C2×Q8—2984no—
206C2×Q8—2981no—
207C2×Q8—2981no—
208C2×Q8—2981no—
209C2×Q8—2981no—
210C2×Q8—1491no—
211C2×Q8—1492no—
212C2×Q8—1492no—
213C2×Q8C22⋊D14911yescharacteristic
214C2×D4—21no—
215C2×D4—2982no—
216C2×D4—2981no—
217C2×D4—1491no—
218C2×D4C22⋊D14911yescharacteristic
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—2982no—
222C22×C4—2982no—
223C22×C4—2981no—
224C22×C4—2981no—
225C22×C4—1492no—
226C22×C4C22×D14911yescharacteristic
227M16—21no—
228M16—21no—
229M16—2981no—
230M16—2981no—
231C2×C8—21no—
232C2×C8—2981no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C42—2981no—
236C42—2981no—
237C23—21no—
238C23—2981no—
239C23D4×D14911yescharacteristic
240Q8—21no—
241Q8—2988no—
242Q8—2982no—
243Q8—2982no—
244Q8—2982no—
245Q8—2981no—
246Q8—2982no—
247Q8—1492no—
248Q8#1455871312yes—
249D4—22no—
250D4—22no—
251D4—21no—
252D4—2988no—
253D4—2982no—
254D4—2982no—
255D4—2981no—
256D4—1492no—
257D4#1455871312yes—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—2988no—
264C2×C4—2988no—
265C2×C4—2981no—
266C2×C4—2982no—
267C2×C4—2982no—
268C2×C4—2982no—
269C2×C4—2982no—
270C2×C4—2982no—
271C2×C4—5961no—
272C2×C4—5961no—
273C2×C4—1494no—
274C2×C4C2×C4×D14911yescharacteristic
275C2×C4D4×D14911yescharacteristic
276C2×C4D4×D14911yescharacteristic
277C2×C4D4×D14911yescharacteristic
278C2×C4C2×C22⋊D14911yescharacteristic
279C2×C4C2×D59611yescharacteristic
280C8—41no—
281C8—5961no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—2982no—
288C22—5961no—
289C22—5961no—
290C22C22⋊C4×D14911yescharacteristic
291C22#1801187911yescharacteristic
292C22#1801188111yescharacteristic
293C4—22no—
294C4—81no—
295C4—2982no—
296C4—2984no—
297C4—5962no—
298C4C22⋊C4×D14911yescharacteristic
299C4C2×#1455871311yescharacteristic
300C4#1801187911yescharacteristic
301C4#1801188111yescharacteristic
302C2—21no—
303C2—21no—
304C2—42no—
305C2—5962no—
306C2#2374948011yescharacteristic
307C2#2374979611yescharacteristic
308C2#2374980611yescharacteristic
subgroupG/H
centerC22#18011879
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#417×C149C2
socleC22×C149#120
prime radicalC2×#18011958C2
cosocleC22×C4×C149C23
hypercenter#417D149
hypocenterC149#1793
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#18011838C2semidirect
3. C2×#18011837C2semidirect
4. #23749624C2semidirect
5. C2×#18011829C2semidirect
6. #23749530C2semidirect
7. #417×C149C2semidirect
11. #18011958C4semidirect
154. C149#1793semidirect
160. #417D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119582
C2×#180118382
C2×#180118372
#237496242
C2×#180118292
#237495302
#417×C1492
#1793149