Finite Group Databasebeta

← C4×#19153837 #37542490

Subgroups — C4×#19153837 #37542490

Order 23168.

500 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153837C211yesmaximal, characteristic
2C4×#15668450C211yesmaximal, characteristic, complemented
3C4×#15668448C211yesmaximal, characteristic, complemented
4C4×#15668439C211yesmaximal, characteristic, complemented
5#26041371C211yesmaximal, characteristic, complemented
6C4×#15668438C211yesmaximal, characteristic, complemented
7SD16×Dic181C211yesmaximal, characteristic, complemented
8#26041366C211yesmaximal, characteristic, complemented
9C4×#15668434C211yesmaximal, characteristic, complemented
10#26041359C211yesmaximal, characteristic, complemented
11#26041314C211yesmaximal, characteristic, complemented
12#26041274C211yesmaximal, characteristic, complemented
13#26041272C211yesmaximal, characteristic, complemented
14C4×C8×D181C211yesmaximal, characteristic, complemented
15C4×SD16×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668448C2211yescharacteristic
18#19153837C418yesdirect product factor
19C2×#15668439C2211yescharacteristic
20C2×#15668438C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×C8×D181C2211yescharacteristic
23C2×C8×D181C2211yescharacteristic
24Q8×Dic181C2211yescharacteristic
25C4×Dic362C2211yescharacteristic
26#19153781C2211yescharacteristic
27C4×D724—21no—
28C4×D724C2211yescharacteristic
29D4×Dic181C2211yescharacteristic
30#19153778—21no—
31#19153778C2211yescharacteristic
32C4×C22⋊D181—21no—
33#19153776—21no—
34#19153774—21no—
35#19153774C2211yescharacteristic
36#19153774C2211yescharacteristic
37#19153772—21no—
38C2×C4×Dic181—21no—
39C42×D181—21no—
40C42×D181C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153749C2211yescharacteristic
43#19153748C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153736C2211yescharacteristic
50C4×#13089678C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C8×Dic181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54C4×Q8×C181C2211yescharacteristic
55C4×D4×C181C2211yescharacteristic
56#106×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C4×C8×C181C2211yescharacteristic
60#15668450—22no—
61#15668450C2×C414yescomplemented
62#15668448—22no—
63#15668448C2×C414yescomplemented
64C2×Dic362C2311yescharacteristic
65C2×D724—21no—
66C2×D724C2311yescharacteristic
67C2×C22⋊D181—21no—
68C22×Dic181—21no—
69C22×Dic181—21no—
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181D411yescharacteristic
74C2×C4×D181D411yescharacteristic
75C2×C4×D181C2311yescharacteristic
76#15668439C2×C414yescomplemented
77#15668438C2×C414yescomplemented
78#15668434C2×C414yescomplemented
79C2×#13089678C2311yescharacteristic
80C2×#13089678C2311yescharacteristic
81C8×D181—22no—
82C8×D181C2×C414yescomplemented
83C4⋊Dic181—21no—
84C4⋊Dic181C2311yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86#15668428—21no—
87#15668428—21no—
88C22⋊Dic181—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181—21no—
96C4×Dic181—21no—
97C4×Dic181—21no—
98C4×Dic181D411yescharacteristic
99C4×Dic181D411yescharacteristic
100C4×Dic181C2311yescharacteristic
101C2×Q8×C181C2311yescharacteristic
102C2×D4×C181C2311yescharacteristic
103C22×C4×C181—21no—
104SD16×C181C2×C414yescomplemented
105C2×C8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C4⋊C4×C181—21no—
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C42×C181—21no—
112C42×C181C2311yescharacteristic
113C22×D181—21no—
114C22×D181C2×D411yescharacteristic
115Dic362—21no—
116Dic362C22×C412yes—
117D724—24no—
118D724—21no—
119D724C22×C412yes—
120C22⋊D181—24no—
121C2×Dic181—21no—
122C2×Dic181—24no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—42no—
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C4×D181—22no—
130C4×D181—24no—
131C4×D181—22no—
132C4×D181—42no—
133C4×D181—42no—
134C4×D181C22×C412yes—
135C4×D181#4112yes—
136#13089678—21no—
137#13089678C22×C412yes—
138C23×C181—21no—
139Q8×C181—21no—
140Q8×C181C22×C412yes—
141D4×C181—21no—
142D4×C181C22×C412yes—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—42no—
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2411yescharacteristic
150C8×C181—21no—
151C8×C181C22×C412yes—
152C22×C181—22no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181C22×D411yescharacteristic
156C2×D181—21no—
157C2×D181—21no—
158C2×D181—22no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181C4×D412yes—
162C4×C181—22no—
163C4×C181—21no—
164C4×C181—41no—
165C4×C181—41no—
166C4×C181#13512yescomplemented
167C4×C181C23×C411yescharacteristic
168C4×C181C2×#4111yescharacteristic
169Dic181—22no—
170Dic181—21no—
171Dic181—41no—
172Dic181—41no—
173Dic181C4×D412yes—
174Dic181#13512yescomplemented
175C2×C181—42no—
176C2×C181C2×C4×D411yescharacteristic
177C2×C181C2×#13511yescharacteristic
178C2×C181C2×#13511yescharacteristic
179D181—22no—
180D181—42no—
181C181C4×#13511yescharacteristic, complemented, Sylow
182C4×#135—1811nomaximal, Sylow
183C2×#135—1811no—
184C4×#41—1811no—
185C4×#41—1811no—
186C4×Q16—1811no—
187C4×Q16—1811no—
188C4×SD16—1811no—
189C4×SD16—1811no—
190C4×SD16—1811no—
191C4×SD16D18111yescharacteristic, complemented
192C4×D8—1811no—
193C4×D8—1811no—
194#427—1811no—
195#416—1811no—
196#416—1811no—
197C2×C4×C8—1811no—
198C2×#41—1811no—
199C2×#41—1811no—
200#135—1818no—
201C2×Q16—1811no—
202C2×SD16—1811no—
203C2×SD16C2×D18111yescharacteristic
204C2×D8—1811no—
205C22×C8—1811no—
206C22×C8—1811no—
207C4×Q8—1811no—
208C4×Q8—1811no—
209C4×Q8—1811no—
210C4×Q8C2×D18111yescharacteristic
211C4×D4—3621no—
212C4×D4—3621no—
213C4×D4—3621no—
214C4×D4—3621no—
215C4×D4—1811no—
216C4×D4—1811no—
217C4×D4—1811no—
218C4×D4C2×D18111yescharacteristic
219#117—3621no—
220#117—3621no—
221#117—1811no—
222#117—1811no—
223C2×C42—3621no—
224C2×C42—3621no—
225C2×C42—1811no—
226#107—1811no—
227#107—1811no—
228#106—1811no—
229#106C2×D18111yescharacteristic
230#103—1811no—
231#103—1811no—
232#103—1811no—
233#103C2×D18111yescharacteristic
234#102—1811no—
235#102—1811no—
236#102—1811no—
237#102C2×D18111yescharacteristic
238C4×C8—1811no—
239C4×C8—1811no—
240C4×C8—1811no—
241C4×C8C2×D18111yescharacteristic
242#41—3622no—
243#41—3622no—
244#41—1814no—
245#41—1814no—
246C2×Q8—1811no—
247C2×Q8C22×D18111yescharacteristic
248C2×D4—3621no—
249C2×D4—3621no—
250C2×D4—1811no—
251C2×D4C22×D18111yescharacteristic
252C22×C4—21no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—3621no—
257C22×C4—3621no—
258C22×C4—1811no—
259C22×C4—1811no—
260C22×C4—1811no—
261Q16—1814no—
262SD16—1814no—
263SD16C4×D18114yescomplemented
264D8—1814no—
265C2×C8—3622no—
266C2×C8—1811no—
267C2×C8—1811no—
268C2×C8—1814no—
269C2×C8C22×D18111yescharacteristic
270C2×C8C22×D18111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—3621no—
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—1811no—
276C4⋊C4—1811no—
277C4⋊C4C22×D18111yescharacteristic
278C4⋊C4C22×D18111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C42—21no—
286C42—3621no—
287C42—3621no—
288C42—3621no—
289C42—3621no—
290C42—3621no—
291C42—1811no—
292C42—1811no—
293C42—1811no—
294C42C22×D18111yescharacteristic
295C23—21no—
296C23—3621no—
297C23—1811no—
298Q8—21no—
299Q8—3621no—
300Q8—1812no—
301Q8C2×C4×D18112yes—
302D4—21no—
303D4—3624no—
304D4—3624no—
305D4—3621no—
306D4—1812no—
307D4C2×C4×D18112yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—3624no—
313C2×C4—3622no—
314C2×C4—3621no—
315C2×C4—3624no—
316C2×C4—3622no—
317C2×C4—3621no—
318C2×C4—3621no—
319C2×C4—1811no—
320C2×C4—1811no—
321C2×C4—1811no—
322C2×C4—1812no—
323C2×C4—1812no—
324C2×C4—7242no—
325C2×C4—7242no—
326C2×C4—7242no—
327C2×C4D4×D18111yescharacteristic
328C2×C4D4×D18111yescharacteristic
329C2×C4C23×D18111yescharacteristic
330C8—21no—
331C8—3621no—
332C8—1812no—
333C8C2×C4×D18112yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—3621no—
338C22—3621no—
339C22—3622no—
340C22—1812no—
341C22—7241no—
342C22—7241no—
343C22C2×D4×D18111yescharacteristic
344C4—22no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—3622no—
349C4—3621no—
350C4—1812no—
351C4—1812no—
352C4—7241no—
353C4—7241no—
354C4#1915383712yesdirect product factor
355C4C22×C4×D18111yescharacteristic
356C4#41×D18111yescharacteristic
357C2—42no—
358C2—3622no—
359C2—7242no—
360C2C4×D4×D18111yescharacteristic
361C2#135×D18111yescharacteristic
362C2C2×#1915383711yescharacteristic
subgroupG/H
centerC2×C4D4×D181
commutatorC4×C181C23×C4
FrattiniC2×C4C23×D181
FittingC4×SD16×C181C2
socleC22×C181C22×D4
prime radicalC2×#19153837C2
cosocleC2×C4×C181C24
hypercenterC4×SD16D181
hypocenterC181C4×#135
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×#15668450C2semidirect
3. C4×#15668448C2semidirect
4. C4×#15668439C2semidirect
5. #26041371C2semidirect
6. C4×#15668438C2semidirect
7. SD16×Dic181C2semidirect
8. #26041366C2semidirect
9. C4×#15668434C2semidirect
10. #26041359C2semidirect
11. #26041314C2semidirect
12. #26041274C2semidirect
13. #26041272C2semidirect
14. C4×C8×D181C2semidirect
15. C4×SD16×C181C2semidirect
18. #19153837C4direct (N × H)
61. #15668450C2×C4semidirect
63. #15668448C2×C4semidirect
76. #15668439C2×C4semidirect
77. #15668438C2×C4semidirect
78. #15668434C2×C4semidirect
82. C8×D181C2×C4semidirect
104. SD16×C181C2×C4semidirect
166. C4×C181#135semidirect
174. Dic181#135semidirect
181. C181C4×#135semidirect
191. C4×SD16D181semidirect
263. SD16C4×D181semidirect
354. C4#19153837direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191538372
C4×#156684502
C4×#156684482
C4×#156684392
#260413712
C4×#156684382
SD16×Dic1812
#260413662
C4×#156684342
#260413592
#260413142
#260412742
#260412722
C4×C8×D1812
C4×SD16×C1812
C4×#135181