Finite Group Databasebeta

← #440×D173 #36362338

Subgroups — #440×D173 #36362338

Order 22144.

544 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D173C211yesmaximal, characteristic
2C4×Q8×D173C211yesmaximal, characteristic, complemented
3C4×D4×D173C211yesmaximal, characteristic
4#26011594C211yesmaximal, characteristic, complemented
5#26011593C211yesmaximal, characteristic, complemented
6#26011592C211yesmaximal, characteristic, complemented
7#26011591C211yesmaximal, characteristic, complemented
8#26011590C211yesmaximal, characteristic, complemented
9#26011589C211yesmaximal, characteristic, complemented
10#26011588C211yesmaximal, characteristic, complemented
11#107×D173C211yesmaximal, characteristic, complemented
12#103×D173C211yesmaximal, characteristic, complemented
13#102×D173C211yesmaximal, characteristic
14#97×D173C211yesmaximal, characteristic, complemented
15#440×C173C211yesmaximal, characteristic, complemented
16C2×Q8×D173C2211yescharacteristic
17C2×D4×D173C2211yescharacteristic
18C22×C4×D173—21no—
19C2×#14583815C2211yescharacteristic
20C2×#14583814C2211yescharacteristic
21C2×#14583813C2211yescharacteristic
22SD16×D173C418yescomplemented
23C2×C8×D173C2211yescharacteristic
24C2×C8×D173C2211yescharacteristic
25Q8×Dic173C2211yescharacteristic, complemented
26C4×Dic346—21no—
27C4×Dic346C2211yescharacteristic, complemented
28#19149644—21no—
29#19149644C2211yescharacteristic, complemented
30C4×D692C2211yescharacteristic
31D4×Dic173C2211yescharacteristic
32#19149641C2211yescharacteristic
33C4×C22⋊D173—21no—
34#19149639—21no—
35C4⋊C4×D173—21no—
36C4⋊C4×D173C2211yescharacteristic
37C4⋊C4×D173C2211yescharacteristic
38C22⋊C4×D173—21no—
39C42×D173—21no—
40C42×D173C2211yescharacteristic
41#19149613C2211yescharacteristic, complemented
42#19149612C2211yescharacteristic, complemented
43#19149612C2211yescharacteristic, complemented
44#19149604C2211yescharacteristic, complemented
45#19149603C2211yescharacteristic, complemented
46#19149602C2211yescharacteristic, complemented
47#19149601C2211yescharacteristic
48#19149600C2211yescharacteristic
49#19149599C2211yescharacteristic
50#19149590C2211yescharacteristic, complemented
51#19149589C2211yescharacteristic, complemented
52#19149589C2211yescharacteristic, complemented
53C2×SD16×C173C2211yescharacteristic
54C4×Q8×C173C2211yescharacteristic, complemented
55C4×D4×C173C2211yescharacteristic
56#107×C173C2211yescharacteristic, complemented
57#103×C173C2211yescharacteristic, complemented
58#102×C173C2211yescharacteristic
59#97×C173C2211yescharacteristic, complemented
60C23×D173—21no—
61C2×Dic346—21no—
62C2×Dic346C2311yescharacteristic
63Q8×D173—22no—
64Q8×D173C2×C414yescomplemented
65C2×D692C2311yescharacteristic
66C2×C22⋊D173—21no—
67D4×D173—22no—
68D4×D173C2×C414yes—
69C22×Dic173—21no—
70C2×C4×D173—21no—
71C2×C4×D173—21no—
72C2×C4×D173—21no—
73C2×C4×D173—21no—
74C2×C4×D173—21no—
75C2×C4×D173—44no—
76C2×C4×D173D411yescharacteristic
77C2×C4×D173D411yescharacteristic
78C2×C4×D173C2311yescharacteristic
79#14583815C2×C414yescomplemented
80#14583814C2×C414yescomplemented
81#14583813C2×C414yescomplemented
82C2×#13063436C2311yescharacteristic
83C2×#13063436C2311yescharacteristic
84C8×D173—22no—
85C8×D173C2×C414yescomplemented
86C4⋊Dic173—21no—
87C4⋊Dic173C2311yescharacteristic
88C4⋊Dic173C2311yescharacteristic
89#14583805—21no—
90#14583805—21no—
91#14583805—21no—
92#14583805—21no—
93C22⋊Dic173—21no—
94#14583803—21no—
95#14583803—21no—
96C4×Dic173—21no—
97C4×Dic173—21no—
98C4×Dic173—21no—
99C4×Dic173D411yescharacteristic
100C4×Dic173D411yescharacteristic
101C4×Dic173C2311yescharacteristic
102C2×Q8×C173C2311yescharacteristic
103C2×D4×C173C2311yescharacteristic
104C22×C4×C173—21no—
105SD16×C173C2×C414yescomplemented
106C2×C8×C173C2311yescharacteristic
107C2×C8×C173C2311yescharacteristic
108C4⋊C4×C173—21no—
109C4⋊C4×C173C2311yescharacteristic
110C4⋊C4×C173C2311yescharacteristic
111C22⋊C4×C173—21no—
112C42×C173—21no—
113C42×C173C2311yescharacteristic
114C22×D173—21no—
115C22×D173—24no—
116C22×D173—42no—
117C22×D173—42no—
118C22×D173C2×D411yescharacteristic
119Dic346—21no—
120Dic346—24no—
121Dic346C22×C412yescomplemented
122D692—21no—
123D692C22×C412yes—
124C22⋊D173—24no—
125C2×Dic173—21no—
126C2×Dic173—21no—
127C2×Dic173—21no—
128C2×Dic173—42no—
129C2×Dic173C2×D411yescharacteristic
130C2×Dic173C2×D411yescharacteristic
131C2×Dic173C2×D411yescharacteristic
132C4×D173—24no—
133C4×D173—22no—
134C4×D173—22no—
135C4×D173—42no—
136C4×D173—42no—
137C4×D173—42no—
138C4×D173—42no—
139C4×D173C22×C412yes—
140C4×D173#4112yes—
141#13063436—21no—
142#13063436C22×C412yescomplemented
143C23×C173—21no—
144Q8×C173—21no—
145Q8×C173C22×C412yescomplemented
146D4×C173—21no—
147D4×C173C22×C412yes—
148C2×C4×C173—21no—
149C2×C4×C173—21no—
150C2×C4×C173—21no—
151C2×C4×C173—42no—
152C2×C4×C173C2×D411yescharacteristic
153C2×C4×C173C2×D411yescharacteristic
154C2×C4×C173C2411yescharacteristic
155C8×C173—21no—
156C8×C173C22×C412yescomplemented
157C22×C173—22no—
158C22×C173—41no—
159C22×C173—41no—
160C22×C173C22×D411yescharacteristic
161C2×D173—22no—
162C2×D173—41no—
163C2×D173—41no—
164C2×D173—48no—
165C2×D173C4×D412yes—
166C2×D173AGL(1,ℤ/8)12yes—
167C2×D173#13712yes—
168C4×C173—22no—
169C4×C173—21no—
170C4×C173—21no—
171C4×C173—41no—
172C4×C173—41no—
173C4×C173C23×C411yescharacteristic
174C4×C173C2×#4111yescharacteristic
175Dic173—22no—
176Dic173—21no—
177Dic173—21no—
178Dic173—41no—
179Dic173—41no—
180Dic173C4×D412yes—
181C2×C173—42no—
182C2×C173C2×C4×D411yescharacteristic
183C2×C173C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C173C2×#13711yescharacteristic
185D173—42no—
186D173#44014yesdirect product factor
187C173C2×#44011yescharacteristic, complemented, Sylow
188C2×#440—1731nomaximal, Sylow
189C22×SD16—1731no—
190C2×C4×Q8—1731no—
191C2×C4×D4—1731no—
192#440—1731no—
193#440—1731no—
194#440—1731no—
195#440—1731no—
196#440—1731no—
197#440—1731no—
198#440—1731no—
199#440D17311yescharacteristic, direct product factor
200C2×#107—1731no—
201C2×#103—1731no—
202C2×#102—1731no—
203C2×#97—1731no—
204C22×Q8—1731no—
205C22×D4—1731no—
206C23×C4—3461no—
207C2×SD16—1731no—
208C2×SD16—1731no—
209C2×SD16—1738no—
210C2×SD16—1731no—
211C2×SD16C2×D17311yescharacteristic
212C22×C8—1731no—
213C22×C8—1731no—
214C4×Q8—3461no—
215C4×Q8—3461no—
216C4×Q8—1731no—
217C4×Q8—1731no—
218C4×Q8—1731no—
219C4×Q8C2×D17311yescharacteristic, complemented
220C4×D4—3461no—
221C4×D4—3461no—
222C4×D4—1731no—
223C4×D4—1731no—
224C4×D4—1731no—
225C4×D4C2×D17311yescharacteristic
226C2×C4⋊C4—3461no—
227C2×C4⋊C4—1731no—
228C2×C4⋊C4—1731no—
229C2×C22⋊C4—3461no—
230C2×C42—3461no—
231C2×C42—1731no—
232#107—1731no—
233#107—1731no—
234#107—1731no—
235#107C2×D17311yescharacteristic, complemented
236#103—1731no—
237#103—1731no—
238#103—1731no—
239#103C2×D17311yescharacteristic, complemented
240#102—1731no—
241#102—1731no—
242#102—1731no—
243#102C2×D17311yescharacteristic
244#97—1731no—
245#97—1731no—
246#97—1731no—
247#97C2×D17311yescharacteristic, complemented
248C24—3461no—
249C2×Q8—3461no—
250C2×Q8—3462no—
251C2×Q8—1734no—
252C2×Q8—1731no—
253C2×Q8C22×D17311yescharacteristic
254C2×D4—3462no—
255C2×D4—3461no—
256C2×D4—1734no—
257C2×D4—1731no—
258C2×D4C22×D17311yescharacteristic
259C22×C4—21no—
260C22×C4—3461no—
261C22×C4—3461no—
262C22×C4—3461no—
263C22×C4—3461no—
264C22×C4—3461no—
265C22×C4—3461no—
266C22×C4—1731no—
267C22×C4—1731no—
268C22×C4—1731no—
269C22×C4—6924no—
270SD16—1734no—
271SD16—1734no—
272SD16—1734no—
273SD16C4×D17314yescomplemented
274C2×C8—3462no—
275C2×C8—1731no—
276C2×C8—1731no—
277C2×C8—1734no—
278C2×C8C22×D17311yescharacteristic
279C2×C8C22×D17311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—3461no—
282C4⋊C4—3461no—
283C4⋊C4—3461no—
284C4⋊C4—3461no—
285C4⋊C4—3461no—
286C4⋊C4—1731no—
287C4⋊C4—1731no—
288C4⋊C4C22×D17311yescharacteristic
289C4⋊C4C22×D17311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—3461no—
292C22⋊C4—3461no—
293C22⋊C4—3461no—
294C42—21no—
295C42—3461no—
296C42—3461no—
297C42—3461no—
298C42—1731no—
299C42—1731no—
300C42—1731no—
301C42C22×D17311yescharacteristic
302C23—21no—
303C23—3464no—
304C23—3461no—
305C23—1731no—
306C23—6922no—
307C23—6922no—
308Q8—21no—
309Q8—3464no—
310Q8—3461no—
311Q8—1732no—
312Q8C2×C4×D17312yescomplemented
313D4—21no—
314D4—3464no—
315D4—3461no—
316D4—1732no—
317D4C2×C4×D17312yes—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—3464no—
323C2×C4—3462no—
324C2×C4—3462no—
325C2×C4—3461no—
326C2×C4—3461no—
327C2×C4—3461no—
328C2×C4—1731no—
329C2×C4—1731no—
330C2×C4—1731no—
331C2×C4—1732no—
332C2×C4—1732no—
333C2×C4—6922no—
334C2×C4—6922no—
335C2×C4—6922no—
336C2×C4—6922no—
337C2×C4—6922no—
338C2×C4D4×D17311yescharacteristic
339C2×C4D4×D17311yescharacteristic
340C2×C4C23×D17311yescharacteristic
341C8—21no—
342C8—3461no—
343C8—1732no—
344C8C2×C4×D17312yescomplemented
345C22—22no—
346C22—41no—
347C22—41no—
348C22—3462no—
349C22—1732no—
350C22—1732no—
351C22—1732no—
352C22—6928no—
353C22—6921no—
354C22—6921no—
355C22C2×D4×D17311yescharacteristic
356C4—22no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—3462no—
362C4—3461no—
363C4—3461no—
364C4—1732no—
365C4—6921no—
366C4—6921no—
367C4C22×C4×D17311yescharacteristic
368C4#41×D17311yescharacteristic
369C2—42no—
370C2—1734no—
371C2—6922no—
372C2C4×D4×D17311yescharacteristic
373C2AGL(1,ℤ/8)×D17311yescharacteristic
374C2#137×D17311yescharacteristic
subgroupG/H
centerC22C2×D4×D173
commutatorC4×C173C23×C4
FrattiniC2×C4C23×D173
Fitting#440×C173C2
socleC22×C173C22×D4
prime radicalC2×D4×D173C22
cosocleC2×C4×C173C24
hypercenter#440D173
hypocenterC173C2×#440
LCSG ▷ C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D173C2semidirect
4. #26011594C2semidirect
5. #26011593C2semidirect
6. #26011592C2semidirect
7. #26011591C2semidirect
8. #26011590C2semidirect
9. #26011589C2semidirect
10. #26011588C2semidirect
11. #107×D173C2semidirect
12. #103×D173C2semidirect
14. #97×D173C2semidirect
15. #440×C173C2semidirect
22. SD16×D173C4semidirect
25. Q8×Dic173C22semidirect
27. C4×Dic346C22semidirect
29. #19149644C22semidirect
41. #19149613C22semidirect
42. #19149612C22semidirect
43. #19149612C22semidirect
44. #19149604C22semidirect
45. #19149603C22semidirect
46. #19149602C22semidirect
50. #19149590C22semidirect
51. #19149589C22semidirect
52. #19149589C22semidirect
54. C4×Q8×C173C22semidirect
56. #107×C173C22semidirect
57. #103×C173C22semidirect
59. #97×C173C22semidirect
64. Q8×D173C2×C4semidirect
79. #14583815C2×C4semidirect
80. #14583814C2×C4semidirect
81. #14583813C2×C4semidirect
85. C8×D173C2×C4semidirect
105. SD16×C173C2×C4semidirect
121. Dic346C22×C4semidirect
142. #13063436C22×C4semidirect
145. Q8×C173C22×C4semidirect
156. C8×C173C22×C4semidirect
186. D173#440direct (N × H)
187. C173C2×#440semidirect
199. #440D173direct (N × H)
219. C4×Q8C2×D173semidirect
235. #107C2×D173semidirect
239. #103C2×D173semidirect
247. #97C2×D173semidirect
273. SD16C4×D173semidirect
312. Q8C2×C4×D173semidirect
344. C8C2×C4×D173semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1732
C4×Q8×D1732
C4×D4×D1732
#260115942
#260115932
#260115922
#260115912
#260115902
#260115892
#260115882
#107×D1732
#103×D1732
#102×D1732
#97×D1732
#440×C1732
C2×#440173