Finite Group Databasebeta

← #463×D173 #36362983

Subgroups — #463×D173 #36362983

Order 22144.

564 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D173C211yesmaximal, characteristic, complemented
2C2×D8×D173C211yesmaximal, characteristic
3#124×D173C211yesmaximal, characteristic, complemented
4C4×D4×D173C211yesmaximal, characteristic, complemented
5#26011709C211yesmaximal, characteristic, complemented
6#26011708C211yesmaximal, characteristic, complemented
7#26011707C211yesmaximal, characteristic, complemented
8#26011706C211yesmaximal, characteristic, complemented
9#26011705C211yesmaximal, characteristic, complemented
10#26011704C211yesmaximal, characteristic, complemented
11#26011703C211yesmaximal, characteristic, complemented
12C4⋊C8×D173C211yesmaximal, characteristic, complemented
13#103×D173C211yesmaximal, characteristic, complemented
14#102×D173C211yesmaximal, characteristic, complemented
15#463×C173C211yesmaximal, characteristic, complemented
16C2×Q8×D173C2211yescharacteristic
17C2×D4×D173C2211yescharacteristic
18C2×D4×D173C2211yescharacteristic
19C22×C4×D173—21no—
20C2×#14583815C2211yescharacteristic, complemented
21C2×#14583814C2211yescharacteristic, complemented
22C2×#14583813C2211yescharacteristic, complemented
23SD16×D173—24no—
24C2×D1384C2211yescharacteristic
25C2×#14583811C2211yescharacteristic
26C2×#14583811C2211yescharacteristic
27D8×D173—24no—
28C2×C8×D173C2211yescharacteristic
29C2×C8×D173C2211yescharacteristic
30#19149668C2211yescharacteristic, complemented
31#19149667C2211yescharacteristic, complemented
32#19149666C2211yescharacteristic, complemented
33#19149665—21no—
34#19149665—21no—
35C4×D692C2211yescharacteristic, complemented
36D4×Dic173C2211yescharacteristic, complemented
37#19149641C2211yescharacteristic, complemented
38C4×C22⋊D173—21no—
39#19149639—21no—
40C4⋊C4×D173C2211yescharacteristic
41C22⋊C4×D173—21no—
42C22⋊C4×D173—21no—
43C22⋊C4×D173—21no—
44C42×D173C2211yescharacteristic
45C4⋊#13063436C2211yescharacteristic, complemented
46#19149608C2211yescharacteristic, complemented
47#19149608C2211yescharacteristic, complemented
48#19149604C2211yescharacteristic, complemented
49#19149603C2211yescharacteristic, complemented
50#19149602C2211yescharacteristic, complemented
51#19149601C2211yescharacteristic, complemented
52#19149600C2211yescharacteristic, complemented
53#19149599C2211yescharacteristic, complemented
54C2×SD16×C173C2211yescharacteristic, complemented
55C2×D8×C173C2211yescharacteristic
56#124×C173C2211yescharacteristic, complemented
57C4×D4×C173C2211yescharacteristic, complemented
58C4⋊C8×C173C2211yescharacteristic, complemented
59#103×C173C2211yescharacteristic, complemented
60#102×C173C2211yescharacteristic, complemented
61C23×D173—21no—
62C23×D173—21no—
63C2×Dic346—21no—
64C2×Dic346C2311yescharacteristic
65Q8×D173—22no—
66Q8×D173—22no—
67C2×D692C2311yescharacteristic
68C2×D692C2311yescharacteristic
69C2×C22⋊D173—21no—
70C2×C22⋊D173—21no—
71D4×D173—22no—
72D4×D173—22no—
73D4×D173—22no—
74D4×D173D414yes—
75C22×Dic173—21no—
76C2×C4×D173—21no—
77C2×C4×D173—21no—
78C2×C4×D173—21no—
79C2×C4×D173—21no—
80C2×C4×D173—44no—
81C2×C4×D173D411yescharacteristic
82C2×C4×D173D411yescharacteristic
83C2×C4×D173C2311yescharacteristic
84#14583815—22no—
85#14583814—22no—
86#14583813—22no—
87D1384—22no—
88#14583811—22no—
89#14583811—22no—
90C2×#13063436C2311yescharacteristic
91C2×#13063436C2311yescharacteristic
92C8×D173—22no—
93C8×D173—22no—
94C4⋊Dic173C2311yescharacteristic
95#14583805—21no—
96C22⋊Dic173—21no—
97C22⋊Dic173—21no—
98C22⋊Dic173—21no—
99#14583803—21no—
100#14583803—21no—
101#14583803—21no—
102#14583803—21no—
103#14583803—21no—
104#14583803—21no—
105C4×Dic173D411yescharacteristic
106C4×Dic173D411yescharacteristic
107C4×Dic173C2311yescharacteristic
108C2×Q8×C173C2311yescharacteristic
109C2×D4×C173C2311yescharacteristic
110C2×D4×C173C2311yescharacteristic
111C22×C4×C173—21no—
112SD16×C173—22no—
113D8×C173—22no—
114C2×C8×C173C2311yescharacteristic
115C2×C8×C173C2311yescharacteristic
116C4⋊C4×C173C2311yescharacteristic
117C22⋊C4×C173—21no—
118C22⋊C4×C173—21no—
119C22⋊C4×C173—21no—
120C42×C173C2311yescharacteristic
121C22×D173—21no—
122C22×D173—24no—
123C22×D173—21no—
124C22×D173—42no—
125C22×D173—42no—
126C22×D173—42no—
127C22×D173—42no—
128C22×D173—42no—
129C22×D173C2×D411yescharacteristic
130Dic346—21no—
131Dic346—21no—
132Dic346—42no—
133D692—21no—
134D692—21no—
135D692—21no—
136D692C2×D412yes—
137C22⋊D173—24no—
138C22⋊D173—42no—
139C2×Dic173—21no—
140C2×Dic173—21no—
141C2×Dic173—42no—
142C2×Dic173C2×D411yescharacteristic
143C2×Dic173C2×D411yescharacteristic
144C2×Dic173C2×D411yescharacteristic
145C4×D173—22no—
146C4×D173—22no—
147C4×D173—42no—
148C4×D173—42no—
149C4×D173—42no—
150C4×D173—42no—
151C4×D173C2×D412yes—
152C4×D173#4112yes—
153#13063436—21no—
154#13063436—21no—
155C23×C173—21no—
156C23×C173—21no—
157Q8×C173—21no—
158Q8×C173—21no—
159D4×C173—21no—
160D4×C173—21no—
161D4×C173—21no—
162D4×C173C2×D412yes—
163C2×C4×C173—21no—
164C2×C4×C173—21no—
165C2×C4×C173—42no—
166C2×C4×C173C2×D411yescharacteristic
167C2×C4×C173C2×D411yescharacteristic
168C2×C4×C173C2411yescharacteristic
169C8×C173—21no—
170C8×C173—21no—
171C22×C173—22no—
172C22×C173—41no—
173C22×C173—41no—
174C22×C173—41no—
175C22×C173—41no—
176C22×C173—41no—
177C22×C173C22×D411yescharacteristic
178C2×D173—22no—
179C2×D173—41no—
180C2×D173—41no—
181C2×D173—48no—
182C2×D173—41no—
183C2×D173—41no—
184C2×D173—41no—
185C2×D173—84no—
186C2×D173#12112yes—
187C2×D173#13512yes—
188C2×D173AGL(1,ℤ/8)12yes—
189C4×C173—21no—
190C4×C173—21no—
191C4×C173—41no—
192C4×C173—41no—
193C4×C173C22×D411yescharacteristic
194C4×C173C2×#4111yescharacteristic
195Dic173—21no—
196Dic173—21no—
197Dic173—41no—
198Dic173—41no—
199Dic173#12112yes—
200C2×C173—42no—
201C2×C173—81no—
202C2×C173C2×#12111yescharacteristic
203C2×C173C2×#13511yescharacteristic
204C2×C173C2×AGL(1,ℤ/8)11yescharacteristic
205D173—42no—
206D173—81no—
207D173#46314yesdirect product factor
208C173C2×#46311yescharacteristic, complemented, Sylow
209C2×#463—1731nomaximal, Sylow
210C22×SD16—1731no—
211C22×D8—1731no—
212C2×#124—1731no—
213C2×C4×D4—1731no—
214#463—1731no—
215#463—1731no—
216#463—1731no—
217#463—1731no—
218#463—1731no—
219#463—1731no—
220#463—1731no—
221#463D17311yescharacteristic, direct product factor
222C2×C4⋊C8—1731no—
223C2×#103—1731no—
224C2×#102—1731no—
225C22×Q8—1731no—
226C22×D4—1731no—
227C22×D4—1731no—
228C23×C4—3461no—
229C2×SD16—3464no—
230C2×SD16—1731no—
231C2×SD16—1731no—
232C2×SD16—1731no—
233C2×SD16C2×D17311yescharacteristic, complemented
234C2×D8—3464no—
235C2×D8—1731no—
236C2×D8—1731no—
237C2×D8—1731no—
238C2×D8C2×D17311yescharacteristic
239C22×C8—1731no—
240C22×C8—1731no—
241#124—3461no—
242#124—3461no—
243#124—1731no—
244#124—1731no—
245#124—1731no—
246#124C2×D17311yescharacteristic, complemented
247C4×D4—3461no—
248C4×D4—3461no—
249C4×D4—1731no—
250C4×D4—1731no—
251C4×D4—1731no—
252C4×D4C2×D17311yescharacteristic, complemented
253C2×C4⋊C4—1731no—
254C2×C22⋊C4—3461no—
255C2×C22⋊C4—3461no—
256C2×C22⋊C4—3461no—
257C2×C42—1731no—
258C4⋊C8—1731no—
259C4⋊C8—1731no—
260C4⋊C8—1731no—
261C4⋊C8C2×D17311yescharacteristic, complemented
262#103—1731no—
263#103—1731no—
264#103—1731no—
265#103C2×D17311yescharacteristic, complemented
266#102—1731no—
267#102—1731no—
268#102—1731no—
269#102C2×D17311yescharacteristic, complemented
270C24—3461no—
271C24—3461no—
272C2×Q8—3461no—
273C2×Q8—3462no—
274C2×Q8—3462no—
275C2×Q8—1731no—
276C2×Q8C22×D17311yescharacteristic
277C2×D4—3462no—
278C2×D4—3462no—
279C2×D4—3462no—
280C2×D4—3461no—
281C2×D4—3461no—
282C2×D4—1734no—
283C2×D4—1731no—
284C2×D4—1731no—
285C2×D4C22×D17311yescharacteristic
286C2×D4C22×D17311yescharacteristic
287C22×C4—21no—
288C22×C4—3461no—
289C22×C4—3461no—
290C22×C4—3461no—
291C22×C4—3461no—
292C22×C4—3461no—
293C22×C4—1731no—
294C22×C4—1731no—
295C22×C4—1731no—
296C22×C4—6924no—
297SD16—22no—
298SD16—3462no—
299SD16—3462no—
300SD16—3462no—
301D8—22no—
302D8—3462no—
303D8—3462no—
304D8—3462no—
305C2×C8—3462no—
306C2×C8—3462no—
307C2×C8—1731no—
308C2×C8—1731no—
309C2×C8C22×D17311yescharacteristic
310C2×C8C22×D17311yescharacteristic
311C4⋊C4—3461no—
312C4⋊C4—1731no—
313C4⋊C4C22×D17311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—3461no—
318C22⋊C4—3461no—
319C22⋊C4—3461no—
320C22⋊C4—3461no—
321C22⋊C4—3461no—
322C22⋊C4—3461no—
323C22⋊C4—3461no—
324C22⋊C4—3461no—
325C22⋊C4—3461no—
326C42—1731no—
327C42—1731no—
328C42—1731no—
329C42C22×D17311yescharacteristic
330C23—21no—
331C23—21no—
332C23—3464no—
333C23—3461no—
334C23—3461no—
335C23—1731no—
336C23—6922no—
337C23—6922no—
338C23—6922no—
339C23—6922no—
340C23—6922no—
341Q8—21no—
342Q8—21no—
343Q8—3461no—
344Q8—3461no—
345Q8—6922no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—3464no—
350D4—3461no—
351D4—3461no—
352D4—3461no—
353D4—1732no—
354D4—6922no—
355D4D4×D17312yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—3462no—
360C2×C4—3462no—
361C2×C4—3461no—
362C2×C4—3461no—
363C2×C4—1731no—
364C2×C4—1731no—
365C2×C4—1731no—
366C2×C4—1732no—
367C2×C4—1732no—
368C2×C4—6922no—
369C2×C4—6922no—
370C2×C4—6922no—
371C2×C4—6922no—
372C2×C4—6922no—
373C2×C4D4×D17311yescharacteristic
374C2×C4D4×D17311yescharacteristic
375C2×C4C23×D17311yescharacteristic
376C8—21no—
377C8—21no—
378C8—3461no—
379C8—3461no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—3462no—
387C22—13844no—
388C22—1732no—
389C22—1732no—
390C22—1732no—
391C22—6928no—
392C22—6921no—
393C22—6921no—
394C22—6921no—
395C22—6921no—
396C22—6921no—
397C22C2×D4×D17311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—3461no—
403C4—3461no—
404C4—1732no—
405C4—6921no—
406C4—6921no—
407C4C2×D4×D17311yescharacteristic
408C4#41×D17311yescharacteristic
409C2—42no—
410C2—81no—
411C2—13841no—
412C2—1734no—
413C2—6922no—
414C2#121×D17311yescharacteristic
415C2#135×D17311yescharacteristic
416C2AGL(1,ℤ/8)×D17311yescharacteristic
subgroupG/H
centerC22C2×D4×D173
commutator, cosocleC2×C4×C173C24
FrattiniC2×C4C23×D173
Fitting#463×C173C2
socleC22×C173C22×D4
prime radicalC2×D8×D173C2
hypercenter#463D173
hypocenterC173C2×#463
LCSG ▷ C2×C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D173C2semidirect
3. #124×D173C2semidirect
4. C4×D4×D173C2semidirect
5. #26011709C2semidirect
6. #26011708C2semidirect
7. #26011707C2semidirect
8. #26011706C2semidirect
9. #26011705C2semidirect
10. #26011704C2semidirect
11. #26011703C2semidirect
12. C4⋊C8×D173C2semidirect
13. #103×D173C2semidirect
14. #102×D173C2semidirect
15. #463×C173C2semidirect
20. C2×#14583815C22semidirect
21. C2×#14583814C22semidirect
22. C2×#14583813C22semidirect
30. #19149668C22semidirect
31. #19149667C22semidirect
32. #19149666C22semidirect
35. C4×D692C22semidirect
36. D4×Dic173C22semidirect
37. #19149641C22semidirect
45. C4⋊#13063436C22semidirect
46. #19149608C22semidirect
47. #19149608C22semidirect
48. #19149604C22semidirect
49. #19149603C22semidirect
50. #19149602C22semidirect
51. #19149601C22semidirect
52. #19149600C22semidirect
53. #19149599C22semidirect
54. C2×SD16×C173C22semidirect
56. #124×C173C22semidirect
57. C4×D4×C173C22semidirect
58. C4⋊C8×C173C22semidirect
59. #103×C173C22semidirect
60. #102×C173C22semidirect
207. D173#463direct (N × H)
208. C173C2×#463semidirect
221. #463D173direct (N × H)
233. C2×SD16C2×D173semidirect
246. #124C2×D173semidirect
252. C4×D4C2×D173semidirect
261. C4⋊C8C2×D173semidirect
265. #103C2×D173semidirect
269. #102C2×D173semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1732
C2×D8×D1732
#124×D1732
C4×D4×D1732
#260117092
#260117082
#260117072
#260117062
#260117052
#260117042
#260117032
C4⋊C8×D1732
#103×D1732
#102×D1732
#463×C1732
C2×#463173