Finite Group Databasebeta

← #2264×D73 #33244120

Subgroups — #2264×D73 #33244120

Order 18688.

462 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#508×D73C211yesmaximal, characteristic
2C2×Q32×D73C211yesmaximal, characteristic, complemented
3#22612251C211yesmaximal, characteristic, complemented
4#22612250C212yesmaximal, complemented
5#22612249C211yesmaximal, characteristic, complemented
6#22612248C211yesmaximal, characteristic, complemented
7#22612247C212yesmaximal, complemented
8Q64×D73C212yesmaximal, complemented
9SD64×D73C212yesmaximal, complemented
10M64×D73C211yesmaximal, characteristic, complemented
11C73×#2264C211yesmaximal, characteristic, complemented
12#135×D73—21no—
13C2×Q16×D73—21no—
14#17989020C2211yescharacteristic
15#17989019C2211yescharacteristic
16#17989018—21no—
17#17989017—21no—
18#17989016C2211yescharacteristic
19C2×Dic584C2211yescharacteristic, complemented
20C2×#14556537—21no—
21Q32×D73—21no—
22Q32×D73—21no—
23Q32×D73C2212yes—
24Q32×D73C2211yescharacteristic
25Q32×D73C2212yescomplemented
26SD32×D73—21no—
27D16×D73C2211yescharacteristic
28C2×C16×D73C2211yescharacteristic
29Dic1168C2212yescomplemented
30#17988427C2212yescomplemented
31#17988427C2212yescomplemented
32#17988426C2212yescomplemented
33#17988425C2212yescomplemented
34#17988424C2212yescomplemented
35#17988421C2211yescharacteristic, complemented
36#17988420C2212yescomplemented
37C32×D73C2212yes—
38#508×C73C2211yescharacteristic
39C2×Q32×C73C2211yescharacteristic, complemented
40Q64×C73C2212yescomplemented
41SD64×C73C2212yescomplemented
42M64×C73C2211yescharacteristic, complemented
43#41×D73—41no—
44C2×Q8×D73—41no—
45#14556614—21no—
46#14556613—21no—
47#14556612—41no—
48#14556611—41no—
49#14556610—21no—
50C2×Dic292—21no—
51C2×#11924018—41no—
52Q16×D73—21no—
53Q16×D73—22no—
54Q16×D73—22no—
55Q16×D73—41no—
56Q16×D73—41no—
57SD16×D73—41no—
58D8×D73—21no—
59C2×C8×D73D411yescharacteristic
60Dic584—21no—
61Dic584C2312yes—
62Dic584C2311yescharacteristic
63#14556537—22no—
64#14556537—22no—
65#14556537—21no—
66#14556536—21no—
67#14556535—21no—
68#14556534—21no—
69D1168C2311yescharacteristic
70#14556532—21no—
71C2×#11924003D411yescharacteristic
72C16×D73D411yescharacteristic
73C16×D73D411yescharacteristic
74C16×D73C2311yescharacteristic
75C16×D73C2311yescharacteristic
76#14556497C2312yes—
77#135×C73—21no—
78C2×Q16×C73—21no—
79Q32×C73—21no—
80Q32×C73C2312yes—
81Q32×C73C2311yescharacteristic
82SD32×C73—21no—
83D16×C73C2311yescharacteristic
84C2×C16×C73C2311yescharacteristic
85C32×C73C2312yes—
86#11924029—41no—
87#11924028—41no—
88#11924028—81no—
89#11924027—41no—
90#11924027—81no—
91C2×Dic146—41no—
92C2×Dic146—81no—
93Q8×D73—41no—
94Q8×D73—42no—
95Q8×D73—42no—
96Q8×D73—81no—
97Q8×D73—81no—
98D4×D73—41no—
99D4×D73—81no—
100C2×C4×D73—81no—
101C2×C4×D73—81no—
102C2×C4×D73D811yescharacteristic
103Dic292—21no—
104Dic292—22no—
105Dic292—41no—
106#11924018—42no—
107#11924018—42no—
108#11924018—41no—
109#11924017—41no—
110#11924016—41no—
111#11924015—41no—
112D584—21no—
113#11924013—41no—
114C2×#10596831D811yescharacteristic
115C8×D73D811yescharacteristic
116C8×D73D811yescharacteristic
117C8×D73C2×D411yescharacteristic
118C8×D73C2×D411yescharacteristic
119#11924003C2×D411yescharacteristic
120#11924003C2×D411yescharacteristic
121#41×C73—41no—
122C2×Q8×C73—41no—
123Q16×C73—21no—
124Q16×C73—22no—
125Q16×C73—41no—
126SD16×C73—41no—
127D8×C73—21no—
128C2×C8×C73C2×D411yescharacteristic
129C16×C73C2×D411yescharacteristic
130C16×C73C2411yescharacteristic
131C22×D73—81no—
132C22×D73D1611yescharacteristic
133Q8×C73—41no—
134Q8×C73—42no—
135Q8×C73—81no—
136D4×C73—41no—
137D4×C73—81no—
138C2×C4×C73—81no—
139C2×C4×C73—81no—
140C2×C4×C73C2×D811yescharacteristic
141C22⋊D73—81no—
142C22⋊D73—81no—
143C22⋊D73—81no—
144C2×Dic73—81no—
145C2×Dic73—81no—
146C2×Dic73D1611yescharacteristic
147D292—41no—
148D292—81no—
149C4×D73—81no—
150C4×D73—82no—
151C4×D73—82no—
152C4×D73—81no—
153C4×D73—81no—
154C4×D73D1611yescharacteristic
155C4×D73D1611yescharacteristic
156C4×D73C2×D811yescharacteristic
157C4×D73C2×D811yescharacteristic
158Dic146—41no—
159Dic146—42no—
160Dic146—81no—
161Dic146—82no—
162Dic146—82no—
163Dic146—81no—
164C8×C73C2×D811yescharacteristic
165C8×C73C22×D411yescharacteristic
166#10596831C2×D811yescharacteristic
167#10596831C2×D811yescharacteristic
168C22×C73—81no—
169C22×C73C2×D1611yescharacteristic
170C2×D73—22no—
171C2×D73—81no—
172C2×D73—162no—
173C2×D73C2×D1611yescharacteristic
174C2×D73C2×D1611yescharacteristic
175C4×C73—82no—
176C4×C73—81no—
177C4×C73C2×D1611yescharacteristic
178C4×C73C22×D811yescharacteristic
179Dic73—82no—
180Dic73—81no—
181Dic73C2×D1611yescharacteristic
182Dic73C2×D1611yescharacteristic
183C2×#2264—731nomaximal, Sylow
184C2×C73—21no—
185C2×C73—161no—
186C2×C73C22×D1611yescharacteristic
187D73—21no—
188D73—161no—
189D73#226412yesdirect product factor
190C2×#508—731no—
191C22×Q32—731no—
192#2264—731no—
193#2264—731no—
194#2264—732no—
195#2264—732no—
196#2264—731no—
197#2264D7311yescharacteristic, direct product factor
198C2×Q64—732no—
199C2×SD64—732no—
200C2×M64—731no—
201C73C2×#226411yescharacteristic, complemented, Sylow
202C2×#135—1461no—
203C22×Q16—1461no—
204#508—731no—
205#508—731no—
206#508—731no—
207#508—1461no—
208#508—1461no—
209#508C2×D7311yescharacteristic
210C2×Q32—732no—
211C2×Q32—732no—
212C2×Q32—731no—
213C2×Q32—731no—
214C2×Q32—1461no—
215C2×Q32—1461no—
216C2×Q32—1461no—
217C2×Q32C2×D7311yescharacteristic, complemented
218C2×SD32—1461no—
219C2×D16—731no—
220C22×C16—731no—
221Q64—732no—
222Q64—732no—
223Q64—732no—
224Q64C2×D7312yescomplemented
225SD64—732no—
226SD64—732no—
227SD64—732no—
228SD64C2×D7312yescomplemented
229M64—731no—
230M64—732no—
231M64C2×D7311yescharacteristic, complemented
232C2×C32—732no—
233C2×#41—2921no—
234C22×Q8—2921no—
235#135—21no—
236#135—2921no—
237#135—2921no—
238#135—1461no—
239#135—1461no—
240#135—1461no—
241C2×Q16—21no—
242C2×Q16—2921no—
243C2×Q16—2921no—
244C2×Q16—2921no—
245C2×Q16—1462no—
246C2×Q16—1462no—
247C2×Q16—1461no—
248C2×Q16—1461no—
249C2×SD16—2921no—
250C2×D8—1461no—
251C22×C8—731no—
252Q32—21no—
253Q32—732no—
254Q32—731no—
255Q32—1462no—
256Q32—1462no—
257Q32—1461no—
258Q32—1461no—
259Q32C22×D7312yes—
260Q32C22×D7311yescharacteristic
261SD32—21no—
262SD32—1461no—
263SD32—1461no—
264SD32—1461no—
265D16—731no—
266D16—1461no—
267D16C22×D7311yescharacteristic
268C2×C16—731no—
269C2×C16—731no—
270C2×C16—731no—
271C2×C16—731no—
272C2×C16—731no—
273C2×C16C22×D7311yescharacteristic
274C32—732no—
275C32C22×D7312yes—
276#41—41no—
277#41—2921no—
278#41—2921no—
279#41—2921no—
280#41—5841no—
281#41—5841no—
282C2×Q8—41no—
283C2×Q8—2921no—
284C2×Q8—2922no—
285C2×Q8—2922no—
286C2×Q8—2921no—
287C2×Q8—5841no—
288C2×Q8—5841no—
289C2×Q8—5841no—
290C2×D4—2921no—
291C2×D4—5841no—
292C22×C4—5841no—
293C22×C4—5841no—
294C22×C4—731no—
295Q16—21no—
296Q16—22no—
297Q16—41no—
298Q16—2922no—
299Q16—2922no—
300Q16—2921no—
301Q16—2921no—
302Q16—1461no—
303Q16—1462no—
304SD16—41no—
305SD16—2921no—
306SD16—2921no—
307SD16—2921no—
308D8—21no—
309D8—2921no—
310D8—1461no—
311C2×C8—731no—
312C2×C8—731no—
313C2×C8—731no—
314C2×C8—731no—
315C2×C8—731no—
316C2×C8D4×D7311yescharacteristic
317C16—731no—
318C16—731no—
319C16D4×D7311yescharacteristic
320C16C23×D7311yescharacteristic
321C23—5841no—
322C23—731no—
323Q8—41no—
324Q8—42no—
325Q8—81no—
326Q8—2921no—
327Q8—2922no—
328Q8—5842no—
329Q8—5842no—
330Q8—5841no—
331Q8—5841no—
332D4—41no—
333D4—81no—
334D4—2921no—
335D4—5841no—
336D4—5841no—
337D4—5841no—
338D4—5841no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—5841no—
342C2×C4—5842no—
343C2×C4—5842no—
344C2×C4—5841no—
345C2×C4—5841no—
346C2×C4—5841no—
347C2×C4—5841no—
348C2×C4—731no—
349C2×C4—731no—
350C2×C4—731no—
351C2×C4—731no—
352C2×C4—731no—
353C2×C4D8×D7311yescharacteristic
354C8—731no—
355C8—731no—
356C8D8×D7311yescharacteristic
357C8C2×D4×D7311yescharacteristic
358C22—81no—
359C22—5841no—
360C22—731no—
361C22—731no—
362C22—11682no—
363C22—1462no—
364C22D16×D7311yescharacteristic
365C4—81no—
366C4—82no—
367C4—5841no—
368C4—5842no—
369C4—731no—
370C4—731no—
371C4D16×D7311yescharacteristic
372C4C2×D8×D7311yescharacteristic
373C2—21no—
374C2—161no—
375C2—732no—
376C2—11681no—
377C2—1461no—
378C2C2×D16×D7311yescharacteristic
subgroupG/H
centerC2C2×D16×D73
commutator, cosocleC16×C73C24
FrattiniC16C23×D73
FittingC73×#2264C2
socleC2×C73C22×D16
prime radical#508×D73C2
hypercenter#2264D73
hypocenterC73C2×#2264
LCSG ▷ C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2264

Complements

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

NH ≅ G/Ntype
2. C2×Q32×D73C2semidirect
3. #22612251C2semidirect
4. #22612250C2semidirect
5. #22612249C2semidirect
6. #22612248C2semidirect
7. #22612247C2semidirect
8. Q64×D73C2semidirect
9. SD64×D73C2semidirect
10. M64×D73C2semidirect
11. C73×#2264C2semidirect
19. C2×Dic584C22semidirect
25. Q32×D73C22semidirect
29. Dic1168C22semidirect
30. #17988427C22semidirect
31. #17988427C22semidirect
32. #17988426C22semidirect
33. #17988425C22semidirect
34. #17988424C22semidirect
35. #17988421C22semidirect
36. #17988420C22semidirect
39. C2×Q32×C73C22semidirect
40. Q64×C73C22semidirect
41. SD64×C73C22semidirect
42. M64×C73C22semidirect
189. D73#2264direct (N × H)
197. #2264D73direct (N × H)
201. C73C2×#2264semidirect
217. C2×Q32C2×D73semidirect
224. Q64C2×D73semidirect
228. SD64C2×D73semidirect
231. M64C2×D73semidirect

Maximal subgroups

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

subgroupindex
#508×D732
C2×Q32×D732
#226122512
#226122502
#226122492
#226122482
#226122472
Q64×D732
SD64×D732
M64×D732
C73×#22642
C2×#226473