Finite Group Databasebeta

← #16807458

Subgroups — #16807458

Order 3328.

3598 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×#261C212yesmaximal
2#13131276C214yesmaximal, complemented
3#13131275C2112yesmaximal, complemented
4#117×#261C216yesmaximal, complemented
5C4×#88237C213yesmaximal, complemented
6C2×#11719057C213yesmaximal, complemented
7C4×#41×D13C211yesmaximal, characteristic
8C2×#41×D13C2211yescharacteristic
9#41×#261C4132yescomplemented
10C2×Q8×#261C2214yes—
11C2×D4×#261C22112yes—
12C2×#88237C2216yes—
13C22×C4×#261C2216yes—
14C4×C13×#41C411yescharacteristic, complemented
15#41×Dic13C411yescharacteristic, complemented
16C4×#6131C412yescomplemented
17C4×Q8×D13C2212yes—
18C4×D4×D13C2216yes—
19C4×#6129C416yescomplemented
20#11719227C413yescomplemented
21D13×#117C2213yes—
22C4×#6127C413yescomplemented
23C2×C42×D13C2213yes—
24C4×C22⋊#261C22112yes—
25C2×(C2×#261)⋊C4C22112yes—
26C4⋊C4×#261C22124yes—
27C22⋊C4×#261C22124yes—
28C4×C4⋊#261C22112yes—
29#11719057C2213yes—
30#11719057C2216yes—
31#11719057C22112yes—
32#11719057C2211yescharacteristic
33C42×#261C2216yes—
34C23×#261C23112yes—
35C2×C13×#41C2×C411yescharacteristic
36#41×D13C2×C4116yes—
37C2×#6131C2×C411yescharacteristic
38C2×Q8×D13C2311yescharacteristic
39C2×#6129C2×C413yes—
40C2×D4×D13C2313yes—
41C2×#6127C2×C413yes—
42C22×C4×D13C2316yes—
43C22×C4×D13C2313yes—
44C2×C22⋊#261C23112yes—
45Q8×#261C2×C4132yescomplemented
46D4×#261C2×C4196yescomplemented
47#88237C2×C4148yescomplemented
48C2×C4⋊#261C23112yes—
49C2×C4×#261C2×C4148yescomplemented
50C2×C4×#261C23124yes—
51C2×C4×#261C2316yes—
52C2×C4×#261C2312yes—
53C2×C4×#261C23112yes—
54C4×Q8×C13C2×C412yescomplemented
55C4×D4×C13C2×C416yescomplemented
56C13×#117C2×C413yescomplemented
57C2×C42×C13C2×C413yescomplemented
58Q8×Dic13C2×C412yescomplemented
59D4×Dic13C2×C416yescomplemented
60C4×C22⋊D13C2×C4112yescomplemented
61#88180C2×C413yescomplemented
62C2×C4×Dic13C2×C413yescomplemented
63C2×C4×Dic13C2×C416yescomplemented
64#88147C2×C416yescomplemented
65#88146C2×C416yescomplemented
66C4⋊C4×D13C2316yes—
67#88141C2×C416yescomplemented
68#88135C2×C4112yescomplemented
69C22⋊C4×D13C2316yes—
70#88131C2×C416yescomplemented
71C4×D52C2×C416yescomplemented
72#88126C2×C416yescomplemented
73C42×D13C2×C413yescomplemented
74C42×D13C2×C413yescomplemented
75C42×D13C2×C416yescomplemented
76C42×D13C2311yescharacteristic
77C42×D13C2313yes—
78C42×D13C2316yes—
79C4×Dic26C2×C416yescomplemented
80(C2×#261)⋊C4C2314yes—
81(C2×#261)⋊C4C23112yes—
82(C2×#261)⋊C4C23124yes—
83#33999—131nomaximal, Sylow
84C23×D13C2413yes—
85C22×#261—424no—
86C22×#261C22×C4148yes—
87C22×#261C2414yes—
88C22×#261C24112yes—
89C13×#41C4218yescomplemented
90C2×Q8×C13C22×C411yescharacteristic
91C2×D4×C13C22×C413yes—
92C22×C4×C13C22×C416yes—
93C22×C4×C13C22×C413yes—
94C2×C22⋊D13C22×C416yes—
95C22×Dic13C22×C416yes—
96C22×Dic13C22×C413yes—
97#6131C4218yescomplemented
98Q8×D13C22×C418yes—
99#6129C42124yescomplemented
100D4×D13C22×C4124yes—
101#6127C42124yescomplemented
102C2×D52C22×C413yes—
103C2×C4×D13—412no—
104C2×C4×D13C22×C416yes—
105C2×C4×D13C22×C416yes—
106C2×C4×D13C22×C413yes—
107C2×C4×D13C22×C413yes—
108C2×C4×D13C22×C4124yes—
109C2×C4×D13C2412yes—
110C2×C4×D13C2416yes—
111C2×C4×D13C2411yescharacteristic
112C2×C4×D13C2413yes—
113C2×Dic26C22×C413yes—
114C22⋊#261C22×C4148yes—
115C4⋊#261C22×C4148yes—
116C4×#261—424no—
117C4×#261C22×C418yes—
118C4×#261C22×C4124yes—
119C4×#261C22×C4148yes—
120C13×C4⋊C4C22×C416yes—
121C13×C22⋊C4C22×C416yes—
122C42×C13C22×C416yes—
123C42×C13C22×C411yescharacteristic
124C42×C13C22×C413yes—
125C22⋊Dic13C22×C416yes—
126#6103C22×C4112yes—
127C4⋊Dic13C22×C416yes—
128#6101C22×C4112yes—
129C4×Dic13C22×C416yes—
130C4×Dic13C22×C412yes—
131C4×Dic13C22×C411yescharacteristic
132C4×Dic13C22×C413yes—
133C4×Dic13C22×C416yes—
134C4×Dic13C22×C416yes—
135C4×Dic13C22×C416yes—
136C2×C4×#41—132no—
137C2×C4×#41—131no—
138#2276—134no—
139#2275—1312no—
140C4×#117—133no—
141C4×#117—136no—
142C2×#376—133no—
143C23×C13C23×C413yes—
144C22×D13—212no—
145C22×D13C23×C4112yes—
146C22×D13C23×C413yes—
147C22×D13C2511yescharacteristic
148C2×#261—224no—
149C2×#261—28no—
150C2×#261—448no—
151C2×#261C23×C418yes—
152C2×#261C23×C4124yes—
153Q8×C13C2×C4214yes—
154D4×C13C2×C42112yes—
155C2×C4×C13—46no—
156C2×C4×C13C2×C42112yes—
157C2×C4×C13C23×C412yes—
158C2×C4×C13C23×C416yes—
159C2×C4×C13C23×C413yes—
160C2×C4×C13C23×C411yescharacteristic
161C22⋊D13C2×C42124yes—
162C2×Dic13—46no—
163C2×Dic13C2×C42112yes—
164C2×Dic13C23×C412yes—
165C2×Dic13C23×C416yes—
166C2×Dic13C23×C411yescharacteristic
167C2×Dic13C23×C413yes—
168D52C2×C42112yes—
169C4×D13—212no—
170C4×D13—24no—
171C4×D13—46no—
172C4×D13—46no—
173C4×D13C2×C42112yes—
174C4×D13C2×C42112yes—
175C4×D13C23×C414yes—
176C4×D13C23×C4112yes—
177Dic26C2×C42112yes—
178C22×#41—131no—
179C4×#41—1332no—
180C4×#41—131no—
181C4×#41—132no—
182C4×#41—136no—
183C4×#41—133no—
184C4×#41—133no—
185C4×#41#26111yescharacteristic, complemented
186C2×C4×Q8—134no—
187C2×C4×Q8—132no—
188C2×C4×D4—1312no—
189C2×C4×D4—136no—
190C2×#117—136no—
191C2×#117—133no—
192C22×C42—136no—
193C22×C42—133no—
194C4×C4⋊C4—1312no—
195C4×C4⋊C4—1324no—
196C4×C22⋊C4—1324no—
197C4×C22⋊C4—1312no—
198#376—131no—
199#376—133no—
200#376—136no—
201#376—1312no—
202C2×#95—1312no—
203C43—136no—
204C22×C13—26no—
205C22×C13C22×C4216yes—
206C22×C13C24×C411yescharacteristic
207C2×D13—26no—
208C2×D13—224no—
209C2×D13C22×C4216yes—
210C2×D13C24×C412yes—
211C2×D13#58514yes—
212#261—28no—
213#261—224no—
214C4×C13—22no—
215C4×C13—26no—
216C4×C13C22×C4216yes—
217C4×C13C22×C4212yes—
218Dic13—22no—
219Dic13—26no—
220Dic13C22×C4216yes—
221Dic13C22×C4212yes—
222C2×#41—1316no—
223C2×#41—131no—
224C2×#41—133no—
225C2×#41—133no—
226C2×#41C2×#26111yescharacteristic
227C22×Q8—131no—
228C22×D4—133no—
229C23×C4—133no—
230C23×C4—1312no—
231C23×C4—136no—
232C4×Q8—1332no—
233C4×Q8—132no—
234C4×Q8—136no—
235C4×Q8—136no—
236C4×Q8C2×#26112yescomplemented
237C4×D4—1396no—
238C4×D4—136no—
239C4×D4—1312no—
240C4×D4—136no—
241C4×D4—1312no—
242C4×D4—136no—
243C4×D4C2×#26116yescomplemented
244#117—1348no—
245#117—133no—
246#117—136no—
247#117—136no—
248#117—136no—
249#117C2×#26113yescomplemented
250C2×C4⋊C4—1312no—
251C2×C4⋊C4—136no—
252C2×C22⋊C4—1312no—
253C2×C22⋊C4—136no—
254C2×C42—136no—
255C2×C42—1312no—
256C2×C42—1348no—
257C2×C42—132no—
258C2×C42—136no—
259C2×C42—133no—
260C2×C42—133no—
261C2×C42—136no—
262C2×C42—136no—
263C2×C42—133no—
264C2×C42—133no—
265C2×C42—131no—
266C2×C42—1324no—
267C2×C42C2×#26113yescomplemented
268#95—134no—
269#95—1324no—
270#95—1312no—
271C2×C13—26no—
272C2×C13C23×C4211yescharacteristic
273C2×C13#342812yes—
274D13—26no—
275D13#342814yes—
276C24—133no—
277#41—138no—
278#41—1324no—
279#41—1324no—
280#41C4×#26118yescomplemented
281C2×Q8—138no—
282C2×Q8—133no—
283C2×Q8C22×#26111yescharacteristic
284C2×D4—136no—
285C2×D4—1324no—
286C2×D4—133no—
287C2×D4C22×#26113yes—
288C22×C4—133no—
289C22×C4—1324no—
290C22×C4—133no—
291C22×C4—133no—
292C22×C4—131no—
293C22×C4—133no—
294C22×C4—134no—
295C22×C4—1312no—
296C22×C4—1348no—
297C22×C4—136no—
298C22×C4—132no—
299C22×C4—136no—
300C22×C4—136no—
301C22×C4—136no—
302C22×C4—5212no—
303C22×C4—5224no—
304C22×C4C22×#26116yes—
305C22×C4C22×#26113yes—
306C4⋊C4—1348no—
307C4⋊C4—1312no—
308C4⋊C4—136no—
309C4⋊C4C22×#26116yes—
310C22⋊C4—1348no—
311C22⋊C4—136no—
312C22⋊C4—1312no—
313C22⋊C4C22×#26116yes—
314C42—138no—
315C42—1324no—
316C42—1348no—
317C42—132no—
318C42—136no—
319C42—136no—
320C42—136no—
321C42—136no—
322C42—131no—
323C42—133no—
324C42—5224no—
325C42C22×#26116yes—
326C42C22×#26111yescharacteristic
327C42C22×#26113yes—
328C13#3399911yescharacteristic, complemented, Sylow
329C23—131no—
330C23—1312no—
331C23—133no—
332C23—2612no—
333C23C23×#26113yes—
334Q8—1312no—
335Q8C2×C4×#26114yes—
336D4—1324no—
337D4—1312no—
338D4C2×C4×#261112yes—
339C2×C4—46no—
340C2×C4—1312no—
341C2×C4—131no—
342C2×C4—133no—
343C2×C4—134no—
344C2×C4—1312no—
345C2×C4—1312no—
346C2×C4—1312no—
347C2×C4—138no—
348C2×C4—1324no—
349C2×C4—132no—
350C2×C4—136no—
351C2×C4—2612no—
352C2×C4—264no—
353C2×C4—2624no—
354C2×C4—268no—
355C2×C4—526no—
356C2×C4—526no—
357C2×C4—526no—
358C2×C4—5248no—
359C2×C4C2×C4×#261112yes—
360C2×C4C23×#26112yes—
361C2×C4C23×#26116yes—
362C2×C4C23×#26113yes—
363C2×C4C23×#26111yescharacteristic
364C22—26no—
365C22—132no—
366C22—134no—
367C22—136no—
368C22—2624no—
369C22—266no—
370C22C22×C4×#26116yes—
371C22C24×#26111yescharacteristic
372C4—22no—
373C4—26no—
374C4—132no—
375C4—136no—
376C4—2624no—
377C4—268no—
378C4—266no—
379C4—262no—
380C4C22×C4×#26112yes—
381C4C22×C4×#26116yes—
382C2—26no—
383C2—134no—
384C2—266no—
385C2C23×C4×#26111yescharacteristic
386C2#1313181612yes—
subgroupG/H
centerC2×C4C23×#261
commutatorC2×C13C23×C42
FrattiniC22C24×#261
FittingC4×C13×#41C4
socleC22×C13C24×C4
prime radicalC2×#41×D13C22
cosocleC22×D13C25
hypercenterC4×#41#261
hypocenterC13#33999
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. #13131276C2semidirect
3. #13131275C2semidirect
4. #117×#261C2semidirect
5. C4×#88237C2semidirect
6. C2×#11719057C2semidirect
9. #41×#261C4semidirect
14. C4×C13×#41C4semidirect
15. #41×Dic13C4semidirect
16. C4×#6131C4semidirect
19. C4×#6129C4semidirect
20. #11719227C4semidirect
22. C4×#6127C4semidirect
45. Q8×#261C2×C4semidirect
46. D4×#261C2×C4semidirect
47. #88237C2×C4semidirect
49. C2×C4×#261C2×C4semidirect
54. C4×Q8×C13C2×C4semidirect
55. C4×D4×C13C2×C4semidirect
56. C13×#117C2×C4semidirect
57. C2×C42×C13C2×C4semidirect
58. Q8×Dic13C2×C4semidirect
59. D4×Dic13C2×C4semidirect
60. C4×C22⋊D13C2×C4semidirect
61. #88180C2×C4semidirect
62. C2×C4×Dic13C2×C4semidirect
63. C2×C4×Dic13C2×C4semidirect
64. #88147C2×C4semidirect
65. #88146C2×C4semidirect
67. #88141C2×C4semidirect
68. #88135C2×C4semidirect
70. #88131C2×C4semidirect
71. C4×D52C2×C4semidirect
72. #88126C2×C4semidirect
73. C42×D13C2×C4semidirect
74. C42×D13C2×C4semidirect
75. C42×D13C2×C4semidirect
79. C4×Dic26C2×C4semidirect
89. C13×#41C42semidirect
97. #6131C42semidirect
99. #6129C42semidirect
101. #6127C42semidirect
185. C4×#41#261semidirect
236. C4×Q8C2×#261semidirect
243. C4×D4C2×#261semidirect
249. #117C2×#261semidirect
267. C2×C42C2×#261semidirect
280. #41C4×#261semidirect
328. C13#33999semidirect

Maximal subgroups

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

subgroupindex
C2×#41×#2612
#131312762
#131312752
#117×#2612
C4×#882372
C2×#117190572
C4×#41×D132
#3399913