Finite Group Databasebeta

← C4×#11718338 #15784749

Subgroups — C4×#11718338 #15784749

Order 3328.

1966 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718338C211yesmaximal, characteristic
2C2×C4×C4⋊Dic13C213yesmaximal, complemented
3C2×C4×#6103C213yesmaximal
4#13113103C213yesmaximal, complemented
5#13113101C211yesmaximal, characteristic, complemented
6#13113082C213yesmaximal
7C4×C13×#95C211yesmaximal, characteristic, complemented
8C23×C4×D13C2211yescharacteristic
9C22×C42×C13C2213yes—
10C22×#6103C2213yes—
11C22×#6103C2213yes—
12C22×C4⋊Dic13C2213yes—
13C22×C4⋊Dic13C2213yes—
14C22×C4×Dic13C2213yes—
15C2×C13×#95C2213yes—
16C2×C13×#95C2211yescharacteristic
17C2×#88071C2213yes—
18C2×#88071C2213yes—
19C2×#88071C2216yes—
20C4×#6103—212no—
21C4×C4⋊Dic13—212no—
22#11718338C418yesdirect product factor
23C24×D13C2311yescharacteristic
24C23×C4×C13C2313yes—
25C23×C4×C13C2313yes—
26C23×C4×C13C2311yescharacteristic
27C23×Dic13C2313yes—
28C23×Dic13C2311yescharacteristic
29C23×Dic13C2313yes—
30C22×C4×D13—26no—
31C22×C4×D13—26no—
32C22×C4×D13Q814yes—
33C2×C42×C13—212no—
34C2×C42×C13D4112yes—
35C2×#6103—26no—
36C2×#6103—26no—
37C2×#6103—26no—
38C2×#6103—26no—
39C2×#6103—26no—
40C2×#6103C2×C4112yes—
41C2×C4⋊Dic13—26no—
42C2×C4⋊Dic13—26no—
43C2×C4⋊Dic13—26no—
44C2×C4⋊Dic13—212no—
45C2×C4⋊Dic13C2×C4112yescomplemented
46C2×C4×Dic13—212no—
47C2×C4×Dic13—26no—
48C13×#95—26no—
49C13×#95C2×C414yescomplemented
50#88071—212no—
51#88071—26no—
52#88071—26no—
53C4×#399—131nomaximal, Sylow
54C24×C13C2411yescharacteristic
55C23×D13—23no—
56C23×D13—23no—
57C23×D13—23no—
58C23×D13—23no—
59C23×D13C22×C412yes—
60C23×D13C2×Q812yes—
61C23×D13#4112yes—
62C22×C4×C13—26no—
63C22×C4×C13—26no—
64C22×C4×C13—26no—
65C22×C4×C13—23no—
66C22×C4×C13—23no—
67C22×C4×C13—26no—
68C22×C4×C13C22×C416yes—
69C22×C4×C13C2×D416yes—
70C22×C4×C13C2×D416yes—
71C22×C4×C13C2×D416yes—
72C22×C4×C13C2×Q812yes—
73C22×C4×C13#4116yes—
74C22×C4×C13#4116yes—
75C22×Dic13—23no—
76C22×Dic13—26no—
77C22×Dic13—26no—
78C22×Dic13—23no—
79C22×Dic13—23no—
80C22×Dic13—26no—
81C22×Dic13—26no—
82C22×Dic13—23no—
83C22×Dic13—23no—
84C22×Dic13—23no—
85C22×Dic13C22×C416yes—
86C22×Dic13C2×Q812yes—
87C22×Dic13#4116yes—
88C2×C4×D13—224no—
89C2×C4×D13—412no—
90C2×C4×D13—44no—
91C42×C13—224no—
92#6103—224no—
93#6103—224no—
94C4⋊Dic13—224no—
95C4⋊Dic13—224no—
96C4×Dic13—412no—
97C2×#399—131no—
98C2×C4×C4⋊C4—133no—
99C2×C4×C22⋊C4—133no—
100#1445—133no—
101#1444—131no—
102#1439—133no—
103C4×#95D1311yescharacteristic, complemented
104C23×C13C23×C411yescharacteristic
105C23×C13C22×D413yes—
106C23×C13C22×Q811yescharacteristic
107C23×C13C2×#4113yes—
108C23×C13C2×#4111yescharacteristic
109C23×C13C2×#4113yes—
110C23×C13C2×#4113yes—
111C22×D13—26no—
112C22×D13—26no—
113C22×D13—26no—
114C22×D13—26no—
115C22×D13—26no—
116C22×D13—26no—
117C22×D13—43no—
118C22×D13—43no—
119C22×D13—46no—
120C22×D13—41no—
121C22×D13—43no—
122C22×D13C4×Q814yes—
123C2×C4×C13—212no—
124C2×C4×C13—26no—
125C2×C4×C13—26no—
126C2×C4×C13—212no—
127C2×C4×C13—26no—
128C2×C4×C13—26no—
129C2×C4×C13—26no—
130C2×C4×C13—46no—
131C2×C4×C13—46no—
132C2×C4×C13C4×D4112yes—
133C2×C4×C13C22⋊Q8112yes—
134C2×C4×C13#123112yes—
135C2×C4×C13#12714yes—
136C2×Dic13—212no—
137C2×Dic13—26no—
138C2×Dic13—26no—
139C2×Dic13—212no—
140C2×Dic13—26no—
141C2×Dic13—43no—
142C2×Dic13—46no—
143C2×Dic13—43no—
144C2×Dic13—43no—
145C2×Dic13—43no—
146C2×Dic13—41no—
147C2×Dic13—46no—
148C2×Dic13—43no—
149C4×D13—416no—
150C24×C4—131no—
151C22×C4⋊C4—133no—
152C22×C4⋊C4—133no—
153C22×C22⋊C4—133no—
154C22×C22⋊C4—133no—
155C22×C42—133no—
156C22×C42C2×D1313yes—
157#399—138no—
158C4×C4⋊C4—2612no—
159C4×C22⋊C4—2612no—
160C2×#95—136no—
161C2×#95—133no—
162C2×#95—133no—
163C2×#95C2×D1313yes—
164C2×#95C2×D1311yescharacteristic
165C22×C13C2×C4×D413yes—
166C22×C13C2×C4×Q811yescharacteristic
167C22×C13C4×#4113yes—
168C22×C13C2×C22⋊Q813yes—
169C22×C13C2×#12313yes—
170C22×C13#52513yes—
171C22×C13#52513yes—
172C22×C13#52916yes—
173C22×C13#52913yes—
174C22×C13C2×#12711yescharacteristic
175C22×C13#53213yes—
176C22×C13#53313yes—
177C2×D13—212no—
178C2×D13—42no—
179C2×D13—42no—
180C2×D13—46no—
181C2×D13—46no—
182C2×D13—42no—
183C2×D13—46no—
184C4×C13—212no—
185C4×C13—46no—
186C4×C13#39918yescomplemented
187Dic13—46no—
188Dic13—42no—
189Dic13—46no—
190C25—131no—
191C23×C4—133no—
192C23×C4—133no—
193C23×C4—131no—
194C23×C4—134no—
195C23×C4—266no—
196C23×C4—266no—
197C23×C4C22×D1313yes—
198C23×C4C22×D1313yes—
199C23×C4C22×D1311yescharacteristic
200C2×C4⋊C4—1312no—
201C2×C4⋊C4—2612no—
202C2×C4⋊C4—266no—
203C2×C4⋊C4—266no—
204C2×C4⋊C4—266no—
205C2×C22⋊C4—1312no—
206C2×C22⋊C4—266no—
207C2×C22⋊C4—266no—
208C2×C22⋊C4—266no—
209C2×C22⋊C4—266no—
210C2×C22⋊C4—266no—
211C2×C42—212no—
212C2×C42—266no—
213C2×C42—2612no—
214C2×C42D52112yes—
215#95—26no—
216#95—266no—
217#95—266no—
218#95—2612no—
219#95C4×D1314yescomplemented
220C2×C13C4×#12313yes—
221C2×C13C4×C22⋊Q813yes—
222C2×C13C4×#12711yescharacteristic
223C2×C13C2×#39911yescharacteristic
224C2×C13#239513yes—
225C2×C13#239613yes—
226C2×C13#239711yescharacteristic
227D13—44no—
228C24—132no—
229C24—132no—
230C24—132no—
231C24—263no—
232C24—263no—
233C24—263no—
234C24—263no—
235C24C23×D1311yescharacteristic
236C22×C4—26no—
237C22×C4—26no—
238C22×C4—26no—
239C22×C4—26no—
240C22×C4—23no—
241C22×C4—23no—
242C22×C4—136no—
243C22×C4—132no—
244C22×C4—136no—
245C22×C4—263no—
246C22×C4—263no—
247C22×C4—263no—
248C22×C4—266no—
249C22×C4—266no—
250C22×C4—263no—
251C22×C4—266no—
252C22×C4—263no—
253C22×C4—263no—
254C22×C4—266no—
255C22×C4—2624no—
256C22×C4—524no—
257C22×C4—5212no—
258C22×C4C2×C4×D1316yes—
259C22×C4C2×D5216yes—
260C22×C4C2×D5216yes—
261C22×C4C2×D5216yes—
262C22×C4#612716yes—
263C22×C4#612916yes—
264C22×C4Q8×D1312yes—
265C4⋊C4—2624no—
266C4⋊C4—2624no—
267C22⋊C4—2624no—
268C22⋊C4—2624no—
269C42—224no—
270C42—5212no—
271C13C4×#39911yescharacteristic, complemented, Sylow
272C23—134no—
273C23—266no—
274C23—266no—
275C23—266no—
276C23—266no—
277C23—266no—
278C23—266no—
279C23—521no—
280C23—523no—
281C23—523no—
282C23—523no—
283C23—526no—
284C23C22×C4×D1311yescharacteristic
285C23C22×D5213yes—
286C23C2×#612713yes—
287C23C2×#612913yes—
288C23C2×Q8×D1311yescharacteristic
289C23#41×D1313yes—
290C23#41×D1311yescharacteristic
291C2×C4—26no—
292C2×C4—26no—
293C2×C4—212no—
294C2×C4—212no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—46no—
299C2×C4—46no—
300C2×C4—266no—
301C2×C4—2612no—
302C2×C4—266no—
303C2×C4—266no—
304C2×C4—2612no—
305C2×C4—523no—
306C2×C4—523no—
307C2×C4—521no—
308C2×C4—523no—
309C2×C4—526no—
310C2×C4—523no—
311C2×C4—526no—
312C2×C4—523no—
313C2×C4—5216no—
314C2×C4C4×D52112yes—
315C2×C4#8812814yes—
316C2×C4#88140112yes—
317C2×C4#88151112yes—
318C22—2612no—
319C22—522no—
320C22—526no—
321C22—526no—
322C22—522no—
323C22—526no—
324C22—522no—
325C22C2×C4×D5213yes—
326C22C2×#8812811yescharacteristic
327C22#1171918213yes—
328C22C2×#8814013yes—
329C22C2×#8815113yes—
330C22#1171922913yes—
331C22#1171922913yes—
332C22C4×#612913yes—
333C22#1171924316yes—
334C22#1171926213yes—
335C22C4×Q8×D1311yescharacteristic
336C22#1171928313yes—
337C4—212no—
338C4—46no—
339C4—522no—
340C4—526no—
341C4—526no—
342C4#1171833818yesdirect product factor
343C2—524no—
344C2C4×#8814013yes—
345C2C4×#8815113yes—
346C2C4×#8812811yescharacteristic
347C2C2×#1171833811yescharacteristic
348C2#1311809613yes—
349C2#1311810813yes—
350C2#1311811711yescharacteristic
subgroupG/H
centerC23×C4C22×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC4×C13×#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4×#95D13
hypocenterC13C4×#399
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic13C2semidirect
4. #13113103C2semidirect
5. #13113101C2semidirect
7. C4×C13×#95C2semidirect
22. #11718338C4direct (N × H)
45. C2×C4⋊Dic13C2×C4semidirect
49. C13×#95C2×C4semidirect
103. C4×#95D13semidirect
186. C4×C13#399semidirect
219. #95C4×D13semidirect
271. C13C4×#399semidirect
342. C4#11718338direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117183382
C2×C4×C4⋊Dic132
C2×C4×#61032
#131131032
#131131012
#131130822
C4×C13×#952
C4×#39913