Finite Group Databasebeta

← C22×#11718466 #16730648

Subgroups — C22×#11718466 #16730648

Order 3328.

2662 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88200C211yesmaximal, characteristic
2C22×C4⋊C4×D13C211yesmaximal, characteristic
3C2×#11718466C2124yesmaximal, direct product factor
4C22×#88057C211yesmaximal, characteristic, complemented
5C22×#88048C211yesmaximal, characteristic, complemented
6C22×#88075C211yesmaximal, characteristic, complemented
7C22×#88060C211yesmaximal, characteristic
8C22×C13×#103C211yesmaximal, characteristic, complemented
9C23×Q8×C13C2211yescharacteristic
10C23×C4×D13—21no—
11C23×C4×D13C2211yescharacteristic
12C23×C8×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C2×#88200—26no—
15C2×#88200C22112yes—
16C22×#6103—21no—
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×#6101—21no—
20C22×#6101—21no—
21C23×#1055C2211yescharacteristic
22C2×C4⋊C4×D13—26no—
23C2×C4⋊C4×D13C22112yes—
24C2×C13×#103C22112yescomplemented
25C2×#88075C22112yescomplemented
26C2×#88060C22112yes—
27C2×#88057C22112yescomplemented
28C2×#88048C22112yescomplemented
29#11718466C22164yesdirect product factor
30C24×D13D411yescharacteristic
31C22×Q8×C13—23no—
32C22×Q8×C13—24no—
33C22×Q8×C13—24no—
34C22×Q8×C13C2316yes—
35C23×C4×C13—21no—
36C23×C4×C13—21no—
37C23×C4×C13C2311yescharacteristic
38C23×Dic13—21no—
39C23×Dic13—21no—
40C23×Dic13D411yescharacteristic
41C22×C4×D13—24no—
42C22×C4×D13—24no—
43C22×C4×D13—212no—
44C22×C4×D13—48no—
45C22×C4×D13D416yes—
46C22×C4×D13C2316yes—
47C22×C8×C13—24no—
48C22×C8×C13C2316yes—
49C2×C13×C4⋊C4—23no—
50C2×C13×C4⋊C4C2316yes—
51#88200—224no—
52#88200C23116yes—
53C2×#6103—212no—
54C2×C4⋊Dic13—23no—
55C2×C4⋊Dic13—23no—
56C2×C4⋊Dic13C2316yes—
57C2×C4⋊Dic13C2316yes—
58C2×#6101—212no—
59C2×#6101—212no—
60C22×#1055—24no—
61C22×#1055C2316yes—
62C4⋊C4×D13—224no—
63C4⋊C4×D13C23116yes—
64C13×#103C23116yescomplemented
65#88075C23116yescomplemented
66#88060C23116yes—
67#88057C23116yescomplemented
68#88048C23116yescomplemented
69C22×#483—131nomaximal, Sylow
70C24×C13C2×D411yescharacteristic
71C23×D13—24no—
72C23×D13—24no—
73C23×D13SD1618yes—
74C23×D13C2×D416yes—
75C2×Q8×C13—26no—
76C2×Q8×C13—212no—
77C2×Q8×C13—212no—
78C2×Q8×C13—412no—
79C2×Q8×C13C2414yes—
80C22×C4×C13—26no—
81C22×C4×C13—26no—
82C22×C4×C13—44no—
83C22×C4×C13—44no—
84C22×C4×C13C2×D413yes—
85C22×C4×C13#4114yes—
86C22×C4×C13#4114yes—
87C22×C4×C13C2413yes—
88C22×Dic13—24no—
89C22×Dic13—26no—
90C22×Dic13—26no—
91C22×Dic13—44no—
92C22×Dic13—44no—
93C22×Dic13C2×D416yes—
94C2×C4×D13—224no—
95C2×C4×D13—212no—
96C2×C4×D13—212no—
97C2×C4×D13—216no—
98C2×C4×D13—448no—
99C2×C4×D13C2×D4112yes—
100C2×C4×D13C2414yes—
101C2×C8×C13—212no—
102C2×C8×C13C2414yes—
103C13×C4⋊C4—26no—
104C13×C4⋊C4C2414yes—
105#6103—216no—
106C4⋊Dic13—26no—
107C4⋊Dic13—26no—
108C4⋊Dic13C2414yes—
109C4⋊Dic13C2414yes—
110#6101—216no—
111#6101—216no—
112C2×#1055—212no—
113C2×#1055C2414yes—
114C22×C22⋊Q8—131no—
115C23×C4⋊C4—131no—
116C2×#483—1324no—
117C22×#106—131no—
118C22×#106—131no—
119C22×#103—131no—
120C22×#103D1311yescharacteristic, complemented
121C22×C22⋊C8—131no—
122C23×C13#12314yes—
123C23×C13C2×SD1614yes—
124C23×C13#13714yes—
125C23×C13C22×D413yes—
126C22×D13—212no—
127C22×D13—212no—
128C22×D13—232no—
129C22×D13C2×SD16124yes—
130C22×D13C22×D414yes—
131Q8×C13—24no—
132Q8×C13—24no—
133Q8×C13—412no—
134C2×C4×C13—24no—
135C2×C4×C13—24no—
136C2×C4×C13—412no—
137C2×C4×C13—412no—
138C2×C4×C13#123112yes—
139C2×C4×C13C22×D413yes—
140C2×C4×C13C2×#4116yes—
141C2×C4×C13C2×#4116yes—
142C2×C4×C13C2511yescharacteristic
143C2×Dic13—212no—
144C2×Dic13—24no—
145C2×Dic13—24no—
146C2×Dic13—412no—
147C2×Dic13—412no—
148C2×Dic13C22×D414yes—
149C4×D13—224no—
150C4×D13—24no—
151C4×D13—24no—
152C4×D13—432no—
153C8×C13—24no—
154#1055—24no—
155C23×Q8C2×D1311yescharacteristic
156C24×C4—131no—
157C24×C4—261no—
158C23×C8—131no—
159C23×C8C2×D1311yescharacteristic
160C2×C22⋊Q8—1312no—
161C2×C22⋊Q8—266no—
162C22×C4⋊C4—131no—
163C22×C4⋊C4—131no—
164C22×C4⋊C4—1312no—
165C22×C4⋊C4—266no—
166C22×C4⋊C4—261no—
167C22×C4⋊C4—261no—
168C22×C4⋊C4C2×D1311yescharacteristic
169C22×C22⋊C4—261no—
170#483—1364no—
171C2×#106—1312no—
172C2×#106—1312no—
173C2×#103—1312no—
174C2×#103C2×D13112yescomplemented
175C2×C22⋊C8—1312no—
176C22×C13#483116yescomplemented
177C22×C13C2×#12316yes—
178C22×C13C22×SD1616yes—
179C22×C13C2×#13716yes—
180C22×C13C23×D411yescharacteristic
181C2×D13—248no—
182C2×D13—24no—
183C2×D13—24no—
184C2×D13C22×SD1618yes—
185C4×C13—44no—
186C4×C13—44no—
187C4×C13C2×#12316yes—
188C4×C13C22×#4111yescharacteristic
189C4×C13C22×#4111yescharacteristic
190Dic13—24no—
191Dic13—44no—
192Dic13—44no—
193C25—131no—
194C22×Q8—23no—
195C22×Q8—24no—
196C22×Q8—24no—
197C22×Q8C22×D1316yes—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—131no—
201C23×C4—136no—
202C23×C4—136no—
203C23×C4—2612no—
204C23×C4—264no—
205C23×C4—264no—
206C23×C4—261no—
207C23×C4—261no—
208C23×C4—528no—
209C23×C4C22×D1311yescharacteristic
210C22×C8—24no—
211C22×C8—136no—
212C22×C8—264no—
213C22×C8C22×D1316yes—
214C22⋊Q8—1316no—
215C22⋊Q8—2624no—
216C2×C4⋊C4—23no—
217C2×C4⋊C4—136no—
218C2×C4⋊C4—136no—
219C2×C4⋊C4—1316no—
220C2×C4⋊C4—2624no—
221C2×C4⋊C4—2612no—
222C2×C4⋊C4—2612no—
223C2×C4⋊C4—263no—
224C2×C4⋊C4—263no—
225C2×C4⋊C4C22×D1316yes—
226C2×C22⋊C4—2612no—
227#106—1316no—
228#106—1316no—
229#103—1316no—
230#103C22×D13116yescomplemented
231C22⋊C8—1316no—
232C2×C13C2×#483112yescomplemented
233C2×C13C22×#12311yescharacteristic
234C2×C13C23×SD1611yescharacteristic
235C2×C13C22×#13711yescharacteristic
236D13—28no—
237C24—138no—
238C24—136no—
239C24—264no—
240C24—264no—
241C24D4×D1311yescharacteristic
242C2×Q8—26no—
243C2×Q8—212no—
244C2×Q8—212no—
245C2×Q8—412no—
246C2×Q8C23×D1314yes—
247C22×C4—26no—
248C22×C4—26no—
249C22×C4—44no—
250C22×C4—44no—
251C22×C4—136no—
252C22×C4—1312no—
253C22×C4—134no—
254C22×C4—2616no—
255C22×C4—264no—
256C22×C4—2624no—
257C22×C4—2612no—
258C22×C4—2612no—
259C22×C4—266no—
260C22×C4—266no—
261C22×C4—5248no—
262C22×C4—524no—
263C22×C4—524no—
264C22×C4#612714yes—
265C22×C4D4×D1313yes—
266C22×C4#612914yes—
267C22×C4C23×D1313yes—
268C2×C8—212no—
269C2×C8—134no—
270C2×C8—2612no—
271C2×C8C23×D1314yes—
272C4⋊C4—26no—
273C4⋊C4—134no—
274C4⋊C4—134no—
275C4⋊C4—2616no—
276C4⋊C4—2616no—
277C4⋊C4—266no—
278C4⋊C4—266no—
279C4⋊C4C23×D1314yes—
280C22⋊C4—2616no—
281C13C22×#48311yescharacteristic, complemented, Sylow
282C23—1324no—
283C23—134no—
284C23—2612no—
285C23—2612no—
286C23—2632no—
287C23#8813714yes—
288C23SD16×D1314yes—
289C23#8817214yes—
290C23C2×D4×D1313yes—
291Q8—24no—
292Q8—24no—
293Q8—412no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—412no—
297C2×C4—412no—
298C2×C4—134no—
299C2×C4—2612no—
300C2×C4—2624no—
301C2×C4—264no—
302C2×C4—264no—
303C2×C4—264no—
304C2×C4—264no—
305C2×C4—5232no—
306C2×C4—5212no—
307C2×C4—5212no—
308C2×C4#88137112yes—
309C2×C4C2×#612716yes—
310C2×C4C2×D4×D1313yes—
311C2×C4C2×#612916yes—
312C2×C4C24×D1311yescharacteristic
313C8—24no—
314C8—264no—
315C22—138no—
316C22—2648no—
317C22—264no—
318C22—264no—
319C22#11718466116yesdirect product factor
320C22C2×#8813716yes—
321C22C2×SD16×D1316yes—
322C22C2×#8817216yes—
323C22C22×D4×D1311yescharacteristic
324C4—44no—
325C4—44no—
326C4—264no—
327C4—524no—
328C4—524no—
329C4C2×#8813716yes—
330C4C22×#612711yescharacteristic
331C4C22×#612911yescharacteristic
332C2—268no—
333C2C2×#11718466112yesdirect product factor
334C2C22×#8813711yescharacteristic
335C2C22×SD16×D1311yescharacteristic
336C2C22×#8817211yescharacteristic
subgroupG/H
centerC24D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#103C2
socleC24×C13C2×D4
prime radicalC24×D13D4
hypercenterC22×#103D13
hypocenterC13C22×#483
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C2×#11718466C2direct (N × H)
4. C22×#88057C2semidirect
5. C22×#88048C2semidirect
6. C22×#88075C2semidirect
8. C22×C13×#103C2semidirect
24. C2×C13×#103C22semidirect
25. C2×#88075C22semidirect
27. C2×#88057C22semidirect
28. C2×#88048C22semidirect
29. #11718466C22direct (N × H)
64. C13×#103C23semidirect
65. #88075C23semidirect
67. #88057C23semidirect
68. #88048C23semidirect
120. C22×#103D13semidirect
174. C2×#103C2×D13semidirect
176. C22×C13#483semidirect
230. #103C22×D13semidirect
232. C2×C13C2×#483semidirect
281. C13C22×#483semidirect
319. C22#11718466direct (N × H)
333. C2C2×#11718466direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882002
C22×C4⋊C4×D132
C2×#117184662
C22×#880572
C22×#880482
C22×#880752
C22×#880602
C22×C13×#1032
C22×#48313