Finite Group Databasebeta

← C22×#11718907 #16729539

Subgroups — C22×#11718907 #16729539

Order 3328.

4766 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88205C212yesmaximal, complemented
2C22×#88198C211yesmaximal, characteristic, complemented
3C2×#11718907C2124yesmaximal, direct product factor
4C22×#88077C212yesmaximal, complemented
5C22×#88076C211yesmaximal, characteristic, complemented
6C22×C13×2−1+4C211yesmaximal, characteristic
7C2×C13×2−1+4—212no—
8C2×C13×2−1+4—26no—
9C2×C13×2−1+4C22112yes—
10C22×C13×#41—22no—
11C22×C13×#41—22no—
12C22×C13×#41C2212yes—
13C23×Q8×C13—22no—
14C23×Q8×C13C2211yescharacteristic
15C23×Dic26C2211yescharacteristic
16C2×#88205—212no—
17C2×#88205C22124yescomplemented
18C2×#88198—26no—
19C2×#88198C22112yescomplemented
20C22×#6107—22no—
21C22×#6105—22no—
22C22×#6101—22no—
23C22×C4×Dic13C2211yescharacteristic
24C22×#6099C2212yes—
25#11718907C22164yesdirect product factor
26C2×#88077C22124yescomplemented
27C2×#88076C22112yescomplemented
28C13×2−1+4—248no—
29C13×2−1+4—248no—
30C13×2−1+4—224no—
31C13×2−1+4C23116yes—
32C2×C13×#41—224no—
33C2×C13×#41—224no—
34C2×C13×#41—224no—
35C2×C13×#41—224no—
36C2×C13×#41—26no—
37C2×C13×#41—26no—
38C2×C13×#41D4112yes—
39C2×C13×#41C23112yes—
40C22×Q8×C13—22no—
41C22×Q8×C13—224no—
42C22×Q8×C13—224no—
43C22×Q8×C13—22no—
44C22×Q8×C13—26no—
45C22×Q8×C13D412yes—
46C22×Q8×C13D416yes—
47C22×Q8×C13C2316yes—
48C22×D4×C13—22no—
49C22×D4×C13—22no—
50C22×D4×C13D412yes—
51C23×C4×C13—24no—
52C23×C4×C13—22no—
53C23×C4×C13D412yes—
54C23×C4×C13C2311yescharacteristic
55C23×Dic13—21no—
56C23×Dic13—21no—
57C22×Dic26—22no—
58C22×Dic26—26no—
59C22×Dic26—23no—
60C22×Dic26C2316yes—
61#88205—248no—
62#88205C23132yescomplemented
63#88198—224no—
64#88198C23116yescomplemented
65C2×#6107—224no—
66C2×#6105—224no—
67C2×#6101—224no—
68C2×C4×Dic13—23no—
69C2×C4×Dic13C2316yes—
70C2×#6099—26no—
71C2×#6099C23112yes—
72C22×#1055—22no—
73#88077C23132yescomplemented
74#88076C23116yescomplemented
75C22×#456—131nomaximal, Sylow
76C24×C13—22no—
77C24×C13C2×D411yescharacteristic
78C13×#41—296no—
79C13×#41—296no—
80C13×#41—232no—
81C13×#41—224no—
82C13×#41—232no—
83C13×#41—212no—
84C13×#41—212no—
85C13×#41C2×D4124yes—
86C13×#41C2418yes—
87C2×Q8×C13—224no—
88C2×Q8×C13—296no—
89C2×Q8×C13—232no—
90C2×Q8×C13—26no—
91C2×Q8×C13—212no—
92C2×Q8×C13—212no—
93C2×Q8×C13—212no—
94C2×Q8×C13—212no—
95C2×Q8×C13C2×D4112yes—
96C2×Q8×C13C2×D4112yes—
97C2×Q8×C13C2414yes—
98C2×D4×C13—224no—
99C2×D4×C13—212no—
100C2×D4×C13—212no—
101C2×D4×C13—26no—
102C2×D4×C13C2×D4112yes—
103C22×C4×C13—248no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—26no—
107C22×C4×C13—212no—
108C22×C4×C13—212no—
109C22×C4×C13C2×D4112yes—
110C22×C4×C13C2×D413yes—
111C22×C4×C13C2×D412yes—
112C22×C4×C13C2×D416yes—
113C22×C4×C13C2413yes—
114C22×Dic13—28no—
115C22×Dic13—26no—
116C22×Dic13—26no—
117C22×Dic13—43no—
118C22×Dic13—41no—
119C2×Dic26—212no—
120C2×Dic26—212no—
121C2×Dic26—26no—
122C2×Dic26—46no—
123C2×Dic26—46no—
124C2×Dic26C2414yes—
125#6107—232no—
126#6105—232no—
127#6101—232no—
128C4×Dic13—26no—
129C4×Dic13C2414yes—
130#6099—212no—
131#6099C2418yes—
132C2×#1055—212no—
133C22×2−1+4D1311yescharacteristic
134C22×#137—132no—
135C22×C4⋊Q8—131no—
136C2×#456—1324no—
137C22×#104—132no—
138C22×#101—131no—
139C23×C13—24no—
140C23×C13—212no—
141C23×C13—48no—
142C23×C13#12013yes—
143C23×C13#12011yescharacteristic
144C23×C13C22×D413yes—
145Q8×C13—232no—
146Q8×C13—212no—
147Q8×C13—224no—
148Q8×C13—28no—
149Q8×C13C22×D418yes—
150D4×C13—232no—
151D4×C13—224no—
152D4×C13—28no—
153D4×C13—212no—
154D4×C13C22×D418yes—
155C2×C4×C13—264no—
156C2×C4×C13—212no—
157C2×C4×C13—212no—
158C2×C4×C13—212no—
159C2×C4×C13—224no—
160C2×C4×C13—28no—
161C2×C4×C13#12016yes—
162C2×C4×C13#12016yes—
163C2×C4×C13C22×D418yes—
164C2×C4×C13C22×D413yes—
165C2×C4×C13C22×D416yes—
166C2×C4×C13C22×D416yes—
167C2×C4×C13C2511yescharacteristic
168C2×Dic13—224no—
169C2×Dic13—24no—
170C2×Dic13—24no—
171C2×Dic13—46no—
172C2×Dic13—46no—
173Dic26—28no—
174Dic26—412no—
175#1055—28no—
176C2×2−1+4—212no—
177C2×2−1+4—26no—
178C2×2−1+4C2×D13112yes—
179C22×#41—22no—
180C22×#41—22no—
181C22×#41C2×D1312yes—
182C23×Q8—22no—
183C23×Q8—131no—
184C23×Q8C2×D1311yescharacteristic
185C2×#137—1324no—
186C2×#137—2612no—
187C22×Q16—262no—
188C22×SD16—262no—
189C22×M16—132no—
190C2×C4⋊Q8—1312no—
191C2×C4⋊Q8—266no—
192C22×C4⋊C4—262no—
193C22×C42—131no—
194#456—1364no—
195C2×#104—1324no—
196C2×#101—1312no—
197C22×C13—26no—
198C22×C13—26no—
199C22×C13—28no—
200C22×C13—424no—
201C22×C13#45614yescomplemented
202C22×C13C2×#12013yes—
203C22×C13C2×#12013yes—
204C22×C13C23×D411yescharacteristic
205C4×C13—28no—
206C4×C13—28no—
207C4×C13C2×#12016yes—
208C4×C13C23×D412yes—
209Dic13—28no—
210Dic13—44no—
2112−1+4—248no—
2122−1+4—248no—
2132−1+4—224no—
2142−1+4C22×D13116yes—
215C2×#41—224no—
216C2×#41—224no—
217C2×#41—224no—
218C2×#41—224no—
219C2×#41—26no—
220C2×#41—26no—
221C2×#41C22⋊D13112yes—
222C2×#41C22×D13112yes—
223C22×Q8—22no—
224C22×Q8—224no—
225C22×Q8—224no—
226C22×Q8—22no—
227C22×Q8—26no—
228C22×Q8—136no—
229C22×Q8—263no—
230C22×Q8—262no—
231C22×Q8—266no—
232C22×Q8C22⋊D1312yes—
233C22×Q8C22⋊D1316yes—
234C22×Q8C22×D1316yes—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4C22⋊D1312yes—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—261no—
241C23×C4—261no—
242C23×C4C22⋊D1312yes—
243C23×C4C22×D1311yescharacteristic
244#137—1332no—
245#137—2648no—
246C2×Q16—2624no—
247C2×SD16—2624no—
248C2×M16—1312no—
249C2×M16—266no—
250C22×C8—262no—
251C4⋊Q8—1316no—
252C4⋊Q8—2624no—
253C2×C4⋊C4—2624no—
254C2×C42—136no—
255C2×C42—263no—
256#104—1332no—
257#101—1316no—
258C2×C13—21no—
259C2×C13—23no—
260C2×C13—48no—
261C2×C13C2×#45616yescomplemented
262C2×C13C22×#12011yescharacteristic
263C24—22no—
264C24C2×C22⋊D1311yescharacteristic
265#41—296no—
266#41—296no—
267#41—232no—
268#41—224no—
269#41—232no—
270#41—212no—
271#41—212no—
272#41C2×C22⋊D13124yes—
273#41C23×D1318yes—
274C2×Q8—224no—
275C2×Q8—296no—
276C2×Q8—232no—
277C2×Q8—26no—
278C2×Q8—212no—
279C2×Q8—212no—
280C2×Q8—212no—
281C2×Q8—212no—
282C2×Q8—134no—
283C2×Q8—266no—
284C2×Q8—2612no—
285C2×Q8—2612no—
286C2×Q8—526no—
287C2×Q8—526no—
288C2×Q8C2×C22⋊D13112yes—
289C2×Q8C2×C22⋊D13112yes—
290C2×Q8C23×D1314yes—
291C2×D4—224no—
292C2×D4—212no—
293C2×D4—212no—
294C2×D4—26no—
295C2×D4C2×C22⋊D13112yes—
296C22×C4—248no—
297C22×C4—26no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—212no—
301C22×C4—212no—
302C22×C4—268no—
303C22×C4—266no—
304C22×C4—266no—
305C22×C4—523no—
306C22×C4—521no—
307C22×C4C2×C22⋊D13112yes—
308C22×C4C2×C22⋊D1313yes—
309C22×C4C2×C22⋊D1316yes—
310C22×C4C2×C22⋊D1312yes—
311C22×C4C23×D1313yes—
312Q16—2632no—
313SD16—2632no—
314M16—138no—
315M16—2612no—
316C2×C8—2612no—
317C4⋊C4—2632no—
318C42—134no—
319C42—266no—
320C13C22×#45611yescharacteristic, complemented, Sylow
321C23—24no—
322C23—212no—
323C23—48no—
324C23#8820713yes—
325C23#8820711yescharacteristic
326C23C22×C22⋊D1313yes—
327Q8—232no—
328Q8—212no—
329Q8—224no—
330Q8—28no—
331Q8—268no—
332Q8—5212no—
333Q8C22×C22⋊D1318yes—
334D4—232no—
335D4—224no—
336D4—28no—
337D4—212no—
338D4C22×C22⋊D1318yes—
339C2×C4—264no—
340C2×C4—212no—
341C2×C4—212no—
342C2×C4—212no—
343C2×C4—224no—
344C2×C4—28no—
345C2×C4—2624no—
346C2×C4—264no—
347C2×C4—264no—
348C2×C4—526no—
349C2×C4—526no—
350C2×C4#8820716yes—
351C2×C4#8820716yes—
352C2×C4C22×C22⋊D1318yes—
353C2×C4C22×C22⋊D1313yes—
354C2×C4C22×C22⋊D1316yes—
355C2×C4C22×C22⋊D1316yes—
356C2×C4C24×D1311yescharacteristic
357C8—268no—
358C22—26no—
359C22—26no—
360C22—28no—
361C22—424no—
362C22#1171890714yesdirect product factor
363C22C2×#8820713yes—
364C22C2×#8820713yes—
365C22C23×C22⋊D1311yescharacteristic
366C4—28no—
367C4—28no—
368C4—268no—
369C4—524no—
370C4C2×#8820716yes—
371C4C23×C22⋊D1312yes—
372C2—21no—
373C2—23no—
374C2—48no—
375C2C2×#1171890716yesdirect product factor
376C2C22×#8820711yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC22×C13×2−1+4C2
socleC23×C13#120
hypercenterC22×2−1+4D13
hypocenterC13C22×#456
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×2−1+4

Complements

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

NH ≅ G/Ntype
1. C22×#88205C2semidirect
2. C22×#88198C2semidirect
3. C2×#11718907C2direct (N × H)
4. C22×#88077C2semidirect
5. C22×#88076C2semidirect
17. C2×#88205C22semidirect
19. C2×#88198C22semidirect
25. #11718907C22direct (N × H)
26. C2×#88077C22semidirect
27. C2×#88076C22semidirect
62. #88205C23semidirect
64. #88198C23semidirect
73. #88077C23semidirect
74. #88076C23semidirect
201. C22×C13#456semidirect
261. C2×C13C2×#456semidirect
320. C13C22×#456semidirect
362. C22#11718907direct (N × H)
375. C2C2×#11718907direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882052
C22×#881982
C2×#117189072
C22×#880772
C22×#880762
C22×C13×2−1+42
C22×#45613