Finite Group Databasebeta

← C4×#11718131 #15778056

Subgroups — C4×#11718131 #15778056

Order 3328.

576 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718131C212yesmaximal
2C4×#88073C211yesmaximal, characteristic
3C4×#88074C211yesmaximal, characteristic
4#13112954C212yesmaximal
5C4×C13×#123C211yesmaximal, characteristic
6C2×C13×#123C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C22×C42×C13C411yescharacteristic, complemented
9C13×#388—21no—
10C13×#387—21no—
11C13×#386C2211yescharacteristic
12C13×#385C411yescharacteristic, complemented
13C13×#381C411yescharacteristic, complemented
14C4×C13×C4⋊C4—21no—
15C4×C13×C22⋊C4—21no—
16C4×C13×C22⋊C4C411yescharacteristic, complemented
17C2×#88074C2212yes—
18C2×#88073C2212yes—
19C4×C22⋊Dic13—21no—
20C4×#6099—21no—
21#11718131C418yesdirect product factor
22#11718122—21no—
23#11718118—21no—
24C22×D4×C13C2311yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C13×#123—22no—
30C13×#123C2×C414yes—
31C4×D4×C13—41no—
32C4×D4×C13—41no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C42×C13—21no—
43C2×C42×C13—21no—
44C2×C42×C13—21no—
45C2×C42×C13—41no—
46C2×C42×C13—41no—
47C2×C42×C13D411yescharacteristic
48C2×C22⋊Dic13—22no—
49C2×C4×Dic13—41no—
50C2×#6099—22no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56#88074—22no—
57#88074C2×C414yes—
58#88073—22no—
59#88073C2×C414yes—
60#88071—41no—
61#88043—41no—
62C4×#1055—41no—
63C4×#352—131nomaximal, Sylow
64C24×C13C22×C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×D4×C13—41no—
67C2×D4×C13—41no—
68C2×D4×C13C22×C412yes—
69C2×D4×C13#4112yes—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—42no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13—41no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13C4212yescomplemented
86C22×C4×C13C22⋊C411yescharacteristic
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22⋊C411yescharacteristic
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×Dic13—42no—
92C13×C4⋊C4—24no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—42no—
95C13×C22⋊C4—21no—
96C13×C22⋊C4—24no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4C4212yescomplemented
102C42×C13—21no—
103C42×C13—21no—
104C42×C13—42no—
105C42×C13—42no—
106C42×C13—41no—
107C42×C13—41no—
108C22⋊Dic13—24no—
109C22⋊Dic13—42no—
110C4×Dic13—82no—
111#6099—24no—
112#6099—42no—
113C2×#1055—42no—
114C4×#123D1311yescharacteristic
115C2×#352—132no—
116C4×#100—131no—
117C4×#99—131no—
118#1390—132no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13C2×C4211yescharacteristic
128C23×C13C2×C22⋊C411yescharacteristic
129C23×C13#11711yescharacteristic
130C23×C13C4×D412yes—
131D4×C13—42no—
132D4×C13—42no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—22no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—42no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—81no—
162C2×C4×C13#9911yescharacteristic
163C2×C4×C13#9911yescharacteristic
164C2×C4×C13C4×D412yes—
165C2×Dic13—44no—
166C2×Dic13—82no—
167C2×Dic13—82no—
168#1055—44no—
169C2×#123C2×D1311yescharacteristic
170C2×C4×D4C2×D1311yescharacteristic
171C22×C42Dic1311yescharacteristic, complemented
172C2×#100—132no—
173C2×#99—132no—
174C4×M16—261no—
175#388—21no—
176#387—21no—
177#386C2×D1311yescharacteristic
178#385Dic1311yescharacteristic, complemented
179#381Dic1311yescharacteristic, complemented
180C4×C4⋊C4—21no—
181C4×C22⋊C4—21no—
182C4×C22⋊C4—261no—
183C4×C22⋊C4Dic1311yescharacteristic, complemented
184#352—138no—
185#343—261no—
186#342—261no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—22no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—42no—
195C22×C13—42no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—81no—
201C22×C13C4×C22⋊C411yescharacteristic
202C22×C13C2×#9911yescharacteristic
203C22×C13#41011yescharacteristic
204C4×C13—21no—
205C4×C13—22no—
206C4×C13—42no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—42no—
211C4×C13—42no—
212C4×C13—81no—
213C4×C13#35212yescomplemented
214Dic13—84no—
215C22×D4C22×D1311yescharacteristic
216C23×C4C2×Dic1311yescharacteristic
217C23×C4C2×Dic1311yescharacteristic
218C23×C4C2×Dic1311yescharacteristic
219C23×C4C22⋊D1311yescharacteristic
220C2×M16—262no—
221#123—22no—
222#123C4×D1314yes—
223C4×D4—41no—
224C4×D4—41no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C22⋊D1311yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—262no—
231C2×C22⋊C4C2×Dic1311yescharacteristic
232C2×C22⋊C4C2×Dic1311yescharacteristic
233C2×C22⋊C4C2×Dic1311yescharacteristic
234C2×C22⋊C4C22⋊D1311yescharacteristic
235C2×C42—21no—
236C2×C42—21no—
237C2×C42—21no—
238C2×C42—41no—
239C2×C42—41no—
240C2×C42—521no—
241C2×C42C22⋊D1311yescharacteristic
242#100—134no—
243#100—262no—
244#99—134no—
245#99—262no—
246#97—521no—
247C4×C8—521no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—521no—
254C2×C13—21no—
255C2×C13—21no—
256C2×C13—42no—
257C2×C13—41no—
258C2×C13—41no—
259C2×C13C4×#9911yescharacteristic
260C2×C13C2×#35211yescharacteristic
261C2×C13#212011yescharacteristic
262C24C22×Dic1311yescharacteristic
263C24C2×C22⋊D1311yescharacteristic
264C2×D4—41no—
265C2×D4—41no—
266C2×D4C2×C4×D1312yes—
267C2×D4#612712yes—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—522no—
284C22×C4C4×Dic1312yescomplemented
285C22×C4C22⋊Dic1311yescharacteristic
286C22×C4C22⋊Dic1311yescharacteristic
287C22×C4C22⋊Dic1311yescharacteristic
288C22×C4C22⋊Dic1311yescharacteristic
289C22×C4C2×C22⋊D1311yescharacteristic
290M16—264no—
291M16—522no—
292C2×C8—522no—
293C4⋊C4—24no—
294C4⋊C4—41no—
295C4⋊C4—42no—
296C22⋊C4—21no—
297C22⋊C4—24no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—41no—
302C22⋊C4—264no—
303C22⋊C4—522no—
304C22⋊C4C4×Dic1312yescomplemented
305C42—21no—
306C42—21no—
307C42—42no—
308C42—42no—
309C42—41no—
310C42—41no—
311C42—1042no—
312C13C4×#35211yescharacteristic, complemented, Sylow
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C2×C4×Dic1311yescharacteristic
322C23#8818011yescharacteristic
323C23C4×C22⋊D1312yes—
324C23C2×C22⋊Dic1311yescharacteristic
325D4—42no—
326D4—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—524no—
357C2×C4—1042no—
358C2×C4—1042no—
359C2×C4#8807411yescharacteristic
360C2×C4#8807411yescharacteristic
361C2×C4C4×C22⋊D1312yes—
362C8—524no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—81no—
377C22C4×C22⋊Dic1311yescharacteristic
378C22C2×#8807411yescharacteristic
379C22#1171890111yescharacteristic
380C4—22no—
381C4—21no—
382C4—42no—
383C4—42no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—42no—
388C4—81no—
389C4—1044no—
390C4#1171813112yesdirect product factor
391C2—21no—
392C2—21no—
393C2—42no—
394C2—41no—
395C2—41no—
396C2C4×#8807411yescharacteristic
397C2C2×#1171813111yescharacteristic
398C2#1311647711yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC23×C13C2×C42
FrattiniC22×D4C22×D13
FittingC4×C13×#123C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenterC4×#123D13
hypocenterC13C4×#352
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
8. C22×C42×C13C4semidirect
12. C13×#385C4semidirect
13. C13×#381C4semidirect
16. C4×C13×C22⋊C4C4semidirect
21. #11718131C4direct (N × H)
85. C22×C4×C13C42semidirect
101. C13×C22⋊C4C42semidirect
171. C22×C42Dic13semidirect
178. #385Dic13semidirect
179. #381Dic13semidirect
183. C4×C22⋊C4Dic13semidirect
213. C4×C13#352semidirect
284. C22×C4C4×Dic13semidirect
304. C22⋊C4C4×Dic13semidirect
312. C13C4×#352semidirect
390. C4#11718131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117181312
C4×#880732
C4×#880742
#131129542
C4×C13×#1232
C4×#35213