Finite Group Databasebeta

← C4×#11718128 #15778051

Subgroups — C4×#11718128 #15778051

Order 3328.

844 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718128C212yesmaximal
2C4×#88073C211yesmaximal, characteristic, complemented
3C4×#88074C211yesmaximal, characteristic, complemented
4#13112954C212yesmaximal, complemented
5C4×C13×#120C211yesmaximal, characteristic
6C24×C4×C13C411yescharacteristic, complemented
7C2×C13×#120C2211yescharacteristic
8C2×C4×D4×C13—21no—
9C2×C4×D4×C13C2211yescharacteristic
10C13×#386—21no—
11C13×#386C2211yescharacteristic
12C13×#385—21no—
13C13×#385C411yescharacteristic, complemented
14C13×#379C411yescharacteristic, complemented
15C4×C13×C22⋊C4—21no—
16C4×C13×C22⋊C4C411yescharacteristic, complemented
17C2×#88074C2212yes—
18C2×#88073C2212yes—
19C4×C22⋊Dic13—21no—
20C4×#6099—21no—
21#11718128C418yesdirect product factor
22#11718122—21no—
23#11718118—21no—
24C25×C13C2×C411yescharacteristic
25C22×D4×C13—21no—
26C22×D4×C13C2311yescharacteristic
27C23×C4×C13—21no—
28C23×C4×C13—21no—
29C23×C4×C13—44no—
30C23×C4×C13—41no—
31C23×C4×C13—41no—
32C23×C4×C13C2×C411yescharacteristic
33C23×C4×C13C2×C411yescharacteristic
34C23×C4×C13D411yescharacteristic
35C13×#120—22no—
36C13×#120C2×C414yes—
37C4×D4×C13—41no—
38C4×D4×C13—41no—
39C4×D4×C13—44no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4C2×C411yescharacteristic
48C2×C13×C22⋊C4C2×C411yescharacteristic
49C2×C13×C22⋊C4D411yescharacteristic
50C2×C42×C13—21no—
51C2×C42×C13D411yescharacteristic
52C2×C22⋊Dic13—22no—
53C2×C4×Dic13—41no—
54C2×#6099—22no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58#88074—22no—
59#88074C2×C414yescomplemented
60#88073—22no—
61#88073C2×C414yescomplemented
62#88071—41no—
63#88043—41no—
64C4×#1055—41no—
65C4×AΣL(1,𝔽16)—131nomaximal, Sylow
66C24×C13—21no—
67C24×C13—21no—
68C24×C13—42no—
69C24×C13—41no—
70C24×C13—42no—
71C24×C13—41no—
72C24×C13C4212yescomplemented
73C24×C13C22×C411yescharacteristic
74C24×C13C2×D411yescharacteristic
75C2×D4×C13—24no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—42no—
79C2×D4×C13—42no—
80C2×D4×C13C22×C412yes—
81C2×D4×C13#4112yes—
82C22×C4×C13—24no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—42no—
91C22×C4×C13—42no—
92C22×C4×C13—42no—
93C22×C4×C13—42no—
94C22×C4×C13—42no—
95C22×C4×C13—42no—
96C22×C4×C13—42no—
97C22×C4×C13—44no—
98C22×C4×C13—44no—
99C22×C4×C13—44no—
100C22×C4×C13—41no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13—44no—
104C22×C4×C13C22⋊C411yescharacteristic
105C22×C4×C13C22⋊C411yescharacteristic
106C22×C4×C13C22⋊C411yescharacteristic
107C22×C4×C13C22⋊C411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×Dic13—42no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—42no—
112C13×C22⋊C4—21no—
113C13×C22⋊C4—24no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—42no—
117C13×C22⋊C4—42no—
118C13×C22⋊C4—42no—
119C13×C22⋊C4—41no—
120C13×C22⋊C4C4212yescomplemented
121C42×C13—21no—
122C42×C13—21no—
123C42×C13—42no—
124C22⋊Dic13—24no—
125C22⋊Dic13—42no—
126C4×Dic13—82no—
127#6099—24no—
128#6099—42no—
129C2×#1055—42no—
130C4×#120D1311yescharacteristic
131C2×AΣL(1,𝔽16)—132no—
132C4×#100—131no—
133C4×#99—131no—
134#1390—132no—
135C23×C13—22no—
136C23×C13—22no—
137C23×C13—22no—
138C23×C13—21no—
139C23×C13—21no—
140C23×C13—21no—
141C23×C13—21no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—44no—
145C23×C13—42no—
146C23×C13—41no—
147C23×C13—44no—
148C23×C13—42no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—42no—
153C23×C13—48no—
154C23×C13—42no—
155C23×C13—41no—
156C23×C13—41no—
157C23×C13—42no—
158C23×C13—42no—
159C23×C13C2×C4211yescharacteristic
160C23×C13C2×C22⋊C411yescharacteristic
161C23×C13#11711yescharacteristic
162C23×C13C4×D412yes—
163D4×C13—42no—
164D4×C13—42no—
165D4×C13—48no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—22no—
169C2×C4×C13—22no—
170C2×C4×C13—22no—
171C2×C4×C13—21no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—44no—
175C2×C4×C13—42no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—48no—
180C2×C4×C13—42no—
181C2×C4×C13—41no—
182C2×C4×C13—42no—
183C2×C4×C13—44no—
184C2×C4×C13—42no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—42no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—81no—
193C2×C4×C13#9911yescharacteristic
194C2×C4×C13#9911yescharacteristic
195C2×C4×C13C4×D412yes—
196C2×Dic13—44no—
197C2×Dic13—82no—
198C2×Dic13—82no—
199#1055—44no—
200C24×C4Dic1311yescharacteristic, complemented
201C2×#120C2×D1311yescharacteristic
202C2×C4×D4—21no—
203C2×C4×D4C2×D1311yescharacteristic
204C2×#100—132no—
205C2×#99—132no—
206C4×M16—261no—
207#386—21no—
208#386C2×D1311yescharacteristic
209#385—21no—
210#385Dic1311yescharacteristic, complemented
211#379Dic1311yescharacteristic, complemented
212C4×C22⋊C4—21no—
213C4×C22⋊C4—261no—
214C4×C22⋊C4Dic1311yescharacteristic, complemented
215AΣL(1,𝔽16)—138no—
216#343—261no—
217#342—261no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—24no—
221C22×C13—22no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—42no—
225C22×C13—41no—
226C22×C13—41no—
227C22×C13—42no—
228C22×C13—42no—
229C22×C13—42no—
230C22×C13—42no—
231C22×C13—44no—
232C22×C13—44no—
233C22×C13—44no—
234C22×C13—44no—
235C22×C13—41no—
236C22×C13—42no—
237C22×C13—41no—
238C22×C13—41no—
239C22×C13—42no—
240C22×C13—41no—
241C22×C13—42no—
242C22×C13—81no—
243C22×C13C4×C22⋊C411yescharacteristic
244C22×C13C2×#9911yescharacteristic
245C22×C13#41011yescharacteristic
246C4×C13—21no—
247C4×C13—22no—
248C4×C13—42no—
249C4×C13—42no—
250C4×C13—41no—
251C4×C13—41no—
252C4×C13—41no—
253C4×C13—81no—
254C4×C13AΣL(1,𝔽16)12yescomplemented
255Dic13—84no—
256C25C2×Dic1311yescharacteristic
257C22×D4—21no—
258C22×D4C22×D1311yescharacteristic
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—44no—
262C23×C4—41no—
263C23×C4—41no—
264C23×C4C2×Dic1311yescharacteristic
265C23×C4C2×Dic1311yescharacteristic
266C23×C4C22⋊D1311yescharacteristic
267C2×M16—262no—
268#120—22no—
269#120C4×D1314yes—
270C4×D4—41no—
271C4×D4—41no—
272C4×D4—44no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4C22⋊D1311yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—262no—
280C2×C22⋊C4C2×Dic1311yescharacteristic
281C2×C22⋊C4C2×Dic1311yescharacteristic
282C2×C22⋊C4C2×Dic1311yescharacteristic
283C2×C22⋊C4C22⋊D1311yescharacteristic
284C2×C42—21no—
285C2×C42—521no—
286C2×C42C22⋊D1311yescharacteristic
287#100—134no—
288#100—262no—
289#99—134no—
290#99—262no—
291#97—521no—
292C4×C8—521no—
293#95—21no—
294#95—21no—
295#95—21no—
296#95—521no—
297C2×C13—21no—
298C2×C13—21no—
299C2×C13—42no—
300C2×C13—44no—
301C2×C13—41no—
302C2×C13—41no—
303C2×C13C4×#9911yescharacteristic
304C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
305C2×C13#212011yescharacteristic
306C24—21no—
307C24—21no—
308C24—42no—
309C24—41no—
310C24—42no—
311C24—41no—
312C24C4×Dic1312yescomplemented
313C24C22×Dic1311yescharacteristic
314C24C2×C22⋊D1311yescharacteristic
315C2×D4—24no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—42no—
319C2×D4—42no—
320C2×D4C2×C4×D1312yes—
321C2×D4#612712yes—
322C22×C4—24no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—44no—
338C22×C4—44no—
339C22×C4—44no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—44no—
344C22×C4—522no—
345C22×C4C22⋊Dic1311yescharacteristic
346C22×C4C22⋊Dic1311yescharacteristic
347C22×C4C22⋊Dic1311yescharacteristic
348C22×C4C22⋊Dic1311yescharacteristic
349C22×C4C2×C22⋊D1311yescharacteristic
350M16—264no—
351M16—522no—
352C2×C8—522no—
353C4⋊C4—41no—
354C4⋊C4—42no—
355C22⋊C4—21no—
356C22⋊C4—24no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C22⋊C4—41no—
363C22⋊C4—264no—
364C22⋊C4—522no—
365C22⋊C4C4×Dic1312yescomplemented
366C42—21no—
367C42—21no—
368C42—42no—
369C42—1042no—
370C13C4×AΣL(1,𝔽16)11yescharacteristic, complemented, Sylow
371C23—22no—
372C23—22no—
373C23—22no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—41no—
379C23—44no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—44no—
385C23—42no—
386C23—41no—
387C23—41no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—48no—
392C23—42no—
393C23—41no—
394C23—41no—
395C23C2×C4×Dic1311yescharacteristic
396C23#8818011yescharacteristic
397C23C4×C22⋊D1312yes—
398C23C2×C22⋊Dic1311yescharacteristic
399D4—42no—
400D4—42no—
401D4—48no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—44no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—48no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—81no—
429C2×C4—524no—
430C2×C4—1042no—
431C2×C4—1042no—
432C2×C4#8807411yescharacteristic
433C2×C4#8807411yescharacteristic
434C2×C4C4×C22⋊D1312yes—
435C8—524no—
436C22—21no—
437C22—21no—
438C22—24no—
439C22—22no—
440C22—21no—
441C22—21no—
442C22—42no—
443C22—41no—
444C22—41no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—44no—
450C22—44no—
451C22—44no—
452C22—44no—
453C22—42no—
454C22—42no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—42no—
459C22—41no—
460C22—81no—
461C22C4×C22⋊Dic1311yescharacteristic
462C22C2×#8807411yescharacteristic
463C22#1171890111yescharacteristic
464C4—22no—
465C4—21no—
466C4—42no—
467C4—42no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—81no—
472C4—1044no—
473C4#1171812812yesdirect product factor
474C2—21no—
475C2—21no—
476C2—42no—
477C2—44no—
478C2—41no—
479C2—41no—
480C2C4×#8807411yescharacteristic
481C2C2×#1171812811yescharacteristic
482C2#1311647711yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC23×C13C2×C42
FrattiniC22×D4C22×D13
FittingC4×C13×#120C2
socleC22×C13C2×#99
prime radicalC2×C13×#120C22
cosocleC22×D4×C13C23
hypercenterC4×#120D13
hypocenterC13C4×AΣL(1,𝔽16)
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
2. C4×#88073C2semidirect
3. C4×#88074C2semidirect
4. #13112954C2semidirect
6. C24×C4×C13C4semidirect
13. C13×#385C4semidirect
14. C13×#379C4semidirect
16. C4×C13×C22⋊C4C4semidirect
21. #11718128C4direct (N × H)
59. #88074C2×C4semidirect
61. #88073C2×C4semidirect
72. C24×C13C42semidirect
120. C13×C22⋊C4C42semidirect
200. C24×C4Dic13semidirect
210. #385Dic13semidirect
211. #379Dic13semidirect
214. C4×C22⋊C4Dic13semidirect
254. C4×C13AΣL(1,𝔽16)semidirect
312. C24C4×Dic13semidirect
365. C22⋊C4C4×Dic13semidirect
370. C13C4×AΣL(1,𝔽16)semidirect
473. C4#11718128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117181282
C4×#880732
C4×#880742
#131129542
C4×C13×#1202
C4×AΣL(1,𝔽16)13