Finite Group Databasebeta

← C4×#16840663 #30606499

Subgroups — C4×#16840663 #30606499

Order 15616.

844 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840663C212yesmaximal
2C4×#14519837C211yesmaximal, characteristic, complemented
3C4×#14519835C211yesmaximal, characteristic, complemented
4#21460904C212yesmaximal, complemented
5C4×#14519747C211yesmaximal, characteristic
6C2×#14519837C2212yes—
7C2×#14519835C2212yes—
8C4×#11758217—21no—
9C4×C22⋊#6923—21no—
10#16840663C418yesdirect product factor
11#16840642—21no—
12#16840640—21no—
13C23×C4×D61C411yescharacteristic, complemented
14C2×#14519747C2211yescharacteristic
15C2×C4×D244—21no—
16C2×C4×C22⋊D61C2211yescharacteristic
17#16839640—21no—
18#16839639C2211yescharacteristic
19#16839637C411yescharacteristic, complemented
20#16839636—21no—
21#16839617C411yescharacteristic, complemented
22C4×#11758198—21no—
23C4×C22⋊C4×C61C411yescharacteristic, complemented
24C2×#11758217—22no—
25C2×C22⋊#6923—22no—
26C2×C4×#6923—41no—
27#14519837—22no—
28#14519837C2×C414yescomplemented
29#14519835—22no—
30#14519835C2×C414yescomplemented
31#14519832—41no—
32C4×#92420—41no—
33(C2×#6923)⋊C4—41no—
34C24×D61C2×C411yescharacteristic
35C22×D244—21no—
36C22×C22⋊D61C2311yescharacteristic
37C23×Dic61C2×C411yescharacteristic
38C22×C4×D61—21no—
39C22×C4×D61—21no—
40C22×C4×D61—44no—
41C22×C4×D61—41no—
42C22×C4×D61—41no—
43C22×C4×D61D411yescharacteristic
44#14519747—22no—
45#14519747C2×C414yes—
46C4×D244—44no—
47C4×C22⋊D61—41no—
48C4×C22⋊D61—41no—
49C2×C4⋊Dic61—21no—
50C2×#11758196D411yescharacteristic
51C2×C22⋊Dic61C2×C411yescharacteristic
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198—21no—
55C2×#11758198—21no—
56C2×#11758198D411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58#14519684—21no—
59#14519684—21no—
60C23×C4×C61C2×C411yescharacteristic
61C2×C22⋊C4×C61C2×C411yescharacteristic
62C2×C22⋊C4×C61C2×C411yescharacteristic
63C2×C42×C61—21no—
64#95×C61—21no—
65C24×C61C22×C411yescharacteristic
66C23×D61—21no—
67C23×D61—21no—
68C23×D61—42no—
69C23×D61—42no—
70C23×D61—41no—
71C23×D61—41no—
72C23×D61C4212yescomplemented
73C23×D61C2×D411yescharacteristic
74C22×#6923—42no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—42no—
80C22×C4×C61C22⋊C411yescharacteristic
81C22×C4×C61C22⋊C411yescharacteristic
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61C22×C412yes—
85C2×C22⋊D61#4112yes—
86C22×Dic61—21no—
87C22×Dic61—42no—
88C22×Dic61—41no—
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C2×D411yescharacteristic
92C2×D244—24no—
93C2×D244—42no—
94C2×D244—42no—
95C2×C4×D61—24no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—42no—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101C2×C4×D61—42no—
102C2×C4×D61—44no—
103C2×C4×D61—44no—
104C2×C4×D61—44no—
105C2×C4×D61—41no—
106C2×C4×D61—41no—
107C2×C4×D61—44no—
108C2×C4×D61—42no—
109C22⋊#6923—24no—
110C22⋊#6923—42no—
111#11758217—24no—
112#11758217—42no—
113C2×#92420—42no—
114C4×#6923—82no—
115C22⋊C4×C61—21no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61C4212yescomplemented
118C42×C61—42no—
119C22⋊Dic61—41no—
120#11758198—24no—
121#11758198—41no—
122#11758198—42no—
123#11758198—42no—
124#11758198—42no—
125C4⋊Dic61—42no—
126#11758196—41no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61C2×C4211yescharacteristic
134C23×C61C2×C22⋊C411yescharacteristic
135C23×C61#11711yescharacteristic
136C22×D61—22no—
137C22×D61—22no—
138C22×D61—22no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—44no—
142C22×D61—44no—
143C22×D61—41no—
144C22×D61—41no—
145C22×D61—42no—
146C22×D61—42no—
147C22×D61—48no—
148C22×D61—42no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—42no—
152C22×D61—42no—
153C22×D61—42no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61C4×D412yes—
157C2×#6923—44no—
158C2×#6923—82no—
159C2×#6923—82no—
160C2×C4×C61—22no—
161C2×C4×C61—22no—
162C2×C4×C61—21no—
163C2×C4×C61—42no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—42no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61#9911yescharacteristic
172C2×C4×C61#9911yescharacteristic
173C22⋊D61—42no—
174C22⋊D61—42no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—22no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—41no—
181C2×Dic61—42no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—42no—
186C2×Dic61C4×D412yes—
187D244—48no—
188C4×D61—44no—
189C4×D61—48no—
190C4×D61—42no—
191C4×D61—44no—
192C4×D61—81no—
193#92420—44no—
194C4×AΣL(1,𝔽16)—611nomaximal, Sylow
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61—42no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61C4×C22⋊C411yescharacteristic
205C22×C61C2×#9911yescharacteristic
206C22×C61#41011yescharacteristic
207C2×D61—24no—
208C2×D61—22no—
209C2×D61—42no—
210C2×D61—42no—
211C2×D61—42no—
212C2×D61—44no—
213C2×D61—44no—
214C2×D61—44no—
215C2×D61—42no—
216C2×D61—41no—
217C2×D61—41no—
218C2×D61—42no—
219C2×D61—42no—
220C2×D61—42no—
221C2×D61—44no—
222C2×D61—81no—
223#6923—84no—
224C4×C61—21no—
225C4×C61—42no—
226C4×C61—41no—
227C4×C61—81no—
228C4×C61AΣL(1,𝔽16)12yescomplemented
229Dic61—22no—
230Dic61—42no—
231Dic61—41no—
232Dic61—41no—
233C4×#120—611no—
234C2×AΣL(1,𝔽16)—612no—
235C4×#100—611no—
236C4×#99—611no—
237#1390—612no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61—41no—
241C2×C61—41no—
242C2×C61C4×#9911yescharacteristic
243C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
244C2×C61#212011yescharacteristic
245D61—42no—
246D61—44no—
247C24×C4—611no—
248C2×#120—611no—
249C2×C4×D4—611no—
250C2×C4×D4—1221no—
251C2×#100—612no—
252C2×#99—612no—
253C4×M16—1221no—
254#386—611no—
255#386—1221no—
256#385—611no—
257#385—1221no—
258#379—611no—
259C4×C22⋊C4—1221no—
260C4×C22⋊C4—1221no—
261C4×C22⋊C4#692311yescharacteristic, complemented
262AΣL(1,𝔽16)—618no—
263#343—1221no—
264#342—1221no—
265C61C4×AΣL(1,𝔽16)11yescharacteristic, complemented, Sylow
266C25—611no—
267C22×D4—611no—
268C22×D4—1221no—
269C23×C4—611no—
270C23×C4—611no—
271C23×C4—1221no—
272C23×C4—1221no—
273C23×C4—2441no—
274C23×C4—2441no—
275C23×C4—2444no—
276C23×C4C2×#692311yescharacteristic
277C2×M16—1222no—
278#120—614no—
279#120—1222no—
280C4×D4—2444no—
281C4×D4—2441no—
282C4×D4—2441no—
283C2×C4⋊C4—611no—
284C2×C4⋊C4—1221no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1222no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—1221no—
292C2×C22⋊C4C2×#692311yescharacteristic
293C2×C22⋊C4C2×#692311yescharacteristic
294C2×C42—21no—
295C2×C42—611no—
296C2×C42—2441no—
297#100—614no—
298#100—1222no—
299#99—614no—
300#99—1222no—
301#97—2441no—
302C4×C8—2441no—
303#95—21no—
304#95—1221no—
305#95—1221no—
306#95—2441no—
307C24—611no—
308C24—612no—
309C24—1221no—
310C24—1221no—
311C24—2441no—
312C24—2441no—
313C24—2442no—
314C24—2442no—
315C24C22×#692311yescharacteristic
316C2×D4—612no—
317C2×D4—612no—
318C2×D4—1224no—
319C2×D4—2442no—
320C2×D4—2442no—
321C2×D4—2441no—
322C2×D4—2441no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—42no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—1224no—
332C22×C4—1221no—
333C22×C4—1221no—
334C22×C4—1221no—
335C22×C4—2442no—
336C22×C4—2442no—
337C22×C4—2442no—
338C22×C4—2442no—
339C22×C4—2442no—
340C22×C4—2444no—
341C22×C4—2444no—
342C22×C4—2444no—
343C22×C4—2444no—
344C22×C4—2442no—
345C22×C4—2442no—
346C22×C4—2441no—
347C22×C4—2441no—
348C22×C4—2441no—
349C22×C4C22⋊#692311yescharacteristic
350C22×C4C22⋊#692311yescharacteristic
351M16—1224no—
352M16—2442no—
353C2×C8—2442no—
354C4⋊C4—2441no—
355C4⋊C4—2442no—
356C22⋊C4—21no—
357C22⋊C4—41no—
358C22⋊C4—1224no—
359C22⋊C4—1224no—
360C22⋊C4—2441no—
361C22⋊C4—2442no—
362C22⋊C4—2442no—
363C22⋊C4—2442no—
364C22⋊C4—2441no—
365C22⋊C4—2442no—
366C22⋊C4C4×#692312yescomplemented
367C42—42no—
368C42—1221no—
369C42—1221no—
370C42—4882no—
371C23—21no—
372C23—21no—
373C23—41no—
374C23—41no—
375C23—612no—
376C23—1222no—
377C23—1222no—
378C23—1221no—
379C23—1221no—
380C23—1222no—
381C23—2441no—
382C23—2441no—
383C23—2442no—
384C23—2441no—
385C23—2441no—
386C23—2442no—
387C23—2444no—
388C23—2444no—
389C23—2442no—
390C23—2442no—
391C23—2442no—
392C23—2448no—
393C23—2442no—
394C23—2441no—
395C23—2441no—
396C23C2×C4×#692311yescharacteristic
397C23C2×C22⋊#692311yescharacteristic
398C23#1451985611yescharacteristic
399D4—2448no—
400D4—2442no—
401D4—2442no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—612no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—1222no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—4881no—
420C2×C4—4882no—
421C2×C4—4882no—
422C2×C4—2444no—
423C2×C4—2448no—
424C2×C4—2444no—
425C2×C4—2441no—
426C2×C4—2442no—
427C2×C4—2441no—
428C2×C4—2442no—
429C2×C4—2444no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2442no—
433C2×C4#1451983611yescharacteristic
434C2×C4#1451983611yescharacteristic
435C8—2444no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—41no—
441C22—41no—
442C22—42no—
443C22—41no—
444C22—41no—
445C22—1224no—
446C22—1222no—
447C22—4881no—
448C22—2442no—
449C22—2442no—
450C22—2442no—
451C22—2442no—
452C22—2444no—
453C22—2444no—
454C22—2444no—
455C22—2444no—
456C22—2441no—
457C22—2442no—
458C22—2441no—
459C22—2442no—
460C22—2442no—
461C22C4×C22⋊#692311yescharacteristic
462C22C2×#1451983611yescharacteristic
463C22#1684074111yescharacteristic
464C4—21no—
465C4—42no—
466C4—41no—
467C4—81no—
468C4—1222no—
469C4—4884no—
470C4—2441no—
471C4—2442no—
472C4—2441no—
473C4#1684066312yesdirect product factor
474C2—21no—
475C2—21no—
476C2—41no—
477C2—41no—
478C2—2442no—
479C2—2444no—
480C2C4×#1451983611yescharacteristic
481C2C2×#1684066311yescharacteristic
482C2#2146207211yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC2×#14519747C22
cosocleC22×C22⋊D61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61C4×AΣL(1,𝔽16)
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×#14519837C2semidirect
3. C4×#14519835C2semidirect
4. #21460904C2semidirect
10. #16840663C4direct (N × H)
13. C23×C4×D61C4semidirect
19. #16839637C4semidirect
21. #16839617C4semidirect
23. C4×C22⋊C4×C61C4semidirect
28. #14519837C2×C4semidirect
30. #14519835C2×C4semidirect
72. C23×D61C42semidirect
117. C22⋊C4×C61C42semidirect
228. C4×C61AΣL(1,𝔽16)semidirect
261. C4×C22⋊C4#6923semidirect
265. C61C4×AΣL(1,𝔽16)semidirect
366. C22⋊C4C4×#6923semidirect
473. C4#16840663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406632
C4×#145198372
C4×#145198352
#214609042
C4×#145197472
C4×AΣL(1,𝔽16)61