Finite Group Databasebeta

← C4×#16840662 #30606497

Subgroups — C4×#16840662 #30606497

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×#16840662C212yesmaximal
2C4×#14519837C211yesmaximal, characteristic, complemented
3C4×#14519835C211yesmaximal, characteristic, complemented
4#21460903C212yesmaximal, complemented
5C4×#14519746C211yesmaximal, characteristic
6C2×#14519837C2212yes—
7C2×#14519835C2212yes—
8C4×#11758217—21no—
9C4×C22⋊#6923—21no—
10#16840662C418yesdirect product factor
11#16840642—21no—
12#16840640—21no—
13C2×#14519746C2211yescharacteristic
14C2×C4×C22⋊D61—21no—
15C2×C4×C22⋊D61C2211yescharacteristic
16#16839641—21no—
17#16839641C2211yescharacteristic
18#16839635—21no—
19#16839635C411yescharacteristic, complemented
20#16839618C411yescharacteristic, complemented
21C4×C22⋊Dic61—21no—
22C4×C22⋊Dic61C411yescharacteristic, complemented
23C24×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—
34C22×C22⋊D61—21no—
35C22×C22⋊D61C2311yescharacteristic
36C22×C4×D61D411yescharacteristic
37#14519746—22no—
38#14519746C2×C414yes—
39C4×C22⋊D61—41no—
40C4×C22⋊D61—41no—
41C4×C22⋊D61—44no—
42C2×#11758196—21no—
43C2×#11758196D411yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61C2×C411yescharacteristic
48C2×C22⋊Dic61C2×C411yescharacteristic
49C2×C22⋊Dic61C2×C411yescharacteristic
50C2×#11758198—21no—
51C2×#11758198D411yescharacteristic
52C2×C4×Dic61—21no—
53C2×C4×Dic61D411yescharacteristic
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C25×C61C2×C411yescharacteristic
58C23×C4×C61—21no—
59C23×C4×C61—21no—
60C23×C4×C61—44no—
61C23×C4×C61—41no—
62C23×C4×C61—41no—
63C23×C4×C61C2×C411yescharacteristic
64C23×C4×C61C2×C411yescharacteristic
65C24×C61—21no—
66C24×C61—21no—
67C24×C61—42no—
68C24×C61—41no—
69C24×C61—42no—
70C24×C61—41no—
71C24×C61C4212yescomplemented
72C24×C61C22×C411yescharacteristic
73C23×D61C2×D411yescharacteristic
74C22×#6923—42no—
75C22×C4×C61—24no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—42no—
80C22×C4×C61—42no—
81C22×C4×C61—42no—
82C22×C4×C61—42no—
83C22×C4×C61—42no—
84C22×C4×C61—42no—
85C22×C4×C61—44no—
86C22×C4×C61—44no—
87C22×C4×C61—44no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—44no—
92C22×C4×C61C22⋊C411yescharacteristic
93C22×C4×C61C22⋊C411yescharacteristic
94C2×C22⋊D61—24no—
95C2×C22⋊D61—41no—
96C2×C22⋊D61—41no—
97C2×C22⋊D61—42no—
98C2×C22⋊D61—42no—
99C2×C22⋊D61C22×C412yes—
100C2×C22⋊D61#4112yes—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61C22⋊C411yescharacteristic
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C2×D411yescharacteristic
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—42no—
109C22⋊#6923—24no—
110C22⋊#6923—42no—
111#11758217—24no—
112#11758217—42no—
113C2×#92420—42no—
114C4×#6923—82no—
115C22⋊Dic61—21no—
116C22⋊Dic61—24no—
117C22⋊Dic61—41no—
118C22⋊Dic61—42no—
119C22⋊Dic61—42no—
120C22⋊Dic61—41no—
121C22⋊Dic61C4212yescomplemented
122#11758198—41no—
123#11758198—42no—
124#11758196—41no—
125#11758196—42no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—42no—
129C23×C61—22no—
130C23×C61—22no—
131C23×C61—22no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—44no—
137C23×C61—42no—
138C23×C61—41no—
139C23×C61—44no—
140C23×C61—42no—
141C23×C61—41no—
142C23×C61—42no—
143C23×C61—48no—
144C23×C61—42no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—42no—
148C23×C61—42no—
149C23×C61C2×C4211yescharacteristic
150C23×C61C2×C22⋊C411yescharacteristic
151C23×C61#11711yescharacteristic
152C22×D61—21no—
153C22×D61—21no—
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—44no—
164C2×C4×C61—42no—
165C2×C4×C61—41no—
166C2×C4×C61—48no—
167C2×C4×C61—42no—
168C2×C4×C61—41no—
169C2×C4×C61—44no—
170C2×C4×C61—42no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61#9911yescharacteristic
174C2×C4×C61#9911yescharacteristic
175C22⋊D61—42no—
176C22⋊D61—42no—
177C22⋊D61—48no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—22no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61C4×D412yes—
191C4×D61—42no—
192C4×D61—81no—
193#92420—44no—
194C4×AΣL(1,𝔽16)—611nomaximal, Sylow
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—24no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—41no—
201C22×C61—41no—
202C22×C61—42no—
203C22×C61—42no—
204C22×C61—42no—
205C22×C61—42no—
206C22×C61—44no—
207C22×C61—44no—
208C22×C61—44no—
209C22×C61—44no—
210C22×C61—42no—
211C22×C61—41no—
212C22×C61—42no—
213C22×C61—41no—
214C22×C61—42no—
215C22×C61C4×C22⋊C411yescharacteristic
216C22×C61C2×#9911yescharacteristic
217C22×C61#41011yescharacteristic
218C2×D61—22no—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—42no—
222C2×D61—81no—
223#6923—84no—
224C4×C61—21no—
225C4×C61—42no—
226C4×C61—41no—
227C4×C61AΣL(1,𝔽16)12yescomplemented
228Dic61—22no—
229Dic61—42no—
230Dic61—41no—
231Dic61—41no—
232Dic61—81no—
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—44no—
241C2×C61—41no—
242C2×C61—41no—
243C2×C61C4×#9911yescharacteristic
244C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
245C2×C61#212011yescharacteristic
246D61—42no—
247C24×C4#692311yescharacteristic, complemented
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—611no—
260C4×C22⋊C4—1221no—
261C4×C22⋊C4—1221no—
262AΣL(1,𝔽16)—618no—
263#343—1221no—
264#342—1221no—
265C61C4×AΣL(1,𝔽16)11yescharacteristic, complemented, Sylow
266C25C2×#692311yescharacteristic
267C22×D4—611no—
268C22×D4—1221no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—44no—
272C23×C4—41no—
273C23×C4—41no—
274C23×C4—611no—
275C23×C4C2×#692311yescharacteristic
276C23×C4C2×#692311yescharacteristic
277C2×M16—1222no—
278#120—614no—
279#120—1222no—
280C4×D4—2441no—
281C4×D4—2441no—
282C4×D4—2444no—
283C2×C4⋊C4—611no—
284C2×C4⋊C4—1221no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—611no—
288C2×C22⋊C4—611no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1222no—
291C2×C22⋊C4—1221no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4—1221no—
294C2×C42—611no—
295C2×C42—1221no—
296C2×C42—2441no—
297#100—614no—
298#100—1222no—
299#99—614no—
300#99—1222no—
301#97—2441no—
302C4×C8—2441no—
303#95—1221no—
304#95—1221no—
305#95—1221no—
306#95—2441no—
307C24—21no—
308C24—21no—
309C24—42no—
310C24—41no—
311C24—42no—
312C24—41no—
313C24—611no—
314C24C4×#692312yescomplemented
315C24C22×#692311yescharacteristic
316C2×D4—612no—
317C2×D4—612no—
318C2×D4—1224no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4—2442no—
322C2×D4—2442no—
323C22×C4—24no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—44no—
334C22×C4—44no—
335C22×C4—44no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—44no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—1221no—
344C22×C4—1221no—
345C22×C4—1221no—
346C22×C4—1221no—
347C22×C4—2442no—
348C22×C4—2442no—
349C22×C4C22⋊#692311yescharacteristic
350C22×C4C22⋊#692311yescharacteristic
351M16—1224no—
352M16—2442no—
353C2×C8—2442no—
354C4⋊C4—2441no—
355C4⋊C4—2442no—
356C22⋊C4—612no—
357C22⋊C4—1224no—
358C22⋊C4—1221no—
359C22⋊C4—1224no—
360C22⋊C4—2441no—
361C22⋊C4—2442no—
362C22⋊C4—2441no—
363C22⋊C4—2442no—
364C22⋊C4—2442no—
365C22⋊C4—2442no—
366C22⋊C4—2441no—
367C42—1221no—
368C42—1221no—
369C42—4882no—
370C42—2442no—
371C23—22no—
372C23—22no—
373C23—21no—
374C23—21no—
375C23—22no—
376C23—41no—
377C23—44no—
378C23—42no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—44no—
383C23—42no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23—48no—
388C23—42no—
389C23—41no—
390C23—41no—
391C23—612no—
392C23—1221no—
393C23—1221no—
394C23—2441no—
395C23—2441no—
396C23C2×C4×#692311yescharacteristic
397C23C2×C22⋊#692311yescharacteristic
398C23#1451985611yescharacteristic
399D4—2442no—
400D4—2442no—
401D4—2448no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—48no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—612no—
416C2×C4—1221no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—1221no—
420C2×C4—1222no—
421C2×C4—4881no—
422C2×C4—4882no—
423C2×C4—4882no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2444no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2442no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4#1451983511yescharacteristic
434C2×C4#1451983511yescharacteristic
435C8—2444no—
436C22—21no—
437C22—21no—
438C22—24no—
439C22—21no—
440C22—21no—
441C22—41no—
442C22—41no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22—44no—
448C22—44no—
449C22—44no—
450C22—44no—
451C22—42no—
452C22—41no—
453C22—42no—
454C22—41no—
455C22—42no—
456C22—1222no—
457C22—4881no—
458C22—2442no—
459C22—2441no—
460C22—2441no—
461C22C4×C22⋊#692311yescharacteristic
462C22C2×#1451983511yescharacteristic
463C22#1684074111yescharacteristic
464C4—21no—
465C4—42no—
466C4—41no—
467C4—1222no—
468C4—4881no—
469C4—4884no—
470C4—2442no—
471C4—2441no—
472C4—2441no—
473C4#1684066212yesdirect product factor
474C2—21no—
475C2—21no—
476C2—44no—
477C2—41no—
478C2—41no—
479C2—2442no—
480C2C4×#1451983511yescharacteristic
481C2C2×#1684066211yescharacteristic
482C2#2146207011yescharacteristic
subgroupG/H
centerC2×C4#14519835
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC24×C4×C61C4
socleC22×C61C2×#99
prime radicalC2×#14519746C22
cosocleC22×C22⋊D61C23
hypercenterC24×C4#6923
hypocenterC61C4×AΣL(1,𝔽16)
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
2. C4×#14519837C2semidirect
3. C4×#14519835C2semidirect
4. #21460903C2semidirect
10. #16840662C4direct (N × H)
19. #16839635C4semidirect
20. #16839618C4semidirect
22. C4×C22⋊Dic61C4semidirect
23. C24×C4×C61C4semidirect
28. #14519837C2×C4semidirect
30. #14519835C2×C4semidirect
71. C24×C61C42semidirect
121. C22⋊Dic61C42semidirect
227. C4×C61AΣL(1,𝔽16)semidirect
247. C24×C4#6923semidirect
265. C61C4×AΣL(1,𝔽16)semidirect
314. C24C4×#6923semidirect
473. C4#16840662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406622
C4×#145198372
C4×#145198352
#214609032
C4×#145197462
C4×AΣL(1,𝔽16)61