Finite Group Databasebeta

← C4×#16840038 #29686906

Subgroups — C4×#16840038 #29686906

Order 15616.

882 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840038C211yesmaximal, characteristic
2C4×#14519810C212yesmaximal
3C2×C4×Dic244C211yesmaximal, characteristic, complemented
4C4×#14519783C211yesmaximal, characteristic
5#21446732C211yesmaximal, characteristic, complemented
6#21446605C211yesmaximal, characteristic, complemented
7#21446475C212yesmaximal, complemented
8#21446333C212yesmaximal
9#21445880C211yesmaximal, characteristic
10C4×#14519695C212yesmaximal, complemented
11C4×#108×C61C211yesmaximal, characteristic, complemented
12C2×#14519810C2212yes—
13C22×Dic244C2211yescharacteristic
14C2×#14519783C2211yescharacteristic
15C2×#14519783C2211yescharacteristic
16C4×#11758222C2211yescharacteristic
17C2×C4×Dic122C2212yes—
18#16840038C418yesdirect product factor
19#16839870—22no—
20#16839864—22no—
21C4×Dic244—22no—
22C4×Dic244—21no—
23C4×Dic244—21no—
24C4×Dic244—21no—
25C4×Dic244—21no—
26C4×#11758190—22no—
27#16839804C2212yes—
28C2×#14519711C2211yescharacteristic
29#16839772C2212yes—
30#16839764C2212yes—
31C2×#14519702C2212yes—
32C2×#14519695C2212yes—
33C2×#14519695C2212yes—
34#16839717C2211yescharacteristic
35#16839717C2211yescharacteristic
36#16839716—21no—
37#16839716—21no—
38C4×#11758194C2211yescharacteristic
39C4×#11758189—21no—
40C4×C8×D61—21no—
41#16839530C2212yes—
42#16839530C2212yes—
43C2×#108×C61C2211yescharacteristic
44C2×#108×C61C2211yescharacteristic
45C4×M16×C61C2212yes—
46C2×C4×C8×C61C2211yescharacteristic
47C61×#341C2212yes—
48C2×#11758222C2311yescharacteristic
49C22×Dic122C2312yes—
50#14519810—24no—
51#14519810C2×C418yes—
52C2×Dic244—22no—
53C2×Dic244—21no—
54C2×Dic244—21no—
55C2×Dic244—22no—
56C2×Dic244C2×C414yescomplemented
57C2×#11758190—22no—
58#14519783—22no—
59#14519783—22no—
60#14519783—22no—
61#14519783C2×C414yes—
62C2×#11758194C2311yescharacteristic
63C2×#11758194C2311yescharacteristic
64C2×#11758189—21no—
65C2×#11758189—21no—
66C2×C8×D61—21no—
67C2×C8×D61—21no—
68C4×Dic122—22no—
69C4×Dic122—22no—
70C4×Dic122—22no—
71C4×Dic122—22no—
72C4×Dic122D411yescharacteristic
73C4×Dic122D411yescharacteristic
74C4×D244D411yescharacteristic
75C4×D244D411yescharacteristic
76C4×C22⋊D61—21no—
77C4×C22⋊D61—21no—
78#14519736C2311yescharacteristic
79#14519734—21no—
80C2×C4⋊Dic61C2312yes—
81C2×#11758196—22no—
82C2×C4×Dic61—22no—
83C42×D61—21no—
84#14519711—21no—
85#14519711—21no—
86#14519711—22no—
87#14519709—22no—
88#14519702—22no—
89#14519702—22no—
90#14519702—22no—
91#14519702—22no—
92#14519702—22no—
93#14519699—22no—
94#14519695—24no—
95#14519695C2×C418yescomplemented
96#14519688—21no—
97#14519687—21no—
98#14519687—21no—
99C4×#92418—21no—
100C8×Dic61—21no—
101C8×Dic61—21no—
102C2×M16×C61C2312yes—
103C2×M16×C61C2312yes—
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C2×C42×C61C2311yescharacteristic
107#108×C61—22no—
108#108×C61C2×C414yescomplemented
109#97×C61—22no—
110C4×C8×C61—22no—
111C4×C8×C61D411yescharacteristic
112C4×C8×C61D411yescharacteristic
113C4×C8×C61D411yescharacteristic
114C4×C8×C61D411yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C22×C4×C61C2411yescharacteristic
118C2×C22⋊D61—21no—
119C22×Dic61—22no—
120C22×Dic61—22no—
121#11758222—21no—
122#11758222—21no—
123#11758222C22×C412yes—
124#11758222#4112yes—
125C2×D244C2×D411yescharacteristic
126C2×C4×D61—21no—
127C2×C4×D61—21no—
128C2×C4×D61—21no—
129C2×Dic122—22no—
130C2×Dic122—22no—
131C2×Dic122—22no—
132C2×Dic122—22no—
133C2×Dic122—22no—
134C2×Dic122C22×C414yes—
135C2×Dic122C2×D411yescharacteristic
136M16×C61—22no—
137M16×C61—22no—
138M16×C61—22no—
139M16×C61C22×C414yes—
140C2×C8×C61—22no—
141C2×C8×C61—21no—
142C2×C8×C61—21no—
143C2×C8×C61—22no—
144C2×C8×C61C22×C412yes—
145C2×C8×C61C2×D411yescharacteristic
146C2×C8×C61C2×D411yescharacteristic
147C2×C8×C61C2×D411yescharacteristic
148C2×C8×C61C2×D411yescharacteristic
149C2×C8×C61#4112yes—
150C42×C61C2×D411yescharacteristic
151C42×C61C2×D411yescharacteristic
152C42×C61C2×D411yescharacteristic
153C42×C61C2×D411yescharacteristic
154C22⋊Dic61—21no—
155#11758198—21no—
156#11758198—21no—
157C4⋊Dic61—22no—
158C4⋊Dic61—22no—
159C4⋊Dic61C2×D411yescharacteristic
160C4⋊Dic61C2×D411yescharacteristic
161#11758196—21no—
162#11758196—21no—
163#11758196—42no—
164#11758196—42no—
165C4×Dic61—21no—
166C4×Dic61—21no—
167C4×Dic61—21no—
168C4×Dic61—42no—
169C4×Dic61—42no—
170#11758194—21no—
171#11758194—21no—
172#11758194C22×C412yes—
173#11758194#4112yes—
174C2×#92418—21no—
175C2×#92418—21no—
176Dic244—28no—
177Dic244—24no—
178Dic244—24no—
179#11758190—28no—
180#11758189—24no—
181#11758189—24no—
182C8×D61—24no—
183C8×D61—24no—
184C23×C61C2×#4111yescharacteristic
185C22×D61—21no—
186C2×C4×C61—22no—
187C2×C4×C61—41no—
188C2×C4×C61#12111yescharacteristic
189C2×C4×C61#12111yescharacteristic
190C2×C4×C61#12111yescharacteristic
191C2×C4×C61#12111yescharacteristic
192C2×C4×C61C23×C411yescharacteristic
193C2×C4×C61C22×D411yescharacteristic
194C2×C4×C61C22×D411yescharacteristic
195C2×C4×C61C2×#4111yescharacteristic
196C2×C4×C61C2×#4111yescharacteristic
197C2×C4×C61C2×#4111yescharacteristic
198C22⋊D61—22no—
199C22⋊D61—22no—
200C2×Dic61—21no—
201C2×Dic61—24no—
202C2×Dic61—21no—
203C2×Dic61—21no—
204C2×Dic61—42no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207C2×Dic61—82no—
208D244—21no—
209D244C4×D412yes—
210C4×D61—22no—
211C4×D61—22no—
212C4×D61—42no—
213C4×D61—42no—
214Dic122—21no—
215Dic122—24no—
216Dic122—24no—
217Dic122—42no—
218Dic122—42no—
219Dic122C4×D412yes—
220C8×C61—24no—
221C8×C61—21no—
222C8×C61—21no—
223C8×C61—42no—
224C8×C61C4×D412yes—
225C8×C61C4×D412yes—
226#92418—22no—
227#92418—22no—
228C4×#473—611nomaximal, Sylow
229C22×C61—21no—
230C22×C61—21no—
231C22×C61C4×#4111yescharacteristic
232C22×C61C2×#12111yescharacteristic
233C22×C61#52911yescharacteristic
234C2×D61—22no—
235C2×D61—41no—
236C2×D61—41no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—21no—
240C4×C61#47312yescomplemented
241C4×C61C2×C4×D411yescharacteristic
242C4×C61C2×C4×D411yescharacteristic
243C4×C61#52511yescharacteristic
244C4×C61#53211yescharacteristic
245Dic61—22no—
246Dic61—41no—
247Dic61—41no—
248Dic61—44no—
249Dic61—82no—
250C2×#473—611no—
251C4×#137—612no—
252C2×C4×Q16—611no—
253C4×#131—611no—
254#1979—611no—
255#1952—611no—
256#1930—612no—
257#1908—612no—
258#1816—611no—
259C4×#108D6111yescharacteristic, complemented
260C4×#101—612no—
261C2×C61—21no—
262C2×C61—21no—
263C2×C61C4×#12111yescharacteristic
264C2×C61C2×#47311yescharacteristic
265C2×C61#306711yescharacteristic
266D61—42no—
267C2×#137—612no—
268C22×Q16—611no—
269C2×#131—611no—
270C2×#131—611no—
271C4×#41—611no—
272C2×C4×Q8—612no—
273#473—618no—
274#441—1222no—
275#440—1222no—
276C4×Q16—1222no—
277C4×Q16—1221no—
278C4×Q16—1221no—
279C4×Q16—1221no—
280C4×Q16—1221no—
281C4×SD16—1222no—
282C2×#108C2×D6111yescharacteristic
283C2×#108C2×D6111yescharacteristic
284#428—612no—
285C2×#107—611no—
286#419—612no—
287#417—612no—
288C2×#103—612no—
289C2×#101—612no—
290C2×#101—612no—
291#405—611no—
292#405—611no—
293#405—1221no—
294#405—1221no—
295C4×M16—611no—
296C4×M16—1221no—
297C4×M16C2×D6112yes—
298C2×C4×C8—1221no—
299C2×C4×C8C2×D6111yescharacteristic
300#343—612no—
301#343—612no—
302#341C2×D6112yes—
303C61C4×#47311yescharacteristic, complemented, Sylow
304C2×#41—611no—
305C22×Q8—612no—
306#137—618no—
307#137—1224no—
308C2×Q16—614no—
309C2×Q16—1222no—
310C2×Q16—1221no—
311C2×Q16—1221no—
312C2×Q16—1222no—
313C2×SD16—1222no—
314#131—614no—
315#131—1222no—
316#131—1222no—
317#131—1222no—
318C2×M16—611no—
319C2×M16—611no—
320C2×M16—1221no—
321C2×M16—1221no—
322C2×M16C22×D6112yes—
323C2×M16C22×D6112yes—
324C22×C8—1221no—
325C22×C8—1221no—
326C22×C8C22×D6111yescharacteristic
327C22×C8C22×D6111yescharacteristic
328C4×Q8—611no—
329C4×Q8—611no—
330C4×Q8—1222no—
331C4×Q8—1222no—
332C4×Q8—1222no—
333C4×Q8—1222no—
334C4×D4—611no—
335C4×D4—611no—
336C4×D4—1221no—
337C4×D4—1221no—
338#117—611no—
339#117—1221no—
340C2×C4⋊C4—612no—
341C2×C4⋊C4—1222no—
342C2×C42—1221no—
343C2×C42—1222no—
344C2×C42C22×D6111yescharacteristic
345#108—22no—
346#108C4×D6114yescomplemented
347#107—1222no—
348#107—1221no—
349#107—1221no—
350#106—1222no—
351#103—1222no—
352#103—1222no—
353#103—1222no—
354#103—1222no—
355#103—1222no—
356#102—1222no—
357#101—618no—
358#101—1224no—
359#97—22no—
360#97—1221no—
361#97—1221no—
362#97—1221no—
363C4×C8—22no—
364C4×C8—1221no—
365C4×C8—1221no—
366C4×C8—1221no—
367C4×C8D24411yescharacteristic
368C4×C8D24411yescharacteristic
369C4×C8D24411yescharacteristic
370C4×C8D24411yescharacteristic
371#41—612no—
372#41—612no—
373#41—1221no—
374#41—1221no—
375C2×Q8—614no—
376C2×Q8—611no—
377C2×Q8—1222no—
378C2×Q8—1222no—
379C2×Q8—1222no—
380C2×Q8—1222no—
381C2×Q8—1222no—
382C2×D4—611no—
383C2×D4—1221no—
384C22×C4—1221no—
385C22×C4—1222no—
386C22×C4—1221no—
387C22×C4—1221no—
388C22×C4—1222no—
389C22×C4#1175822611yescharacteristic
390C22×C4#1175822611yescharacteristic
391C22×C4C23×D6111yescharacteristic
392Q16—1228no—
393Q16—1224no—
394Q16—1224no—
395SD16—1228no—
396M16—22no—
397M16—22no—
398M16—22no—
399M16—612no—
400M16—612no—
401M16—1224no—
402M16—1221no—
403M16—1221no—
404M16—1224no—
405M16C2×C4×D6114yes—
406C2×C8—22no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—22no—
410C2×C8—1224no—
411C2×C8—1221no—
412C2×C8—1221no—
413C2×C8—1224no—
414C2×C8C2×C4×D6112yes—
415C2×C8C2×D24411yescharacteristic
416C2×C8C2×D24411yescharacteristic
417C2×C8C2×D24411yescharacteristic
418C2×C8C2×D24411yescharacteristic
419C2×C8#1175822212yes—
420C4⋊C4—611no—
421C4⋊C4—611no—
422C4⋊C4—1221no—
423C4⋊C4—1221no—
424C4⋊C4—1222no—
425C4⋊C4—1222no—
426C4⋊C4—2442no—
427C4⋊C4—2442no—
428C22⋊C4—1221no—
429C22⋊C4—1221no—
430C22⋊C4—1221no—
431C42—1221no—
432C42—1221no—
433C42—1221no—
434C42—2442no—
435C42—2442no—
436C42C2×D24411yescharacteristic
437C42C2×D24411yescharacteristic
438C42D4×D6111yescharacteristic
439C42D4×D6111yescharacteristic
440C23—1221no—
441C23C2×#1175822611yescharacteristic
442Q8—612no—
443Q8—1221no—
444Q8—1224no—
445Q8—1224no—
446Q8—2442no—
447Q8—2442no—
448D4—612no—
449D4—1222no—
450D4—1222no—
451D4—1221no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—1221no—
455C2×C4—1222no—
456C2×C4—1222no—
457C2×C4—1224no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—4882no—
461C2×C4—2442no—
462C2×C4—2442no—
463C2×C4—2442no—
464C2×C4—2442no—
465C2×C4—2442no—
466C2×C4#1451975211yescharacteristic
467C2×C4#1451975211yescharacteristic
468C2×C4#1451975211yescharacteristic
469C2×C4#1451975211yescharacteristic
470C2×C4C22×C4×D6111yescharacteristic
471C2×C4C2×D4×D6111yescharacteristic
472C2×C4C22×D24411yescharacteristic
473C2×C4#41×D6111yescharacteristic
474C2×C4#41×D6111yescharacteristic
475C2×C4C2×#1175822211yescharacteristic
476C8—24no—
477C8—21no—
478C8—21no—
479C8—42no—
480C8—1222no—
481C8—1222no—
482C8C4×D24412yes—
483C8C4×D24412yes—
484C22—21no—
485C22—21no—
486C22—1222no—
487C22—2441no—
488C22—2441no—
489C22C4×#1175822611yescharacteristic
490C22C2×#1451975211yescharacteristic
491C22#1684029911yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—1222no—
496C4—4882no—
497C4—2444no—
498C4—2441no—
499C4—2441no—
500C4#1684003812yesdirect product factor
501C4C4×D4×D6111yescharacteristic
502C4C2×C4×D24411yescharacteristic
503C4#1684027411yescharacteristic
504C4#1684030911yescharacteristic
505C2—21no—
506C2—21no—
507C2—2442no—
508C2C4×#1451975211yescharacteristic
509C2C2×#1684003811yescharacteristic
510C2#2145554011yescharacteristic
subgroupG/H
centerC2×C4#14519752
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#108×C61C2
socleC22×C61C2×#121
prime radicalC2×#11758222C23
cosocleC22×C4×C61C24
hypercenterC4×#108D61
hypocenterC61C4×#473
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#108

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic244C2semidirect
5. #21446732C2semidirect
6. #21446605C2semidirect
7. #21446475C2semidirect
10. C4×#14519695C2semidirect
11. C4×#108×C61C2semidirect
18. #16840038C4direct (N × H)
56. C2×Dic244C2×C4semidirect
95. #14519695C2×C4semidirect
108. #108×C61C2×C4semidirect
240. C4×C61#473semidirect
259. C4×#108D61semidirect
303. C61C4×#473semidirect
346. #108C4×D61semidirect
500. C4#16840038direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168400382
C4×#145198102
C2×C4×Dic2442
C4×#145197832
#214467322
#214466052
#214464752
#214463332
#214458802
C4×#145196952
C4×#108×C612
C4×#47361