Finite Group Databasebeta

← C4×#16840034 #29686898

Subgroups — C4×#16840034 #29686898

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×#16840034C211yesmaximal, characteristic
2C4×#14519808C212yesmaximal
3C4×#14519783C211yesmaximal, characteristic
4#21446735C211yesmaximal, characteristic, complemented
5#21446602C211yesmaximal, characteristic, complemented
6#21446471C212yesmaximal, complemented
7#21446337C212yesmaximal
8#21445884C211yesmaximal, characteristic
9C4×#14519713C211yesmaximal, characteristic, complemented
10C4×#14519696C212yesmaximal, complemented
11C2×C4×Q16×C61C211yesmaximal, characteristic, complemented
12C2×#14519808C2212yes—
13C2×#14519783C2211yescharacteristic
14C2×#14519783C2211yescharacteristic
15C4×#11758222C2211yescharacteristic
16#16840034C418yesdirect product factor
17#16839867—22no—
18#16839860—22no—
19C4×#11758202—22no—
20C4×#11758201—22no—
21C2×#14519713C2211yescharacteristic
22C2×#14519713C2211yescharacteristic
23#16839802C2212yes—
24#16839771C2212yes—
25#16839761C2212yes—
26C2×#14519696C2212yes—
27C2×#14519696C2212yes—
28#16839717C2211yescharacteristic
29#16839717C2211yescharacteristic
30#16839716—21no—
31#16839716—21no—
32C4×#11758194C2212yes—
33C4×#11758194C2211yescharacteristic
34C4×#11758189—21no—
35C4×C8×D61—21no—
36#16839531C2212yes—
37#16839531C2212yes—
38#16839527C2212yes—
39C22×Q16×C61C2211yescharacteristic
40C2×C4×Q8×C61C2212yes—
41C4×Q16×C61—21no—
42C4×Q16×C61—21no—
43C4×Q16×C61—21no—
44C4×Q16×C61—21no—
45C2×#107×C61C2211yescharacteristic
46C2×#103×C61C2212yes—
47C2×C4×C8×C61C2211yescharacteristic
48C2×#11758222C2311yescharacteristic
49#14519808—24no—
50#14519808C2×C418yes—
51C2×#11758202—22no—
52C2×#11758201—22no—
53#14519783—22no—
54#14519783—22no—
55#14519783—22no—
56#14519783C2×C414yes—
57C2×#11758194C2312yes—
58C2×#11758194C2311yescharacteristic
59C2×#11758194C2312yes—
60C2×#11758194C2311yescharacteristic
61C2×#11758189—21no—
62C2×#11758189—21no—
63C2×C8×D61—21no—
64C2×C8×D61—21no—
65C4×Dic122D411yescharacteristic
66C4×Dic122D411yescharacteristic
67C4×D244D411yescharacteristic
68C4×D244D411yescharacteristic
69C4×C22⋊D61—21no—
70C4×C22⋊D61—21no—
71#14519736C2311yescharacteristic
72#14519734—21no—
73C42×D61—21no—
74#14519713—22no—
75#14519713C2×C414yescomplemented
76#14519710—22no—
77#14519708—22no—
78#14519701—22no—
79#14519701—22no—
80#14519700—22no—
81#14519697—22no—
82#14519696—24no—
83#14519696C2×C418yescomplemented
84#14519688—21no—
85#14519688—22no—
86#14519687—21no—
87#14519687—21no—
88C4×#92418—21no—
89C4×#92418—22no—
90C8×Dic61—21no—
91C8×Dic61—21no—
92C22×Q8×C61C2312yes—
93C2×Q16×C61—21no—
94C2×Q16×C61—21no—
95C2×Q16×C61—22no—
96C2×Q16×C61C2×C414yescomplemented
97C22×C8×C61C2311yescharacteristic
98C22×C8×C61C2311yescharacteristic
99C4×Q8×C61—22no—
100C4×Q8×C61—22no—
101C4×Q8×C61—22no—
102C4×Q8×C61—22no—
103C2×C4⋊C4×C61—22no—
104C2×C4⋊C4×C61C2312yes—
105C2×C42×C61—22no—
106C2×C42×C61C2311yescharacteristic
107#107×C61—21no—
108#107×C61—21no—
109#103×C61—22no—
110#103×C61—22no—
111C4×C8×C61D411yescharacteristic
112C4×C8×C61D411yescharacteristic
113C4×C8×C61D411yescharacteristic
114C4×C8×C61D411yescharacteristic
115C2×Q8×C61—22no—
116C2×Q8×C61—22no—
117C2×Q8×C61—22no—
118C2×Q8×C61—22no—
119C2×Q8×C61—22no—
120C2×Q8×C61C22×C414yes—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61#4111yescharacteristic
124C22×C4×C61#4111yescharacteristic
125C22×C4×C61C2411yescharacteristic
126C2×C22⋊D61—21no—
127#11758222—21no—
128#11758222—21no—
129#11758222C22×C412yes—
130#11758222#4112yes—
131C2×D244C2×D411yescharacteristic
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×Dic122C2×D411yescharacteristic
136Q16×C61—24no—
137Q16×C61—24no—
138C2×C8×C61—21no—
139C2×C8×C61—21no—
140C2×C8×C61C22×C412yes—
141C2×C8×C61C2×D411yescharacteristic
142C2×C8×C61C2×D411yescharacteristic
143C2×C8×C61C2×D411yescharacteristic
144C2×C8×C61C2×D411yescharacteristic
145C2×C8×C61#4112yes—
146C4⋊C4×C61—22no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61—42no—
149C4⋊C4×C61—42no—
150C42×C61—42no—
151C42×C61—42no—
152C42×C61C2×D411yescharacteristic
153C42×C61C2×D411yescharacteristic
154C42×C61C2×D411yescharacteristic
155C42×C61C2×D411yescharacteristic
156C22⋊Dic61—21no—
157#11758202—28no—
158#11758201—28no—
159#11758198—21no—
160#11758198—21no—
161C4⋊Dic61C2×D411yescharacteristic
162C4⋊Dic61C2×D411yescharacteristic
163#11758196—21no—
164#11758196—21no—
165C4×Dic61—21no—
166C4×Dic61—21no—
167C4×Dic61—21no—
168#11758194—22no—
169#11758194—21no—
170#11758194—21no—
171#11758194—22no—
172#11758194—22no—
173#11758194C22×C414yes—
174#11758194C22×C412yes—
175#11758194#4112yes—
176C2×#92418—21no—
177C2×#92418—21no—
178C2×#92418—22no—
179C2×#92418—22no—
180#11758189—24no—
181#11758189—24no—
182C8×D61—24no—
183C8×D61—24no—
184C23×C61C2×#4111yescharacteristic
185C22×D61—21no—
186Q8×C61—24no—
187Q8×C61—24no—
188Q8×C61—42no—
189Q8×C61—42no—
190C2×C4×C61—22no—
191C2×C4×C61—24no—
192C2×C4×C61—41no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—82no—
197C2×C4×C61#12111yescharacteristic
198C2×C4×C61#12111yescharacteristic
199C2×C4×C61#12111yescharacteristic
200C2×C4×C61#12111yescharacteristic
201C2×C4×C61C23×C411yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C2×C4×C61C22×D411yescharacteristic
204C2×C4×C61C2×#4111yescharacteristic
205C2×C4×C61C2×#4111yescharacteristic
206C2×C4×C61C2×#4111yescharacteristic
207C22⋊D61—22no—
208C22⋊D61—22no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—21no—
212D244—21no—
213D244C4×D412yes—
214C4×D61—22no—
215C4×D61—22no—
216C4×D61—42no—
217C4×D61—42no—
218Dic122—21no—
219Dic122C4×D412yes—
220C8×C61—21no—
221C8×C61—21no—
222C8×C61C4×D412yes—
223C8×C61C4×D412yes—
224#92418—22no—
225#92418—24no—
226#92418—22no—
227#92418—42no—
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—44no—
241C4×C61—82no—
242C4×C61#47312yescomplemented
243C4×C61C2×C4×D411yescharacteristic
244C4×C61C2×C4×D411yescharacteristic
245C4×C61#52511yescharacteristic
246C4×C61#53211yescharacteristic
247Dic61—22no—
248Dic61—41no—
249Dic61—41no—
250C2×#473—611no—
251C4×#137—612no—
252C2×C4×Q16D6111yescharacteristic, complemented
253C4×#131—611no—
254#1979—611no—
255#1952—611no—
256#1930—612no—
257#1908—612no—
258#1816—611no—
259C4×#108—611no—
260C4×#101—612no—
261C2×C61—21no—
262C2×C61—21no—
263C2×C61C4×#12111yescharacteristic
264C2×C61C2×#47311yescharacteristic
265C2×C61#306711yescharacteristic
266D61—42no—
267C2×#137—612no—
268C22×Q16C2×D6111yescharacteristic
269C2×#131—611no—
270C2×#131—611no—
271C4×#41—611no—
272C2×C4×Q8C2×D6112yes—
273#473—618no—
274#441—1222no—
275#440—1222no—
276C4×Q16—21no—
277C4×Q16—21no—
278C4×Q16—21no—
279C4×Q16—21no—
280C4×Q16—1222no—
281C4×SD16—1222no—
282C2×#108—611no—
283C2×#108—611no—
284#428—612no—
285C2×#107C2×D6111yescharacteristic
286#419—612no—
287#417—612no—
288C2×#103C2×D6112yes—
289C2×#101—612no—
290C2×#101—612no—
291#405—611no—
292#405—611no—
293#405—1221no—
294#405—1221no—
295C4×M16—611no—
296C4×M16—612no—
297C4×M16—1221no—
298C2×C4×C8—1221no—
299C2×C4×C8C2×D6111yescharacteristic
300#343—612no—
301#343—612no—
302#341—612no—
303C61C4×#47311yescharacteristic, complemented, Sylow
304C2×#41—611no—
305C22×Q8C22×D6112yes—
306#137—618no—
307#137—1224no—
308C2×Q16—22no—
309C2×Q16—21no—
310C2×Q16—21no—
311C2×Q16—1222no—
312C2×Q16C4×D6114yescomplemented
313C2×SD16—1222no—
314#131—614no—
315#131—1222no—
316#131—1222no—
317#131—1222no—
318C2×M16—611no—
319C2×M16—611no—
320C2×M16—612no—
321C2×M16—612no—
322C2×M16—1221no—
323C2×M16—1221no—
324C22×C8—1221no—
325C22×C8—1221no—
326C22×C8C22×D6111yescharacteristic
327C22×C8C22×D6111yescharacteristic
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×Q8—611no—
333C4×Q8—611no—
334C4×D4—611no—
335C4×D4—611no—
336C4×D4—1221no—
337C4×D4—1221no—
338#117—611no—
339#117—1221no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4C22×D6112yes—
342C2×C42—22no—
343C2×C42—1221no—
344C2×C42C22×D6111yescharacteristic
345#108—614no—
346#108—1222no—
347#107—21no—
348#107—21no—
349#107—1222no—
350#106—1222no—
351#103—22no—
352#103—22no—
353#103—1222no—
354#103—1222no—
355#103—1222no—
356#102—1222no—
357#101—618no—
358#101—1224no—
359#97—1221no—
360#97—1221no—
361#97—1222no—
362#97—1221no—
363C4×C8—1221no—
364C4×C8—1221no—
365C4×C8—1222no—
366C4×C8—1221no—
367C4×C8C22⋊D6111yescharacteristic
368C4×C8C22⋊D6111yescharacteristic
369C4×C8C22⋊D6111yescharacteristic
370C4×C8C22⋊D6111yescharacteristic
371#41—612no—
372#41—612no—
373#41—1221no—
374#41—1221no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—611no—
381C2×Q8C2×C4×D6114yes—
382C2×D4—611no—
383C2×D4—1221no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—1221no—
387C22×C4—1221no—
388C22×C4—1221no—
389C22×C4#1175822411yescharacteristic
390C22×C4#1175822411yescharacteristic
391C22×C4C23×D6111yescharacteristic
392Q16—24no—
393Q16—24no—
394Q16—1228no—
395SD16—1228no—
396M16—612no—
397M16—614no—
398M16—612no—
399M16—1224no—
400M16—1221no—
401M16—1222no—
402M16—1221no—
403M16—1224no—
404M16—1222no—
405M16—1222no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—1224no—
409C2×C8—1222no—
410C2×C8—1221no—
411C2×C8—1221no—
412C2×C8—1224no—
413C2×C8—1222no—
414C2×C8C2×C4×D6112yes—
415C2×C8#1175822212yes—
416C2×C8C2×C22⋊D6111yescharacteristic
417C2×C8C2×C22⋊D6111yescharacteristic
418C2×C8C2×C22⋊D6111yescharacteristic
419C2×C8C2×C22⋊D6111yescharacteristic
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—42no—
423C4⋊C4—42no—
424C4⋊C4—611no—
425C4⋊C4—611no—
426C4⋊C4—1221no—
427C4⋊C4—1221no—
428C22⋊C4—1221no—
429C22⋊C4—1221no—
430C22⋊C4—1221no—
431C42—42no—
432C42—42no—
433C42—1221no—
434C42—1221no—
435C42—1221no—
436C42D4×D6111yescharacteristic
437C42D4×D6111yescharacteristic
438C42C2×C22⋊D6111yescharacteristic
439C42C2×C22⋊D6111yescharacteristic
440C23—1221no—
441C23C2×#1175822411yescharacteristic
442Q8—24no—
443Q8—24no—
444Q8—42no—
445Q8—42no—
446Q8—612no—
447Q8—1221no—
448D4—612no—
449D4—1222no—
450D4—1222no—
451D4—1221no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—82no—
459C2×C4—1221no—
460C2×C4—1222no—
461C2×C4—1222no—
462C2×C4—1221no—
463C2×C4—1221no—
464C2×C4—2442no—
465C2×C4—2442no—
466C2×C4#1451974811yescharacteristic
467C2×C4#1451974811yescharacteristic
468C2×C4#1451974811yescharacteristic
469C2×C4#1451974811yescharacteristic
470C2×C4C22×C4×D6111yescharacteristic
471C2×C4C2×D4×D6111yescharacteristic
472C2×C4C22×C22⋊D6111yescharacteristic
473C2×C4#41×D6111yescharacteristic
474C2×C4#41×D6111yescharacteristic
475C2×C4C2×#1175822211yescharacteristic
476C8—21no—
477C8—21no—
478C8—1224no—
479C8—1222no—
480C8—1222no—
481C8—2442no—
482C8C4×C22⋊D6112yes—
483C8C4×C22⋊D6112yes—
484C22—21no—
485C22—21no—
486C22—1222no—
487C22—2441no—
488C22—2441no—
489C22C4×#1175822411yescharacteristic
490C22C2×#1451974811yescharacteristic
491C22#1684029411yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—44no—
496C4—82no—
497C4—1222no—
498C4—2441no—
499C4—2441no—
500C4#1684003412yesdirect product factor
501C4C4×D4×D6111yescharacteristic
502C4C2×C4×C22⋊D6111yescharacteristic
503C4#1684026911yescharacteristic
504C4#1684030911yescharacteristic
505C2—21no—
506C2—21no—
507C2—2442no—
508C2C4×#1451974811yescharacteristic
509C2C2×#1684003411yescharacteristic
510C2#2145553511yescharacteristic
subgroupG/H
centerC2×C4#14519748
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×Q16×C61C2
socleC22×C61C2×#121
prime radicalC2×#11758222C23
cosocleC22×C4×C61C24
hypercenterC2×C4×Q16D61
hypocenterC61C4×#473
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
4. #21446735C2semidirect
5. #21446602C2semidirect
6. #21446471C2semidirect
9. C4×#14519713C2semidirect
10. C4×#14519696C2semidirect
11. C2×C4×Q16×C61C2semidirect
16. #16840034C4direct (N × H)
75. #14519713C2×C4semidirect
83. #14519696C2×C4semidirect
96. C2×Q16×C61C2×C4semidirect
242. C4×C61#473semidirect
252. C2×C4×Q16D61semidirect
303. C61C4×#473semidirect
312. C2×Q16C4×D61semidirect
500. C4#16840034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168400342
C4×#145198082
C4×#145197832
#214467352
#214466022
#214464712
#214463372
#214458842
C4×#145197132
C4×#145196962
C2×C4×Q16×C612
C4×#47361