Finite Group Databasebeta

← C4×#17989630 #34020488

Subgroups — C4×#17989630 #34020488

Order 18688.

1046 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989630C212yesmaximal
2C4×#14556679C211yesmaximal, characteristic, complemented
3C4×#14556678C211yesmaximal, characteristic, complemented
4C4×#14556661C211yesmaximal, characteristic, complemented
5#22625734C212yesmaximal, complemented
6#22625708C212yesmaximal, complemented
7#22625706C212yesmaximal, complemented
8C4×#14556656C211yesmaximal, characteristic, complemented
9C4×#14556655C211yesmaximal, characteristic, complemented
10C4×C8×#64408C211yesmaximal, characteristic, complemented
11C4×#14556612C211yesmaximal, characteristic
12C2×#14556679C2212yes—
13C2×#14556678C2212yes—
14#17989630C4116yesdirect product factor
15C2×#14556661C2212yes—
16C2×#14556656C2212yes—
17C2×#14556655C2212yes—
18#17989552—22no—
19#17989552C2212yes—
20#17989552C2212yes—
21#17989551—22no—
22C4×#11924038—21no—
23C4×#11924038C2211yescharacteristic
24C4×#11924038C2211yescharacteristic
25C4×#11924037—21no—
26C4×#11924036—21no—
27C4×#11924036C2211yescharacteristic
28C2×C4×#10596833—21no—
29C2×C8×#64408C2212yes—
30C2×C8×#64408C2212yes—
31C42×#64408C2211yescharacteristic
32#17989463C2212yes—
33#17989457C2212yes—
34#17989457C2212yes—
35C2×#14556612C2211yescharacteristic
36C4×#11924029C2211yescharacteristic
37C4×#11924027C2211yescharacteristic
38C4×#11924018C411yescharacteristic, complemented
39#17988679C411yescharacteristic, complemented
40C4×#11924017C411yescharacteristic, complemented
41SD16×Dic73C411yescharacteristic, complemented
42#17988674C411yescharacteristic, complemented
43C4×#11924013C411yescharacteristic, complemented
44#17988667C411yescharacteristic, complemented
45#17988622C2211yescharacteristic
46#17988582C2211yescharacteristic
47#17988580C2211yescharacteristic
48C4×C8×D73C2211yescharacteristic
49C4×SD16×C73C411yescharacteristic, complemented
50#14556679—24no—
51#14556679C2×C418yescomplemented
52#14556678—24no—
53#14556678C2×C418yescomplemented
54C2×#11924038—22no—
55C2×#11924038C2312yes—
56C2×#11924038C2312yes—
57C2×#11924037—22no—
58C2×#11924036—22no—
59C2×#11924036C2312yes—
60C22×#10596833—22no—
61C2×C4×#64408—21no—
62C2×C4×#64408—21no—
63C2×C4×#64408C2312yes—
64#14556661C2×C418yescomplemented
65#14556656C2×C418yescomplemented
66#14556655C2×C418yescomplemented
67#14556646—22no—
68#14556646—22no—
69#14556646—21no—
70#14556646—21no—
71C4×#10596833—22no—
72C4×#10596833—22no—
73C4×#10596833—21no—
74C4×#10596833—21no—
75C4×#10596833D411yescharacteristic
76C4×#10596833D411yescharacteristic
77C4×#10596833D412yes—
78C8×#64408—24no—
79C8×#64408C2×C418yescomplemented
80C2×#11924029C2311yescharacteristic
81C2×#11924027C2311yescharacteristic
82#14556612C2×C418yes—
83C2×#11924018C2×C411yescharacteristic
84C2×#11924017C2×C411yescharacteristic
85C2×#11924013C2×C411yescharacteristic
86C2×C8×D73C2311yescharacteristic
87C2×C8×D73C2311yescharacteristic
88Q8×Dic73C2×C411yescharacteristic
89C4×Dic146C2×C411yescharacteristic
90#14556556C2×C411yescharacteristic
91C4×D292—21no—
92C4×D292C2×C411yescharacteristic
93D4×Dic73C2×C411yescharacteristic
94#14556553—21no—
95#14556553C2×C411yescharacteristic
96C4×C22⋊D73—21no—
97#14556551—21no—
98#14556549—21no—
99#14556549C2311yescharacteristic
100#14556549C2311yescharacteristic
101#14556547—21no—
102C2×C4×Dic73—21no—
103C42×D73—21no—
104C42×D73C2311yescharacteristic
105#14556524C2×C411yescharacteristic
106#14556524C2×C411yescharacteristic
107#14556523C2×C411yescharacteristic
108#14556516C2×C411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556514C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556512C2×C411yescharacteristic
113#14556511C2×C411yescharacteristic
114C4×#10596831C2×C411yescharacteristic
115C8×Dic73C2×C411yescharacteristic
116C8×Dic73C2×C411yescharacteristic
117C2×SD16×C73C2×C411yescharacteristic
118C4×Q8×C73C2×C411yescharacteristic
119C4×D4×C73C2×C411yescharacteristic
120#106×C73C2×C411yescharacteristic
121#103×C73C2×C411yescharacteristic
122#102×C73C2×C411yescharacteristic
123C4×C8×C73C2×C411yescharacteristic
124C22×#64408—22no—
125#11924038—22no—
126#11924038—22no—
127#11924038—28no—
128#11924038C22×C414yes—
129#11924038C22×C414yes—
130#11924037—28no—
131#11924036—28no—
132#11924036C22×C414yes—
133#11924036#4114yes—
134C2×#10596833—22no—
135C2×#10596833—22no—
136C2×#10596833—28no—
137C2×#10596833C2×D412yes—
138C2×#10596833C2×D412yes—
139C4×#64408—24no—
140C4×#64408—24no—
141C4×#64408—22no—
142C4×#64408C22×C414yes—
143#11924029—22no—
144#11924029C22×C414yes—
145#11924027—22no—
146#11924027C22×C414yes—
147C2×Dic146C22×C411yescharacteristic
148C2×D292—21no—
149C2×D292C22×C411yescharacteristic
150C2×C22⋊D73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73#4111yescharacteristic
157C2×C4×D73#4111yescharacteristic
158C2×C4×D73C2411yescharacteristic
159#11924018C4214yescomplemented
160#11924017C4214yescomplemented
161#11924013C4214yescomplemented
162C2×#10596831C22×C411yescharacteristic
163C2×#10596831C22×C411yescharacteristic
164C8×D73—22no—
165C8×D73C22×C414yes—
166C4⋊Dic73—21no—
167C4⋊Dic73C22×C411yescharacteristic
168C4⋊Dic73C22×C411yescharacteristic
169#11924007—21no—
170#11924007—21no—
171C22⋊Dic73—21no—
172#11924005—21no—
173#11924005—21no—
174#11924005—21no—
175#11924005—21no—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C4×Dic73—21no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73C22×C411yescharacteristic
182C4×Dic73C2×D411yescharacteristic
183C4×Dic73C2×D411yescharacteristic
184C2×Q8×C73C22×C411yescharacteristic
185C2×D4×C73C22×C411yescharacteristic
186C22×C4×C73—21no—
187SD16×C73C4214yescomplemented
188C2×C8×C73C22×C411yescharacteristic
189C2×C8×C73C22×C411yescharacteristic
190C4⋊C4×C73—21no—
191C4⋊C4×C73C22×C411yescharacteristic
192C4⋊C4×C73C22×C411yescharacteristic
193C22⋊C4×C73—21no—
194C42×C73—21no—
195C42×C73C22×C411yescharacteristic
196C23×C73—21no—
197C22×D73—21no—
198C22×D73C2×#4111yescharacteristic
199C2×#64408—24no—
200C2×#64408—24no—
201C2×#64408—24no—
202Q8×C73—21no—
203Q8×C73C2×C4212yes—
204D4×C73—21no—
205D4×C73C2×C4212yes—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—42no—
210C2×C4×C73C4×D411yescharacteristic
211C2×C4×C73C4×D411yescharacteristic
212C2×C4×C73C23×C411yescharacteristic
213C22⋊D73—24no—
214C2×Dic73—21no—
215C2×Dic73—24no—
216C2×Dic73—21no—
217C2×Dic73—21no—
218C2×Dic73—42no—
219C2×Dic73C4×D411yescharacteristic
220C2×Dic73C4×D411yescharacteristic
221C2×Dic73C22×D411yescharacteristic
222D292—24no—
223D292—21no—
224D292C2×C4212yes—
225C4×D73—22no—
226C4×D73—24no—
227C4×D73—22no—
228C4×D73—42no—
229C4×D73—42no—
230C4×D73C23×C412yes—
231C4×D73C2×#4112yes—
232Dic146—21no—
233Dic146C2×C4212yes—
234#10596833—24no—
235#10596833—24no—
236#10596833C4×D414yes—
237#10596833C4×D414yes—
238C8×C73—21no—
239C8×C73C2×C4212yes—
240#10596831—21no—
241#10596831C2×C4212yes—
242C22×C73—22no—
243C22×C73—41no—
244C22×C73—41no—
245C22×C73C2×C4×D411yescharacteristic
246C2×D73—21no—
247C2×D73—21no—
248C2×D73—22no—
249C2×D73—41no—
250C2×D73—41no—
251C2×D73C4×#4112yes—
252#64408—28no—
253C4×C73—21no—
254C4×C73—22no—
255C4×C73—41no—
256C4×C73—41no—
257C4×C73#44312yescomplemented
258C4×C73C22×C4211yescharacteristic
259C4×C73C4×#4111yescharacteristic
260Dic73—21no—
261Dic73—22no—
262Dic73—41no—
263Dic73—41no—
264Dic73#44312yescomplemented
265Dic73C2×C4×D412yes—
266C4×#443—731nomaximal, Sylow
267C2×C73—42no—
268C2×C73C42×D411yescharacteristic
269C2×C73C2×#44311yescharacteristic
270C2×C73C2×#44311yescharacteristic
271D73—22no—
272D73—42no—
273C2×#443—732no—
274C4×#135—731no—
275C4×#131—731no—
276C4×#131—731no—
277C4×#108—731no—
278#1772—732no—
279#1764—732no—
280#1764—732no—
281C4×#104—731no—
282C4×#104—731no—
283C42×C8—731no—
284C73C4×#44311yescharacteristic, complemented, Sylow
285C2×#135—731no—
286C2×#131—732no—
287C2×#131—732no—
288C4×#41—731no—
289C4×#41—731no—
290#443—7316no—
291C4×Q16—731no—
292C4×Q16—731no—
293C4×SD16—731no—
294C4×SD16—731no—
295C4×SD16—731no—
296C4×SD16#6440811yescharacteristic, complemented
297C4×D8—731no—
298C4×D8—731no—
299C2×#108—732no—
300#427—731no—
301C2×#104—732no—
302C2×#104—732no—
303#416—731no—
304#416—731no—
305#405—732no—
306#405—732no—
307#405—1462no—
308#405—1462no—
309C4×M16—731no—
310C4×M16—731no—
311C4×M16—1461no—
312C4×M16—1461no—
313C2×C4×C8—731no—
314C2×C4×C8—732no—
315C2×C4×C8—731no—
316C2×C4×C8—732no—
317C2×C4×C8—1461no—
318C2×C4×C8—1461no—
319C43—731no—
320#341—732no—
321#339—732no—
322#339—732no—
323C2×#41—731no—
324C2×#41—731no—
325#135—738no—
326C2×Q16—731no—
327C2×SD16—731no—
328C2×SD16C2×#6440811yescharacteristic
329C2×D8—731no—
330#131—738no—
331#131—738no—
332#131—1464no—
333#131—1464no—
334C2×M16—732no—
335C2×M16—732no—
336C2×M16—1462no—
337C2×M16—1462no—
338C22×C8—732no—
339C22×C8—731no—
340C22×C8—731no—
341C22×C8—1462no—
342C22×C8—1462no—
343C4×Q8—731no—
344C4×Q8—731no—
345C4×Q8—731no—
346C4×Q8C2×#6440811yescharacteristic
347C4×D4—731no—
348C4×D4—731no—
349C4×D4—731no—
350C4×D4—1461no—
351C4×D4—1461no—
352C4×D4—1461no—
353C4×D4—1461no—
354C4×D4C2×#6440811yescharacteristic
355#117—731no—
356#117—731no—
357#117—1461no—
358#117—1461no—
359C2×C42—731no—
360C2×C42—732no—
361C2×C42—1461no—
362C2×C42—1461no—
363C2×C42—1461no—
364C2×C42—1461no—
365#108—738no—
366#107—731no—
367#107—731no—
368#106—731no—
369#106C2×#6440811yescharacteristic
370#104—738no—
371#104—738no—
372#103—731no—
373#103—731no—
374#103—731no—
375#103C2×#6440811yescharacteristic
376#102—731no—
377#102—731no—
378#102—731no—
379#102C2×#6440811yescharacteristic
380#97—1461no—
381#97—1461no—
382#97—1462no—
383#97—1462no—
384C4×C8—731no—
385C4×C8—731no—
386C4×C8—732no—
387C4×C8—738no—
388C4×C8—731no—
389C4×C8—731no—
390C4×C8—731no—
391C4×C8—1461no—
392C4×C8—1461no—
393C4×C8—1464no—
394C4×C8—1462no—
395C4×C8—1462no—
396C4×C8C2×#6440811yescharacteristic
397#41—734no—
398#41—734no—
399#41—1462no—
400#41—1462no—
401C2×Q8—731no—
402C2×Q8C22×#6440811yescharacteristic
403C2×D4—731no—
404C2×D4—1461no—
405C2×D4—1461no—
406C2×D4C22×#6440811yescharacteristic
407C22×C4—21no—
408C22×C4—731no—
409C22×C4—731no—
410C22×C4—731no—
411C22×C4—1461no—
412C22×C4—1461no—
413C22×C4—1461no—
414C22×C4—1461no—
415C22×C4—1461no—
416C22×C4—1462no—
417Q16—734no—
418SD16—734no—
419SD16C4×#6440814yescomplemented
420D8—734no—
421M16—734no—
422M16—734no—
423M16—1468no—
424M16—1468no—
425M16—1462no—
426M16—1462no—
427C2×C8—732no—
428C2×C8—732no—
429C2×C8—734no—
430C2×C8—734no—
431C2×C8—731no—
432C2×C8—734no—
433C2×C8—731no—
434C2×C8—1462no—
435C2×C8—1468no—
436C2×C8—1468no—
437C2×C8—1462no—
438C2×C8—1462no—
439C2×C8C22×#6440811yescharacteristic
440C2×C8C22×#6440811yescharacteristic
441C4⋊C4—21no—
442C4⋊C4—731no—
443C4⋊C4—731no—
444C4⋊C4—1461no—
445C4⋊C4—1461no—
446C4⋊C4—1461no—
447C4⋊C4C22×#6440811yescharacteristic
448C4⋊C4C22×#6440811yescharacteristic
449C22⋊C4—21no—
450C22⋊C4—1461no—
451C22⋊C4—1461no—
452C22⋊C4—1461no—
453C22⋊C4—1461no—
454C22⋊C4—1461no—
455C42—21no—
456C42—731no—
457C42—731no—
458C42—731no—
459C42—734no—
460C42—1461no—
461C42—1461no—
462C42—1461no—
463C42—1461no—
464C42—1462no—
465C42—1464no—
466C42—1464no—
467C42—1461no—
468C42C22×#6440811yescharacteristic
469C23—21no—
470C23—731no—
471C23—1461no—
472Q8—21no—
473Q8—732no—
474Q8—1461no—
475Q8C2×C4×#6440812yes—
476D4—21no—
477D4—732no—
478D4—1464no—
479D4—1464no—
480D4—1461no—
481D4C2×C4×#6440812yes—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—42no—
486C2×C4—2922no—
487C2×C4—2922no—
488C2×C4—2922no—
489C2×C4—731no—
490C2×C4—731no—
491C2×C4—732no—
492C2×C4—732no—
493C2×C4—731no—
494C2×C4—1462no—
495C2×C4—1464no—
496C2×C4—1461no—
497C2×C4—1461no—
498C2×C4—1464no—
499C2×C4—1464no—
500C2×C4—1464no—
501C2×C4—1464no—
502C2×C4—1461no—
503C2×C4—1462no—
504C2×C4D4×#6440811yescharacteristic
505C2×C4D4×#6440811yescharacteristic
506C2×C4C23×#6440811yescharacteristic
507C8—21no—
508C8—734no—
509C8—734no—
510C8—732no—
511C8—1464no—
512C8—1464no—
513C8—1461no—
514C8C2×C4×#6440812yes—
515C22—22no—
516C22—41no—
517C22—41no—
518C22—2921no—
519C22—2921no—
520C22—732no—
521C22—1462no—
522C22—1461no—
523C22—1461no—
524C22C2×D4×#6440811yescharacteristic
525C4—22no—
526C4—21no—
527C4—41no—
528C4—41no—
529C4—2921no—
530C4—2921no—
531C4—732no—
532C4—732no—
533C4—1468no—
534C4—1462no—
535C4—1461no—
536C4#1798963012yesdirect product factor
537C4C22×C4×#6440811yescharacteristic
538C4#41×#6440811yescharacteristic
539C2—42no—
540C2—2922no—
541C2—1462no—
542C2C4×D4×#6440811yescharacteristic
543C2C2×#1798963011yescharacteristic
544C2D73⋊#44311yescharacteristic
subgroupG/H
centerC2×C4D4×#64408
commutatorC4×C73C22×C42
FrattiniC2×C4C23×#64408
FittingC4×SD16×C73C4
socleC22×C73C2×C4×D4
prime radicalC2×#14556612C22
cosocleC2×C4×D73C24
hypercenterC4×SD16#64408
hypocenterC73C4×#443
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×#14556679C2semidirect
3. C4×#14556678C2semidirect
4. C4×#14556661C2semidirect
5. #22625734C2semidirect
6. #22625708C2semidirect
7. #22625706C2semidirect
8. C4×#14556656C2semidirect
9. C4×#14556655C2semidirect
10. C4×C8×#64408C2semidirect
14. #17989630C4direct (N × H)
38. C4×#11924018C4semidirect
39. #17988679C4semidirect
40. C4×#11924017C4semidirect
41. SD16×Dic73C4semidirect
42. #17988674C4semidirect
43. C4×#11924013C4semidirect
44. #17988667C4semidirect
49. C4×SD16×C73C4semidirect
51. #14556679C2×C4semidirect
53. #14556678C2×C4semidirect
64. #14556661C2×C4semidirect
65. #14556656C2×C4semidirect
66. #14556655C2×C4semidirect
79. C8×#64408C2×C4semidirect
159. #11924018C42semidirect
160. #11924017C42semidirect
161. #11924013C42semidirect
187. SD16×C73C42semidirect
257. C4×C73#443semidirect
264. Dic73#443semidirect
284. C73C4×#443semidirect
296. C4×SD16#64408semidirect
419. SD16C4×#64408semidirect
536. C4#17989630direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179896302
C4×#145566792
C4×#145566782
C4×#145566612
#226257342
#226257082
#226257062
C4×#145566562
C4×#145566552
C4×C8×#644082
C4×#145566122
C4×#44373