Finite Group Databasebeta

← C4×#17989330 #33248689

Subgroups — C4×#17989330 #33248689

Order 18688.

2664 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989330C211yesmaximal, characteristic
2#22613104C216yesmaximal, complemented
3#22613101C213yesmaximal, complemented
4#22613072C211yesmaximal, characteristic, complemented
5#22613070C212yesmaximal, complemented
6#22613069C213yesmaximal, complemented
7C4×#14556578C213yesmaximal, complemented
8C4×#14556577C216yesmaximal, complemented
9C4×#14556560C212yesmaximal, complemented
10C4×#14556559C213yesmaximal, complemented
11C4×#120×C73C211yesmaximal, characteristic, complemented
12C23×C4×D73C2211yescharacteristic, complemented
13#17989330C4116yesdirect product factor
14C2×#14556578C2213yes—
15C2×#14556577C2216yes—
16C2×#14556560C2212yes—
17C2×#14556559C2213yes—
18C2×C4×Dic146C2213yescomplemented
19C2×C4×C22⋊D73C2216yes—
20#17988492C2213yescomplemented
21#17988491C2216yescomplemented
22#17988490C2213yes—
23#17988487C2216yes—
24#17988481C2216yescomplemented
25#17988481C2216yescomplemented
26#17988480C2216yescomplemented
27#17988479C2216yescomplemented
28#17988476C2216yescomplemented
29#17988475C2216yescomplemented
30#17988467C2213yes—
31#17988466C2216yes—
32#17988463C2216yes—
33#17988460C2216yescomplemented
34#17988459C2213yescomplemented
35#17988458C2216yescomplemented
36#17988452C2213yescomplemented
37#17988451C2216yescomplemented
38#17988443C2212yescomplemented
39#17988442C2213yescomplemented
40C4×#11924005C2216yescomplemented
41C4×C22⋊Dic73C2213yescomplemented
42C4×C22⋊Dic73C2216yescomplemented
43C42×Dic73C2213yescomplemented
44C24×C4×C73C2211yescharacteristic, complemented
45C2×#120×C73C2211yescharacteristic
46C2×C4×D4×C73C2213yes—
47#386×C73C2213yes—
48#385×C73C2213yescomplemented
49#379×C73C2211yescharacteristic, complemented
50C4×C22⋊C4×C73C2213yescomplemented
51C24×D73C2311yescharacteristic
52C22×Dic146C2313yes—
53C22×C22⋊D73C2316yes—
54C23×Dic73C2311yescharacteristic
55C22×C4×D73—46no—
56C22×C4×D73C2312yes—
57C22×C4×D73C2312yes—
58#14556578C2×C4124yescomplemented
59#14556577C2×C4148yescomplemented
60#14556560C2×C4116yescomplemented
61#14556559C2×C4124yescomplemented
62C4×Dic146—46no—
63C4×C22⋊D73—412no—
64C2×C4⋊Dic73C2313yes—
65C2×#11924007C2316yes—
66C2×#11924007C2316yes—
67C2×C22⋊Dic73C2313yes—
68C2×C22⋊Dic73C2316yes—
69C2×C22⋊Dic73C2316yes—
70C2×C22⋊Dic73C2313yes—
71C2×C22⋊Dic73C2316yes—
72C2×#11924005C2316yes—
73C2×#11924005C2316yes—
74C2×#11924005C2316yes—
75C2×C4×Dic73C2316yes—
76C2×C4×Dic73C2316yes—
77C2×C4×Dic73C2313yes—
78C2×C4×Dic73C2313yes—
79#14556498C2316yes—
80#14556498C2316yes—
81#14556498C2316yes—
82#14556498C2316yes—
83#14556498C2316yes—
84C25×C73C2311yescharacteristic
85C22×D4×C73C2313yes—
86C23×C4×C73—46no—
87C23×C4×C73C2313yes—
88C23×C4×C73C2311yescharacteristic
89C23×C4×C73C2313yes—
90#120×C73C2×C418yescomplemented
91C4×D4×C73—46no—
92C2×C4⋊C4×C73C2313yes—
93C2×C22⋊C4×C73C2313yes—
94C2×C22⋊C4×C73C2313yes—
95C2×C22⋊C4×C73C2313yes—
96C2×C22⋊C4×C73C2313yes—
97C2×C42×C73C2313yes—
98#95×C73C2316yes—
99C23×D73—43no—
100C23×D73—43no—
101C23×D73C22×C414yescomplemented
102C23×D73C2412yes—
103C2×Dic146—43no—
104C2×Dic146—43no—
105C2×Dic146C22×C4112yescomplemented
106C2×C22⋊D73—46no—
107C2×C22⋊D73—46no—
108C2×C22⋊D73C22×C4124yes—
109C22×Dic73—43no—
110C22×Dic73C2412yes—
111C22×Dic73C2416yes—
112C22×Dic73C2416yes—
113C2×C4×D73—212no—
114C2×C4×D73—46no—
115C2×C4×D73—416no—
116C4⋊Dic73—43no—
117#11924007—46no—
118#11924007—46no—
119C22⋊Dic73—46no—
120C22⋊Dic73—43no—
121C22⋊Dic73—46no—
122C22⋊Dic73C22×C4112yescomplemented
123C22⋊Dic73C22×C4124yescomplemented
124#11924005—46no—
125#11924005—46no—
126#11924005C22×C4124yescomplemented
127C4×Dic73—212no—
128C4×Dic73—46no—
129C4×Dic73—43no—
130C4×Dic73C22×C4112yescomplemented
131C24×C73—43no—
132C24×C73—43no—
133C24×C73C22×C414yescomplemented
134C24×C73C2413yes—
135C24×C73C2411yescharacteristic
136C2×D4×C73—43no—
137C2×D4×C73—43no—
138C2×D4×C73C22×C4112yes—
139C22×C4×C73—26no—
140C22×C4×C73—26no—
141C22×C4×C73—212no—
142C22×C4×C73—46no—
143C22×C4×C73—43no—
144C22×C4×C73—416no—
145C22×C4×C73C2413yes—
146C22×C4×C73C2413yes—
147C22×C4×C73C2411yescharacteristic
148C22×C4×C73C2413yes—
149C22×C4×C73C2411yescharacteristic
150C4⋊C4×C73—43no—
151C22⋊C4×C73—43no—
152C22⋊C4×C73—43no—
153C22⋊C4×C73—43no—
154C22⋊C4×C73C22×C4112yescomplemented
155C42×C73—26no—
156C23×C73—23no—
157C23×C73—23no—
158C23×C73—26no—
159C23×C73—23no—
160C23×C73—23no—
161C23×C73—26no—
162C23×C73—412no—
163C23×C73—44no—
164C23×C73—412no—
165C23×C73C23×C416yes—
166C23×C73C23×C412yes—
167C23×C73C2511yescharacteristic
168C22×D73—26no—
169C22×D73—26no—
170C22×D73—412no—
171C22×D73—44no—
172C22×D73—412no—
173C22×D73C23×C414yes—
174D4×C73—412no—
175C2×C4×C73—23no—
176C2×C4×C73—23no—
177C2×C4×C73—23no—
178C2×C4×C73—23no—
179C2×C4×C73—23no—
180C2×C4×C73—26no—
181C2×C4×C73—26no—
182C2×C4×C73—412no—
183C2×C4×C73—412no—
184C2×C4×C73—44no—
185C2×C4×C73C23×C416yes—
186C2×C4×C73H(5,𝔽2)16yes—
187C22⋊D73—424no—
188C2×Dic73—26no—
189C2×Dic73—26no—
190C2×Dic73—26no—
191C2×Dic73—26no—
192C2×Dic73—26no—
193C2×Dic73—26no—
194C2×Dic73—44no—
195C2×Dic73C23×C4112yes—
196C4×D73—48no—
197C4×D73—48no—
198Dic146—412no—
199C22×C73—212no—
200C22×C73—26no—
201C22×C73—26no—
202C22×C73—416no—
203C22×C73—41no—
204C22×C73—43no—
205C22×C73—43no—
206C22×C73—43no—
207C22×C73—46no—
208C22×C73C24×C411yescharacteristic
209C22×C73C2×H(5,𝔽2)13yes—
210C22×C73#58513yes—
211C2×D73—212no—
212C2×D73—416no—
213C2×D73—42no—
214C2×D73—46no—
215C4×C73—26no—
216C4×C73—41no—
217C4×C73—43no—
218C4×C73—43no—
219C4×C73H(3,𝔽4)14yescomplemented
220Dic73—212no—
221Dic73—42no—
222Dic73—46no—
223C4×H(3,𝔽4)—731nomaximal, Sylow
224C2×C73—42no—
225C2×C73—46no—
226C2×C73C4×H(5,𝔽2)13yes—
227C2×C73C2×H(3,𝔽4)11yescharacteristic
228C2×C73#352913yes—
229D73—44no—
230C2×H(3,𝔽4)—731no—
231#2379—733no—
232#2379—736no—
233#2375—733no—
234#2375—732no—
235#2375—731no—
236C4×#124—736no—
237C4×#124—733no—
238C4×#120—732no—
239C4×#120—733no—
240C4×#120D7311yescharacteristic, complemented
241C73C4×H(3,𝔽4)11yescharacteristic, complemented, Sylow
242C24×C4—731no—
243C24×C4C2×D7311yescharacteristic, complemented
244H(3,𝔽4)—7316no—
245C2×#124—733no—
246C2×#124—736no—
247C2×#120—732no—
248C2×#120—733no—
249C2×#120C2×D7311yescharacteristic
250C2×C4×Q8—733no—
251C2×C4×D4—736no—
252C2×C4×D4C2×D7313yes—
253#391—733no—
254#391—736no—
255#390—733no—
256#390—736no—
257#388—736no—
258#388—736no—
259#388—736no—
260#388—736no—
261#388—736no—
262#388—736no—
263#386—733no—
264#386—736no—
265#386—736no—
266#386C2×D7313yes—
267#385—736no—
268#385—736no—
269#385—733no—
270#385C2×D7313yescomplemented
271#382—733no—
272#382—736no—
273#379—732no—
274#379—733no—
275#379C2×D7311yescharacteristic, complemented
276C4×C22⋊C4—736no—
277C4×C22⋊C4—733no—
278C4×C22⋊C4—736no—
279C4×C22⋊C4C2×D7313yescomplemented
280C43—733no—
281C25—731no—
282C25C22×D7311yescharacteristic
283C22×Q8—733no—
284C22×D4—736no—
285C22×D4C22×D7313yes—
286C23×C4—46no—
287C23×C4—2926no—
288C23×C4—731no—
289C23×C4—732no—
290C23×C4—732no—
291C23×C4C22×D7313yes—
292C23×C4C22×D7311yescharacteristic
293C23×C4C22×D7313yes—
294#124—7324no—
295#124—7348no—
296#120—7316no—
297#120—7324no—
298#120C4×D7318yescomplemented
299C4×Q8—2926no—
300C4×D4—46no—
301C4×D4—29212no—
302C2×C4⋊C4—736no—
303C2×C4⋊C4—736no—
304C2×C4⋊C4—733no—
305C2×C4⋊C4C22×D7313yes—
306C2×C22⋊C4—736no—
307C2×C22⋊C4—733no—
308C2×C22⋊C4—736no—
309C2×C22⋊C4—736no—
310C2×C22⋊C4—736no—
311C2×C22⋊C4—733no—
312C2×C22⋊C4—736no—
313C2×C22⋊C4—736no—
314C2×C22⋊C4C22×D7313yes—
315C2×C22⋊C4C22×D7313yes—
316C2×C22⋊C4C22×D7313yes—
317C2×C22⋊C4C22×D7313yes—
318C2×C42—736no—
319C2×C42—733no—
320C2×C42—733no—
321C2×C42—736no—
322C2×C42C22×D7313yes—
323#95—736no—
324#95—736no—
325#95—736no—
326#95—736no—
327#95—736no—
328#95C22×D7316yes—
329C24—43no—
330C24—43no—
331C24—2923no—
332C24—2923no—
333C24—734no—
334C24—732no—
335C24C2×C4×D7314yescomplemented
336C24C23×D7311yescharacteristic
337C24C23×D7313yes—
338C2×Q8—2923no—
339C2×Q8—2923no—
340C2×Q8—7312no—
341C2×D4—43no—
342C2×D4—43no—
343C2×D4—2926no—
344C2×D4—2926no—
345C2×D4—7324no—
346C2×D4C2×C4×D73112yes—
347C22×C4—26no—
348C22×C4—26no—
349C22×C4—212no—
350C22×C4—46no—
351C22×C4—43no—
352C22×C4—416no—
353C22×C4—2926no—
354C22×C4—29216no—
355C22×C4—2923no—
356C22×C4—736no—
357C22×C4—732no—
358C22×C4—736no—
359C22×C4—14612no—
360C22×C4C23×D7311yescharacteristic
361C22×C4C23×D7313yes—
362C22×C4C23×D7313yes—
363C22×C4C23×D7313yes—
364C22×C4C23×D7311yescharacteristic
365C4⋊C4—43no—
366C4⋊C4—2926no—
367C4⋊C4—2926no—
368C4⋊C4—2923no—
369C22⋊C4—43no—
370C22⋊C4—43no—
371C22⋊C4—43no—
372C22⋊C4—2926no—
373C22⋊C4—2926no—
374C22⋊C4—2923no—
375C22⋊C4—2926no—
376C22⋊C4—2926no—
377C22⋊C4—7312no—
378C22⋊C4—7324no—
379C22⋊C4—7324no—
380C22⋊C4C2×C4×D73112yescomplemented
381C42—26no—
382C42—2923no—
383C42—2926no—
384C42—7312no—
385C42—14612no—
386C23—23no—
387C23—23no—
388C23—26no—
389C23—23no—
390C23—23no—
391C23—26no—
392C23—412no—
393C23—44no—
394C23—412no—
395C23—29212no—
396C23—2924no—
397C23—29212no—
398C23—734no—
399C23—1466no—
400C23—1466no—
401C23C22×C4×D7312yes—
402C23C22×C4×D7316yes—
403C23C24×D7311yescharacteristic
404Q8—29212no—
405D4—412no—
406D4—29224no—
407C2×C4—23no—
408C2×C4—23no—
409C2×C4—23no—
410C2×C4—23no—
411C2×C4—23no—
412C2×C4—26no—
413C2×C4—26no—
414C2×C4—412no—
415C2×C4—412no—
416C2×C4—44no—
417C2×C4—2928no—
418C2×C4—2924no—
419C2×C4—2928no—
420C2×C4—7312no—
421C2×C4—1466no—
422C2×C4—1466no—
423C2×C4—1466no—
424C2×C4—1466no—
425C2×C4—1466no—
426C2×C4—1466no—
427C2×C4C22×C4×D7316yes—
428C2×C4#1455663616yes—
429C22—26no—
430C22—26no—
431C22—212no—
432C22—416no—
433C22—43no—
434C22—41no—
435C22—43no—
436C22—46no—
437C22—43no—
438C22—29216no—
439C22—2922no—
440C22—2926no—
441C22—14612no—
442C22C23×C4×D7311yescharacteristic
443C22C2×#1455663613yes—
444C22#1798942313yes—
445C4—26no—
446C4—43no—
447C4—41no—
448C4—43no—
449C4—2922no—
450C4—2926no—
451C4—14612no—
452C4#1798933014yesdirect product factor
453C2—46no—
454C2—42no—
455C2—2924no—
456C2C4×#1455663613yes—
457C2C2×#1798933011yescharacteristic
458C2#2262406913yes—
subgroupG/H
centerC22×C4C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC4×#120×C73C2
socle, cosocleC23×C73C25
prime radicalC2×#17989330C2
hypercenterC4×#120D73
hypocenterC73C4×H(3,𝔽4)
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
2. #22613104C2semidirect
3. #22613101C2semidirect
4. #22613072C2semidirect
5. #22613070C2semidirect
6. #22613069C2semidirect
7. C4×#14556578C2semidirect
8. C4×#14556577C2semidirect
9. C4×#14556560C2semidirect
10. C4×#14556559C2semidirect
11. C4×#120×C73C2semidirect
12. C23×C4×D73C22semidirect
13. #17989330C4direct (N × H)
18. C2×C4×Dic146C22semidirect
20. #17988492C22semidirect
21. #17988491C22semidirect
24. #17988481C22semidirect
25. #17988481C22semidirect
26. #17988480C22semidirect
27. #17988479C22semidirect
28. #17988476C22semidirect
29. #17988475C22semidirect
33. #17988460C22semidirect
34. #17988459C22semidirect
35. #17988458C22semidirect
36. #17988452C22semidirect
37. #17988451C22semidirect
38. #17988443C22semidirect
39. #17988442C22semidirect
40. C4×#11924005C22semidirect
41. C4×C22⋊Dic73C22semidirect
42. C4×C22⋊Dic73C22semidirect
43. C42×Dic73C22semidirect
44. C24×C4×C73C22semidirect
48. #385×C73C22semidirect
49. #379×C73C22semidirect
50. C4×C22⋊C4×C73C22semidirect
58. #14556578C2×C4semidirect
59. #14556577C2×C4semidirect
60. #14556560C2×C4semidirect
61. #14556559C2×C4semidirect
90. #120×C73C2×C4semidirect
101. C23×D73C22×C4semidirect
105. C2×Dic146C22×C4semidirect
122. C22⋊Dic73C22×C4semidirect
123. C22⋊Dic73C22×C4semidirect
126. #11924005C22×C4semidirect
130. C4×Dic73C22×C4semidirect
133. C24×C73C22×C4semidirect
154. C22⋊C4×C73C22×C4semidirect
219. C4×C73H(3,𝔽4)semidirect
240. C4×#120D73semidirect
241. C73C4×H(3,𝔽4)semidirect
243. C24×C4C2×D73semidirect
270. #385C2×D73semidirect
275. #379C2×D73semidirect
279. C4×C22⋊C4C2×D73semidirect
298. #120C4×D73semidirect
335. C24C2×C4×D73semidirect
380. C22⋊C4C2×C4×D73semidirect
452. C4#17989330direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893302
#226131042
#226131012
#226130722
#226130702
#226130692
C4×#145565782
C4×#145565772
C4×#145565602
C4×#145565592
C4×#120×C732
C4×H(3,𝔽4)73