Finite Group Databasebeta

← C4×#17989324 #33248665

Subgroups — C4×#17989324 #33248665

Order 18688.

2568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989324C211yesmaximal, characteristic
2#22613124C212yesmaximal, complemented
3#22613108C211yesmaximal, characteristic, complemented
4#22613082C216yesmaximal, complemented
5#22613081C213yesmaximal, complemented
6#22613068C213yesmaximal, complemented
7C4×#14556585C212yesmaximal, complemented
8C4×#14556572C213yesmaximal, complemented
9C4×#14556563C216yesmaximal, complemented
10C4×#14556559C213yesmaximal, complemented
11C4×#127×C73C211yesmaximal, characteristic, complemented
12C23×C4×D73C2211yescharacteristic
13#17989324C4116yesdirect product factor
14C2×#14556585C2212yes—
15C2×#14556572C2213yes—
16C2×#14556563C2216yes—
17C2×#14556559C2213yes—
18C2×C4×C22⋊D73C2216yes—
19C22×C4×Dic73C2213yescomplemented
20#17988487C2216yes—
21#17988482C2216yescomplemented
22#17988481C2216yescomplemented
23#17988478C2216yes—
24#17988477C2216yes—
25#17988475C2216yes—
26#17988471C2216yescomplemented
27#17988468C2216yescomplemented
28#17988467C2213yes—
29#17988467C2213yes—
30#17988467C2216yescomplemented
31#17988464C2216yes—
32#17988463C2216yes—
33#17988459C2213yes—
34#17988459C2213yescomplemented
35#17988458C2216yes—
36#17988455C2212yescomplemented
37#17988448C2213yescomplemented
38#17988445C2216yescomplemented
39#17988442C2213yes—
40C4×#11924007C2216yescomplemented
41C4×#11924005C2216yes—
42C4×C22⋊Dic73C2213yes—
43C4×C22⋊Dic73C2213yescomplemented
44C2×#127×C73C2211yescharacteristic
45C2×C4×D4×C73C2213yes—
46C2×C4×D4×C73C2213yescomplemented
47#390×C73C2213yes—
48#390×C73C2213yescomplemented
49#384×C73C2211yescharacteristic, complemented
50C43×C73C2211yescharacteristic, complemented
51C24×D73C2311yescharacteristic
52C22×C22⋊D73C2316yes—
53C23×Dic73C2311yescharacteristic
54C23×Dic73C2313yes—
55C23×Dic73C2313yes—
56C22×C4×D73—46no—
57C22×C4×D73C2312yes—
58C22×C4×D73C2312yes—
59#14556585C2×C4116yescomplemented
60#14556572C2×C4124yescomplemented
61#14556563C2×C4148yescomplemented
62#14556559C2×C4124yescomplemented
63C4×C22⋊D73—412no—
64C2×#11924007C2316yes—
65C2×#11924007C2316yes—
66C2×#11924007C2316yes—
67C2×C22⋊Dic73C2313yes—
68C2×C22⋊Dic73C2313yes—
69C2×C22⋊Dic73C2316yes—
70C2×C22⋊Dic73C2313yes—
71C2×C22⋊Dic73C2313yes—
72C2×#11924005C2316yes—
73C2×#11924005C2316yes—
74C2×#11924005C2316yes—
75C2×C4×Dic73—46no—
76C2×C4×Dic73C2316yes—
77C2×C4×Dic73C2316yes—
78#14556498C2316yes—
79#14556498C2316yes—
80#14556498C2316yes—
81#14556498C2316yes—
82#14556498C2316yes—
83#14556498C2316yes—
84C22×D4×C73C2313yes—
85C22×D4×C73C2313yes—
86C23×C4×C73C2311yescharacteristic
87C23×C4×C73C2313yes—
88#127×C73C2×C418yescomplemented
89C4×D4×C73—46no—
90C4×D4×C73—46no—
91C2×C4⋊C4×C73C2313yes—
92C2×C4⋊C4×C73C2313yes—
93C2×C22⋊C4×C73C2313yes—
94C2×C22⋊C4×C73C2316yes—
95C2×C22⋊C4×C73C2313yes—
96C2×C42×C73C2313yes—
97C2×C42×C73C2313yes—
98C2×C42×C73C2311yescharacteristic
99C23×D73—43no—
100C23×D73—43no—
101C23×D73C22×C414yes—
102C23×D73C2412yes—
103C2×C22⋊D73—46no—
104C2×C22⋊D73—46no—
105C2×C22⋊D73C22×C4124yes—
106C22×Dic73—43no—
107C22×Dic73—43no—
108C22×Dic73—43no—
109C22×Dic73—43no—
110C22×Dic73—46no—
111C22×Dic73C22×C4112yescomplemented
112C22×Dic73C2416yes—
113C22×Dic73C2412yes—
114C22×Dic73C2416yes—
115C2×C4×D73—212no—
116C2×C4×D73—46no—
117C2×C4×D73—416no—
118#11924007—46no—
119#11924007—46no—
120#11924007C22×C4124yescomplemented
121C22⋊Dic73—43no—
122C22⋊Dic73—43no—
123C22⋊Dic73—46no—
124C22⋊Dic73C22×C4112yes—
125C22⋊Dic73C22×C4112yescomplemented
126#11924005—46no—
127#11924005—46no—
128#11924005C22×C4124yes—
129C4×Dic73—212no—
130C4×Dic73—46no—
131C24×C73C2411yescharacteristic
132C24×C73C2413yes—
133C2×D4×C73—43no—
134C2×D4×C73—43no—
135C2×D4×C73—43no—
136C2×D4×C73—43no—
137C2×D4×C73C22×C4112yes—
138C2×D4×C73C22×C4112yescomplemented
139C22×C4×C73—26no—
140C22×C4×C73—212no—
141C22×C4×C73—26no—
142C22×C4×C73C2413yes—
143C22×C4×C73C2411yescharacteristic
144C22×C4×C73C2413yes—
145C22×C4×C73C2413yes—
146C22×C4×C73C2411yescharacteristic
147C4⋊C4×C73—43no—
148C4⋊C4×C73—43no—
149C22⋊C4×C73—43no—
150C22⋊C4×C73—46no—
151C22⋊C4×C73—43no—
152C42×C73—26no—
153C42×C73—43no—
154C42×C73C22×C414yescomplemented
155C23×C73—26no—
156C23×C73—23no—
157C23×C73—23no—
158C23×C73—23no—
159C23×C73—23no—
160C23×C73—26no—
161C23×C73C23×C412yes—
162C23×C73C23×C416yes—
163C23×C73C2511yescharacteristic
164C22×D73—26no—
165C22×D73—26no—
166C22×D73—412no—
167C22×D73—44no—
168C22×D73—412no—
169C22×D73C23×C414yes—
170D4×C73—412no—
171D4×C73—412no—
172C2×C4×C73—23no—
173C2×C4×C73—23no—
174C2×C4×C73—23no—
175C2×C4×C73—23no—
176C2×C4×C73—26no—
177C2×C4×C73—23no—
178C2×C4×C73—26no—
179C2×C4×C73—412no—
180C2×C4×C73—44no—
181C2×C4×C73C23×C416yes—
182C2×C4×C73H(5,𝔽2)16yes—
183C22⋊D73—424no—
184C2×Dic73—26no—
185C2×Dic73—26no—
186C2×Dic73—26no—
187C2×Dic73—26no—
188C2×Dic73—26no—
189C2×Dic73—26no—
190C2×Dic73—412no—
191C2×Dic73—44no—
192C2×Dic73—412no—
193C2×Dic73C23×C4112yes—
194C4×D73—48no—
195C4×D73—48no—
196C22×C73—26no—
197C22×C73—212no—
198C22×C73—26no—
199C22×C73—41no—
200C22×C73—43no—
201C22×C73—43no—
202C22×C73—43no—
203C22×C73—46no—
204C22×C73C24×C411yescharacteristic
205C22×C73C2×H(5,𝔽2)13yes—
206C22×C73#58513yes—
207C2×D73—212no—
208C2×D73—416no—
209C2×D73—42no—
210C2×D73—46no—
211C4×C73—26no—
212C4×C73—41no—
213C4×C73—43no—
214C4×C73—43no—
215C4×C73#56014yescomplemented
216Dic73—212no—
217Dic73—42no—
218Dic73—46no—
219C4×#560—731nomaximal, Sylow
220C2×C73—42no—
221C2×C73—46no—
222C2×C73C4×H(5,𝔽2)13yes—
223C2×C73C2×#56011yescharacteristic
224C2×C73#352913yes—
225D73—44no—
226C2×#560—731no—
227#2383—732no—
228#2380—731no—
229#2377—736no—
230#2376—733no—
231#2375—733no—
232C4×#127D7311yescharacteristic, complemented
233C4×#126—732no—
234C4×#123—733no—
235C4×#121—736no—
236C4×#120—733no—
237C73C4×#56011yescharacteristic, complemented, Sylow
238C24×C4—731no—
239#560—7316no—
240C2×#127C2×D7311yescharacteristic
241C2×#126—732no—
242C2×#123—733no—
243C2×#121—736no—
244C2×#120—733no—
245C2×C4×D4—736no—
246C2×C4×D4C2×D7313yes—
247C2×C4×D4C2×D7313yescomplemented
248C22×C42—733no—
249#390—736no—
250#390C2×D7313yes—
251#390C2×D7313yescomplemented
252#389—736no—
253#388—736no—
254#388—736no—
255#388—736no—
256#388—736no—
257#387—736no—
258#387—736no—
259#386—733no—
260#386—733no—
261#386—736no—
262#386—736no—
263#386—736no—
264#385—736no—
265#385—733no—
266#385—733no—
267#384C2×D7311yescharacteristic, complemented
268#383—732no—
269#381—733no—
270#380—736no—
271#379—733no—
272C4×C4⋊C4—736no—
273C4×C22⋊C4—733no—
274C4×C22⋊C4—733no—
275C4×C22⋊C4—736no—
276C43C2×D7311yescharacteristic, complemented
277C25—731no—
278C22×D4—736no—
279C22×D4C22×D7313yes—
280C22×D4C22×D7313yes—
281C23×C4—2926no—
282C23×C4—731no—
283C23×C4—733no—
284C23×C4—732no—
285C23×C4—733no—
286C23×C4—732no—
287C23×C4C22×D7313yes—
288C23×C4C22×D7311yescharacteristic
289#127C4×D7318yescomplemented
290#126—7316no—
291#123—7324no—
292#121—7348no—
293#120—7324no—
294C4×D4—46no—
295C4×D4—46no—
296C4×D4—29212no—
297C2×C4⋊C4—736no—
298C2×C4⋊C4—736no—
299C2×C4⋊C4—736no—
300C2×C4⋊C4C22×D7313yes—
301C2×C4⋊C4C22×D7313yes—
302C2×C22⋊C4—736no—
303C2×C22⋊C4—733no—
304C2×C22⋊C4—733no—
305C2×C22⋊C4—736no—
306C2×C22⋊C4—736no—
307C2×C22⋊C4—733no—
308C2×C22⋊C4—733no—
309C2×C22⋊C4—736no—
310C2×C22⋊C4C22×D7313yes—
311C2×C22⋊C4C22×D7313yes—
312C2×C22⋊C4C22×D7316yes—
313C2×C42—2926no—
314C2×C42—736no—
315C2×C42—736no—
316C2×C42C22×D7313yes—
317C2×C42C22×D7313yes—
318C2×C42C22×D7311yescharacteristic
319#95—736no—
320#95—736no—
321#95—736no—
322#95—736no—
323#95—736no—
324#95—736no—
325C24—2923no—
326C24—2923no—
327C24—734no—
328C24—732no—
329C24C23×D7311yescharacteristic
330C24C23×D7313yes—
331C2×D4—43no—
332C2×D4—43no—
333C2×D4—43no—
334C2×D4—43no—
335C2×D4—2926no—
336C2×D4—2926no—
337C2×D4—7324no—
338C2×D4C2×C4×D73112yes—
339C2×D4C2×C4×D73112yescomplemented
340C22×C4—26no—
341C22×C4—212no—
342C22×C4—26no—
343C22×C4—2926no—
344C22×C4—29216no—
345C22×C4—2923no—
346C22×C4—2923no—
347C22×C4—2923no—
348C22×C4—2926no—
349C22×C4—2923no—
350C22×C4—7312no—
351C22×C4—736no—
352C22×C4—736no—
353C22×C4—732no—
354C22×C4—14612no—
355C22×C4C23×D7311yescharacteristic
356C22×C4C23×D7313yes—
357C22×C4C23×D7313yes—
358C22×C4C23×D7313yes—
359C22×C4C23×D7311yescharacteristic
360C4⋊C4—43no—
361C4⋊C4—43no—
362C4⋊C4—2926no—
363C4⋊C4—2926no—
364C4⋊C4—7324no—
365C22⋊C4—43no—
366C22⋊C4—46no—
367C22⋊C4—43no—
368C22⋊C4—2926no—
369C22⋊C4—2926no—
370C22⋊C4—2923no—
371C22⋊C4—2923no—
372C22⋊C4—2926no—
373C22⋊C4—7312no—
374C22⋊C4—7312no—
375C22⋊C4—7324no—
376C42—26no—
377C42—43no—
378C42—2926no—
379C42—14612no—
380C42C2×C4×D7314yescomplemented
381C23—26no—
382C23—23no—
383C23—23no—
384C23—23no—
385C23—23no—
386C23—26no—
387C23—29212no—
388C23—2924no—
389C23—29212no—
390C23—734no—
391C23—1466no—
392C23—1466no—
393C23C22×C4×D7312yes—
394C23C22×C4×D7316yes—
395C23C24×D7311yescharacteristic
396D4—412no—
397D4—412no—
398D4—29224no—
399C2×C4—23no—
400C2×C4—23no—
401C2×C4—23no—
402C2×C4—23no—
403C2×C4—26no—
404C2×C4—23no—
405C2×C4—26no—
406C2×C4—44no—
407C2×C4—412no—
408C2×C4—2928no—
409C2×C4—2924no—
410C2×C4—29212no—
411C2×C4—2928no—
412C2×C4—29212no—
413C2×C4—7312no—
414C2×C4—1466no—
415C2×C4—1466no—
416C2×C4—1466no—
417C2×C4—1466no—
418C2×C4—1466no—
419C2×C4—1466no—
420C2×C4C22×C4×D7316yes—
421C2×C4#1455663616yes—
422C22—26no—
423C22—212no—
424C22—26no—
425C22—41no—
426C22—43no—
427C22—43no—
428C22—43no—
429C22—46no—
430C22—29216no—
431C22—2922no—
432C22—2926no—
433C22—14612no—
434C22C23×C4×D7311yescharacteristic
435C22C2×#1455663613yes—
436C22#1798942313yes—
437C4—26no—
438C4—41no—
439C4—43no—
440C4—43no—
441C4—2922no—
442C4—2926no—
443C4—14612no—
444C4#1798932414yesdirect product factor
445C2—42no—
446C2—46no—
447C2—2924no—
448C2C4×#1455663613yes—
449C2C2×#1798932411yescharacteristic
450C2#2262406713yes—
subgroupG/H
centerC22×C4C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC4×#127×C73C2
socle, cosocleC23×C73C25
prime radicalC2×#17989324C2
hypercenterC4×#127D73
hypocenterC73C4×#560
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
2. #22613124C2semidirect
3. #22613108C2semidirect
4. #22613082C2semidirect
5. #22613081C2semidirect
6. #22613068C2semidirect
7. C4×#14556585C2semidirect
8. C4×#14556572C2semidirect
9. C4×#14556563C2semidirect
10. C4×#14556559C2semidirect
11. C4×#127×C73C2semidirect
13. #17989324C4direct (N × H)
19. C22×C4×Dic73C22semidirect
21. #17988482C22semidirect
22. #17988481C22semidirect
26. #17988471C22semidirect
27. #17988468C22semidirect
30. #17988467C22semidirect
34. #17988459C22semidirect
36. #17988455C22semidirect
37. #17988448C22semidirect
38. #17988445C22semidirect
40. C4×#11924007C22semidirect
43. C4×C22⋊Dic73C22semidirect
46. C2×C4×D4×C73C22semidirect
48. #390×C73C22semidirect
49. #384×C73C22semidirect
50. C43×C73C22semidirect
59. #14556585C2×C4semidirect
60. #14556572C2×C4semidirect
61. #14556563C2×C4semidirect
62. #14556559C2×C4semidirect
88. #127×C73C2×C4semidirect
111. C22×Dic73C22×C4semidirect
120. #11924007C22×C4semidirect
125. C22⋊Dic73C22×C4semidirect
138. C2×D4×C73C22×C4semidirect
154. C42×C73C22×C4semidirect
215. C4×C73#560semidirect
232. C4×#127D73semidirect
237. C73C4×#560semidirect
247. C2×C4×D4C2×D73semidirect
251. #390C2×D73semidirect
267. #384C2×D73semidirect
276. C43C2×D73semidirect
289. #127C4×D73semidirect
339. C2×D4C2×C4×D73semidirect
380. C42C2×C4×D73semidirect
444. C4#17989324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893242
#226131242
#226131082
#226130822
#226130812
#226130682
C4×#145565852
C4×#145565722
C4×#145565632
C4×#145565592
C4×#127×C732
C4×#56073