Finite Group Databasebeta

← C73×#62595 #32971999

Subgroups — C73×#62595 #32971999

Order 18688.

1966 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3517C211yesmaximal, characteristic, complemented
2C73×#3499C211yesmaximal, characteristic, complemented
3C73×#3359C212yesmaximal, complemented
4C73×#3358C212yesmaximal, complemented
5C73×#3332C216yesmaximal, complemented
6C73×#3330C216yesmaximal, complemented
7C73×#3239C213yesmaximal, complemented
8C73×#3214C213yesmaximal, complemented
9C73×#3171C213yesmaximal, complemented
10C73×#3141C213yesmaximal, complemented
11C73×#2971C211yesmaximal, characteristic, complemented
12C2×2−1+4×C73—21no—
13#557×C73C2211yescharacteristic
14#553×C73—23no—
15#550×C73—21no—
16#550×C73C2213yes—
17#550×C73C2211yescharacteristic
18D4×Q8×C73—21no—
19D4×Q8×C73C2212yes—
20#547×C73—23no—
21#547×C73C2213yes—
22#547×C73C2216yes—
23#540×C73—23no—
24#536×C73—23no—
25#532×C73C2213yes—
26#532×C73C2213yes—
27C2×C4⋊Q8×C73C2213yes—
28#529×C73C2213yes—
29#520×C73—21no—
30C4×#41×C73C2211yescharacteristic
31#501×C73C2213yes—
32#496×C73C2213yes—
33#490×C73C2211yescharacteristic
34#489×C73C2216yes—
35#489×C73C2213yes—
36#487×C73C2216yes—
37#486×C73C2216yes—
38#484×C73C2216yes—
39#481×C73C2216yes—
40#475×C73C2216yes—
41#474×C73C2216yes—
42#469×C73C2216yes—
43#468×C73C2216yes—
44#461×C73C2216yes—
45#459×C73C2216yes—
46#449×C73C22112yes—
47C8×Q8×C73C2212yes—
48C4×SD16×C73C2216yes—
49C4×D8×C73C2216yes—
50#436×C73C2216yes—
51#432×C73C2213yes—
52#417×C73C22112yes—
53C4×M16×C73C2213yes—
542−1+4×C73—48no—
55C2×#41×C73—21no—
56C2×#41×C73—26no—
57C2×#41×C73—23no—
58C2×#41×C73D411yescharacteristic
59C2×#41×C73C2316yes—
60C22×Q8×C73—22no—
61C22×Q8×C73—23no—
62C2×SD16×C73C2316yes—
63C2×D8×C73C2316yes—
64C2×M16×C73C2316yes—
65C4⋊Q8×C73—23no—
66C4⋊Q8×C73—23no—
67C4⋊Q8×C73C2313yes—
68C4⋊Q8×C73C2316yes—
69C4⋊Q8×C73C2313yes—
70#127×C73—23no—
71#127×C73C2313yes—
72#127×C73C2311yescharacteristic
73#126×C73—23no—
74#125×C73—23no—
75#125×C73C2311yescharacteristic
76#124×C73—23no—
77#124×C73C2313yes—
78#123×C73—23no—
79#123×C73—212no—
80#123×C73—26no—
81C22⋊Q8×C73—26no—
82C22⋊Q8×C73—26no—
83C22⋊Q8×C73C2313yes—
84#121×C73—23no—
85#121×C73—23no—
86#121×C73—23no—
87#121×C73—23no—
88#121×C73—23no—
89#121×C73—26no—
90#121×C73C2316yes—
91#121×C73C2313yes—
92C4×Q8×C73—21no—
93C4×Q8×C73D411yescharacteristic
94C4×Q8×C73C2313yes—
95C4×Q8×C73C2311yescharacteristic
96C4×D4×C73—23no—
97C4×D4×C73—23no—
98C4×D4×C73—23no—
99C4×D4×C73—23no—
100C4×D4×C73—23no—
101C4×D4×C73D413yes—
102C4×D4×C73C2313yes—
103C4×D4×C73C2316yes—
104C4×D4×C73C2313yes—
105#117×C73—23no—
106#117×C73D413yes—
107C2×C4⋊C4×C73—23no—
108C2×C4⋊C4×C73—23no—
109C2×C4⋊C4×C73C2316yes—
110C2×C42×C73C2313yes—
111#107×C73C2316yes—
112#106×C73C2316yes—
113C4⋊C8×C73C2316yes—
114#103×C73C2316yes—
115#103×C73C23112yes—
116#102×C73C2316yes—
117#102×C73C23112yes—
118#102×C73C2312yes—
119#102×C73C2312yes—
120C22⋊C8×C73C2316yes—
121#97×C73C2311yescharacteristic
122#97×C73C2313yes—
123C4×C8×C73C2316yes—
124#41×C73—24no—
125#41×C73—412no—
126#41×C73—412no—
127#41×C73—424no—
128#41×C73—44no—
129C2×Q8×C73—26no—
130C2×Q8×C73—23no—
131C2×Q8×C73—412no—
132C2×Q8×C73—48no—
133C2×Q8×C73C2×D411yescharacteristic
134C2×Q8×C73C2413yes—
135C2×D4×C73—26no—
136C2×D4×C73—23no—
137C2×D4×C73—26no—
138C2×D4×C73—21no—
139C2×D4×C73—23no—
140C2×D4×C73—21no—
141C2×D4×C73—23no—
142C2×D4×C73C2×D413yes—
143C2×D4×C73C2413yes—
144C2×D4×C73C2412yes—
145C22×C4×C73—26no—
146C22×C4×C73—23no—
147C22×C4×C73—26no—
148C22×C4×C73—26no—
149C22×C4×C73C2×D413yes—
150C22×C4×C73C2×D413yes—
151C22×C4×C73C2413yes—
152SD16×C73—46no—
153D8×C73—46no—
154M16×C73—46no—
155C2×C8×C73C2412yes—
156C2×C8×C73C2416yes—
157C4⋊C4×C73—23no—
158C4⋊C4×C73—23no—
159C4⋊C4×C73—23no—
160C4⋊C4×C73—26no—
161C4⋊C4×C73—26no—
162C4⋊C4×C73—21no—
163C4⋊C4×C73—21no—
164C4⋊C4×C73—23no—
165C4⋊C4×C73—23no—
166C4⋊C4×C73C2×D413yes—
167C4⋊C4×C73C2×D413yes—
168C4⋊C4×C73C2416yes—
169C4⋊C4×C73C2411yescharacteristic
170C4⋊C4×C73C2411yescharacteristic
171C22⋊C4×C73—23no—
172C22⋊C4×C73—23no—
173C22⋊C4×C73—23no—
174C22⋊C4×C73—23no—
175C22⋊C4×C73—26no—
176C22⋊C4×C73—23no—
177C22⋊C4×C73—26no—
178C22⋊C4×C73C2×D416yes—
179C42×C73—23no—
180C42×C73C2×D413yes—
181C42×C73C2×D413yes—
182C42×C73C2413yes—
183C42×C73C2411yescharacteristic
184C23×C73—22no—
185C23×C73—23no—
186C23×C73C22×D413yes—
187Q8×C73—26no—
188Q8×C73—46no—
189Q8×C73—412no—
190Q8×C73AGL(1,ℤ/8)14yes—
191D4×C73—26no—
192D4×C73—22no—
193D4×C73—26no—
194D4×C73—22no—
195D4×C73—42no—
196D4×C73—42no—
197D4×C73—412no—
198D4×C73—46no—
199D4×C73—83no—
200D4×C73—83no—
201D4×C73—86no—
202C2×C4×C73—26no—
203C2×C4×C73—26no—
204C2×C4×C73—21no—
205C2×C4×C73—23no—
206C2×C4×C73—21no—
207C2×C4×C73—26no—
208C2×C4×C73—43no—
209C2×C4×C73—412no—
210C2×C4×C73—412no—
211C2×C4×C73—46no—
212C2×C4×C73—86no—
213C2×C4×C73C22×D411yescharacteristic
214C2×C4×C73C22×D411yescharacteristic
215C2×C4×C73C22×D413yes—
216C2×C4×C73C22×D413yes—
217C2×C4×C73C22×D413yes—
218C2×C4×C73C2511yescharacteristic
219C8×C73—22no—
220C8×C73—26no—
221C22×C73—23no—
222C22×C73—23no—
223C22×C73—23no—
224C22×C73—42no—
225C22×C73—43no—
226C22×C73—43no—
227C22×C73—42no—
228C22×C73—42no—
229C22×C73—43no—
230C22×C73C23×D411yescharacteristic
231C4×C73—21no—
232C4×C73—23no—
233C4×C73—23no—
234C4×C73—21no—
235C4×C73—41no—
236C4×C73—43no—
237C4×C73—41no—
238C4×C73—46no—
239C4×C73C2×AGL(1,ℤ/8)16yes—
240C4×C73#58512yes—
241#62595C7311yesmaximal, characteristic, direct product factor, Sylow
242C2×C73—43no—
243C2×C73—82no—
244C2×C73—83no—
245C2×C73#350011yescharacteristic
246C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
247C2×C73#358611yescharacteristic
248#3517C2×C7311yescharacteristic, complemented
249#3499C2×C7311yescharacteristic, complemented
250#3359C2×C7312yescomplemented
251#3358C2×C7312yescomplemented
252#3332C2×C7316yescomplemented
253#3330C2×C7316yescomplemented
254#3239C2×C7313yescomplemented
255#3214C2×C7313yescomplemented
256#3171C2×C7313yescomplemented
257#3141C2×C7313yescomplemented
258#2971C2×C7311yescharacteristic, complemented
259C73#6259511yescharacteristic, direct product factor, Sylow
260C2×2−1+4—21no—
261#557C22×C7311yescharacteristic
262#553—23no—
263#550—21no—
264#550C22×C7313yes—
265#550C22×C7311yescharacteristic
266D4×Q8—21no—
267D4×Q8C22×C7312yes—
268#547—23no—
269#547C22×C7313yes—
270#547C22×C7316yes—
271#540—23no—
272#536—23no—
273#532C22×C7313yes—
274#532C22×C7313yes—
275C2×C4⋊Q8C22×C7313yes—
276#529C22×C7313yes—
277#520—21no—
278C4×#41C22×C7311yescharacteristic
279#501C22×C7313yes—
280#496C22×C7313yes—
281#490C22×C7311yescharacteristic
282#489C22×C7313yes—
283#489C22×C7316yes—
284#487C22×C7316yes—
285#486C22×C7316yes—
286#484C22×C7316yes—
287#481C22×C7316yes—
288#475C22×C7316yes—
289#474C22×C7316yes—
290#469C22×C7316yes—
291#468C22×C7316yes—
292#461C22×C7316yes—
293#459C22×C7316yes—
294#449C22×C73112yes—
295C8×Q8C22×C7312yes—
296C4×SD16C22×C7316yes—
297C4×D8C22×C7316yes—
298#436C22×C7316yes—
299#432C22×C7313yes—
300#417C22×C73112yes—
301C4×M16C22×C7313yes—
3022−1+4—48no—
303C2×#41—21no—
304C2×#41—26no—
305C2×#41—23no—
306C2×#41D4×C7311yescharacteristic
307C2×#41C23×C7316yes—
308C22×Q8—22no—
309C22×Q8—23no—
310C2×SD16C23×C7316yes—
311C2×D8C23×C7316yes—
312C2×M16C23×C7316yes—
313C4⋊Q8—23no—
314C4⋊Q8—23no—
315C4⋊Q8C23×C7313yes—
316C4⋊Q8C23×C7313yes—
317C4⋊Q8C23×C7316yes—
318#127—23no—
319#127C23×C7311yescharacteristic
320#127C23×C7313yes—
321#126—23no—
322#125—23no—
323#125C23×C7311yescharacteristic
324#124—23no—
325#124C23×C7313yes—
326#123—23no—
327#123—212no—
328#123—26no—
329C22⋊Q8—26no—
330C22⋊Q8—26no—
331C22⋊Q8C23×C7313yes—
332#121—23no—
333#121—23no—
334#121—23no—
335#121—23no—
336#121—23no—
337#121—26no—
338#121C23×C7313yes—
339#121C23×C7316yes—
340C4×Q8—21no—
341C4×Q8D4×C7311yescharacteristic
342C4×Q8C23×C7313yes—
343C4×Q8C23×C7311yescharacteristic
344C4×D4—23no—
345C4×D4—23no—
346C4×D4—23no—
347C4×D4—23no—
348C4×D4—23no—
349C4×D4D4×C7313yes—
350C4×D4C23×C7313yes—
351C4×D4C23×C7316yes—
352C4×D4C23×C7313yes—
353#117—23no—
354#117D4×C7313yes—
355C2×C4⋊C4—23no—
356C2×C4⋊C4—23no—
357C2×C4⋊C4C23×C7316yes—
358C2×C42C23×C7313yes—
359#107C23×C7316yes—
360#106C23×C7316yes—
361C4⋊C8C23×C7316yes—
362#103C23×C7316yes—
363#103C23×C73112yes—
364#102C23×C7316yes—
365#102C23×C73112yes—
366#102C23×C7312yes—
367#102C23×C7312yes—
368C22⋊C8C23×C7316yes—
369#97C23×C7311yescharacteristic
370#97C23×C7313yes—
371C4×C8C23×C7316yes—
372#41—24no—
373#41—412no—
374#41—412no—
375#41—424no—
376#41—44no—
377C2×Q8—26no—
378C2×Q8—23no—
379C2×Q8—412no—
380C2×Q8—48no—
381C2×Q8C2×D4×C7311yescharacteristic
382C2×Q8C24×C7313yes—
383C2×D4—26no—
384C2×D4—23no—
385C2×D4—26no—
386C2×D4—21no—
387C2×D4—23no—
388C2×D4—21no—
389C2×D4—23no—
390C2×D4C2×D4×C7313yes—
391C2×D4C24×C7313yes—
392C2×D4C24×C7312yes—
393C22×C4—26no—
394C22×C4—23no—
395C22×C4—26no—
396C22×C4—26no—
397C22×C4C2×D4×C7313yes—
398C22×C4C2×D4×C7313yes—
399C22×C4C24×C7313yes—
400SD16—46no—
401D8—46no—
402M16—46no—
403C2×C8C24×C7312yes—
404C2×C8C24×C7316yes—
405C4⋊C4—23no—
406C4⋊C4—23no—
407C4⋊C4—23no—
408C4⋊C4—26no—
409C4⋊C4—26no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—23no—
413C4⋊C4—23no—
414C4⋊C4C2×D4×C7313yes—
415C4⋊C4C2×D4×C7313yes—
416C4⋊C4C24×C7316yes—
417C4⋊C4C24×C7311yescharacteristic
418C4⋊C4C24×C7311yescharacteristic
419C22⋊C4—23no—
420C22⋊C4—23no—
421C22⋊C4—23no—
422C22⋊C4—23no—
423C22⋊C4—26no—
424C22⋊C4—23no—
425C22⋊C4—26no—
426C22⋊C4C2×D4×C7316yes—
427C42—23no—
428C42C2×D4×C7313yes—
429C42C2×D4×C7313yes—
430C42C24×C7313yes—
431C42C24×C7311yescharacteristic
432C23—22no—
433C23—23no—
434C23C22×D4×C7313yes—
435Q8—26no—
436Q8—46no—
437Q8—412no—
438Q8AGL(1,ℤ/8)×C7314yes—
439D4—26no—
440D4—22no—
441D4—26no—
442D4—22no—
443D4—42no—
444D4—42no—
445D4—412no—
446D4—46no—
447D4—83no—
448D4—86no—
449D4—83no—
450C2×C4—26no—
451C2×C4—26no—
452C2×C4—21no—
453C2×C4—23no—
454C2×C4—21no—
455C2×C4—26no—
456C2×C4—43no—
457C2×C4—412no—
458C2×C4—412no—
459C2×C4—46no—
460C2×C4—86no—
461C2×C4C22×D4×C7311yescharacteristic
462C2×C4C22×D4×C7311yescharacteristic
463C2×C4C22×D4×C7313yes—
464C2×C4C22×D4×C7313yes—
465C2×C4C22×D4×C7313yes—
466C2×C4C25×C7311yescharacteristic
467C8—22no—
468C8—26no—
469C22—23no—
470C22—23no—
471C22—23no—
472C22—43no—
473C22—42no—
474C22—42no—
475C22—43no—
476C22—42no—
477C22—43no—
478C22C23×D4×C7311yescharacteristic
479C4—23no—
480C4—21no—
481C4—21no—
482C4—23no—
483C4—43no—
484C4—46no—
485C4—41no—
486C4—41no—
487C4C2×AGL(1,ℤ/8)×C7316yes—
488C4#585×C7312yes—
489C2—43no—
490C2—83no—
491C2—82no—
492C2C73×#350011yescharacteristic
493C2C22×AGL(1,ℤ/8)×C7311yescharacteristic
494C2C73×#358611yescharacteristic
subgroupG/H
center, socleC22×C73C23×D4
commutator, Frattini, cosocleC2×C4C25×C73
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C4×#41×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3517C2semidirect
2. C73×#3499C2semidirect
3. C73×#3359C2semidirect
4. C73×#3358C2semidirect
5. C73×#3332C2semidirect
6. C73×#3330C2semidirect
7. C73×#3239C2semidirect
8. C73×#3214C2semidirect
9. C73×#3171C2semidirect
10. C73×#3141C2semidirect
11. C73×#2971C2semidirect
241. #62595C73direct (N × H)
248. #3517C2×C73semidirect
249. #3499C2×C73semidirect
250. #3359C2×C73semidirect
251. #3358C2×C73semidirect
252. #3332C2×C73semidirect
253. #3330C2×C73semidirect
254. #3239C2×C73semidirect
255. #3214C2×C73semidirect
256. #3171C2×C73semidirect
257. #3141C2×C73semidirect
258. #2971C2×C73semidirect
259. C73#62595direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35172
C73×#34992
C73×#33592
C73×#33582
C73×#33322
C73×#33302
C73×#32392
C73×#32142
C73×#31712
C73×#31412
C73×#29712
#6259573