Finite Group Databasebeta

← C73×#25050 #32934454

Subgroups — C73×#25050 #32934454

Order 18688.

720 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
1C73×#3098C212yesmaximal, complemented
2C73×#3060C211yesmaximal, characteristic
3C73×#2952C211yesmaximal, characteristic, complemented
4C73×#2078C212yesmaximal, complemented
5C73×#2040C212yesmaximal, complemented
6C73×#1974C211yesmaximal, characteristic, complemented
7C73×#1951C211yesmaximal, characteristic, complemented
8C73×#1860C212yesmaximal, complemented
9C73×#1846C211yesmaximal, characteristic, complemented
10C73×#1815C211yesmaximal, characteristic, complemented
11C73×#1764C211yesmaximal, characteristic, complemented
12C2×#135×C73C2211yescharacteristic
13C2×#131×C73C2211yescharacteristic
14#537×C73C2212yes—
15#520×C73C2212yes—
16#485×C73—22no—
17#484×C73—22no—
18#482×C73—22no—
19#480×C73—22no—
20#470×C73—21no—
21#469×C73—21no—
22#465×C73—22no—
23#442×C73—21no—
24#441×C73—21no—
25C4×SD16×C73—22no—
26C2×#108×C73C2211yescharacteristic
27#428×C73C2212yes—
28C2×#107×C73C2212yes—
29C2×#106×C73C2211yescharacteristic
30C2×#106×C73C2211yescharacteristic
31C2×#104×C73C2212yes—
32C2×#104×C73C2211yescharacteristic
33#417×C73C2212yes—
34#417×C73C2212yes—
35#417×C73C2212yes—
36#416×C73C2211yescharacteristic
37#408×C73C2212yes—
38#405×C73C2211yescharacteristic
39C2×C4×C8×C73C2211yescharacteristic
40#382×C73C2212yes—
41#343×C73C2212yes—
42#343×C73C2212yes—
43#341×C73C2211yescharacteristic
44#339×C73C2211yescharacteristic
45C2×#41×C73C2312yes—
46C2×#41×C73C2311yescharacteristic
47#135×C73—22no—
48#135×C73—22no—
49C2×Q16×C73D411yescharacteristic
50C2×SD16×C73D412yes—
51C2×D8×C73D411yescharacteristic
52#131×C73—22no—
53#131×C73—22no—
54C2×M16×C73—21no—
55C2×M16×C73C2311yescharacteristic
56C2×M16×C73C2312yes—
57C2×M16×C73C2311yescharacteristic
58C22×C8×C73—21no—
59C22×C8×C73C2311yescharacteristic
60C22×C8×C73C2311yescharacteristic
61C22⋊Q8×C73—22no—
62C22⋊Q8×C73—22no—
63#121×C73—22no—
64#121×C73—22no—
65#121×C73—42no—
66C4×Q8×C73—22no—
67C4×D4×C73—22no—
68C4×D4×C73—42no—
69#117×C73—22no—
70#117×C73C2311yescharacteristic
71C2×C4⋊C4×C73—22no—
72C2×C4⋊C4×C73C2312yes—
73C2×C4⋊C4×C73C2312yes—
74C2×C42×C73C2311yescharacteristic
75#108×C73—22no—
76#107×C73—22no—
77#107×C73—22no—
78#107×C73—22no—
79#106×C73—21no—
80#106×C73—21no—
81#106×C73—21no—
82#106×C73—21no—
83#106×C73—22no—
84#104×C73—24no—
85#104×C73—22no—
86#103×C73—22no—
87#103×C73—22no—
88#103×C73—22no—
89#103×C73D412yes—
90#102×C73—22no—
91#102×C73—22no—
92#102×C73—22no—
93#102×C73D412yes—
94C22⋊C8×C73—22no—
95C22⋊C8×C73—22no—
96#97×C73—21no—
97C4×C8×C73—21no—
98C4×C8×C73—22no—
99#95×C73—42no—
100#41×C73—22no—
101#41×C73—21no—
102#41×C73—21no—
103#41×C73—21no—
104#41×C73—22no—
105#41×C73—22no—
106#41×C73—22no—
107#41×C73—21no—
108C2×Q8×C73C2×D411yescharacteristic
109C2×Q8×C73C2×D412yes—
110C2×D4×C73—22no—
111C2×D4×C73—21no—
112C2×D4×C73—42no—
113C2×D4×C73C2×D411yescharacteristic
114C2×D4×C73C2×D412yes—
115C22×C4×C73—21no—
116C22×C4×C73—22no—
117C22×C4×C73—21no—
118C22×C4×C73—22no—
119C22×C4×C73—22no—
120C22×C4×C73—42no—
121C22×C4×C73C2411yescharacteristic
122Q16×C73—22no—
123SD16×C73—24no—
124D8×C73—22no—
125M16×C73—22no—
126M16×C73—21no—
127M16×C73—22no—
128M16×C73—21no—
129M16×C73—21no—
130M16×C73—21no—
131M16×C73—42no—
132C2×C8×C73—21no—
133C2×C8×C73—21no—
134C2×C8×C73—21no—
135C2×C8×C73—22no—
136C2×C8×C73—21no—
137C2×C8×C73—42no—
138C2×C8×C73C2×D412yes—
139C2×C8×C73C2×D411yescharacteristic
140C2×C8×C73C2×D411yescharacteristic
141C2×C8×C73#4112yes—
142C2×C8×C73#4112yes—
143C4⋊C4×C73—22no—
144C4⋊C4×C73—22no—
145C4⋊C4×C73—22no—
146C4⋊C4×C73—22no—
147C4⋊C4×C73—42no—
148C4⋊C4×C73—42no—
149C4⋊C4×C73C2×D412yes—
150C22⋊C4×C73—21no—
151C22⋊C4×C73—42no—
152C22⋊C4×C73—42no—
153C22⋊C4×C73—42no—
154C42×C73—21no—
155C42×C73—21no—
156C42×C73—42no—
157C42×C73#4112yes—
158C23×C73—22no—
159C23×C73—21no—
160C23×C73H(5,𝔽2)11yescharacteristic
161Q8×C73—22no—
162Q8×C73—21no—
163Q8×C73—21no—
164Q8×C73—22no—
165D4×C73—22no—
166D4×C73—21no—
167D4×C73—21no—
168D4×C73—22no—
169D4×C73—42no—
170D4×C73—41no—
171D4×C73—42no—
172D4×C73—41no—
173D4×C73—162no—
174C2×C4×C73—22no—
175C2×C4×C73—22no—
176C2×C4×C73—21no—
177C2×C4×C73—22no—
178C2×C4×C73—42no—
179C2×C4×C73—41no—
180C2×C4×C73—42no—
181C2×C4×C73—42no—
182C2×C4×C73—41no—
183C2×C4×C73—42no—
184C2×C4×C73—42no—
185C2×C4×C73—82no—
186C2×C4×C73—82no—
187C2×C4×C73—162no—
188C2×C4×C73C22×D411yescharacteristic
189C2×C4×C73C22×D411yescharacteristic
190C2×C4×C73C2×#4111yescharacteristic
191C2×C4×C73C2×#4111yescharacteristic
192C2×C4×C73C2×#4111yescharacteristic
193C2×C4×C732−1+411yescharacteristic
194C8×C73—22no—
195C8×C73—41no—
196C8×C73—42no—
197C8×C73—41no—
198C8×C73#12312yes—
199C8×C73#12312yes—
200C22×C73—22no—
201C22×C73—41no—
202C22×C73—42no—
203C22×C73—42no—
204C22×C73—42no—
205C22×C73—42no—
206C22×C73#54211yescharacteristic
207C22×C73D4211yescharacteristic
208C22×C73#55311yescharacteristic
209C4×C73—42no—
210C4×C73—42no—
211C4×C73—41no—
212C4×C73—42no—
213C4×C73—82no—
214C4×C73—82no—
215C4×C73C2×#12311yescharacteristic
216C4×C73#53211yescharacteristic
217C4×C73#54711yescharacteristic
218C4×C73#54711yescharacteristic
219#25050C7311yesmaximal, characteristic, direct product factor, Sylow
220C2×C73—21no—
221C2×C73—21no—
222C2×C73—82no—
223C2×C73—81no—
224C2×C73#242211yescharacteristic
225C2×C73#329012yes—
226#3098C2×C7312yescomplemented
227#3060C2×C7311yescharacteristic
228#2952C2×C7311yescharacteristic, complemented
229#2078C2×C7312yescomplemented
230#2040C2×C7312yescomplemented
231#1974C2×C7311yescharacteristic, complemented
232#1951C2×C7311yescharacteristic, complemented
233#1860C2×C7312yescomplemented
234#1846C2×C7311yescharacteristic, complemented
235#1815C2×C7311yescharacteristic, complemented
236#1764C2×C7311yescharacteristic, complemented
237C73#2505011yescharacteristic, direct product factor, Sylow
238C2×#135C22×C7311yescharacteristic
239C2×#131C22×C7311yescharacteristic
240#537C22×C7312yes—
241#520C22×C7312yes—
242#485—22no—
243#484—22no—
244#482—22no—
245#480—22no—
246#470—21no—
247#469—21no—
248#465—22no—
249#442—21no—
250#441—21no—
251C4×SD16—22no—
252C2×#108C22×C7311yescharacteristic
253#428C22×C7312yes—
254C2×#107C22×C7312yes—
255C2×#106C22×C7311yescharacteristic
256C2×#106C22×C7311yescharacteristic
257C2×#104C22×C7312yes—
258C2×#104C22×C7311yescharacteristic
259#417C22×C7312yes—
260#417C22×C7312yes—
261#417C22×C7312yes—
262#416C22×C7311yescharacteristic
263#408C22×C7312yes—
264#405C22×C7311yescharacteristic
265C2×C4×C8C22×C7311yescharacteristic
266#382C22×C7312yes—
267#343C22×C7312yes—
268#343C22×C7312yes—
269#341C22×C7311yescharacteristic
270#339C22×C7311yescharacteristic
271C2×#41C23×C7312yes—
272C2×#41C23×C7311yescharacteristic
273#135—22no—
274#135—22no—
275C2×Q16D4×C7311yescharacteristic
276C2×SD16D4×C7312yes—
277C2×D8D4×C7311yescharacteristic
278#131—22no—
279#131—22no—
280C2×M16—21no—
281C2×M16C23×C7311yescharacteristic
282C2×M16C23×C7311yescharacteristic
283C2×M16C23×C7312yes—
284C22×C8—21no—
285C22×C8C23×C7311yescharacteristic
286C22×C8C23×C7311yescharacteristic
287C22⋊Q8—22no—
288C22⋊Q8—22no—
289#121—22no—
290#121—22no—
291#121—42no—
292C4×Q8—22no—
293C4×D4—22no—
294C4×D4—42no—
295#117—22no—
296#117C23×C7311yescharacteristic
297C2×C4⋊C4—22no—
298C2×C4⋊C4C23×C7312yes—
299C2×C4⋊C4C23×C7312yes—
300C2×C42C23×C7311yescharacteristic
301#108—22no—
302#107—22no—
303#107—22no—
304#107—22no—
305#106—21no—
306#106—21no—
307#106—21no—
308#106—21no—
309#106—22no—
310#104—24no—
311#104—22no—
312#103—22no—
313#103—22no—
314#103—22no—
315#103D4×C7312yes—
316#102—22no—
317#102—22no—
318#102—22no—
319#102D4×C7312yes—
320C22⋊C8—22no—
321C22⋊C8—22no—
322#97—21no—
323C4×C8—21no—
324C4×C8—22no—
325#95—42no—
326#41—22no—
327#41—21no—
328#41—21no—
329#41—21no—
330#41—22no—
331#41—22no—
332#41—22no—
333#41—21no—
334C2×Q8C2×D4×C7311yescharacteristic
335C2×Q8C2×D4×C7312yes—
336C2×D4—22no—
337C2×D4—21no—
338C2×D4—42no—
339C2×D4C2×D4×C7311yescharacteristic
340C2×D4C2×D4×C7312yes—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—42no—
347C22×C4C24×C7311yescharacteristic
348Q16—22no—
349SD16—24no—
350D8—22no—
351M16—22no—
352M16—21no—
353M16—22no—
354M16—21no—
355M16—21no—
356M16—21no—
357M16—42no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—22no—
362C2×C8—21no—
363C2×C8—42no—
364C2×C8C2×D4×C7312yes—
365C2×C8C2×D4×C7311yescharacteristic
366C2×C8C2×D4×C7311yescharacteristic
367C2×C8#41×C7312yes—
368C2×C8#41×C7312yes—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4C2×D4×C7312yes—
376C22⋊C4—21no—
377C22⋊C4—42no—
378C22⋊C4—42no—
379C22⋊C4—42no—
380C42—21no—
381C42—21no—
382C42—42no—
383C42#41×C7312yes—
384C23—22no—
385C23—21no—
386C23H(5,𝔽2)×C7311yescharacteristic
387Q8—22no—
388Q8—21no—
389Q8—21no—
390Q8—22no—
391D4—22no—
392D4—21no—
393D4—21no—
394D4—22no—
395D4—42no—
396D4—41no—
397D4—42no—
398D4—41no—
399D4—162no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—162no—
414C2×C4C22×D4×C7311yescharacteristic
415C2×C4C22×D4×C7311yescharacteristic
416C2×C4C2×#41×C7311yescharacteristic
417C2×C4C2×#41×C7311yescharacteristic
418C2×C4C2×#41×C7311yescharacteristic
419C2×C42−1+4×C7311yescharacteristic
420C8—22no—
421C8—41no—
422C8—42no—
423C8—41no—
424C8#123×C7312yes—
425C8#123×C7312yes—
426C22—22no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—41no—
431C22—42no—
432C22#542×C7311yescharacteristic
433C22D42×C7311yescharacteristic
434C22#553×C7311yescharacteristic
435C4—42no—
436C4—42no—
437C4—42no—
438C4—41no—
439C4—82no—
440C4—82no—
441C4C2×#123×C7311yescharacteristic
442C4#532×C7311yescharacteristic
443C4#547×C7311yescharacteristic
444C4#547×C7311yescharacteristic
445C2—21no—
446C2—21no—
447C2—82no—
448C2—81no—
449C2C73×#242211yescharacteristic
450C2C73×#329012yes—
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#3060C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3098C2semidirect
3. C73×#2952C2semidirect
4. C73×#2078C2semidirect
5. C73×#2040C2semidirect
6. C73×#1974C2semidirect
7. C73×#1951C2semidirect
8. C73×#1860C2semidirect
9. C73×#1846C2semidirect
10. C73×#1815C2semidirect
11. C73×#1764C2semidirect
219. #25050C73direct (N × H)
226. #3098C2×C73semidirect
228. #2952C2×C73semidirect
229. #2078C2×C73semidirect
230. #2040C2×C73semidirect
231. #1974C2×C73semidirect
232. #1951C2×C73semidirect
233. #1860C2×C73semidirect
234. #1846C2×C73semidirect
235. #1815C2×C73semidirect
236. #1764C2×C73semidirect
237. C73#25050direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#30982
C73×#30602
C73×#29522
C73×#20782
C73×#20402
C73×#19742
C73×#19512
C73×#18602
C73×#18462
C73×#18152
C73×#17642
#2505073