Finite Group Databasebeta

← C73×#19506 #32928910

Subgroups — C73×#19506 #32928910

Order 18688.

686 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3214C211yesmaximal, characteristic, complemented
2C73×#3205C211yesmaximal, characteristic, complemented
3C73×#3205C211yesmaximal, characteristic, complemented
4C73×#2981C211yesmaximal, characteristic, complemented
5C73×#1701C212yesmaximal, complemented
6C73×#1687C212yesmaximal, complemented
7C73×#1681C212yesmaximal, complemented
8C73×#1667C212yesmaximal, complemented
9C73×#1572C211yesmaximal, characteristic, complemented
10C73×#1555C211yesmaximal, characteristic, complemented
11C73×#1553C211yesmaximal, characteristic, complemented
12#532×C73C2211yescharacteristic
13#532×C73C2211yescharacteristic
14C2×#127×C73C2211yescharacteristic
15#496×C73—21no—
16#493×C73—21no—
17#493×C73C2211yescharacteristic
18#493×C73C2211yescharacteristic
19#489×C73—21no—
20#486×C73—21no—
21#486×C73C2211yescharacteristic
22#486×C73C2211yescharacteristic
23#461×C73C2212yescomplemented
24#459×C73—22no—
25#459×C73C2212yes—
26#459×C73C2212yes—
27#459×C73C2212yescomplemented
28#449×C73—22no—
29#447×C73—22no—
30#447×C73—22no—
31#436×C73C2212yescomplemented
32#435×C73—22no—
33C8×D4×C73C2212yescomplemented
34#432×C73C2211yescharacteristic
35#432×C73C2211yescharacteristic
36#431×C73C2211yescharacteristic
37#431×C73C2211yescharacteristic
38#408×C73—22no—
39#335×C73C2212yescomplemented
40#334×C73C2212yescomplemented
41#332×C73C2212yescomplemented
42#331×C73C2212yes—
43#331×C73C2212yes—
44#331×C73C2212yescomplemented
45C2×#41×C73—21no—
46C2×#41×C73—21no—
47C22×D4×C73—21no—
48C22×D4×C73—21no—
49C22×D4×C73—21no—
50C2×SD16×C73—22no—
51C2×D8×C73—22no—
52C2×D8×C73—22no—
53C2×D8×C73—22no—
54C2×D8×C73—22no—
55C2×D8×C73—22no—
56C2×M16×C73—22no—
57C22×C8×C73—22no—
58C4⋊Q8×C73D411yescharacteristic
59C4⋊Q8×C73C2311yescharacteristic
60#127×C73—21no—
61#127×C73—21no—
62#127×C73—21no—
63#127×C73D411yescharacteristic
64#127×C73C2311yescharacteristic
65#127×C73C2311yescharacteristic
66#127×C73C2311yescharacteristic
67#124×C73—21no—
68#124×C73—21no—
69#121×C73—21no—
70#121×C73—21no—
71#121×C73—21no—
72#121×C73D412yes—
73C4×D4×C73—21no—
74C4×D4×C73—21no—
75C4×D4×C73—21no—
76C4×D4×C73C2312yes—
77C2×C42×C73C2311yescharacteristic
78C4⋊C8×C73D412yes—
79C4⋊C8×C73C2312yes—
80C4⋊C8×C73C2312yes—
81C4⋊C8×C73C2312yes—
82#103×C73—22no—
83#102×C73—22no—
84#102×C73—22no—
85#102×C73—22no—
86#102×C73—22no—
87#102×C73—22no—
88C22⋊C8×C73—21no—
89C22⋊C8×C73—21no—
90C22⋊C8×C73—21no—
91C22⋊C8×C73—22no—
92C22⋊C8×C73—22no—
93C22⋊C8×C73D412yes—
94#97×C73—21no—
95#97×C73—21no—
96C4×C8×C73—21no—
97C4×C8×C73C2311yescharacteristic
98C4×C8×C73C2311yescharacteristic
99C24×C73—41no—
100#41×C73—82no—
101#41×C73—82no—
102C2×Q8×C73—21no—
103C2×Q8×C73—21no—
104C2×D4×C73—22no—
105C2×D4×C73—21no—
106C2×D4×C73—21no—
107C2×D4×C73—21no—
108C2×D4×C73—21no—
109C2×D4×C73—21no—
110C2×D4×C73—21no—
111C2×D4×C73—21no—
112C2×D4×C73—21no—
113C2×D4×C73—21no—
114C2×D4×C73—21no—
115C2×D4×C73—21no—
116C2×D4×C73—41no—
117C2×D4×C73—41no—
118C2×D4×C73—41no—
119C2×D4×C73—41no—
120C2×D4×C73—82no—
121C2×D4×C73—82no—
122C2×D4×C73—82no—
123C2×D4×C73C2×D412yes—
124C22×C4×C73—22no—
125C22×C4×C73—41no—
126C22×C4×C73C2×D411yescharacteristic
127C22×C4×C73C2×D411yescharacteristic
128C22×C4×C73#4111yescharacteristic
129SD16×C73—82no—
130D8×C73—82no—
131D8×C73—82no—
132D8×C73—82no—
133D8×C73—82no—
134D8×C73—82no—
135M16×C73—82no—
136C2×C8×C73—22no—
137C2×C8×C73—22no—
138C2×C8×C73—22no—
139C2×C8×C73—82no—
140C2×C8×C73C2×D412yes—
141C2×C8×C73C2×D412yes—
142C4⋊C4×C73—21no—
143C4⋊C4×C73—21no—
144C4⋊C4×C73—21no—
145C4⋊C4×C73C2×D412yes—
146C22⋊C4×C73—22no—
147C22⋊C4×C73—22no—
148C22⋊C4×C73—41no—
149C22⋊C4×C73—41no—
150C42×C73C2×D411yescharacteristic
151C42×C73C2×D411yescharacteristic
152C42×C73#4111yescharacteristic
153C42×C73C2411yescharacteristic
154C23×C73—22no—
155C23×C73—41no—
156C23×C73—41no—
157C23×C73—41no—
158C23×C73—82no—
159C23×C73—82no—
160C23×C73—82no—
161C23×C73#12111yescharacteristic
162Q8×C73—42no—
163Q8×C73—81no—
164D4×C73—22no—
165D4×C73—22no—
166D4×C73—42no—
167D4×C73—42no—
168D4×C73—42no—
169D4×C73—42no—
170D4×C73—42no—
171D4×C73—42no—
172D4×C73—81no—
173D4×C73—81no—
174D4×C73—81no—
175D4×C73—81no—
176D4×C73—81no—
177D4×C73—82no—
178D4×C73—82no—
179D4×C73—82no—
180D4×C73—82no—
181D4×C73—82no—
182C2×C4×C73—22no—
183C2×C4×C73—22no—
184C2×C4×C73—22no—
185C2×C4×C73—41no—
186C2×C4×C73—42no—
187C2×C4×C73—42no—
188C2×C4×C73—41no—
189C2×C4×C73—82no—
190C2×C4×C73#12111yescharacteristic
191C2×C4×C73#12111yescharacteristic
192C2×C4×C73#12111yescharacteristic
193C2×C4×C73C22×D411yescharacteristic
194C2×C4×C73C22×D411yescharacteristic
195C2×C4×C73C2×#4111yescharacteristic
196C8×C73—22no—
197C8×C73—22no—
198C8×C73—42no—
199C8×C73—42no—
200C8×C73—42no—
201C22×C73—21no—
202C22×C73—21no—
203C22×C73—21no—
204C22×C73—42no—
205C22×C73—42no—
206C22×C73—42no—
207C22×C73—81no—
208C22×C73—81no—
209C22×C73—81no—
210C22×C73—81no—
211C22×C73—81no—
212C22×C73—81no—
213C22×C73—81no—
214C22×C73—81no—
215C22×C73—81no—
216C22×C73—164no—
217C22×C73C2×#12111yescharacteristic
218C4×C73—21no—
219C4×C73—21no—
220C4×C73—21no—
221C4×C73—21no—
222C4×C73—42no—
223C4×C73—81no—
224C4×C73#57612yes—
225C4×C73#57612yes—
226#19506C7311yesmaximal, characteristic, direct product factor, Sylow
227C2×C73—41no—
228C2×C73—82no—
229C2×C73—161no—
230C2×C73—161no—
231C2×C73—161no—
232C2×C73#304111yescharacteristic
233C2×C73#305811yescharacteristic
234C2×C73#306811yescharacteristic
235#3214C2×C7311yescharacteristic, complemented
236#3205C2×C7311yescharacteristic, complemented
237#3205C2×C7311yescharacteristic, complemented
238#2981C2×C7311yescharacteristic, complemented
239#1701C2×C7312yescomplemented
240#1687C2×C7312yescomplemented
241#1681C2×C7312yescomplemented
242#1667C2×C7312yescomplemented
243#1572C2×C7311yescharacteristic, complemented
244#1555C2×C7311yescharacteristic, complemented
245#1553C2×C7311yescharacteristic, complemented
246C73#1950611yescharacteristic, direct product factor, Sylow
247#532C22×C7311yescharacteristic
248#532C22×C7311yescharacteristic
249C2×#127C22×C7311yescharacteristic
250#496—21no—
251#493—21no—
252#493C22×C7311yescharacteristic
253#493C22×C7311yescharacteristic
254#489—21no—
255#486—21no—
256#486C22×C7311yescharacteristic
257#486C22×C7311yescharacteristic
258#461C22×C7312yescomplemented
259#459—22no—
260#459C22×C7312yes—
261#459C22×C7312yes—
262#459C22×C7312yescomplemented
263#449—22no—
264#447—22no—
265#447—22no—
266#436C22×C7312yescomplemented
267#435—22no—
268C8×D4C22×C7312yescomplemented
269#432C22×C7311yescharacteristic
270#432C22×C7311yescharacteristic
271#431C22×C7311yescharacteristic
272#431C22×C7311yescharacteristic
273#408—22no—
274#335C22×C7312yescomplemented
275#334C22×C7312yescomplemented
276#332C22×C7312yescomplemented
277#331C22×C7312yes—
278#331C22×C7312yes—
279#331C22×C7312yescomplemented
280C2×#41—21no—
281C2×#41—21no—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4—21no—
285C2×SD16—22no—
286C2×D8—22no—
287C2×D8—22no—
288C2×D8—22no—
289C2×D8—22no—
290C2×D8—22no—
291C2×M16—22no—
292C22×C8—22no—
293C4⋊Q8D4×C7311yescharacteristic
294C4⋊Q8C23×C7311yescharacteristic
295#127—21no—
296#127—21no—
297#127—21no—
298#127D4×C7311yescharacteristic
299#127C23×C7311yescharacteristic
300#127C23×C7311yescharacteristic
301#127C23×C7311yescharacteristic
302#124—21no—
303#124—21no—
304#121—21no—
305#121—21no—
306#121—21no—
307#121D4×C7312yes—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4C23×C7312yes—
312C2×C42C23×C7311yescharacteristic
313C4⋊C8D4×C7312yes—
314C4⋊C8C23×C7312yes—
315C4⋊C8C23×C7312yes—
316C4⋊C8C23×C7312yes—
317#103—22no—
318#102—22no—
319#102—22no—
320#102—22no—
321#102—22no—
322#102—22no—
323C22⋊C8—21no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326C22⋊C8—22no—
327C22⋊C8—22no—
328C22⋊C8D4×C7312yes—
329#97—21no—
330#97—21no—
331C4×C8—21no—
332C4×C8C23×C7311yescharacteristic
333C4×C8C23×C7311yescharacteristic
334C24—41no—
335#41—82no—
336#41—82no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×D4—22no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—82no—
356C2×D4—82no—
357C2×D4—82no—
358C2×D4C2×D4×C7312yes—
359C22×C4—22no—
360C22×C4—41no—
361C22×C4C2×D4×C7311yescharacteristic
362C22×C4C2×D4×C7311yescharacteristic
363C22×C4#41×C7311yescharacteristic
364SD16—82no—
365D8—82no—
366D8—82no—
367D8—82no—
368D8—82no—
369D8—82no—
370M16—82no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—82no—
375C2×C8C2×D4×C7312yes—
376C2×C8C2×D4×C7312yes—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4C2×D4×C7312yes—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C42C2×D4×C7311yescharacteristic
386C42C2×D4×C7311yescharacteristic
387C42#41×C7311yescharacteristic
388C42C24×C7311yescharacteristic
389C23—22no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—82no—
394C23—82no—
395C23—82no—
396C23#121×C7311yescharacteristic
397Q8—42no—
398Q8—81no—
399D4—22no—
400D4—22no—
401D4—42no—
402D4—42no—
403D4—42no—
404D4—42no—
405D4—42no—
406D4—42no—
407D4—81no—
408D4—81no—
409D4—81no—
410D4—81no—
411D4—81no—
412D4—82no—
413D4—82no—
414D4—82no—
415D4—82no—
416D4—82no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—82no—
425C2×C4#121×C7311yescharacteristic
426C2×C4#121×C7311yescharacteristic
427C2×C4#121×C7311yescharacteristic
428C2×C4C22×D4×C7311yescharacteristic
429C2×C4C22×D4×C7311yescharacteristic
430C2×C4C2×#41×C7311yescharacteristic
431C8—22no—
432C8—22no—
433C8—42no—
434C8—42no—
435C8—42no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—164no—
452C22C2×#121×C7311yescharacteristic
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—42no—
458C4—81no—
459C4#576×C7312yes—
460C4#576×C7312yes—
461C2—41no—
462C2—82no—
463C2—161no—
464C2—161no—
465C2—161no—
466C2C73×#304111yescharacteristic
467C2C73×#305811yescharacteristic
468C2C73×#306811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3214C2semidirect
2. C73×#3205C2semidirect
3. C73×#3205C2semidirect
4. C73×#2981C2semidirect
5. C73×#1701C2semidirect
6. C73×#1687C2semidirect
7. C73×#1681C2semidirect
8. C73×#1667C2semidirect
9. C73×#1572C2semidirect
10. C73×#1555C2semidirect
11. C73×#1553C2semidirect
23. #461×C73C22semidirect
27. #459×C73C22semidirect
31. #436×C73C22semidirect
33. C8×D4×C73C22semidirect
39. #335×C73C22semidirect
40. #334×C73C22semidirect
41. #332×C73C22semidirect
44. #331×C73C22semidirect
226. #19506C73direct (N × H)
235. #3214C2×C73semidirect
236. #3205C2×C73semidirect
237. #3205C2×C73semidirect
238. #2981C2×C73semidirect
239. #1701C2×C73semidirect
240. #1687C2×C73semidirect
241. #1681C2×C73semidirect
242. #1667C2×C73semidirect
243. #1572C2×C73semidirect
244. #1555C2×C73semidirect
245. #1553C2×C73semidirect
246. C73#19506direct (N × H)
258. #461C22×C73semidirect
262. #459C22×C73semidirect
266. #436C22×C73semidirect
268. C8×D4C22×C73semidirect
274. #335C22×C73semidirect
275. #334C22×C73semidirect
276. #332C22×C73semidirect
279. #331C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#32142
C73×#32052
C73×#29812
C73×#17012
C73×#16872
C73×#16812
C73×#16672
C73×#15722
C73×#15552
C73×#15532
#1950673