Finite Group Databasebeta

← C73×#33767 #32943171

Subgroups — C73×#33767 #32943171

Order 18688.

564 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3061C211yesmaximal, characteristic
2C73×#3059C211yesmaximal, characteristic, complemented
3C73×#2237C211yesmaximal, characteristic, complemented
4C73×#2236C211yesmaximal, characteristic, complemented
5C73×#2235C211yesmaximal, characteristic, complemented
6C73×#2234C211yesmaximal, characteristic, complemented
7C73×#2220C211yesmaximal, characteristic, complemented
8C73×#2219C211yesmaximal, characteristic, complemented
9C73×#2217C211yesmaximal, characteristic, complemented
10C73×#2216C211yesmaximal, characteristic, complemented
11C73×#2189C211yesmaximal, characteristic, complemented
12C73×#2189C211yesmaximal, characteristic, complemented
13C73×#2188C211yesmaximal, characteristic, complemented
14C73×#2185C211yesmaximal, characteristic, complemented
15C73×#2113C211yesmaximal, characteristic, complemented
16C2×#135×C73C2211yescharacteristic
17C22×Q16×C73C2211yescharacteristic
18C2×#131×C73C2211yescharacteristic
19#537×C73—21no—
20#536×C73—21no—
21C2×Q32×C73C2211yescharacteristic
22C2×Q32×C73C2211yescharacteristic
23C2×SD32×C73C2211yescharacteristic
24C2×SD32×C73C2211yescharacteristic
25C2×M32×C73C2211yescharacteristic
26C22×C16×C73C2211yescharacteristic
27#470×C73—21no—
28#470×C73—21no—
29#468×C73—21no—
30#468×C73—21no—
31#467×C73C2211yescharacteristic
32#467×C73C2211yescharacteristic
33#467×C73C2211yescharacteristic
34#467×C73C2211yescharacteristic
35#467×C73C2211yescharacteristic
36#467×C73C2211yescharacteristic
37#466×C73C2211yescharacteristic
38#466×C73C2211yescharacteristic
39#427×C73C2211yescharacteristic
40C2×#107×C73C2211yescharacteristic
41#419×C73—21no—
42#417×C73—21no—
43#367×C73C2211yescharacteristic
44#367×C73C2211yescharacteristic
45#366×C73C2211yescharacteristic
46#366×C73C2211yescharacteristic
47#358×C73C2211yescharacteristic
48#358×C73C2211yescharacteristic
49#358×C73C2211yescharacteristic
50#358×C73C2211yescharacteristic
51#358×C73C2211yescharacteristic
52#358×C73C2211yescharacteristic
53#357×C73C2211yescharacteristic
54#357×C73C2211yescharacteristic
55C22⋊C16×C73C2211yescharacteristic
56C22⋊C16×C73C2211yescharacteristic
57C22⋊C16×C73C2211yescharacteristic
58C22⋊C16×C73C2211yescharacteristic
59C2×#41×C73—21no—
60C2×#41×C73D411yescharacteristic
61C22×Q8×C73—21no—
62#135×C73—41no—
63#135×C73—41no—
64C2×Q16×C73—21no—
65C2×Q16×C73—41no—
66C2×Q16×C73—41no—
67C2×Q16×C73C2311yescharacteristic
68C2×Q16×C73C2311yescharacteristic
69C2×Q16×C73C2311yescharacteristic
70C2×SD16×C73—21no—
71C2×D8×C73C2311yescharacteristic
72#131×C73—41no—
73#131×C73—41no—
74C2×M16×C73D411yescharacteristic
75C2×M16×C73D411yescharacteristic
76C2×M16×C73D411yescharacteristic
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C4⋊Q8×C73—41no—
81#124×C73—41no—
82#123×C73—41no—
83#123×C73—41no—
84C22⋊Q8×C73—21no—
85C22⋊Q8×C73—21no—
86C22⋊Q8×C73—21no—
87C22⋊Q8×C73—21no—
88C22⋊Q8×C73—21no—
89C22⋊Q8×C73—21no—
90C22⋊Q8×C73—41no—
91#121×C73—21no—
92#121×C73—21no—
93#121×C73—41no—
94#121×C73—41no—
95#121×C73—41no—
96#117×C73—21no—
97C2×C4⋊C4×C73—21no—
98Q32×C73—41no—
99Q32×C73—41no—
100SD32×C73—41no—
101SD32×C73—41no—
102M32×C73—41no—
103C2×C16×C73—41no—
104C2×C16×C73C2311yescharacteristic
105C2×C16×C73C2311yescharacteristic
106C2×C16×C73C2311yescharacteristic
107C2×C16×C73C2311yescharacteristic
108#107×C73—21no—
109#107×C73C2311yescharacteristic
110#107×C73C2311yescharacteristic
111#107×C73C2311yescharacteristic
112#107×C73C2311yescharacteristic
113#106×C73—21no—
114#103×C73—21no—
115#103×C73—21no—
116#103×C73—21no—
117#103×C73—21no—
118#103×C73—21no—
119#103×C73—21no—
120#102×C73—21no—
121#102×C73—21no—
122#41×C73—41no—
123#41×C73—41no—
124#41×C73—42no—
125#41×C73—42no—
126C2×Q8×C73—21no—
127C2×Q8×C73—21no—
128C2×Q8×C73—21no—
129C2×Q8×C73—42no—
130C2×Q8×C73—42no—
131C2×Q8×C73—41no—
132C2×Q8×C73D811yescharacteristic
133C2×D4×C73—21no—
134C2×D4×C73—41no—
135C2×D4×C73—41no—
136C2×D4×C73—41no—
137C2×D4×C73D811yescharacteristic
138C2×D4×C73D811yescharacteristic
139C2×D4×C73D811yescharacteristic
140C22×C4×C73—41no—
141C22×C4×C73—41no—
142C22×C4×C73—41no—
143C22×C4×C73C2×D411yescharacteristic
144C22×C4×C73C2×D411yescharacteristic
145C22×C4×C73C2×D411yescharacteristic
146Q16×C73—21no—
147Q16×C73—21no—
148Q16×C73—21no—
149Q16×C73—21no—
150Q16×C73—21no—
151Q16×C73—21no—
152Q16×C73—42no—
153SD16×C73—42no—
154D8×C73—21no—
155D8×C73—21no—
156M16×C73—41no—
157M16×C73—41no—
158M16×C73—41no—
159C2×C8×C73—21no—
160C2×C8×C73—21no—
161C2×C8×C73—21no—
162C2×C8×C73—21no—
163C2×C8×C73—21no—
164C2×C8×C73—21no—
165C2×C8×C73C2×D411yescharacteristic
166C2×C8×C73C2×D411yescharacteristic
167C2×C8×C73C2×D411yescharacteristic
168C2×C8×C73C2411yescharacteristic
169C4⋊C4×C73—21no—
170C4⋊C4×C73—21no—
171C4⋊C4×C73—21no—
172C4⋊C4×C73—21no—
173C4⋊C4×C73—41no—
174C4⋊C4×C73—41no—
175C4⋊C4×C73—41no—
176C4⋊C4×C73—41no—
177C4⋊C4×C73—41no—
178C4⋊C4×C73—41no—
179C4⋊C4×C73—41no—
180C22⋊C4×C73—41no—
181C22⋊C4×C73—41no—
182C22⋊C4×C73—41no—
183C22⋊C4×C73—41no—
184C22⋊C4×C73—41no—
185C22⋊C4×C73—41no—
186C22⋊C4×C73—41no—
187C22⋊C4×C73—41no—
188C22⋊C4×C73—41no—
189C42×C73—41no—
190C16×C73—21no—
191C16×C73—21no—
192C16×C73—21no—
193C16×C73—21no—
194C23×C73—41no—
195C23×C73C2×D811yescharacteristic
196C23×C73C2×D811yescharacteristic
197C23×C73C2×D811yescharacteristic
198Q8×C73—41no—
199Q8×C73—41no—
200Q8×C73—41no—
201Q8×C73—41no—
202Q8×C73—41no—
203Q8×C73—41no—
204Q8×C73—41no—
205Q8×C73—82no—
206D4×C73—41no—
207D4×C73—41no—
208D4×C73—41no—
209D4×C73—41no—
210D4×C73—41no—
211D4×C73—82no—
212D4×C73—161no—
213D4×C73—161no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—82no—
228C2×C4×C73—82no—
229C2×C4×C73—161no—
230C2×C4×C73C2×D811yescharacteristic
231C2×C4×C73C2×D811yescharacteristic
232C2×C4×C73C2×D811yescharacteristic
233C2×C4×C73C22×D411yescharacteristic
234C8×C73—21no—
235C8×C73—21no—
236C8×C73—21no—
237C8×C73H(5,𝔽2)11yescharacteristic
238C8×C73H(5,𝔽2)11yescharacteristic
239C22×C73—21no—
240C22×C73—21no—
241C22×C73—21no—
242C22×C73—21no—
243C22×C73—21no—
244C22×C73—21no—
245C22×C73—21no—
246C22×C73—21no—
247C22×C73—21no—
248C22×C73—81no—
249C22×C73—81no—
250C22×C73—81no—
251C22×C73C22×D811yescharacteristic
252C4×C73—21no—
253C4×C73—21no—
254C4×C73—21no—
255C4×C73—81no—
256C4×C73—81no—
257C4×C73—81no—
258C4×C73—81no—
259C4×C73—81no—
260C4×C73—81no—
261C4×C73—81no—
262C4×C73#53411yescharacteristic
263C4×C73#57511yescharacteristic
264#33767C7311yesmaximal, characteristic, direct product factor, Sylow
265C2×C73—41no—
266C2×C73—41no—
267C2×C73—41no—
268C2×C73—161no—
269C2×C73#318611yescharacteristic
270C2×C73#341611yescharacteristic
271C2×C73#341711yescharacteristic
272#3061C2×C7311yescharacteristic
273#3059C2×C7311yescharacteristic, complemented
274#2237C2×C7311yescharacteristic, complemented
275#2236C2×C7311yescharacteristic, complemented
276#2235C2×C7311yescharacteristic, complemented
277#2234C2×C7311yescharacteristic, complemented
278#2220C2×C7311yescharacteristic, complemented
279#2219C2×C7311yescharacteristic, complemented
280#2217C2×C7311yescharacteristic, complemented
281#2216C2×C7311yescharacteristic, complemented
282#2189C2×C7311yescharacteristic, complemented
283#2189C2×C7311yescharacteristic, complemented
284#2188C2×C7311yescharacteristic, complemented
285#2185C2×C7311yescharacteristic, complemented
286#2113C2×C7311yescharacteristic, complemented
287C73#3376711yescharacteristic, direct product factor, Sylow
288C2×#135C22×C7311yescharacteristic
289C22×Q16C22×C7311yescharacteristic
290C2×#131C22×C7311yescharacteristic
291#537—21no—
292#536—21no—
293C2×Q32C22×C7311yescharacteristic
294C2×Q32C22×C7311yescharacteristic
295C2×SD32C22×C7311yescharacteristic
296C2×SD32C22×C7311yescharacteristic
297C2×M32C22×C7311yescharacteristic
298C22×C16C22×C7311yescharacteristic
299#470—21no—
300#470—21no—
301#468—21no—
302#468—21no—
303#467C22×C7311yescharacteristic
304#467C22×C7311yescharacteristic
305#467C22×C7311yescharacteristic
306#467C22×C7311yescharacteristic
307#467C22×C7311yescharacteristic
308#467C22×C7311yescharacteristic
309#466C22×C7311yescharacteristic
310#466C22×C7311yescharacteristic
311#427C22×C7311yescharacteristic
312C2×#107C22×C7311yescharacteristic
313#419—21no—
314#417—21no—
315#367C22×C7311yescharacteristic
316#367C22×C7311yescharacteristic
317#366C22×C7311yescharacteristic
318#366C22×C7311yescharacteristic
319#358C22×C7311yescharacteristic
320#358C22×C7311yescharacteristic
321#358C22×C7311yescharacteristic
322#358C22×C7311yescharacteristic
323#358C22×C7311yescharacteristic
324#358C22×C7311yescharacteristic
325#357C22×C7311yescharacteristic
326#357C22×C7311yescharacteristic
327C22⋊C16C22×C7311yescharacteristic
328C22⋊C16C22×C7311yescharacteristic
329C22⋊C16C22×C7311yescharacteristic
330C22⋊C16C22×C7311yescharacteristic
331C2×#41—21no—
332C2×#41D4×C7311yescharacteristic
333C22×Q8—21no—
334#135—41no—
335#135—41no—
336C2×Q16—21no—
337C2×Q16—41no—
338C2×Q16—41no—
339C2×Q16C23×C7311yescharacteristic
340C2×Q16C23×C7311yescharacteristic
341C2×Q16C23×C7311yescharacteristic
342C2×SD16—21no—
343C2×D8C23×C7311yescharacteristic
344#131—41no—
345#131—41no—
346C2×M16D4×C7311yescharacteristic
347C2×M16D4×C7311yescharacteristic
348C2×M16D4×C7311yescharacteristic
349C22×C8C23×C7311yescharacteristic
350C22×C8C23×C7311yescharacteristic
351C22×C8C23×C7311yescharacteristic
352C4⋊Q8—41no—
353#124—41no—
354#123—41no—
355#123—41no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—41no—
363#121—21no—
364#121—21no—
365#121—41no—
366#121—41no—
367#121—41no—
368#117—21no—
369C2×C4⋊C4—21no—
370Q32—41no—
371Q32—41no—
372SD32—41no—
373SD32—41no—
374M32—41no—
375C2×C16—41no—
376C2×C16C23×C7311yescharacteristic
377C2×C16C23×C7311yescharacteristic
378C2×C16C23×C7311yescharacteristic
379C2×C16C23×C7311yescharacteristic
380#107—21no—
381#107C23×C7311yescharacteristic
382#107C23×C7311yescharacteristic
383#107C23×C7311yescharacteristic
384#107C23×C7311yescharacteristic
385#106—21no—
386#103—21no—
387#103—21no—
388#103—21no—
389#103—21no—
390#103—21no—
391#103—21no—
392#102—21no—
393#102—21no—
394#41—41no—
395#41—41no—
396#41—42no—
397#41—42no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×Q8—42no—
403C2×Q8—41no—
404C2×Q8D8×C7311yescharacteristic
405C2×D4—21no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4D8×C7311yescharacteristic
410C2×D4D8×C7311yescharacteristic
411C2×D4D8×C7311yescharacteristic
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4C2×D4×C7311yescharacteristic
416C22×C4C2×D4×C7311yescharacteristic
417C22×C4C2×D4×C7311yescharacteristic
418Q16—21no—
419Q16—21no—
420Q16—21no—
421Q16—21no—
422Q16—21no—
423Q16—21no—
424Q16—42no—
425SD16—42no—
426D8—21no—
427D8—21no—
428M16—41no—
429M16—41no—
430M16—41no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8C2×D4×C7311yescharacteristic
438C2×C8C2×D4×C7311yescharacteristic
439C2×C8C2×D4×C7311yescharacteristic
440C2×C8C24×C7311yescharacteristic
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4—41no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C42—41no—
462C16—21no—
463C16—21no—
464C16—21no—
465C16—21no—
466C23—41no—
467C23C2×D8×C7311yescharacteristic
468C23C2×D8×C7311yescharacteristic
469C23C2×D8×C7311yescharacteristic
470Q8—41no—
471Q8—41no—
472Q8—41no—
473Q8—41no—
474Q8—41no—
475Q8—41no—
476Q8—41no—
477Q8—82no—
478D4—41no—
479D4—41no—
480D4—41no—
481D4—41no—
482D4—41no—
483D4—82no—
484D4—161no—
485D4—161no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—161no—
502C2×C4C2×D8×C7311yescharacteristic
503C2×C4C2×D8×C7311yescharacteristic
504C2×C4C2×D8×C7311yescharacteristic
505C2×C4C22×D4×C7311yescharacteristic
506C8—21no—
507C8—21no—
508C8—21no—
509C8H(5,𝔽2)×C7311yescharacteristic
510C8H(5,𝔽2)×C7311yescharacteristic
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22C22×D8×C7311yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4#534×C7311yescharacteristic
535C4#575×C7311yescharacteristic
536C2—41no—
537C2—41no—
538C2—41no—
539C2—161no—
540C2C73×#318611yescharacteristic
541C2C73×#341611yescharacteristic
542C2C73×#341711yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
prime radicalC73×#3061C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×#41×C73 ◁ C2×#131×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3059C2semidirect
3. C73×#2237C2semidirect
4. C73×#2236C2semidirect
5. C73×#2235C2semidirect
6. C73×#2234C2semidirect
7. C73×#2220C2semidirect
8. C73×#2219C2semidirect
9. C73×#2217C2semidirect
10. C73×#2216C2semidirect
11. C73×#2189C2semidirect
12. C73×#2189C2semidirect
13. C73×#2188C2semidirect
14. C73×#2185C2semidirect
15. C73×#2113C2semidirect
264. #33767C73direct (N × H)
273. #3059C2×C73semidirect
274. #2237C2×C73semidirect
275. #2236C2×C73semidirect
276. #2235C2×C73semidirect
277. #2234C2×C73semidirect
278. #2220C2×C73semidirect
279. #2219C2×C73semidirect
280. #2217C2×C73semidirect
281. #2216C2×C73semidirect
282. #2189C2×C73semidirect
283. #2189C2×C73semidirect
284. #2188C2×C73semidirect
285. #2185C2×C73semidirect
286. #2113C2×C73semidirect
287. C73#33767direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#30612
C73×#30592
C73×#22372
C73×#22362
C73×#22352
C73×#22342
C73×#22202
C73×#22192
C73×#22172
C73×#22162
C73×#21892
C73×#21882
C73×#21852
C73×#21132
#3376773